Preprints
https://doi.org/10.5194/hess-2020-584
https://doi.org/10.5194/hess-2020-584

  13 Nov 2020

13 Nov 2020

Review status: a revised version of this preprint is currently under review for the journal HESS.

Reinterpreting the Budyko Framework

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 Budyko framework posits that a catchment's long-term mean evapotranspiration (E) is primarily governed by the availabilities of water and energy, represented by long-term mean precipitation (P) and potential evapotranspiration (E0), respectively. This assertion is supported by the distinctive clustering pattern that catchments take in Budyko space. Several semi-empirical, non-parametric curves have been shown to generally represent this clustering pattern but cannot explain deviations from the central tendency. Parametric Budyko equations attempt to generalize the non-parametric framework, through the introduction of a catchment-specific parameter (n or w). Prevailing interpretations of Budyko curves suggest that the explicit functional forms represent trajectories through Budyko space for individual catchments undergoing changes in aridity index, (E0/P), while n and w values represent catchment biophysical features; however, neither of these interpretations arise from the derivation of the Budyko equations. In this study, we re-examine, reinterpret, and test these two key components of the current Budyko framework both theoretically and empirically. In our theoretical test, we use a biophysical model for E to demonstrate that n and w values can change without invoking changes in landscape biophysical features and that catchments are not required to follow Budyko curve trajectories. Our empirical test uses data from 728 reference catchments in the United Kingdom and United States to illustrate that catchments rarely follow Budyko curve trajectories and that n and w are not transferable between catchments or across time for individual catchments. This non-transferability implies n and w are proxy variables for E/P, rendering the parametric Budyko equations under-determined and lacking of predictive ability. Finally, we show that the parametric Budyko equations are non-unique, suggesting their physical interpretations are unfounded. Overall, we conclude that, while the shape of Budyko curves generally captures the global behavior of multiple catchments, their specific functional forms are arbitrary and not reflective of the dynamic behavior of individual catchments.

Nathan G. F. Reaver et al.

 
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Nathan G. F. Reaver et al.

Nathan G. F. Reaver et al.

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Short summary
The Budyko curve emerges globally from the behavior of multiple catchments. Single parameter Budyko equations extrapolate the curve concept to individual catchments, interpreting curves and parameters as representing climatic and biophysical impacts and on water availability, respectively. We tested these two key components theoretically and empirically, finding catchments are not required to follow Budyko curves and usually do not, implying the parametric framework lacks predictive ability.