Estimating the monthly pan evaporation with limited climatic data in dryland based on the extended long short-term memory model enhanced with meta-heuristic algorithms

Accurate estimation of evaporation is of great significance for understanding regional drought, and managing and applying limited water resources in dryland. However, the application of the traditional estimation approaches is limited due to the lack of required meteorological parameters or experimental conditions. In this study, a novel hybrid model was proposed to estimate the monthly pan Ep in dryland by integrating long short-term memory (LSTM) with grey wolf optimizer (GWO) algorithm and Kendall-τ correlation coefficient, where the GWO algorithm was employed to find the optimal hyper-parameters of LSTM, and Kendall-τ correlation coefficient was used to determine the input combination of meteorological variables. The model performance was compared to the performance of other methods based on the evaluation metrics, including root mean squared error (RMSE), the normalized mean squared error (NMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), and Nash–Sutcliffe coefficient of efficiency (NSCE). The results indicated that the optimal input meteorological parameters of the hybrid Kendall-τ-GWO-LSTM models are the monthly average temperature, the minimum air temperature, the maximum air temperature, the minimum values of RMSE, NMSE, MAE, and MAPE are 38.28, 0.20, 26.62, and 19.96%, and the maximum NSCE is 0.89, suggesting that the hybrid Kendall-τ-GWO-LSTM exhibit better model performance than the other hybrid models. Thus, the hybrid Kendall-τ-GWO-LSTM model was highly recommended for estimating pan Ep with limited meteorological information in dryland. The present investigation provides a novel method to estimate the monthly pan Ep with limited meteorological variables in dryland by coupling a deep learning model with meta-heuristic algorithms and the data preprocessing techniques.