scholarly journals Evaluation of Generalized Extreme (GEV), Log-Pearson Type 3 (LP3), Pearson Type 3(P3) and Gumbel (EV1) Distributions for Development of IDF Equations for Warri, Nigeria

2021 ◽  
pp. 386-395
Author(s):  
Itolima Ologhadien
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Series Data ◽  
Economic Losses ◽  
Precipitation Series ◽  
Return Periods ◽  
Water Drainage ◽  
Pearson Type ◽  
Idf Curves ◽  
Type 3

The application of Gumbel (EVI) to the development of rainfall intensity– duration – frequency (IDF) curves has often been criticized on theoretical and empirical grounds as it may underestimate the largest extreme rainfall amounts. The consequences of underestimation are economic losses, property damages, and loss of life. Therefore, it is important that water resources engineering infrastructure be accurately design to avoid these consequences. This paper evaluates the performances of four probability distributions; GEV, EV1, LP3 and P3 using the annual maxima precipitation series of 26 years for Warri Metropolis obtained from Nigerian Meteorological Agency (NiMet). The strength and weakness of the four probability distributions were examined with the goodness of fit (GOF) module of Easyfit software which implemented Kolmogorov - Smirnov (KS) and Anderson - Darling (AD) tests at 5% significance level. The Easyfit software fitted the precipitation series data to the four probability distributions and ranked the four probability distributions across the fifteen rainfall durations. Results show that for both KS and AD tests, GEV distribution was found to be best-fit distribution and it was applied to the development of IDF curves in Warri Metropolis, Nigeria. Furthermore, the IDF values obtained were applied in the development of three-parameter IDF models for return periods of 10 - , 15 -, 20 -, 25 - , 50 -, and 100-years. The mean absolute error, Nash – Sutcliffe Efficiency (NSE) and Root Mean Square Error (RMSE) indices computed for the IDF models increase with increasing return periods. The IDF curves and models depicted the general attributes of IDF curves and models. This study could be of significant academic value and improvement to professional practice in the design of storm water drainage systems. Therefore, the developed IDF curves and models are recommended to the Warri Urban Authority for inclusion in her stormwater handbooks and manuals.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Vitthal Anwat ◽  
Pramodkumar Hire ◽  
Uttam Pawar ◽  
Rajendra Gunjal
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Western India ◽  
Type I ◽  
Return Periods ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

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 Best fitting probability distributions for annual maximum discharge data of the river Kopili, Assam

2009 ◽  
Vol 1 (1) ◽  
pp. 50-52
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Annual Maximum ◽  
Discharge Data ◽  
Generalized Pareto ◽  
Maximum Discharge ◽  
Pearson Type ◽  
Best Fitting ◽  
Log Normal

In this study our main objective is to determine the best fitting probability distribution for annual maximum flood discharge data of river Kopili, Assam. Various probability distributions i.e. Gumbel (G), generalized extreme value (GEV), normal (N), log-normal (LN3), generalized logistic (GLO), generalized pareto (GPA) and Pearson type-III (PE3) have been used for our study. The L-moments methods have been used for estimating the parameters of all the distributions. The root mean square error (RMSE), model efficiency and D-index (fit in the top six values) together with L-moment ratio diagram is used for goodness of fit measure. It has been observed that Generalized Pareto is the best fitting probability distribution for annual maximum discharge data of river Kopili.

scholarly journals Analysis of Rainfall Time Series with Application to Calculation of Return Periods

2021 ◽  
Vol 13 (14) ◽  
pp. 8051
Author(s):  
Ramón Egea Egea Pérez ◽  
Mónica Cortés-Molina ◽  
Francisco J. Navarro-González
Keyword(s):  
Mediterranean Climate ◽  
Probability Distributions ◽  
Direct Analysis ◽  
Rainfall Time Series ◽  
Precipitation Series ◽  
Return Periods ◽  
Precipitation Regime ◽  
Peak Over Threshold ◽  
Rain Events ◽  
Main Components

