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
Slide 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
Slide 3
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
Slide 4
Big-Leaf Circuit Aerodynamic resistance for momentum
Quasi-Laminar Boundary Layer Resistance Surface Resistance, Rs
Conductance Form of Evaporation Equation, Demand
Slide 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
Slide 6
ESPM 129 Biometeorology Various Conductance/Resistance form for
Latent Heat Exchange
Slide 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
Slide 8
ESPM 129 Biometeorology Linearize Leaf-Air Vapor Pressure
Difference Linearize LongWave Energy Emission from Surface
Slide 9
ESPM 129 Biometeorology9 Linearize with 1 st order Taylors
Expansion Series
Slide 10
ESPM 129 Biometeorology Eliminate e s (T s ) e a from Ohms Law
LE equation
Slide 11
ESPM 129 Biometeorology Solve for Ts-Ta Define Psychrometric
Constant e s = s
Slide 12
ESPM 129 Biometeorology Substitute Ts-Ta in LE
Slide 13
ESPM 129 Biometeorology Simplify and Re-Arrange
Slide 14
ESPM 129 Biometeorology Shake and Stir Solve and remove
Ts-Ta
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
Slide 17
ESPM 129 Biometeorology Taylors Series Expansion to Linearize
Non-Linear Functions
Slide 18
ESPM 129 Biometeorology Linearize Leaf-Air Vapor Pressure
Difference Linearize LongWave Energy Emission from Surface
Slide 19
ESPM 129 Biometeorology
Slide 20
Penman-Monteith vs Quadratic Solution
Slide 21
ESPM 129 Biometeorology Relative Error in LE, PM with
Tsfc-Tair
Slide 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
Slide 23
ESPM 129 Biometeorology Aerodynamic Resistance for Momentum, R
a,m u*: friction velocity, m/s
Slide 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
Slide 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
Slide 26
ESPM 129 Biometeorology
Slide 27
Massman, 1999
Slide 28
ESPM 129 Biometeorology Surface Conductance May Not Equal the
Canopy stomatal Conductance
ESPM 129 Biometeorology Why the Radiative Temperature Does Not
Equal Aerodynamic Temperature
Slide 31
ESPM 129 Biometeorology Aerodynamic Temperature does not Equal
Radiative Temperature
Slide 32
ESPM 129 Biometeorology McNaughton-Jarvis Omega Theory
Resolving the Conflict: Evaporation driven by the Supply of Energy
or the Demand by the Atmosphere
Slide 33
ESPM 129 Biometeorology Resolving the Conflict Evaporation
driven by the Supply of Energy or the Demand by the Atmosphere
Slide 34
Conceptual Diagram of PBL Interactions H and LE:
Analytical/Quadratic version of Penman-Monteith Equation
Slide 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
Growth of PBL ESPM 228 Adv Topics Micromet & Biomet
Slide 38
Slide 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
Slide 40
Forests Transpire effectively, causing evaporative cooling,
which in humid regions may form clouds and reduce planetary
albedo
Slide 41
Theoretical Difference in Air Temperature: Grass vs Savanna:
Grass T air is much cooler if we only consider albedo Summer
Conditions
Slide 42
And Smaller Temperature Difference, like field measurements, if
we consider PBL, R c, R a and albedo.!! Summer Conditions
Slide 43
Tsfc can vary by 10 C by changing Ra and Rs
Slide 44
Tsfc can vary by 10 C by changing albedo and Rs
Slide 45
Tair can vary by 3 C by changing albedo and Rs
Slide 46
Tair can vary by 3 C by changing Ra and Rs
Slide 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 Ohms Law for water
vapor Surface Conditions and Fluxes are NOT independent of the
dynamics of the Planetary Boundary Layer