Repetition

GEO3020/4020

Lecture 1: Meteorological elements

2

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.

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

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Meteorological variables

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Radiation

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

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30% 70%

Daily clear-sky solar radiation

• Important contributor to the energy balance at the earth surface;

• Difficult to measure;• Method for estimating it on a horisontal and slope

surface at an arbritary place is given in Appendix E.

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7

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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Empirical adjustments

• The total daily clear sky radiation flux at the surface , are derived from

• Empirical relationships (adjusting for the effect of clouds and vegetation) have been developed, e.g.

where global short wave radiation on the surface and , Extraterrestrial Radiation, n = actual sunshine hour and N= max sunshine hour (can be read from table for a given location and season).

'csK

21)-(E ...

'''

bsgcs KKK

'gK

N

nbaKK ETg

''

'ETK

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Relation between K, Kin, Kcs, KET

• KET = Extraterrestrial (potential) solar radiation• Kcs = clear sky short wave radiation flux on a horizontal surface on earth• Kin = adjusted Kcs for slope, aspect, clouds and vegetation• K = net flux of solar energy entering the surface, e.g. snowpack

• Normally K < Kin < Kcs < KETKET = extraterrestrial (potential) solar radiation

Kin = measured solar radiation

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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

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

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Meteorological variablesMeasurements

Lena M. Tallaksen

Chapter 5.4.2 & 7.3.4, Appendix D.4; Dingman

GEO3020/4020

Lecture 2: I. Energy balance

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30% 70%

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Albedo is the

shortwave reflectance

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Shortwave radiation input, K Net solar radiation, K

K = Kin - Kout = Kin·(1-) (5-27)

• Where K is net flux of solar energy entering the body

• Kin – flux of solar energy incident on the surface (= global radiation)

• Kout – reflected flux

• – albedo, depends on the properties of the surface

K can be measured by pyranometers, but more common to estimate

Kcs represents the clear-sky shortwave radiation fluxKin, adjusted for the slope and aspect:

Λ, latitude, J day of year, , slope inclination angle, , slope azimuth angle

C, fraction of sky covered with cloudsF, fraction of sky obscured by forest canopy,

are functions

29)-(5 )1()()(),,(),( 321 FfCffJKK cs

inK

321 ,, fff

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Shortwave radiation input, K

• The function is derived using the concept of equivalent latitude,

• The function , the effect of cloud cover can be estimated using empirical relations like,

or

• The function effect of forest canopy, an example for pine,

• The albedo, , changes with location, season, vegetation, ….

,,1 f)2.( EAppendixAeq

Cf2

N

nbaCf 2 CbaCf 12

Ff3

FFf 91.3exp3

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Practical considerations

• Empirical equation for Shortwave radiation

C = fraction of sky covered with clouds

KCS = total daily clear sky incident radiation on a horizontal plane at

the earth surface

29)-(5 )-(1)1()()(),,(),( 321 incs KFfCffJKK

26)-(7 168.0355.0 csin KCK

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Longwave radiation exchange, L Net longwave radiation – equals to incoming atmospheric longwave radiation

minus the portion of that reflected and the radiation flux emitted by the surface

L = Lin – Lout = Lat – (1-s)Lat - Ls (7-28)

where:

Lat - incoming atmospheric longwave radiation flux,

Ls - outgoing radiation from the surface

s - emissivity of surface

L, Lat, Ls can be measured by pyranometers, but more common to estimate using equations like:

where:

at - emissivity of the atmosphere and canopy

s - emissivity of the surface

σ - Stefan-Boltzmann constant

Tat ,Ts – temperature of the atmosphere and water surface

(5.35) )2.273( 4 atatin TL

(5.36) )1()2.273( 4insssout LTL

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Longwave radiation exchange, L

Combine the two equations (5.35 and 5.36) we get:

where, Stefan-Boltzmann constant (4.90×10-9 MJ m-2 day-1 K-4)

Tat, effective radiating temp of atmosphere and canopy (˚C)Ts, temperature of surface (˚C)

29)-(7 )2.273()2.273( 44 ssatsat TTL

Table D-1 for s values, the question remains how to calculate at.

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Table d1

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Longwave radiation exchange, L

• Clear sky, no forest canopy

• Cloudy sky, no forest canopy

• Cloudy sky, forest canopy (general equation)

where ea is near surface saturation atmospheric vapor pressure

and Ta is air temperature in °C, F is the ratio of the horizontally projected area of forest canopy to the total area of interest, C is degree of cloud cover

38)-(5 2.273

72.17

1

a

aat T

e

39)-(5 )C0.22(1 2.273

72.1 27

1

a

aat T

e

40)-(5 (missing) F)C0.22(1 2.273

72.1)1( 27

1

a

aat T

eF

7)-(D 2.273

3.17exp611.0

71

a

aa T

Te

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Sensible heat, H

Sensible-heat exchange by turbulent transfer, H:

and from equation (D-49)

where

a = density of air;

Ca = heat capacity of air;

k = 0.4;

zd = zero plane displacement

height

52)-(D saaH 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.

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Zveg

Zd

Z0

velocity

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Latent heat, LE

Latent heat exchange by turbulent transfer, LE

and from equation (D-42)

where

a = density of air;

λv = latent heat of vaporization;

P = atmospheric pressure

k = 0.4;

zd = zero plane displacement

height

45)-(D saaLE 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 = horisontal windspeed,

ea = air vapor pressure

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

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Exchange of (sensible) heat with the ground, G

• Positive or negative depending on the temperature of the air

and soil surface (often negligible compared to other terms).

