A Novel Local‐Inertial Formulation Representing Subgrid Scale Topographic Effects for Urban Flood Simulation

• Published in: Water resources research Vol. 60; no. 5
• Main Authors: Nithila Devi, N., Kuiry, Soumendra Nath
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 01.05.2024
• Subjects: Accuracy; Canals; Computational efficiency; Computer applications; Computing costs; Depth; Elevation; Flood forecasting; flood inundation; Flooding; Floodplains; Floods; Highways; Hydraulic properties; Hydraulics; local‐inertial model; Mathematical models; Roads & highways; Shallow water; Shallow water equations; Streets; subgrid model; Terrain; Topographic effects; Topography; Two dimensional models; Urban areas; urban flooding
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2023WR035334

The local‐inertial approximations of the shallow water equations (SWEs) have been used for flood forecasting at larger spatial scales owing to the improved computational efficiency and similar accuracy compared to the full 2D SWEs. With the availability of high‐resolution elevation data, the complex terrain of urban areas with various small‐scale features is represented well. Even for a local‐inertial model, utilizing such high‐resolution elevation data in flood simulations of urbanized areas increases the computational cost. A subgrid‐based local‐inertial formulation that permits large numerical grid size for computations while preserving the within‐grid topography is proposed to circumvent this. The subgrid topography can be incorporated into the coarse numerical grid computations by estimating the hydraulic properties, namely, volume and face area, based on water surface elevation variations of the associated high‐resolution terrain. The pre‐stored hydraulic properties are then used to dynamically update the hydraulic variables during the execution of the local‐inertial model. Idealized and real‐world test cases were simulated to illustrate the advantages of the proposed model. The proposed subgrid model performs better in capturing flood depth around subgrid‐scale features such as streets, highways, minor canals, etc., than the simple grid‐averaged local‐inertial models of the same grid size. The proposed model is faster than the existing local‐inertial model (e.g., LISFLOOD‐FP) (∼21–34 times) and the full 2D model (e.g., HEC‐RAS 2D) (∼361–660 times) of similar accuracy in the slow‐rising flood applications. Thus, the subgrid local‐inertial model holds promise in real‐time flood inundation forecasting, resolving smaller urban features. Plain Language Summary Quick and accurate flood forecasting is crucial in highly populated urban areas with several small terrain features like roads, streets, highways, canals, etc. The simulation of flood depth and extent can be made faster by using simplified equations or dividing the domain into larger grids. The equations will be solved over each grid, generating flood depth and flow. However, opting for a large grid will not capture smaller within‐grid terrain elements. Therefore, this paper proposes a novel subgrid‐based local‐inertial model that uses simplified equations and operates at a large grid while still representing the within‐grid terrain. The subgrid‐inertial model simulates flooding around the smaller features of urban areas with less time than finer grid full 2D models. Meanwhile, the existing local‐inertial models operating at large grids often fail to resolve urban terrain features. Thus, using limited computing facilities, the proposed subgrid‐inertial model is highly suited for real‐time riverine flood forecasting in urbanized floodplains. Key Points A subgrid‐based local‐inertial formulation that makes computations at coarse grids while capturing the within‐grid terrain is proposed It is faster than a full 2D model and can resolve complex urban terrain (streets, canals, roads) where existing coarse grid models fail It improves mass flux estimation of coarse grids and holds promise in real‐time forecasting of slow‐rising urban floods