Evaporation Slides prepared by Daene C. McKinney and Venkatesh Merwade Reading: Applied Hydrology Sections 4.1 and 4.2.

Evaporation

• Slides prepared by Daene C. McKinney and Venkatesh Merwade

• Reading: Applied Hydrology Sections 4.1 and 4.2

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

CS

w

a

AEm wv

dtdh

E

nRsH

Sensibleheat to air

Net radiationVapor flow rate

Heat conductedto ground

G

Methods of Estimating Evaporation

• Energy Balance Method

• Aerodynamic method

• Combined method

Energy Method

• CV contains liquid and vapor phase water• Continuity - Liquid phase

CS

wCV

wv ddt

dm dAV

0

dt

dhAw No flow of liquid No flow of liquid

water through CSwater through CS

AEm wv

Edt

dh hw

a

vm

dt

dhE

nRsH

G

Energy Method

• Continuity - Vapor phase

CS

avw qAE dAV

0Steady flow of airSteady flow of air

over waterover water

AEw

CS

avCV

avv qdqdt

dm dAV

CS

avw

qA

E dAV

1

CS

avv qm dAV

hw

a

vm

dt

dhE

nRsH

G

CSu

CVu

dgzVe

dgzVedt

d

dt

dW

dt

dH

AV

)2/(

)2/(

2

2

Energy Method• Energy Eq.

0

hw

a

vm

dtdh

E

nRsH

G

.,0;0 consthV

CV

wu dedt

d

dt

dH

GHRdt

dHsn

GHR sn

Energy Method• Energy Eq. for Water in CV

Assume:Assume:1. Constant temp of water in CV1. Constant temp of water in CV2. Change of heat is change in internal energy of water 2. Change of heat is change in internal energy of water evaporatedevaporated

hw

a

vm

dtdh

E

nRsH

G

vvmldt

dH

GHRdt

dHsn

GHRml snvv AEm w

GHRAl

E snwv

1

RecallRecall::

wv

nr l

RE

Neglecting sensible and Neglecting sensible and ground heat fluxesground heat fluxes

Transport Processes

• Sun is the major source of energy in hydrologic cycle

• Energy transport takes place through:– Conduction– Convection– Radiation

EnergyEnergy

Energy & Mass

Energy & Mass

Energy & Mass

Mass

LandOcean

Energy & Mass

Sun

Flux• The rate of flow of extensive property per unit area

of surface through which it passes is called the flux.

area

flowrateFlux

A

Qq

A

dtdE /

2VA

QV

A

Vm

A

Qm

Volumetric flux

Mass flux

Momentum flux

Energy flux

Mass flux = density x volumetric flux

Momentum flux = mass flux x velocity

Conduction• Heat is transferred as

molecules with higher temperature collide with lower temperature molecules

• Results from random molecular motion in substances

• Eg. Heating of earth’s land surface

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

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

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 turb 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.

Velocity Profile

• Determining momentum transfer requires knowing velocity profile

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

/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

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

zz

qqK

dz

dqKm

vvwa

vwa

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

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

AEm w

aasa eeBE

22

22

ln

622.0

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

Kl

pKC

622.0

2)3.237(

4098

T

e

dT

de 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 degC, – Rel. Humidity = 40%,

• Use Combo Method to find Evaporation

kJ/kg 244110)25*36.22500(

237010501.23

6

x

Txlv

mm/day10.7997*102441

2003

xl

RE

wv

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%,

• 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

Pa3167ase

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

Kl

pKC

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

3.10.2

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/