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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

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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

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P-M Basics Surface Energy Balance Ohms 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

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

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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

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

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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

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

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ESPM 129 Biometeorology9 Linearize with 1 st order Taylors Expansion Series

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ESPM 129 Biometeorology Eliminate e s (T s ) e a from Ohms Law LE equation

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

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ESPM 129 Biometeorology Substitute Ts-Ta in LE

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ESPM 129 Biometeorology Simplify and Re-Arrange

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ESPM 129 Biometeorology Shake and Stir Solve and remove Ts-Ta

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

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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

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ESPM 129 Biometeorology Taylors Series Expansion to Linearize Non-Linear Functions

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

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ESPM 129 Biometeorology

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Penman-Monteith vs Quadratic Solution

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

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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

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

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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

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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

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ESPM 129 Biometeorology

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Massman, 1999

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

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

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

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ESPM 129 Biometeorology Aerodynamic Temperature does not Equal Radiative Temperature

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

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

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

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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

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

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Growth of PBL ESPM 228 Adv Topics Micromet & Biomet

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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

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

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

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

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Tsfc can vary by 10 C by changing Ra and Rs

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Tsfc can vary by 10 C by changing albedo and Rs

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Tair can vary by 3 C by changing albedo and Rs

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Tair can vary by 3 C by changing Ra and Rs

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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 Ohms Law for water vapor Surface Conditions and Fluxes are NOT independent of the dynamics of the Planetary Boundary Layer