a. How does this compare with the Longwave Upwelling at the Surface output variable? If
they are different, why?
b. Does the Upwelling Longwave flux change as CO$_2$ goes up? Why?
c. Are the two experiments (CO2rad and CO2phys) similar or different, and why?
3. We are going to calculate potential evapotranspiration from the Penman-Monteith
equation. It will be helpful as a first step to calculate e*(T) for the modeled surface air
temperature called the Clausius Clayperyon curve:
$e_s(T) = e_s(T_0) \cdot exp[\frac{\lambda}{R_v} (\frac{1}{T_0} - \frac{1}{T})]$
where $e_s(T_0)$=0.6108, T is in Kelvin, $T_0$=273.15K, and latent heat of vaporization
Also calculate the local slope of the Clausius Clayperyon curve (de*(T)/dT):
$\Delta = \frac{\lambda}{R_v} \frac{e^*(T)}{T^2}$
This is the form of Penman-Monteith that we looked at in class:
$PET = \frac{1}{\lambda} [\frac{\Delta (LH + SH) + \rho_a C_p e^*(T_a)(1 - RH)C_H|u|}{\Delta + \gamma (1 + r_s C_H|u|)}$
for which you also need to solve the drag coefficient $C_H$ (which depends on some
assumptions about height of measurements, momentum roughness length, scalar
roughness length, and the von Karman constant k):
$C_H = \frac{k^2}{ln(z_w - d/z_{om}) \cdot ln(z_h - d/z_{oh})}$
as well as calculate the density of air calculated from the ideal gas law:
$\rho_a = \frac{1.01 \rho_s}{R_v T}$
and explicitly specifies stomatal resistance $r_s$.
This equation is starting to get pretty thick with constants, so instead lets use this slightly
less specific version that lumps many of these constants together:
$PET = 0.0352 \frac{\Delta (LH + SH) + \frac{900}{T} |u|e_s(T_a)(1 - RH)}{\Delta + \gamma (1 + 0.34|u|)}$
