Nonlinearities of Penman and Penman-Monteith Equations across Multiple Timescales

The nonlinear Penman and Penman-Monteith equations, widely used for estimating surface evapotranspiration at regional and global scales, were derived from turbulent transport of heat fluxes and thus apply to subhourly scale. However, these equations have been directly applied with hydrometeorological variables averaged at longer time intervals, leading to biases due to their nonlinearities. To address this problem, we used global eddy covariance flux data and Taylor expanded Penman and Penman-Monteith equations to explore their nonlinear components and the biases associated with the timescales mismatch. We found relatively small biases when applying Penman equation at longer timescale, in which the biases in equilibrium evapotranspiration mainly stem from the temperature-radiation covariance, whereas the biases in evapotranspiration due to drying power of air primarily come from the higher-order terms. Most of these biases can be corrected by linear regressions of first-order approximations. For Penman-Monteith equations, the corresponding biases are relatively larger but can be significantly reduced when daytime median stomatal conductance is used along with the first-order approximation of Penman-Monteith equation, suggesting the importance of diurnal variation of latent heat fluxes. The nonlinearity explored here serves as a reminder of the mismatched timescales for applying Penman and Penman-Monteith equations.