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.

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 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 Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River

2019 ◽  
Vol 1 (12) ◽  
Author(s):  
Mahmood Ul Hassan ◽  
Omar Hayat ◽  
Zahra Noreen
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Goodness Of Fit ◽  
Direct Method ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Goodness Of Fit Tests ◽  
Pearson Type

AbstractAt-site flood frequency analysis is a direct method of estimation of flood frequency at a particular site. The appropriate selection of probability distribution and a parameter estimation method are important for at-site flood frequency analysis. Generalized extreme value, three-parameter log-normal, generalized logistic, Pearson type-III and Gumbel distributions have been considered to describe the annual maximum steam flow at five gauging sites of Torne River in Sweden. To estimate the parameters of distributions, maximum likelihood estimation and L-moments methods are used. The performance of these distributions is assessed based on goodness-of-fit tests and accuracy measures. At most sites, the best-fitted distributions are with LM estimation method. Finally, the most suitable distribution at each site is used to predict the maximum flood magnitude for different return periods.

Flood Frequency Analysis of the Mahi Basin by Using Log Pearson Type III Probability Distribution

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Uttam Pawar ◽  
Pramodkumar Hire
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Return Period ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Series Data ◽  
Period Range ◽  
Type Iii ◽  
Pearson Type ◽  
Data Points

Flood frequency analysis is one of the techniques of examination of peak stream flow frequency and magnitude in the field of flood hydrology, flood geomorphology and hydraulic engineering. In the present study, Log Pearson Type III (LP-III) probability distribution has applied for flood series data of four sites on the Mahi River namely Mataji, Paderdi Badi, Wanakbori and Khanpur and of three sites on its tributaries such as Anas at Chakaliya, Som at Rangeli and Jakham at Dhariawad. The annual maximum series data for the record length of 26-51 years have been used for the present study. The time series plots of the data indicate that two largest ever recorded floods were observed in the year 1973 and 2006 on the Mahi River. The estimated discharges of 100 year return period range between 3676 m3/s and 47632 m3/s. The return period of the largest ever recorded flood on the Mahi River at Wankbori (40663 m3/s) is 127-yr. The recurrence interval of mean annual discharges (Qm) is between 2.73-yr and 3.95-yr, whereas, the return period of large floods (Qlf) range from 6.24-yr to 9.33-yr. The magnitude-frequency analysis curves represent the reliable estimates of the high floods. The fitted lines are fairly close to the most of the data points. Therefore, it can be reliably and conveniently used to read the recurrence intervals for a given magnitude and vice versa.

scholarly journals Flood Frequency Analysis of River Niger, Shintaku Gauging Station, Kogi State, Nigeria

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Andy O Ibeje
Keyword(s):  
Frequency Distribution ◽  
Goodness Of Fit ◽  
Climatic Factors ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Optimal Model ◽  
Frequency Curve ◽  
Type Iii ◽  
Pearson Type ◽  
Niger River

The study outlines a frequency distribution study on the highest annual flood statistics in Niger River located at Shintaku hydrologic Station for period of 58years. In order to determine the optimal model for highest annual flood analysis Generalised extreme value, Log normal, Gumbel maximum, Generalised Pareto and Log Pearson III, were tested. Based on error produced by criteria of goodness of Fit tests, the optimal model was determined. Results obtained indicated that Log Pearson type III was best to model maximum flood magnitude of Niger River at Shintaku station. The flood frequency curve was therefore derived using Log Pearson type III frequency distribution. Flood frequency curve showed that return periods of 50 and 100 years with the probabilities of 2% and1% respectively, yielded discharges of 15300m3/s and 15600m3/s respectively. These results were strongly influenced by their topographical, geographical and climatic factors. The findings of this work will be useful for design engineers in deciding the dimension of hydraulic structures such as spillway, dams, canals, bridges and levees among others. Future studies are required to include flood forecasting in the development of inundation maps for Niger River.Keywords—Return period, Frequency Distribution, Flood, Niger River, Flood Modeling

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 Best Fitted Distribution For Meteorological Data In Kuala Krai

2021 ◽  
Vol 3 (1) ◽  
pp. 16-25
Author(s):  
Siti Mariam Norrulashikin ◽  
Fadhilah Yusof ◽  
Siti Rohani Mohd Nor ◽  
Nur Arina Bazilah Kamisan
Keyword(s):  
Climate Change ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Meteorological Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

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 Identification of the Most Suitable Probability Distribution Models for Maximum, Minimum, and Mean Streamflow

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 734 ◽  
Author(s):  
Langat ◽  
Kumar ◽  
Koech
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Information Criterion ◽  
Distribution Functions ◽  
Flood Frequency Analysis ◽  
Distribution Models ◽  
Selection Procedures ◽  
Tana River ◽  
Best Fit ◽  
Maximum Minimum

Hydrological studies are useful in designing, planning, and managing water resources, infrastructure, and ecosystems. Probability distribution models are applied in extreme flood analysis, drought investigations, reservoir volumes studies, and time-series modelling, among other various hydrological studies. However, the selection of the most suitable probability distribution and associated parameter estimation procedure, as a fundamental step in flood frequency analysis, has remained the most difficult task for many researchers and water practitioners. This paper explains the current approaches that are used to identify the probability distribution functions that are best suited for the estimation of maximum, minimum, and mean streamflows. Then, it compares the performance of six probability distributions, and illustrates four fitting tests, evaluation procedures, and selection procedures through using a river basin as a case study. An assemblage of the latest computer statistical packages in an integrated development environment for the R programming language was applied. Maximum likelihood estimation (MLE), goodness-of-fit (GoF) tests-based analysis, and information criteria-based selection procedures were used to identify the most suitable distribution models. The results showed that the gamma (Pearson type 3) and lognormal distribution models were the best-fit functions for maximum streamflows, since they had the lowest Akaike Information Criterion values of 1083 and 1081, and Bayesian Information Criterion (BIC) values corresponding to 1087 and 1086, respectively. The Weibull, GEV, and Gumbel functions were the best-fit functions for the annual minimum flows of the Tana River, while the lognormal and GEV distribution functions the best-fit functions for the annual mean flows of the Tana River. The choices of the selected distribution functions may be used for forecasting hydrologic events and detecting the inherent stochastic characteristics of the hydrologic variables for predictions in the Tana River Basin. This paper also provides a significant contribution to the current understanding of predicting extreme hydrological events for various purposes. It indicates a direction for hydro-meteorological scientists within the current debate surrounding whether to use historical data and trend estimation techniques for predicting future events with issues of non-stationarity and underlying stochastic processes.

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