18 Nov 2020
18 Nov 2020
Technical Note: Analytical Inversion of the Parametric Budyko Equations
- 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
- 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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RC1: 'Review', Anonymous Referee #1, 29 Nov 2020
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AC1: 'Response to Anonymous Referee #1', Nathan Reaver, 04 Mar 2021
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AC1: 'Response to Anonymous Referee #1', Nathan Reaver, 04 Mar 2021
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RC2: 'Interactive comment on “Technical Note: Analytical Inversion of the Parametric Budyko Equations”', Anonymous Referee #2, 21 Dec 2020
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AC2: 'Response to Anonymous Referee #2', Nathan Reaver, 04 Mar 2021
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AC2: 'Response to Anonymous Referee #2', Nathan Reaver, 04 Mar 2021
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RC3: 'review comment', Anonymous Referee #3, 19 Jan 2021
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AC3: 'Response to Anonymous Referee #3', Nathan Reaver, 04 Mar 2021
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AC3: 'Response to Anonymous Referee #3', Nathan Reaver, 04 Mar 2021
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RC4: 'review of reaves techincal note', Anonymous Referee #4, 03 Feb 2021
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AC4: 'Response to Anonymous Referee #4', Nathan Reaver, 04 Mar 2021
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AC4: 'Response to Anonymous Referee #4', Nathan Reaver, 04 Mar 2021
Nathan G. F. Reaver et al.
Nathan G. F. Reaver et al.
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