Optimization methods for shallow water flow modeling

The calibration of shallow water flow models is a computationally intensive yet essential process for ensuring the model applicability and its reliability, particularly in multi-parameter calibration. It involves optimizing model parameters to enhance the agreement between simulated results and observed data. Despite significant advancements in hydrological and hydrodynamic modeling, automatic calibration for shallow water flow models remains challenging due to high computational costs and model complexity. This research addresses these challenges by applying global optimization methods to the automatic calibration of shallow water flow models, aiming to enable calibration with many parameters and/or reduce the effort of manual calibration for a small number of model parameters. To achieve this, a Python-based optimization framework, ActSwm (Automatic Calibration Tool for Shallow Water Flow Models), was developed. ActSwm integrates global optimization methods from the SciPy library, enabling automated parameter calibration for hms (Hydroinformatics Modeling System) and TELEMAC-2D in a user-friendly, open-source environment. With six built-in global optimization methods (Basin Hopping, Differential Evolution, Dual Annealing, SHGO, DIRECT, and Brute Force) and support for flexible objective functions (Root Mean Square Error (RMSE), Nash-Sutcliffe Efficiency (NSE), and Kling-Gupta Efficiency (KGE)), ActSwm streamlines the calibration process while minimizing the need for manual intervention. The effectiveness of ActSwm was demonstrated through multiple case studies, where it was applied to low-, medium-, and high-dimensional optimization problems. In the calibration of three, seven, and ten parameters, results showed that tuning hybrid optimization parameters significantly improved computational efficiency, reducing iteration numbers by 70–90 % while maintaining or even improving accuracy. Additionally, the use of different objective functions provided deeper insight into their influence on the calibration performance, further enhancing the tool’s adaptability. ActSwm’s scalability was demonstrated across three application domains of increasing computational complexity: a rainfall-runoff model applied to an alpine catchment using hms, another rainfall-runoff model incorporating infiltration processes applied to a plot experiment also using hms, and a coupled hydrodynamic-water quality model using TELEMAC-2D. This progression highlights the framework’s adaptability to a wide range of hydro- and environmental modeling problems, including a plot experiment, a catchment and a river-lake system. Across all case studies, Dual Annealing and Differential Evolution were the fastest to converge and maintained good average accuracy, notwithstanding run-to-run variability. In contrast, SHGO and DIRECT were deterministic, yielding identical results across runs and, in the rainfall-runoff applications, under both RMSE and NSE; in the river-lake water-quality case, both remained stable. Basin Hopping was only used in the rainfall-runoff studies with three and seven parameters; while accurate and fast, it was sensitive to initial parameter values. Brute-force search was applied with RMSE in the three-parameter case and was not practical because its cost grows quickly with additional parameters or higher accuracy. The results indicate that ActSwm provides an efficient and effective solution for the automatic calibration of computationally expensive shallow water models. While this study primarily focuses on applications for shallow water flow models, the framework is adaptable to other high-dimensional simulation models that require optimization within constrained computational resources. Future research should explore the role of objective function selection in further enhancing optimization efficiency and robustness.