Hindawi Publishing CorporationAdvances in MeteorologyVolume 2013 Article ID 512656 12 pageshttpdxdoiorg1011552013512656
Research ArticleThe Development of a Hybrid EnKF-3DVAR Algorithm forStorm-Scale Data Assimilation
Jidong Gao12 Ming Xue13 and David J Stensrud2
1 Center for Analysis and Prediction of Storms University of Oklahoma Norman OK 73072 USA2NOAANational Severe Storm Laboratory National Weather Center 120 David L Boren Boulevard Norman OK 73072 USA3 School of Meteorology University of Oklahoma Norman OK 73072 USA
Correspondence should be addressed to Jidong Gao jidonggaonoaagov
Received 17 May 2013 Revised 15 September 2013 Accepted 25 September 2013
Academic Editor Kun Zhao
Copyright copy 2013 Jidong Gao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A hybrid 3DVAR-EnKF data assimilation algorithm is developed based on 3DVAR and ensemble Kalman filter (EnKF) programswithin the Advanced Regional Prediction System (ARPS)The hybrid algorithm uses the extended alpha control variable approachto combine the static and ensemble-derived flow-dependent forecast error covariancesThe hybrid variational analysis is performedusing an equal weighting of static and flow-dependent error covariance as derived from ensemble forecasts The method is firstapplied to the assimilation of simulated radar data for a supercell storm Results obtained using 3DVAR (with static covarianceentirely) hybrid 3DVAR-EnKF and the EnKF are compared When data from a single radar are used the EnKF method providesthe best results for themodel dynamic variables while the hybridmethod provides the best results for hydrometeor related variablesin termof rms errors Although storm structures can be established reasonablywell using 3DVAR the rms errors are generallyworsethan seen from the other two methods With two radars the results from 3DVAR are closer to those from EnKF Our tests indicatethat the hybrid scheme can reduce the storm spin-up time because it fits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning of the assimilation cycles
1 Introduction
The effective assimilation of radar data into a numericalweather prediction (NWP) model requires advanced dataassimilation (DA) techniques such as variational and ensem-ble Kalman filter methods A three-dimensional variational(3DVAR) system which includes a mass continuity equationand other appropriate model equations as weak constraintshas been developed in recent years [1ndash5] This systemwas designed with special considerations for assimilatingradar data into a convective-scale nonhydrostatic modelmdashthe Advanced Regional Prediction System (ARPS)mdashand hasbeen used to provide initial conditions for numerous real-time convective-scale data forecasts These forecasts havebeen produced since 2008 using grid spacing that varied from4 to 1 km for domains covering the entire continental UnitedStates as part of the NOAA Hazardous Weather Testbed(HWT) Spring Experiments [6 7] For the HWT SpringExperiments Level-II radial velocity and reflectivity data
from over 120 operational Weather Surveillance Radar-1988Doppler (WSR-88D) radars were analyzed using the 3DVARsystem and ensemble forecasts were produced by addingadditional initial condition perturbations to this 3DVARanalysis The ARPS 3DVAR system has also been used in alarge number of real case studies with encouraging results[2 3 8 9] Barker et al [10] and Xiao et al [11] also appliedthe 3DVARmethod to assimilate Doppler radar observationsinto the Weather Research and Forecasting (WRF) model[12]Themajor advantage of the 3DVARmethod is its compu-tational efficiency and the ease by which weak constraints canbe included However the truly flow-dependent backgrounderror covariances were not included in either ARPS 3DVARor WRF 3DVAR systems at that time
Compared to 3DVAR the more advanced 4DVAR tech-nique incorporates the full prediction model into the assim-ilation system and implicitly includes the effects of flow-dependent error covariances through the use of both the
2 Advances in Meteorology
forward and backward models In recent years the 4DVARtechnique has helped improve global forecasts at severaloperational NWP centers including the European Centre forMedium-Range Weather Forecasts Meteo-France Meteoro-logical Service of Canada and Japan Meteorological Agency(JMA) [13] Research has also focused on storm-scale radardata assimilation using the 4DVAR method by Sun andCrook [14ndash16] In these studies both radial velocity andreflectivity data were assimilated into a convective cloud-resolving model Despite some encouraging results 4DVARfor convective-scale applications has been limited to theuse of simple microphysics in almost all cases becausethe strong nonlinearity within sophisticated microphysicsschemes makes the minimization process difficult Hondaand Koizumi [17] report difficulties including slow conver-gence when including complex ice microphysics within theinner loop of the 4DVAR systemwhenusing a nonhydrostaticmodel at JMA
The ensemble Kalman filter (EnKF) is an advanced dataassimilation method that shares many of the advantages of4DVAR It has gained considerable popularity in recent yearsin meteorology and oceanography since first proposed byEvensen [18] For convective storms very encouraging resultshave been obtained in recent studies using the ensembleKalman filter method in analyzing wind temperature mois-ture fields and evenmicrophysics variables from radar obser-vations of convective storms [19ndash26] One of the advantagesof the EnKF method over variational methods is that it canexplicitly evolve and carry the background error covariancesthrough the assimilation cycles However one of the majorsources of error with ensemble-based DA is covariancematrix rank deficiency or sampling error as a result of arelatively small ensemble size [27 28] This problem can bemore severe with storm-scale data assimilation because thedegrees of freedom of the system are typically even largerrelative to the practical ensemble sizeThe commonly utilizedremedy to the rank deficiency problem is to apply covariancelocalization by a Schur product as introduced byHoutekamerand Mitchell [27] This solution however prevents the use ofdistant correlations that are physically meaningful Furtherthe modification to the spatial covariances within a cut-offradius by a Schur product also introduces imbalances andthe effect is more substantial when the localization is morerestrictive [28] This problem may be remedied or reducedwhen using a hybrid 3DVAR and EnKF method
As discussed above the 3DVAR method is attractive forconvective scale assimilation because of its computationalefficiency and the ease by which weak constraints can beadded However the major shortcoming is that the back-ground error covariances are stationary and isotropic anderror covariances related to the model equations cannotbe simply defined In addition for convective-scale radardata assimilation only observations of radial velocity andreflectivity are typically measured while all other state vari-ables have to be ldquoretrievedrdquo in this case the flow-dependentbackground error covariances such as that derived from aforecast ensemble are especially important Oneway to blendthe advanced features of both variational and EnKF methodsand to overcome their respective shortcomings is to employ
a hybrid ensemble 3DVAR framework In such a frameworka combination of the static background error covariance andthe flow-dependent error covariance derived from an ensem-ble is used within the variational analysis For large-scale dataassimilation such an approach was initially demonstratedfor a quasigeostrophic system by Hamill and Snyder [29]and further developed by Lorenc [30] Buehner [31] andZupanski [32] with different formulations Another relativelynew approach estimates the four-dimensional background-error covariances from the ensemble members to produce a4D analysis with the variational data assimilation approachIn this method the tangent-linear or adjoint versions ofthe forecast model are no longer needed This approachwas called the En-4DVar approach [33ndash35] but was recentlyrenamed as 4DEnVar [36]
Wang et al [37] showed that the formulations proposedby Hamill and Snyder [29] Lorenc [30] and Buehner [31]though different in implementation and computational costare mathematically equivalent Barker et al [38] Li et al[39] and Zhang et al [40] recently reported the capability ofthe WRF hybrid system for mesoscale applications Furtherstudies have demonstrated the potential advantages of thehybrid method over both the pure variational and pureensemble methods for mesoscale and global applicationsespecially for small ensemble size [41ndash44] However theapplication of hybrid methods to convective scale dataassimilation has so far been limited The purpose of thispaper is to demonstrate the potential usefulness of the hybridEnKF-3DVARmethod for convective scale data assimilationespecially when assimilating radar data
The rest of this paper is organized as follows In Section 2we introduce the hybrid EnKF-3DVAR system developed inthis study Section 3 describes the DA experiment designExperiment results and quantitative performance areassessed in Section 4 We conclude in Section 5 with a sum-mary and outlook for future work
2 The Hybrid EnKF-3DVAR Scheme
In the implementation of the hybrid method for convectivescale the ensemble covariance is incorporated in the varia-tional framework using the extended control variablemethod[30 31 37] A convenient approach initially suggested byBuehner [31] is to combine the ensemble-derived and staticcovariancematrices through the augmentation of state vectorfrom k to (k w) within the 3DVAR cost function which canbe written as
119869 =1
2k119879k +1
2w119879w + 12[119867 (x119887 + Δx) minus y119900]
119879
times Rminus1 [119867 (x119887 + Δx) minus y119900] + 119869119888
(1)
where
Δx = Δx1+ Δx2= 1205731B12k + 120573
2P12w (2)
is the analysis increment of state vector x B is the static3DVAR background error covariance matrix and P is thecovariance matrix derived from an ensemble of forecastsThe
Advances in Meteorology 3
control variable k is defined in association with B and wis the augmented control vector associated with P The sizeof k is the number of analysis variables multiplied by theirdimension and the size of w is the ensemble size multipliedby the dimension of variables By using control variablesk and w instead of Δx
1and Δx
2in (2) the minimization
