Abstract:
Frequent and intensified flood disasters driven by global climate change have posed severe challenges to regional flood control and water resources management. The Taihu Basin, as one of China’s most economically and ecologically significant regions, is highly vulnerable to extreme hydrological events, making accurate, extended lead-time water level forecasting essential for disaster prevention and mitigation. However, existing forecasting approaches often suffer from reduced accuracy and stability under long lead times and extreme water level fluctuations. To address these limitations, this study proposes a novel hybrid model—WD-iNARX-WR (Wavelet Decomposition–improved Nonlinear Auto-Regressive model with Exogenous Inputs–Wavelet Reconstruction)—which incorporates optimized time-delay embedding for both inputs and outputs, an adaptive hidden-layer configuration tailored to the complexity of each component, and a refined learning algorithm designed to enhance nonlinear mapping capability, long-term memory retention, and generalization performance, thereby improving multi-step-ahead forecasting of Taihu water levels. The proposed approach begins with the systematic selection of meteorological, hydrological, and operational scheduling variables that significantly influence basin water levels. These multi-source predictors are subjected to multi-level wavelet decomposition, with an optimal wavelet basis and decomposition scale determined according to the statistical and spectral characteristics of the data. This process isolates low-frequency approximation components that capture long-term hydrological trends and high-frequency detail components representing short-term variability. Each component is then modeled independently using an improved NARX neural network, featuring optimized time-delay embedding, adaptive hidden-layer configuration, and an enhanced learning algorithm to strengthen nonlinear mapping capability, long-term memory retention, and generalization performance. Unlike the conventional NARX architecture, where all inputs share a uniform delay, the iNARX network assigns distinct time delays to each exogenous input and the output variable, enabling a more flexible temporal representation of different driving factors. Historical datasets are used for rigorous training and validation, ensuring that both persistent trends and transient fluctuations are effectively captured. Finally, the predicted components are recombined via wavelet reconstruction to produce the final forecast series, preserving the multi-scale structure of the hydrological process. Model performance was evaluated for lead times of 1–7 days and benchmarked against a traditional backpropagation (BP) neural network and the original iNARX model. Results indicate that: (1) For shorter lead times, all three models achieved relatively good forecasting performance, indicating that neural network models with nonlinear mapping capabilities have certain advantages in predicting hydrological time series. (2) For longer lead times, the iNARX and WD-iNARX-WR models showed clear advantages over the BP model, reflecting the superiority of the iNARX network structure with its strong generalization ability and long-term memory capacity. (3) When observed water levels exhibited large fluctuations and extreme values, the BP model’s predicted hydrograph showed oscillations, the iNARX model’s predictions displayed a sawtooth pattern, whereas the WD-iNARX-WR model produced relatively smooth curves that closely matched the observed water levels. This demonstrates that the use of wavelet transform can capture useful information at multiple resolutions, thereby significantly enhancing forecasting capability. (4) The WD-iNARX-WR model exhibited superior forecasting performance across different lead times, with particularly notable improvements in accuracy for long lead times and during extreme water level events. For 4–7 day lead times, the accuracy of WD-iNARX-WR was 8.5% higher than that of BP and 2.5% higher than that of iNARX. This study not only validates the feasibility and superiority of coupling wavelet decomposition with an improved NARX network but also provides a robust technical framework for operational flood forecasting in the Taihu Basin. The model’s reliable performance under long lead times and extreme hydrological conditions offers valuable support for optimizing water resources allocation, enhancing early warning systems, and developing intelligent disaster management platforms.