Stochastic Modelling of Rainfall Patterns and Flood Risk in Calabar River Basin, Cross River State

Flooding in the Calabar River Basin, Cross River State, South South Nigeria, causes recurrent displacement, property destruction, and disruption of economic activities, with the frequency and intensity of flood events increasing over the past decade in line with regional climate change trends. This study develops a stochastic model for daily rainfall occurrence and intensity using Markov chain first-order and second-order models combined with gamma distribution fitting for rainfall amounts on wet days. Daily rainfall data from five meteorological stations in the basin spanning 2010 to 2023 are obtained from the Nigerian Meteorological Agency. The two-state Markov chain classifies each day as wet or dry, with transition probabilities estimated by maximum likelihood. Gamma distribution parameters for wet-day rainfall amounts are estimated separately for three seasonal windows corresponding to the long dry season, long rainy season, and short dry season. Monte Carlo simulation generates 10,000 synthetic rainfall series of 30-year length, from which extreme quantile estimates and return period analysis are derived. The 50-year return period daily rainfall for Calabar is estimated at 187.4 millimetres, 23 percent higher than the design value currently used in local drainage infrastructure. The study recommends revising drainage design standards and implementing early warning systems linked to stochastic rainfall thresholds. Keywords: stochastic rainfall modelling, Markov chain, flood risk, Calabar River Basin, return period.