procedure is preconditioned by B12 and P12 respectivelyThis technique was first proposed in the context of dataassimilation by Derber and Rosati [45] The definition of(B)12 is the same as Gao et al [1] If no localization is appliedto the ensemble covariance P12 is simply a rectangularmatrix whose columns are the ensemble perturbation vectorsdivided by radic119873 minus 1 where119873 is the ensemble size The local-ization of the ensemble covariance in a variational systemwith preconditioning is discussed in Lorenc [30] Buehner[31] and Wang et al [37] The procedure and cost of doingso were also discussed in these papers For computationalefficiency we also use the recursive filter for covariancelocalization as suggested in Wang et al [41]
In (2) there are two factors 1205731and 120573
2that define the
weights placed on the static background error covariance andthe ensemble covariance To conserve the total background-error variance 120573
1and 120573
2are constrained by
1205732
1+ 1205732
2= 1 (3)
A similar constraint was applied in Hamill and Snyder [29]This approach for combining two covariancematrices to forma hybrid covariance provides flexibility since it allows fordifferent relative contributions from two covariancematricesWhen 120573
1= 1 the analysis is back to a 3DVAR analysis
scheme when 1205732= 1 the analysis is mathematically equiv-
alent to a EnKF scheme and in between we have a hybridscheme that incorporates a mixture of both static and flow-dependent error covariances When 120573
2= 1 the scheme is
essentially a variational formulation of an ensemble-basedanalysis scheme and it can be called 3DEnVAR Though thedimension of the control variables is increased the form ofthe background term of the cost function remains unchangedfrom that of 3DVAR so that codes from an existing 3DVARsystem can readily be utilized [30]
In the current study the hybrid system will assimilateboth radar reflectivity and radial velocity data Withinthis system flow-dependent background-error covariancesin particular cross covariances between microphysical anddynamic variables will be derived and utilized The single-resolution version of the EnKF system of Gao and Xue [46]is used for updating the ensemble perturbations in the dataassimilation cycles In Gao and Xue [46] an efficient dual-resolution (DR) data assimilation algorithm was developedbased on the ensemble square root Kalman filter method andtested using simulated radar radial velocity data for a super-cell storm Within the algorithm radar observations wereassimilated on both high-resolution and lower-resolutiongrids using ensemble Kalman filter algorithms and the flow-dependent background error covariance estimated from thelower resolution ensemble In that paper the DRmethod wascompared to a standard full-resolution ensemble square rootKalman filter method which is used in this study
Different from other hybrid systems [40 41] for thishybrid method an extra model integration for the length ofthe analysis cycle is needed to produce a control forecast andanalysis cycle The EnKF analyses are performed to updateanalysis perturbations for each ensemble member Then thecost function (1) is minimized to obtain optimal analyses ofcontrol vectors k and w and the optimal analysis incrementΔx is derived from (2) The ensemble mean analysis isreplaced with the hybrid EnKF-3DVAR analysis Finally theinitial conditions for the ensemble and one control forecastare obtained The above steps are repeated for each dataassimilation cycle (Figure 1)
3 Model and Experimental Design
31 PredictionModel andTruth Simulation forOSSEs We testour hybrid EnKF-3DVAR algorithm and compare its resultswith those of 3DVAR and EnKF schemes using simulateddata from a classic supercell storm of May 20 1977 near DelCity Oklahoma [47] The ARPS prediction model is usedin a 3D cloud model mode and the prognostic variablesinclude three velocity components 119906 V and 119908 perturbationpotential temperature 1205791015840 pressure 119901 and six categories ofwater substances that is water vapor specific humidity 119902Vand mixing ratios for cloud water 119902
119888 rainwater 119902
119903 cloud
ice 119902119894 snow 119902
119904 and hail 119902
ℎ The microphysical processes are
parameterized using the single-moment three-category icescheme of Ying Lin et al [48] More details on the model canbe found in Xue et al [49 50]
For our experiments the model domain is 57 times 57 times16 km3 The horizontal grid spacing is 1 km and the meanvertical grid spacing is 500m The truth simulation runis initialized from a modified real sounding plus a 4Kellipsoidal thermal bubble centered at 119909 = 48 119910 = 16and 119911 = 15 km with radii of 10 km in 119909 and 119910 and 15 kmin the 119911 direction Open conditions are used at the lateralboundaries The length of simulation is 2 hours A constantwind of 119906 = 3msminus1 and V = 14msminus1 is subtracted from theobserved sounding to keep the primary storm cell near thecenter of model grid The evolution of the simulated stormsis similar to those documented in Xue et al [50] During thetruth simulation the initial convective cell strengthens overthe first 30min The strength of the cell then decreases overthe next 30min or so which is associated with the splittingof the cell at around 55min The right moving (relative tothe storm motion vector which is towards north-northeast)cell tends to dominate the system and its updraft reachesa peak value of over 40msminus1 at 90min The initial cloudstarts to form at about 10min and rainwater forms at about15min Ice phase fields appear at about 20minA similar truthsimulation was also used in Gao et al [51] Tong and Xue [21]and Gao and Xue [46]
32 Simulation of Radar Observations The simulated radialvelocity observations are assumed to be available on the gridpoints The simulated radial velocity V
119903 is calculated from
V119903= 119906 sin120601 cos 120583 + V cos120601 cos 120583 + 119908 sin 120583 (4)
4 Advances in Meteorology
EnKF
ana
lysis
VAR-EnKF VAR-EnKF VAR-EnKF
Cycles for single analysis and forecast
Cycles for analysis and forecast ensemble
Cov
aria
nce
Repl
ace m
ean
Cov
aria
nce
Cov
aria
nce
Repl
ace m
ean
Repl
ace m
ean
EnKF
ana
lysis
EnKF
ana
lysis
Figure 1 Illustration of cycle used in a hybrid EnKF-3DVAR analysis scheme
where 120583 is the elevation angle 120601 is the azimuth angle of radarbeams and 119906 V and w are the model-simulated velocitiesinterpolated to the scalar points of the staggered model gridRandom errors drawn from a normal distribution with zeromean and a standard deviation of 1msminus1 are added to thesimulated data Since V
119903is sampled directly from the model
velocity fields hydrometeor sedimentation is not involvedThe ground-based radar is located at the southwest cornerof the computational domain that is at the origin of the119909-119910 coordinates The simulated reflectivity observations arecalculated based on Smith et al [52] and Ferrier [53] Forreflectivity random errors drawn from a normal distributionwith zero mean and a standard deviation of 3 dBZ are addedto the simulated data The radial velocity data are assimilatedand are only available where the truth reflectivity is greaterthan zero in the analysis domainWe also use only the data atevery other grid point from the 1 km truth simulation grid inhorizontal so that the total data used are one-fourth of totalmodel grid points
33 Design of Assimilation Experiments We start the initialensemble forecast at 20min of the model integration timewhen the storm cell is well developed To initialize theensemble members random noise is first added to the ini-tially horizontally homogeneous first guess defined using theenvironmental soundingA 2Dfive-point smoother is appliedto the resultant fields similar to a method used by Zupanskiet al [54] The random noise is sampled from Gaussiandistributions with zero mean and standard deviations of5msminus1 for 119906 V and 119908 and 3K for potential temperatureThese perturbation variances are somewhat larger than thoseused in Tong and Xue [21] but the standard deviation ofthe final perturbations is not necessarily larger because ofthe smoothing Other variables including the microphysicalvariables are not perturbed at the initial timeThe radial andreflectivity observations are calculated and assimilated usinga 5min cycle in all three data assimilation schemes The firstanalysis is performed at 20min and 20 ensemble membersare used A cut-off radius of 8 km is used in most of ourexperiments
We perform two set of experiments The first group ofexperiments is performed to compare the performance ofthree different schemes when observations from a singleDoppler radar are used The second group of experimentswill be performed when observations from two Dopplerradars are used For comparison purposes all three methods(3DVAR EnKF and Hybrid EnKF-3DVAR) are performedwith 16 data assimilation cycles where each cycle has a 5minanalysis-prediction interval The total assimilation period is75min
4 Results
41 Single Observation Experiment Figure 2 provides anal-ysis results of a single observation with three model vari-ables showing that ensemble information can provide flow-dependent estimates of the background-error covariance andthat both the EnKF and hybrid 3DVAR-EnKF methods canutilize such information to provide flow-dependent analysisincrements Because mass continuity equation is used asa weak constraint in 3DVAR [1] the 3DVAR method canalso provide a kind of flow-dependent anisotropic non-Gaussian type covariance structure for both 119906 componentand 119908 component (Figures 2(a) and 2(b)) However the3DVAR cannot provide increments for potential temperature(Figure 2(d)) though updated potential temperature can beobtained through a cycled 3DVAR analysis (built up byintegration of a convective NWPmodel ARPS in this study)The EnKF provides a flow-dependent covariance structure(Figures 2(b) 2(e) and 2(h)) and the hybrid 3DVAR-EnKFprovides a covariance structure in between the other twostructures In addition both EnKF and hybrid 3DVAR-EnKFcan provide increments for unobserved variables such aspotential temperature which is not directly related to radialvelocity (Figures 2(h) and 2(i)) Because the mass continuityequation is used as a weak constraint in 3DVAR this actuallyprovides a physical constraint for three components of windfield Similar to Buehner [31] and to take advantage of both3DVAR and EnKF methods 5050 weightings are chosen inthe cost function
Advances in Meteorology 5
200200
510
410
310
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10510410310
28
21011010
= minus0758 = 622 = 139Min Max Inc(km)
(km
)
(a)
510
410
310
210
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1051041031021011010
= minus105 = 392 = 0994Min Max Inc(km)
(km
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1051041031021011010
(km)
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Min = minus383 Max = 511 Inc = 179
(c)
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1051041031021011010
(km)
