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Zimmermann Hydrological Modeling 1
Dr. Lothar ZimmermannBavarian Forest Institute
Phone:
08161-71-4914
For questions:
Introduction Hydrological Modelling
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Lecture: Hydrological Modeling
Short description:
Overview in application of hydrological models in
water ressources management in order to quantify
effects of land use and climate change on water
budget (ground water recharge) and flood
generation
Aim of the course:
General knowledge about hydrological
problems and their solution by models
practical work experience with a model
introduction towards sophisticated models
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What is Hydrological Modeling Good for?
Climate and land use change and its
impacts on the water budget, dischargeand water quality
Extremes
Flood forecast and protection
Drought and low flows
River management
Ground water management
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Structure of the lecture
1. Water budget and its components (Review)
2. Model theory for water budget models
3. Change of land use and effects for water and
element budget
4. Climate change scenarios
5. Practical examples with BROOK90
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Precipitation
(rain, snow)Transpiration and
Interception fromplants
Evaporation from bare soil
Overland flowTranspiration and
Interzeption from
plantsSoil Percolation
Interflow
Soil Percolation
Capillary rise
Groundwater flow
Soil PercolationSoil Percolation
River flow,
discharge
Water Circle Components of a Landscape
(mod. after Bremicker 1999)
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Water budget components in the Eastern U.S
(Hewlett 1982)
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Precipitation: Measurement of Rainfall
Unit: 1 l/m2*d = 1 mm/d
German Hellmann collector 200cm
(Maidment 1982)
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Precipitation: Correction for systematic undercatch
Mean rain gauge deficiency for
snowfall of US gauges in dependence on wind speed Wind shield
3 main errors:
Wind 10%Evaporation 2-3%
Interception 2-3%
(Maidment 1982) (Dyck&Peschke 1995)
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Precipitation: Measurement of snow height and
water equivalent
Snowpack depth
Water equivalent:
Depth of water produced by the melted snow
Water equivalent=snow density [kg/m**3]*snow depth [m]
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Areal Precipitation: IDW Inverse Distance Weighting
Catchment with precipitation gauges
point precipitation
Catchment with areal precipitation
?
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Variability of Precipitation
Precipitation DWD-Weihenstephan year/vegetation period in comparison
to long-term average (1951-80 resp. since 1995 : 1961-90)
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Evapotranspiration: Measurement
Lysimeter Evaporation pan
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Evapotranspiration: Energy and Water Budget
R G H L E.E R S PW
Energy balance
Water balance
Rn: radiation balance, net radiation [W/m2]
G: heat flow in the ground [W/m
2
]H: sensible heat flux [W/m2]
L.E: latent heat flux [W/m2]
Energyflux densities
Fluxes
Energy
flux densities
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Potential evapotranspiration
Maximum possible evapotranspiration under given climatic conditions
2 * If
Short-cut grass is in the midst of a large, unbroken, similarly
vegetated stretch of land
Soil moisture is so plentiful that uptake by plants is not inhibited
Advantage:Calculation by meteorological quantities(air temperature, relative humidity, net or global radiation, sunshine
duration, windspeed)
Definition:
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Potential evapotranspiration: Upper limit
Rn: net radiation [W m
-2
]
L
RnradiationnetofequivalentWater
The water equivalent of net radiation is the upper limit for potential evapotrans-
piration if sensible (H) and ground heat flux (G) is neglected (see energy balance).
It describes that all net incoming radiative energy is completely used for the
evaporation of water, so it assumes that no bodies are warmed (heat flow in the
ground G) or that air is warmed and bubbles up as eddy (sensible heat flow). Forreal calculations the terms of H and G cannot be neglected.
