Research ArticleAdjusting of Wind Input Source Term inWAVEWATCH III Model for the Middle-Sized WaterBody on the Basis of the Field Experiment
Alexandra Kuznetsova12 Georgy Baydakov12 Vladislav Papko1 Alexander Kandaurov12
Maxim Vdovin12 Daniil Sergeev12 and Yuliya Troitskaya12
1 Institute of Applied Physics of the Russian Academy of Sciences 46 Ulyanov Street Nizhny Novgorod 603950 Russia2Nizhny Novgorod State University 23 Gagarina Avenue Nizhny Novgorod 603950 Russia
Correspondence should be addressed to Alexandra Kuznetsova alexandrahydroapplsci-nnovru
Received 20 August 2015 Accepted 18 November 2015
Academic Editor Alan Blumberg
Copyright copy 2016 Alexandra Kuznetsova et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Adjusting of wind input source term in numerical model WAVEWATCH III for the middle-sized water body is reported For thispurpose the field experiment on Gorky Reservoir is carried out Surface waves are measured along with the parameters of theairflow The measurement of wind speed in close proximity to the water surface is performed On the basis of the experimentalresults the parameterization of the drag coefficient depending on the 10m wind speed is proposed This parameterization is usedinWAVEWATCH III for the adjusting of the wind input source term within WAM 3 and Tolman and Chalikov parameterizationsThe simulation of the surface wind waves within tuned to the conditions of the middle-sized water body WAVEWATCH III isperformed using three built-in parameterizations (WAM 3 Tolman and Chalikov and WAM 4) and adjusted wind input sourceterm parameterizations Verification of the applicability of the model to the middle-sized reservoir is performed by comparing thesimulated data with the results of the field experiment It is shown that the use of the proposed parameterization 119862
119863(11988010) improves
the agreement in the significant wave height119867119878from the field experiment and from the numerical simulation
1 Introduction
Prediction of surfacewindwaves on the inlandwater bodies isrecognized as an important problem involvingmany environ-mental applications such as safety of the inland navigationand protection from the banks erosion Lake waves alsostrongly affect the processes of exchange of momentum heatand moisture in the low atmosphere and thus determinemicroclimate of the adjacent areas which should be takeninto account in planning structure of recreation zones [1]
The major physical problem of numerical wave modelingin inland water bodies is associated with short fetches whenparameters of wave excitation and development are stronglydifferent from long-fetch condition typical for the open ocean[2] Typically in these conditions the numerical descriptionof waves in lakes and reservoirs is based on empirical models
(see eg [3 4]) But the empirical relationships are based onthe averaged characteristics that cannot predict the extremesimportant for many tasks of operational meteorology (stormconditions such as Great Lakes storm discussed in [5])and numerical wave models are required Now there area number of examples of application of third generationmodels for waves forecast in large lakes So WAVEWATCHIII [2] is used successfully for the wave forecasts on theGreat Lakes in the USA [6 7] The data for a current wavesituation is presented on the open website and is updatedevery three hours [8] Furthermore WAVEWATCH III andSWAN [9] are applied to Caspian Sea and Ladoga Laketo analyze the wind and waves climate hindcasting [10]Nevertheless lakes and reservoirs of smaller sizes (less than100 km linear size the so-called middle-sized reservoirs) alsohave examples of hurricane-force wind and severe surface
Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 8539127 13 pageshttpdxdoiorg10115520168539127
2 Advances in Meteorology
wave states conditions The first attempt of application of aglobal wave model WAM [11] for the wave forecasting on amiddle-sized reservoir was reported recently in [12]
Among the peculiarities of the low-fetch waves at themiddle-sized reservoirs is the stronger wind input which isproportional to the ratio of wind friction velocity (or 10mwind speed) to the wave phase velocity [2] Another featureis the enhanced nonlinearity caused by higher steepness ofthe waves Then the tuning of the ocean wave model to theinland water conditions should be twofold adjusting of thewind source and ldquocollision integralrdquo Dissipation due to wavebreaking can be expected to be similar towave conditions dueto their universal nature
One more problem of tuning of numerical models tothe conditions of middle-sized reservoirs and lakes is thesmall amount of experimental data that can be used for itsverification Rare examples of such experiments are studied[13 14] which show the specificity of wind-wave interactionin the indicated circumstances In this paper we present atuning of the wind input term inWAVEWATCH III model tothe conditions of the middle-sized reservoir on an exampleof Gorky Reservoir belonging to the Volga Cascade Thetuning is based on the data of the field experiment held byour groupThe methods of the experiment are different fromthose used in [13 14] and they focus on the study of airflowin close proximity to water surfaceThe comparison of resultsof the numerical experiments with the results of the fieldexperiments on Gorky Reservoir is presented
The paper has the following structure In Section 2 thebasic parameterizations of wind and wave interactions inWAVEWATCH III v314 are presented In Section 3 thestudied reservoir and the field experiment setup with itsinstrumentation andmethods are described In Section 4 thefield data processing and the results of the field experimentare presented In Section 5 numerical experiment withintuned to the conditions of the middle-sized reservoirWAVE-WATCH III is set out In Section 6 the adjustment of windinput source term in tunedWAVEWATCH III and the resultsof numerical experiments within tuned WAVEWATCH IIIandwithin a tunedWAVEWATCH III with the adjusted windinput are presented
2 Wind Input Parameterizationsin WAVEWATCH III
WAVEWATCH III [2 15 16] is based on the numericalsolution of the equation for the spectral density ofwave action119873 in the approximation of phase averaging
120597119873
120597119905+ nabla119909119873 +
120597
120597120590119873 +
120597
120597120579
120579119873 =1
120590(119878in + 119878dis + 119878nl) (1)
The lefthand side of (1) describes the kinematics ofwaves120590 is the radian frequency and 120579 is the wave direction In theright hand side there are terms that describe the wind-wavegrowth 119878in dissipation mainly due to wave breaking 119878dis and4-wave nonlinear interaction of waves 119878nl
This paper focuses on the wind input parameterizationswhose parameters can be adjusted on the basis of the field
measurements data Generally the term describing the windinput is determined as
119878in = 120573 (119896 120579)119873 (119896 120579) 120590 (2)
where 120573(119896 120579) is the dimensionless wind-wave growth rateparameter approximated in WAVEWATCH III v314 bydifferent parameterizations (WAM 3 Tolman and Chalikovand WAM 4) Among them the WAM 3 parameterization[17ndash19] is defined by two empirical formulas The first one isfor the wind-wave growth rate
120573 (119896 120579) = 119862in120588119886
120588119908
max[0 (28119906lowast
119888phcos (120579 minus 120579
119908) minus 1)] (3)
where 119862in = 025 is a constant 120588119886120588119908is the ratio of the
densities of air and water 119906lowastis the friction velocity 119888ph
is the phase velocity and 120579119908is the main wind direction
The second one is a relation between the 10m wind speed11988010
and a friction velocity 119906lowast
= 11988010radic119862119863provided by the
empirical formula of the parameterization of the surface dragcoefficient 119862
119863 proposed in [19]
119862119863= 0001 times (08 + 065119880
10) (4)
In the Tolman and Chalikov parameterization [20] thedimensionless coefficient depends on the drag coefficientand on the dimensionless frequency of the spectral com-ponents In the WAM 4 parameterization [21] the wind-waves interaction parameter 120573 is presented by the adjustedMiles formula To calculate the roughness parameter thefeedback of the wind-waves spectra is taken into account aswell So in the considered parameterizations the wind inputis determined by the wind-wave interaction parameter 120573 andby the dependence 119906
lowast(11988010) which is defined by 119862
119863
3 Field Experiment
The tuning of WAVEWATCH III to the conditions of themiddle-sized reservoir was performed for conditions ofGorky Reservoir on the basis of field experiment
Measurements were carried out in 2012ndash2014 from Mayto October in the waters of Gorky Reservoir It has anelongated shape (Figure 1) which allows studyingwindwavesof different fetch depending on the wind direction GorkyReservoir is an artificial lake in the central part of the VolgaRiver formed by the dam of Nizhny Novgorod HydroelectricStation Its lake part is 85 km long and up to 15 km wideThe mean depth of the reservoir varies in the range of4ndash20 meters and the depth in the area of measurementsis 9ndash12 meters depending on the season and the point ofmeasurement
31 Instrumentation Instrumentation was placed on a buoystation with the original design based on the oceanographicFroude buoy Froude buoy is a mast submerged in water andheld in a vertical position by the float close to the surfaceand by the load on the depth (Figures 2(a) and 2(b)) Buoyrsquostotal length is 12m and the length of the part above the water
Advances in Meteorology 3
(a)
Point ofmeasurements
1km
(b)
Figure 1 (a) Gorky Reservoir (Google Earth data) (b) Zoom view of the measurements area
(a)
Balanceweight
Float
Wirewave gauge
Ultrasonicwind sensors
Separate float
Water surface
12m
53
m
227
m
13
m
085
m
01
m
(b)
Figure 2 Froude buoy (a) real view of the operating state and (b) scheme
is 53m The resonant frequency of the vertical oscillationsis 025Hz which corresponds to a wavelength of 25m Onthe buoy mast 4 ultrasonic speed sensors (WindSonic GillInstruments Production) are located at heights of 085m13m 227m and 526m over the mean water surface A fifthsensor is located on the float tracking waveform that allowsmeasuring the wind speed in close proximity to the watersurface The distance from the float to the buoy mast is 1mthe height of thewind speedmeasuring zone is 10 cm from thewater surfaceThe buoy is also equipped with air temperaturesensors (at heights of 01m (float) 085m and 13m) watertemperature sensors and three-channel wire wave gauge thatallows us to retrieve the wave space-time spectra