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Min = minus147 Max = 139 Inc = 0571
(d)
510
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1051041031021011010
= minus192 = 193 = 0768Min Max Inc(km)
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1051041031021011010
= minus405 = 390 = 159Min Max Inc(km)
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1051041031021011010
(km)
(km
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(g)
510
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1051041031021011010
Min = minus142 Max(km)
(km
)
= 0265 Inc = 0336
(h)
510
410
310
210
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1051041031021011010
= minus189 = 221 = 0819Min Max Inc(km)
(km
)
(i)
Figure 2 Wind vectors 119906-component increment by using (a) 3DVAR (b) EnKF and (c) hybrid 3DVAR-EnKF 119908-component increment byusing (d) 3DVAR (e) EnKF and (f) hybrid 3DVAR-EnKF and potential temperature increment by using (g) 3DVAR (h) EnKF and (i) hybrid3DVAR-EnKF by assimilating a single radial velocity at the black dot
42 Experiments with Single Radar As stated above the firstgroup of experiments is performed with radial velocity andreflectivity data from a single radar Figure 3 shows the finalassimilation results after 16 assimilation cycles with 5minprediction-analysis intervals The low-level flow reflectivity
patterns and the strength of the cold pool from both EnKFand hybrid EnKF-3DVAR agree very well with the simulatedtruth (Figure 3(a)) and are better than the result using 3DVAR(Figure 3(b)) although this 3DVAR can also establish thestorm structures reasonablywellThemost obvious difference
6 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
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5050 160 320 480
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Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
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Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
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Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
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(km
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Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
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2
3
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20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
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8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
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rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
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1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
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45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
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= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
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First level above ground (surface)757065
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= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
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(km)
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(km)
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= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
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(c)
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= 1366
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IncMin = minus6567
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minus20
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(km)
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Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
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4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
forward and backward models In recent years the 4DVARtechnique has helped improve global forecasts at severaloperational NWP centers including the European Centre forMedium-Range Weather Forecasts Meteo-France Meteoro-logical Service of Canada and Japan Meteorological Agency(JMA) [13] Research has also focused on storm-scale radardata assimilation using the 4DVAR method by Sun andCrook [14ndash16] In these studies both radial velocity andreflectivity data were assimilated into a convective cloud-resolving model Despite some encouraging results 4DVARfor convective-scale applications has been limited to theuse of simple microphysics in almost all cases becausethe strong nonlinearity within sophisticated microphysicsschemes makes the minimization process difficult Hondaand Koizumi [17] report difficulties including slow conver-gence when including complex ice microphysics within theinner loop of the 4DVAR systemwhenusing a nonhydrostaticmodel at JMA
The ensemble Kalman filter (EnKF) is an advanced dataassimilation method that shares many of the advantages of4DVAR It has gained considerable popularity in recent yearsin meteorology and oceanography since first proposed byEvensen [18] For convective storms very encouraging resultshave been obtained in recent studies using the ensembleKalman filter method in analyzing wind temperature mois-ture fields and evenmicrophysics variables from radar obser-vations of convective storms [19ndash26] One of the advantagesof the EnKF method over variational methods is that it canexplicitly evolve and carry the background error covariancesthrough the assimilation cycles However one of the majorsources of error with ensemble-based DA is covariancematrix rank deficiency or sampling error as a result of arelatively small ensemble size [27 28] This problem can bemore severe with storm-scale data assimilation because thedegrees of freedom of the system are typically even largerrelative to the practical ensemble sizeThe commonly utilizedremedy to the rank deficiency problem is to apply covariancelocalization by a Schur product as introduced byHoutekamerand Mitchell [27] This solution however prevents the use ofdistant correlations that are physically meaningful Furtherthe modification to the spatial covariances within a cut-offradius by a Schur product also introduces imbalances andthe effect is more substantial when the localization is morerestrictive [28] This problem may be remedied or reducedwhen using a hybrid 3DVAR and EnKF method
As discussed above the 3DVAR method is attractive forconvective scale assimilation because of its computationalefficiency and the ease by which weak constraints can beadded However the major shortcoming is that the back-ground error covariances are stationary and isotropic anderror covariances related to the model equations cannotbe simply defined In addition for convective-scale radardata assimilation only observations of radial velocity andreflectivity are typically measured while all other state vari-ables have to be ldquoretrievedrdquo in this case the flow-dependentbackground error covariances such as that derived from aforecast ensemble are especially important Oneway to blendthe advanced features of both variational and EnKF methodsand to overcome their respective shortcomings is to employ
a hybrid ensemble 3DVAR framework In such a frameworka combination of the static background error covariance andthe flow-dependent error covariance derived from an ensem-ble is used within the variational analysis For large-scale dataassimilation such an approach was initially demonstratedfor a quasigeostrophic system by Hamill and Snyder [29]and further developed by Lorenc [30] Buehner [31] andZupanski [32] with different formulations Another relativelynew approach estimates the four-dimensional background-error covariances from the ensemble members to produce a4D analysis with the variational data assimilation approachIn this method the tangent-linear or adjoint versions ofthe forecast model are no longer needed This approachwas called the En-4DVar approach [33ndash35] but was recentlyrenamed as 4DEnVar [36]
Wang et al [37] showed that the formulations proposedby Hamill and Snyder [29] Lorenc [30] and Buehner [31]though different in implementation and computational costare mathematically equivalent Barker et al [38] Li et al[39] and Zhang et al [40] recently reported the capability ofthe WRF hybrid system for mesoscale applications Furtherstudies have demonstrated the potential advantages of thehybrid method over both the pure variational and pureensemble methods for mesoscale and global applicationsespecially for small ensemble size [41ndash44] However theapplication of hybrid methods to convective scale dataassimilation has so far been limited The purpose of thispaper is to demonstrate the potential usefulness of the hybridEnKF-3DVARmethod for convective scale data assimilationespecially when assimilating radar data
The rest of this paper is organized as follows In Section 2we introduce the hybrid EnKF-3DVAR system developed inthis study Section 3 describes the DA experiment designExperiment results and quantitative performance areassessed in Section 4 We conclude in Section 5 with a sum-mary and outlook for future work
2 The Hybrid EnKF-3DVAR Scheme
In the implementation of the hybrid method for convectivescale the ensemble covariance is incorporated in the varia-tional framework using the extended control variablemethod[30 31 37] A convenient approach initially suggested byBuehner [31] is to combine the ensemble-derived and staticcovariancematrices through the augmentation of state vectorfrom k to (k w) within the 3DVAR cost function which canbe written as
119869 =1
2k119879k +1
2w119879w + 12[119867 (x119887 + Δx) minus y119900]
119879
times Rminus1 [119867 (x119887 + Δx) minus y119900] + 119869119888
(1)
where
Δx = Δx1+ Δx2= 1205731B12k + 120573
2P12w (2)
is the analysis increment of state vector x B is the static3DVAR background error covariance matrix and P is thecovariance matrix derived from an ensemble of forecastsThe
Advances in Meteorology 3
control variable k is defined in association with B and wis the augmented control vector associated with P The sizeof k is the number of analysis variables multiplied by theirdimension and the size of w is the ensemble size multipliedby the dimension of variables By using control variablesk and w instead of Δx
1and Δx
2in (2) the minimization
procedure is preconditioned by B12 and P12 respectivelyThis technique was first proposed in the context of dataassimilation by Derber and Rosati [45] The definition of(B)12 is the same as Gao et al [1] If no localization is appliedto the ensemble covariance P12 is simply a rectangularmatrix whose columns are the ensemble perturbation vectorsdivided by radic119873 minus 1 where119873 is the ensemble size The local-ization of the ensemble covariance in a variational systemwith preconditioning is discussed in Lorenc [30] Buehner[31] and Wang et al [37] The procedure and cost of doingso were also discussed in these papers For computationalefficiency we also use the recursive filter for covariancelocalization as suggested in Wang et al [41]
