Modeling spatial distribution of flow depth in fluvial systems using a hybrid two-dimensional hydraulic-multigene genetic programming approach

Abstract

Modeling spatial distribution of flow depth in fluvial systems is crucial for flow mitigation, river rehabilitation, and design of water resources infrastructure. Flow depth in fluvial systems can be typically estimated using hydrological or physics-based hydraulic models. However, hydrological models may not be able to provide satisfactory predictions for catchments with limited data because they normally ignored the strict conservation of momentum. Traditional fully physics-based hydraulic models are often very computationally expensive, limiting their wide usage in practical applications. In this study, a novel method, based on a hybrid two-dimensional (2D) hydraulic-multigene genetic programming (MGGP) approach, is proposed and employed to model the spatial distribution of flow depth in fluvial systems. A 2D hydraulic model was constructed using the TELEMAC-2D software and validated against field measurements. The validated model was then assumed to reflect the real physical processes and utilized to carry out additional computations to obtain spatial distribution of flow depth under different discharge scenarios, which provided a sufficient synthetic dataset for training machine learning models based on the MGGP technique. The study area (a segment of the Ottawa River near the island named Île Kettle) was divided into 34 sub-regions to further reduce the computational costs of the training processes and the complexity of the evolved models. The numerical data were distributed to the corresponding sub-regions, and an MGGP-based model was trained for each sub-region. These models are compact explicit arithmetic equations that can be readily transferable and can immediately output the flow depth at any point in the corresponding sub-region as functions of the flow rate, longitudinal, and transversal coordinates. The best MGGP model for each sub-region amongst all the generated models was identified using the Pareto optimization approach. The results showed that the best MGGP models satisfactorily reproduced the training data and predicted the testing data (the root mean square errors were 0.303 m and 0.306 m, respectively), demonstrating the predictive capability of the approach. A comparison between MGGP and single-gene genetic programming (SGGP) approaches and confidence analysis were also reported, which demonstrated the good performance of the proposed approach. Furthermore, it took about 53 min for the hydraulic model to complete each simulation, but it took only about 0.56 s using the final model; the total size of the hydraulic output files for 12 different sizes was 432, 948 KB, but the total size of the script file for the final model was only about 46 KB. Therefore, the present study found that the hybrid 2D hydraulic-MGGP approach was satisfactorily accurate, fast to run, and easy to use, and thus, it is a promising tool for modeling spatial distribution of flow depth in fluvial systems.