Penman-Monteith (FAO-56): The Reference Standard

Penman-Monteith is the combination equation: it merges the energy budget and the aerodynamic mass-transfer term into a single expression, which is why it is the reference standard for evaporation and evapotranspiration (Allen et al., 1998, FAO-56).

The equation

The numerator adds an energy term ($\Delta(R_n - G)$) to an aerodynamic term (driven by the vapour-pressure deficit $e_s - e_a$ and the aerodynamic resistance $r_a$). The denominator weights the two with the saturation-curve slope $\Delta$ and the psychrometric constant $\gamma$.

Inputs & data needed

A full meteorological set: net radiation, air temperature, humidity, and wind speed, plus the derived terms $\Delta$, $\gamma$, $r_a$ and (for vegetation) $r_s$. For open water, the surface resistance $r_s$ is dropped and an open-water albedo is used to compute $R_n$; the vegetated form over-predicts open-water loss.

Worked example (structure)

A full numeric run involves roughly ten intermediate quantities (saturation and actual vapour pressure, $\Delta$, $\gamma$, net short- and long-wave radiation, aerodynamic resistance). The procedure is:

1. From air temperature, compute $e_s$, $e_a$, and the slope $\Delta$.
2. From latitude, day-of-year and sunshine/radiation, compute $R_n$ using an open-water albedo (~0.06).
3. From wind speed and measurement height, compute the aerodynamic resistance $r_a$.
4. Substitute into the equation (with $r_s = 0$ for open water) to get $ET$ in mm/day.

FAO-56 Chapter 4 gives every sub-equation and a fully worked tabulation; we link to it rather than reproduce it.

Accuracy & when to use

When you have full data and apply the open-water adaptation, Penman-Monteith is the benchmark other methods are calibrated against. Reserve it for sites with a proper weather station. With less data, step down to Priestley-Taylor (radiation), mass-transfer (wind), or Hargreaves-Samani (temperature only). See the overview for how they trade off.