PET versus AET, Penman's method

PET versus AET

Penman's method

Penman's method estimates PET by combining the energy balance (net radiation $H_n$) with the aerodynamic term $E_a$ (drying power of the air):

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

• $A$ is the slope of the saturation vapour pressure curve at air temperature (mm Hg/°C), and $\gamma = 0.49$ mm Hg/°C is the psychrometric constant.
• Net radiation (mm/day):

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

where $H_a$ is the extraterrestrial radiation, $r$ the reflection coefficient, $n/N$ the sunshine ratio and $\sigma = 2.01\times10^{-9}$ mm/day/K⁴.

• Aerodynamic term: $E_a = 0.35(1 + u_2/160)(e_w - e_a)$ with $u_2$ in km/day and $e_a = RH\times e_w$.

Steps: (1) get $T$, RH, $n$, $u_2$, latitude; (2) read $e_w$, $A$, $H_a$, $N$ from tables; (3) find $e_a$; (4) compute $H_n$; (5) compute $E_a$; (6) compute PET. It is widely used because it needs only routine weather data and gives good results for daily and monthly periods.