scholarly journals Development of a General Equation for Intensity-Duration-Frequency (IDF): Iraq

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Hasan Mahdi
Keyword(s):  
Water Resource Management ◽  
Goodness Of Fit ◽  
Flash Flood ◽  
Repeated Cycle ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Chi Squared ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Anderson Darling

In the field of water resource management, rainfall intensity-duration-frequency (IDF) curves are of great importance, especially in the design of hydraulic structures and the assessment of flash-flood risks. The aim of this study is to obtain IDF curves and find empirical equations for rain duration for Al-Najaf city in the southwest of Iraq. Rainfall data for 30 years, from 1989 to 2018, were collected. The practical reduction equation of the Indian Meteorological Department (IMD), with six methods of probability distribution, was used for short intervals (0.25, 0.5, 1, 2, 3, 6, 12, and 24 hours) with a specified recurrence period (100, 50, 25, 10, 5, and 2 years). The Kolmogorov-Smirnov, chi-squared, and Anderson-Darling goodness of fit tests were used with the help of EasyFit 5.6 software. The findings revealed that the highest intensity of rainfall occurs during a repeated cycle of 100 years with a duration of 0.25 hours, while the lowest intensity of rainfall occurs during a repeated cycle of 2 years with a duration of 24 hours. In the results obtained from the six methods, as well as the superiority of the log Pearson type III method, the consistency of the fit tests showed some convergence.

scholarly journals MENENTUKAN DISTRIBUSI REPRESENTATIF FREQUENSI CURAHAN HUJAN HARIAN MAKSIMUM DENGAN METODEHISTOGRAM DAN METODE PARAMETIK DI PROVINSI SUMATERA BARAT

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Selpa Dewi
Keyword(s):  
Goodness Of Fit ◽  
Type Iii ◽  
Pearson Type ◽  
Chi Squared ◽  
Anderson Darling

Penelitian ini bertujuan untuk menentukan distribusi yang representatif frequensi curahan hujan harian maksimum di Provinsi Sumatera Barat. Data yang digunakan untuk penelitian ini diambil dari data hujan maksimum harian selama 20 sampai 40 tahunan, dengan 24 stasiun penakar hujan untuk provinsi Sumatera Barat. Data masing-masing stasiun kemudian disusun dalam dua jenis deret data, yaitu deret data annual maxima dan deret data annual exceedances. Dari hasil uji deret data ini diharapkan mengikuti satu atau beberapa dari distribusi yang umum dipakai dalam hidrologi rekayasa, yaitu distribusi normal, normal-log, Gumbel, Gama-II, Gama-III dan distribusi Log-Pearson Type III (LP-III). Dengan mengunakan uji kecocokan (goodness of fit), uji parametrik, Chi-Squared test, Kolmogorov-Smirnovtest dan Anderson-Darling test ditambah dengan metode histrogram (visual).Kata kunci:Intensitas hujan distribusi representative annual maxima, annual exceendances, goodness of fitprovinsi Sumatera Barat.

scholarly journals Stochastic Generation of Low Stream Flow Data of Iokastis Stream, Kavala City, NE Greece

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 579
Author(s):  
Thomas Papalaskaris ◽  
Theologos Panagiotidis
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Specific Area ◽  
Low Flow ◽  
Urban Stream ◽  
Flow Data ◽  
Goodness Of Fit Tests ◽  
Chi Squared ◽  
Anderson Darling

Only a few scientific research studies, especially dealing with extremely low flow conditions, have been compiled so far, in Greece. The present study, aiming to contribute in this specific area of hydrologic investigation, generates synthetic low stream flow time series of an entire calendar year considering the stream flow data recorded during a center interval period of the year 2015. We examined the goodness of fit tests of eleven theoretical probability distributions to daily low stream flow data acquired at a certain location of the absolutely channelized urban stream which crosses the roads junction formed by Iokastis road an Chrisostomou Smirnis road, Agios Loukas residential area, Kavala city, NE Greece, using a 3-inches conventional portable Parshall flume and calculated the corresponding probability distributions parameters. The Kolmogorov-Smirnov, Anderson-Darling and Chi-Squared, GOF tests were employed to show how well the probability distributions fitted the recorded data and the results were demonstrated through interactive tables providing us the ability to effectively decide which model best fits the observed data. Finally, the observed against the calculated low flow data are plotted, compiling a log-log scale chart and calculate statistics featuring the comparison between the recorded and the forecasted low flow data.

scholarly journals Exploiting the information content of hydrological "outliers" for goodness-of-fit testing

2010 ◽  
Vol 7 (4) ◽  
pp. 4851-4874 ◽  
Author(s):  
F. Laio ◽  
P. Allamano ◽  
P. Claps
Keyword(s):  
Goodness Of Fit ◽  
Probabilistic Models ◽  
Small Samples ◽  
Goodness Of Fit Tests ◽  
Maximum Value ◽  
Parent Distribution ◽  
Fit Testing ◽  
Chi Squared ◽  
Anderson Darling ◽  
Hydrological Applications

