Power‐Function Expansion of the Polynomial Complementary Relationship of Evaporation
József Szilágyi, Ning Ma, Richard D. Crago, Russell J. Qualls
Abstract
Abstract The linear form of the nondimensional complementary relationship (CR) follows from an isenthalpic process of evaporation under a constant surface available energy and unchanging wind. Mixing of external moisture into the boundary layer (BL) alters the dry‐end second‐type boundary condition yielding a polynomial that can be further generalized into a three‐parameter (Priestley‐Taylor α, a , b ) power function (PF 3 ), capable of responding to the level of such admixing. With the help of FLUXNET data and setting a = 2 for a possible recapture of the linear and/or polynomial versions of the CR, it is demonstrated that the resulting two‐parameter PF (i.e., PF 2 ) excels among the CR‐based two‐parameter models considered in this study. PF 2 is then employed with a globally set constant value of α = 1.1 and 0.5° monthly data across Australia, while calibrating b against the multiyear water‐balance evaporation rate on a cell‐by‐cell basis. The resulting bi‐modal histogram peaks first near b = 2 (recapturing the polynomial CR) when moisture admixing is significant, and then at b → 1 (yielding the linear CR) when mixing effects are negligible. Unlike the linear or polynomial CR versions, PF 2 can respond to the general efficiency of external moisture admixing through its parameter b , making it applicable even near sudden discontinuities in surface moisture. A new duality emerges with the PF 2 : while α accounts for the effect of entrainment of free tropospheric drier air into the BL on the resulting wet‐environment evaporation rate, b does so for moisture on the drying‐environment evaporation rates.