This paper presents a study of the characteristics of rainfall in a typical Mediterranean climate, characterized by infrequent and irregular rain in the territorial area and its intensity. One of the main components of this type of climate is short-duration and high-intensity rain events that cause a large amount of damage to property and human lives, seriously affecting the operation of infrastructure and the activity of society in general. The objective of this study was to design a methodology based on peak over threshold (POT) analysis. This methodology allows us to establish reference precipitation values and more approximate return periods in the absence of sufficiently extensive historical precipitation series. In addition, the frequency of these extreme events or return periods is established. The characteristics of the precipitation regime make direct analysis difficult. Thus, the functions of the probability distributions underlying the described phenomena are improved.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

scholarly journals Selection Selection of Probabilistic Model of Extreme Floods in Benue River Basin, Nigeria

2021 ◽  
Vol 6 (1) ◽  
pp. 7-18
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Frequency Analysis ◽  
Probabilistic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Extreme Floods ◽  
Pearson Type ◽  
Selection Of

The selection of optimum probabilistic model of extreme floods as a crucial step for flood frequency analysis has remained a formidable challenge for the scientific and engineering communities to address. Presently, there is no scientific consensus about the choice of probability distribution model that would accurately simulate flood discharges at a particular location or region. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the design quantile - probability relationship. 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 Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria. Additionally, Q-Q plots were used to compliment the selection process. The choice of optimum probability distribution model was based 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). Goodness – of – fit assessment reveals that GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. In comparison with WMO (1989) survey of countries on distribution types currently in use for frequency analysis of extremes of floods shows that GEV is standard in one country, while PR3 is a standard in 7 countries, and LP3 is standard in 7 countries. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

scholarly journals Evaluation of Plotting Position Formulae for Pearson Type 3 Distribution in Three Hydrological Stations on the Niger River

2021 ◽  
pp. 117-128
Author(s):  
Itolima Ologhadien
Keyword(s):  
Goodness Of Fit ◽  
Absolute Error ◽  
Distribution Model ◽  
Pearson Type ◽  
Simulated Series ◽  
The Individual ◽  
Individual Scores ◽  
Type 3 ◽  
River Niger ◽  
Relative Root

In this study, eight unbiased plotting position formulae recommended for Pearson Type 3 distribution were evaluated by comparing the simulated series of each formula with the annual maximum series (AMS) of River Niger at Baro, Koroussa and Shintaku hydrological stations, each having data length of 51years, 53 years and 58 years respectively. The parameters of Pearson Type 3 distribution were computed by the method of moments with corrections for skewness. While the fitting of Pearson Type 3 distribution proceeds with the development of flood – return period (Q-T) relationship, followed by application of the derived Q- T relation to compute simulated discharges for comparison with AMS of the study stations. The plotting position formulae were evaluated on the basis of optimum values of the statistically goodness-of-fit of probability plot correlation coefficient (PPCC), relative root mean square error (RRMSE), percent bias (PBIAS), mean absolute error (MAE) and Nash-sutcliffe efficiency (NSE), across the stations. The plotting position formulae were ranked on scale of 1 to 8. Thus a plotting formula that best simulates the empirical observations using the goodness-of-measures was scored “1” and so on. The individual scores per plotting position were summed across the gof tests to obtain the total score.    The study show that Chegodayev is the best plotting position formula for Baro, Weibull is the best plotting position Formula for Kourassou and Shintaku hydrological stations. The overall performances of the eight plotting position formulae across the hydrological stations show that weibull distribution is the overall best having scored 27, seconded by Chegodayev with 30 and thirdly, Beard with 38. The Pearson Type 3 distribution had been found one of the best probability distribution model of flood flow in Nigeria and this study was conducted to gain in-depth knowledge of the distribution. Finally, this study recommends extension of the studies to Log-Pearson Type 3 distribution.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document