EXTENSION OF A COUPLED REACTION–DIFFUSION–ADVECTION FRAMEWORK FOR ENSO (EL NIÑO–SOUTHERN OSCILLATION DYNAMICS AND CLIMATE-DRIVEN FLOOD RISK IN KENYA

This study develops a human-centered mathematical framework for connecting El Niño–Southern Oscillation (ENSO) variability with rainfall anomalies and climate-driven flood risk in Kenya. The work extends a coupled reaction–diffusion–advection (RDA) formulation into a reduced ocean–atmosphere–land system. Rather than treating El Niño as a single index followed by a simple rainfall correlation, the proposed framework represents climate variability as a coupled process involving forcing, transport, diffusion, reaction, memory and feedback. The state vector includes Pacific sea-surface temperature anomaly, subsurface ocean heat, atmospheric circulation, pressure, Indian Ocean Dipole (IOD), moisture, Kenyan rainfall, runoff, surface-water depth and flood risk. An illustrative 2010–2024 Kenya dataset is included to demonstrate the complete data-to-model workflow using rainfall records from Nairobi, Kitale, Kisii, Mombasa and Voi together with ENSO and IOD indices. These values are explicitly synthetic and are not presented as official Kenya Meteorological Department (KMD) observations. The numerical section demonstrates finite-difference discretisation, DuFort–Frankel treatment, stability through spectral-radius analysis and convergence through grid refinement. A statistical benchmark provides ENSO and IOD coefficients, R², RMSE, MAE, cross-validation and event-detection results. The study is deliberately transparent about uncertainty: the illustrative results demonstrate methodology rather than operational forecast skill. The proposed framework provides a practical foundation for calibrating a Kenya-specific ENSO-to-rainfall-to-flood early-warning model using verified KMD observations