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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2018-598
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2018-598
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 05 Dec 2018

Research article | 05 Dec 2018

Review status
This discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

Derivation of the mean annual water-energy balance equation based on an Ohms-type approach

Xu Shan, Xindong Li, and Hanbo Yang Xu Shan et al.
  • State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Abstract. The Budyko hypothesis has been widely used to describe precipitation partitioning at the catchment scale. Many empirical and analytical formulas have been proposed to describe the Budyko hypothesis. Based on dimensional analysis and mathematic reasoning, previous studies have given an analytical derivation, i.e., the Mezentsev-Choudhury-Yang (MCY) equation. However, few hydrological processes are involved in the derivation. Note that similar to electrical circuits and atmospheric motions, this study tried to give a new derivation of the Budyko hypothesis based on an analogy of the Ohms-type approach and the homogeneity assumption. The derived equation has the same form as the MCY equation but has a more physical explanation than the mathematic reasoning proposed in previous studies. In addition, under conditions without the homogeneity constraint, a more general expression is
E=P(b+kE)0) [Pn+(b+kE)0)n](1/n), where E, E0 and P are evaporation, potential evaporation and precipitation, respectively, and n, k and b are constants.

Xu Shan et al.
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Xu Shan et al.
Xu Shan et al.
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Short summary
The Budyko hypothesis has been generally used to quantify how much precipitation transforms into evaporation in one catchment. To approach this hypothesis, previous studies proposed analytical formulas derived based on mathematic reasoning. Differently, this study drew a new derivation for this hypothesis based on fundamental physical principles. It clearly reveals the underlying assumptions in the previous mathematic reasoning and promotes hydrologic understanding on this hypothesis.
The Budyko hypothesis has been generally used to quantify how much precipitation transforms into...
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