Hydrological Basis of Different Budyko Equations: The Spatial Variability of Available Water for Evaporation

The available water for evaporation within a catchment is spatially variable. However, how the spatial variability of available water affects mean annual evaporation is not fully understood. For a specific catchment, a suitable distribution function defined for non-negative random variables can be determined through statistical methods to represent the spatial variability of the available water when the point-scale data are available. This article proposes that the distribution function representing the spatial variability of available water for evaporation determines the functional form of Budyko equation based on the one-stage precipitation partitioning concept. Specifically, the available water for evaporation following a single-parameter distribution function leads to a deterministic Budyko equation; whereas a two-parameter distribution function of available water for evaporation leads to a single-parameter Budyko equation. We identified the property of distribution function for symmetric Budyko equation, which suggests that precipitation partitioning and energy partitioning in the hydrological cycle follow the same functional form with respect to aridity index and humidity index, respectively. The lower bound of Budyko curve is explained as a result of probable distributions of available water for evaporation due to catchment co-evolution.