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

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.