This document discusses various processes of evaporation and methods for estimating evaporation and evapotranspiration rates. It defines evaporation, transpiration, and sublimation and describes factors that influence evaporation like energy supply, transport of vapor, and vegetated surfaces. Methods for estimating evaporation rates include the energy balance method, aerodynamic method, and combined method. The document also provides an example calculation using the combined method.

1. Evaporation

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

3. 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 Flow
u

4. Evaporation from a Water
Surface
• Simplest form of evaporation
– From free liquid of permanently saturated
surface

5. 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 
dt
dh
E 
nRsH
Sensible
heat to air
Net radiation Vapor flow rate
Heat conducted
to ground
G

6. Methods of Estimating Evaporation
• Energy Balance Method
• Aerodynamic method
• Combined method

7. Energy Method
• CV contains liquid and vapor phase water
• Continuity - Liquid phase
  
CS
w
CV
wv d
dt
d
m dAV
0
dt
dh
Aw No flow of liquid
water through CS
AEm wv 
E
dt
dh

hw
a
vm
dt
dh
E 
nRsH
G

8. Energy Method
• Continuity - Vapor phase
 
CS
avw qAE dAV
0
Steady flow of air
over water
AEw
  
CS
av
CV
avv qdq
dt
d
m dAV
 
CS
av
w
q
A
E dAV

1
 
CS
avv qm dAV
hw
a
vm
dt
dh
E 
nRsH
G

9.  
 
CS
u
CV
u
dgzVe
dgzVe
dt
d
dt
dW
dt
dH
AV



)2/(
)2/(
2
2
Energy Method
• Energy Eq.
0
hw
a
vm
dt
dh
E 
nRsH
G
.,0;0 consthV 
 
CV
wu de
dt
d
dt
dH

GHR
dt
dH
sn 
GHR sn 

10. Energy Method
• Energy Eq. for Water in CV
Assume:
1. Constant temp of water in CV
2. Change of heat is change in internal energy of water evaporated
hw
a
vm
dt
dh
E 
nRsH
G
vvml
dt
dH

GHR
dt
dH
sn 
GHRml snvv  AEm w
 GHR
Al
E sn
wv


1
Recall:
wv
n
r
l
R
E


Neglecting sensible and ground heat
fluxes

11. 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

12. 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
qq
K
dz
dq
Km
vv
wa
v
wa


 
12
12
zz
uu
K
dz
du
K mama


 
 
 12
21
uuK
qqK
m
m
vvw




13. Aerodynamic Method
• Log-velocity profile
• Momentum flux
nR
E
Net radiation
Evaporation
Air Flow
 
 12
21
uuK
qqK
m
m
vvw










oZ
Z
ku
u
ln
1
*
 
 
2
12
12
ln 




 

ZZ
uuk
a
  
  2
12
12
2
ln
21
ZZK
uuqqkK
m
m
vvaw 



Thornthwaite-Holzman Equation
u
Z

14. Aerodynamic Method
• Often only available at 1
elevation
• Simplifying
nR
E
Net radiation
Evaporation
Air Flow
  
  2
12
12
2
ln
21
ZZK
uuqqkK
m
m
vvaw 



uqv and
 
  2
2
2
2
ln
622.0
o
aasa
ZZP
ueek
m




AEm w
 aasa eeBE 
  2
2
2
2
ln
622.0
ow
a
ZZP
uk
B



2@pressurevapor Zea 

15. 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
n
r
l
R
EE


 aasa eeBEE 
wv
hp
Kl
pKC
622.0

2
)3.237(
4098
T
e
dT
de ss


rEE


 3.1
Priestly & Taylor

16. 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/kg244110)25*36.22500(
237010501.2
3
6


x
Txlv
mm/day10.7
997*102441
200
3

xl
R
E
wv
n
r


17. 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 11
24
2
2
2
2
2
 

x
xZZP
uk
B
ow
a


Pa3167ase
Pa12673167*4.0*  asha eRe

18. 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/degC1.67
102441*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*4098
2



738.0



mm/day2.745.7*262.010.7*738.0 




 ar EEE



262.0
 


19. 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/day10.7rE 738.0



mm/day80.610.7*738.0*3.1 E

20. 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

21. Potential Evapotranspiration
• Multiply reference crop ET by a Crop Coefficient and a
Soil Coefficient rcs ETkkET 
3.10.2
t;CoefficienCrop


c
c
k
k
10
t;CoefficienSoil


s
s
k
k
ETActualET
ETCropReference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)
CropCoefficient,kc