Probability and non-probability rainfall intensity-duration-frequency modeling for port-harcourt metropolis, Nigeria

Abstract

This study is all about rainfall intensity – duration - frequency (IDF) modeling based on probability and non-probability distribution function (PDF, and nPDF). A set of sixteen year rainfall amounts and durations for Port Harcourt metropolis was adopted for the modeling. The study involved the application of the following distribution functions: Gumbel Extreme Value Type-1 (Gumbel EVT-1), Normal, Pearson Type-3 (PT-3), Log Pearson Type-3(LPT-3), and Log-Normal (L-N), respectively. And the nPDF in the form of Talbot simple quotient, power, and Sherman quotient-power models. To implement the PDF modeling it was necessary to generate frequency factors for each of the five models. This was followed by non-linear regression analysis which involved the use of Excel Solver with optimization technique in Microsoft Excel applied to estimate the parameters of the IDF models. All the PDF-IDF models were calibrated using the Sherman’s equation as general models for which the intensity value is a function of return period and rainfall duration. A comparative analysis was carried out between PDF and nPDF IDF models predicted intensities that showed a good match with observed intensities. The Normal distribution IDF model ranked the best with respect to mean squared error (MSE=92.71) and goodness of fit (R2=0.970) in PDF model category, while Gumbel EVT-1 model was second best (MSE=109.39, R2=0.975), and showed better result on each of the specified return period (2, 5, 8 and 16 years). In all, no significant difference amongst the predicted intensities of the various IDF models (PDF and nPDF models).