Lumped variable representing the integrative effects of climate and underlying surface system: Interpreting Budyko model parameter from earth system science perspective

Parametric Budyko models express the ratio of annual actual evapotranspiration (ET) to annual precipitation (P) as a function of dryness index, i.e., annual potential evapotranspiration (ET0)/P (denoted as DI) and model parameter at a catchment. Generally the model parameter is assumed to reflect factors besides DI, especially the underlying surface features. However, recent studies have revealed its relations with DI, which forces us to further examine its connotation. We revisited the derivation of three parametric Budyko equations and found that model parameter was essentially a lumped variable representing the integrative effects of climate and underlying surface system. Then taking 15 typical catchments in the Chinese Loess Plateau as the study area, we explored the controls of Budyko-Fu model parameter (w) and their differences in temporal (between-years) and spatial (between-catchments) processes. As expected, w was affected by both climate and underlying surface factors. Specifically, DI, climate seasonality and asynchrony index (SAI) and Normalized Difference Vegetation Index (NDVI) influenced w in both temporal and spatial processes; besides, catchment relief ratio (CR) and relative infiltration capacity (ks/ir) also affected w in spatial process. SAI was strongly correlated with DI and its close relationship with w essentially conveyed DI's influence. Considering the inherent connection between DI and the inverse w, DI was not included in the empirical formula for w. SAI and NDVI remained independent in temporal process and the empirical formula for w with these two factors modeled annual ET well (MAE = 15.03 mm). In spatial process, SAI, NDVI, CR, and ks/ir were interconnected and by using any one the spatial variation of ET was captured adequately (MAE = 11.16, 11.74, 11.27, and 10.43 mm, respectively). Our results demonstrate theoretically and empirically the importance of viewing Budyko model parameter from earth system science perspective and focusing on the differences of its controls in spatiotemporal processes.