Penman Equation - Details

Details

Numerous variations of the Penman equation are used to estimate evaporation from water, and land. Specifically the Penman-Monteith equation refines weather based potential evapotranspiration (PET) estimates of vegetated land areas. It is widely regarded as one of the most accurate models, in terms of estimates.

The original equation was developed by Howard Penman at the Rothamsted Experimental Station, Harpenden, UK.

The equation for evaporation given by Penman is:

E_{mass}=\frac{m R_n + \rho_a c_p \left(\delta e \right) g_a }{\lambda_v \left(m + \gamma \right) }

where:

m = Slope of the saturation vapor pressure curve (Pa K-1)
Rn = Net irradiance (W m-2)
ρa = density of air (kg m-3)
cp = heat capacity of air (J kg-1 K-1)
ga = momentum surface aerodynamic conductance (m s-1)
δe = vapor pressure deficit (Pa)
λv = latent heat of vaporization (J kg-1)
γ = psychrometric constant (Pa K-1)

which (if the SI units in parentheses are used) will give the evaporation Emass in units of kg/(m²·s), kilograms of water evaporated every second for each square meter of area.

Remove λ to obviate that this is fundamentally an energy balance. Replace λv with L to get familiar precipitation units ETvol, where Lv=λvρwater. This has units of m/s, or more commonly mm/day, because it is flux m3/s per m2=m/s.

This equation assumes a daily time step so that net heat exchange with the ground is insignificant, and a unit area surrounded by similar open water or vegetation so that net heat & vapor exchange with the surrounding area cancels out. Some times people replace Rn with and A for total net available energy when a situation warrants account of additional heat fluxes.

temperature, wind speed, relative humidity impact the values of m, g, cp, ρ, and δe.

Read more about this topic:  Penman Equation

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