Inundation Flooding in Urban Environments using on-lattice Density Functional Theory

Abstract

We propose a statistical physics-based computational approach called on-lattice density functional theory (DFT) for evaluating the risk of inundation flooding in urban environments. Originally developed in Materials Science for porous materials this DFT model is herein upscaled from the nanoscale to the city scale. We show that the strength of such an equilibrium-based approach, which discards the timedependence of flooding, stems from a combination of three aspects. First, the model has a minimum of input quantities and an efficient computational time. Second, the model comes with an ease of modeling a variety of city elements that are critical for inundation flooding (e.g., buildings, pavements, permeable soils, and drainage systems). Finally, the model has physically meaningful output parameters, such as the adsorption-desorption isotherms, which can be linked to a city’s drainage capacity and steady-state gauge heights. Also, the resulting isotherms exhibit a pronounced hysteresis, indicating the irreversibility of the flooding and draining properties at city scale. This hysteresis loop is of great importance since it provides a powerful means to qualitatively identifying the risk of inundation flooding.