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Evaporation Theory

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. Penman- Monteith Equation.

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Evaporation Theory

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  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 ESPM 129 Biometeorology

  5. Canopy resistance/conductance for water vapor, Gw • Boundary layer resistance, Ra • Stomatal resistance, Rs • Boundary layer conductance,Ga • Stomatal conductance, Gs R, s/m G, m/s ESPM 129 Biometeorology

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

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

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

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

  10. Eliminate es(Ts) –ea from Ohm’s Law LE equation ESPM 129 Biometeorology

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

  12. Substitute Ts-Ta in LE ESPM 129 Biometeorology

  13. Simplify and Re-Arrange ESPM 129 Biometeorology

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

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

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

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

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

  19. ESPM 129 Biometeorology

  20. Penman-Monteithvs Quadratic Solution ESPM 129 Biometeorology

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

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

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

  24. 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 ESPM 129 Biometeorology

  25. ESPM 129 Biometeorology

  26. ESPM 129 Biometeorology

  27. ESPM 129 Biometeorology Massman, 1999

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

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

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

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

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

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

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

  35. Mixed Layer Budget Eq. Flux in from the top Time rate Of change Flux in the bottom 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

  38. 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 (Tsfc) 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 vsSavanna: Grass Tair is much cooler if we only consider albedo Summer Conditions

  42. And Smaller Temperature Difference, like field measurements, if we consider PBL, Rc, Raand 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. 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 ESPM 129 Biometeorology

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