ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE June 2024. Vol. 20(2):403-416 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 403 GENERATION OF RAINFALL INTENSITY-DURATION FREQUENCY MODELS FOR PORT HARCOURT CITY IN SOUTH- SOUTH NGERIA C. C. Emeka-Chris Department of Agricultural and Bioresources Engineering, Michael Okpara University of Agriculture, Umudike, Nigeria *Corresponding author's email address: cemekachris1@gmail.com ARTICLE INFORMATION Submitted 8 May, 2024 Revised 27 May, 2024 Accepted 30 May, 2024 Keywords: Rainfall Intensity Duration Frequency Model Gumbel Distribution ABSTRACT Inadequate meteorological data poses a significant challenge for engineers in accurately designing, operating, and planning water resources, particularly against extreme rainfall events. This study focuses on Generating Intensity Duration Frequency (IDF) Models for Port Harcourt City in South Nigeria. Daily rainfall data spanning thirty-two years (1983-2014) were collected from the Nigeria Meteorological Agency (NIMET) Oshodi, Lagos State. The annual maximum series method was employed to select datasets for rainfall analysis. Two statistical distributions, Gumbel and Log Pearson Type III, were utilized to calculate observed rainfall intensity values at durations of 10, 15, 20, 30, 60, 120, 180, 240, 300, and 360 minutes, considering return periods of 2, 5, 10, 20, 50, and 100 years. Non-linear regression analysis using Microsoft Excel's Optimization Technique Solver wizard was performed to derive parameters for the IDF models for each duration and return period. Metrics such as chi-square (χ2), coefficient of determination (R2), and Root Mean Square Error (RMSE) were analyzed in order to assess the performance of the models. For the Gumbel distribution, R2 values ranged from 0.76 to 1.00, with RMSE from 0.20 to 11.73. The Log Pearson Type III distribution showed perfect R2of 1 and RMSE ranging from 0.23 to 9.68, indicating superior performance in terms of R2 and RMSE. While there were no significant differences among the predicted intensities of various IDF models, the Log Pearson Type III Model is recommended for predicting rainfall intensities in Port Harcourt due to its superior performance metrics. These IDF Models serve as valuable tools for engineers and hydrologists in estimating stormwater runoff, designing drainage systems, managing reservoirs, and planning water resources development to mitigate flooding and its impacts. Moreover, they can enhance the teaching of land drainage courses for engineering students, providing practical demonstrations and improving their understanding of the subject matter. 1.0 Introduction Precipitation is an important component in the hydrologic cycle. Brian et al. (2006) posited that rainfall frequency analyses are desirable in the development plus designing of different water resources schemes, this includes storm sewers, culverts, and other hydraulic structures. A life- threatening precipitation happening endangers the quality of water, annihilation of assets, loss of lives due to flooding and pollution (Brian et al., 2006). According to Panel et al. (2016) the valuation of dangerous precipitation is a vital issue in hydrologic risk investigation and design. Additionally, they noted that the assessment of rainfall excesses as embodied in the intensity- duration-frequency (IDF) relationship has been the main objective of applied and theoretical hydrology. Similarly, Elsebaie (2012) noted that rainfall intensity-duration-frequency curves are http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com mailto:%20salami.lukman@adelekeuniversity.edu.ng mailto:%20salami.lukman@adelekeuniversity.edu.ng Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 404 graphical demonstrations of the quantity of rainwater that falls within a specified period of time in catchment areas. Prodanovic and Simonovic, (2007) suggested, that to design flood protection structures involving hydrologic flows, rainfall events statistics (that is, in relations to intensity, duration, and period of return) are required. Additionally, Elsebaie (2012) noted that, graphically the measure of precipitation that falls within a catchment range in a specified period of time are denoted by Rainfall – Intensity - Duration-Frequency (IDF) curves. He added that, IDF curves are an