Evaporation

• What is evaporation?• How is evaporation measured?• How is evaporation estimated?

• Reading: Applied Hydrology Sections 3.5 and 3.6

• With assistance from Dan Siegel and Marcy Litvak

Evaporation

• What is evaporation?• How is evaporation measured?• How is evaporation estimated?

Evaporation

Evaporation – process by which liquid water becomes water vapor– Transpiration – process by which liquid water

passes from liquid to vapor through plant metabolism

– Evapotranspiration – evaporation through plants and trees, and directly from the soil and land surface

– Potential Evaporation – evaporation from an open water surface or from a well-watered grass surface

Factors Influencing Evaporation

• Energy supply for vaporization (latent heat)– Solar radiation

• Transport of vapor away from evaporative surface– Wind velocity over surface– Specific humidity gradient

above surface• Vegetated surfaces

– Supply of moisture to the surface

– Evapotranspiration (ET)• Potential Evapotranspiration

(PET) – moisture supply is not limited

nR

E

Net radiation

Evaporation

Air Flowu

Evapotranspiration (ET)

Over land surfaces, we cannot distinguish between water vapor that evaporated from the soil and water vapor that was transpired through plants

Evaporation

• What is evaporation?• How is evaporation measured?• How is evaporation estimated?

Evaporation from an Open Water Surface

• Simplest form of evapotranspiration– This is the amount of water lost from lakes and reservoirs– Often estimating by measuring the loss from a National

Weather Service Class A pan

• This is referred to as Potential Evapotranspiration (ETp) because it is the maximum potential rate of ET under the given meteorological conditions

Lysimeters

Measurement of evapotranspiration

Flux Towers (Marcy Litvak)

Flux tower instruments

IRGA

3-D Sonic anemometer

Net radiometerPyrronometer

Quantumsensor

Flux tower instruments

Air Temperature at 1m and 10m

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5

10

15

20

25

30

35

40

t_hmp_10m

Freeman Ranc Flux Tower (Marcy Litvak)

Vapor Pressure and Saturated Vapor Pressure (kPa)

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/040

1

2

3

4

5

6

e_Avge_sat_Avg

Relative Humidity at 1m and 10m

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/040

0.2

0.4

0.6

0.8

1

rh_hmp_10m

Average = 0.61

Average = 0.71

Wind Speed (m/s)

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5

10

15

20

25

Net Radiation (W/m2)

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/04

-100

0

100

200

300

400

500

600

700

800

ET -Eddy covariance method

• Measurement of vertical transfer of water vapor driven by convective motion

• Directly measure flux by sensing properties of eddies as they pass through a measurement level on an instantaneous basis

• Statistical tool

Basic Theory

Mean

Fluctuation

Instantaneous signal

InstantaneousPerturbation from

The mean

All atmospheric entities show short-period fluctuations about their long term mean value

Time averaged property

Turbulent mixing

Propterties carried by eddies:Mass, density ρVertical velocity w

Volumetric content qv

Temperature T

Sensible Heat Flux (W/m2)

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/04

-200

-100

0

100

200

300

400

500

Latent Heat Flux (W/m2)

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/04

-200

-100

0

100

200

300

400

500

Evaporation (mm/day)

8/5/04 8/6/04 8/7/04 8/8/04 8/9/04 8/10/04 8/11/04 8/12/04 8/13/04 8/14/04 8/15/04

-4

0

4

8

12

16

20

Average = 3.15 mm/day

Energy Balance Method

Can directly measure these variables

How do you partition H and E??

Evaporation

• What is evaporation?• How is evaporation measured?• How is evaporation estimated?

Energy Balance Method

28.4 W  𝑚2  

×𝐽 /𝑠𝑊

×1𝑔

2450 𝐽×

3600 𝑠1h𝑟

×24 h𝑟1𝑑𝑎𝑦

×𝑚3

1000𝑘𝑔×

1𝑘𝑔1000𝑔

×1000𝑚𝑚

1𝑚=1

𝑚𝑚𝑑𝑎𝑦

𝜌 𝑤

𝐸𝑇=E28.4

=1

28.4(𝑅𝑛−𝐺− 𝐻−𝑊 )

The maximum radiative evaporation rate Er =

Velocity Profile

• Determining momentum transfer requires knowing velocity profile

• Flow of air over land or water – log velocity profile

0 1 2 3 40

1

2

3

4

Velocity (u)

Ele

va

tio

n (

z))ln()(

0

*

z

z

k

uzu

/0* u Shear velocity

Von Karman constant Roughness heightk

)ln()(0

*

z

z

k

uzu

0Wall shear stress

0z

zk

u

dz

du 1* Velocity gradient

Aerodynamic Method

• Include transport of vapor away from water surface as function of: – Humidity gradient above

surface– Wind speed across surface

• Upward vapor flux

• Upward momentum flux12

21

zz

qqK

dz

dqKm

vvwa

vwa

nR

E

Net radiation

Evaporation

Air Flow

12

12

zz

uuK

dz

duK mama

12

21

uuK

qqKm

m

vvw

Aerodynamic Method

• Log-velocity profile

• Momentum flux

nR

E

Net radiation

Evaporation

Air Flow

12

21

uuK

qqKm

m

vvw

oZ

Z

ku

uln

1

*

2

12

12

ln

ZZ

uuka

212

122

ln21

ZZK

uuqqkKm

m

vvaw

Thornthwaite-Holzman Equation

u

Z

Aerodynamic Method

• Often only available at 1 elevation

• Simplifying

AEm w

nR

E

Net radiation

Evaporation

Air Flow

212

122

ln21

ZZK

uuqqkKm

m

vvaw

uqv and

22

22

ln

622.0

o

aasa

ZZP

ueekm

aasa eeBE

22

22

ln

622.0

ow

a

ZZP

ukB

2 @ pressure vapor Zea

What is B?

