Integration of an improved transformer with physical models for the spatiotemporal simulation of urban flooding depths

The Caochangmen area in the Gulou District, Nanjing City, China, is a typical flood-prone and well-defined region. This paper addresses the limitations of the current "single-driver" approach in simulating urban waterlogging, proposing a modeling methodology that integrates physical coupling models with data-driven techniques. The objective is to conduct comprehensive simulation research on urban flooding depth that leverages the respective strengths of both physical and data-driven models. A 1D pipe network runoff model and 2D surface runoff model were coupled to create an integrated model under a physical coupling framework. Based on a dataset of urban-rainfall-induced flooding depths, two data-driven modules were designed: a convolutional neural network (CNN) and improved transformer. To address the parameter uncertainty in the “model-data” coupling approach, two optimization methods were proposed for optimizing sensitive physical model parameters and the performance of the deep learning models, facilitating the spatiotemporal simulation of urban flood depths. The proposed physically calibrated module exhibits a nearly linear relationship with observed water depths, confirming the suitability of the calibrated parameters for the physical driver of the integrated model within the study area. The improved transformer integrated model outperformed the CNN integrated model, achieving excellent efficiency and high accuracy. This research employed a dual-engine driving approach, wherein physical models and data are mutually integrated and mutually reinforced. This demonstration underscores the potential of the synergy between deep learning and physical knowledge in urban flooding simulation studies.