One-Parameter Analytical Derivation in Modified Budyko Framework for Unsteady-State Streamflow Elasticity in Humid Catchments

The changes in climate and catchment properties have altered the hydrological processes significantly at different spatiotemporal scales around the world. In particular for finer time scales, changes in water storage, which has been commonly neglected for long-term temporal scales, may play an important role on hydrological processes. Nevertheless, few studies addressed this question in modifying the Budyko framework, with most of them remaining a steady-state assumption on catchment characteristics. Here, we derive new analytical formulas of unsteady-state streamflow elasticity in a modified Budyko framework, incorporating both storage change and one specific parameter for catchment properties. We study 78 humid catchments in the USA with simulation data of daily hydrological processes from a probability-distribution-based hydrological model (the modified HyMOD). As indicated by results, the annual storage change ratio is linearly correlated with the annual aridity index, and this relationship can be used to estimate elasticity coefficients with our formulas. The estimated elasticity coefficients perform well in simulating the annual streamflow with the power-law model. For different catchments, variability of the unsteady-state elasticity is higher than that of the steady-state elasticity. Unsteady-state streamflow coefficients show significant linear correlation with catchment properties, such as the average slope, average elevation, and catchment area. This study provides a new analytical approach to investigate the interannual stability of catchments with varying climate and catchment properties.