A TimeGAN-enhanced cross-attention time-frequency transformer for multi-step monthly runoff forecasting in the Huaihe river basin

Study region The upper Huaihe River Basin (HRB), China, with runoff observations from the Xincai (XC) and Zhoukou (ZK) hydrological stations. Study focus Data-driven models have shown considerable potential for runoff forecasting, yet their performance in monthly runoff prediction remains constrained by hydrological non-stationarity and limited data availability. To address these challenges, this study proposes a Cross-Attention Time-Frequency Transformer (CA-TFAformer, CTF) framework that jointly exploits the trend, seasonal, and residual components obtained from Seasonal-Trend decomposition using Loess (STL). A time-frequency attention (TFA) mechanism is developed to extract dominant temporal and frequency-domain characteristics, while a cross-attention (CA) mechanism is introduced to capture interactions among runoff components. Furthermore, a TimeGAN-based data augmentation strategy is employed to enrich training samples and improve model generalization. New hydrological insights for the region Monthly runoff dynamics in the upper HRB are jointly characterized by long-term trends, seasonal variability, and irregular fluctuations, indicating the importance of explicitly modeling the interactions among these runoff components. Results indicate that incorporating both time-frequency information and inter-component dependencies substantially improves forecasting performance. In addition, TimeGAN-generated samples provide additional representation of high-flow conditions in the augmented training set, resulting in more robust forecasting and improved flood peak prediction. These findings demonstrate the value of integrating runoff component interactions and data augmentation for reliable medium- and long-term runoff forecasting in non-stationary hydrological environments.