hydrological modeling chapter1 2

8/12/2019 Hydrological Modeling Chapter1 2

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Zimmermann Hydrological Modeling 1

Dr. Lothar ZimmermannBavarian Forest Institute

Phone:

08161-71-4914

For questions:

[email protected]

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



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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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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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hydrological modeling chapter1 2

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