In (2) there are two factors 1205731and 120573
2that define the
weights placed on the static background error covariance andthe ensemble covariance To conserve the total background-error variance 120573
1and 120573
2are constrained by
1205732
1+ 1205732
2= 1 (3)
A similar constraint was applied in Hamill and Snyder [29]This approach for combining two covariancematrices to forma hybrid covariance provides flexibility since it allows fordifferent relative contributions from two covariancematricesWhen 120573
1= 1 the analysis is back to a 3DVAR analysis
scheme when 1205732= 1 the analysis is mathematically equiv-
alent to a EnKF scheme and in between we have a hybridscheme that incorporates a mixture of both static and flow-dependent error covariances When 120573
2= 1 the scheme is
essentially a variational formulation of an ensemble-basedanalysis scheme and it can be called 3DEnVAR Though thedimension of the control variables is increased the form ofthe background term of the cost function remains unchangedfrom that of 3DVAR so that codes from an existing 3DVARsystem can readily be utilized [30]
In the current study the hybrid system will assimilateboth radar reflectivity and radial velocity data Withinthis system flow-dependent background-error covariancesin particular cross covariances between microphysical anddynamic variables will be derived and utilized The single-resolution version of the EnKF system of Gao and Xue [46]is used for updating the ensemble perturbations in the dataassimilation cycles In Gao and Xue [46] an efficient dual-resolution (DR) data assimilation algorithm was developedbased on the ensemble square root Kalman filter method andtested using simulated radar radial velocity data for a super-cell storm Within the algorithm radar observations wereassimilated on both high-resolution and lower-resolutiongrids using ensemble Kalman filter algorithms and the flow-dependent background error covariance estimated from thelower resolution ensemble In that paper the DRmethod wascompared to a standard full-resolution ensemble square rootKalman filter method which is used in this study
Different from other hybrid systems [40 41] for thishybrid method an extra model integration for the length ofthe analysis cycle is needed to produce a control forecast andanalysis cycle The EnKF analyses are performed to updateanalysis perturbations for each ensemble member Then thecost function (1) is minimized to obtain optimal analyses ofcontrol vectors k and w and the optimal analysis incrementΔx is derived from (2) The ensemble mean analysis isreplaced with the hybrid EnKF-3DVAR analysis Finally theinitial conditions for the ensemble and one control forecastare obtained The above steps are repeated for each dataassimilation cycle (Figure 1)
3 Model and Experimental Design
31 PredictionModel andTruth Simulation forOSSEs We testour hybrid EnKF-3DVAR algorithm and compare its resultswith those of 3DVAR and EnKF schemes using simulateddata from a classic supercell storm of May 20 1977 near DelCity Oklahoma [47] The ARPS prediction model is usedin a 3D cloud model mode and the prognostic variablesinclude three velocity components 119906 V and 119908 perturbationpotential temperature 1205791015840 pressure 119901 and six categories ofwater substances that is water vapor specific humidity 119902Vand mixing ratios for cloud water 119902
119888 rainwater 119902
119903 cloud
ice 119902119894 snow 119902
119904 and hail 119902
ℎ The microphysical processes are
parameterized using the single-moment three-category icescheme of Ying Lin et al [48] More details on the model canbe found in Xue et al [49 50]
For our experiments the model domain is 57 times 57 times16 km3 The horizontal grid spacing is 1 km and the meanvertical grid spacing is 500m The truth simulation runis initialized from a modified real sounding plus a 4Kellipsoidal thermal bubble centered at 119909 = 48 119910 = 16and 119911 = 15 km with radii of 10 km in 119909 and 119910 and 15 kmin the 119911 direction Open conditions are used at the lateralboundaries The length of simulation is 2 hours A constantwind of 119906 = 3msminus1 and V = 14msminus1 is subtracted from theobserved sounding to keep the primary storm cell near thecenter of model grid The evolution of the simulated stormsis similar to those documented in Xue et al [50] During thetruth simulation the initial convective cell strengthens overthe first 30min The strength of the cell then decreases overthe next 30min or so which is associated with the splittingof the cell at around 55min The right moving (relative tothe storm motion vector which is towards north-northeast)cell tends to dominate the system and its updraft reachesa peak value of over 40msminus1 at 90min The initial cloudstarts to form at about 10min and rainwater forms at about15min Ice phase fields appear at about 20minA similar truthsimulation was also used in Gao et al [51] Tong and Xue [21]and Gao and Xue [46]
32 Simulation of Radar Observations The simulated radialvelocity observations are assumed to be available on the gridpoints The simulated radial velocity V
119903 is calculated from
V119903= 119906 sin120601 cos 120583 + V cos120601 cos 120583 + 119908 sin 120583 (4)
4 Advances in Meteorology
EnKF
ana
lysis
VAR-EnKF VAR-EnKF VAR-EnKF
Cycles for single analysis and forecast
Cycles for analysis and forecast ensemble
Cov
aria
nce
Repl
ace m
ean
Cov
aria
nce
Cov
aria
nce
Repl
ace m
ean
Repl
ace m
ean
EnKF
ana
lysis
EnKF
ana
lysis
Figure 1 Illustration of cycle used in a hybrid EnKF-3DVAR analysis scheme
where 120583 is the elevation angle 120601 is the azimuth angle of radarbeams and 119906 V and w are the model-simulated velocitiesinterpolated to the scalar points of the staggered model gridRandom errors drawn from a normal distribution with zeromean and a standard deviation of 1msminus1 are added to thesimulated data Since V
119903is sampled directly from the model
velocity fields hydrometeor sedimentation is not involvedThe ground-based radar is located at the southwest cornerof the computational domain that is at the origin of the119909-119910 coordinates The simulated reflectivity observations arecalculated based on Smith et al [52] and Ferrier [53] Forreflectivity random errors drawn from a normal distributionwith zero mean and a standard deviation of 3 dBZ are addedto the simulated data The radial velocity data are assimilatedand are only available where the truth reflectivity is greaterthan zero in the analysis domainWe also use only the data atevery other grid point from the 1 km truth simulation grid inhorizontal so that the total data used are one-fourth of totalmodel grid points
33 Design of Assimilation Experiments We start the initialensemble forecast at 20min of the model integration timewhen the storm cell is well developed To initialize theensemble members random noise is first added to the ini-tially horizontally homogeneous first guess defined using theenvironmental soundingA 2Dfive-point smoother is appliedto the resultant fields similar to a method used by Zupanskiet al [54] The random noise is sampled from Gaussiandistributions with zero mean and standard deviations of5msminus1 for 119906 V and 119908 and 3K for potential temperatureThese perturbation variances are somewhat larger than thoseused in Tong and Xue [21] but the standard deviation ofthe final perturbations is not necessarily larger because ofthe smoothing Other variables including the microphysicalvariables are not perturbed at the initial timeThe radial andreflectivity observations are calculated and assimilated usinga 5min cycle in all three data assimilation schemes The firstanalysis is performed at 20min and 20 ensemble membersare used A cut-off radius of 8 km is used in most of ourexperiments
We perform two set of experiments The first group ofexperiments is performed to compare the performance ofthree different schemes when observations from a singleDoppler radar are used The second group of experimentswill be performed when observations from two Dopplerradars are used For comparison purposes all three methods(3DVAR EnKF and Hybrid EnKF-3DVAR) are performedwith 16 data assimilation cycles where each cycle has a 5minanalysis-prediction interval The total assimilation period is75min
4 Results
41 Single Observation Experiment Figure 2 provides anal-ysis results of a single observation with three model vari-ables showing that ensemble information can provide flow-dependent estimates of the background-error covariance andthat both the EnKF and hybrid 3DVAR-EnKF methods canutilize such information to provide flow-dependent analysisincrements Because mass continuity equation is used asa weak constraint in 3DVAR [1] the 3DVAR method canalso provide a kind of flow-dependent anisotropic non-Gaussian type covariance structure for both 119906 componentand 119908 component (Figures 2(a) and 2(b)) However the3DVAR cannot provide increments for potential temperature(Figure 2(d)) though updated potential temperature can beobtained through a cycled 3DVAR analysis (built up byintegration of a convective NWPmodel ARPS in this study)The EnKF provides a flow-dependent covariance structure(Figures 2(b) 2(e) and 2(h)) and the hybrid 3DVAR-EnKFprovides a covariance structure in between the other twostructures In addition both EnKF and hybrid 3DVAR-EnKFcan provide increments for unobserved variables such aspotential temperature which is not directly related to radialvelocity (Figures 2(h) and 2(i)) Because the mass continuityequation is used as a weak constraint in 3DVAR this actuallyprovides a physical constraint for three components of windfield Similar to Buehner [31] and to take advantage of both3DVAR and EnKF methods 5050 weightings are chosen inthe cost function
Advances in Meteorology 5
200200
510
410
310
210
110
10510410310
28
21011010
= minus0758 = 622 = 139Min Max Inc(km)
(km
)
(a)
510
410
310
210
110
1051041031021011010
= minus105 = 392 = 0994Min Max Inc(km)
(km
)
(b)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus383 Max = 511 Inc = 179
(c)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus147 Max = 139 Inc = 0571
(d)
510
410
310
210
110
1051041031021011010
= minus192 = 193 = 0768Min Max Inc(km)
(km
)
(e)
510
410
310
210
110
1051041031021011010
= minus405 = 390 = 159Min Max Inc(km)
(km
)
(f)
510
410
310
210
110
1051041031021011010
(km)
(km
)
(g)
510
410
310
210
110
1051041031021011010
Min = minus142 Max(km)
(km
)
= 0265 Inc = 0336
(h)
510
410
310
210
110
1051041031021011010
= minus189 = 221 = 0819Min Max Inc(km)
