Robust Parameter Estimation of the Nonlinear Muskingum Model Using a Stabilized Conjugate Gradient Method

This study presents a robust and efficient framework for parameter estimation of the nonlinear Muskingum model using a stabilized Conjugate Gradient (CG) method with a safeguarded update strategy. The proposed approach addresses numerical instability and convergence issues commonly observed in optimization methods. Three real-world flood events are employed to evaluate model performance. The results demonstrate that the CG method provides accurate predictions with significantly lower computational cost compared to Particle Swarm Optimization (PSO), while maintaining stable convergence behavior. Sensitivity analysis indicates that the nonlinear exponent (m) is the most influential parameter, followed by the weighting parameter (X), whereas the storage constant (K) has comparatively lower sensitivity. The findings confirm the efficiency, robustness, and practical applicability of the proposed method for real-world flood routing problems.