important tool for the engineers when designing urban drainage works. According to (Koutsoyiannis, 2003) the IDF relationship is a mathematical connection between the precipitation intensity I, the duration d, and the return period T. In addition, Al-Dokhayel (1986) accomplished a research on the estimation of rainfall depth duration frequency (DDF) relationships intended for Qasim region in Kingdom of Saudi Arabia (KSA) on different return periods, by the use of two continuous probability distributions, namely, Gumbel distribution and Log Pearson Type III (LPT III) distributions. He found that, between the two distributions under study, the LPT III distribution technique provided greater precipitation estimations with lesser standard errors. Similarly, David et al. (2019) noted that the institution of IDF relationships commenced in the nineteen thirties, subsequently many sets of connections have been lumped together globally. Consequently, Elsebaie (2012) posited that the establishment of the IDF was formally on the basis of frequency investigation of precipitation at a particular station observed throughout a long period, normally the annual maximum of the series (AMS) or adequately high values greater than threshold. According to Akpan and Okoro (2013), Nwaogazie and Duru (2002) and Nwoke and Okoro (2012) developed Rainfall Intensity Frequency Models based on statistical method of least squares. In Nigeria, current studies on rainfall IDF development have been done in Southern Nigeria, with little information made available about rainfall intensities in particular for short durations. The insufficient accessible IDF curves for selected parts of the country are very costly and plotting of the curves was done manually. Hence, this method of developing IDF curves manually is prone to error. The broad objective of this research was to generate Intensity- Duration – Frequency (IDF) curves and models for estimating the precipitation intensities for Port Harcourt city, using two statistical methods, that is Gumbel distribution and Log Pearson Type 111 distribution. 2. Materials and Method 2.1 Description of the Study Area The area studied is Port Harcourt city. The city is the capital and largest city of Rivers State, in Nigeria. It is the fifth most populous city in Nigeria after Lagos, Kano, Ibadan and Benin (Statista, 2021 and world population review.com, 2021). It lies along the Bonny River and is located in the oil rich Niger Delta at latitude 04o451to 04o 601N and Longitude 06o 501E to 08o 0107oE (Figure 1). It is located 64 kilometres from the Atlantic Ocean and situated 15.0 metres above sea level. Port Harcourt experiences rainy season from March to October and receives 2293.6mm of rainfall per year (Abah et al., 2019). Only the months of November to February truly qualify as dry season months in the city and the so-called dry season are not free from occasional rainfall. Port Harcourt has three hydro- vegetation zones such as beach ridge, salt water and fresh water. file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:%20kunleoluyori@gmail.com Emeka-Chris: Generation of Rainfall Intensity-Duration Frequency Models for Port Harcourt City in South- South Ngeria. AZOJETE, 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 405 Figure 1: Map of Port Harcourt City Local Government Area and its environs Source: Abah et al. (2019) 2.2 Data Collection The required data in this research are the precipitation depths for smaller durations namely, 5, 10, 15, 20, 30, 60, 120, 180, 240, 300 and 360 minutes. Precipitation data were collected from Nigeria Meteorological Agency Lagos, Nigeria. Thirty-two years span of records was used for the studied location between 1983-2014. 2.3 Development of IDF curves Two common frequency analysis techniques were used in the development of the relationship between rainfall intensity, storm duration, and return periods from rainfall data for the region under study. These techniques are the Gumbel distribution and the LPT III distribution. 