(km
)
(i)
Figure 2 Wind vectors 119906-component increment by using (a) 3DVAR (b) EnKF and (c) hybrid 3DVAR-EnKF 119908-component increment byusing (d) 3DVAR (e) EnKF and (f) hybrid 3DVAR-EnKF and potential temperature increment by using (g) 3DVAR (h) EnKF and (i) hybrid3DVAR-EnKF by assimilating a single radial velocity at the black dot
42 Experiments with Single Radar As stated above the firstgroup of experiments is performed with radial velocity andreflectivity data from a single radar Figure 3 shows the finalassimilation results after 16 assimilation cycles with 5minprediction-analysis intervals The low-level flow reflectivity
patterns and the strength of the cold pool from both EnKFand hybrid EnKF-3DVAR agree very well with the simulatedtruth (Figure 3(a)) and are better than the result using 3DVAR(Figure 3(b)) although this 3DVAR can also establish thestorm structures reasonablywellThemost obvious difference
6 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
control variable k is defined in association with B and wis the augmented control vector associated with P The sizeof k is the number of analysis variables multiplied by theirdimension and the size of w is the ensemble size multipliedby the dimension of variables By using control variablesk and w instead of Δx
1and Δx
2in (2) the minimization
procedure is preconditioned by B12 and P12 respectivelyThis technique was first proposed in the context of dataassimilation by Derber and Rosati [45] The definition of(B)12 is the same as Gao et al [1] If no localization is appliedto the ensemble covariance P12 is simply a rectangularmatrix whose columns are the ensemble perturbation vectorsdivided by radic119873 minus 1 where119873 is the ensemble size The local-ization of the ensemble covariance in a variational systemwith preconditioning is discussed in Lorenc [30] Buehner[31] and Wang et al [37] The procedure and cost of doingso were also discussed in these papers For computationalefficiency we also use the recursive filter for covariancelocalization as suggested in Wang et al [41]
In (2) there are two factors 1205731and 120573
2that define the
weights placed on the static background error covariance andthe ensemble covariance To conserve the total background-error variance 120573
1and 120573
2are constrained by
1205732
1+ 1205732
2= 1 (3)
A similar constraint was applied in Hamill and Snyder [29]This approach for combining two covariancematrices to forma hybrid covariance provides flexibility since it allows fordifferent relative contributions from two covariancematricesWhen 120573
1= 1 the analysis is back to a 3DVAR analysis
scheme when 1205732= 1 the analysis is mathematically equiv-
alent to a EnKF scheme and in between we have a hybridscheme that incorporates a mixture of both static and flow-dependent error covariances When 120573
2= 1 the scheme is
essentially a variational formulation of an ensemble-basedanalysis scheme and it can be called 3DEnVAR Though thedimension of the control variables is increased the form ofthe background term of the cost function remains unchangedfrom that of 3DVAR so that codes from an existing 3DVARsystem can readily be utilized [30]
In the current study the hybrid system will assimilateboth radar reflectivity and radial velocity data Withinthis system flow-dependent background-error covariancesin particular cross covariances between microphysical anddynamic variables will be derived and utilized The single-resolution version of the EnKF system of Gao and Xue [46]is used for updating the ensemble perturbations in the dataassimilation cycles In Gao and Xue [46] an efficient dual-resolution (DR) data assimilation algorithm was developedbased on the ensemble square root Kalman filter method andtested using simulated radar radial velocity data for a super-cell storm Within the algorithm radar observations wereassimilated on both high-resolution and lower-resolutiongrids using ensemble Kalman filter algorithms and the flow-dependent background error covariance estimated from thelower resolution ensemble In that paper the DRmethod wascompared to a standard full-resolution ensemble square rootKalman filter method which is used in this study
Different from other hybrid systems [40 41] for thishybrid method an extra model integration for the length ofthe analysis cycle is needed to produce a control forecast andanalysis cycle The EnKF analyses are performed to updateanalysis perturbations for each ensemble member Then thecost function (1) is minimized to obtain optimal analyses ofcontrol vectors k and w and the optimal analysis incrementΔx is derived from (2) The ensemble mean analysis isreplaced with the hybrid EnKF-3DVAR analysis Finally theinitial conditions for the ensemble and one control forecastare obtained The above steps are repeated for each dataassimilation cycle (Figure 1)
3 Model and Experimental Design
31 PredictionModel andTruth Simulation forOSSEs We testour hybrid EnKF-3DVAR algorithm and compare its resultswith those of 3DVAR and EnKF schemes using simulateddata from a classic supercell storm of May 20 1977 near DelCity Oklahoma [47] The ARPS prediction model is usedin a 3D cloud model mode and the prognostic variablesinclude three velocity components 119906 V and 119908 perturbationpotential temperature 1205791015840 pressure 119901 and six categories ofwater substances that is water vapor specific humidity 119902Vand mixing ratios for cloud water 119902
119888 rainwater 119902
119903 cloud
ice 119902119894 snow 119902
119904 and hail 119902
ℎ The microphysical processes are
parameterized using the single-moment three-category icescheme of Ying Lin et al [48] More details on the model canbe found in Xue et al [49 50]
For our experiments the model domain is 57 times 57 times16 km3 The horizontal grid spacing is 1 km and the meanvertical grid spacing is 500m The truth simulation runis initialized from a modified real sounding plus a 4Kellipsoidal thermal bubble centered at 119909 = 48 119910 = 16and 119911 = 15 km with radii of 10 km in 119909 and 119910 and 15 kmin the 119911 direction Open conditions are used at the lateralboundaries The length of simulation is 2 hours A constantwind of 119906 = 3msminus1 and V = 14msminus1 is subtracted from theobserved sounding to keep the primary storm cell near thecenter of model grid The evolution of the simulated stormsis similar to those documented in Xue et al [50] During thetruth simulation the initial convective cell strengthens overthe first 30min The strength of the cell then decreases overthe next 30min or so which is associated with the splittingof the cell at around 55min The right moving (relative tothe storm motion vector which is towards north-northeast)cell tends to dominate the system and its updraft reachesa peak value of over 40msminus1 at 90min The initial cloudstarts to form at about 10min and rainwater forms at about15min Ice phase fields appear at about 20minA similar truthsimulation was also used in Gao et al [51] Tong and Xue [21]and Gao and Xue [46]
32 Simulation of Radar Observations The simulated radialvelocity observations are assumed to be available on the gridpoints The simulated radial velocity V
119903 is calculated from
V119903= 119906 sin120601 cos 120583 + V cos120601 cos 120583 + 119908 sin 120583 (4)
4 Advances in Meteorology
EnKF
ana
lysis
VAR-EnKF VAR-EnKF VAR-EnKF
Cycles for single analysis and forecast
Cycles for analysis and forecast ensemble
Cov
aria
nce
Repl
ace m
ean
Cov
aria
nce
Cov
aria
nce
Repl
ace m
ean
Repl
ace m
ean
EnKF
ana
lysis
EnKF
ana
lysis
Figure 1 Illustration of cycle used in a hybrid EnKF-3DVAR analysis scheme
where 120583 is the elevation angle 120601 is the azimuth angle of radarbeams and 119906 V and w are the model-simulated velocitiesinterpolated to the scalar points of the staggered model gridRandom errors drawn from a normal distribution with zeromean and a standard deviation of 1msminus1 are added to thesimulated data Since V
119903is sampled directly from the model
velocity fields hydrometeor sedimentation is not involvedThe ground-based radar is located at the southwest cornerof the computational domain that is at the origin of the119909-119910 coordinates The simulated reflectivity observations arecalculated based on Smith et al [52] and Ferrier [53] Forreflectivity random errors drawn from a normal distributionwith zero mean and a standard deviation of 3 dBZ are addedto the simulated data The radial velocity data are assimilatedand are only available where the truth reflectivity is greaterthan zero in the analysis domainWe also use only the data atevery other grid point from the 1 km truth simulation grid inhorizontal so that the total data used are one-fourth of totalmodel grid points
33 Design of Assimilation Experiments We start the initialensemble forecast at 20min of the model integration timewhen the storm cell is well developed To initialize theensemble members random noise is first added to the ini-tially horizontally homogeneous first guess defined using theenvironmental soundingA 2Dfive-point smoother is appliedto the resultant fields similar to a method used by Zupanskiet al [54] The random noise is sampled from Gaussiandistributions with zero mean and standard deviations of5msminus1 for 119906 V and 119908 and 3K for potential temperatureThese perturbation variances are somewhat larger than thoseused in Tong and Xue [21] but the standard deviation ofthe final perturbations is not necessarily larger because ofthe smoothing Other variables including the microphysicalvariables are not perturbed at the initial timeThe radial andreflectivity observations are calculated and assimilated usinga 5min cycle in all three data assimilation schemes The firstanalysis is performed at 20min and 20 ensemble membersare used A cut-off radius of 8 km is used in most of ourexperiments
We perform two set of experiments The first group ofexperiments is performed to compare the performance ofthree different schemes when observations from a singleDoppler radar are used The second group of experimentswill be performed when observations from two Dopplerradars are used For comparison purposes all three methods(3DVAR EnKF and Hybrid EnKF-3DVAR) are performedwith 16 data assimilation cycles where each cycle has a 5minanalysis-prediction interval The total assimilation period is75min
4 Results
