Evaporation Theory Dennis Baldocchi Department of Environmental Science, Policy and Management...
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- Slide 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
- 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
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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
- 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
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- ESPM 129 Biometeorology Substitute Ts-Ta in LE
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- ESPM 129 Biometeorology Simplify and Re-Arrange
- Slide 14
- 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
- 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
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- 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
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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
- Slide 26
- ESPM 129 Biometeorology
- Slide 27
- Massman, 1999
- Slide 28
- ESPM 129 Biometeorology Surface Conductance May Not Equal the
Canopy stomatal Conductance
- Slide 29
- ESPM 129 Biometeorology High Ps Capacity Dry Soil Low Ps
Capacity Wet Soil
- Slide 30
- 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
- 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
- Slide 36
- PBL Budgets w/o subsidence ESPM 228 Adv Topics Micromet &
Biomet
- Slide 37
- 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