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

2019 ◽  
pp. 457-466
Author(s):  
A. O. David ◽  
Ify L. Nwaogazie ◽  
J. C. Agunwamba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Rainfall Intensity ◽  
Mean Squared Error ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Pearson Type ◽  
Intensity Duration Frequency ◽  
Type 3

The rainfall Intensity-Duration-Frequency (IDF) relationship is widely used for adequate estimation of rainfall intensity over a particular catchment. A 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Akure station. Twenty five year annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the excel solver software wizard. A total of six (6) return period specific and one (1) general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using Gumbel Extreme Value Type-1 and Log Pearson Type -3 distributions. Anderson Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.982 to 0.985 for GEVT -1 and 0.978 to 0.989 for Log Pearson type -3 while the Mean Squared Error from 33.56 to 156.50 for GEVT -1 and 43.01 to 150.63 Log Pearson Type III distributions respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Akure metropolis.

scholarly journals Modelling Rainfall Intensity by Optimization Technique in Abeokuta, South-West, Nigeria

2019 ◽  
pp. 1-10
Author(s):  
A. O. David ◽  
Ify L. Nwaogazie ◽  
J. C. Agunwamba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Rainfall Intensity ◽  
Mean Squared Error ◽  
Optimization Technique ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Pearson Type ◽  
Type 3

The design of water resources engineering control structures is best achieved with adequate estimation of rainfall intensity over a particular catchment. To develop the rainfall intensity, duration and frequency (IDF) models, 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Abeokuta. The annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the Excel Optimization Solver wizard. Specific and general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using the Gumbel Extreme Value Type -1 and Log Pearson Type -3 distributions. The Anderson-Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.973 – 0.993 and the Mean Squared Error, MSE from 84.49 – 134.56 for the Gumbel and 0.964 – 0.997 with MSE of 42.88 – 118.68 for Log Pearson Type -3 distribution, respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Abeokuta metropolis.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

scholarly journals Flood Flow Probability Distribution Model Selection on Niger/Benue River Basins in Nigeria

2021 ◽  
pp. 76-94
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
River Basins ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Distribution Model ◽  
Distribution Models ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Flood frequency analysis is a crucial component of flood risk management which seeks to establish a quantile relationship between peak discharges and their exceedance (or non-exceedance) probabilities, for planning, design and management of infrastructure in river basins. This paper evaluates the performance of five probability distribution models using the method of moments for parameter estimation, with five GoF-tests and Q-Q plots for selection of best –fit- distribution. The probability distributions models employed are; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value( GEV). The five statistical goodness – of – fit tests, namely; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR) were used to identify the most suitable distribution models. The study was conducted using annual maximum series of nine gauge stations in both Benue and Niger River Basins in Nigeria. The study reveals that GEV was the best – fit distribution in six gauging stations, LP3 was best – fit distribution in two gauging stations, and PR3 is best- fit distribution in one gauging station. This study has provided a significant contribution to knowledge in the choice of distribution models for predicting extreme hydrological events for design of water infrastructure in Nigeria. It is recommended that GEV, PR3 and LP3 should be considered in the development of regional flood frequency using the existing hydrological map of Nigeria.

Best-fit probability distribution model for predicting annual maximum rainfall of Pusa (Bihar)

2018 ◽  
Vol 3 (01) ◽  
pp. 100-104
Author(s):  
J. Kumar ◽  
R. Suresh ◽  
Jyoti .
Keyword(s):  
Probability Distribution ◽  
Gumbel Distribution ◽  
Annual Rainfall ◽  
Annual Maximum ◽  
Distribution Models ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Pearson Type ◽  
Annual Maximum Rainfall ◽  
Pearson Type Iii Distribution

