scholarly journals Fitting statistical distribution of extreme rainfall data for the purpose of simulation

2020 ◽  
Vol 18 (3) ◽  
pp. 1367
Author(s):  
S.M. Shaharudin ◽  
N Ahmad ◽  
N.S. Mohamed ◽  
Hairulnizam Mahdin
Keyword(s):  
Goodness Of Fit ◽  
Graphical Representation ◽  
Classical Method ◽  
Probability Distributions ◽  
Peninsular Malaysia ◽  
Statistical Distribution ◽  
Rainfall Data ◽  
Suitable Model ◽  
Generalized Pareto ◽  
Torrential Rainfall

<span>In this study, several types of probability distributions were used to fit the daily torrential rainfall data from 15 monitoring stations of Peninsular Malaysia from the period of 1975 to 2007. The study of fitting statistical distribution is important to find the most suitable model that could anticipate extreme events of certain natural phenomena such as flood and tsunamis. The aim of the study is to determine which distribution fits well with the daily torrential Malaysian rainfall data. Generalized Pareto, Lognormal and Gamma distributions were the distributions that had been tested to fit the daily torrential rainfall amount in Peninsular Malaysia. First, the appropriate distribution of the daily torrential rainfall was identified within the selected distributions for rainfall stations. Then, data sets were generated based on probability distributions that mimic a daily torrential rainfall data. Graphical representation and goodness of fit tests were used in finding the best fit model. The Generalized Pareto was found to be the most appropriate distribution in describing the daily torrential rainfall amounts of Peninsular Malaysia. The outputs can be beneficial for the purpose of generating several sets of simulated data matrices that mimic the same characteristics of rainfall data in order to assess the performance of the modification method compared to classical method. </span>

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 Estimate of intense rainfall equation parameters for rainfall stations of the Paraíba State, Brazil

2017 ◽  
Vol 47 (1) ◽  
pp. 15-21
Author(s):  
Alcinei Ribeiro Campos ◽  
João Batista Lopes da Silva ◽  
Glenio Guimarães Santos ◽  
Rafael Felippe Ratke ◽  
Itauane Oliveira de Aquino
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Daily Rainfall ◽  
Water Source ◽  
Rainfall Data ◽  
Intense Rainfall ◽  
Probability Models ◽  
Temporal And Spatial Distribution ◽  
Intensity Duration Frequency ◽  
Log Normal

ABSTRACT Rainfall is the primary water source for hydrographic basins. Hence, the quantification and knowledge of its temporal and spatial distribution are indispensable in dimensioning hydraulic projects. This study aimed at assessing the fit of a series of rainfall data to different probability models, as well as estimating parameters of the intensity-duration-frequency (IDF) equation for rain stations of the Paraíba State, Brazil. The rainfall data of each station were obtained from the Brazilian Water Agency databanks. To estimate the maximum daily rainfall of each station and return period (5, 10, 15, 25, 50 and 100 years), the following probability distributions were used: Gumbel, Log-Normal II, Log-Normal III, Pearson III and Log-Pearson III. The estimation of rainfall in durations of 5-1,440 min was carried out by daily rainfall disaggregation. The adjustment of the IDF equation was performed via nonlinear multiple regression, using the nonlinear generalized reduced gradient interaction method. When compared to the data observed, the intense rainfall equations for most stations showed goodness of fit with coefficients of determination above 0.99, which supports the methodology applied in this study.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

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 Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows

2014 ◽  
Vol 18 (1) ◽  
pp. 353-365 ◽  
Author(s):  
U. Haberlandt ◽  
I. Radtke
Keyword(s):  
Time Series ◽  
Frequency Analysis ◽  
Model Calibration ◽  
Hydrological Model ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Rainfall Data ◽  
Flood Frequency Analysis ◽  
Peak Flows ◽  
Hourly Rainfall

Abstract. Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the application for derived flood frequency analysis.

scholarly journals Spatial Interpolation on Rainfall Data over Peninsular Malaysia Using Ordinary Kriging

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Suhaila Jamaludin ◽  
Hanisah Suhaimi
Keyword(s):  
Spatial Analysis ◽  
Ordinary Kriging ◽  
Spatial Interpolation ◽  
Rainfall Intensity ◽  
Peninsular Malaysia ◽  
Rainfall Data ◽  
Kriging Method ◽  
Intensity Index ◽  
Dry Conditions ◽  
Two Indices

This study presents the spatial analysis of the rainfall data over Peninsular Malaysia. 70 rainfall stations were utilized in this study. Due to the limited number of rainfall stations, the Ordinary Kriging method which is one of the techniques in Spatial Interpolation was used to estimate the values of the rainfall data and to map their spatial distribution. This spatial analysis was analysed according to the two indices that describe the wet events and another two indices that characterize dry conditions. Large areas at the east experienced high rainfall intensity compared to the areas in the west, northwest and southwest. The small value that has been obtained in Aridity Intensity Index (AII) reflects that the high amount of rainfall in the eastern areas is not contributed by low-intensity events (less than 25th percentile). In terms of number of consecutive dry days, Northwestern areas in Peninsular Malaysia recorded the highest value. This finding explains the occurrence of a large number of floods and soil erosions in the eastern areas.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals A comparative study of different imputation methods for daily rainfall data in east-coast Peninsular Malaysia

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Siti Mariana Che Mat Nor ◽  
Shazlyn Milleana Shaharudin ◽  
Shuhaida Ismail ◽  
Nurul Hila Zainuddin ◽  
Mou Leong Tan
Keyword(s):  
Missing Values ◽  
Nearest Neighbor ◽  
East Coast ◽  
Daily Rainfall ◽  
Absolute Error ◽  
Peninsular Malaysia ◽  
Partial Least Square ◽  
Least Square ◽  
Rainfall Data ◽  
Efficiency Coefficient

Rainfall data are the most significant values in hydrology and climatology modelling. However, the datasets are prone to missing values due to various issues. This study aspires to impute the rainfall missing values by using various imputation method such as Replace by Mean, Nearest Neighbor, Random Forest, Non-linear Interactive Partial Least-Square (NIPALS) and Markov Chain Monte Carlo (MCMC). Daily rainfall datasets from 48 rainfall stations across east-coast Peninsular Malaysia were used in this study. The dataset were then fed into Multiple Linear Regression (MLR) model. The performance of abovementioned methods were evaluated using Root Mean Square Method (RMSE), Mean Absolute Error (MAE) and Nash-Sutcliffe Efficiency Coefficient (CE). The experimental results showed that RF coupled with MLR (RF-MLR) approach was attained as more fitting for satisfying the missing data in east-coast Peninsular Malaysia.

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.

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