EVAPORATION

Evaporation

• Terminology– Evaporation – process by which liquid water

passes directly to the vapor phase– Transpiration - process by which liquid water

passes from liquid to vapor through plant metabolism

– Sublimation - process by which water passes directly from the solid phase to the vapor phase

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

Evaporation from a Water Surface

• Simplest form of evaporation– From free liquid of permanently saturated surface

Evaporation from a Pan

• National Weather Service Class A type• Installed on a wooden platform in a

grassy location• Filled with water to within 2.5 inches of

the top• Evaporation rate is measured by manual

readings or with an analog output evaporation gauge

h

Area, A

CSw

a

AEm wv

dtdhE

nRsHSensible

heat to airNet radiationVapor flow rate

Heat conductedto ground

G

Methods of Estimating Evaporation

• Energy Balance Method• Aerodynamic method• Combined method

Energy Method• Continuity - Vapor contains liquid and vapor phase

water• Continuity - Liquid phase

CS

wCV

wv ddtdm dAV

0dtdhAw No flow of liquid

water through CS

AEm wv

Edtdh

hw

a

vm

dtdhE

nRsH

G

Energy Method

• Continuity - Vapor phase

CS

avw qAE dAV

0Steady flow of air

over water

AEw

CS

avCV

avv qdqdtdm dAV

CS

avw

qA

E dAV

1

CS

avv qm dAV

hw

a

vm

dtdhE

nRsH

G

CSu

CVu

dgzVe

dgzVedtd

dtdW

dtdH

AV

)2/(

)2/(

2

2

Energy Method• Energy Eq.

0

hw

a

vm

dtdhE

nRsH

G

.,0;0 consthV

CV

wu dedtd

dtdH

GHRdtdH

sn

GHR sn

Energy Method• Energy Eq. for Water in CV

Assume:1. Constant temp of water in CV2. Change of heat is change in internal energy of water evaporated

hw

a

vm

dtdhE

nRsH

G

vvmldtdH

GHRdtdH

sn

GHRml snvv AEm w

GHRAl

E snwv

1

Recall:

wv

nr l

RE

Neglecting sensible and ground heat fluxes

Wind as a Factor in Evaporation

• Wind has a major effect on evaporation, E– Wind removes vapor-laden air by convection – This Keeps boundary layer thin – Maintains a high rate of water transfer from liquid

to vapor phase– Wind is also turbulent

• Convective diffusion is several orders of magnitude larger than molecular diffusion

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 flux

nR

E

Net radiation

Evaporation

Air Flow

12

21

zzqq

KdzdqKm vv

wav

wa

12

12zzuuK

dzduK mama

12

21

uuKqqK

mm

vvw

Aerodynamic Method

• Log-velocity profile

• Momentum flux

nR

E

Net radiation

Evaporation

Air Flow

12

21

uuKqqK

mm

vvw

oZZ

kuu ln1*

2

12

12ln

ZZuuk

a 212

122

ln21

ZZK

uuqqkKm

m

vvaw

Thornthwaite-Holzman Equation

u

Z

Aerodynamic Method

• Often only available at 1 elevation

• Simplifying

nR

E

Net radiation

Evaporation

Air Flow

212

122

ln21

ZZK

uuqqkKm

m

vvaw

uqv and

22

22

ln622.0

o

aasa

ZZPueekm

AEm w

aasa eeBE

22

22

ln622.0

ow

a

ZZP

ukB

2 @ pressure vapor Zea

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

ar EEE

wv

nr l

REE

aasa eeBEE

wv

hp

KlpKC

622.0

2)3.237(4098

Te

dTde ss

rEE

3.1

Priestly & Taylor

Example

– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200

W/m2, – Air Temp = 25 oC, – Rel. Humidity = 40%,

• Use Energy Method to find Evaporation

kJ/kg 24412500006.0250016.02536.28.2500

00006.00016.036.28.250032

32

TTTlv

mm/day10.7997102441

2003

wv

nr l

RE

Example

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

• Use Aerodynamic 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*622.0ln

622.0 1124

2

22

22

x

xZZP

ukB

ow

a

PakPaT

Teas 31671678.3]3.23725

2527.17exp[6108.03.237

27.17exp6108.0

PaeRe asha 126731674.0

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*622.0103.101*1005

622.0 3

3

xx

KlpKC

wv

hp

• Use Combo Method to find Evaporation

Pa/degC7.188)253.237(

3167*40982

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

Evapotranspiration

• Evapotranspiration– Combination of evaporation from soil surface and

transpiration from vegetation– Governing factors

• Energy supply and vapor transport• Supply of moisture at evaporative surfaces

– Reference crop• 8-15 cm of healthy growing green grass with abundant water

– Combo Method works well if B is calibrated to local conditions

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

Coefficient rcs ETkkET

3.10.2t;Coefficien Crop

c

ck

k

10t;Coefficien Soil

s

sk

k

ET Actual ET

ET Crop Reference rETCORN

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 Co

effic

ient

, kc