GEO3020/4020

Evapotranspiration

• Definition and Controlling factors• Measurements• Physics of evaporation• Estimation of free water evaporation, potential and actual evapotransp.• Processes and estimation methods for bare soil, transpiration,

interception

I. Meteorological Elements

II. Energy Balance

III. Evapotranspiration

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is determined by the energy and mass transport at the surface:

Weather

Meteorological variables are used to describe the weather and to calculate the components of the energy and water balance equation.

Energy transportLE: 15%H: 60%Oceans: 25%

• Precipitation• Radiation• Air temperature• Air humidity• Wind• Air pressure

3

Meteorological variables

4

Radiation

Why do we want to calculate the radiation budget at the land surface?

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30% 70%

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Summary

= Extraterrestrial Radiation on a horizontal plane

= Extraterrestrial Radiation on a sloping plane

= Total daily clear sky incident radiation on a horizontal

plane at the earth surface

= global short wave radiation at the earth surface

= backscattered radiation (= )

and

'ETK

ETK

'csK

'gK

''''' 5.0 ETETsdirdifg KKKKK

'bsK

'''bsgsc KKK

'5.0 gs K

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• Structure of the atmosphere• Composition• Vertical structure

• Pressure-temperature relation (Ideal gas law)• Adiabatic lapse rate (dry & wet)

• Vapour – Vapour pressure, ea

– Sat. vapour pressure, ea*– Absolute humidity, ρv – Specific humidity, q = ρa/ρv – Relative humidity, Wa = ea/ea*– Dew point temperature, Td

GEO3020/4020

Lecture 2: I. Energy balance II. Evapotranspiration

Energy balance equation

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0/ tQAGLEHLK w

where:

K net shortwave radiationL net longwave radiationLE latent heat transferH sensible heat transferG soil fluxAw advective energyΔQ/Δt change in stored energy

Units: [EL-2T-1]

Bowen ratio = H/LE replace H = B∙LE

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Controlling factors of evaporation

I. Meteorological situation• Energy availability• How much water vapour can be received

– Temperature– Vapour pressure deficit– Wind speed and turbulence

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Controlling factors of evaporationII. Physiographic and plant characteristics• Characteristics that influence available energy

– albedo– heat capacity

• How easily can water be evaporated– size of the evaporating surface– surroundings– roughness (aerodynamic resistance)– salt content– stomata

• Water supply– free water surface (lake, ponds or intercepted water)– soil evaporation– transpiration

The wind speed immediately above the surface. • The humidity gradient away from the surface.

– The rate and quantity of water vapor entering into the atmosphere both become higher in drier air.

• Water availability. – Evapotranspiration cannot occur if water is not available.

EvapotranspirationMeasurements

Free water evaporation- Pans and tanks- Evaporimeters

Evapotranspiration (includes vegetation)- Lysimeters- Remote sensing

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GEO3020/4020

Lecture 3: Free water Evaporation

Flux of water molecules over a surface

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15

Zveg

Zd

Z0

velocity

22)-(D ln1

0*

z

zzu

kv dm

m

Momentum, sensible heat and water vapour (latent heat) transfer by turbulence (z-direction)

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Steps in the derivation of LE• Fick’s law of diffusion for matter (transport due to differences in the concentration of water vapour);• Combined with the equation for vertical transport of water vapour due to turbulence (Fick’s law of

diffusion for momentum), gives:

DWV/DM (and DH/DM) = 1 under neutral atmospheric conditions

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42)-(D )e-(e

ln

622.0ms2

0

2

zzz

vk

PD

DLE

da

maV

M

WV

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Latent heat, LE

Latent heat exchange by turbulent transfer, LE

where

where

a = density of air;

λv = latent heat of vaporization;

P = atmospheric pressure

k = 0.4;

zd = zero plane displacement

height

45)-(D asaLE eevKLE

43)-(D

ln

622.02

0

2

zzz

k

PK

da

aVLE

z0 = surface-roughness height;

za = height above ground surface

at which va & ea are measured;

va = windspeed,

ea = air vapor pressure

es = surface vapor pressure (measured at z0 + zd)

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Sensible heat, H

Sensible-heat exchange by turbulent transfer, H (derived based on the diffusion equation for energy and momentum):

where

where

a = density of air;

Ca = heat capacity of air;

k = 0.4;

zd = zero plane displacement

height

52)-(D asaH TTvKH

50)-(D

ln

2

0

2

z

zz

kcK

da

aaH

z0 = surface-roughness height;

za = height above ground surface

at which va & Ta are measured;

va = windspeed,

Ta = air temperatures and

Ts = surface temperatures.

