A hybrid approach to enhance streamflow simulation in data-constrained Himalayan basins: combining the Glacio-hydrological Degree-day Model and recurrent neural networks

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Abstract. The Glacio-hydrological Degree-day Model (GDM) is a distributed model, but it is prone to uncertainties due to its conceptual nature, parameter estimation, and limited data in the Himalayan basins. To enhance accuracy without sacrificing interpretability, we propose a hybrid model approach that combines GDM with recurrent neural networks (RNNs), hereafter referred to as GDM–RNN. Three RNN types – a simple RNN model, a gated recurrent unit (GRU) model, and a long short-term memory (LSTM) model – are integrated with GDM. Rather than directly predicting streamflow, RNNs forecast GDM's residual errors. We assessed performance across different data availability scenarios, with promising results. Under limited-data conditions (1 year of data), GDM–RNN models (GDM–simple RNN, GDM–LSTM, and GDM–GRU) outperformed standalone GDM and machine learning models. Compared with GDM's respective Nash–Sutcliffe efficiency (NSE), R2, and percent bias (PBIAS) values of 0.80, 0.63, and −4.78, the corresponding values for the GDM–simple RNN were 0.85, 0.82, and −6.21; for GDM–LSTM, they were 0.86, 0.79, and −6.37; and for GDM–GRU, they were 0.85, 0.8, and −5.64. Machine learning models yielded similar results, with the simple RNN at 0.81, 0.7, and −16.6; LSTM at 0.79, 0.65, and −21.42; and GRU at 0.82, 0.75, and −12.29, respectively. Our study highlights the potential of machine learning with respect to enhancing streamflow predictions in data-scarce Himalayan basins while preserving physical streamflow mechanisms.