Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields

Abstract

The mitigation of societal damage from urban floods requires fast hydraulic models for emergency and planning purposes. The simplified mathematical model Cellular Automata is combined with Motion Cost fields, which score the difficulty to traverse an area, to the urban inundation model CAMC. It is implemented with simple matrix and logic operations to achieve high computational efficiency. The development concentrated on an application in dense urban built-up areas with numerous buildings. CAMC is efficient and flexible enough to be used in a “live” urban flood warning system with current weather conditions. A case study is conducted in the German city of Wuppertal with about 12,000 buildings. The water depth estimation of every time step are visualized in a web-interface on the basis of the virtual globe NASA WorldWind. CAMC is compared with the shallow water equations-based model ANUGA. CAMC is approximatively 5 times faster than ANUGA at high spatial resolution and able to maintain numerical stability. The Nash-Sutcliffe coefficient (0.61), Root Mean Square Error (0.39 m) and Index of Agreement (0.65) indicate acceptable agreement for water depth estimation but identify different areas where important deviations occur. The estimation of velocity performs considerably less well (0.34 for Nash-Sutcliffe coefficient, 0.13 ms − 1 for Root Mean Square Error, and 0.39 for Index of Agreement) because CA ignores momentum conservation.

A Digital Template for the Generic Multi-Risk (GenMR) Framework: A Virtual Natural Environment

“…The motion cost can include soil characteristics, such as roughness and infiltration potential. The weights for water distribution are a function of the motion cost at the central and neighbor cells [ 62 ], which, in the simplest case, is proportional to the normalized gradients. The simulation stops when all the surplus water has reached the coast.…”

A rapid flood inundation model for urban flood analyses

“…In the application of flood simulation, numerous models have been developed based on different rules. Examples include the ranking system [11] , minimization [ 23 , 34 ], weighted parameters [12] , and the motion cost file [16] . The DBM method swiftly generates a maximum inundation map using a mass conservation and topographical data.…”

A Simplified Representation of Pressure Flow from Surface Slopes in Urban Sewer Systems

“…Most RFIMs route the surface flow to derive flood inundation information, taking advantage of the greater availability of high-resolution topographic data and high-performance computing resources [34]. The surface flow can be routed by the simplified forms of 2D shallow water equation, including diffusive wave [35][36][37][38], kinematic wave [39,40] and inertial wave [41][42][43], and also by the Cellular Automata approaches [44][45][46][47]. In these models, surface flow is typically routed on a regular cell basis, but the computational efficiency is still a challenge for large areas represented by high-resolution topographic data.…”