Derivation of the Penman-Monteith equation with the thermodynamic approach. II. Numerical solutions and evaluation

Authors: ZERIHUN, DAWIT - University Of Arizona; SANCHEZ, CHARLES - University Of Arizona; French, Andrew

Submitted to: American Society of Civil Engineers Journal of Irrigation and Drainage
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/13/2022
Publication Date: 3/10/2023
Citation: Zerihun, D., Sanchez, C.A., French, A.N. 2023. Derivation of the Penman-Monteith equation with the thermodynamic approach. II: Numerical solutions and evaluation. American Society of Civil Engineers Journal of Irrigation and Drainage. 149(5).Article 04023008. https://doi.org/10.1061/JIDEDH.IRENG-9888.
DOI: https://doi.org/10.1061/JIDEDH.IRENG-9888

Interpretive Summary: The Penman-Monteith Equation (PM) is widely used to estimate water vapor flux between land surface soils, plants, and the overlying atmosphere. The flux is commonly referred to as evapotranspiration (ET). Though its derivation and implementation have been evaluated and verified over decades, the solution of PM incorporates a simplified linearity assumption for the computation of a critical parameter (Delta), namely the slope of the saturation vapor pressure vs. air temperature. Possibly a more rigorous numerical solution to equations underlying PM could improve ET estimates. A series of simulations were conducted to evaluate this possibility. The results showed small uncertainties, usually less than 8%, suggesting that the existing simplified estimation of the Delta parameter is still recommended. Outcome from this research will have interest to researchers and students investigating ways to improve ET models.

Technical Abstract: A review of the derivation of the Penman-Monteith equation based on the thermodynamic approach of Monteith is presented in the companion paper. The resultant set of equations consisting of the latent heat flux, lf, sensible heat flux, qf, final air temperature, Ta, and ' equations cannot be solved directly, because the value of ' is not known. A pair of alternative numerical solutions, with different levels of complexity (referred here as model i and ii), were developed and evaluated here. Results of model verification showed that each of the alternative models produced outputs that are practically identical and also in close agreement with a reference solution. Furthermore, 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, for estimating evaporation from a wet surface. However, owing to its simplicity, model i is recommended here for further use. A comparison of the outputs of model i with those of the conventional model (i.e., the approach widely used to evaluate the Penman-Monteith and related equations) shows that difference in the approaches implemented in the two models has maximum effect on estimates of qf (where the mean absolute residual is 18.1%), a negligible effect on Ta (with an average residual of 0.7%), and a limited effect on lf, in which the mean residual is 8.2%. Because both model i and the conventional model involve a level of approximation in the determination of ', a direct comparison of the two models cannot provide an answer to the question: which model is more accurate? However, considering the approximations incurred in estimating ' with each of these models and in the input weather parameters, the fact that the average residual for the rather more important of the variables (i.e., the latent heat flux, lf) is only 8.2% suggests that the absolute residuals (of lf) are perhaps within the margins of error of the lf estimates obtained with these models. This implies that, for most applications, both the conventional model and model i can be considered to be equally acceptable from the standpoint of accuracy. However, the conventional model appears to be preferable, because of its simplicity. Authors, nonetheless, would emphasize the fact that results presented here are limited and hence preliminary in nature.