1 Evapotranspiration Be able to calculate evaporation from open water surfaces and transpiration from vegetation, using a method appropriate for the information available

2 Standard Evaporation RatesPotential Evaporation Eo [mm/day] is the quantity of water evaporated per unit area, per unit time from an idealized, extensive free water surface under existing atmospheric conditions. Reference Crop Evaporation Erc [mm/day] is the rate of evaporation from an idealized grass crop with a fixed crop height of 0.12 m, an albedo of 0.23, and a surface resistance of 69 s/m These assume No shortage of water Ignore influence of evaporation on meteorological parameters Actual Evaporation E [mm/day]

3 ET involves Energy exchanges and energy balanceTurbulent diffusion into the atmosphere Adjustment and balance Rn G + -

4 Evaporative Energy FluxMJ/kg Evaporation rate E mm/day or m/s L/T Mass evaporation rate wE kg/m2/day M L-2 T-1 Latent heat transfer rate LE = v wE kJ/m2/hr or W/m E L-2 T-1

5 Energy Budget for a Unit AreaA = LE + H [MJ m-2 day-1] A = Rn – G – S – P – Ad Often A = Rn – G Ad – loss of energy associated with horizontal air movement. Significant in an “oasis” situation, generally neglected. P – energy absorbed by biochemical processes in the plants, typically 2% of net radiation Rn – net incoming radiation LE – outgoing energy as evaporation S – energy temporarily stored within the volume G – outgoing heat conduction into the soil

6 Turbulent transfer near the ground𝑣 𝑎 = 1 𝑘 𝑢 ∗ ln 𝑧− 𝑧 𝑑 𝑧 𝑜 𝑘=0.4 von Karman 𝑣 𝑎 𝑧 𝑑 ≈0.7 𝑧 𝑣𝑒𝑔 𝑧 𝑜 ≈0.1 𝑧 𝑣𝑒𝑔 𝑧 𝑜 𝑧 𝑑 𝑧 𝑣𝑒𝑔 From Chow et al., 1988

7 Turbulent convection transports heat, vapor and momentum𝑣 𝑎 Ta ea 𝑧 𝑚 Ts es

8 Vapor Transport Td ea Ta es(Ta) The vapor pressure at the surface is es(Ts); the vapor pressure of the overlying air is relative humidity times es(Ta). The rate of evaporation is proportional to es – ea.

9 Mass Transfer / Aerodynamic Method

10 - psychrometric constantBowen Ratio - psychrometric constant Using standard values for P and v the value is [kPa/K]

11 Bowen Ratio Energy Balance MethodA = Rn – G = LE + H = LE(1+)

12

13 Combination Method ConceptsRn – G = LE + H es(Ta) es(Ts) Ts Ta

14 Combination or Penman Method

15 Priestley Taylor MethodThis is also sometimes taken as an estimate of equilibrium potential evapotranspiration for well watered surface

16 From Brutsaert, 2005

17 From Brutsaert, 2005

18 Summary of ET EquationsBowen Ratio Mass Transfer Combination Priestly Taylor What happens in these equations if the wind speed doubles?

19 Evapotranspiration FeedbacksRn G + - Conditions adjust to varying inputs. Calculations can interpret adjustments, but should not be used to predict the effect of changing one variable without considering the adjustments of connected variables

20 Water Balance Evaporation𝐸 = 𝑃 + 𝑆 𝑊 𝑖𝑛 +𝐺 𝑊 𝑖𝑛 −𝑆 𝑊 𝑜𝑢𝑡 −𝐺 𝑊 𝑜𝑢𝑡 −∆𝑉 Errors in quantifying the water balance terms all accumulate in the evaporation estimate

21 Eddy Correlation Approach𝐸 ~ 𝑤′𝑞′ 𝑤 ′ is vertical wind velocity component fluctuation 𝑞 ′ is specific humidity fluctuation

22 Evaporation Pan U.S. Class A pan 1.21 m 255 mm 150 mm

23 Method Information RequirementsMass Transfer Bowen Ratio / Energy Balance RN Combination