41 Single Observation Experiment Figure 2 provides anal-ysis results of a single observation with three model vari-ables showing that ensemble information can provide flow-dependent estimates of the background-error covariance andthat both the EnKF and hybrid 3DVAR-EnKF methods canutilize such information to provide flow-dependent analysisincrements Because mass continuity equation is used asa weak constraint in 3DVAR [1] the 3DVAR method canalso provide a kind of flow-dependent anisotropic non-Gaussian type covariance structure for both 119906 componentand 119908 component (Figures 2(a) and 2(b)) However the3DVAR cannot provide increments for potential temperature(Figure 2(d)) though updated potential temperature can beobtained through a cycled 3DVAR analysis (built up byintegration of a convective NWPmodel ARPS in this study)The EnKF provides a flow-dependent covariance structure(Figures 2(b) 2(e) and 2(h)) and the hybrid 3DVAR-EnKFprovides a covariance structure in between the other twostructures In addition both EnKF and hybrid 3DVAR-EnKFcan provide increments for unobserved variables such aspotential temperature which is not directly related to radialvelocity (Figures 2(h) and 2(i)) Because the mass continuityequation is used as a weak constraint in 3DVAR this actuallyprovides a physical constraint for three components of windfield Similar to Buehner [31] and to take advantage of both3DVAR and EnKF methods 5050 weightings are chosen inthe cost function
Advances in Meteorology 5
200200
510
410
310
210
110
10510410310
28
21011010
= minus0758 = 622 = 139Min Max Inc(km)
(km
)
(a)
510
410
310
210
110
1051041031021011010
= minus105 = 392 = 0994Min Max Inc(km)
(km
)
(b)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus383 Max = 511 Inc = 179
(c)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus147 Max = 139 Inc = 0571
(d)
510
410
310
210
110
1051041031021011010
= minus192 = 193 = 0768Min Max Inc(km)
(km
)
(e)
510
410
310
210
110
1051041031021011010
= minus405 = 390 = 159Min Max Inc(km)
(km
)
(f)
510
410
310
210
110
1051041031021011010
(km)
(km
)
(g)
510
410
310
210
110
1051041031021011010
Min = minus142 Max(km)
(km
)
= 0265 Inc = 0336
(h)
510
410
310
210
110
1051041031021011010
= minus189 = 221 = 0819Min Max Inc(km)
(km
)
(i)
Figure 2 Wind vectors 119906-component increment by using (a) 3DVAR (b) EnKF and (c) hybrid 3DVAR-EnKF 119908-component increment byusing (d) 3DVAR (e) EnKF and (f) hybrid 3DVAR-EnKF and potential temperature increment by using (g) 3DVAR (h) EnKF and (i) hybrid3DVAR-EnKF by assimilating a single radial velocity at the black dot
42 Experiments with Single Radar As stated above the firstgroup of experiments is performed with radial velocity andreflectivity data from a single radar Figure 3 shows the finalassimilation results after 16 assimilation cycles with 5minprediction-analysis intervals The low-level flow reflectivity
patterns and the strength of the cold pool from both EnKFand hybrid EnKF-3DVAR agree very well with the simulatedtruth (Figure 3(a)) and are better than the result using 3DVAR(Figure 3(b)) although this 3DVAR can also establish thestorm structures reasonablywellThemost obvious difference
6 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
Figure 1 Illustration of cycle used in a hybrid EnKF-3DVAR analysis scheme
where 120583 is the elevation angle 120601 is the azimuth angle of radarbeams and 119906 V and w are the model-simulated velocitiesinterpolated to the scalar points of the staggered model gridRandom errors drawn from a normal distribution with zeromean and a standard deviation of 1msminus1 are added to thesimulated data Since V
119903is sampled directly from the model
velocity fields hydrometeor sedimentation is not involvedThe ground-based radar is located at the southwest cornerof the computational domain that is at the origin of the119909-119910 coordinates The simulated reflectivity observations arecalculated based on Smith et al [52] and Ferrier [53] Forreflectivity random errors drawn from a normal distributionwith zero mean and a standard deviation of 3 dBZ are addedto the simulated data The radial velocity data are assimilatedand are only available where the truth reflectivity is greaterthan zero in the analysis domainWe also use only the data atevery other grid point from the 1 km truth simulation grid inhorizontal so that the total data used are one-fourth of totalmodel grid points
33 Design of Assimilation Experiments We start the initialensemble forecast at 20min of the model integration timewhen the storm cell is well developed To initialize theensemble members random noise is first added to the ini-tially horizontally homogeneous first guess defined using theenvironmental soundingA 2Dfive-point smoother is appliedto the resultant fields similar to a method used by Zupanskiet al [54] The random noise is sampled from Gaussiandistributions with zero mean and standard deviations of5msminus1 for 119906 V and 119908 and 3K for potential temperatureThese perturbation variances are somewhat larger than thoseused in Tong and Xue [21] but the standard deviation ofthe final perturbations is not necessarily larger because ofthe smoothing Other variables including the microphysicalvariables are not perturbed at the initial timeThe radial andreflectivity observations are calculated and assimilated usinga 5min cycle in all three data assimilation schemes The firstanalysis is performed at 20min and 20 ensemble membersare used A cut-off radius of 8 km is used in most of ourexperiments
We perform two set of experiments The first group ofexperiments is performed to compare the performance ofthree different schemes when observations from a singleDoppler radar are used The second group of experimentswill be performed when observations from two Dopplerradars are used For comparison purposes all three methods(3DVAR EnKF and Hybrid EnKF-3DVAR) are performedwith 16 data assimilation cycles where each cycle has a 5minanalysis-prediction interval The total assimilation period is75min
4 Results
41 Single Observation Experiment Figure 2 provides anal-ysis results of a single observation with three model vari-ables showing that ensemble information can provide flow-dependent estimates of the background-error covariance andthat both the EnKF and hybrid 3DVAR-EnKF methods canutilize such information to provide flow-dependent analysisincrements Because mass continuity equation is used asa weak constraint in 3DVAR [1] the 3DVAR method canalso provide a kind of flow-dependent anisotropic non-Gaussian type covariance structure for both 119906 componentand 119908 component (Figures 2(a) and 2(b)) However the3DVAR cannot provide increments for potential temperature(Figure 2(d)) though updated potential temperature can beobtained through a cycled 3DVAR analysis (built up byintegration of a convective NWPmodel ARPS in this study)The EnKF provides a flow-dependent covariance structure(Figures 2(b) 2(e) and 2(h)) and the hybrid 3DVAR-EnKFprovides a covariance structure in between the other twostructures In addition both EnKF and hybrid 3DVAR-EnKFcan provide increments for unobserved variables such aspotential temperature which is not directly related to radialvelocity (Figures 2(h) and 2(i)) Because the mass continuityequation is used as a weak constraint in 3DVAR this actuallyprovides a physical constraint for three components of windfield Similar to Buehner [31] and to take advantage of both3DVAR and EnKF methods 5050 weightings are chosen inthe cost function
Advances in Meteorology 5
200200
510
410
310
210
110
10510410310
28
21011010
= minus0758 = 622 = 139Min Max Inc(km)
(km
)
(a)
510
410
310
210
110
1051041031021011010
= minus105 = 392 = 0994Min Max Inc(km)
(km
)
(b)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus383 Max = 511 Inc = 179
(c)
510
410
310
210
110
1051041031021011010
(km)
(km
)
Min = minus147 Max = 139 Inc = 0571
(d)
510
410
310
210
110
1051041031021011010
= minus192 = 193 = 0768Min Max Inc(km)
(km
)
(e)
510
410
310
210
110
1051041031021011010
= minus405 = 390 = 159Min Max Inc(km)
(km
)
(f)
510
410
310
210
110
1051041031021011010
(km)
(km
)
(g)
510
410
310
210
110
1051041031021011010
Min = minus142 Max(km)
(km
)
= 0265 Inc = 0336
(h)
510
410
310
210
110
1051041031021011010
= minus189 = 221 = 0819Min Max Inc(km)
(km
)
(i)
Figure 2 Wind vectors 119906-component increment by using (a) 3DVAR (b) EnKF and (c) hybrid 3DVAR-EnKF 119908-component increment byusing (d) 3DVAR (e) EnKF and (f) hybrid 3DVAR-EnKF and potential temperature increment by using (g) 3DVAR (h) EnKF and (i) hybrid3DVAR-EnKF by assimilating a single radial velocity at the black dot
42 Experiments with Single Radar As stated above the firstgroup of experiments is performed with radial velocity andreflectivity data from a single radar Figure 3 shows the finalassimilation results after 16 assimilation cycles with 5minprediction-analysis intervals The low-level flow reflectivity
patterns and the strength of the cold pool from both EnKFand hybrid EnKF-3DVAR agree very well with the simulatedtruth (Figure 3(a)) and are better than the result using 3DVAR(Figure 3(b)) although this 3DVAR can also establish thestorm structures reasonablywellThemost obvious difference
6 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
Figure 2 Wind vectors 119906-component increment by using (a) 3DVAR (b) EnKF and (c) hybrid 3DVAR-EnKF 119908-component increment byusing (d) 3DVAR (e) EnKF and (f) hybrid 3DVAR-EnKF and potential temperature increment by using (g) 3DVAR (h) EnKF and (i) hybrid3DVAR-EnKF by assimilating a single radial velocity at the black dot
42 Experiments with Single Radar As stated above the firstgroup of experiments is performed with radial velocity andreflectivity data from a single radar Figure 3 shows the finalassimilation results after 16 assimilation cycles with 5minprediction-analysis intervals The low-level flow reflectivity
patterns and the strength of the cold pool from both EnKFand hybrid EnKF-3DVAR agree very well with the simulatedtruth (Figure 3(a)) and are better than the result using 3DVAR(Figure 3(b)) although this 3DVAR can also establish thestorm structures reasonablywellThemost obvious difference
6 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 637Min = minus7282 Max = 05903
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 = 614
Inc = 1000Umin
= minus767 Umax
= 1888
Vmin
= minus2256 Vmax
= 1585
Min = minus7301 Max Max
= 07146
minus20
minus40
minus20
minus20
minus20
minus40
(km)
(b)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 632
Inc = 1000Umin
= minus1065 Umax
= 2231
Vmin
= minus2164 Vmax
= 1413
Min = minus6779 Max = 06719
minus20
minus20
minus20
minus20
minus40
(km)
(c)
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
Min = 000 Max = 634
Inc = 1000Umin
= minus1125 Umax
= 2132
Vmin
= minus2244 Vmax
= 1561
Min = minus6674 Max = 06627
minus20
minus40
minus40
minus20
minus20
(km)
(d)
Figure 3 Horizontal winds (vectors msminus1) perturbation potential temperature (contours at 1-K intervals) and simulated reflectivity (shadedcontours dBZ) at 250mAGL for (a) the truth simulation (b) the 3DVAR analysis (c) the EnKF analysis and (d) the hybrid EnKF-3DVARanalysis for the single radar experiment The time shown is at 100min (the end of data assimilation cycles) Wind vectors are shown every2 km