In present study an attempt has been made to evaluate the suitable probability distribution models for predicting 1, 2, 3, 4, 5, 6 and 7-days annual maximum rainfall amounts based on 39 years (1964 to 2002) daily rainfall data. Three probability distribution models namely: Log Normal distribution, Log Pearson Type-III distribution and Gumbel distribution models were considered to evaluate their goodness of fit. The Weibull’s method was used for computation of observed rainfall values at1, 5, 20, 30, 50, 95 and 99 percent probability levels. The Log Pearson type –III distribution was found suitable for 1 and 2 days maximum annual rainfall, while Gumbel distribution was found to be the best for predicting 3, 4, 5, 6 and 7- days annual maximum rainfall amounts. The relationships between annual maximum rainfall and return periods were also developed. The non – linear relationships (i.e. logarithmic) were found to be most suitable for all the cases.

scholarly journals Comparative Evaluation of Probability Distribution Models of Flood flow in Lower Niger Basin

2021 ◽  
Vol 6 (2) ◽  
pp. 107-117
Author(s):  
Itolima Ologhadien
Keyword(s):  
Water Resources ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Distribution Models ◽  
Optimum Distribution ◽  
Water Resources Systems ◽  
Type Iii ◽  
Pearson Type

The choice of optimum probability distribution model that would accurately simulate flood discharges at a particular location or region has remained a challenging problem to water resources engineers. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the quantile - probability relationship for planning, design and management of water resources systems, risk assessment in flood plains and flood insurance. This paper presents the evaluation of five probability distributions models: Gumbel (EV1), 2-parameter lognormal (LN2), log pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of five hydrological stations in the lower Niger River Basin in Nigeria. The choice of optimum probability distribution model was made on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR), and probability plot correlation coefficient (PPCC). The results show that GEV is the optimum distribution in 3 stations, and LP3 in 2 stations. On the overall GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. Furthermore, GEV simulated discharges were in closest agreement with the observed flood discharges. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

Rainfall Intensity-Duration-Frequency Models for Ibadan Using Optimization Technique

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
A.O David
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Optimization Technique ◽  
Extreme Value ◽  
Engineering Structures ◽  
Distribution Ranges ◽  
Pearson Type ◽  
Intensity Duration Frequency ◽  
Type 3

Hydraulic engineering structures always depend on type and velocity of flow water arising from rainfall activities in a given catchment. Twenty-five (25) year Ibadan daily rainfall data (amount & duration) was collected from Nigerian Meteorological Agency (NIMET) Abuja and subjected to frequency analysis for the development of intensity – duration – frequency models. Mean rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the Excel Optimization Solver wizard. Gumbel Extreme Value Type 1 and Log- Pearson Type 3 distributions were used to develop specified and non-specified IDF models for return periods of 2, 5, 10, 25, 50 and 100 years. These models have not been developed for Ibadan. The values for the coefficient of determination (R2) and mean squared error (MSE) were used to test the fitness of the probability distribution functions. Gumbel Extreme Value Type – 1 has values of R2 and MSE ranging from 0.989 to 0.998 & 3.54 to 102.30 while R2 and MSE values for Log – Pearson type 3 distribution ranges from 0.978 to 0.989 & 6.09 to 213.10. The probability distribution models are recommended for the prediction of rainfall intensities of Ibadan metropolis for the Ministry of Works for adequate design purposes.

scholarly journals Evaluation of Best-Fit Probability Distribution Models for the Prediction of Inflows of Kainji Reservoir, Niger State, Nigeria

2017 ◽  
Vol 10 ◽  
pp. 117862211769103
Author(s):  
Mohammed J Mamman ◽  
Otache Y Martins ◽  
Jibril Ibrahim ◽  
Mohammed I Shaba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Type I ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Hydropower Dams ◽  
Log Normal ◽  
Near Future ◽  
Best Fit ◽  
Analysis Of Time Series

