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 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 Frequency analysis of annual one day to five consecutive days maximum rainfall for Gandak river basin

2014 ◽  
Vol 3 (2) ◽  
pp. 93 ◽  
Author(s):  
Shivika Singla ◽  
Raktim Halder ◽  
Rakesh Khosa ◽  
Rumani Singla ◽  
Rudraksh Rajeev
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Frequency Estimation ◽  
Distribution Functions ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Thiessen Polygon ◽  
Chi Square Test ◽  
Arc Gis ◽  
Best Fit

The present study has been conducted for rainfall intensity and frequency estimation for the Gandak basin, a region prone to high floods with an unrealized and unexplored hydro-potential. The two popular gridded precipitation datasets i.e.: (1) APHRODITE, and (2) IMD, for the years 1969-2005, has been used to calculate the mean basin precipitation through the Thiessen polygon method on the ARC-GIS interface. This computed data was used to find out the 1-day, 2-day to 5-day consecutive maximum precipitation series and hence fitted into various well-known probability distribution functions viz., Normal, Gamma, Exponential, etc. According to the best fit data in these functions, the quantiles were determined corresponding to a return period of 2, 10, 20, 25, 50 and 100 years. The two widely used tests: Chi-square Test and Kolmogorov-Smirnov Test were employed to further check the goodness of fit of the series in the distributions. The results reveal that the best fit for 1-day was achieved with the normal distribution, for 2-day with GEV and with GPAR for the remaining maximum consecutive days rainfall. Such studies have thus proven to be substantially facilitative in planning for the safe and economic design of various engineered structures such as bridges, culverts, levees, canals, irrigation and drainage works and effective reservoir management. Keywords: Floods, Frequency, Hydrology, Probability Distribution, Rainfall.

scholarly journals Potential of plotting positions for intensity-duration-frequency curves with short rainfall records

2017 ◽  
Vol 13 (4-1) ◽  
pp. 394-399
Author(s):  
Noratiqah Mohd Ariff ◽  
Abdul Aziz Jemain ◽  
Mohd Aftar Abu Bakar
Keyword(s):  
Probability Distribution ◽  
Empirical Distribution ◽  
Annual Rainfall ◽  
Annual Maximum ◽  
Distribution Fitting ◽  
Maximum Rainfall ◽  
Gev Distribution ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Annual Maximum Rainfall

Intensity-duration-frequency (IDF) curves represent the relationship between storm intensity, storm duration and return period. The IDF curves available are mostly done by fitting series of annual maximum rainfall intensity to parametric distributions. However, the length of annual rainfall records, especially for small scaled data, are not always enough. Rainfall records of less than 50 years are usually deemed insufficient to unequivocally identify the probability distribution of the annual rainfall. Thus, this study introduces an alternative approach that replaces the need for parametric fitting by using empirical distribution based on plotting positions to represent annual maximum rainfall series. Subsequently, these plotting positions are used to build IDF curves. The IDF curves found are then compared to the IDF curves yielded from the parametric GEV distribution which is a common basis for IDF curves. This study indicates that IDF curves obtained using plotting positions are similar to IDF curves found using GEV distribution for storm events. Hence, researchers could model and subsequently build IDF curves for annual rainfall records of less than 50 years by using plotting positions and avoid any probability distribution fitting of insufficient data.

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 Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey

2018 ◽  
Vol 19 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Ebru Eris ◽  
Hafzullah Aksoy ◽  
Bihrat Onoz ◽  
Mahmut Cetin ◽  
Mehmet Ishak Yuce ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Distribution Functions ◽  
Low Flow ◽  
Probability Distribution Functions ◽  
Low Flows ◽  
Intermittent Rivers ◽  
Log Normal ◽  
Best Fit

Abstract This study attempts to find out the best-fit probability distribution function to low flows using the up-to-date data of intermittent and non-intermittent rivers in four hydrological basins from different regions in Turkey. Frequency analysis of D = 1-, 7-, 14-, 30-, 90- and 273-day low flows calculated from the daily flow time series of each stream gauge was performed. Weibull (W2), Gamma (G2), Generalized Extreme Value (GEV) and Log-Normal (LN2) are selected among the 2-parameter probability distribution functions together with the Weibull (W3), Gamma (G3) and Log-Normal (LN3) from the 3-parameter probability distribution function family. Selected probability distribution functions are checked for their suitability to fit each D-day low flow sequence. LN3 mostly conforms to low flows by being the best-fit among the selected probability distribution functions in three out of four hydrological basins while W3 fits low flows in one basin. With the use of the best-fit probability distribution function, the low flow-duration-frequency curves are determined, which have the ability to provide the end-users with any D-day low flow discharge of any given return period.

scholarly journals Analysis of Annual Maximum Rainfall for Frequency Distribution to Determine the Best-fitted Probability Distribution for Different Sites in Pakistan.

2021 ◽  
Author(s):  
Tasir khan ◽  
Yejuan Wang ◽  
Mohammad Anwar
Keyword(s):  
Probability Distribution ◽  
Mean Square Error ◽  
Goodness Of Fit ◽  
Mean Square ◽  
Annual Maximum ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Hourly Rainfall ◽  
Annual Maximum Rainfall ◽  
Peak Weight

Abstract In the project of irrigation and addition structure of hydraulic, it is important to assess the specific probability of extreme rainfall. The novelty of this study is the use of KS, Chi-square, root mean square error (RMSE), and peak weight root means square error (PWRMSE) to evaluate the fit theoretical and Empirical distributions. Thirty-seven years of meteorological data from 1980 to 2017, the frequency analysis of the annual maximum rainfall in 10 regions of Pakistan was conducted. Used eight formulas to predict the annual return period of the maximum hourly precipitation every year. Five different probability distribution functions (PDF) are used to predict the probability distribution of the annual maximum hourly rainfall. Use the chi-square test and Kolmogorov- Smirnov to assess the goodness of fit. It shows that the log-logistics distribution is the overall best-fitting PDF of the annual maximum hourly rainfall in most areas of Pakistan. Besides, the peak weight relative mean square error and root mean square error goodness of fit test indicators both indicate that most suitable distribution of the probability function of all stations analysis is similar. The value of root means square error (RMSE) is almost always smaller than peak weight root means square error (PWRMSE). This is due to the higher weighting of value above the average value in the PWRMSE goodness of fit index, while for the RMSE goodness of fit index individual value has an equal weight.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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