Asian Journal of Probability and Statistics

The aim of the study was to analyze annual maximum rainfall data in the megacities of India to determine susceptibility to extreme rainfall events, finding best probability distribution models for forecasting the future, and offer suggestions for flood risk management policy. This is a retrospective analytical study that uses data from Indian Meteorological Department on the annual maximum rainfall at 20 sites of six megacities of India over several decades. The parameters related to the distribution models are determined through parametric estimation techniques to calculate maximum rainfall events in millimeters across twenty rain gauge stations. Goodness-of-fit tests based analysis (Kolmogorov–Smirnov test and Anderson-Darling test), information based criterion (Akaike Information Criteria and Bayesian Information Criteria) and graphical techniques (Probability Density Function, Cumulative Density Function, Probability Difference, P-P and Q-Q plots) were used to validate the suitability of distributions including Generalized Extreme Value (GEV), two-parameter Gumbel maximum (Gumbel 2P), three-parameter Frechet (Frechet 3P), three-parameter Gamma (Gamma3P), three-parameter Weibull (Weibull3P), Log-Logistic 3P (LL3P), and two-parameter lognormal (LN2) for each city and conducted simulation studies in R Programming for checking whether distribution imitate the observed values of rainfall events. Return periods of 10, 25, 50, 100, 200, 500 and 1000 years were calculated to predict future trends and assess rainfall events risk. Result shows GEV distribution for eight rain gauge stations (40%), Log-logistic for six stations (30%), Weibull 3P for three stations (15%), Gamma3P for two stations (10%) and Frechet 3P for one station (5%) are the best fit probability distribution models for annual maximum rainfall events among twenty rain gauge stations. The study emphasizes how crucial it is to implement city specific flood management plans in the megacities of India to mitigate the impact of extreme rainfall events with the following estimated rainfall levels and corresponding return periods were found for particular megacities: Hyderabad Begumpet Aero reported 241.5 mm in 2000, which corresponds to 241.77 mm with a 100-year return period; Bengaluru C.O. recorded 178.9 mm in 1997, which is equivalent to an expected rainfall of 178.95 mm with a 50-year return period; In 1976, Chennai Nungambakkam recorded 452.4 mm, which translates to 452.50 mm during a 50-year return period; In 1981, Delhi Palam Aero recorded 215.6 mm, which translates to 215.80 mm during a 100-year return period; Kolkata Uluberia recorded 409.3 mm in 1978, which corresponds to 409.50 mm with a 50-year return time, while Mumbai Santacruz Aero recorded 944.2 mm in 2005, which corresponds to 944.72 mm with a 200-year return period, especially in light of climate change.