Calibration of Channel Manning’s Roughness Coefficients Using Population Simplex Evolution, Finite Volume Method, and Their Integration with Convolutional Neural Networks and Transformer

The roughness coefficient is a vital parameter in river dynamics calculations, and its accuracy is crucial for simulating water flow. Various factors contribute to channel roughness, and the underlying mechanisms are quite complex. There is a strong spatiotemporal correlation, which complicates the calculations, particularly when hydrological data is lacking or insufficient. In this study, we solved the two-dimensional shallow-water equations using the Population Simplex Evolution (PSE) with the Finite Volume Method (FVM). This approach allowed us to obtain samples for calibrating channel roughness coefficients. To enhance the analysis, we introduced a Convolutional Neural Network (CNN) to reduce the dimensionality of input parameters and extract the temporal characteristics of the flow series. Notably, we integrated a Transformer to capture the spatial characteristics of the time series. By combining the PSE-FVM with the CNN-Transformer, we effectively calibrated the roughness coefficients. Our findings indicated that the integrated PSE-FVM and CNN-Transformer model achieved high accuracy and efficiency in this calibration process. Specifically, the cross-correlation coefficients exceeded 0.90 for calibration results from September to December 2020. We recorded an average absolute deviation of 7 cm between the calculated and measured maximum water levels, and the average calibration runtime ratio was approximately 0.19% when comparing the CNN-Transformer to the PSE-FVM. Importantly, this approach could be used for rivers with incomplete hydrological data. Our work highlighted spatiotemporal correlations between roughness coefficients and their influencing factors, thereby facilitating the integration of river dynamics models with intelligent algorithms. Therefore, these findings may serve as a valuable reference for river numerical analysis, flood impact assessment, and the development of digital twins and information systems for water-related engineering projects.