is the reflectivity field in the center ofmodel domainThe areaof reflectivity values greater than 55 dBZ is over extended ina peanut-shaped region for 3DVAR The spread of potentialtemperature is little bit far to the south-southwest directionin the southwest corner (Figure 3(b)) But the strength of thecold pool in 3DVAR as indicated by minimum perturbationpotential of minus730∘ is closer to the truth simulation (minus728∘)than seen in either EnKF or the hybrid EnKF-3DVAR
The rms errors of the analyzed fields with data from asingle radar are shown in Figure 4 The rms error calculationis limited to the regions where the truth reflectivity exceeds10 dBZ Figure 4 shows that the rms errors formodel variables119906 V119908 120579 and 119902V and reflectivity119885 (derived from the hydrom-eteor mixing ratios) generally decrease with the cycles inall three experiments The errors for 3DVAR decrease moreslowly and remain at a higher level at the end of assimilation
Advances in Meteorology 7
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
Figure 4 The rms errors of the analysis and forecast for the 3DVAR (red) EnKF (green) hybrid EnKF-3DVAR (blue) methods averagedover points at which the reflectivity is greater than 10 dBZ for (a) 119906-wind component (b) V-wind component (c) vertical wind speed (d)potential temperature (e) water vapor mixing ratio and (f) reflectivity
cycles than those for the ensemble based methods for mostof model variables For example the rms error of 119908 is closeto 3msminus1 at 100min for 3DVAR method while that in EnKFand hybrid EnKF-3DVAR is close to 13msminus1 The rms errorsof 119902V for 3DVAR is 04 gkg and that in ∘EnKF and hybridEnKF-3DVAR is below 02 kkg While these differences aresignificant the error levels late in the assimilation period forEnKF and hybrid EnKF-3DVAR are unrealistically low dueto the perfect model assumption For real data cases wheremodel error exists the analysis errors are likely to be much
larger (see for example Dowell et al [22 23]) For systemscontaining discrete intense updrafts the rms error tendsto exaggerate errors because of small spatial displacementandor structure discrepancies such as those seen in Figure 4So the results for 3DVARmay still be reasonable It should benoted that for most of model variables the performance ofEnKF and hybrid methods is very close to each other withEnKF a little bit better Interestingly the differences amongthe rms errors for 119885 in different experiments are smallest(Figure 4(f)) The rms error of 119885 is decreased to about
8 Advances in Meteorology
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
First level above ground (surface)75706560555045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000= minus7282
= 637 Max Max = 05903
MinMin
Inc = 1000Umin
= minus1007 Umax
= 2085
Vmin
= minus2194 Vmax
= 1373
minus20
minus20
minus20
minus40
minus40
minus40
(km)
(a)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1115 Umax
= 2152
Vmin
= minus2155 Vmax
= 1442
Min
IncMin = minus6549
= 637 Max Max = 06395
minus20
minus20
minus20
minus40
minus40
minus40
minus20
(km)
(b)
First level above ground (surface)
(km)
757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000
= 1000Umin
= minus1006 Umax
= 2150
Vmin
= minus2114 Vmax
= 1439
Min
IncMin = minus6536
= 634 Max
Max Max = 07219
minus20
minus20minus40
minus40
minus40
(c)
First level above ground (surface)757065
5560
5045403530252015
480
320
160
0000
5050 160 320 480
(km
)
Ref (dBZ shaded)ptprt (K contour)U-V (ms vector)
= 000 = 638
= 1000Umin
= minus1077 Umax
= 2179
Vmin
= minus2286 Vmax
= 1366
Min
IncMin = minus6567
Max Max = 06563
minus20
minus20
minus40
minus40
(km)
(d)
Figure 5 The same as Figure 3 but for the experiment with two radars
5 dBZ in all three experiments The variation of rms errorsis volatile for 3DVAR especially near the very beginning ofthe assimilation The method can decrease the errors fromabout 40 dBZ to 10 dBZ in two data assimilation cycles butthe errors quickly increase to above 20 dBZ after the 5 minmodel integration step The rms errors for the EnKF methoddecrease more smoothly throughout the data assimilationcycles because of its statistical nature Perhaps the advantageof hybrid method is most obvious for reflectivity as it fitsthe observed reflectivity field more closely than the other two
methods Though the evolution of rms errors is also volatilefor the first 10 minutes it quickly settles down and its rmserrors are the lowest among all three methods
43 Experiments with Two Radars The second group ofexperiments is performedwith radar data from two simulatedDoppler radars Figure 5 shows the final assimilation resultsafter 16 assimilation cycles As expected the low-level flowreflectivity patterns and the strength of the cold pool look
Advances in Meteorology 9
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = u
(a)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var =
(b)
1
2
3
4
5
6
7
8
20 30 40 50 60 70 80 90 100
rms
Var = w
(c)
05
1
15
2
25
3
35
4
20 30 40 50 60 70 80 90 100
rms
Var = 120579998400
(d)
02
04
06
08
1
12
20 30 40 50 60 70 80 90 100
rms
Var = q
(e)
5
10
15
20
25
30
35
40
45
20 30 40 50 60 70 80 90 100
rms
Var = Z
(f)
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
Figure 6 The same as Figure 4 but for the experiment with two radars
much better (Figure 5(b)) for 3DVAR (Figure 5(b)) espe-cially for the reflectivity field The pattern for potential tem-perature is improved when compared with the single radarexperiment (Figure 3(b)) but is still not as good as the truthsimulation (Figure 5(a)) and that for EnKF (Figure 5(c)) andthe hybrid EnKF-3DVAR (Figure 5(d)) So with more dataused the results for 3DVAR are improved Again the mostobvious improvement is for the reflectivity field in the centerof model domainThe area with reflectivity values larger than55 dBZ is more similar to the shape of truth simulation Thestorm structure for all three methods is well established by
the end of data assimilation at 100min of reference modelassimilation timeThe variation of rms errors for the analyzedfields using data from two radars is shown in Figure 6 It is notsurprising that the rms errors for model 119906 and V are muchimproved for 3DVAR For the first several data assimilationcycles the errors for 3DVAR are the lowest With morecycles the errors for the hybrid method become the lowestamong threemethods Formost of variables (except potentialtemperature) the errors for 3DVAR decrease more quicklythan seen in the other two methods for the first several dataassimilation cycles but then remain at higher levels for later
10 Advances in Meteorology
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
DA cycles The variation of rms errors is less volatile whendata from two radars are used compared to when data froma single radar is used for 3DVARThe other features are quitesimilar to the cases when data from a single radar are used
5 Summary and Future Work
A hybrid EnKF-3DVAR data assimilation system has beendeveloped based on existing 3DVAR and ensemble Kalmanfilter (EnKF) programs within the ARPS model The algo-rithm uses the extended control variable approach to com-bine the static and ensemble-derived flow-dependent forecasterror covariances [30 31 37]
The method is applied to the assimilation of radar datafrom a simulated supercell storm Two groups of experimentsare performed using different amounts of radar data Resultsobtained using 3DVAR (with static covariances entirely)hybrid EnKF-3DVAR and EnKF are compared When datafrom a single radar are used results show that after 16 cyclesof data assimilation the EnKF and hybrid schemes providesimilar results When evaluated in term of rms errors theEnKF provides slightly better results for the model dynamicvariables while the hybrid provides slightly better resultsfor the hydrometeor related variables Though the stormstructures can be established reasonably well using 3DVARits rms errors are generally worse than those from the othertwo methods When data from two radars are used the rmserrors for the hybrid method are smallest for most of themodel variables With two radars the results from 3DVARare close to those fromEnKFThese tests also indicate that thehybrid scheme can reduce the storm spin-up time because itfits the observations especially the reflectivity observationsbetter than the EnKF and the 3DVAR at the beginning ofthe assimilation cycles Thus precipitation exists from thebeginning of the model integration
Our future studies will try to answer a number of keyquestions within the hybrid EnKF-3DVAR framework justdescribedThey include the following (1)What is the optimalchoice for the relative weight of the static and flow-dependentcovariances for storm scale radar data assimilation (2)Whatis the optimal combination of ensemble size and grid spacingfor a specific computational cost (3) How does the overallperformance of the proposed method compare with 3DVARand EnKF methods when model error is present Moresensitivity experiments will be performed to answer thesequestions in the near future and results will likely help usto solve the challenges of applying this method to real-worldscenarios Even if these questions are successfully answeredthe high computational cost of this method is still likely tobe a big hurdle For this we will apply the dual-resolutionstrategy as developed for the EnKF scheme in Gao and Xue[46] A new strategy for hybrid data assimilation proposedby Penny [55] also will be tested within a storm scale dataassimilation framework in the near future
Acknowledgments
This research was funded by the NOAA Warn-on-Forecastproject The first two authors were partially supported by
[1] J Gao M Xue K Brewster and K K Droegemeier ldquoA three-dimensional variational data analysis method with recursivefilter for Doppler radarsrdquo Journal of Atmospheric and OceanicTechnology vol 21 no 3 pp 457ndash469 2004
[2] M Hu M Xue J Gao and K Brewster ldquo3DVAR and cloudanalysis with WSR-88D level-II data for the prediction of theFort Worth Texas tornadic thunderstorms Part IIimpact ofradial velocity analysis via 3DVARrdquo Monthly Weather Reviewvol 134 no 2 pp 699ndash721 2006
[3] M Hu and M Xue ldquoImpact of configurations of rapid inter-mittent assimilation ofWSR-88D radar data for the 8 May 2003Oklahoma city tornadic thunderstorm caserdquo Monthly WeatherReview vol 135 no 2 pp 507ndash525 2007
[4] G Ge and J Gao ldquoLatest development of 3DVAR system forARPS and its application to a tornadic supercell stormrdquo inProceedings of the 22nd Conference on Weather Analysis andForecasting18th Conference on Numerical Weather Prediction2007