WindSonic is two-component ultrasonic sensor with 4measurement accuracy and velocity resolution of 001msOperating range of wind speed measurements 0ndash60msincludesmeasurements in calm conditions Resistive temper-ature sensors measure the environmental temperature with
resolution of 001∘C and 3 measurement accuracy Wavegauge consists of three pairs of resistive wire sensors locatedat the vertices of an equilateral triangle with a side of 62mmand the data sampling rate is 100Hz
32 Surface Wave Spectra Three-dimensional frequency-wavenumber spectra were retrieved from wave gauge databy the algorithm similar to the wavelet directional method(WDM) suggested in [22] The details of the applied methodare described in [23] Time series of water elevation from eachpair of wire sensors were processed by the window FFT withthe windowwidth 2119873 (119873 is an integer) with 50 overlappingThe complex amplitudes of harmonics at each frequency120596 119860120596(119909119899 119910119899) exp(119894120601
120596(119909119899 119910119899))were calculated here119860
120596is the
wave magnitude 120601120596is the wave phase 119899 = 1 2 3 is
the number of the wave sensors and (119909119899 119910119899) are the 119899-
sensorrsquos Cartesian coordinates Suppose that the wave fieldis a superposition of harmonic waves with the wavenumbers
4 Advances in Meteorology
01 1
00001
0001
001
01
simfminus506
simfminus511
E(f
)(m
minus2 s)
1E minus 005
f (Hz)
(a)
0001 001 01
00001
0001
simkminus309
simkminus313
1E minus 005
1E minus 006
1E minus 007
E(k)
(m3 )
k (cmminus1)
(b)
Figure 3 Wave spectra for 11988010= 6-7ms averaged over 60 minutes (a) 1D frequency spectrum and (b) 1D wavenumber spectrum
= (119896119909 119896119910) and one harmonic wave dominates in each
interrogation window and then their phases are
120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)
Thus the wavenumber components can be calculated bythe phase difference at different wave sensors To obtain thedirectional spectra the Cartesian coordinates (119896
119909 119896119910) were
transformed to the polar coordinates (119896 120579) and then 3Dspectrum 119864(120590 119896 120579) was obtained similar to [22] by binningthe amplitudes squared into calculated bins in 119896 and 120579Integration of119864(120590 119896 120579) overwavenumber or frequency yieldsfrequency 119864(120590 120579) or wavenumber 119864(119896 120579) directional spec-tra respectively Integrating over 120579 gives the 1D frequencyand wavenumber spectra correspondingly (examples are inFigure 3)The system allows estimating the parameters of thewave whose length exceeds the double distance 119889 betweenthe sensors
119896max =120587
119889= 05 cmminus1 (6)
The developed algorithm is based on the supposition thatthe dominatingwave field within the interrogationwindow ata given frequency 120590 is a harmonic wave which is correct for arather short time interval due to grouping of the surface wavefield Several periods of the energy-wave should fit into theinterrogationwindow For typical values of the observed peakfrequency 119891
119901= 035ndash08Hz (or the observed peak period 119879
119901
= 125ndash280 s) the size of interrogation window is selected tobe 2048 s (2048 points)
Frequency and wavenumber spectra shown in Figure 3are obtained by processing of two consecutive recordings 60minutes long It should be noted that the asymptotic behaviorof frequency spectrum and wavenumber spectrum (120590minus5 119896minus3)correspond to Philips saturation spectrum (see eg [24])but they do not correspond to Toba spectrum (see eg [25])which is typical for the ocean conditions
For the comparison with the numerical modeling resultsthe values of significant wave height119867
119878are estimated as four-
standard deviation of the water surface elevation which arecalculated as the integral of the frequency spectrum
119867119878= 4 (int119864 (120590) 119889120590)
12
(7)
33 Parameters of Low Atmosphere over the Inland WaterBody The location of wind velocity sensors corresponds tothe structure of the airflow It is well known (see eg [26])that the velocity profile in the constant flux layer (wherethe turbulent momentum flux 120591turb = 120588air⟨119906
1015840
1199091199061015840
119911⟩ does not
depend on the vertical coordinate 119911 here 120588air is the air densityand 119906
1015840
119909and 119906
1015840
119911are the fluctuations of horizontal and vertical
components of the wind velocity resp) has a logarithmicform
119880 (119911) =119906lowast
120581ln( 119911
1199110
) (8)
where 119906lowast
= radic120591turb120588air = radic⟨11990610158401199091199061015840119911⟩ is the friction velocity
determined by the turbulentmomentumflux 1199110is the surface
roughness parameter and 120581 is the von Karman constant In[27] a distortion of the velocity field in the presence of arough surface is considered and it is shown that in case ofa monochromatic wave propagating along the wind for thestream function 120593 averaged over the turbulent fluctuationsan equation can be written as
(119880 minus 119888) (1198892120593
1198891205782minus 1198962120593) minus
1198892119880
1198891205782120593 = 0 (9)
where119880(120578) is the dependence of wind speed on height abovethe surface (in curvilinear coordinates) 119888 is phase velocityof the wave and 119896 is wavenumber When the magnitude
Advances in Meteorology 5
119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an
approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where
119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])
119906lowast120581
(119896120578)2
|119880 minus 119888|
≪ 1
or 119906lowast120581
(119896120578)2
|119880 minus 119888|
≫ 1
(10)
and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float
It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]
(lowast
120581ln( 119911
1199110
) minus 119888)
10038161003816100381610038161003816100381610038161003816119911=120576
=120581lowast119911
1205762
10038161003816100381610038161003816100381610038161003816119911=120576
(11)
where 119888 and lowastdenote typical values of the mentioned
above variables In the conditions of the Gorky Reservoir (= 2-3mminus1
lowast= 01ndash04ms) the evaluation of the height
of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location
It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors
To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)
minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and
119863sim (
119909
119863)
13
(12)
the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded
01 1 10Height (m)
2
3
4
5
6
7
8
9
Win
d ve
loci
ty (m
s)
U10 = 86msU10 = 72msU10 = 64ms
U10 = 55msU10 = 41ms
Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions
space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence
120574 =1198801015840
1198800
= 03 (119909
119863)
minus23
exp(minus 1199032
22) (13)
is used where 119863 = 04(119909119863)13 1198800is the estimated wind
speed in the unperturbed flow and 1198801015840 is the magnitude
of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)
minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top
4 Field Data Processing and Results
Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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EcologyInternational Journal of
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EarthquakesJournal of
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Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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MineralogyInternational Journal of
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MeteorologyAdvances in
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ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
2 Advances in Meteorology
wave states conditions The first attempt of application of aglobal wave model WAM [11] for the wave forecasting on amiddle-sized reservoir was reported recently in [12]
Among the peculiarities of the low-fetch waves at themiddle-sized reservoirs is the stronger wind input which isproportional to the ratio of wind friction velocity (or 10mwind speed) to the wave phase velocity [2] Another featureis the enhanced nonlinearity caused by higher steepness ofthe waves Then the tuning of the ocean wave model to theinland water conditions should be twofold adjusting of thewind source and ldquocollision integralrdquo Dissipation due to wavebreaking can be expected to be similar towave conditions dueto their universal nature
One more problem of tuning of numerical models tothe conditions of middle-sized reservoirs and lakes is thesmall amount of experimental data that can be used for itsverification Rare examples of such experiments are studied[13 14] which show the specificity of wind-wave interactionin the indicated circumstances In this paper we present atuning of the wind input term inWAVEWATCH III model tothe conditions of the middle-sized reservoir on an exampleof Gorky Reservoir belonging to the Volga Cascade Thetuning is based on the data of the field experiment held byour groupThe methods of the experiment are different fromthose used in [13 14] and they focus on the study of airflowin close proximity to water surfaceThe comparison of resultsof the numerical experiments with the results of the fieldexperiments on Gorky Reservoir is presented
The paper has the following structure In Section 2 thebasic parameterizations of wind and wave interactions inWAVEWATCH III v314 are presented In Section 3 thestudied reservoir and the field experiment setup with itsinstrumentation andmethods are described In Section 4 thefield data processing and the results of the field experimentare presented In Section 5 numerical experiment withintuned to the conditions of the middle-sized reservoirWAVE-WATCH III is set out In Section 6 the adjustment of windinput source term in tunedWAVEWATCH III and the resultsof numerical experiments within tuned WAVEWATCH IIIandwithin a tunedWAVEWATCH III with the adjusted windinput are presented
2 Wind Input Parameterizationsin WAVEWATCH III
WAVEWATCH III [2 15 16] is based on the numericalsolution of the equation for the spectral density ofwave action119873 in the approximation of phase averaging
120597119873
120597119905+ nabla119909119873 +
120597
120597120590119873 +
120597
120597120579
120579119873 =1
120590(119878in + 119878dis + 119878nl) (1)
