1. Evaporation and Transpiration Evapotranspiration or ET
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

2. 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.

3. Part of The Hydrologic Cycle
Atmospheric Moisture
100
Precipitation on land
Infiltration W a t e r b l
Groundwater flow
1 Groundwater
discharge
Surface discharge 61
Evapotranspiration from land 39
Moisture over land
385
Precipitation
on ocean
424
Evaporation
from ocean
Surface
runoff
Impervious
strata
Groundwater
Recharge P
Snow
melt
Runoff
Evap ET
Evap
Streams
Runoff
Lake GW
Reservoir
Figure 1-1 from Bedient:

4. 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

5. Factors affecting ET Energy available for phase change
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).

6. 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)
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,
Brutsaert, W., (1982), Evaporation into the Atmosphere, Kluwer Academic Publishers, 299 p.

7. Global Energy Balance
How much evaporation is represented by the latent heat flux of 82 W/m2?
From Lindzen (1990), Bulleting AMS 71(3):

8. World Water Balance
From Brutsaert, 2005

9. 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

10. 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-)
[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)
n – bright sunshine hours per day
N – total day length
So– extraterrestrial radiation [MJ m-2 day-1]
Refer to Shuttleworth 1993

11.  Eqn. E-3
Day Angle 
Eqn E-1 ro
Eo=(ro/r)2 Eqn. E-2 r
From Dingman, 1994

12. 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

13. 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

14. Direct approach to radiation calculation
Slope illumination angle z
Surface
Normal
North
Solar azimuth angle A
Slope azimuth angle 
Slope angle 

15. 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

16. Clear sky attenuation of solar radiation passing through atmosphere
0.5 sK'ET
K'ET
K'dir =  K'ET
0.5 sK'ET
0.5 a sK'g
and s - appendix E
optical air mass
precipitable water
dust
backscattering
Optical air mass – Dingman Fig E-4

17. Longwave Radiation Rn = Sn + Ln Net Radiation
Atmosphere and ground emit black body radiation
Surface usually warmer than atmosphere -> net loss of energy as thermal radiation from the ground.
 - 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]
ed – vapor pressure [kPa]
ae = 0.34
be = -0.14
Rn = Sn + Ln
Net Radiation
Refer to Shuttleworth 1993 for details

18. Solar Radiation Review Questions
Write a definition of and use a diagram or diagrams as necessary to depict
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).