2.3.1 Gumbel theory of distribution Gumbel assumption methodology was adopted to perform the flood probability studies. In addition, Elsebaie (2012) noted that this is because the method of the analysis is widely accepted for IDF analysis owing to its appropriateness for modeling maxima. The Gumbel methodology determines the 2, 5, 10, 25, 50 and 100 year return intervals for each duration period and hence requires several calculations. The frequency precipitation for duration with a definite return period is expressed by the following formula PT = Pave + KS (1) Where, K =Gumbel frequency factor given by: K = √6 π [0.5772 + 𝐼𝑛[𝐼𝑛 [ 𝑇 𝑇−1 (8)]]] (2) Where, Pave = the average of the maximum precipitation corresponding to a specific duration. In utilizing Gumbel’s distribution, the arithmetic average (Pave) in Equation (3) was used: Pave = 1 𝑛 ∑ Pn i=1 i (3) Where, Pi = the individual extreme value of rainfall and n is the number of events or years of record. The standard deviation, S of P data was calculated using Equation (4) http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 406 S = [ 1 𝑛−1 ∑ (𝑃𝑖 − 𝑃𝑎𝑣𝑒𝑛 𝑖=1 )22 1 ] (4) The frequency factor (K), which is a function of the return period and sample size, was multiplied by the standard deviation to give the departure of a desired return period rainfall from the average. Then the rainfall intensities, I (mm/h) for return period T were obtained from: IT = 𝑃𝑇 𝑇𝑑 (5) Where, Td is duration in hours, PT is frequency precipitation values and IT is intensities for different durations. From the raw data, the maximum precipitation (P) and the statistical variables (average and standard deviation) for each of the duration 0.25hr, 0.5hr, 1hr, 2hr, 4hr, and 6hr) were computed. 2.3.2 Log Pearson type III The Log Pearson Type III probability model was utilized in the calculation of the precipitation intensity at different precipitation durations and return periods to form the historic IDF curves for the designated localities. Logarithmically transformed data was used in determination of the mean and the standard deviation. The simplified expression for this latter distribution is given as: P* = log (Pi) (6) P*T = P*ave + KT S (7) P*ave = 1 𝑛 ∑ 𝑃 ∗𝑛 𝑖=1 (8) S* = [ 1 𝑛−1 ∑ (P ∗ − 𝑛 𝑖=1 P*ave)21/2 ] (9) Where, P*T is frequency precipitation and P*ave is the average of the maximum precipitation corresponding to a specific duration based on the logarithmically transformed Pi values; i.e. P* of Equation (6). KT is the Pearson frequency factor which depends on return period (T) and skewness coefficient (Cs). The skewness coefficient (Cs) is required to compute the frequency factor for this distribution. The skewness coefficients were computed using Equation (1) as suggested by (Burke and Burke, 2008). 𝐶𝑠 = 𝑛 ∑ (𝑃∗𝑖−𝑃𝑎𝑣𝑒 𝑛𝑖 𝑖 )³ (𝑛−1)(𝑛−2)(𝑆∗)³ (10) The computed frequency precipitation P*T values and intensities (IT) for six different durations and six return periods using LPT III methodology. 2.4 Intensity-Duration –Frequency (IDF) Model Development The Intensity-Duration-Frequency (IDF) formulae are the empirical equations demonstrating a correlation between the variables. Several commonly used IDF equations relating the file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:%20kunleoluyori@gmail.com Emeka-Chris: Generation of Rainfall Intensity-Duration Frequency Models for Port Harcourt City in South- South Ngeria. AZOJETE, 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 407 rainfall intensities, the frequencies, and durations are available in literature (Burke and Burke, 2008; Nhat et al., 2006 and Mohammad, 2016). The commonly used IDF equations is Sherman equation, which is given as: i = 𝑎𝑇𝑏 (𝑡+𝑑)𝑐 (11) Where, i = intensity of rainfall in mm/hr; t = duration of rainfall in minutes; T = return period of rainfall in years; a, b, c, and d, are the regional IDF parameters to be determined. Equation (11) which is the most general form of IDF equation has been used to develop the IDF equations by optimization method. 2.4.1 Application of Excel Solver Optimization Technique to estimate IDF Parameters The excel solver methods are mainly the Generalized Reduced Gradient (GRG Solver) for optimization of nonlinear equations and the linear programming Solver (LP Solver) for linear equations. Due to the fact that IDF equations are nonlinear, the GRG Solver was used in this work to get the optimum of the parameters for the models. 