# Evaporation Theory Dennis Baldocchi Department of Environmental Science

- Slides: 47

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 • 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

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

Big-Leaf Circuit Aerodynamic resistance for momentum Quasi-Laminar Boundary Layer Resistance Surface Resistance, Rs Conductance Form of Evaporation Equation, Demand ESPM 129 Biometeorology

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

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

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

Linearize Leaf-Air Vapor Pressure Difference Linearize Long. Wave Energy Emission from Surface ESPM 129 Biometeorology

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

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

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

Substitute Ts-Ta in LE ESPM 129 Biometeorology

Simplify and Re-Arrange ESPM 129 Biometeorology

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

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

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

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

Linearize Leaf-Air Vapor Pressure Difference Linearize Long. Wave Energy Emission from Surface ESPM 129 Biometeorology

ESPM 129 Biometeorology

Penman-Monteith vs Quadratic Solution ESPM 129 Biometeorology

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

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

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

Reynolds number Re Inertial to visous forces Schmidt Sc Kinematic viscosity to molecular diffusivity Prandtl Pr Kinematic viscosity to thermal diffusivity Sherwood Sh Dimensionless mass transfer conductance (conductance divided by the ratio of the molecular diffusivity and a length scale, l) Grasshof Gr Buoyant force times an inertial force to the square of the viscous force Nusselt Nu Dimensionless heat transfer conductacne ESPM 129 Biometeorology 25

ESPM 129 Biometeorology

Massman, 1999 ESPM 129 Biometeorology

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

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

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

Aerodynamic Temperature does not Equal Radiative Temperature ESPM 129 Biometeorology

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

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

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

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

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

Growth of PBL ESPM 228 Adv Topics Micromet & Biomet

ESPM 228 Adv Topics Micromet & Biomet

• 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

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

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

And Smaller Temperature Difference, like field measurements, if we consider PBL, Rc, Ra and albedo…. !! Summer Conditions

Tsfc can vary by 10 C by changing Ra and Rs

Tsfc can vary by 10 C by changing albedo and Rs

Tair can vary by 3 C by changing albedo and Rs

Tair can vary by 3 C by changing Ra and Rs

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