The modified Penman method estimates how much water evaporates and transpires from a surface by merging a radiation balance with an aerodynamic mass‑transfer term. It uses everyday weather data and a standard grass reference to generate a reference evapotranspiration value that can be adapted to any crop.
Core idea of the method
Evaporation is driven by two forces. The first is the energy available at the surface, captured by net radiation minus soil heat flux. The second is the ability of moving air to carry away the newly formed vapor, described by wind speed and vapor‑pressure deficit. The modified Penman equation balances these two components so that neither dominates the result.
Reference crop and standardisation
To make the calculation universal, the method assumes a reference surface: a well‑watered grass strip 0.12 m tall, albedo 0.23, and a surface resistance of 70 s m⁻¹. This removes crop‑specific traits from the base calculation, yielding a single value called reference evapotranspiration (ETo).
Required meteorological inputs
Typical weather stations provide all needed data: maximum and minimum air temperatures, relative humidity, wind speed at 2 m, and net short‑wave radiation or sunshine duration. From these, the equation derives actual vapor pressure, the slope of the saturation vapor pressure curve (Δ), and the psychrometric constant (γ).
Equation structure
The modified Penman formula can be written as:
ETo = [Δ(Rn – G) + ρa Cp (es – ea) / ra] / [Δ + γ(1 + rs/ra)]
where Rn is net radiation, G soil heat flux, ρa air density, Cp specific heat of air, es – ea vapor‑pressure deficit, ra aerodynamic resistance, and rs surface resistance (fixed at 70 s m⁻¹ for the reference crop).
From ETo to crop water need
Once ETo is known, the actual water requirement for a particular crop is obtained by multiplying with a crop coefficient (Kc) that reflects the crop’s growth stage and canopy characteristics: ETc = Kc × ETo. Kc values are supplied by FAO tables for common crops.
Practical use and limits
Because it relies on readily available weather data, the modified Penman method is widely used for irrigation scheduling, drought assessment, and climate studies. However, it assumes a uniform surface and may under‑estimate evaporation from highly irregular or water‑rich surfaces. For fine‑scale hydrology, more detailed models may be required.