2.4.2 Calibration of the Sherman (1932) Model Sherman (1932) model as given in equation (14) was calibrated using GRG Solver optimization method to obtain optimum values for the regional parameters namely a, b, c, and d for the models. Thus, the objective function becomes: Min SSE = ∑ (iobs −iest)2n i=1 (12) Where, iobs is observed intensity corresponding to any duration and iest is estimated intensity corresponding to any duration. Solving equation (12) produces the optimum values for the parameters a, b, c, and d achieved through an iterative process that produces the least squared error. 2.5 Model Performance Analysis The performance of the Intensity Duration Frequency (IDF) models given by Gumbel distribution and Log Pearson Type 111 Distribution (LPT 111) were evaluated by obtaining empirical data from the models and then goodness of Fit test, Correlation Coefficient, and Root Mean Square Error (RMSE) analysis were carried out. To determine the best-fit distribution, the observed distributions were fitted to the theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution. A Goodness-of-fit test between observed and expected frequencies is based on the chi-square quantity, which is expressed as: χ2 = Σk i= (𝑂𝑖−𝐸𝑖)2 𝐸𝑖 (13) Where, χ2 = random variable whose sampling distribution is approximated very closely by the chi- square distribution. Oi and Ei = observed and expected frequencies for the ith class interval in the histogram. K = the number of class intervals. Mohammad (2016) provided programmable formulae to obtain the coefficient of http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 408 determination (R2 ) and Root Mean Square Error (RMSE) as follows: R2 = ∑ (𝐼𝑜𝑏𝑠−𝐼𝑎𝑣𝑔)2−∑ (𝐼𝑜𝑏𝑠−𝐼𝑝𝑟𝑒𝑑)2𝑛 𝑖=1 𝑛 𝑖=1 ∑ (𝐼𝑜𝑏𝑠−𝐼𝑎𝑣𝑔)2𝑛 𝑖=1 (14) RMSE = √ 1 𝑁 ∑ (𝐼𝑖 − 𝐼∗)2𝑁 𝑖=1 (15) The theoretical description of Correlation Coefficient (CC) is as given in equation (16) CC = ∑ ( (𝐼𝑜𝑏𝑠−𝐼𝑎𝑣𝑔𝑜𝑏𝑠)( 𝐼𝑝𝑟𝑒𝑑− 𝐼𝑎𝑣𝑔𝑝𝑟𝑒𝑑 ) √∑ (𝐼𝑜𝑏𝑠−𝐼𝑎𝑣𝑔 𝑜𝑏𝑠) 2 +𝑁 𝑖=1 ∑ (𝐼𝑝𝑟𝑒𝑑−𝐼𝑎𝑣𝑔 𝑝𝑟𝑒𝑑) 2𝑁 𝑖=1 𝑁 𝑖=1 (16) Where, Iobs is the observed precipitation intensity of ith event, Ipred is the predicted precipitation intensity of the ith event, Iavg obs is the average observed precipitation intensity and Iavg pred is the average of predicted precipitation intensity. 3. Results and discussion 3.1 Intensity Duration Frequency IDF Curves by Gumbel and Log Pearson Type (LPT) 111 Methods for Port Harcourt. The results of the Intensity Duration- Frequency curves by Gumbel and Log Pearson Type methods for Port Harcourt city are shown in Figures 2 and 3, respectively. Figure 2: IDF curves by Gumbel method at Port-Harcourt Figure 3.1b: IDF curves by LPT III method at Port-Harcourt 1 10 100 1000 1 10 100 1000 In te n si ty ( m m /h r) Duration (min) 2-Years 5-Years 10-Years 25-Years 50-Years 100-Years 1 10 100 1000 1 10 100 1000 In te n si ty ( m m /h r) Duration (min) 2-Years 5-Years 10-Years 25-Years 50-Years 100-Years file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:%20kunleoluyori@gmail.com Emeka-Chris: Generation of Rainfall Intensity-Duration Frequency Models for Port Harcourt City in South- South Ngeria. AZOJETE, 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 409 Figures 2 and 3 show results of the IDF curves obtained by Gumbel and LPT 111 methods for the region. According to the IDF curves rainfall estimates are increasing with increase in the return period and the rainfall intensities decrease with rainfall durations in all return periods. The trends of the results from the two methods have good consistency. The IDF curves proved the basic principle in hydrology that high intensity rainfalls had shorter durations. It also showed that rainfall intensities increase with return periods. This is in line with findings of similar research carried out by Ogbozige (2021), Mohammed et al. (2021), Majeed et al. (2021), Agarwal et al. (2021), Al-wagdany (2020) and Gratein et al. (2019). 3.2 Rainfall Intensity Duration Frequency Models and their Parameter Values The parameter values used in deriving the Gumbel and Log Pearson Type III models, including the models for Port Harcourt region is shown in Table 1. Table 1: Parameters values used in deriving models for rainfall intensity at Port Harcourt City. S/No. Location Distribution Parameters Models a b c d 1. Port Harcourt Gumbel 135 1.72 0.83 46.35 𝐼 = 135𝑇𝑟 1.72 (𝑡 + 46.35)0.83 Log Pearson Type III 140 1.23 0.73 30.33 𝐼 = 140𝑇𝑟 1.23 (𝑡 + 30.33)0.73 The Gumbel and Log Pearson Type 111 models, including the parameter values used in deriving the models for the region studied are shown in Table 1. The parameter values used in deriving the models are a, b, c and d. Parameters b (1.72), c (0.83), and d (46.35) values using Gumbel distribution are higher than values obtained using Log Pearson Type 111 method for Port Harcourt region. 