Geog595 Ecological Modeling
Spring 2010
Due: March 3, 2010
Lab 4 Modeling ET with Penman-Monteith Equation
1. Objectives
(1) To implement the Penman-Monteith equation with C to model ET for leave surface.
(2) To understand the important interactions of biophysical processes that control ET.
(3) To scale up ET from leaves to Canopy
2. Theory
Transpiration of water from leaf surfaces to the free atmosphere is determined by two processes: (1) the size and distribution of stoma, and (2) the aerodynamic conditions at the leaf surface. The control of stoma on transpiration was emphasized by plant physiologists, while the control of aerodynamic conditions was emphasized by meteorologists. Moteith (1965) expanded the Penman (1948) model to become the Penman-Monteith Equation that first reconciled the two processes in modeling transpiration through leaves as
(1)
Where Δ (Pa/K) is the slope of saturated vapor pressure at air temperature. Rnet (W/m2) is the net radiation on the leaf surface. The psychrometric constant is γ (Pa/K). cp is air specific heat in J/kg/K. The vapor pressure of air is ea, and es(Tl) is the saturated vapor pressure inside stoma at the leaf temperature. If we assume the leaf temperature is equal to the air temperature, (es(Tl) – ea) is simply the vapor pressure deficit of the air. Ra and Rs are the aerodynamic and stomatal resistance (s/m), respectively. For a vegetated canopy with a height of H0 and a wind speed of u at H0, Ra can be modeled as
(2)
Where d0 is zero plane displacement, d0=0.7H0, and z0 is the surface roughness, z0=0.1H0. Kv is von Karman constant, Kv=0.41.
The wind speed in Eq (2) is the wind speed at the top of the canopy. Usually the wind speed is measure above the canopy. We call the height where the wind speed (us) is measured the screen height (Hs). Assuming that the speed decreases with height exponentially, the wind speed at the top of canopy can be estimated as
(3)
There are several models that simulate the stomatal conductance (gs) or resistance (Ra) The relationship between conductance and resistance is gs=1/Ra. We will use a recent stomatal conductance model by Leuning (1995) as in the following
(4)
where g0 is the cuticular conductance at the time when stoma are closed, g0=0.01 mol/m2/s. Ca is CO2 concentration in the atmosphere in ppm. Γ is the CO2 compensation point in ppm (. A is the net photosynthesis rate in μmol/m2/s. D is vapor pressure deficit in Pascal. D0 is an empirical parameters, D0=1500 Pa. The unit of gs is in mol/m2/s. The empirical parameter, a1, characterize the rate of gs changes with A.
3. Numerical Experiment
In this lab, we will use the weather and photosynthesis data collected on the eddy flux tower at Duke Forest to simulate transpiration with the models as described in Eqs (1-4) and using the measured latent heat flux measured at the same tower to evaluate our model.
(1) Run the model penman_monteith with default parameter values using WindLaiTaVpdAnRnet2001.txt as the input file. Save the output file and then compare the simulated LE with the measured LE as in file LE-May2001.txt. Please generate a scatter plot with modeled LE on the x-axis, and the measured LE on the y-axis. Please add trend with regression equation and R2 value with intercept forced to zero.
(2) Do the same simulation as above and set m as 6.0 and 12.0. Please compare the outputs with the observed data and describe how sensitive ET is to m.
(3) Resume m to its default value (m=9), and set Ca to 280 and 560 ppm, and compare the results. Discuss the implications of the rising CO2 concentration in the atmosphere to water resources.