Abstract Extreme rainfall events have intensified in both frequency and magnitude as a consequence of climate change, resulting in escalating flood risk and substantial socio-economic losses worldwide. Reliable prediction and quantitative assessment of flood hazards are therefore essential for effective disaster preparedness, mitigation, and climate-resilient planning. This study develops a comprehensive mathematical modeling framework for analyzing extreme rainfall and flood dynamics under changing climatic conditions. Rainfall intensity is incorporated as a climate-driven forcing parameter and coupled with hydrodynamic flood propagation equations to describe surface runoff and inundation processes. The governing equations, based on conservation of mass and momentum, are solved numerically using finite difference techniques, with all simulations implemented in MATLAB. A non-dimensional formulation highlights the dominant controlling parameters, including the rainfall forcing parameter Froude number (Fr), and friction parameter which collectively govern flow acceleration, flood depth, and energy dissipation. Numerical results demonstrate that increases in and (Fr) significantly amplify flood depth, flow velocity, and inundation extent, while higher enhances resistance and water accumulation, underscoring the nonlinear sensitivity of flood risk to climatic and hydraulic controls. The proposed framework provides a robust theoretical and computational tool for flood risk assessment, supporting early warning systems, urban drainage design, and climate adaptation strategies.