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 (R 2 =0.970) in PDF model category, while Gumbel EVT-1 model was second best (MSE=109.39, R 2 =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).

A Review Study on Stationary and Non-Stationary IDF Models Used in Rainfall Data Analysis around the World from 1951-2020

“…In the USA, [18] adopted the AMS rainfall analysis method to develop a scaling model of a rainfall IDF relationship; [19] used the AMS construction method to develop a generalized framework for estimating IDF curves and their uncertainties using Bayesian inference. Like in USA and other Countries, the AMS method as the most prevalent rainfall analysis method has been of immense utility by Nigerian scholars to develop IDF models for Nigerian cities [20,21,22,23,24].…”

“…Also, another major short coming of the IDF models developed from return period T obtained from this method of empirical continuous probability distribution function (ECPDE) are that they are return period specific and are seriously limited by the years of data collection. The IDF models showed higher prediction at lower durations of 10 -40 minutes [23]. Typical empirical equations calibrated for IDF modeling are those of power and quotientpower governing equations.…”

“…Frequency factor ( ) is a function of standard deviation and return period. Recently in Nigeria, pioneering effort has been observed in the use of the stochastic IDF modeling approach to develop IDF models for some cities such as Lokoja, Port Harcourt, Akure and Abeokuta [22,23,24]. [23] in their study found that the probability distribution function (PDF) IDF models showed higher prediction at higher durations of 50 -120 minutes and also predicted higher rainfall intensities for longer return period of 25, 50, and 100 years that were far beyond years of data collection.…”

Development of Models for Rainfall Intensity- duration-frequency for Akure, South-west, Nigeria

“…Where: I = rainfall intensity (mm/hr); T = return period (years) and d = duration (minutes). Examples of three different types of empirical equations was documented by [12,13].…”

“…Gumbel distribution is one commonly used probability distribution for obtaining the rainfall intensity values. The rainfall intensity values were obtained using Equation (2.1) [12]. The Gumbel's frequency factor is obtained using Equation (2.2).…”