The analysis of time series is essential for building mathematical models to generate synthetic hydrologic records, to forecast hydrologic events, to detect intrinsic stochastic characteristics of hydrologic variables, as well as to fill missing and extend records. To this end, various probability distribution models were fitted to river inflows of Kainji Reservoir in New Bussa, Niger State, Nigeria. This is to evaluate the probability function that is best suitable for the prediction of their values and subsequently using the best model to predict for both the expected maximum and minimum monthly inflows at some specific return periods. Three models, ie, Gumbel extreme value type I (EVI), log-normal (LN), and normal (N), were evaluated for the inflows and the best model was selected based on the statistical goodness-of-fit test. The values of goodness-of-fit test for Kainji hydropower dam are as follows: r = 0.96, R2 = 0.99, SEE = 0.0087, χ2 = 0.0054, for Gumbel (EVI); r = 0.79, R2 = 0.85, SEE = 0.02, χ2 = 0.31 for LN; and r = 0.0.75, R2 = 0.0.68, SEE = 0.056, χ2 = 1376.39 for N. For the Kainji hydropower dams, the Gumbel (EVI) model gave the best fit. These probability distribution models can be used to predict the near-future reservoir inflow at the Kainji hydropower dams.

scholarly journals The Effect of Sample Size on Bivariate Rainfall Frequency Analysis of Extreme Precipitation

Proceedings ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 19 ◽  
Author(s):  
Nikoletta Stamatatou ◽  
Lampros Vasiliades ◽  
Athanasios Loukas
Keyword(s):  
Sample Size ◽  
Frequency Analysis ◽  
Extreme Precipitation ◽  
Goodness Of Fit ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Rainfall Frequency ◽  
Rainfall Frequency Analysis ◽  
Pseudo Likelihood Estimation

The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices.

Temporal and spatial variations in annual rainfall distribution in Erbil province

2018 ◽  
Vol 47 (1) ◽  
pp. 59-67
Author(s):  
Tariq H Karim ◽  
Dawod R Keya ◽  
Zahir A Amin
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Kendall Test ◽  
Distribution Functions ◽  
Annual Rainfall ◽  
Maximum Rainfall ◽  
Probability Distribution Functions ◽  
Goodness Of Fit Tests ◽  
Annual Maximum Rainfall ◽  
Best Fit

This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions, namely Normal, Lognormal (LN), one-parameter gamma (1P-G), 2P-G, 3P-G, Log Pearson, Weibull, Pareto, and Beta, were assessed. On the basis of maximum overall score, obtained by adding individual point scores from three selected goodness-of-fit tests, the best fit probability distribution was identified. Results showed that the 2P-G distribution and LN distribution were the best fit probability distribution functions for annual rainfall for the region. The analysis of annual rainfall records in Erbil city spanning from 1964 to 2013, covering three periods, also revealed significant temporal changes in the shape and scale parameter patterns of the fitted gamma distribution. Based on the reliable annual rainfall data in the region, the shape and scale parameters were then regionalized, hence it is possible to find the parameter values for any desired location within the study area. The Mann–Kendall test results indicated that there was a decreasing trend in rainfall over most of the study area in recent decades.

scholarly journals Probabilistic Assessment of Degree of Bending in Tubular X-Joints of Offshore Structures Subjected to Bending Loads

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hamid Ahmadi ◽  
Amirreza Ghaffari
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Accurate Determination ◽  
Offshore Structures ◽  
Fatigue Reliability ◽  
Distribution Models ◽  
Estimated Parameters ◽  
Jacket Structures ◽  
Kolmogorov Smirnov ◽  
Bending Loads

Fatigue life of tubular joints in offshore structures is significantly influenced by the degree of bending (DoB). The DoB exhibits considerable scatter calling for greater emphasis in accurate determination of its governing probability distribution which is a key input for the fatigue reliability analysis of a tubular joint. Although the tubular X-joints are commonly found in offshore jacket structures, as far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB in tubular X-joints. In the present paper, results of parametric equations available for the calculation of the DoB have been used to develop probability distribution models for the DoB in the chord member of tubular X-joints subjected to four types of bending loads. Based on a parametric study, a set of samples was prepared and density histograms were generated for these samples using Freedman-Diaconis method. Twelve different probability density functions (PDFs) were fitted to these histograms. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs have been proposed for the DoB in tubular X-joints subjected to bending loads.

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