Accurate runoff prediction in nonlinear and nonstationary environments using a novel hybrid model

Accurate runoff prediction is essential for water resource management and ecological conservation. However, the challenges posed by the nonlinear, non-stationary, and multiscale nature of runoff processes hinder the achievement of high prediction accuracy. To address these challenges, this study proposes a novel combined prediction model named OVMD-IAPO-TCN-GRU, which integrates optimized variational modal decomposition (OVMD), an improved Arctic Puffin Optimization Algorithm (IAPO), and a deep learning neural network that combines temporal convolutional networks (TCN) and gated recurrent units (GRU). The model’s framework optimizes and enhances each component’s functionality. Initially, the IAPO algorithm is employed to optimize the key parameters of the VMD, thereby effectively separating hydrological processes across various time scales. This step significantly improves the decomposition quality of non-stationary runoff sequences, reducing modal aliasing and distortion in feature extraction. Subsequently, the well-decomposed non-smooth runoff data is processed by the TCN-GRU module, which leverages gated recurrent units to capture long-term dependencies, while the TCN component improves the extraction of significant multivariate time-series features. Furthermore, the TCN-GRU parameters are further fine-tuned using the IAPO algorithm, thus enhancing the model’s ability to fit nonlinear relationships and improving its generalization performance. Combining each smoothed subsequence obtained from decomposition with the optimal features extracted, the OVMD-IAPO-TCN-GRU model delivers accurate runoff predictions by superimposing the predictions from each mode. The IAPO algorithm enhances the optimization capabilities of the Arctic Puffin algorithm by introducing effective initialization strategies and updating behavioural conversion factors, which improves parameter optimization accuracy. Case studies were conducted at the Hongjiadu and Yingluoxia sites to validate the model’s effectiveness. The performance was assessed using four evaluation metrics, nine benchmark models, and four advanced combined optimization models. The results indicate that the proposed model achieves a Nash-Sutcliffe efficiency coefficient (NSEC) and correlation coefficient (R) exceeding 0.96 and outperforms comparison models across all metrics. Specifically, the root mean square error (RMSE) is reduced by 66.29% and 64.73% compared to the TCN-GRU model. These findings highlight the model’s significant potential for efficient and accurate runoff prediction across different watersheds, emphasizing its superiority in runoff forecasting.