The lefthand side of (1) describes the kinematics ofwaves120590 is the radian frequency and 120579 is the wave direction In theright hand side there are terms that describe the wind-wavegrowth 119878in dissipation mainly due to wave breaking 119878dis and4-wave nonlinear interaction of waves 119878nl
This paper focuses on the wind input parameterizationswhose parameters can be adjusted on the basis of the field
measurements data Generally the term describing the windinput is determined as
119878in = 120573 (119896 120579)119873 (119896 120579) 120590 (2)
where 120573(119896 120579) is the dimensionless wind-wave growth rateparameter approximated in WAVEWATCH III v314 bydifferent parameterizations (WAM 3 Tolman and Chalikovand WAM 4) Among them the WAM 3 parameterization[17ndash19] is defined by two empirical formulas The first one isfor the wind-wave growth rate
120573 (119896 120579) = 119862in120588119886
120588119908
max[0 (28119906lowast
119888phcos (120579 minus 120579
119908) minus 1)] (3)
where 119862in = 025 is a constant 120588119886120588119908is the ratio of the
densities of air and water 119906lowastis the friction velocity 119888ph
is the phase velocity and 120579119908is the main wind direction
The second one is a relation between the 10m wind speed11988010
and a friction velocity 119906lowast
= 11988010radic119862119863provided by the
empirical formula of the parameterization of the surface dragcoefficient 119862
119863 proposed in [19]
119862119863= 0001 times (08 + 065119880
10) (4)
In the Tolman and Chalikov parameterization [20] thedimensionless coefficient depends on the drag coefficientand on the dimensionless frequency of the spectral com-ponents In the WAM 4 parameterization [21] the wind-waves interaction parameter 120573 is presented by the adjustedMiles formula To calculate the roughness parameter thefeedback of the wind-waves spectra is taken into account aswell So in the considered parameterizations the wind inputis determined by the wind-wave interaction parameter 120573 andby the dependence 119906
lowast(11988010) which is defined by 119862
119863
3 Field Experiment
The tuning of WAVEWATCH III to the conditions of themiddle-sized reservoir was performed for conditions ofGorky Reservoir on the basis of field experiment
Measurements were carried out in 2012ndash2014 from Mayto October in the waters of Gorky Reservoir It has anelongated shape (Figure 1) which allows studyingwindwavesof different fetch depending on the wind direction GorkyReservoir is an artificial lake in the central part of the VolgaRiver formed by the dam of Nizhny Novgorod HydroelectricStation Its lake part is 85 km long and up to 15 km wideThe mean depth of the reservoir varies in the range of4ndash20 meters and the depth in the area of measurementsis 9ndash12 meters depending on the season and the point ofmeasurement
31 Instrumentation Instrumentation was placed on a buoystation with the original design based on the oceanographicFroude buoy Froude buoy is a mast submerged in water andheld in a vertical position by the float close to the surfaceand by the load on the depth (Figures 2(a) and 2(b)) Buoyrsquostotal length is 12m and the length of the part above the water
Advances in Meteorology 3
(a)
Point ofmeasurements
1km
(b)
Figure 1 (a) Gorky Reservoir (Google Earth data) (b) Zoom view of the measurements area
(a)
Balanceweight
Float
Wirewave gauge
Ultrasonicwind sensors
Separate float
Water surface
12m
53
m
227
m
13
m
085
m
01
m
(b)
Figure 2 Froude buoy (a) real view of the operating state and (b) scheme
is 53m The resonant frequency of the vertical oscillationsis 025Hz which corresponds to a wavelength of 25m Onthe buoy mast 4 ultrasonic speed sensors (WindSonic GillInstruments Production) are located at heights of 085m13m 227m and 526m over the mean water surface A fifthsensor is located on the float tracking waveform that allowsmeasuring the wind speed in close proximity to the watersurface The distance from the float to the buoy mast is 1mthe height of thewind speedmeasuring zone is 10 cm from thewater surfaceThe buoy is also equipped with air temperaturesensors (at heights of 01m (float) 085m and 13m) watertemperature sensors and three-channel wire wave gauge thatallows us to retrieve the wave space-time spectra
WindSonic is two-component ultrasonic sensor with 4measurement accuracy and velocity resolution of 001msOperating range of wind speed measurements 0ndash60msincludesmeasurements in calm conditions Resistive temper-ature sensors measure the environmental temperature with
resolution of 001∘C and 3 measurement accuracy Wavegauge consists of three pairs of resistive wire sensors locatedat the vertices of an equilateral triangle with a side of 62mmand the data sampling rate is 100Hz
32 Surface Wave Spectra Three-dimensional frequency-wavenumber spectra were retrieved from wave gauge databy the algorithm similar to the wavelet directional method(WDM) suggested in [22] The details of the applied methodare described in [23] Time series of water elevation from eachpair of wire sensors were processed by the window FFT withthe windowwidth 2119873 (119873 is an integer) with 50 overlappingThe complex amplitudes of harmonics at each frequency120596 119860120596(119909119899 119910119899) exp(119894120601
120596(119909119899 119910119899))were calculated here119860
120596is the
wave magnitude 120601120596is the wave phase 119899 = 1 2 3 is
the number of the wave sensors and (119909119899 119910119899) are the 119899-
sensorrsquos Cartesian coordinates Suppose that the wave fieldis a superposition of harmonic waves with the wavenumbers
4 Advances in Meteorology
01 1
00001
0001
001
01
simfminus506
simfminus511
E(f
)(m
minus2 s)
1E minus 005
f (Hz)
(a)
0001 001 01
00001
0001
simkminus309
simkminus313
1E minus 005
1E minus 006
1E minus 007
E(k)
(m3 )
k (cmminus1)
(b)
Figure 3 Wave spectra for 11988010= 6-7ms averaged over 60 minutes (a) 1D frequency spectrum and (b) 1D wavenumber spectrum
= (119896119909 119896119910) and one harmonic wave dominates in each
interrogation window and then their phases are
120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)
Thus the wavenumber components can be calculated bythe phase difference at different wave sensors To obtain thedirectional spectra the Cartesian coordinates (119896
119909 119896119910) were
transformed to the polar coordinates (119896 120579) and then 3Dspectrum 119864(120590 119896 120579) was obtained similar to [22] by binningthe amplitudes squared into calculated bins in 119896 and 120579Integration of119864(120590 119896 120579) overwavenumber or frequency yieldsfrequency 119864(120590 120579) or wavenumber 119864(119896 120579) directional spec-tra respectively Integrating over 120579 gives the 1D frequencyand wavenumber spectra correspondingly (examples are inFigure 3)The system allows estimating the parameters of thewave whose length exceeds the double distance 119889 betweenthe sensors
119896max =120587
119889= 05 cmminus1 (6)
The developed algorithm is based on the supposition thatthe dominatingwave field within the interrogationwindow ata given frequency 120590 is a harmonic wave which is correct for arather short time interval due to grouping of the surface wavefield Several periods of the energy-wave should fit into theinterrogationwindow For typical values of the observed peakfrequency 119891
119901= 035ndash08Hz (or the observed peak period 119879
119901
= 125ndash280 s) the size of interrogation window is selected tobe 2048 s (2048 points)
Frequency and wavenumber spectra shown in Figure 3are obtained by processing of two consecutive recordings 60minutes long It should be noted that the asymptotic behaviorof frequency spectrum and wavenumber spectrum (120590minus5 119896minus3)correspond to Philips saturation spectrum (see eg [24])but they do not correspond to Toba spectrum (see eg [25])which is typical for the ocean conditions
For the comparison with the numerical modeling resultsthe values of significant wave height119867
119878are estimated as four-
standard deviation of the water surface elevation which arecalculated as the integral of the frequency spectrum
119867119878= 4 (int119864 (120590) 119889120590)
12
(7)
33 Parameters of Low Atmosphere over the Inland WaterBody The location of wind velocity sensors corresponds tothe structure of the airflow It is well known (see eg [26])that the velocity profile in the constant flux layer (wherethe turbulent momentum flux 120591turb = 120588air⟨119906
1015840
1199091199061015840
119911⟩ does not
depend on the vertical coordinate 119911 here 120588air is the air densityand 119906
1015840
119909and 119906
1015840
119911are the fluctuations of horizontal and vertical
components of the wind velocity resp) has a logarithmicform
119880 (119911) =119906lowast
120581ln( 119911
1199110
) (8)
where 119906lowast
= radic120591turb120588air = radic⟨11990610158401199091199061015840119911⟩ is the friction velocity
determined by the turbulentmomentumflux 1199110is the surface
roughness parameter and 120581 is the von Karman constant In[27] a distortion of the velocity field in the presence of arough surface is considered and it is shown that in case ofa monochromatic wave propagating along the wind for thestream function 120593 averaged over the turbulent fluctuationsan equation can be written as
(119880 minus 119888) (1198892120593
1198891205782minus 1198962120593) minus
1198892119880
1198891205782120593 = 0 (9)
where119880(120578) is the dependence of wind speed on height abovethe surface (in curvilinear coordinates) 119888 is phase velocityof the wave and 119896 is wavenumber When the magnitude
Advances in Meteorology 5
119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an
approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where
119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])
119906lowast120581
(119896120578)2
|119880 minus 119888|
≪ 1
or 119906lowast120581
(119896120578)2
|119880 minus 119888|
≫ 1
(10)
and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float
It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]
(lowast
120581ln( 119911
1199110
) minus 119888)
10038161003816100381610038161003816100381610038161003816119911=120576
=120581lowast119911
1205762
10038161003816100381610038161003816100381610038161003816119911=120576
(11)
where 119888 and lowastdenote typical values of the mentioned
above variables In the conditions of the Gorky Reservoir (= 2-3mminus1
lowast= 01ndash04ms) the evaluation of the height
of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location
It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors
To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)
minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and
