Derivation of the Penman–Monteith Equation with the Thermodynamic Approach. II: Numerical Solutions and Evaluation

Abstract

A review of the derivation of the Penman–Monteith equation with the thermodynamic approach of Monteith is presented in a companion manuscript. The resultant set of equations (expressed in terms of latent heat flux, lf, sensible heat flux, qf, final air temperature, Ta, and the slope parameter related to the saturation vapor pressure curve, Δ) represents a coupled system. Thus, a pair of alternative numerical solutions, with different levels of complexity, were developed and evaluated in the study reported here. Results showed that the alternative models (labeled as model 1 and 2) produced outputs that are essentially identical and also in close agreement with a reference solution. Intercomparison of the alternative models based on the criteria of numerical efficiency and robustness suggests that each model represents a comparable alternative to the other to estimate evaporation. However, owing to its simplicity, model 1 was selected for further consideration. A comparison of the outputs of model 1 with those of the conventional model (i.e., the approach widely used to evaluate the Penman–Monteith set of equations), based on data sets covering a range of evaporation conditions, showed that the difference in the approaches implemented in the two models has a significant effect on estimates of qf, a limited effect on lf, and a negligible effect on Ta. Notably, the results also showed that the mean absolute residual for latent heat flux, lf (i.e., the mean of the absolute residuals between estimates obtained with model 1 and the conventional model) is relatively small (only about 8.2%), suggesting that differences between lf estimates computed with model 1 and the conventional model should generally be within the margin of error of the conventional model.