Evaporation and Transpiration
Evapotranspiration or ET
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62% of precipitation that falls on the continents is
evaporated
Understanding and predicting climate change
Q=P-ET. P-ET is the water available for use
ET "loss" supports ecosystems and agriculture
Reservoir losses
The antecedent "wetness" that determines what
happens to runoff depends on ET
Even during a single storm ET may exceed runoff
Learning Objectives
• Be able to calculate incoming solar
radiation as a driver of evaporation and
snowmelt based on of geographic location
(latitude and longitude), date, time of day
and atmospheric conditions
• Be able to calculate evaporation from open
water surfaces and transpiration from
vegetation, using a method appropriate for
the information available.
Part of The Hydrologic Cycle
Atmospheric Moisture
39
Moisture over land
100
Precipitation on land
P
61
Evapotranspiration from land
385
Precipitation
on ocean
Snow
melt
Surface
runoff
Runoff
Precipitation
Evap
ET
424
Evaporation
from ocean
Evap
Infiltration
Streams
Groundwater
Recharge
Runoff
38
Groundwater flow
Lake
Impervious
strata
GW
Surface discharge
1 Groundwater
discharge
Reservoir
Figure 1-1 from Bedient: http://hydrology.rice.edu/bedient/
Physical principles used
• Conservation of mass
• Conservation of energy
• Ideal gas law as it pertains to water
vapor
• Latent heat of phase change
(vaporization)
• Turbulent transfer near the ground
Factors affecting ET
• Energy available for phase change
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Solar Radiation
Surface energy balance
• Water available at surface to evaporate
or in root zone to transpire
• "Dryness" of the air – saturation vapor
deficit
• Capacity of the atmosphere to transport
away evaporated moisture. (wind speed,
turbulence, diffusion).
ET References
• Shuttleworth, W. J., (1993), "Evaporation," in Handbook of
Hydrology, Chapter 4, Edited by D. R. Maidment, McGraw-Hill,
New York.
• Dingman, S. L., (2002)
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Chapter 7. Evapotranspiration
Appendix D.4. Physics of Evaporation
Appendix D.6. Physics of Turbulent Transfer near the ground.
Appendix E. Radiation on sloping surfaces
• Allen, R. G., I. A. Walter, R. L. Elliot, T. A. Howell, D. Itenfisu
and M. Jensen, ed. (2005), ASCE Standardized Reference
Evapotranspiration Equation, American Society of Civil Engineers,
http://www.kimberly.uidaho.edu/water/asceewri/ascestzdetmain20
05.pdf.
• Brutsaert, W., (1982), Evaporation into the Atmosphere, Kluwer
Academic Publishers, 299 p.
Global Energy Balance
How much evaporation is represented by the latent heat flux of 82
W/m2?
From Lindzen (1990), Bulleting AMS 71(3): 288-299
World Water Balance
From Brutsaert, 2005
Solar Radiation
• Be able to calculate incoming solar radiation
as a driver of evaporation and snowmelt based
on of geographic location (latitude and
longitude), date, time of day and atmospheric
conditions
Shortwave Radiation at a Point
• Extraterrestrial radiation So is a function of date
(season) time, latitude, slope and aspect.
• St at surface is So modified by absorption by
atmospheric gases, particularly water vapor,
through scattering by air molecules and dust
particles, and additionally by clouds when they are
present.
• Net shortwave takes into account losses after
reflection (albedo) Sn = St(1-)
n
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S t   as  bs  S o
N

[MJ m-2 day-1 or W m-2]
as – fraction of So on overcast days (n=0)
as+bs – fraction of So on clear days
n/N – (1 - cloudiness fraction)
Refer to Shuttleworth 1993
n – bright sunshine hours per day
N – total day length
So– extraterrestrial radiation [MJ m-2 day-1]
 Eqn. E-3
Day Angle
ro
r
Γ=
2 𝜋 𝐽−1
365
(E-1)
Eo=(ro/r)2 Eqn. E-2
From Dingman, 1994
Zenith angle  Eqn. E-4
 Eqn. E-3
Latitude 
Sunrise Thr Eqn E-5a
Sunset Ths Eqn E-5b
Horizontal plane radiation
Instantaneous kET' Eqn E-6
Daily total KET' Eqn E-7
Equivalent plane at latitude eq
Sloping surface
angle 
eq
Latitude 
Slope Sunrise Tsr Eqn E-24a
Equivalent sloping plane radiation
Daily total KET Eqn E-25
Slope Sunset Tss Eqn E-24b
Direct approach to radiation calculation
Slope illumination angle z
Surface
Normal
North
Solar azimuth angle A
Slope azimuth angle 
Slope angle 
Accounting for terrain shading
Plan
N
A
x
L
Sun
x/L = cos(A-p/2)
L=x/cos(A-p/2) in the am
L=-x/cos(A-p/2) in the pm
Side view

H
h
L
h = atan(H/L)
Solve iteratively for when p/2- > h to figure out when a
distant horizon obscures the sun
Clear sky attenuation of solar radiation passing
through atmosphere
K'ET
K'dir =  K'ET
0.5 sK'ET
0.5 sK'ET
 and s - appendix E
• optical air mass
• precipitable water
• dust
• backscattering
0.5 a sK'g
Optical air mass – Dingman Fig E-4
Longwave Radiation
• Atmosphere and ground emit
black body radiation
• Surface usually warmer than
atmosphere -> net loss of energy
as thermal radiation from the
ground.
Ln  Li  Lo   f  (T  273.2) 4
 - adjustment for cloud cover
’ – net emmissivity between the atmosphere
and the ground
 - Stefan-Boltzmann constant
4.903 x 10-9 [MJ m-2 K-4 day-1]
T – mean air temperature [oC]
 '  ae  be ed
ed – vapor pressure [kPa]
ae = 0.34
be = -0.14
Refer to Shuttleworth 1993 for details
Rn = Sn + Ln
Net Radiation
Solar Radiation Review Questions
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Write a definition of and use a diagram or diagrams as necessary to depict
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Solar declination
Day angle
Eccentricity (in the context of solar radiation)
Equivalent latitude in the equivalent plane concept
Longitude difference in the equivalent plane concept
Zenith angle
Illumination angle for a sloping surface
Explain the difference between results from equation E-6 with equivalent latitude
and equation E-25 as evaluated in Cell C42 in SolarRad spreadsheet. (on the day
we evaluated values were 54 MJ/m2/day vs 13.4 MJ/m2/day
Explain the difference between the extra terrestrial radiation evaluated for a
sloping surface using the SOLARRAD spreadsheet (Cell C42) and the direct
approach (CELL E126).
Explain the difference between the extra terrestrial radiation evaluated for a
sloping surface using the SOLARRAD spreadsheet (Cell C42) and the clear sky
radiation (CELL C47).