119863sim (
119909
119863)
13
(12)
the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded
01 1 10Height (m)
2
3
4
5
6
7
8
9
Win
d ve
loci
ty (m
s)
U10 = 86msU10 = 72msU10 = 64ms
U10 = 55msU10 = 41ms
Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions
space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence
120574 =1198801015840
1198800
= 03 (119909
119863)
minus23
exp(minus 1199032
22) (13)
is used where 119863 = 04(119909119863)13 1198800is the estimated wind
speed in the unperturbed flow and 1198801015840 is the magnitude
of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)
minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top
4 Field Data Processing and Results
Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 3
(a)
Point ofmeasurements
1km
(b)
Figure 1 (a) Gorky Reservoir (Google Earth data) (b) Zoom view of the measurements area
(a)
Balanceweight
Float
Wirewave gauge
Ultrasonicwind sensors
Separate float
Water surface
12m
53
m
227
m
13
m
085
m
01
m
(b)
Figure 2 Froude buoy (a) real view of the operating state and (b) scheme
is 53m The resonant frequency of the vertical oscillationsis 025Hz which corresponds to a wavelength of 25m Onthe buoy mast 4 ultrasonic speed sensors (WindSonic GillInstruments Production) are located at heights of 085m13m 227m and 526m over the mean water surface A fifthsensor is located on the float tracking waveform that allowsmeasuring the wind speed in close proximity to the watersurface The distance from the float to the buoy mast is 1mthe height of thewind speedmeasuring zone is 10 cm from thewater surfaceThe buoy is also equipped with air temperaturesensors (at heights of 01m (float) 085m and 13m) watertemperature sensors and three-channel wire wave gauge thatallows us to retrieve the wave space-time spectra
WindSonic is two-component ultrasonic sensor with 4measurement accuracy and velocity resolution of 001msOperating range of wind speed measurements 0ndash60msincludesmeasurements in calm conditions Resistive temper-ature sensors measure the environmental temperature with
resolution of 001∘C and 3 measurement accuracy Wavegauge consists of three pairs of resistive wire sensors locatedat the vertices of an equilateral triangle with a side of 62mmand the data sampling rate is 100Hz
32 Surface Wave Spectra Three-dimensional frequency-wavenumber spectra were retrieved from wave gauge databy the algorithm similar to the wavelet directional method(WDM) suggested in [22] The details of the applied methodare described in [23] Time series of water elevation from eachpair of wire sensors were processed by the window FFT withthe windowwidth 2119873 (119873 is an integer) with 50 overlappingThe complex amplitudes of harmonics at each frequency120596 119860120596(119909119899 119910119899) exp(119894120601
120596(119909119899 119910119899))were calculated here119860
120596is the
wave magnitude 120601120596is the wave phase 119899 = 1 2 3 is
the number of the wave sensors and (119909119899 119910119899) are the 119899-
sensorrsquos Cartesian coordinates Suppose that the wave fieldis a superposition of harmonic waves with the wavenumbers
4 Advances in Meteorology
01 1
00001
0001
001
01
simfminus506
simfminus511
E(f
)(m
minus2 s)
1E minus 005
f (Hz)
(a)
0001 001 01
00001
0001
simkminus309
simkminus313
1E minus 005
1E minus 006
1E minus 007
E(k)
(m3 )
k (cmminus1)
(b)
Figure 3 Wave spectra for 11988010= 6-7ms averaged over 60 minutes (a) 1D frequency spectrum and (b) 1D wavenumber spectrum
= (119896119909 119896119910) and one harmonic wave dominates in each
interrogation window and then their phases are
120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)
Thus the wavenumber components can be calculated bythe phase difference at different wave sensors To obtain thedirectional spectra the Cartesian coordinates (119896
119909 119896119910) were
transformed to the polar coordinates (119896 120579) and then 3Dspectrum 119864(120590 119896 120579) was obtained similar to [22] by binningthe amplitudes squared into calculated bins in 119896 and 120579Integration of119864(120590 119896 120579) overwavenumber or frequency yieldsfrequency 119864(120590 120579) or wavenumber 119864(119896 120579) directional spec-tra respectively Integrating over 120579 gives the 1D frequencyand wavenumber spectra correspondingly (examples are inFigure 3)The system allows estimating the parameters of thewave whose length exceeds the double distance 119889 betweenthe sensors
119896max =120587
119889= 05 cmminus1 (6)
The developed algorithm is based on the supposition thatthe dominatingwave field within the interrogationwindow ata given frequency 120590 is a harmonic wave which is correct for arather short time interval due to grouping of the surface wavefield Several periods of the energy-wave should fit into theinterrogationwindow For typical values of the observed peakfrequency 119891
119901= 035ndash08Hz (or the observed peak period 119879
119901
= 125ndash280 s) the size of interrogation window is selected tobe 2048 s (2048 points)
Frequency and wavenumber spectra shown in Figure 3are obtained by processing of two consecutive recordings 60minutes long It should be noted that the asymptotic behaviorof frequency spectrum and wavenumber spectrum (120590minus5 119896minus3)correspond to Philips saturation spectrum (see eg [24])but they do not correspond to Toba spectrum (see eg [25])which is typical for the ocean conditions
For the comparison with the numerical modeling resultsthe values of significant wave height119867
119878are estimated as four-
standard deviation of the water surface elevation which arecalculated as the integral of the frequency spectrum
119867119878= 4 (int119864 (120590) 119889120590)
12
(7)
33 Parameters of Low Atmosphere over the Inland WaterBody The location of wind velocity sensors corresponds tothe structure of the airflow It is well known (see eg [26])that the velocity profile in the constant flux layer (wherethe turbulent momentum flux 120591turb = 120588air⟨119906
1015840
1199091199061015840
119911⟩ does not
depend on the vertical coordinate 119911 here 120588air is the air densityand 119906
1015840
119909and 119906
1015840
119911are the fluctuations of horizontal and vertical
components of the wind velocity resp) has a logarithmicform
119880 (119911) =119906lowast
120581ln( 119911
1199110
) (8)
where 119906lowast
= radic120591turb120588air = radic⟨11990610158401199091199061015840119911⟩ is the friction velocity
determined by the turbulentmomentumflux 1199110is the surface
roughness parameter and 120581 is the von Karman constant In[27] a distortion of the velocity field in the presence of arough surface is considered and it is shown that in case ofa monochromatic wave propagating along the wind for thestream function 120593 averaged over the turbulent fluctuationsan equation can be written as
(119880 minus 119888) (1198892120593
1198891205782minus 1198962120593) minus
1198892119880
1198891205782120593 = 0 (9)
where119880(120578) is the dependence of wind speed on height abovethe surface (in curvilinear coordinates) 119888 is phase velocityof the wave and 119896 is wavenumber When the magnitude
Advances in Meteorology 5
119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an
approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where
119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])
119906lowast120581
(119896120578)2
|119880 minus 119888|
≪ 1
or 119906lowast120581
(119896120578)2
|119880 minus 119888|
≫ 1
(10)
and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float
It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]
(lowast
120581ln( 119911
1199110
) minus 119888)
10038161003816100381610038161003816100381610038161003816119911=120576
=120581lowast119911
1205762
10038161003816100381610038161003816100381610038161003816119911=120576
(11)
where 119888 and lowastdenote typical values of the mentioned
above variables In the conditions of the Gorky Reservoir (= 2-3mminus1
lowast= 01ndash04ms) the evaluation of the height
of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location
It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors
To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)
minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and
119863sim (
119909
119863)
13
(12)
the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded
01 1 10Height (m)
2
3
4
5
6
7
8
9
Win
d ve
loci
ty (m
s)
U10 = 86msU10 = 72msU10 = 64ms
U10 = 55msU10 = 41ms
Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions
space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence
120574 =1198801015840
1198800
= 03 (119909
119863)
minus23
exp(minus 1199032
22) (13)
is used where 119863 = 04(119909119863)13 1198800is the estimated wind
speed in the unperturbed flow and 1198801015840 is the magnitude
of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)
minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top
4 Field Data Processing and Results
Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Volume 2014
Mining
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International Journal of
Geophysics
OceanographyInternational Journal of
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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
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Advances in
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Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
4 Advances in Meteorology
01 1
00001
0001
001
01
simfminus506
simfminus511
E(f
)(m
minus2 s)
1E minus 005
f (Hz)
(a)
0001 001 01
00001
0001
simkminus309
simkminus313
1E minus 005
1E minus 006
1E minus 007
E(k)
(m3 )
k (cmminus1)
(b)
Figure 3 Wave spectra for 11988010= 6-7ms averaged over 60 minutes (a) 1D frequency spectrum and (b) 1D wavenumber spectrum
= (119896119909 119896119910) and one harmonic wave dominates in each
interrogation window and then their phases are
120601120596(119909119899 119910119899) = 119896119909119909119899+ 119896119910119910119899 (5)
Thus the wavenumber components can be calculated bythe phase difference at different wave sensors To obtain thedirectional spectra the Cartesian coordinates (119896
119909 119896119910) were
transformed to the polar coordinates (119896 120579) and then 3Dspectrum 119864(120590 119896 120579) was obtained similar to [22] by binningthe amplitudes squared into calculated bins in 119896 and 120579Integration of119864(120590 119896 120579) overwavenumber or frequency yieldsfrequency 119864(120590 120579) or wavenumber 119864(119896 120579) directional spec-tra respectively Integrating over 120579 gives the 1D frequencyand wavenumber spectra correspondingly (examples are inFigure 3)The system allows estimating the parameters of thewave whose length exceeds the double distance 119889 betweenthe sensors
