Influencing Factors of the Controlling Parameter in Budyko Framework

Budyko-Fu equation is one of the Budyko models and widely used to describe the coupled water-energy balance at catchment scale. Traditionally the controlling parameter in Fus equation is assumed to represent the underlying surface conditions of a catchment. However, some recent studies have shown that is still a function of multiple factors, in which vegetation cover and climate seasonality are two major ones. It could promote the effective application of Budyko-fu formula to build an empirical equation of by easily available relevant information. Here, taking 15 basins in the Loess Plateau as examples, the relationships between climate seasonality indexes and aridity index(AI) were analyzed, and the interaction between AI and vegetation cover(NDVI) as well as their effects on catchment water balance were explored. The results showed:(1) The current two indexes of climate seasonality, seasonality index(SI) and seasonality and asynchrony index(SAI), were both affected by AI, and their linear relationships with AI were highly significant in the processes of both spatial and temporal (p<0.01). It is difficult to use SI and SAI to accurately quantify the match degree of intra-annual distribution of water and energy. The relationships between the two indexes and were mainly a reflection of that between AI and .(2) In terms of inter-annual variation, AI and NDVI were independent factors with the insignificant relationship in most catchments. In terms of spatial variation, the power function relationship between AI and NDVI reached a highly significant level(p<0.01).(3) There existed a power function relationship between AI and in the spatial process(p<0.05) and temporal process in most catchments(p<0.05). NDVI had a linear relationship with in the spatial process(p<0.01) and temporal process in about half of the catchments(p<0.05).(4) The relationship between SAI and was stronger than that between SI and in both inter-annual and spatial variations, indicating the influence of phase difference in the intra-annual distribution of water-energy on catchment water balance. The exact structure of climate seasonal index needs to be reconsidered.