A Historical Perspective on the Calculation of Evapotranspiration Using the Combination Method

The term potential evapotranspiration (ETp), introduced by Thornthwaite in 1948, stands for the maximum rate of water loss by evaporation from the land surface under given atmospheric conditions. Conversely, the ETa represents values of ET that applied to well-watered agricultural crops facilitate the planning and efficient use of water in crop production. It takes account of the role of leaf stomata in causing ETa to be less than ETp. Historically, the methods of relating ETp to weather parameters were empirical and lacked general validity. However, Howard Penman in 1948 and Mikhail and Budyko in 1958 independently proposed methods to calculate ETp based on known physical principles and standard climatological data, commonly referred to as the combination method. The solution was obtained by combining the equations for the transport of water vapor and sensible heat from or to the land surface with an expression for the radiative energy balance of that surface. Penman derived an explicit equation for ETp by making the assumption that the ratio between the temperature gradient between the surface and the air above and the corresponding humidity gradient, given saturation at the surface, would equal the value of the Clausius-Clapeyron equation at the ambient air temperature. The object of this assumption was the elimination of the surface temperature (Ts) from the set of equations used in the calculation of ETp. However, the validity of this procedure is questionable under hot and arid conditions. Furthermore, the validity of the assumption of using a linear expansion of the saturation vapor pressure curve versus the air temperature has been questioned. The method proposed by Budyko suggested, without making any assumptions, an energy balance equation that contains two unknowns, ETp and Ts, and the Groff-Gratch equation that relates the saturation humidity at the surface to that temperature. Starting with an initial value for Ts, the value of both unknowns is found by iteration, resulting in a value for ETp that satisfies the energy balance. We have shown that the linearity assumption introduced by Penman can result in a 25% under-calculation of ET and that the iterative procedure suggested by Budyko gives accurate values of ET. We tested our method with alfalfa in Bushland TX and Tempe AZ. Our results show that for a well-watered crop the iterative method we proposed to calculate crop ET is accurate. The method is simple to implement and requires no more computing power than a spreadsheet. This is a preferred method to calculate ET and requires input values that are routinely measured in weather stations that are part of regional ET networks.