Interaction of vegetation, climate and topography on evapotranspiration modelling at different time scales within the Budyko framework

Vegetation, climate and topography have been empirically formulated into the controlling parameter of the Budyko model (omega) to estimate evapotranspiration (ET). However, these variables, if simultaneously employed, may induce multicollinearity problems because of their potential interactions. Further, these interactions may vary with different time scales and subsequently result in the inaccurate estimation of to omega. As such, we investigated the interactions of vegetation, climate and topography and their corresponding effects on ET modelling at different time scales by employing vegetation coverage (M), an improved climate seasonality and asynchrony index (SAI), the fraction of precipitation falling as snow (f(s)) and relative basin relief (BR/(B) over barR), in 30 catchments in China's Loess Plateau. We found that, on annual scale, M and SAI were significantly related to omega, while being independent from each other; in consequence, both of them should be parameterized into the Budyko model on the annual scale for better ET modelling. However, the links between M and SAI became stronger with increased time scales, the parameterization of omega should thus be reformatted for longer periods. When extended to a 30-year period, omega was closely related to the above variables, but M was highly inter correlated with SAI and BR/(B) over barR, and f(s) was significantly related to BR/(B) over barR. The independent M and f(s) were finally selected to fit omega, which allowed mean annual ET to be accurately modelled on long-term scale. Identification of the dominant factors applicable at different time scales can simplify the empirical parameterization of the Budyko formula and thereby facilitate more accurate estimation of ET.