Improving monthly river discharge forecasts using Fourier-based smoothing and deep learning

ABSTRACT Reliable monthly discharge forecasting is crucial for water-resource planning, reservoir operation, and flood management in the Mahanadi River basin. This study evaluates six deep learning models, long short-term memory (LSTM), gated recurrent unit (GRU), Transformer, and their Fourier-transformed (FT) counterparts (FT-LSTM, FT-GRU, FT-TRANS) across three major gauging stations: Kurubhata, Boranda, and Tikarapara. The Fourier Transform is applied to smooth the time-series data, reducing short-term fluctuations while highlighting dominant seasonal and periodic trends before feeding them into the models. This pre-processing step enables the models to focus on the primary discharge dynamics, thereby improving prediction accuracy. Results show that Fourier-based models outperform their standard versions at all stations. Specifically, FT-GRU achieves the highest accuracy at Kurubhata, while FT-LSTM consistently delivers superior and stable performance at Boranda and Tikarapara. The smoothing process enhances the ability of models to capture monsoon-driven seasonal peaks and strengthens their generalisation under varying flow conditions. Overall, the integration of Fourier-based smoothing with deep learning architectures significantly improves the quality of monthly discharge forecasts, reduces errors during both low- and high-flow periods, and provides a practical tool for hydrologists, water managers, and planners in water-resource management and flood risk reduction.