Preprints
https://doi.org/10.5194/hess-2020-585
https://doi.org/10.5194/hess-2020-585
18 Nov 2020
 | 18 Nov 2020
Status: this discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

Technical Note: Analytical Inversion of the Parametric Budyko Equations

Nathan G. F. Reaver, David A. Kaplan, Harald Klammler, and James W. Jawitz

Abstract. The non-parametric Budyko framework provides empirical relationships between a catchment's long-term mean evapotranspiration (E) and the aridity index, defined as the ratio of mean rainfall depth (P) to mean potential evapotranspiration (E0). The parametric Budyko equations attempt to generalize this framework by introducing a catchment-specific parameter (n or w), intended to represent differences in catchment climate and landscape features. Many studies have developed complex regression relationships for the catchment-specific parameter in terms of biophysical features, all of which use known values of P, E0, and E to numerically invert the parametric Budyko equations to obtain values of n or w. In this study, we analytically invert both forms of the parametric Budyko equations, producing expressions for n and w only in terms of P, E0, and E. These expressions allow for n and w to be explicitly expressed in terms of biophysical features through the dependence of P, E0, and E on those same features.

Nathan G. F. Reaver, David A. Kaplan, Harald Klammler, and James W. Jawitz
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
 
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
Nathan G. F. Reaver, David A. Kaplan, Harald Klammler, and James W. Jawitz
Nathan G. F. Reaver, David A. Kaplan, Harald Klammler, and James W. Jawitz

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Latest update: 28 Mar 2024
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Short summary
The parametric Budyko equations contain a single parameter (n or w), interpreted as depending on biophysical features, however, these relationships have remained elusive. We analytically invert the parametric Budyko equations, expressing n and w only in terms of the mean values of potential (E0) and actual evapotranspiration (E) and precipitation (P). These expressions allow n and w to be explicitly related to biophysical features through the dependence of P, E0, and E on those same features.