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

The accurate quantification of actual evapotranspiration (ET) is crucial for water resources management in agricultural production and ecological construction. Estimating 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, which is the value of the independent variable x when the dependent variable y is equal to zero 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 and vice versa. Based on the data from 15 catchments in the Loess Plateau of China, we validate this relationship between two CR models. Meanwhile, we evaluate the formulation for xmin proposed by Crago et al. (2016) (xmin-d) and the results show that the range of variation for xmin-d values is smaller than that for the xmin values obtained by inverse method from the models (xmin-i) in the interannual process. The mean xmin-i value of RCR-C2016 is larger than that of RCR-S2017, while the mean xmin-d value is 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. The empirical function for xmin is expressed only using the AI in the spatial variations at a mean annual scale. Cross-validation results show that the rescaled CR models with the empirical functions of xmin can more accurately estimate ET and simulate its interannual and spatial changes.