3.3 Model Performance/Validation for Port Harcourt IDF Models The results of the computed indicators of goodness of fit between Gumbel and Log Pearson Type III Models, namely Chi Square (χ2), Root Mean Square Error (RMSE), Correlation Coefficient (R) and Coefficient of Determination (R2) are given in Tables 2a and 3, respectively. Tables 2 and 3 show the model performance / validation of IDF Model obtained for Port Harcourt region using Gumbel and Log Pearson Type III distributions respectively. Table 2: Model Performance/ Validation for Port Harcourt IDF Model Obtained by Gumbel method Duration (min) Location Distribution Model validation 10 15 20 30 60 120 180 240 300 360 Port-Harcourt Gumbel χ2 0.98 2.69 0.96 7.49 4.10 1.05 0.27 0.25 0.01 0.50 RMSE 4.68 7.59 4.28 11.73 7.82 3.00 1.34 1.20 0.20 1.43 R 1.00 1.00 1.00 0.99 0.87 0.98 0.99 1.00 1.00 1.00 R2 1.00 1.00 1.00 0.98 0.76 0.97 0.99 1.00 1.00 1.00 Pvalue 0.96 0.75 0.97 0.19 0.54 0.96 1.00 1.00 1.00 0.99 http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 410 Table 3: Model Performance/Validation for Port Harcourt IDF Model Obtained by Log Pearson Type 111 Method Tables 2 and 3 show the model performance / validation of IDF Model obtained for Port Harcourt region using Gumbel and Log Pearson Type 111 distributions respectively. Goodness of fit tests was used to choose the best statistical distribution among those techniques. As can be seen in Tables 2 and 3, most of the data fit both Gumbel and Log Pearson Type 111 distributions at 5% level of significance. However, the data at 30minutes and 60minutes durations do not give good fit using Gumbel distribution for Port Harcourt region. Also, the data for 15 minutes and 30 minutes durations do not give good fit using Log Pearson Type 111 distribution for Port Harcourt. The correlation coefficient (R) and coefficient of determination (R2) obtained from the fitted IDF Models adopting Gumbel distribution are high and ranged from 0.97 to 1.00 except at 60 minutes duration with R as 0.87 and R2 as 0.76, respectively. However, the correlation coefficient and coefficient of determination obtained from the fitted IDF Model adopting Log Pearson Type 111 distribution have perfect value of 1. The values of root mean square errors (RMSE) obtained are lower for durations from 30minutes to 360 minutes using Log Pearson Type 111, except for durations of 300minutes when compared to Gumbel distribution. The results show the goodness of fit of the formulae to estimate the rainfall intensities of the region of study, especially for higher durations and frequencies of 2 to 100 years. 3.4 Comparison of Observed and Predicted Rainfall Intensities The results of the predicted rainfall intensities for different durations and return Periods are shown in Table 4 and 5. Also some selected index values of predicted intensities for comparison of short, medium and higher durations are shown in Table 6. Location Distribution Model validation Duration (min) 10 15 20 30 60 120 180 240 300 360 Port-Harcourt Log Pearson Type III χ2 2.60 4.29 2.23 4.17 0.42 0.39 0.03 0.10 0.01 0.10 RMSE 7.86 9.68 6.70 8.58 2.35 1.86 0.45 0.78 0.23 0.67 R 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 R2 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 P-value 0.76 0.51 0.82 0.52 0.99 1.00 1.00 1.00 1.00 1.00 file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:%20kunleoluyori@gmail.com Emeka-Chris: Generation of Rainfall Intensity-Duration Frequency Models for Port Harcourt City in South- South Ngeria. AZOJETE, 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 411 Table 4: Predicted Intensity-Duration frequencies for different return periods by Gumbel method at Port-Harcourt Return Period (Years) 2 5 10 25 50 100 Duration (min) Observed Predicted Observed Predicted Observed Predicted Observed Predicted Observed Predicted Observed Predicted 10 86.382 83.96554981 110.701 106.8743 126.84 122.0707 147.192 141.1825201 162.282 155.5011 177.294 174.8547 15 74.664 78.78027513 94.128 99.97962 107.044 114.0438 123.328 131.7165551 135.408 144.9406 147.42 156.6058 20 71.565 