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.
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
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
Pa3167ase
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/day10.7rE 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
ETActualET
ETCropReferencerET
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