Penman-Monteith Equation

Penman-Monteith equation is a widely used formula for estimating evapotranspiration (ET), which is the process of water moving from the soil through plants and into the atmosphere.  It combines both the energy and mass transfer approaches, providing a comprehensive way to calculate how much water is lost from soil, plants, and water bodies through evaporation and transpiration.

This Equation was Developed by Combining Two Models

Penman's Equation (1948)  -  Originally used to calculate evaporation from open water or wet surfaces.
Monteith's Modification (1965)  -  Improved the model to account for plant resistance to water loss (stomatal resistance) and the effect of vegetation on the energy balance.

 

Penman-Monteith equation
\( ET_0 \;=\; [ 0.408\;m\;( R_n - G ) + \gamma\; (900\;/\;T+273)\; u_2 \;( e_s - e_a ) ] \;/\; [ m + \gamma \; (1 + 0.34\;u_2) ]  \)
Symbol	English	Metric
\( ET_0 \) = Reference Evapotranspiration	-	\(mm\;/\;d\)
\( m \) = Slope of Saturated Vapor Pressure Curve	-	\(kPa\;/\;C\)
\( R_n \) = Net Radiation at the Crop Surface (Incoming and Outgoing Solar Radiation)	-	\(MJ\;/\;m^2\;/\;d\)
\( G \) = Sensible Heat Flux into the Soil	-	\(MJ\;/\;m^2\;/\;d\)
\( \gamma \)  (Greek symbol gamma) = Psychrometric Constant	-	\(kPa\;/\;C\)
\( T \) = Mean Daily Air Temperature at 2 Meters Height	-	\(C\)
\( u_2 \) = Wind Speed at 2 Meters Height	-	\(m\;/\;s\)
\( e_s \) = Saturation Vapor Pressure	-	\(kPa\)
\( e_a \) = Actual Vapor Pressure	-	\(kPa\)