Selection of estimation method

• Type of surface• Availability of water• Stored-energy• Water-advected energy

Additional elements to consider:1) Purpose of study

2) Available data

3) Time period of interest

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Estimation of free water evaporation

• Water balance method• Mass-transfer methods

• Energy balance method• Combination (energy +

mass balance) method• Pan evaporation method

Defined by not accounting for stored energy

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Mass-transfer methodPhysical based equation:

or

Empirical equation:

- Different versions and expressions exist for KE and the empirical constants b0 and b1; mainly depending on wind, va and actual vapour pressure, ea

saaE eevKE saaLE eevKLE

(1802)Dalton ref. )( 10 saa eevbbE

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Calculation of evaporation using energy balance methodSubstitute the different terms into the following equation, the evaporation can

be calculated

where

22)-(7 /

vw

w tQAHGLKE

15)-(7 / tQAHGLKLE w

Latent Heat of Vaporization :v= 2.495 - (2.36 × 10-3) Ta

[MJkg-1] or 2495 J/g at 0oC

LE has units [EL-2T-1]

E [LT-1] = LE/ρwλv

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Penman combination methodPenman (1948) combined the mass-transfer and energy balance approaches to get an equation that did not require surface temp.:

I. Simplifies the original energy balance equation:

thus neglecting ground-heat conduction G, water-advected energy Aw, and change in energy storage Q/t.

II. The sensible-heat transfer flux, H, is given by:

I. + II. gives the Penman equation:

1)-(7B1 vw

HLKE

2)-(7B1 asaH TTvKH

33)-(7

)(

1)( *

vw

aaavwE WevKLKE

Penman equation – input data

• Net radiation (K+L)

(measured or alternative cloudiness, C or sunshine hours, n/N can be used);

• Temperature, Ta (gives ea*)

• Humidity, e.g. relative humidity, Wa = ea/ea*

(gives ea and thus the saturation deficit, (ea* - ea)

• Wind velocity, va

Measurements are only taken at one height interval and data are available at standard weather stations

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GEO3020/4020

Lecture 4: Evapotranspiration- bare soil- transpiration - interception

Lena M. Tallaksen

Chapter 7.4 – 7.8; Dingman

Influence of Vegetation

• Albedo• Roughness• Stomata• Root system• LAI • GAI

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Aerodynamic and surface resistance

Modelling transpiration

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Rearrange to give:

)e-(e

ln

622.0ms2

0

2

zzz

vk

PD

DLE

dm

maV

M

WV

)e-(e

and

)e-(e

ln

622.0

as

as2

0

2

C KE

v

z

zz

k

D

D

P

LEE

atat

m

daM

WV

w

a

wV

Atmospheric conductance, Cat

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ln25.6

2

0

zzz

vC

dm

mat

Orignal Penman

Penman (physical based wind function)

Penman (atmospheric conductance)

Penman equation – 3 versions

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)(

1)( *

vw

aaavwE WevKLKE

)(

1)( *

vw

aaataa WeCcLKE

)(

1)()( *

vw

aa WeufLKE

Penman-Monteith

Penman

Penman-Monteith

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55)-(7

)(

1)( *

vw

aaataa WeCcLKE

where

56)-(7 1

1)( *

CLAIfC

CC

WeCcLKE

leafscan

can

atvw

aaataa

”Big leaf” concept

Interception: Measuring and Modelling

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Function of:

i)Vegetation type and age (LAI)

ii)Precipitation intensity, frequency, duration and type

Replacement or addition to transpiration?

Estimation of potential evapotranspiration

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Definition: function of vegetation – reference crop

Operational definitions (PET)

1.Temperature based methods (daily, monthly)Empirical

2.Radiation based methods (daily)Homogeneous, well watered surfaces, e.g. P-T

3. Combination method (daily)Penman or Penman-Monteith (Cleaf: no soil moisture deficit)

4. Pan methods

Estimation of actual evapotranspiration (ET)

• Potential-evapotranspiration approaches– Empirical relationships between P-PET– Monthly water balance– Soil moisture functions– Complementary approach

• Water balance approaches – Lysimeter – Water balance for the soil moisture zone, atmosphere, land

• Turbulent-Transfer/Energy balance approaches– Penman-Monteith– Bowen ratio– Eddy correlation

• Water quality approaches

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Lena M. Tallaksen

Chapter 9.1-9.2; Dingman

GEO3020/4020

Lecture 10: Rainfall-runoff processes

• Basic aspect of catchment response

– hillslope (and stream network)

• Hydrograph separation

– The Base Flow Index (BFI)

• Linear reservoir model

• Mechanisms producing event response

• (Rainfall-runoff modeling)

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Streamflow response to precipitation (rain or snow) input

Definition of terms

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Refer Table 9-1

- Time instants, t- Time durations, T

Hydrograph separation Flow components

Methods for continuous separation similarly divide the total streamflow into one rapid, qef (event flow) and one delayed component, qbf (base flow). The delayed flow component represents the proportion of flow that originates from stored sources (e.g. groundwater).

4,00E+04

4,50E+04

5,00E+04

5,50E+04

6,00E+04

6,50E+04

Rapid response

Base flow

The Base Flow IndexBFI = Vbase flow /Vtotal flow

Isotopic and chemical methods (Box 9.1)

Linear reservoir model of catchment response• Box 9-2

– Catchment response time, T*– Influence of storm size and timing– Influence of drainage basin characteristics

• Summary of their influence is given in Table 9.2

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Mechanisms producing event responseIII. Subsurface flow

I. Channel precipitation

II. Overland flow (surface runoff)

A. Hortonian

B. Saturation excess

III. Subsurface flow

A. Saturated zone1. Local groundwater mounds

2. Perched saturated zones

B. Unsaturated zone1. Matrix (Darcian) flow

2. Macropore flow

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Questions?

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