The traditional Muskingum model has difficulty representing complex hydraulic behaviors under high-flow conditions because it relies on simplified assumptions and fixed parameters. To address the pronounced nonlinearity and non-stationarity of flood routing in the arid Tarim River Basin, a hybrid forecasting framework was developed by coupling the Muskingum method with multiple machine learning algorithms (Ridge, LASSO, RF, and LSTM) to predict and correct Muskingum residuals. Global Muskingum parameters were identified using the L-BFGS-B algorithm to represent basin-scale routing characteristics. For rolling forecast, a multidimensional feature space was constructed by integrating routing gradients and hydraulic interaction terms. The results indicated that all hybrid models outperformed the traditional Muskingum method across lead times. The Ridge-based hybrid model achieved the best performance at short lead times, with the Nash–Sutcliffe efficiency (NSE) at a 4 h lead time increasing from 0.56 for the physical baseline to 0.977. For longer lead times (12–24 h), the LASSO-based hybrid model demonstrated higher robustness, which was attributed to L1-regularization-based feature selection. The key scientific contribution of this work lies in proposing a lead-time-dependent adaptive modeling strategy, revealing the structural characteristics of the residuals of the Muskingum model, and demonstrating that, in the study basin, simple linear models outperform complex models in multi-step correction. Overall, the proposed framework alleviates systematic underestimation during high-flow periods and provides a predictive scheme for arid-region rivers that preserves physical interpretability while improving forecasting accuracy.
Wang et al. (Thu,) studied this question.