74.22266278 90.215 93.96795 102.591 107.0701 118.02 123.5249021 129.774 135.8244 141.282 142.618 30 72.624 66.57923988 91.556 83.98306 104.12 95.53717 119.964 110.0404577 131.712 120.8618 143.398 122.3677 60 50.865 51.07672082 64.083 64.07358 72.856 72.71203 83.919 83.56395718 92.122 91.6294 70.341 89.48134 120 32.678 35.17853278 41.195 44.05725 46.847 49.96015 53.975 57.40454873 59.26 62.90963 64.517 62.30258 180 25.935 27.01030311 32.693 33.89063 37.178 38.46038 42.833 44.24513759 47.027 48.50819 51.199 49.64461 240 22.938 22.00838133 28.616 27.689 32.384 31.45697 37.136 36.24202741 40.659 39.75916 44.164 42.05611 300 18.895 18.61875859 23.734 23.49087 26.945 26.71826 30.995 30.82797277 33.998 33.84244 36.985 36.90138 360 17.29 16.16426144 21.795 20.45039 24.784 23.28608 28.555 26.90547973 31.35 29.55577 34.131 33.12582 http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 412 Table 5: Predicted Intensity-Duration frequencies for different return periods by LPT III method at Port-Harcourt Return period (years) 2 5 10 25 50 100 Duration (min) Observed Predicted Observed Predicted Observed Predicted Observed Predicted Observed Predicted Observed Predicted 10 93.82 88.7856 118.928 112.5219 135.293 128.0203 156.419 148.055 171.905 162.92524 187.623 177.5798 15 75.344 81.5423 95.512 103.3653 108.656 117.5917 125.62 135.944 138.052 149.13244 150.68 163.0634 20 71.213 75.5563 90.273 95.78784 102.697 108.9643 118.73 125.936 130.483 137.84965 142.414 151.0655 30 71.784 66.2023 90.998 83.93016 103.522 95.46815 119.682 110.3 129.428 120.41026 143.558 132.3153 60 50.816 49.3025 64.269 62.46537 73.114 71.04943 84.333 82.0608 92.683 89.409988 101.158 98.44184 120 32.657 33.9709 41.397 42.96677 47.095 48.8773 54.447 56.4645 59.837 61.708828 65.309 67.7292 180 26.175 26.568 33.18 33.55299 37.747 38.17439 43.639 44.1175 47.96 48.416597 52.345 52.9129 240 21.525 22.1083 27.286 27.88576 31.041 31.73105 35.887 36.6852 39.44 40.416534 43.047 43.99422 300 19.321 19.0897 23.935 24.05273 27.229 27.37287 31.48 31.6576 34.596 34.998441 37.76 37.96152 360 17.252 16.893 21.87 21.26524 24.88 24.20328 28.764 28.0007 31.612 31.050985 34.502 33.57369 file:///C:/user/Downloads/azojete143/www.azojete.com.ng mailto:%20kunleoluyori@gmail.com Emeka-Chris: Generation of Rainfall Intensity-Duration Frequency Models for Port Harcourt City in South- South Ngeria. AZOJETE, 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 413 The rainfall intensity of any duration and return period is predicted by the aid of the developed IDF models. The factors that enhance the distribution of the observed and predicted rainfall intensities are duration and return period. Observed and predicted rainfall intensities were compared as way of verification of the developed models. For the studied location in Tables 4 and 5, it was noted that rainfall intensity decreases with increasing durations and for a given duration the higher return period yielded corresponding higher intensity values. From Table 5, the highest predicted intensity values were given by Log Pearson Type 111. Table 6: Comparison of selected index values of predicted intensities (mm/hr) for short, medium and higher durations Method Station 10min duration 60min duration 300 min duration 100-year return period 100-year return period 100-year return period Gumbel Log Pearson Type 111 Port Harcourt Port Harcourt 174.85 177.58 89.48 98.44 36.9 37.96 Table 6 shows the comparative predicted intensities by Gumbel and Log Pearson Type111 Models for short, medium and higher durations. In Table 4 at 10 minutes duration and 100- year return period, the predicted intensities by Gumbel model was 174.85mm/hr. The predicted intensities at the same 10minutes duration and 100-year return period by Log Pearson Type 111 was 177.58mm/hr. Also, for 60minutes duration and 100-year return period, the predicted intensities by Gumbel was 89.48mm/hr. While at the same 60minutes duration and 100-year return period, the predicted intensities by Log Pearson Type 111 was 98.44mm/hr. Finally, at 300minutes duration and 100 years return period, the predicted intensities by Gumbel was 36.90mm/hr. While at the same 300minutes duration and 100-year return period, the predicted intensities by Log Pearson Type 111 was 37.96mm/hr. The predicted intensities values given in tables 3.4 establishes the consistent superiority of Log Pearson Type 111 model over Gumbel model in predicting higher intensity values at short, medium and higher durations in the studied location. This observation was also established in the works for Port Harcourt, Ikeja and Lahore city IDF models by Nwaogazie et al. (2019); David and Nwaogazie (2020) and Ahmed and Ali (2016) respectively. 