Procedure of Penman's method

Penman's method combines the energy balance (net radiation) and the aerodynamic (mass transfer) methods to estimate evaporation or potential evapotranspiration (PET) from standard weather data. It needs no surface temperature.

$$PET = \frac{A\,H_n + E_a\,\gamma}{A + \gamma}$$

Procedure

1. Collect data: mean monthly air temperature $T$, relative humidity RH, observed sunshine hours $n$, wind speed $u_2$ at 2 m, latitude, and the reflection coefficient $r$ of the surface.
2. Find from tables: saturation vapour pressure $e_w$ at $T$ (mm Hg), the slope $A = de_w/dT$ at $T$, the extraterrestrial radiation $H_a$ (mm of evaporable water/day) for the latitude and month, and the possible sunshine hours $N$.
3. Actual vapour pressure: $e_a = RH \times e_w$.
4. Net radiation (mm/day):

$$H_n = H_a(1-r)\left(0.29\cos\varphi + 0.52\frac{n}{N}\right) - \sigma T_a^4(0.56 - 0.092\sqrt{e_a})\left(0.1 + 0.9\frac{n}{N}\right)$$

with $\sigma = 2.01\times10^{-9}$ mm/day/K$^4$ and $T_a$ in kelvin.

5. Aerodynamic term:

$$E_a = 0.35\left(1 + \frac{u_2}{160}\right)(e_w - e_a)$$

with $u_2$ in km/day.

6. Compute $PET$ using the equation above with $\gamma = 0.49$ mm Hg/$^\circ$C (psychrometric constant).
7. For the monthly value multiply by the number of days. For open-water evaporation, use $r = 0.05$; for crops use $r$ of the crop (0.15-0.25) and multiply by a crop coefficient if actual crop ET is required.