119896max =120587
119889= 05 cmminus1 (6)
The developed algorithm is based on the supposition thatthe dominatingwave field within the interrogationwindow ata given frequency 120590 is a harmonic wave which is correct for arather short time interval due to grouping of the surface wavefield Several periods of the energy-wave should fit into theinterrogationwindow For typical values of the observed peakfrequency 119891
119901= 035ndash08Hz (or the observed peak period 119879
119901
= 125ndash280 s) the size of interrogation window is selected tobe 2048 s (2048 points)
Frequency and wavenumber spectra shown in Figure 3are obtained by processing of two consecutive recordings 60minutes long It should be noted that the asymptotic behaviorof frequency spectrum and wavenumber spectrum (120590minus5 119896minus3)correspond to Philips saturation spectrum (see eg [24])but they do not correspond to Toba spectrum (see eg [25])which is typical for the ocean conditions
For the comparison with the numerical modeling resultsthe values of significant wave height119867
119878are estimated as four-
standard deviation of the water surface elevation which arecalculated as the integral of the frequency spectrum
119867119878= 4 (int119864 (120590) 119889120590)
12
(7)
33 Parameters of Low Atmosphere over the Inland WaterBody The location of wind velocity sensors corresponds tothe structure of the airflow It is well known (see eg [26])that the velocity profile in the constant flux layer (wherethe turbulent momentum flux 120591turb = 120588air⟨119906
1015840
1199091199061015840
119911⟩ does not
depend on the vertical coordinate 119911 here 120588air is the air densityand 119906
1015840
119909and 119906
1015840
119911are the fluctuations of horizontal and vertical
components of the wind velocity resp) has a logarithmicform
119880 (119911) =119906lowast
120581ln( 119911
1199110
) (8)
where 119906lowast
= radic120591turb120588air = radic⟨11990610158401199091199061015840119911⟩ is the friction velocity
determined by the turbulentmomentumflux 1199110is the surface
roughness parameter and 120581 is the von Karman constant In[27] a distortion of the velocity field in the presence of arough surface is considered and it is shown that in case ofa monochromatic wave propagating along the wind for thestream function 120593 averaged over the turbulent fluctuationsan equation can be written as
(119880 minus 119888) (1198892120593
1198891205782minus 1198962120593) minus
1198892119880
1198891205782120593 = 0 (9)
where119880(120578) is the dependence of wind speed on height abovethe surface (in curvilinear coordinates) 119888 is phase velocityof the wave and 119896 is wavenumber When the magnitude
Advances in Meteorology 5
119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an
approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where
119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])
119906lowast120581
(119896120578)2
|119880 minus 119888|
≪ 1
or 119906lowast120581
(119896120578)2
|119880 minus 119888|
≫ 1
(10)
and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float
It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]
(lowast
120581ln( 119911
1199110
) minus 119888)
10038161003816100381610038161003816100381610038161003816119911=120576
=120581lowast119911
1205762
10038161003816100381610038161003816100381610038161003816119911=120576
(11)
where 119888 and lowastdenote typical values of the mentioned
above variables In the conditions of the Gorky Reservoir (= 2-3mminus1
lowast= 01ndash04ms) the evaluation of the height
of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location
It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors
To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)
minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and
119863sim (
119909
119863)
13
(12)
the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded
01 1 10Height (m)
2
3
4
5
6
7
8
9
Win
d ve
loci
ty (m
s)
U10 = 86msU10 = 72msU10 = 64ms
U10 = 55msU10 = 41ms
Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions
space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence
120574 =1198801015840
1198800
= 03 (119909
119863)
minus23
exp(minus 1199032
22) (13)
is used where 119863 = 04(119909119863)13 1198800is the estimated wind
speed in the unperturbed flow and 1198801015840 is the magnitude
of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)
minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top
4 Field Data Processing and Results
Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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MineralogyInternational Journal of
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Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 5
119880101584010158401198962(119880 minus 119888) is much greater or much less than 1 an
approximate solution is the function 120593 = 119860(119880minus119888)119890minus119896120578 where
119860 is wave amplitude In the case of the logarithmic velocityprofile this condition takes the form (see [27])
119906lowast120581
(119896120578)2
|119880 minus 119888|
≪ 1
or 119906lowast120581
(119896120578)2
|119880 minus 119888|
≫ 1
(10)
and it is performed well enough at the height of the orderof the wave amplitude and higher Thus the perturbationis the bending of the flow lines along the rough surfaceand it decreases exponentially with altitude Therefore to fixspeed sensor relatively to the mean streamlines the speed ata distance from surface must be measured at a fixed horizonand the measurements close to the surface should be carriedout using a tracking waveform sensor located on the float
It is important that the lower sensor should not be locatedin the wave boundary layer The magnitude of the waveboundary layer 120576 can be estimated in accordance with [28]
(lowast
120581ln( 119911
1199110
) minus 119888)
10038161003816100381610038161003816100381610038161003816119911=120576
=120581lowast119911
1205762
10038161003816100381610038161003816100381610038161003816119911=120576
(11)
where 119888 and lowastdenote typical values of the mentioned
above variables In the conditions of the Gorky Reservoir (= 2-3mminus1
lowast= 01ndash04ms) the evaluation of the height
of the wave boundary layer gives a value 120576 sim 1mm thatis significantly less than the height of the lower sensormeasuring wind speed location
It should be noted that the buoy is connected to thevessel by the cable and is located at a fixed distance of30 meters the cross section of the vessel is approximatelyequal to 3 times 3m Thus the buoy is located at a distanceof about 10 characteristic dimensions from the obstacleAccording to the recommendations of Gill Instruments [29]it is enough to consider the airflow to be unperturbed but themeasurements show the presence of small (3ndash6) deviationsof the measured profile from the logarithmic form evenin a steady wind and neutral stratification (Figure 4) Thisdeviation consists of the speed increasing at a height of 526mon 3ndash6 compared with the logarithmic approximationApparently this is due to the effect of the vessel shielding onthe 4 lower sensors
To estimate the perturbations introduced by vessel theformulas of the defect rate attenuation in the turbulent wakeare used It is known [30] that the perturbation introduced bythe body in the unlimited turbulent flow decreases in propor-tion (119909119863)
minus23 along the flow and in proportion exp(minus119903222)along the cross sectionHere119863 is the characteristic size of thebody 119909 and 119903 are the cylindrical coordinates is a width ofthe Gaussian function and
119863sim (
119909
119863)
13
(12)
the coefficients of the proportionality are determined empiri-cally In the case of airflow vessel shielding in a semibounded
01 1 10Height (m)
2
3
4
5
6
7
8
9
Win
d ve
loci
ty (m
s)
U10 = 86msU10 = 72msU10 = 64ms
U10 = 55msU10 = 41ms
Figure 4 Examples of the deviation of the wind velocity profile(5 minutes averaging) from the logarithmic form under differentconditions
space it is fair to expect that the nature of the turbulentwake is the same but the appropriate factors must be chosenSince the top speed sensor is located outside the vesselshielding zone and the lower four are well approximated bya logarithmic dependence the value should be between theheights of the fourth and fifth sensors The linear coefficientis selected so that the velocity profiles are well approximatedby a logarithmic dependence in average Finally to determinethemagnitude of the perturbation introduced by the vessel inthe airflow the dependence
120574 =1198801015840
1198800
= 03 (119909
119863)
minus23
exp(minus 1199032
22) (13)
is used where 119863 = 04(119909119863)13 1198800is the estimated wind
speed in the unperturbed flow and 1198801015840 is the magnitude
of the perturbation Note that the selected coefficients aresimilar to those obtained in [31] for the wake behind thesphere To determine the wind velocity in the unperturbedflow the wind speed measured by sensors is multiplied bythe coefficient 120572 = (1 minus 120574)
minus1 The coefficients 120572 for thevarious sensors are equal to 1069 1065 1061 1047 and 1009respectively from the bottom up to the top
4 Field Data Processing and Results
Investigation of the wind flow parameters is carried outby profiling General recording of wind speed is up to 5-hour duration and is divided into 5-minute sections (300measuring points) with a 50 of overlap As a result of
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
6 Advances in Meteorology
0 1 2 3 4 5 6 7 8 9 10 11 120
000050001
000150002
000250003
000350004
000450005
00055
Binning Gorky Reservoir sensors 2 3 4 and 5Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 5 Comparison of the retrieved dependence 119862119863(11988010) with
and without the lower sensor gray diamonds denote the binning ofdatawith the lower sensor (the standard deviation as the error gates)black solid circles are the binning of the data without the lowersensor (the standard deviation as the error gates) gray circles arethe results of field experiment [13] gray crosses are the results of fieldexperiment [14] dashed line is the empiric oceanic parameterizationCOARE 30
the averaging 5 values of wind speed corresponding to fivehorizons of measurements are received for each sectionThe resulting averaged profile is approximated by function(8) with the parameters of the approximation 119906