3.5: Comparison of IDF Curves obtained with Published IDF Curves The comparison of IDF curves obtained with published IDF curves by Mbajiorgu and Okonkwo (2010) is shown in Table 7. Table 7: Comparison of Mbajiorgu and Okonkwo (2010) estimated intensities with Intensities predicted by Gumbel distribution. Method Station 10-yr 15min 2-yr, 30mins 5-yr, 1hr 25-yr, 1hr 100yr,6hr Mbajiorgu and Okonkwo Port Harcourt 122.4 71.6 62.8 82.5 34.4 Gumbel Distribution Port Harcourt 114.0 66.6 64.1 83.6 33.1 Mbajiorgu and Okonkwo (2010) used the Gumbel method to develop IDF curves for some selected locations in Nigeria. Port Harcourt is common to his work, so comparison was made using results of predicted intensities developed by Gumbel distribution models for Port Harcourt. Table 7 shows the intensities estimated by Mbajiorgu and Okonkwo (2010) using Gumbel method and predicted intensities from this work by Gumbel distribution model. From the table, the intensities predicted by Gumbel distribution models for the selected location of study are lower than those of Mbajiorgu and Okonkwo (2010) at both shorter and higher rainfall durations. This could be as a result of differences in number of years of records of data http://www.azojete.com.ng/ file:///C:/Users/Engr.%20Samuel/Documents/Engr%20Oyeniyi/azojete/AZOJETE%20ARCHIVE/UPLOAD/VOL%2020%20NO%201/PUBLISH/niyiolabisi@gmail.com Arid Zone Journal of Engineering, Technology and Environment, June 2024; Vol. 20(2):403-416. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: cemekachris1@gmail.com 414 collected. Mbajiorgu and Okonkwo (2010) did not exactly specify the number of years of rainfall data used; rather the work stated that the length of available records used varies from 22 to 30 years. In this study, 33 years of daily rainfall data was used. Also, according to David and Nwaogazie (2020)) at times values of rainfall recorded at some stations may be incorrectly observed. However, the differences are not statistically significant at 5% level of significance. It was also noted that for a given return period, intensities decrease as duration increases. This is in line with what Mbajiorgu and Okonkwo (2010) obtained as shown in Table 7. Storms of 10-years return period and 15minutes duration gave the highest intensities than storms of 100- years return period and 6 hours duration. Therefore, models developed by Gumbel and Log Pearson Type 111 distributions are in agreement with Probability Distribution Function (PDF) theory which shows higher intensities occurring at shorter duration and lower intensities at longer duration. 4. Conclusion This work shows the procedure for the development of rainfall intensity duration frequency models for Port Harcourt in South -South Nigeria. In this study, IDF models were developed for studied location. These models are guides for estimating the rainfall intensities for any specific return period at different durations. The highest intensity occurs at return periods of 100 years with durations of 10minutes (0.15hr), while the lowest intensity occurs at return period of 2 years with durations of 360minutes (6.0hr). 5. Engineering implications of Findings The IDF Models developed will serve as tools for the Engineers and Hydrologists in estimating storm water runoff from a watershed for the design of drainage systems, reservoir management and planning of water resources development. This will mitigate flooding and its consequences. Also, the findings when applied as demonstration tools in teaching land drainage courses to Engineering students, will enhance their understanding and appreciation of the course. References Abah, AE., Woken, GN. and Sounyo, II. 2019. Fasciola Infection in Goats Slaughtered from Port Harcourt Metropolis Rivers State, Nigeria. International Journal of Health, 5(11): 76-80 DOI:10.14202/IJOH.2019.76-80. www.onehealthjournal.org/vol.5/11.pdf Agarwal, S., Kumar, S. and Singh, U. 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