Hybrid Deep Learning Versus Empirical Methods for Daily Potential Evapotranspiration Estimation in the Nakdong River Basin, South Korea

Abstract

This study compares the performance of empirical and hybrid deep learning (DL) models in estimating daily potential evapotranspiration (PET) in the Nakdong River Basin (NRB), South Korea, with the FAO-56 Penman-Monteith (PM) method as a reference. Two empirical models, Priestley-Taylor (P-T) and Hargreaves-Samani (H-S), and two DL models, a standalone Long Short-Term Memory (LSTM) network and a hybrid Convolutional Neural Network Bidirectional LSTM with an attention mechanism, were trained on a meteorological dataset (1973-2024) across 13 meteorological stations. Four input combinations (C1, C2, C3, and C4) were tested to assess the model's robustness under varying data availability conditions. The results indicate that empirical models performed poorly, with a basin-wide RMSE of 5.04-5.79 mm/day and negative NSE (-10.37 to -13.99), and are therefore poorly suited to NRB. In contrast, DL models achieved significant improvements in accuracy. The hybrid CNN-BiLSTM Attention Mechanism (C1) produced the highest performance, with R2 = 0.820, RMSE = 0.672 mm/day, NSE = 0.820, and KGE = 0.880, which was better than the standalone LSTM (R2 = 0.756; RMSE = 0.782 mm/day). The generalization of heterogeneous climates was also verified through spatial analysis, in which the NSE at the station level consistently exceeded 0.70. The hybrid DL model was found to be highly accurate in representing the temporal variability and seasonal patterns of PET and is therefore more suitable for operational hydrological modeling and water-resource planning in the NRB.