Modified Horton’s infiltration model integrated with a Sub-Grid shallow water equation solver for High-Resolution flooding simulation

Abstract

Infiltration models are crucial components of rainfall-runoff models based on shallow water equations, combined with direct-rainfall for flooding simulations. While the original Horton’s model is frequently used, various modifications have been proposed to deal with its limitations for intermittent rainfall patterns. We evaluate two modifications, from well-known Storm Water Management Model or SWMM and from Diskin and Nazimov, against the original Horton’s model both theoretically and with numerical experiments. We find the formulation from Diskin and Nazimov as most suitable for real-world applications. In this paper, we describe an adaptation of the Diskin and Nazimov infiltration model through a Surface Detention Box model to integrate it into a shallow water equation solver, that accounts for detailed topographic information using a sub-grid approach. The Surface Detention Box model in this paper is generalized to account for sources and sinks other than infiltration. We verify the efficiency of our implementation for a catchment in Australia with intermittent and extreme rainstorms. We also demonstrate the accuracy, efficiency and the precise volume conservation of our method for high-resolution grids and large computational time steps, enabled by the predictor–corrector solver. In conclusion, we present a robust and efficient scheme for practical flood simulations, including various sources and sinks such as rainfall and infiltration. Our approach is a strong foundation for operational flood forecasting with high resolution Digital Terrain Models.