Estimation of time-varying parameter in Budyko framework using long short-term memory network over the Loess Plateau, China

Abstract

Accurate estimation of the basin-specific parameter in the Budyko framework (e.g., parameter n in the Choudhury-Yang equation) is critical to quantify precipitation partitioning into evapotranspiration (E) and runoff. However, n is difficult to estimate due to complex interactions between the water balance and various environmental factors. In this study, we identified the controlling factors of n using random forest during 1981–2015 for 30 basins in the Loess Plateau of China. We then used the long short-term memory (LSTM) network combined with an 11-year moving window to develop a model to estimate time-varying n. This model was further incorporated into the Choudhury-Yang equation to simulate E. Our results showed that correlations between parameter n and environmental factors presented obvious spatial heterogeneity. Three land use type factors (i.e., the proportions of cropland, shrubland, and built-up land area), two climatic factors (i.e., precipitation and potential evapotranspiration), and a water use factor (i.e., irrigation water use) were identified as the controlling factors for n. Based on these controls, the LSTM model outperformed the traditional multiple linear regression model (MLR model) in estimating time-varying n, with root mean square error (RMSE) of 0.31/0.49 and coefficient of determination (R2) of 0.88/0.67 for the LSTM/MLR model, respectively. Moreover, compared with the original Choudhury-Yang equation (using constant n calibrated by long-term average water balance), the improved equation (using time-varying n estimated by the LSTM) better reproduced the time series of water balance-based E. This study could enhance the applicability of the Budyko framework and provide scientific guidance for water resources management.