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

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 100 Precipitation on land Infiltration W a t e r b l Groundwater flow 1 Groundwater discharge 38 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: 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 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) 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/ascestzdetmain2005.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-) [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

 Eqn. E-3 Day Angle ro Eo=(ro/r)2 Eqn. E-2 r 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 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

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

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).