From energy balance: L.ET=Rn-G-H G, H neglected
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Potential evapotranspiration: Formulae I
Haude: [mm/d]
e: vapour pressure at 2 pm localtime [hPa]
es: saturation vapour pressure at 2 pm [hPa]
f: monthly proportional factor (empirical)
ETP f e es( )
Vapour deficit driven by air temperature and therefore
indirectly by radiation
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Empirical monthly factors dependent on vegetation type
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Haude: Empirical monthly factors also dependent on altitude
Upper physical limit of ET
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Potential evapotranspiration: Formulae II
Priestley-Taylor
: 1.26 (arid: 1.74)
s: slope of vapour pressure curve e(T) [hPa*K-1]
: psychrometric constant [hPa*K-1]
Rn: net radiation [Wm-2]
G: ground heat flow [Wm-2]
GRns
s
ETP *
Psychrometric constant :
= air pressure p [Pa]* specific heat of air at constant pressure [J*kg-1*K-1] / (m*L) [J*kg-1]
m: ratio of individual gas constants for water vapor and dry air =0.622
= 0.016286 * p/L p=1013.25 hPa, T=15.2C = 0.67hPa*K-1
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PenmanETP
s RL
f u e e
s
ns* ( ) ( )
Potential evapotranspiration: Formulae III
From all three formulae for potential evapotranspiration PENMAN is the most
pyhsically based one since it considers
radiation
vapour deficit
ventilation (wind)as the three meteorological driving forces of evapotranspiration.
Wind function f(u)=0.26 (1+0,54u) [mm/hPa] u in m/s
Slope of the saturation vapor curve s=4098T / (237.3+T) [hPa/K] T in C
Latent heat of water L=2501-2.37T [kJ/kg]
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Evapotranspiration: Comparison of ETP
Potential Evapotranspiration Schluchsee/Black Forest
0
100
200
300
400
500
600
700
800
900
88 89 90 91 92 93 94 95 mean
Hydrological Years
m
m/a Rn / L
PenmanPriestley-Taylor
Haude forest
Water balance P-R
Variability of Evapotranspiration
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Variability of Evapotranspiration
Evapotranspiration acc. to Haude and climatic water balance DWD
Weihenstephan 1991-2001
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Soil water
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Soil Retention: Measurement of Soil Moisture
DataloggerSatellit
Tensiometer,TDR-Sonde
5
13
18
9
5cmThermofhler10cmThermofhler,TDR-Sonde20cmTensiometer,TDR-Sonde
3m2m
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Measurement of soil water content by
TDR (Time Domain Reflectometry)
Quantity: volumetric water content [cm3/cm3 or volume-%)
Principle:
Retardation of propagation velocity of
electromagnetic waves in wet soil
High dielectric constant of water ( =82) compared todry soil ( < 5) and air ( = 1)
Strong correlation between dielectric constant in thesoil and volumetric water content
Annual variation of soil water content
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Annual variation of soil water content
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Matric potential
The matric potential describes
with how much energy, as a result
of the soils capillary and
adhesive forces, water is hold by
the soil
[hPa, cm WC]
(Hewlett 1982)
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A18
180 185 190 195 200 205 210
Rasterpunkte
2
4
6
8
10
1214
16
18
Woche
-800
-700
-600
-500
-400
-300
-200
-100
0
Erosionspillway
Gleyic
featuresm.
NN 465
460
455
Surface Morphology
and stratigraphy
influence soil moisture
and runoff generation
Change of Matric Potentials within a Field
Transect of tensiometers in 90 cm depth: change of matric potentials in dependent on
site and slope position
Annual variation of
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Annual variation of
Open-field precipitation
Potential evapotranspiration
Matric potential (soil moisture)
Snow cover
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Runoff: Measurement of Flow Velocity I
R Runoff, discharge = flow velocity * river profile area A
(width*water depth)
R = v * A
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Runoff: Measurement of Flow Velocity II
(Hewlett 1982)
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Runoff: Stage-Discharge Curve I
Discharge [m3/s] = f (Water level (Stage))
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Runoff: Stage-Discharge Curve II
(Hewlett 1982)
E l f it i t d l t fl
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Here, discharge and element concentration are
continuously monitored and stored in a data
logger.
