Evaluating the role of watershed properties in long-term water balance through a Budyko equation based on two-stage partitioning of precipitation

In this paper, a four-parameter Budyko equation is derived for mean annual water balance by applying the proportionality relationship to a two-stage partitioning of precipitation. The four dimensionless parameters include the Horton index (H, defined as the ratio of evaporation to total wetting) and (the ratio of initial evaporation to total wetting) for slow runoff, and (the ratio of initial wetting to total wetting) and (the ratio of total wetting to its potential) for fast runoff. The derived four-parameter equation balances model parsimony and representation of dominant hydrologic processes and provides a framework to disentangle the roles of climate variability, vegetation, soil, and topography on long-term water balance in gauged watersheds. The four parameters are determined for 165 watersheds by using observations of precipitation, potential evaporation, streamflow, and soil properties. Based on the principal component regression analysis, average time interval between rainfall events, slope, normalized difference vegetation index, and wilting point are identified as the dominant controlling factors on H and ; saturated hydraulic conductivity and the difference between field capacity and residual soil moisture are identified as the dominant controlling factors on ; and is controlled by effective soil water storage capacity, frequency of rainfall events, and climate seasonality. The combination of four-parameter Budyko equation and the principal component regression equations provides a model to assess the long-term responses of evaporation and runoff to climate and watershed property changes in ungauged watersheds.