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

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, ${\mathcal{l}}_f$, sensible heat flux, $q_f$, final air temperature, $T_a$, and the slope parameter related to the saturation vapor pressure curve, $\mathrm{\Delta }$) 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 $q_f$, a limited effect on ${\mathcal{l}}_f$, and a negligible effect on $T_a$. Notably, the results also showed that the mean absolute residual for latent heat flux, ${\mathcal{l}}_f$ (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 ${\mathcal{l}}_f$ estimates computed with model 1 and the conventional model should generally be within the margin of error of the conventional model.