• If soil temperature is increasing downward (due to thermal energy stored during the summer) heat is transferred upwards at a rate:

• kG is the thermal conductivity of the soil (E L-1 T-1 -1), depends on soil texture, soil density, and moisture content and vary widely with season and place.

48)-(5 dz

dTkG GG

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Water-advected energy, Aw (lakes)

Net water-advected energy Aw [E L-2 T-1] is found from:

where:

w density of water [M L-3]cw – specific heat of water [E M-1 θ-1]w – average precipitation rate [L T-1]SW and GW – surface water and ground water inflows and outflowsTs – temperatures of the respective inflows and outflows [θ]

out in out in gwoutgwinswoutswinawww TGWTGWTSWTSWTwcA

Heat input by rain, R (snowpack)

i.rainwater is first cooled to the snow temperature (Eq. 5-47a)ii.if the snow is below zero, then freezing may occur and latent heat realised (Eq. 5-47b)

Change in stored energy, ΔQ

Energy can be stored in e.g. a snowpack, lake or soil

• Snow (warming phase)

• Lake

where: hm snow water equivalentci heat capacity of iceV lake volume, TL average lake temperature, AL lake area.subscripts 1 and 2 designate values at the beginning and end of t

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)32.7(1122 LLL

ww TVTVA

cQ

)19.5(12 TThcQ mwi

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]

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Calculation of evaporation using the energy balance method

Evaporation can be calculated solving for LE:

where:

22)-(7 /

vw

w tQAHGLKE

15)-(7 / tQAHGLKLE w

Latent Heat of Vaporization :v= 2.501 - (2.361 × 10-3) Ta

LE has units [EL-2T-1]

E [LT-1] = LE/ρwλv

Lena M. Tallaksen

Chapter 7. – 7.1.2, 7.3.6; Dingman

GEO3020/4020

Lecture 2: II. Evapotranspiration- Definitions- Governing factors- Measurements

Global water balance

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114

1255

1141

275 490

765

mm/year

Water balance for Norway, 1931 -60

33Otnes & Ræstad, 1978

Evaporation - Norway

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Global distribution of evaporation (cm)

35Encyclopedia Britannica Inc.

Temporal variation – bare soil

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Temporal variation – Lake Ontario

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Evaporation and evapotranspirationSummary

– Evapotranspiration is a collective term for all the processes by which water in the liquid or solid phase at or near the earth’s surface (rivers and lakes, bare soils, and vegetative surfaces) becomes atmospheric water vapor.

– Evapotranspiration is a second largest term in the global water balance; about 62% of precipitation that falls on the continents is evapotranspired.

– Evapotranspiration is the term that links earth surface’s water balance and energy balance.

– It is much more difficult to measure evapotranspiration than to measure precipitation and streamflow.

– There are numerous methods/models available in calculating evapotranspiration, of which the most well-known methods will be discussed in the class.

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Governing factors of evaporation

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

– Temperature– Vapour pressure deficit– Wind speed and turbulence

Optimal conditions: ?

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Governing 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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Definitions• Potential evapotranspiration, PE, is the rate at which

evapotranspiration would occur from a large area completely and uniformly covered with growing vegetation which has access to an unlimited supply of soil water and without advection or heat-storage effects (i.e. the rate is depedent on the vegetation)

• Actual evapotranspiration, ET, is the rate at which evapotranspiration occurs (i.e. describes all the processes by which liquid water at or near the land surface becomes atmospheric water vapor).

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Pan evaporation methods

Pan evaporationEpan = W – [V2-V1]

where

W = precipitation during t

V1 = the storage at the beginning of t

V2 = the storage at the end of t

For American Class-A pan, Kohler et al. (1955) developed an empirical equation to account for energy exchange through sides of a pan, and adjust daily pan evaporation, Epan, to free water evaporation, Efw [mm day-1] (Equations 7-41 and 7-42).

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Pan evaporation methods

Pan coefficient

Elake/Epan = kp

where

k is a coefficient that varies with seasons and lake.

Its annual average over the US is about 0.7

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Pan evaporation methods

4646

Pan evaporation methods

Example of pan coefficient in the Yangtze River catchment in China

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Lysimeter

One of the most reliable way of measuring potential or actual evapotranspiration is to use large containers (sometimes on the order of several metres across) called lysimeters;

Evapotranspiration is calculated by subtraction considering the different components of the water balance.

A lysimeter is most accurate when vegetation is grown in a large set up which allows the rainfall input and water lost through the soil to be easily calculated from the difference between the weight before and after a given period.

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input (Rainfall R and Additional water A) and output (Percolated water P) collected in the receiver, then PE can be estimated from the equation:

PE = R + A – P

Lysimeter for measuring potential evapotranspiration

R A

P

49Figure. Schematic of a weighable gravitation lysimeter.

Lysimeter for measuring actual evapotranspiration

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Estimation of evapotranspiration by remote sensing

Remote sensing has two potentially very important roles in estimating evapotranspiration (Engman, 1995).

First, remotely sensed measurements offer methods for extending point measurements or empirical relationships to much larger areas, including those areas where measured meteorological data may be sparse.

Secondly, remotely sensed measurements may be used to measure variables in the energy and moisture balance models of ET, such as as radiometric surface temperature, albedo, and vegetation index.