Evaluation of the Generalized and Rescaled Complementary Evaporation Relationships

Abstract

AbstractA rigorous approach to the complementary relationship (CR) in land surface evaporation was introduced by Brutsaert (2015, https://doi.org/10.1002/2015WR017720) in which the problem was cast in nondimensional form for generality, boundary conditions (BCs) were established from physical constraints, and a suitable mathematical solution was formulated. Building on Brutsaert's insightful foundation, Crago et al. (2016, https://doi.org/10.1002/2016WR019753) showed the need, for rational reasons, to modify Brutsaert's BCs by introducing Emax, an upper limit to the apparent potential evaporation corresponding to an actual evaporation of 0. Following the rigorous approach of Brutsaert, this paper presents the derivation and resulting CR. The BC associated with Emax requires a solution that is rescaled with regard to Brutsaert's dimensionless framework and represents a fundamentally different solution from that of Brutsaert. In essence, this formulation acknowledges a pattern of organized variability, which exists within the data when scaled in Brutsaert's dimensionless framework, and our rescaled CR reorganizes the data, collapsing it toward a more universal representation. Our rescaled CR, implemented with two versions of Emax, one based on mass transfer and another on the Penman equation, is evaluated alongside Brutsaert's original formulation. Multiyear data sets from seven Fluxnet sites in Australia, ranging from a sparsely vegetated ephemeral tropical wetland to a temperate forest with a 75‐m‐tall canopy were used to test the formulations on a weekly basis. All three formulations performed adequately. Overall, the rescaled model with Emax based on the Penman equation performed best; it extracts more information with no additional observational data requirements.