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).

This paper mainly investigated the basic information about non-stationary trend change point patterns. After performing the investigation, the corresponding results show the existence of a trend, its magnitude, and change points in 24-hourly annual maximum series (AMS) extracted from monthly maximum series (MMS) data for thirty years rainfall data for Uyo metropolis. Trend analysis was performed using Mann-Kendall (MK) test and Sen's slope estimator (SSE) used to obtain the trend magnitude, while the trend change point analysis was conducted using the distribution-free cumulative sum test (CUSUM) and the sequential Mann-Kendall test (SQMK). A free CUSUM plot date of change point of rainfall trend as 2002 at 90% confidence interval was obtained from where the increasing trend started and became more pronounced in the year 2011, another change point year from the SQMK plot with the trend intensifying. The SSE gave an average rate of change in rainfall as 2.1288 and 2.16 mm/year for AMS and MMS time series data respectively. Invariably, the condition for Non-stationary concept application is met for intensity-duration-frequency modeling.

The design of structures for flood mitigation depends on the adequate estimation of rainfall intensity over a given catchment which is achieved by the rainfall intensity duration frequency modelling. In this study, an extensive comparative analyses were carried out on the predictive performance of three PDF – IDF model types, namely: Gumbel Extreme Value Type 1 (GEVT – 1), Log-Pearson Type 3 (LPT – 3) and Normal Distribution (ND) in 14 selected cities in Southern Nigeria. This is to rank the order of best performance. The principle of general model development was adopted in which rainfall intensities at different durations and specified return periods were used as input data set. This is not same as return period specific model that involves rainfall intensities for various durations and a given return period. The predicted rainfall intensity values with the PDF – IDF model types indicate high goodness of fit (R2) and Mean Squared Errors (MSE) ranging from: (a) R2 = 0.875 – 0.992; MSE = 33.17 – 224.6 for GEVT – 1; (b) R2 = 0.849 – 0.990; MSE = 65.34 – 405.5 for LPT – 3 and (c) R2 = 0.839 – 0.992; MSE = 29.23 – 200.2 for ND. The comparative analysis of all the 42 general models (14 locations versus 3 model types) considered showed that the order of best performance is LPT – 3 1st, GEVT - 1 2nd and ND 3rd for each return period (10, 50 and 100 years). The Kruskal Wallis test of significance indicates that no significant difference exists in the predictive performance of the three General models across the board. This may be due to the fact that the fourteen locations of the study area are bordering with the Atlantic Ocean and seems to have similar climatology. These developed General models are recommended for the computation of intensities in the fourteen locations for the design of flood control structures; and the order of preference should be LPT – 3 > GEVT – 1 > ND.

This article focuses on an overview of the processes of generating rainfall intensity-duration-frequency (IDF) models, the different types and applications. IDF model is an important tool applied in the design of either hydrologic or hydraulic design such as prediction of rainfall intensities to estimate peak runoff volumes for mitigation of flooding. IDF models evolved from stationary – parametric (empirical) and non-parametric (stochastic) models, to non-stationary models in which variables vary with time. Each category controls the ways models predict rainfall intensities, and reveals their strength and weaknesses. IDF models must therefore, be chosen in terms of the project objective, data availability, size of the study, location, output needed, and the desired simplicity. For instance, while the parametric model predicts better for shorter durations and return periods only, the non-parametric models predict better for both shorter and longer durations and return periods. For projects requiring change of input data over time and evaluation of uncertainty bounds, risk assessment, including incorporation of changes in extreme precipitation, the non-stationary model approach must be selected. Also, of importance for catchments without rainfall amount and corresponding duration records but has daily (24-hourly) record of rainfall depth, the Indian Meteorological Department (IMD) method of shorter duration disaggregation can be adopted to generate in-put data for the development of IDF curves for such a location. Therefore, each model type has limitations that may make it unsuitable for some projects. Reviewing input data and output requirements, and simplicity are all necessary to decide on which model type should be selected.

The aim of this study is the establishment of the existence of trend and variability on a typical 24-hourly sorted thirty years (1986-2015) annual maximum series (AMS) and maximum monthly series (MMS) rainfall data for Uyo metropolis in Nigeria. Data were downscaled into shorter durations of 0.25, 0.5, …,12 hours. The statistical tool applied for the study was the Mann-Kendall (MK) test and Sen Slope estimator. The results showed that there exists increasing trend for all durations analyzed with consistency in the test statistic results. The MK statistic lZl  for the AMS varied between 3.1701 and 3.2827 while that of MMS was 4.756, were greater than critical Z = 1.96. Also, the computed p-value for the AMS varied between 0.0012 and 0.0015, and were lower than the significant level of alpha,  = 0.05. Thus, the null hypothesis of no trend was rejected. Similarly, the Sen Slope estimator gave an average rate of change in rainfall as 2.1288 and 2.16 mm/year for AMS and MMS time series data, respectively. The result from the Sen Slope estimator indicated that the magnitude of the trend decreased as the duration of rainfall increased such that shorter duration exhibited more trend than higher duration. The results of the MK trend and Sen Slope analysis proved that both test exhibited high degree of consistency with statistically significant positive trend and variability. These results have provided further evidence of an accelerated alarming rate in climate change increasing trend in Uyo metropolis and perhaps the environs. Therefore, planning for effective and accurate rainfall prediction for annual maximum time series data with established variability in trend will require adoption of non-stationary concept to account for the influence of changing climatic parameters in intensity-duration-frequency (IDF) modeling.