automaticsampler
Datalogger
60V-weir
Laptop
pressuregauge
WieseBrache
Acker 19
Acker 20
Fichtenwald
BW4
A1A2A3
A4
A5A6
A7BN
BE6
BW1Waldrand
Lage der Wehre und Drnagen
100 m100 m
Example for monitoring water and element fluxes
Position of weirs and drains
V-notch sharp crested weir
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V-notch, sharp crested weir
Q=1.34*h2.48
Defined relation
between h and Q
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Catchment area
(Hewlett 1982)
C t h t I
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Catchment I
Surface catchment
Underground catchment
permeable
impermeable
Ground water
Water divide
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Catchment II
Definition:
A catchment is the area in horizontal projection in km, limited
by water divides through which at a certain point of the river all
discharge originates
The water divide can be constructed in a topographical map
including isohypses. It starts from a point at the river (river
profile) by cutting the isohypses vertically.
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Surface and Subsurface Catchment
G d t D fi iti I
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Groundwater Definitions I
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Fl i i d d l
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Flow regime in dependence on geology
Salt river:impermeable, shallow soils
(clayey glacial till)
Manistee River:
deep, permeabale soils
Structure of the lecture
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Zimmermann Hydrological Modeling 47
Structure of the lecture
1. Water budget and its components (Review)
2. Model theory for water budget models
3. Change of land use and effects for water and
element budget
4. Climate change scenarios
5. Practical examples with BROOK90
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Natural Land use change
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Bavarian Forest
National Park
No counter-
measures against
bark beetles
Water Budget Model as Scenario Tool
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g
State of the System
Hydrometeorology River bed parameter Basin characterisitics
Discharge
Input for Water quality and ground water models
Change in the state of the system (scenario) controllable
Operational forecast
What is a system a process a model?
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Zimmermann Hydrological Modeling 51
What is a system, a process, a model?
Input p Output qSystem
P-q=dS/dt
A model describes a system and its processes.
A system is an unit of elements which is separated from its environment and
relates an input of element, energy or information to an output of element, energy
or information in its time pattern to each other.
A process is defined as quantitative or qualitative change with time. For
hydrological processes, in most cases, the coordinates of a water body or
particle are changed, together with a change in temperature, pressure or other
properties of water. They are often non-linear.
The operation of the system is modelled.
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Model requirements
A model should include:
basic laws (cont inui ty , geometry, boundary co ndi t ions)
st ructure of the sy stem
parameters of the system
A model is an idealized abstraction of reality. Models should berepresetative of real systems.
Hydrological System
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Hydrological System
A catchment (watershed) or a defined section between two
gauges at a river or a lake is a system.
It consists out of subsystems like land surface (plant canopy),soil, groundwater, river bed, epi- and hypolimnion etc.
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Classification of hydrological models
Aim of the model application?
real-time forecasting, scenarios, planning
Which type of system is modelled?
aquifers, catchment, river section
Which hydrological process or variable?
infiltration, ET, ground water recharge
Which degree of deterministic behaviour (cause-effect
relationships)?
Overview of hydrological models
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Deterministic Models
(Cause-Effect-Relations
Stochastic Models
(Statistical relations)
Fundamental
Laws (Hydrodynam.)
Conceptual
Models
Black Box
Models
Distributed Models
(areal-detailed information)
Lumped Models
(no/coarse spatial partitioning)
Elementary
Unit Areas
Larger
Subareas
Statistical
distribution
No
DistributionRaster
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Description of process in dependence on spatial
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process resolution (acc.to Becker 1995)
Conceptual models>1000 km2>30 kmmacro
Physically based
conceptual models0,01-1000 km20,1 30 kmmeso
Basic
physical laws< 0,01 km2< 100 mmicro
Process
description
AreaLengthScale
Discretization in space and time
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Discretization in space and time
Discretization in time
According to the aim of the modeling different time steps have to be
used (e.g. floods, urban drainage down to minutes, water budget
daily to monthly)
Discretization in space
Input data, parameters which describe the basin (topography, land
use, soils)and resulting fluxes of energy and mass are spatially
heterogeneous
Raster, homogeneous areas, largersubareas or statistical distribution
Example spatial discretization
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Subcatchments as block
models
Zones or hydrotopes,
for element transport furtherseparated into segments or
cascades
Regular raster
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Complex hydrological factors: hydrotopes
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Errors in hydrological models
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Error of model:
Decreases with increasing model complexity
Error of measurement (input data)
Increases with increasing model complexity since datademand increase
Total errorerror
Model complexity
Input error
model error
Lumped Water Budget Model
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Deterministic Models
(Cause-Effect-Relations
Stochastic Models
(Statistical relations)
Fundamental
Laws (Hydrodynam.)
