Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Andréassian, Vazken; Sari, Tewfik

doi:10.5194/hess-23-2339-2019

Cited by 18 publications

(14 citation statements)

References 8 publications

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“…Even Eqs. ( 5) and ( 6), which are generally regarded as essentially interchangeable when using the approximate relationship, w ≈ n+0.72 (Yang et al, 2008;Andréassian and Sari, 2019), give nonequivalent trajectories, particularly for small values of the catchment-specific parameter. The contradiction between Eqs.…”

Section: Nonuniqueness Of the Parametric Budyko Equationsmentioning

confidence: 99%

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Reaver

Kaplan

Klammler

et al. 2022

Hydrol. Earth Syst. Sci.

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Abstract. The Budyko framework posits that a catchment's long-term mean evapotranspiration (ET) is primarily governed by the availabilities of water and energy, represented by long-term mean precipitation (P) and potential evapotranspiration (PET), respectively. This assertion is supported by the distinctive clustering pattern that catchments take in Budyko space. Several semi-empirical, nonparametric 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 nonparametric 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 the aridity index, PETP, while the 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 reexamine, reinterpret, and test these two key assumptions of the current Budyko framework both theoretically and empirically. In our theoretical test, we use a biophysical model for ET 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 (UK) and United States (US) 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 nontransferability implies that n and w are proxy variables for ETP, rendering the parametric Budyko equations underdetermined and lacking predictive ability. Finally, we show that the parametric Budyko equations are nonunique, 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.

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Section: Nonuniqueness Of the Parametric Budyko Equationsmentioning

confidence: 99%

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Reaver

Kaplan

Klammler

et al. 2022

Hydrol. Earth Syst. Sci.

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“…Zhang et al, 2008;Zheng et al, 2018) and the Mezentsev-Choudhury-Yang equation (3) (Luo et al, 2020;Roderick & Farquhar, 2011;Wang et al, 2020;Xing et al, 2018;Xiong et al, 2020). These equations can be found under different names in the litterature such as Tixeront-Fu equation for (2) or Turc-Mezentsev for (3) (Andréassian & Sari, 2019).…”

Section: One Parameter Equationmentioning

confidence: 99%

Budyko framework based analysis of the effect of climate change on watershed characteristics and their impact on discharge over Europe

Collignan

Polcher

Quintana‐Seguí

2022

Preprint

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In a context of climate change, the stakes surrounding water availability are getting higher. Decomposing and quantifying the effects of climate on discharge allows to better understand their impact on water resources. We propose a methodology to separate the effect of change in annual mean of climate variables from the effect of intra-annual distribution of precipitations. It combines the Budyko framework with outputs from a Land Surface Model (LSM). The LSM is used to reproduces the behavior of 2134 reconstructed watersheds over Europe between 1902 and 2010, with climate inputs as the only source of change. We fit to the LSM outputs a one parameter approximation to the Budyko framework. It accounts for the evolution of annual mean in precipitation (P) and potential evapotranspiration (PET). We introduce a time-varying parameter in the equation which represents the effect of long-term variations in the intra-annual distribution of P and PET. To better assess the effects of changes in annual means or in intra-annual distribution of P, we construct synthetic forcings fixing one or the other. The results over Europe show that the changes in discharge due to climate are dominated by the trends in the annual averages of P. The second main climate driver is PET, except over the Mediterranean area where changes in intra-annual variations of P have a higher impact on discharge than trends in PET. Therefore the effects of changes in intra-annual distribution of climate variables are not to be neglected when looking at changes in annual discharge.

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“…Afterwards other researchers developed new equations in various forms within the Budyko framework. For example, based on new data and considering the constraints of water and energy availability (Andreassian and Sari, 2019), Turc (1954) empirically proposed, the following equation:…”

Section: -Budyko Framework Under Steady State Conditions: a Short Ove...mentioning

confidence: 99%

Budyko framework; towards non-steady state conditions

Mianabadi

Davary

Pourreza‐Bilondi

et al. 2020

Journal of Hydrology

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Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Cited by 18 publications

References 8 publications

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Budyko framework based analysis of the effect of climate change on watershed characteristics and their impact on discharge over Europe

Budyko framework; towards non-steady state conditions

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