Probabilistic daily runoff forecasting in high-altitude cold regions using a hybrid model combining DBO and transformer variants

The Tailan River Basin in the Aksu region and the Yulong Kashi River in the Hotan River Basin of Xinjiang are located at respective geographical coordinates of 80°21'44" to 81°10'14" E, 40°41'41" to 42°15'13" N, and 77.25° to 81.75° E, 34.75° to 36.25° N. To tackle the complexity of runoff prediction in high-altitude cold regions, alongside the limitations of existing machine learning approaches, where nonlinear relationships, long-term dependencies, and sparse observational data pose significant challenges, previous models have consistently struggled to account for these issues. In response, we propose a hybrid runoff prediction model that combines Dung Beetle Optimization (DBO)'s optimization capabilities, Temporal Convolutional Networks (TCN)’s proficiency in extracting local temporal features, and the Transformer’s ability to capture long-term dependencies. In addition, the Bootstrap method is employed to merge point prediction outcomes for interval runoff forecasting, providing robust uncertainty estimates to address data limitations in these regions. The DBO-TCN-Transformer model consistently attains a Nash-Sutcliffe Efficiency (NSE) above 0.81, showcasing enhanced performance over traditional models. Across various forecast periods, the model’s NSE values are 6.9–26.9 % higher than those of the TCN and Transformer models, offering more reliable short-term and long-term predictions. Furthermore, the Bootstrap algorithm’s probabilistic approach provides valuable insights into forecast uncertainty, a crucial feature for managing water resources and mitigating flood risks in high-altitude cold regions with complex hydrological dynamics. • Hybrid DBO-TCN-Transformer model improves runoff forecasting accuracy. • Significant NSE improvements of 6.9 %-26.9 % over TCN and Transformer models. • Bootstrap approach provides enhanced uncertainty quantification. • Applicable for both short-term and long-term water resource management. • Suitable for high-altitude cold regions with complex hydrological dynamics.