Evaluation and Improvement of the Method for Selecting the Ridge Parameter in System Differential Response Curves

The selection of an appropriate ridge parameter plays a crucial role in ridge estimation. A smaller ridge parameter leads to larger residuals, while a larger ridge parameter reduces the unbiasedness of the estimation. This paper proposes a constrained L-curve method to accurately select the optimal ridge parameter. Additionally, the constrained L-curve method, traditional L-curve method, and ridge trace method are individually coupled with the system differential response curve to update the streamflow in the Jianyang Basin using the SWAT model. Multiple evaluation criteria are employed to analyze the efficacy of the three methods for correction. The results demonstrate that the constrained L-curve method accurately identifies the optimal ridge parameter in the actual model. Furthermore, the coupling of the constrained L-curve method with the system differential response curve exhibits markedly superior accuracy of simulated streamflow compared to the traditional L-curve and ridge trace methods, with the mean Nash–Sutcliffe efficiency (NSE) improving from 0.71 to 0.88 after correction. The constrained L-curve method, which incorporates the physical interpretation of the estimated parameters, effectively identifies the optimal ridge parameter in practical scenarios. As a result, it demonstrates superior usability and applicability when compared to the traditional L-curve method.