lowast(friction
velocity) and 1199110(surface roughness) The values of the 10m
wind speed 11988010
and of the drag coefficient 119862119863are retrieved
from the resulting approximationThe impact of data obtained from different horizons
on the resulting approximation of the wind velocity profileis analyzed Figure 5 shows a comparison of the retrieveddependence 119862
119863(11988010) for two combinations of speed sensors
with and without the lower sensor The points on the plot arethe result of the binning of the wind speed data within a cellwith size of Δ119880
10= 05ms The error gates correspond to
the standard deviation Also the results of field experiments[13 14] and empiric oceanic parameterization COARE 30[32] are shown in Figure 5 It is evident that without thelower sensor data the values 119862
119863(11988010) are characterized by
a slightly greater spread and are located higher and moreclose to the results of [13 14 32] while taking the lowersensor into account shows lower values of the drag coefficientIn [13] the sensors are located at the heights of 089m upto 10m from the mean water level in [14] the sensors arelocated at heights from 05m up to 4m In both cases all thesensors are firmly fixed on the masts and the approximationis performed throughout the wind speed profile
Figure 6 shows a comparison of the retrieved dependence119862119863(11988010) using two lower sensors only and using all five
sensors The use of two sensors only reveals significant dif-ferences in the wind parameters recovery in the weak windsarea the scatter and absolute value of 119862
119863(11988010) decreases In
the field of moderate and strong winds the retrieved values
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
0003
Binning Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2 3 4 and 5Lake George [13]Lake Washington [14]COARE 30
U10 (ms)
CD
Figure 6 Comparison of retrieved dependence 119862119863(11988010) using two
and five sensors gray solid circles are the binning of the five-sensordata (the standard deviation as the error gates) black diamonds arethe binning of the two-sensor data (the standard deviation as theerror gates) gray circles are the results of the field experiment [13]gray crosses are the results of the field experiment [14] dashed lineis the empiric oceanic parameterization COARE 30
of drag coefficient differ slightly despite the small increase inthe measurement error
These results can be explained by the deviation of windvelocity profile from the logarithmic form It may be causedby the stratification of the surface layer of the atmosphereand impact of the coastline as well as gustiness of thewind because the lower part of the profile adapts morequickly to the changing conditions of waves and the airflowparameters determine themomentum transfer from thewindto the waves exactly at the water-air boundary Consequentlyfurther analysis of the dependence 119862
119863(11988010) was based on the
measured data from sensors 1 and 2Throughout the 2012ndash2014 years the dataset consisting of
approximately 100 hours of recordings in the range of windvelocities 1ndash12ms for different fetch values (119871 fetch = 1ndash50 km)and stratification conditions (119879air minus 119879water = (minus5) minus 15
∘C) isobtainedThe resulting dependence119862
119863(11988010) using two lower
sensors is received and shown in Figure 7The approximationof the obtained data is made by a function
119862119863= 000124119880
minus1
10+ 000034 + 0000049119880
10 (14)
The result of binning of the wind speed data within a cellwith size Δ119880
10= 05ms and the standard deviation as the
error gates are shown in Figure 7The dependence (14) is usedbelow to adjust the wind input in WAVEWATCH III
5 Tuning of WAVEWATCH IIINumerical Experiment
The tuning of WAVEWATCH III to the conditions of theGorky Reservoir consists of the following factors In the opencode the minimum value of a significant wave height 119867
119878is
adjusted in a number of blocks where the lowest value of
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 7
0 1 2 3 4 5 6 7 8 9 10 11 120
00005
0001
00015
0002
00025
Gorky Reservoir sensors 1 2Fit Gorky Reservoir sensors 1 2Binning Gorky Reservoir sensors 1 2COARE 30
U10 (ms)
CD
Figure 7 Detailed retrieved dependence 119862119863(11988010) gray diamonds
denote the dependence received using two lower sensors solid line isan approximation of the obtained data by a function 119862
119863= 000124 sdot
119880minus1
10+ 000034 + 0000049 sdot 119880
10 black circles denote binning of the
two-sensor data (the standard deviation as the error gates) dashedline is the empiric oceanic parameterization COARE 30
119867119878is directly indicated For a description of the reservoir
the topographic grid of the Gorky Reservoir with dimensions72 times 108 and increments of 000833∘ (which corresponds toapproximately 800m by 900m for the considered latitudes)is used The grid is taken from the NOAA data ldquoGlobal LandOne-Kilometer Base Elevation (GLOBE)rdquo Topographic gridof Gorky Reservoir is shown in Figure 8 There is no reliableinformation about the bathymetry of the considered areaalthough the navigational maps show that the depth is bigenough to consider an approximation of deepwaterThus theconstant depth of 9m is taken
The frequency range is changed to 02ndash4Hz in accordancewith the experimentally observed range which is split in 31frequencies in the simulation and ismodeled by a logarithmicformula for the frequency growth
120590119873= (120575)119873minus1
1205901 (15)
where the growth rate is determined to be 120575 = 11 inaccordance with the recommendations of [2] 30 angulardirections of the wave field are consideredThe initial seedingis triggered and evolved in the wind In practice to simulatewind waves on the surface of the seas and oceans thereanalysis data is typically used as a wind forcing In themiddle-sized inland waters this approach is not applicablebecause of its too low spatial resolution (25∘) In additionin this area there are only two weather stations (Volga GMOYuryevets) but they are on the coast and it was found outthat the wind speed on the coast is different from those overthe waters of the reservoir In this regard the magnitude anddirection of the wind data are taken from the field experimentand are considered to be homogeneous over the whole waterarea of the reservoir In fact the wind field is expected tobe heterogeneous as such factors like the elongated shapeof the reservoir and the high banks can lead to a significantspatial variability of thewind field It should be noted that this
GrADS COLAIGES 2014-04-24-2047
4345∘ E
434∘ E
4335∘ E
433∘ E
4325∘ E
432∘ E
4315∘ E
431∘ E
4305∘ E
43∘ E
4295∘ E
429∘ E
566∘N
567∘N
568∘N
569∘N
57∘N
571∘N
572∘N
573∘N
574∘N
cellComputational
Figure 8 Topographical grid of Gorky Reservoir Computationalcell with a size of 000833∘ is shown
assumption of the homogeneity of the wind forcing over thepond can be a source of errors in the numerical experiment
As the wind above the reservoir is characterized by astrong mutability the averaging of the wind speed in theexperiment is performed in the interval of 15 minutes Thusthe simulation is held with input data updated every 15minutes measured in field experiment 10m wind speedand direction the water-air temperature difference Thecomparison is made for the following output 1D spectraelevations significant wave height and the average waveperiod All data is obtained at the point corresponding tothe point of observations and is averaged in the range of 15minutes to match the similarity with the averaged data of thefield experiment
6 Adjusting of Wind Input Source Term inTuned WAVEWATCH III
For the further tuning ofWAVEWATCH III a comparison ofthe used parameterizations of wind input is performed Forthis coefficients determiningWAVEWATCH III parameteri-zations of wind input (119862
119863and 120573) are displayed at each step of
the numerical simulation Figure 9(a) shows the dependence120573(120590119906lowast119892) for three considered parameterizations results of
numerical simulations for Tolman and Chalikov parameteri-zations and theoretically estimated curves for parameteriza-tionsWAM3 andWAM4 Figure 9(b) shows the dependence119862119863(11988010) of WAVEWATCH III and the proposed parameter-
ization 119862119863(11988010) obtained as a result of field measurements
(14) It can be seen that different parameterization of120573 and119862119863
used in WAVEWATCH III v314 gives similar values in theconditions of middle-sized reservoirs (120590119906
lowast119892 = 01ndash015 119880
10
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
8 Advances in Meteorology
01 1
WAM 3Tolman and ChalikovWAM 4
120590ulowastg
1E minus 005
00001
0001
001
01
120573
(a)
0 2 4 6 8 100
00005
0001
00015
0002
00025
WAM 3Tolman and Chalikov
WAM 4Experimental
U10 (ms)
CD
(b)
Figure 9 (a) Dependence of the wind-wave interaction coefficient on the dimensionless friction velocity for different parameterizations (b)Dependence of the surface drag coefficient 119862
119863on the wind speed 119880
10 WAM 3 is indicated by a dashed line Tolman and Chalikov by circles
and WAM 4 by crosses
= 1ndash10ms) At the same time the proposed parameterizationof119862119863gives significantly lower values (onasymp50) formoderate
and strong wind speeds 11988010
gt 4msThen wind-waves regime is studied for built-in param-
eterizations WAM 3 Tolman and Chalikov and WAM 4 Inthe tunedWAVEWATCH III we also used the adjusted windinput parameterization consisting of the use of the proposedexperimental parameterization 119862
119863within parameterizations
WAM 3 and Tolman and Chalikov As it was shown inSection 2 WAM 3 is based on the explicit formula andTolman and Chalikov is based on the implicit formula of119862119863(11988010)These formulas aremodified directly in the program
code Thus instead of built-in parameterizations of 119862119863in
the model the new proposed parameterization (14) is usedFigures 10(a) and 10(b) show the results of the modelingand field measurements for the days 130613 and 200614which are typical for the biggest part of the considered dataThe lower plots show the measured values of the wind usedin the simulation and the plots on the top show a changefor the retrieved values of 119867
119878 obtained both from the field
experiment and from the numerical experiments In themodel calculation119867
119878is based on a formula
119867119878= 4radic119864 (16)
The same value gives the calculation of119867119878in the experi-
