Hargreaves-Samani: The Temperature-Only Method

Hargreaves-Samani is the temperature-only fallback: when humidity, wind and radiation data are unavailable, it estimates reference evapotranspiration from air temperature and the daily temperature range alone.

The equation

$R_a$ is extraterrestrial radiation — the top-of-atmosphere solar radiation, fixed by latitude and day of year and read from a table. The temperature range $(T_{\max}-T_{\min})^{0.5}$ acts as a proxy for the missing cloud and humidity information.

Inputs & data needed

Just daily maximum and minimum temperature, plus latitude and day of year to look up $R_a$. That minimal demand is the entire point of the method.

Worked example

For $T_{\max} = 32\,^\circ\text{C}$, $T_{\min} = 18\,^\circ\text{C}$ (so $T_{\text{mean}} = 25\,^\circ\text{C}$) and $R_a = 16\ \text{mm/day}$ equivalent (≈ $40\ \text{MJ/m}^2/\text{day} \times 0.408$):

Note $R_a$ must be expressed as a mm/day equivalent (multiply MJ/m²/day by 0.408).

Accuracy & when to use

Use Hargreaves-Samani only when richer data are missing — it is less accurate than the radiation- and wind-based methods, and it returns reference ET (a vegetated-surface concept), so it needs adapting before it represents open-water loss (see reference vs. open-water ET). When better data exist, prefer Priestley-Taylor, mass-transfer or Penman-Monteith.