NONLINEAR PRESSURE-COUPLED URBAN FLOOD MODELLING USING A CROSS-DOMAIN CO2 PLUME OPERATOR: A RISK CLASSIFICATION FRAMEWORK FOR NAIROBI, KENYA

Cities are flooding more often. Climate variability, expanding built-up land, ageing drainage and growing impervious cover all push runoff past what urban catchments can absorb (IPCC, 2023; Freeze & Cherry, 1979). The flood models in routine use are mostly gravity-driven shallow-water schemes, and they say little about the subsurface pressure that keeps water ponded and decides where it eventually settles (Bates et al., 2010). We develop a nonlinear, pressure-coupled flood model that borrows a CO2 plume operator taken from geological carbon-sequestration modelling (Funk et al., 2015). Rather than treat the surface and the subsurface separately, we place climate forcing, rainfall, surface flow, infiltration, drainage limits and pressure evolution inside a single reaction-diffusion-advection system and solve them at once. We ran the model over Nairobi City County, feeding it CHIRPS rainfall, SRTM elevation, Landsat land-use and the city drainage network (Chow et al., 1988). The DuFort-Frankel finite-difference scheme was chosen because it holds the nonlinear coupling stable. The output is a flood-risk map of Nairobi, with Kibera, Mathare and Mukuru standing out as the extreme-risk zones. Against observed flooding the model gave a Mean Absolute Percentage Error of 2.07%, so the simulated and recorded behaviour line up closely.