Wet-surface evaporation equations related to the Penman equation can be represented graphically on vapor pressure () versus temperature () graphs (Qualls & Crago, 2020). Here, actual regional evaporation is represented graphically on (, ) graphs using the Complementary Relationship (CR) between actual and apparent potential evaporation. The CR proposed by the authors can be represented in a simple and intuitive geometric form, in which lines representing the regional latent heat flux, , and the wet surface (Priestley & Taylor, 1972) evaporation rate, , intersect at =0. This approach allows a graphical estimate of (or the corresponding mathematical formulation) without the need to know either the wet surface or the apparent potential evaporation rates. The wet surface temperature is needed, and a calculation method for it is provided. The formulation works well using monthly data from seven sites in Australia, even when the same value of the Priestley & Taylor parameter α is used for all sites.

The polynomial form of the nondimensional complementary relationship (CR) follows from an isenthalpic process of evaporation under a constant surface available energy and unchanging wind. The exact polynomial expression results from rationally derived first and second-order boundary conditions (BC). By keeping the BCs, the polynomial can be extended into a two-parameter (a and b) power function for added flexibility. When a = b = 2 it reverts to the polynomial version. With the help of Australian FLUXNET data it is demonstrated that the power-function formulation excels among CR-based two-parameter models considered, even when a = 2 is prescribed to reduce the number of parameters to calibrate to two. The same power-function approach (a = 2) is then employed with a combination of different gridded monthly potential evaporation terms across Australia, while calibrating b against the multiyear simplified water-balance evaporation rate on a cell-by-cell basis. The resulting bi-modal histogram of the b values peaks first near b = 2 and then at b → 1 (secondary modus), confirming earlier findings that occasionally a linear version (i.e., b = 1) of the CR yields the best estimates. It is further demonstrated that the linear form emerges when regional-scale transport of moist air is negligible toward the study area during its drying, while the more typical nonlinear CR version prevails otherwise. A thermodynamic-based explanation is yet to be found as to why the flexible power function curves (i.e., b ≠ 2) converge to the polynomial one (b = 2) in such cases.