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Rescaling the complementary relationship for land surface evaporation
Author(s) -
Crago R.,
Szilagyi J.,
Qualls R.,
Huntington J.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr019753
Subject(s) - evaporation , potential evaporation , function (biology) , mathematics , thermodynamics , calibration , surface (topology) , boundary value problem , chemistry , physics , mathematical analysis , geometry , statistics , evolutionary biology , biology
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 y = 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 x min . The value of x min 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 x min is required. It is shown that the scatter in x ‐ y plots using experimental data is reduced when x is replaced by X = ( x − x min )/(1 − x min ). This rescaling results in data falling along the line y = 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.