1. Evaporation Theory Dennis Baldocchi Department of Environmental Science, Policy and Management University of California, Berkeley Shortcourse on ADAPTIVE MANAGEMENT OF MEDITERRANEAN FOREST ECOSYSTEMS TO CLIMATE CHANGE Zaragosa, Spain May, 2010

2. Penman-Monteith Equation Reconciles balance between evaporation driven by available energy supply and limited by the demand imposed by a network of physiological and aerodynamic resistances and humidity deficit ESPM 129 Biometeorology

3. P-M Basics Surface Energy Balance Ohm’s Law Resistance Analog Linearization of saturation vapor pressure, as a function of leaf temperature Linearization of longwave energy emission as a function of leaf temperature Solve for E by eliminating (Tsfc-Tair) ESPM 129 Biometeorology

4. Big-Leaf Circuit Aerodynamic resistance for momentum Quasi-Laminar Boundary Layer Resistance Surface Resistance, Rs Conductance Form of Evaporation Equation, Demand

5. ESPM 129 Biometeorology5 Canopy resistance/conductance for water vapor, G w Boundary layer resistance, R a Stomatal resistance, R s Boundary layer conductance,G a Stomatal conductance, G s R, s/m G, m/s

6. ESPM 129 Biometeorology Various Conductance/Resistance form for Latent Heat Exchange

7. ESPM 129 Biometeorology Penman Monteith Equation Surface Energy Balance, Supply, W m -2 E, latent heat flux density H, sensible heat flux density S, soil heat flux density Rg: global solar radiation  : albedo L: Longwave radiation  : emissivity

8. ESPM 129 Biometeorology Linearize Leaf-Air Vapor Pressure Difference Linearize LongWave Energy Emission from Surface

9. ESPM 129 Biometeorology9 Linearize with 1 st order Taylor’s Expansion Series

10. ESPM 129 Biometeorology Eliminate e s (T s ) –e a from Ohm’s Law LE equation

11. ESPM 129 Biometeorology Solve for Ts-Ta Define Psychrometric Constant e s ’ = s

12. ESPM 129 Biometeorology Substitute Ts-Ta in LE

13. ESPM 129 Biometeorology Simplify and Re-Arrange

14. ESPM 129 Biometeorology ‘Shake and Stir’ Solve and remove Ts-Ta

15. ESPM 129 Biometeorology Gw = f(Gs, Gh) Penman-Montieth Eq = f( surface, boundary layer conductances)

16. ESPM 129 Biometeorology On to Quadratic Solution, when Ts-Ta is large like in the Mediterranean Incoming Short - + Long-wave minus outgoing Short-Wave Energy W m -2

17. ESPM 129 Biometeorology Taylor’s Series Expansion to Linearize Non-Linear Functions

18. ESPM 129 Biometeorology Linearize Leaf-Air Vapor Pressure Difference Linearize LongWave Energy Emission from Surface

19. ESPM 129 Biometeorology

20. Penman-Monteith vs Quadratic Solution

21. ESPM 129 Biometeorology Relative Error in LE, PM with Tsfc-Tair

22. ESPM 129 Biometeorology Boundary Layer Resistance for heat or vapor is the sum of the aerodynamic resistance, R a,m, and the Quasi-Laminar resistance, R b

23. ESPM 129 Biometeorology Aerodynamic Resistance for Momentum, R a,m u*: friction velocity, m/s

24. ESPM 129 Biometeorology Quasi-Laminar Boundary Layer Resistance, Rb,, s/m Sc: Schmidt Number Pr: Prandtl Number Zo: roughness length for momentum Zc: roughness length for mass transfer B: Stanton Number

25. ESPM 129 Biometeorology25 Reynolds numberReInertial to visous forces SchmidtScKinematic viscosity to molecular diffusivity PrandtlPrKinematic viscosity to thermal diffusivity SherwoodShDimensionless mass transfer conductance (conductance divided by the ratio of the molecular diffusivity and a length scale, l) GrasshofGrBuoyant force times an inertial force to the square of the viscous force NusseltNuDimensionless heat transfer conductacne

26. ESPM 129 Biometeorology

27. Massman, 1999

28. ESPM 129 Biometeorology Surface Conductance May Not Equal the Canopy stomatal Conductance

29. ESPM 129 Biometeorology High Ps Capacity Dry Soil Low Ps Capacity Wet Soil

30. ESPM 129 Biometeorology Why the Radiative Temperature Does Not Equal Aerodynamic Temperature

31. ESPM 129 Biometeorology Aerodynamic Temperature does not Equal Radiative Temperature

32. ESPM 129 Biometeorology McNaughton-Jarvis Omega Theory Resolving the Conflict: Evaporation driven by the Supply of Energy or the Demand by the Atmosphere

33. ESPM 129 Biometeorology Resolving the Conflict Evaporation driven by the Supply of Energy or the Demand by the Atmosphere

34. Conceptual Diagram of PBL Interactions H and LE: Analytical/Quadratic version of Penman-Monteith Equation

35. Mixed Layer Budget Eq. Time rate Of change Flux in the bottom Flux in from the top Growth - subsidence ESPM 228 Adv Topics Micromet & Biomet

36. PBL Budgets w/o subsidence ESPM 228 Adv Topics Micromet & Biomet

37. Growth of PBL ESPM 228 Adv Topics Micromet & Biomet

39. The Energetics of afforestation/deforestation is complicated Forests have a low albedo, are darker and absorb more energy But, Ironically the darker forest maybe cooler (T sfc ) than a bright grassland due to evaporative cooling

40. Forests Transpire effectively, causing evaporative cooling, which in humid regions may form clouds and reduce planetary albedo

41. Theoretical Difference in Air Temperature: Grass vs Savanna: Grass T air is much cooler if we only consider albedo Summer Conditions

42. And Smaller Temperature Difference, like field measurements, if we consider PBL, R c, R a and albedo….!! Summer Conditions

43. Tsfc can vary by 10 C by changing Ra and Rs

44. Tsfc can vary by 10 C by changing albedo and Rs

45. Tair can vary by 3 C by changing albedo and Rs

46. Tair can vary by 3 C by changing Ra and Rs

47. ESPM 129 Biometeorology Summary Evaporation can be measured with –Aerodynamic and Energy Balance Methods, as well as eddy covariance Penman-Monteith Equation unites theories relating to evaporation on the basis of energy balance and Ohm’s Law for water vapor Surface Conditions and Fluxes are NOT independent of the dynamics of the Planetary Boundary Layer