A Recursive Method to Calculate Evapotranspiration.

The simultaneous solution of the equations that define the surface energy balance and turbulent transport of heat and water vapor to calculate evapotranspiration (ET) is known as the ‘combination method’ and was first introduced by H. Penman in 1948. He was able to eliminate the surface temperature (T_s) from the set of equations 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. This procedure to calculate evaporation is referred to as the Explicit Combination Method (ECM). In 1951 and in 1956, M. I. Budyko supplanted this explicit solution, without making any assumptions, using an energy balance equation with two unknowns, ET and the surface temperature T_s. He used the Goff-Gratch equation that relates the saturation humidity at the surface to that temperature. Starting with an initial value for T_s, the value of both unknowns is found by iteration, resulting in a value for ET that satisfies the energy balance. Budyko coined his procedure the ‘complex method’ and his iterative procedure is referred to as the Recursive Combination Method (RCM). Regardless of whether the ECM or RCM are used to calculate ET, errors in weather input data (radiation, temperature, humidity and wind-speed) can cause large errors in the calculation of ET. We examine errors in the calculation of ET using ECM and RCM associated with incorrect input of air humidity.