Relations of rescaled to non-rescaled complementary models and improvement of evapotranspiration estimates by incorporating both climatic and land surface conditions

The estimation of actual evapotranspiration (ET) using both rescaled and non-rescaled complementary relationship (CR) models has become a hotspot in the research on terrestrial ET. This study explores the relationship between these two CR models and improves the method for calculating xmin in rescaled CR models. The rescaled and non-rescaled CR models can be functionally interconvertible, i.e., the non-rescaled CR model enables the rescaled simulation of ET and the rescaled CR model can also conduct a non-rescaled simulation. The parameter b or c in the non-rescaled CR models plays a role similar to xmin in the rescaled models. Based on the data from 15 catchments in the Loess Plateau of China, we validate this relationship between the two CR models. Meanwhile, we evaluate the formulation for xmin proposed by Crago et al. (2016) (the Cragos xmin values) and the results show that the range of variation for the Cragos xmin values is smaller than that for the xmin values obtained by inverse method from the models (the inversed xmin values) in the interannual process. The inversed xmin values of RCR-C2016 are mostly larger than that of RCR-S2017, while the Cragos xmin values are in between these two values. The empirical function for xmin is developed using the aridity index (AI) and normalized difference vegetation index (NDVI) as independent variables in the interannual fluctuations. On the mean annual scale, the empirical function for xmin is expressed only using the AI. Cross-validation results show that the rescaled CR models combined with xmin determined by the empirical functions can more accurately estimate ET and simulate its interannual and spatial changes. (Supported by Project 41971049 of NSFC)