Reinterpreting the Budyko Framework

Abstract

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.

Climate Controls on River Chemistry

“…Here we relate mean solute concentrations to climate conditions at each site using a widely used relationship, Budyko equation. Various forms of Budyko equations relate the long‐term ratio of evaporative index to aridity index (Chen & Sivapalan, 2020; Gentine et al., 2012; Reaver et al., 2020). Here we used the original form (Budyko, 1974): $$$\frac{ET}{P}=\frac{1}{{\left[{\left(\frac{P}{PET}\right)}^{\beta }+1\right]}^{1/\beta }}$$$ where P is precipitation, ET is evapotranspiration, the summation of evaporation (from open water, bare soil, and vegetated surfaces), transpiration (from within plant leaves), and sublimation from ice and snow surfaces.…”

“…Here we relate mean solute concentrations to climate conditions at each site using a widely used relationship, Budyko equation. Various forms of Budyko equations relate the long-term ratio of evaporative index to aridity index (Chen & Sivapalan, 2020;Gentine et al, 2012;Reaver et al, 2020). Here we used the original form (Budyko, 1974):…”

Ecosystem adaptation to climate change: the sensitivity of hydrological predictions to time-dynamic model parameters

“…While the Budyko framework is a well-established concept, recent studies by Berghuijs et al (2020) and Reaver et al (2020) show that it should be cautiously applied in changing systems. The Budyko framework reflects the long-term hydrological partitioning under dynamic equilibrium conditions.…”

Exploring the role of soil storage capacity for explaining deviations from the Budyko curve using a simple water balance model

“…Physiographic catchment characteristics that affect the water balance are nevertheless manifold and interrelated, and it thus appears inappropriate to represent those by a single parameter. Reaver et al (2020) https://doi.org/10.5194/hess-2021-174 Preprint. Discussion started: 30 March 2021 c Author(s) 2021.…”