Conceptual
Models
Black Box
Models
Distributed Models
(areal-detailed information)
Lumped Models
(no/coarse spatial partitioning)
Elementary
Unit Areas
Larger
Subareas
Statistical
distribution
No
Distribution
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Input data- in general
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Process variablesPrecipitation, global radiation or sunshine duration, relative humidity, air
temperature, wind
Physical plot or basin characteristicsCatchment area, latitude, slope, exposition, mean elevation height, land use,
porosity of the soil, field capacity, permanent wilting point, root depth, land use,
LAI etc.
Model parameterprecipitation correction, interception and land surface storage capacity, storage
constants, percentage of overland flow, temperature limit for snow/rain, snow
melt temperature, day degree factor for snow melt, retention factor for snow
cover, starting values for the storages
Test and control dataDischarge, percentage of ground water flow, soil moisture and
evapotranspiration measurements at certain points
Lumped Water Budget Model BROOK90
Short description
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p
Modeling of subsystem:Precipitation
Precipitation PREC has to be
corrected for systematic
undercatch outside the model
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while pre-processing the
meteorological input data, then
division into snowfall fraction(SFAL) and rainfall (RFAL),
these are further divided into
the fractions which are
intercepted (SINT, RINT) and
which fall through the canopy
(RTHR, RTHR). Throughfall isfurther reduced by the amount
of rain which is stored within
the snow cover(SNOW). The
snow cover is reduced by
evaporation (SNVP) and
snow melt (SMLT) while thelast is added with the remaining
throughfall to the net rainfall
(RNET).
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Modeling of subsystem:Runoff formation
Net rainfall RNET is dividedinto surface runoff (SRFL) and
into infiltration into the soil
(SLFL). The soil water
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( )
storage (SWATI (1->n))
consists of several layers. The
infiltration SLFL which can beregarded as fast deep
infiltration by macropores is
divided into two components
within the soil: first infiltration
by macropores in each layer
(INFL(1->n)) of the soil matrix,second a fast downslope
bypass flow through pipes
(BYFL(1->n)) which does not
enter the soil matrix. Within the
soil we have a vertical matrix
flow (VRFL(I)), when layersare saturated another
downslope, slow flow (DSFL)
is generated.
Lumped Water Budget Model BROOK90Flow components
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SRFL:
Overland flow
BYFL:Bypass flow
SLFL:
surface infiltration
INFL:
macropore infiltrationVRFL:
vertical matric flow
DSFL:
slope parallel interflow
GWFL:ground water flow
FLOW=SRFL+BYFL+DSFL+GWFL
Modeling of subsystem:Evapotranspiration
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From each soil layer according
to root density water is
withdrawn throughtranspiration (TRAN(I->n)),
from the first soil layer in
addition also soil evaporation
(SLVP) takes place, if snow
cover is present snow
evaporation (SNVP) as well,the interception storages
(INTR, INTS) are emptied as
well by interception
evaporation (IRVP, ISVP)
Input data- Brook90
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Process variables [unit] in dfile.dat
global radiation [MJ cm-2d-1]maximum and minimum of air temperature [C]
vapour pressure [kPa]
wind speed [m/s]
precipitation [mm/d]
Discharge [mm/d]
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