ment (7) As it can be seen from Figure 10 usually the valuesof the significant wave height in simulations with built-inparameterizations are overestimated But it can be seen thatthe use of the proposed parameterization 119862
119863(11988010) improves
the agreement with the field experiment The dependence119867119878(119905) (Figure 10) shows that at the beginning of the time
interval of the measurements (first 50 minutes) the waveregime is developing only while the experimental valuesare already much higher First of all this is due to the factthat the wind prehistory for the simulations (before thestart of the measurements) for both dates is taken fromthe weather stations and as it is mentioned in Section 5
the wind speed on the coast is different from those overthe waters of the reservoir We also associate the differencebetween the simulation output and experimental values withthe inaccuracy of wind forcing due to the fact that the windis set to be homogeneous the waves that come from otherparts of the reservoir are not large enough To better matchthe results inhomogeneous wind field is required
Table 1 describes the evaluation of the difference in theapplying of different parameterizations of wind input sourceterm for two test dates 130613 and 200614 It can beseen that WAM 3 typically overestimates the values of 119867
119878
compared with the experimental data for both dates whereasthe use of the proposed new119862
119863improves the accordance very
wellAt the same time Tolman and Chalikov parameterization
underestimates the part of the values for 130613 but theuse of new 119862
119863improves the total standard deviation (STD)
for all the day of 130613 For 200614 the use of new 119862119863
makes the underestimation of Tolman and Chalikov in thebeginning of the time interval bigger because it decreasesthe value of the energy entering the system (the new 119862
119863lies
lower than 119862119863in Tolman and Chalikov as it is shown in
Figure 9(b)) This worsens the STD for Tolman and Chalikovwith new 119862
119863for 200614 It should be mentioned that
built-in Tolman and Chalikov source term performs wellenough for the conditions of the middle-sized water body Itmay be due to the particular properties of the dependenceof 119862119863
on 11988010
in Tolman and Chalikov parameterization(see Figure 9(b)) Tolman and Chalikov parameterizationunderestimates the growth rate at low wind speeds (119880
10lt
3ms) and overestimates it at higher wind speeds (11988010
gt
4ms) in comparison with the proposed new 119862119863
in theadjusted WAM 3 Possibly these effects compensate eachother and give close results for the integral value of 119867
119878
Nevertheless new 119862119863is applied in the framework of this
parameterization and shows different results for the datesof 130613 and 200614 (Table 1) but for the analysis of all
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 9
Table 1 Standard deviation of119867119878
WAM 3 + new 119862119863
WAM 3 Tolman and Chalikov + new 119862119863
Tolman and Chalikov WAM 4130613 028 036 019 023 032200614 023 041 025 020 020
0 60 120 180 240 300Internal time (min)
0 60 120 180 240 300Internal time (min)
004
008
012
016
02
024
02468
10
Win
d ve
loci
ty (m
s)
130613
HS
(m)
ExperimentTolman and Chalikov + new CD
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
(a)
Internal time (min)0 60 120 180 240 300
Internal time (min)0 60 120 180 240 300
01
02
03
04
05
06
56789
10
Win
d ve
loci
ty (m
s)
200614
HS
(m)
WAM 3Tolman and ChalikovWAM 4ExperimentTolman and Chalikov + new CD
WAM 3 + new CD
ExperimentTolman and Chalikov + new CD
(b)
Figure 10 The upper graphs dependence of119867119878on time Results of field experiments are marked by crosses the simulated values of119867
119878for
parameterizations WAM 3 (dark gray dashed line) WAM 3 with new 119862119863(dark gray solid line) Tolman and Chalikov (black dashed line)
Tolman and Chalikov with new 119862119863(black solid line) and WAM 4 (long dotted line) The lower graphs evolution of wind given by the field
experiment specified as input for WAVEWATCH III (a) 130613 (b) 200614
the measured data with the simulation data it improves thecoincidence (as shown in Figure 12(b))
The resulting values of WAM 4 application are usuallylocated between the results of WAM 3 and Tolman andChalikov and here in both cases the same situation is realized(the analysis of all data is shown in Figure 12(c))
Figure 11 shows a comparison of the wave spectra atthe point of measurements at a fixed time with the spectraobtained from a numerical experiment for built-in param-eterizations WAM 3 Tolman and Chalikov and WAM 4and for the adjusted parameterizations WAM 3 Tolman andChalikov with the new dependence 119862
119863(11988010) as in formula
(14) This improvement in the prediction of wave spectrais observed for the new parameterization 119862
119863(11988010) for the
biggest part of the considered data (Figure 11(a)) The spectrain the beginning of the time interval that correspond to
the situation in Figure 10 where the experimental valuesexceed the estimated values of119867
119878 are shown in Figure 11(b)
However along with improving the prediction of wind-wave characteristics there is still a situation in which thesimulated values of119867
119878are overestimated compared with the
experimental values this situation is reflected in the spectrain Figure 11(c)
For all of the considered experiments a comparison of theintegral characteristics (119867
119878and the mean wave period 119879
119898) is
performed The mean wave period 119879119898is simulated using the
following formula
119879119898= 1198791198980minus1
= (int
119891119903
119891min
119864 (119891) 119889119891)
minus1
int
119891119903
119891min
119864 (119891)119891minus1119889119891 (17)
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
10 Advances in Meteorology
1
0
0002
0004
0006
0008
001
f (Hz)
E(m
2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(a)
1
0
0004
0008
0012
0016
002
f (Hz)E
(m2 s)
WAM 3Tolman and ChalikovWAM 4Experiment
WAM 3 + new CD
Tolman and Chalikov + new CD
(b)
WAM 3Tolman and ChalikovWAM 4Experiment
1
0
0004
0008
0012
0016
002
f (Hz)
E(m
2 s)
WAM 3 + new CD
Tolman and Chalikov + new CD
(c)
Figure 11 1D wave spectra The experimental spectrum is indicated by light-gray bold solid wide line the simulated spectrum with theparameterizations WAM 3 gray dashed line WAM 3 with the new 119862
119863 gray solid line Tolman and Chalikov dark gray dashed line Tolman
and Chalikov with the new 119862119863 dark gray solid line and WAM 4 a long dotted line (a) The improved prediction of the wave spectra with
the use of the new parameterization of 119862119863 (b) spectra of the beginning of the time interval where the spectra from the field experiment are
higher than the spectra from the numerical experiment (c) the spectra from the numerical experiment are higher than the spectra from thefield experiment
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 11
0 01 02 03 04 05 060
01
02
03
04
05
06
WAM 3HS
experiment (m)
WAM 3 + new CD
08 1 12 14 16 18 2 22 2408
112141618
22224
Trexperiment (s)
WAM 3
WAM 3 + new CD
HS
WA
M3
(m)
Tr
WA
M3
(s)
STD = 052
STD = 039
STD = 019
STD = 025(a)
0 01 02 03 040
01
02
03
04
Tolman and ChalikovHS
experiment (m)
HS
Tolm
anan
dCh
alik
ov(m
)Tolman and Chalikov + new CD
06 08 1 12 14 16 18 2 22 240608
112141618
22224
Tr
Tolm
anan
dCh
alik
ov(s
)
Trexperiment (s)
Tolman and Chalikov
Tolman and Chalikov + new CD
STD = 040
STD = 037
STD = 026
STD = 028(b)
STD = 025
WAM 4
WAM 4
01 02 03 040HS
experiment (m)
0
01
02
03
04
081
12141618
22224
1 12 14 16 18 2 22 2408Tr
experiment (s)H
SW
AM
4(m
)Tr
WA
M4
(s)
STD = 046
(c)
Figure 12 119867119878(top graph) and 119879
119898(bottom graph) in comparison with the data of field experiment for (a) parameterizations WAM 3
(diamonds) and WAM 3 with the new 119862119863(crosses) (b) parameterizations Tolman and Chalikov (diamonds) and Tolman and Chalikov
with the new 119862119863(crosses) and (c) parameterization WAM 4 (diamonds)
On Figure 12 the 119909-axis represents the values obtained inthe field experiments and 119910-axis represents the results of thenumerical simulations On the top plots in Figure 12 for allthe considered parameterizations (both built-in and with theuse of a new parameterization) values of119867
119878in the output of
the numerical simulation are compared with those obtainedfrom the experimentThe lower plots are for the values of119879
119898
For all built-in parameterizations the overestimation of thesignificant wave height and the underestimation of the meanwave period are typical and the STD of119867
119878forWAM3 is 52
for Tolman and Chalikov is 40 and forWAM 4 is 46Theuse of the new parameterization reduces the STD of 119867
119878for
WAM 3 from 52 to 39 and for Tolman and Chalikov from40 to 37 This is an expected result as in the numericalexperiment with the use of new parameterization of 119862
119863 the
wave growth increment is defined more precisely that meansthat the amount of energy entering the system is simulatedmore accurately
However the lower graphs in Figure 12 show that theprediction of mean wave periods has significant discrepancywith the measured ones and the use of the new parameteri-zation of 119862
119863(11988010) does not make sufficient changes Perhaps
this is due to the fact that the adaptation of WAVEWATCHIII to marine environment is reflected not only in thefunction of the wind input but also in taking into accountthe specific parameters of numerical nonlinear scheme DIA[33 34] because nonlinear processes are responsible forthe redistribution of the energy received from the windin the spectrum WAVEWATCH III considers the wavecharacteristic of marine and ocean conditions which havea lower slope compared to the waves on the middle-sizedinland waters The coefficients of proportionality in thescheme DIA are adjusted to the sea conditions Steeper wavesof middle-sized reservoir may require a different adjustmentof parameters corresponding to a situation with strongernonlinearity which should lead to more rapid frequencies
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
12 Advances in Meteorology
downshift Consequently mean wave periods will decreaseAt the same time we can expect that such a tuning of thenumerical nonlinear scheme should not affect the quality ofthe predictions of 119867
119878 which indicates the amount of energy
received by the system but should lead to a better predictionof mean wave periods This hypothesis will be tested in thesubsequent numerical experiments
7 Conclusions
