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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/hess-2020-585
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-585
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  18 Nov 2020

18 Nov 2020

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This preprint is currently under review for the journal HESS.

Technical Note: Analytical Inversion of the Parametric Budyko Equations

Nathan G. F. Reaver1,2, David A. Kaplan2, Harald Klammler2,3, and James W. Jawitz4 Nathan G. F. Reaver et al.
  • 1Water Institute, University of Florida, Gainesville, Florida, USA
  • 2Engineering School of Sustainable Infrastructure and Environment (ESSIE), University of Florida, Gainesville, Florida, USA
  • 3Department of Geosciences, Federal University of Bahia, Salvador, Bahia, Brazil
  • 4Soil and Water Science Department, University of Florida, Gainesville, Florida, USA

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 et al.

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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.
The parametric Budyko equations contain a single parameter (n or w), interpreted as depending on...
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