Abstract. Validation of probabilistic models based on goodness-of-fit tests is an essential step for the frequency analysis of extreme events. The outcome of standard testing techniques, however, is mainly determined by the the behavior of the hypothetical model, FX(x), in the central part of the distribution, while the behavior in the tails of the distribution, which is indeed very relevant in hydrological applications, is relatively unimportant for the results of the tests. The maximum-value test, originally proposed as a technique for outlier detection, is a suitable, but seldom applied, technique that addresses this problem. The test is specifically targeted to verify if the maximum (or minimum) values in the sample are consistent with the hypothesis that the distribution FX(x) is the real parent distribution. The application of this test is hindered by the fact that the critical values for the test should be numerically obtained when the parameters of FX(x) are estimated on the same sample used for verification, which is the standard situation in hydrological applications. We propose here a simple, analytically explicit, technique to suitably account for this effect, based on the application of censored L-moments estimators of the parameters. We demonstrate, with an application that uses artificially generated samples, the superiority of this modified maximum-value test with respect to the standard version of the test. We also show that the test has comparable or larger power with respect to other goodness-of-fit tests (e.g., chi-squared test, Anderson-Darling test, Fung and Paul test), in particular when dealing with small samples (sample size lower than 20–25) and when the parent distribution is similar to the distribution being tested.

scholarly journals Statistical Study of Rainfall Control: The Dagum Distribution and Applicability to the Southwest of Spain

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 453 ◽  
Author(s):  
Fernando López-Rodríguez ◽  
Justo García-Sanz-Calcedo ◽  
Francisco Moral-García ◽  
Antonio García-Conde
Keyword(s):  
Goodness Of Fit ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Statistical Distributions ◽  
Statistical Tool ◽  
Goodness Of Fit Tests ◽  
Dagum Distribution ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

It is of vital importance in statistical distributions to fit rainfall data to determine the maximum amount of rainfall expected for a specific hydraulic work. Otherwise, the hydraulic capacity study could be erroneous, with the tragic consequences that this would entail. This study aims to present the Dagum distribution as a new statistical tool to calculate rainfall in front of frequent statistical distributions such as Gumbel, Log-Pearson Type III, Gen Extreme Value (GEV) and SQRT-ET max. The study was performed by collecting annual rainfall data from 52 meteorological stations in the province of Badajoz (Spain), using the statistical goodness-of-fit tests of Anderson–Darling and Kolmogorov–Smirnov to establish the degree of fitness of the Dagum distribution, applied to the maximum annual rainfall series. The results show that this distribution obtained a flow 21.92% greater than that with the traditional distributions. Therefore, in the Southwest of Spain, the Dagum distribution fits better to the observed rainfall data than other common statistical distributions, with respect to precision and calculus of hydraulics works and river flood plains.

scholarly journals Exploiting the information content of hydrological ''outliers'' for goodness-of-fit testing

2010 ◽  
Vol 14 (10) ◽  
pp. 1909-1917 ◽  
Author(s):  
F. Laio ◽  
P. Allamano ◽  
P. Claps
Keyword(s):  
Goodness Of Fit ◽  
Probabilistic Models ◽  
Small Samples ◽  
Goodness Of Fit Tests ◽  
Maximum Value ◽  
Parent Distribution ◽  
Fit Testing ◽  
Chi Squared ◽  
Anderson Darling ◽  
Hydrological Applications

Abstract. Validation of probabilistic models based on goodness-of-fit tests is an essential step for the frequency analysis of extreme events. The outcome of standard testing techniques, however, is mainly determined by the behavior of the hypothetical model, FX(x), in the central part of the distribution, while the behavior in the tails of the distribution, which is indeed very relevant in hydrological applications, is relatively unimportant for the results of the tests. The maximum-value test, originally proposed as a technique for outlier detection, is a suitable, but seldom applied, technique that addresses this problem. The test is specifically targeted to verify if the maximum (or minimum) values in the sample are consistent with the hypothesis that the distribution FX(x) is the real parent distribution. The application of this test is hindered by the fact that the critical values for the test should be numerically obtained when the parameters of FX(x) are estimated on the same sample used for verification, which is the standard situation in hydrological applications. We propose here a simple, analytically explicit, technique to suitably account for this effect, based on the application of censored L-moments estimators of the parameters. We demonstrate, with an application that uses artificially generated samples, the superiority of this modified maximum-value test with respect to the standard version of the test. We also show that the test has comparable or larger power with respect to other goodness-of-fit tests (e.g., chi-squared test, Anderson-Darling test, Fung and Paul test), in particular when dealing with small samples (sample size lower than 20–25) and when the parent distribution is similar to the distribution being tested.

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 Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

scholarly journals Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1735 ◽  
Author(s):  
Julia Lutz ◽  
Lars Grinde ◽  
Anita Verpe Dyrrdal
Keyword(s):  
Bayesian Inference ◽  
Goodness Of Fit ◽  
Bayesian Method ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Current Method ◽  
Credible Interval ◽  
Computational Method ◽  
Goodness Of Fit Tests ◽  
Idf Curves

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

scholarly journals Estimation of flood frequency using statistical method: Mahanadi River basin, India

2020 ◽  
Vol 3 (1) ◽  
pp. 189-207
Author(s):  
Sandeep Samantaray ◽  
Abinash Sahoo
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Central India ◽  
Extreme Value ◽  
Flood Frequency ◽  
Goodness Of Fit Test ◽  
Mahanadi River ◽  
Goodness Of Fit Tests ◽  
Study Results ◽  
Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

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