The paper shows the tuning of WAVEWATCH III to theconditions of the middle-sized reservoir on the exampleof the Gorky Reservoir which is specified in the modelusing real topographic grid NOAA ldquoGLOBErdquo In carryingout the calculations the default values of model parametersare modified on the basis of field measurements on thereservoir In particular the minimum value of significantwave height is adjusted and frequency range changed to 02ndash4Hz The initial seeding is developing under the influence ofunsteady uniform wind given by the experiment The wavefield is simulated using both the built-in parameterizationsof wind input adapted to the conditions of the open oceanand the parameterization using the new form of the surfacedrag coefficient (14) which is obtained from a series of fieldexperiments
Field experiments in the Gorky Reservoir show that thevalues of 119862
119863in moderate and strong winds are on asymp50
lower than those typical for the ocean conditions In thecourse of the experiment wave characteristics (frequency andwavenumber spectra the mean wave period and significantwave height) were obtained for different wind conditions Itis found out that the spectra have the asymptotic behaviorsimilar to Phillips saturation spectrum Field experiments inthe Gorky Reservoir show that the values of 119862
119863in moderate
and strong winds are on asymp50 lower than those typical forthe ocean conditions
The results of the numerical experiments are comparedwith the results obtained in the field experiments on theGorky Reservoir The use of the built-in parameterizationsshows a significant overestimation of the simulated 119867
119878
comparedwith the experimental resultsWe interpret it by theoverestimation of the turbulent wind stress (friction velocity119906lowast) and accordingly of the wind input The use of the
new parameterization119862119863(11988010) based on field measurements
on the reservoir reduces the values of 119906lowastand hence wind
increment of surface waves That improves the agreementin 119867119878from the field experiment and from the numerical
simulation Comparison of the simulationwith built-in oceanparameterizations of the wind input overestimates values ofthe mean wave period 119879
119898as well At the same time the
adjustment of the wind input does not affect significantly theagreement of119879
119898values in the results of numerical simulation
and in the field experiment We interpret this by the fact thatthe nonlinear scheme is also adjusted to the conditions ofseas and oceans and we plan to make the adjustment of theparameters of the numerical nonlinear scheme DIA to theconditions of the middle-sized reservoir
Another source of possible errors of numerical exper-iment should also be noted Due to the lack of sufficient
experimental data the wind speed is assumed to be uniformover the entire water area of the reservoir with the temporalvariability defined from the experiment In fact nonuniformdistribution of the wind is expected as factors such as theelongated shape of the reservoir and the high banks canlead to a significant spatial variability of the scale with orderof 1 km or less The use of the wind from the reanalysisdata is also impossible because of too low spatial resolution(25∘) Taking into account the high spatial variability is achallenging problem To solve it it is planned to use theatmospheric models of high and ultrahigh spatial resolution(eg atmospheric model Weather Research amp Forecasting(WRF) with block LES (Large Eddy Simulation))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the Grant of the Government ofthe Russian Federation (Contract 11G34310048) PresidentGrant for young scientists (MK-355020145) and RFBR(13-05-00865 13-05-12093 14-05-91767 14-05-31343 15-35-20953 and 15-45-02580) The field experiment is supportedby Russian Science Foundation (Agreement no 15-17-20009)and numerical simulations are partially supported by RussianScience Foundation (Agreement no 14-17-00667)
References
[1] K Hunter EdHydrodynamics of the Lakes CISM Courses andLectures no 286 International Centre for Mechanical SciencesUdine Italy 1984
[2] H Tolman and WAVEWATCH III Development Group UserManual and System Documentation of WAVEWATCH III Ver-sion 418 Marine Modeling and Analysis Branch Environmen-tal Modeling Center College Park Md USA 2014
[3] S A Poddubnyi and E V Sukhova Modeling the Effect ofHydrodynamical and Anthropogenic Factors on Distribution ofHydrobionts in Reservoirs (Userrsquos Manual) Papanin Institute ofBiology of Inland Waters 2002
[4] E N Sutyrina ldquoThe estimation of characteristics of theBratskoye Reservoir wave regimerdquo Izvestiya Irkutskogo Gosu-darstvennogo Universiteta vol 4 pp 216ndash226 2011
[5] MNewton-MatzaDisasters and Tragic Events An Encyclopediaof Catastrophes inAmericanHistory ABC-CLIO Santa BarbaraCalif USA 2014
[6] G M Jose-Henrique A Alves H L Chawla et al ldquoThe greatlakes wavemodel at NOAANCEP challenges and future devel-opmentsrdquo in Proceedings of the 12th International Workshop onWave Hindcasting and Forecasting Kohala Coast Hawaii USA2011
[7] J-H GM Alves A Chawla H L Tolman D Schwab G Langand G Mann ldquoThe operational implementation of a GreatLakes wave forecasting system at NOAANCEPrdquo Weather andForecasting vol 29 no 6 pp 1473ndash1497 2014
[8] httppolarncepnoaagovwavesviewershtml-glw-latest-hs-grl-
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Advances in Meteorology 13
[9] SWAN Team SWANmdashUser Manual Environmental FluidMechanics Section Delft University of Technology Delft TheNetherlands 2006
[10] L J Lopatoukhin A V Boukhanovsky E S Chernyshova andS V Ivanov ldquoHindcasting of wind and wave climate of seasaround Russiardquo in Proceedings of the 8th InternationalWorkshopon Waves Hindcasting and Forecasting Oahu Hawaii USANovember 2004
[11] H Gunter S Hasselmann and P A E M Janssen ldquoTheWAM model cycle 4rdquo Tech Rep 4 DKRZ WAM ModelDocumentation Hamburg Germany 1992
[12] T J Hesser M A Cialone and M E Anderson Lake St ClairStorm Wave and Water Level Modeling The US Army Researchand Development Center (ERDC) 2013
[13] A V Babanin and V K Makin ldquoEffects of wind trend andgustiness on the sea drag lake George studyrdquo Journal ofGeophysical Research vol 113 no 2 Article ID C02015 2008
[14] S S Atakturk and K B Katsaros ldquoWind stress and surfacewaves observed on Lake Washingtonrdquo Journal of PhysicalOceanography vol 29 no 4 pp 633ndash650 1999
[15] H L Tolman ldquoA third-generation model for wind waveson slowly varying unsteady and inhomogeneous depths andcurrentsrdquo Journal of Physical Oceanography vol 21 no 6 pp782ndash797 1991
[16] H L Tolman ldquoUser manual and system documentation ofWAVEWATCH III TM version 314rdquo Tech Note 276 NOAANWS NCEP MMAB 2009
[17] R L Snyder F W Dobson J A Elliott and R B LongldquoArray measurements of atmospheric pressure fluctuationsabove surface gravity wavesrdquo Journal of Fluid Mechanics vol102 pp 1ndash59 1981
[18] G J Komen S Hasselmann and K Hasselmann ldquoOn theexistence of a fully developed wind-sea spectrumrdquo Journal ofPhysical Oceanography vol 14 no 8 pp 1271ndash1285 1984
[19] J Wu ldquoWind-stress coefficients over sea surface from breeze tohurricanerdquo Journal of Geophysical Research vol 87 no 12 pp9704ndash9706 1982
[20] H L Tolman and D V Chalikov ldquoSource terms in a third-generation wind-wave modelrdquo Journal of Physical Oceanogra-phy vol 26 no 11 pp 2497ndash2518 1996
[21] P A E M Janssen The Interaction of Ocean Waves and WindCambridge University Press Cambridge UK 2004
[22] M A Donelan W M Drennan and A K Magnusson ldquoNon-stationary analysis of the directional properties of propagatingwavesrdquo Journal of Physical Oceanography vol 26 no 9 pp 1901ndash1914 1996
[23] Y I Troitskaya D A Sergeev A A Kandaurov G A BaidakovM A Vdovin and V I Kazakov ldquoLaboratory and theoreticalmodeling of air-sea momentum transfer under severe windconditionsrdquo Journal of Geophysical Research Oceans vol 117 no6 Article ID C00J21 2012
[24] OM Phillips ldquoSpectral and statistical properties of the equilib-rium range in wind-generated gravity wavesrdquo Journal of FluidMechanics vol 156 pp 505ndash531 1985
[25] P Janssen The Interaction of Ocean Waves and Wind Cam-bridge University Press Cambridge UK 2004
[26] O G SuttonMicrometeorology A Study of Physical Processes inthe Lowest Layers of the Earthrsquos Atmosphere McGraw-Hill NewYork NY USA 1953
[27] T B Benjamin ldquoShearing flow over a wavy boundaryrdquo Journalof Fluid Mechanics vol 6 pp 161ndash205 1959
[28] S E Belcher and J C RHunt ldquoTurbulent shear flowover slowlymoving wavesrdquo Journal of FluidMechanics vol 251 pp 109ndash1481993
[29] WindSonicUserManual Doc no 1405-PS-0019 Issue 21March2013
[30] E J Hopfinger J-B Flor J-M Chomaz and P BonnetonldquoInternal waves generated by a moving sphere and its wake in astratified fluidrdquo Experiments in Fluids vol 11 no 4 pp 255ndash2611991
[31] G R Spedding ldquoThe evolution of initially turbulent bluff-body wakes at high internal Froude numberrdquo Journal of FluidMechanics vol 337 pp 283ndash301 1997
[32] C W Fairall E F Bradley J E Hare A A Grachev and J BEdson ldquoBulk parameterization of airndashsea fluxes updates andverification for the COARE algorithmrdquo Journal of Climate vol16 no 4 pp 571ndash591 2003
[33] S Hasselmann and K Hasselmann ldquoComputations and param-eterizations of the nonlinear energy transfer in a gravity-wavespectrum Part I A new method for efficient computationsof the exact nonlinear transfer integralrdquo Journal of PhysicalOceanography vol 15 no 11 pp 1369ndash1377 1985
[34] S Hasselmann K Hasselmann J H Allender and T P BarnettldquoComputations and parameterizations of the nonlinear energytransfer in a gravity-wave spectrum Part II parameterizationsof the nonlinear energy transfer for application inwavemodelsrdquoJournal of Physical Oceanography vol 15 no 11 pp 1378ndash13911985
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ClimatologyJournal of
EcologyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EarthquakesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom
Applied ampEnvironmentalSoil Science
Volume 2014
Mining
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal of
Geophysics
OceanographyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Atmospheric SciencesInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MineralogyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MeteorologyAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geological ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geology Advances in