Hydrological Basis of the Budyko Curve: Data-Guided Exploration of the Mediating Role of Soil Moisture

We present a data-guided framework to explore the hydrological basis of the Budyko curve, focusing on the role of soil moisture in mediating the partitioning of precipitation into runoff and evaporation and the role of climate in this partitioning. The conceptual framework for the derivation of the Budyko curve builds on empirically based power law relationships for long-term average scaled runoff (Q/P) and scaled evaporation (E/E_p), both as functions of long-term average (equilibrium) soil moisture. A second component of the framework is an empirical power law relationship between equilibrium soil moisture and the aridity index, E_p/P. Combinations of these empirical power law relationships with the long-term water balance equation give rise to a form of the Budyko curve, which is a close approximation to Budyko's original relationship and is mathematically similar to the Turc-Pike equation, thus supporting the role of equilibrium soil moisture in giving rise to the Budyko curve. In the remainder of the paper, for special cases of the parameter values of the power law relationships, we independently derive both the soil moisture dependence on E_p/P as well as the Budyko curve itself that not only reproduces a new Budyko-type curve, but can also explain the spread of the empirical data points away from the mean curve. The paper also raises fresh questions about how the empirical power law relationships that govern the soil-mediated precipitation partitioning may have emerged and the role of vegetation in that mediation.