Rescaling the complementary relationship for land surface evaporation

Recent research into the complementary relationship (CR) between actual and apparent potential evaporation has resulted in numerous alternative forms for the CR. Inspired by Brutsaert (2015), who derived a general CR in the form y5 function (x), where x is the ratio of potential evaporation to apparent potential evaporation and y is the ratio of actual to apparent potential evaporation, an equation is proposed to calculate the value of x at which y goes to zero, denoted xmin. The value of xmin varies even at an individual observation site, but can be calculated using only the data required for the Penman (1948) equation as expressed here, so no calibration of xmin is required. It is shown that the scatter in x-y plots using experimental data is reduced when x is replaced by X5 (x2 xmin)/(12 xmin). This rescaling results in data falling along the line y5 X, which is proposed as a new version of the CR. While a reinterpretation of the fundamental boundary conditions proposed by Brutsaert (2015) is required, the physical constraints behind them are still met. An alternative formulation relating y to X is also discussed.