Mathematical Modelling for Flood Risk Prediction and Urban Drainage Management in Nigeria: A Conceptual and Illustrative Framework

Flooding is one of the most destructive recurring environmental hazards facing Nigerian cities, yet much of the existing Nigerian literature on the subject remains descriptive rather than predictive. This paper sets out a conceptual and mathematical framework for predicting flood risk and supporting urban drainage management decisions in Nigeria, built around three complementary, well-established techniques: the Rational Method runoff equation, simple linear regression of rainfall against runoff, and the Gumbel extreme-value distribution for estimating rainfall return periods. After reviewing the conceptual, theoretical and empirical literature on flooding and mathematical modelling, the paper formally specifies each model and then works through a fully hypothetical numerical example, using assumed but literature-consistent parameter values, purely to demonstrate how the equations behave and what kind of planning insight they can yield once populated with real, site-specific data. The illustration shows, in principle, that peak runoff is highly sensitive to the proportion of impervious surface in a catchment, that rainfall intensity and runoff volume can be linked through a simple, testable statistical relationship, and that the estimated recurrence interval of extreme rainfall rises sharply, rather than proportionally, with event magnitude. The paper argues that this combination of classical hydrological and statistical tools offers Nigerian planning authorities an accessible, low cost complement to more data- and computation-intensive approaches such as GIS-based terrain modelling and machine learning, provided the models are calibrated and validated against verified local rainfall and stream-gauge records before being used for actual design or policy decisions.