• Imagine ET as an electrical analog

• The potential difference V = (eas – ea)

• The resistance of the atmosphere to heat transfer is ra

• ET, the flux, is analogous to the current, so

ET = V / R = (eas – ea)/ra

Thus

aasa eeBE

𝐵 1/𝑟𝑎

Combined Method

• Evaporation is calculated by– Aerodynamic method

• Energy supply is not limiting– Energy method

• Vapor transport is not limiting

• Normally, both are limiting, so use a combination method

w

hp

K

pKC

622.0

ar EEET

wv

nr l

REE

aasa eeBEE

2)3.237(

4098

T

e

dT

de ss

rEET

3.1

Priestley & Taylor

Example

– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,

kJ/kg 244110)25*36.22500(

237010501.23

6

x

Tx

• Use Combo Method to find Evaporation

mm/day10.7997*102441

2003

x

RE

w

nr

Example (Cont.)

– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,

Pa3167ase

• Use Combo Method to find Evaporation

mm/day45.7

)day1/s86400(*)m1/mm1000(*126731671054.4 11

xEa

sm/Pa1054.4

1032ln997*3.101

3*19.1*4.0*622.0

ln

622.0 1124

2

22

22

x

xZZP

ukB

ow

a

Pa12673167*4.0* asha eRe

Example (Cont.)

– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,

Pa/degC1.67102441*622.0

103.101*1005

622.0 3

3

x

x

K

pKC

w

hp

Pa/degC7.188)253.237(

3167*40982

• Use Combo Method to find Evaporation

738.0

mm/day2.745.7*262.010.7*738.0

ar EEE

262.0

Example

– Net Radiation = 200 W/m2, – Air Temp = 25 degC,

• Use Priestly-Taylor Method to find Evaporation rate for a water body

rEE

3.1 Priestly & Taylor

mm/day10.7rE 738.0

mm/day80.610.7*738.0*3.1 E

Methods of Estimating Actual ET

• Penman-Monteith• Crop Coefficients• Lysimeters• Flux Towers• Satellites

Penman-Monteith Equation

𝐸=∆(𝑅¿¿𝑛−𝐺)+𝜌𝑎𝑐𝑝 (𝑒𝑎𝑠−𝑒𝑎)/𝑟𝑎

𝛾+∆(1+𝑟 𝑠

𝑟𝑎

)¿

• A surface resistance term rs is added to Combined Method to account for soil and vegetation’s tendency to hold onto water

• rs varies based on vegetation cover and soil moisture content

• The wind speed is u at height z • The wind speed is 0 at height zo, which is called the

surface roughness• k=0.41 is the Van Karman constant

Crop Coefficients

• Multiply reference crop ET by a Crop Coefficient and a Soil Coefficient

rcs ETkkET

0 20 40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1CORN

Time Since Planting (Days)

Cro

p C

oef

fici

ent,

kc

3.10.2

t;Coefficien Crop

c

c

k

k

10

t;Coefficien Soil

s

s

k

k

ET Actual ET

ET Crop Reference rET

http://www.ext.colostate.edu/pubs/crops/04707.html

Conduction of mass, momentum and energy

• Flux is proportional to the gradient of a potential

dz

du

dz

dCDfm

dz

dTkfh

Momentum flux (laminar flow)

Newton’s law of viscosity

Mass flux Fick’s law of diffusion

Energy flux Fourier’s law of heat conduction

m is dynamic viscosity, D is diffusion coefficient, and k is heat conductivity. Dynamic viscosity (m) is related to kinematic viscosity (n) as m = r n

The direction of transport of extensive properties is transverse to the direction of flow.

Convection

• Energy transfer through the action of turbulent eddies or mass movement of fluids with different velocities.

• Turbulence – mechanism causing greater rate of exchange of mass, energy, and momentum than molecular exchanges

• Unlike conduction, convection requires flowing fluid• Eg. Convection causes vertical air circulation in which

warm air rises and cool air sinks, resulting in vertical transport and mixing of atmospheric properties

Convection of mass, momentum and energy

dz

duKmturb

dz

dCKf wm

dz

dTKCf hph

Momentum flux (turbulent flow)

Km is momentum diffusivity or eddy viscosity

Mass flux

Energy flux Kh is heat diffusivity

Kw is mass diffusivity

• Km is 4-6 orders of magnitude greater than .n

• tturb is the dominant momentum transfer in surface water flow and air flow.

The direction of transport of extensive properties is transverse to the direction of flow.

Potential Evapotranspiration

• Multiply reference crop ET by a Crop Coefficient and a Soil Coefficient

rcs ETkkET

3.10.2

t;Coefficien Crop

c

c

k

k

10

t;Coefficien Soil

s

s

k

k

ET Actual ET

ET Crop Reference rET

http://www.ext.colostate.edu/pubs/crops/04707.html

CORN

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160

Time Since Planting (Days)

Cro

p C

oef

fici

ent,

kc

Resources on the web

• Evaporation maps from NWS climate prediction center– http://www.cpc.ncep.noaa.gov/soilmst/e.shtml

• Climate maps from NCDC– http://www.nndc.noaa.gov/cgi-bin/climaps/climaps.pl

• Evapotranspiration variability in the US– http://geochange.er.usgs.gov/sw/changes/natural/et/