Evaluating biases in Penman and Penman–Monteith evapotranspiration rates at different timescales

The Penman and Penman–Monteith equations are widely used for estimating surface evapotranspiration (ET) at regional and global scales. These nonlinear equations were derived from the turbulent transport of heat fluxes and, in theory, need to be applied to a temporal scale ranging from half hour to an hour. However, these equations have been frequently applied with hydrometeorological variables averaged at daily, monthly, and even decadal time intervals, resulting in biases due to their nonlinearities. In this study, we used global reanalysis data and Taylor expanded Penman and Penman–Monteith equations to explore their nonlinear components and the biases associated with the timescale mismatches. We found that global average biases for approximating Penman equation range from 0.72 to 1.31 mm day⁻¹ from daily to annual timescales, which mainly stem from the temperature–radiation, temperature–vapor pressure deficit (VPD), and aerodynamic conductance–VPD covariances. For Penman–Monteith equation, the corresponding biases vary from 0.47 to 0.53 mm day⁻¹, which may be associated with the addition of stomatal conductance–VPD covariances. As a reference, the global averages from Penman and Penman–Monteith at hourly timescale over one year are 7.1 and 1.7 mm day⁻¹. Large biases also exist around the world across various climate zones, where one or multiple covariances between meteorological variables makes the first-order approximations of Penman and Penman–Monteith equations less accurate. This analysis serves as a reminder of nonlinearities in Penman and Penman–Monteith equations, hence the requirement of data at high temporal resolution for estimating potential or actual evapotranspiration.