TCN-CMA-ES; a novel flood routing approach integrating temporal convolutional networks (TCNs) with covariance matrix adaptation evolution strategy (CMA-ES)

Abstract Flood routing is fundamental to water-resource management, early-warning systems, and infrastructure planning because it estimates downstream flow dynamics from upstream river conditions. This study proposes TCN–CMA-ES, a hybrid flood-routing framework that integrates Temporal Convolutional Networks (TCN) with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The proposed model was applied to three flood-routing configurations involving six gauging stations across the Homochitto, Mississippi, and Ohio River systems. In each configuration, upstream discharge and gage-height hydrographs were used to estimate downstream discharge and gage height. The model was trained and tested over four routing horizons (10, 30, 60, and 120 time-step lags), and its performance was evaluated using Nash–Sutcliffe Efficiency (NSE), Kling–Gupta Efficiency (KGE), Mean Absolute Relative Error (MARE), Percent Bias (PBIAS), and Root Mean Square Error (RMSE). During testing, the best-performing configuration at the 30-step lag achieved RMSE = 1.28 m³/s, NSE = 0.83, KGE = 0.42, MARE = 5.18%, and PBIAS = 4.49%, while longer routing horizons (60–120 steps) also maintained strong predictive performance, confirming the robustness of the framework. Compared with standalone TCN and conventional benchmark models, the hybrid TCN–CMA-ES approach improved both discharge and gage-height routing accuracy, particularly at intermediate and extended lead times. These results highlight the potential practical value of the proposed framework for flood routing, early-warning systems, and reservoir-operation planning. However, additional computational benchmarking is required before confirming its suitability for operational real-time applications.