[5] G Ge J Gao and M Xue ldquoDiagnostic pressure equation as aweak constraint in a storm-scale three dimensional variationalradar data assimilation systemrdquo Journal of Atmospheric andOceanic Technology vol 29 pp 1075ndash1092 2012
[6] M Xue F Kong K Thomas et al ldquoCAPS realtime storm-scaleensemble and high-resolution forecasts as part of the NOAAhazardous weather testbed spring experimentrdquo in Proceedingsof the 24th Conference on Severe Local Storms AMS SavannahGa USA 2008
[7] F Kong M Xue K W Thomas et al ldquoA realtime storm-scale ensemble forecast system 2009 spring experimentrdquo inProceedings of the 23rd Conference on Weather Analysis andForecasting19th Conference on Numerical Weather PredictionAmerican Meteorological Society Omaha Neb USA 2009
[8] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoImpact of CASA radar and Oklahoma Mesonet data assimila-tion on the analysis and prediction of tornadic mesovortices inan MCSrdquo Monthly Weather Review vol 139 no 11 pp 3422ndash3445 2011
[9] A D Schenkman M Xue A Shapiro K Brewster and J GaoldquoThe analysis and prediction of the 8-9 May 2007 Oklahomatornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVARrdquo Monthly WeatherReview vol 139 no 1 pp 224ndash246 2011
[10] D M Barker W Huang Y R Guo A J Bourgeois and QXiao ldquoA three-dimensional variational data assimilation systemforMM5 implementation and initial resultsrdquo MonthlyWeatherReview vol 132 pp 897ndash914 2004
[11] Q Xiao Y-H Kuo J Sun et al ldquoAssimilation of Doppler radarobservations with a regional 3DVAR system impact of Dopplervelocities on forecasts of a heavy rainfall caserdquo Journal of AppliedMeteorology vol 44 no 6 pp 768ndash788 2005
[12] W C Skamarock J B Klemp J Dudhia et al ldquoA description ofthe advanced research WRFrdquo Version 2 2005
[13] F Rabier ldquoOverview of data assimilation developments innumerical weather prediction centersrdquo in Proceedings of the 4thWMO International Symposium Assimilation of Observations inMeteorology and Oceanography Prague Czech Republic 2005
Advances in Meteorology 11
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
[14] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom Doppler radar observations using a cloud model andits adjoint Part I model development and simulated dataexperimentsrdquo Journal of the Atmospheric Sciences vol 54 no12 pp 1642ndash1661 1997
[15] J Sun andN A Crook ldquoDynamical andmicrophysical retrievalfrom doppler radar observations using a cloud model and itsadjoint Part II retrieval experiments of an observed Floridaconvective stormrdquo Journal of the Atmospheric Sciences vol 55no 5 pp 835ndash852 1998
[16] J Sun ldquoInitialization and numerical forecasting of a supercellstorm observed during STEPSrdquo Monthly Weather Review vol133 no 4 pp 793ndash813 2005
[17] Y Honda and K Koizumi ldquoThe impact of the assimilation ofprecipitation data and Radar reflectivity with a pre-operational4DVAR for the JMA nonhydrostatic modelrdquo in Proceedings ofthe 10th Symposium on Integrated Observing and AssimilationSystems for Atmosphere Oceans Land Surface (IOAS-AOLS rsquo06)2006
[18] G Evensen ldquoSequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to fore-cast error statisticsrdquo Journal of Geophysical Research vol 99 no5 pp 10143ndash10162 1994
[19] C Snyder and F Zhang ldquoAssimilation of simulated Dopplerradar observations with an ensemble Kalman filterrdquo MonthlyWeather Review vol 131 no 8 pp 1663ndash1677 2003
[20] F Zhang C Snyder and J Sun ldquoImpacts of initial estimate andobservations on the convective-scale data assimilation with anensemble Kalman filterdquo Monthly Weather Review vol 132 pp1238ndash1253 2004
[21] M Tong and M Xue ldquoEnsemble Kalman filter assimilation ofDoppler radar data with a compressible nonhydrostatic modelOSS experimentsrdquo Monthly Weather Review vol 133 no 7 pp1789ndash1807 2005
[22] D Dowell F Zhang L J Wicker C Snyder and N A CrookldquoWind and temperature retrievals in the 17 May 1981 ArcadiaOklahoma supercell ensemble Kalman filter experimentsrdquoMonthly Weather Review vol 132 pp 1982ndash2005 2004
[23] D C Dowell L J Wicker and C Snyder ldquoEnsemble kalmanfilter assimilation of radar observations of the 8 may 2003oklahoma city supercell influences of reflectivity observationson storm-scale analysesrdquoMonthly Weather Review vol 139 no1 pp 272ndash294 2011
[24] N Yussouf and D J Stensrud ldquoImpact of phased-array radarobservations over a short assimilation period observing systemsimulation experiments using an ensemble Kalman filterrdquoMonthly Weather Review vol 138 no 2 pp 517ndash538 2010
[25] N SnookMXue andY Jung ldquoAnalysis of a tornadicmesoscaleconvective vortex based on ensemble kalman filter assimilationof CASA X-band and WSR-88D radar datardquo Monthly WeatherReview vol 139 no 11 pp 3446ndash3468 2011
[26] N Snook M Xue and Y Jung ldquoEnsemble probabilistic fore-casts of a tornadic mesoscale convective system from ensembleKalman filter analyses using WSR-88D and CASA radar datardquoMonthly Weather Review vol 140 pp 2126ndash2146 2012
[27] P L Houtekamer and H L Mitchell ldquoA sequential ensem-ble Kalman filter for atmospheric data assimilationrdquo MonthlyWeather Review vol 129 no 1 pp 123ndash137 2001
[28] H L Mitchell P L Houtekamer and G Pellerin ldquoEnsemblesize balance and model-error representation in an ensembleKalman filterrdquo Monthly Weather Review vol 130 no 11 pp2791ndash2808 2002
[29] T M Hamill and C Snyder ldquoA hybrid ensemble Kalman filter-3D variational analysis schemerdquo Monthly Weather Review vol128 no 8 pp 2905ndash2919 2000
[30] A C Lorenc ldquoThe potential of the ensemble Kalman filter forNWPmdasha comparison with 4D-Varrdquo Quarterly Journal of theRoyal Meteorological Society vol 129 no 595 pp 3183ndash32032003
[31] M Buehner ldquoEnsemble-derived stationary and flow-dependent background-error covariances evaluation in aquasi-operational NWP settingrdquo Quarterly Journal of the RoyalMeteorological Society vol 131 no 607 pp 1013ndash1043 2005
[32] M Zupanski ldquoMaximum likelihood ensemble filter theoreticalaspectsrdquoMonthly Weather Review vol 133 no 6 pp 1710ndash17262005
[33] X Tian A Dai D Yang and Z Xie ldquoEffects of precipitation-bias corrections on surface hydrology over northern latitudesrdquoJournal of Geophysical Research vol 112 no 14 pp 1984ndash20122007
[34] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part I tech-nical formulation and preliminary testrdquo Monthly WeatherReview vol 136 no 9 pp 3363ndash3373 2008
[35] C Liu Q Xiao and B Wang ldquoAn ensemble-based four-dimensional variational data assimilation scheme Part IIobserving system simulation experiments with advancedresearch WRF (ARW)rdquo Monthly Weather Review vol 137 no5 pp 1687ndash1704 2009
[36] N E Bowler J Flowerdew and S R Pring ldquoTests of differentflavours of EnKF on a simple modelrdquo Quarterly Journal of theRoyal Meteorological Society vol 139 no 675 pp 1505ndash15192013
[37] X Wang C Snyder and T M Hamill ldquoOn the theoreticalequivalence of differently proposed ensemblemdash3DVAR hybridanalysis schemesrdquo Monthly Weather Review vol 135 no 1 pp222ndash227 2007
[38] D M Barker and Coauthors ldquoTheWeather Research and Fore-castingmodelrsquos community variationalensemble data assimila-tion system WRFDArdquo Bulletin of the American MeteorologicalSociety vol 93 pp 831ndash843 2012
[39] Y Li XWang andMXue ldquoAssimilation of radar radial velocitydata with the WRF hybrid ensemble-3DVAR system for theprediction of hurricane Ike (2008)rdquo Monthly Weather Reviewvol 140 pp 3507ndash3524 2012
[40] F Zhang M Zhang and J Poterjoy ldquoE4DVar coupling anensemble kalman filter with four-dimensional variational dataassimilation in a limited-area weather prediction model andcomparison to E4DVarrdquo Monthly Weather Review vol 141 pp900ndash917 2013
[41] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart I observation system simulation experimentrdquo MonthlyWeather Review vol 136 pp 5116ndash5131 2008
[42] X Wang D M Barker C Snyder and T M Hamill ldquoA hybridETKF-3DVAR data assimilation scheme for the WRF modelPart II real observation experimentsrdquoMonthlyWeather Reviewvol 136 pp 5116ndash5131 2008
[43] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartI description and single-observation experimentsrdquo MonthlyWeather Review vol 138 no 5 pp 1550ndash1566 2010
12 Advances in Meteorology
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
[44] M Buehner P L Houtekamer C Charette H L Mitchell andB He ldquoIntercomparison of variational data assimilation andthe ensemble Kalman filter for global deterministic NWP PartII one-month experiments with real observationsrdquo MonthlyWeather Review vol 138 no 5 pp 1567ndash1586 2010
[45] J C Derber and A Rosati ldquoA global oceanic data assimilationsystemrdquo Journal of Physical Oceanography vol 19 pp 1333ndash13471989
[46] J Gao and M Xue ldquoAn efficient dual-resolution approach forensemble data assimilation and tests with simulated Dopplerradar datardquo Monthly Weather Review vol 136 no 3 pp 945ndash963 2008
[47] P S Ray ldquoThe morphology of several tornadic storms on 20May 1977rdquo Journal of the Atmospheric Sciences vol 38 no 8 pp1643ndash1663 1981
[48] Y L Ying Lin P S Ray and K W Johnson ldquoInitialization of amodeled convective storm using Doppler radar-derived fieldsrdquoMonthly Weather Review vol 121 no 10 pp 2757ndash2775 1993
[49] M Xue K K Droegemeier and V Wong ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction model Part Imodel dynamics and verificationrdquo Meteorology and Atmo-spheric Physics vol 75 no 3-4 pp 161ndash193 2000
[50] M Xue K K Droegemeier V Wong et al ldquoThe advancedregional prediction system (ARPS)mdasha multi-scale nonhydro-static atmospheric simulation and prediction tool Part IImodel physics and applicationsrdquo Meteorology and AtmosphericPhysics vol 76 no 3-4 pp 143ndash165 2001
[51] J Gao M Xue A Shapiro Q Xu and K K DroegemeierldquoThree-dimensional simple adjoint velocity retrievals fromsingle-Doppler radarrdquo Journal of Atmospheric and OceanicTechnology vol 18 no 1 pp 26ndash38 2001
[52] P L Jr Smith C GMyers andH D Orville ldquoRadar reflectivityfactor calculations in numerical cloud models using bulkparameterization of precipitation processesrdquo Journal of AppliedMeteorology vol 14 pp 1156ndash1165 1975
[53] B S Ferrier ldquoA double-moment multiple-phase four-class bulkice scheme Part I descriptionrdquo Journal of the AtmosphericSciences vol 51 no 2 pp 249ndash280 1994
[54] M Zupanski S J Fletcher I M Navon et al ldquoInitiation ofensemble data assimilationrdquo Tellus A vol 58 no 2 pp 159ndash1702006
[55] S Penny ldquoThe hybrid local ensemble transform kalman filterrdquoMonthly Weather Review Accepted
