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Power-function expansion of the nondimensional complementary relationship of evaporation: the emergence of dual attractors
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  • Jozsef Szilagyi,
  • Ning Ma,
  • Richard D Crago,
  • Russell J. Qualls
Jozsef Szilagyi
University of Nebraska/Budapest University of Technology and Economics

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Ning Ma
Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences
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Richard D Crago
Bucknell University
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Russell J. Qualls
University of Idaho
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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.