Understanding the Budyko Equation

The Budyko equation has achieved iconic status in hydrology for its concise and accurate representation of the relationship between annual evapotranspiration and long-term-average water and energy balance at catchment scales. Accelerating anthropogenic land-use and climate change have sparked a renewed interest in predictive applications of the Budyko equation to analyze future scenarios important to water resource management. These applications, in turn, have inspired a number of attempts to derive mathematical models of the Budyko equation from a variety of specific assumptions about the original Budyko hypothesis. Here, we show that the Budyko equation and all extant models of it can be derived rigorously from a single mathematical assumption concerning the Budyko hypothesis. The implications of this fact for parametric models of the Budyko equation also are explored.