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.

scholarly journals Modeling of probability in obtaining intensity-duration-frequency relationships of rainfall occurrence for Pelotas, RS, Brazil

2019 ◽  
Vol 23 (7) ◽  
pp. 499-505
Author(s):  
Viviane R. Dorneles ◽  
Rita de C. F. Damé ◽  
Claudia F. A. Teixeira-Gandra ◽  
Patrick M. Veber ◽  
Gustavo B. Klumb ◽  
...  
Keyword(s):  
Empirical Model ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Return Periods ◽  
Intense Rainfall ◽  
Maximum Rainfall ◽  
Rainfall Occurrence ◽  
Historical Series ◽  
Intensity Duration Frequency ◽  
Log Normal

ABSTRACT Based on historical series, for each locality, equations can characterize the relationship between intensity, duration and frequency of rainfall occurrence. The objective of this study was to present two equations that can describe the occurrence of intense rainfall in Pelotas, RS state, over the period 1982-2015. The two equations were denominated conventional and hybrid, depending on the probabilistic model used. Following the conventional methodology, the parameters of Normal, Log-Normal, Gumbel and Gamma probability distributions were adjusted by the maximum likelihood method for return periods of 2, 5, 10, 20, 25, 50 and 100 years. The maximum intensity values for the hybrid equation were obtained using the empirical model of Weibull, considering return periods of 2, 5, 10, 20 and 25 years. On the other hand, the same theoretical distributions used in the conventional equation were applied to return periods of 50 and 100 years. The Kolmogorov-Smirnov test was used to select the best fitting distribution for the data. In order to verify the information acquired through the Weibull empirical model in comparison to the theoretical distributions, the t-test was applied to the angular coefficients. Significant differences were not verified between the values of maximum rainfall intensities obtained using the two methodologies, for the pre-established durations and return periods. Thus, considering the maximum rainfall intensities values (durations of 5-1440 min) and return periods of 2-100 years in the municipality of Pelotas, RS, Brazil, both the hybrid and the conventional intense rainfall equations can be used.

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 The Fitting of a Truncated Log?Normal Curve to Daily Rainfall Data

1956 ◽  
Vol 9 (1) ◽  
pp. 151 ◽  
Author(s):  
SC Das
Keyword(s):  
Curve Fitting ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Normal Curve ◽  
Daily Rainfall Data ◽  
Log Normal

In a previous paper (Das 1955) the author discussed a problem of curve fitting which arose in testing the hypothesis proposed by Bowen (1953) concerning daily rainfall data.

scholarly journals Fit Adequacy of Dichotomous Logit Response Models of the Regressor Bernoulli and Binomial Probability Distributions

2016 ◽  
Vol 16 ◽  
pp. 38-48
Author(s):  
G. Uzodinma Ugwuanyim ◽  
Chukwudi Justin Ogbonna
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Models ◽  
Response Models ◽  
Explanatory Variables ◽  
Fit Statistics ◽  
Binomial Distributions ◽  
Multiple Correlation Analysis ◽  
Work Done ◽  
Best Fit

Logit models belong to the class of probability models that determine discrete probabilities over a limited number of possible outcomes. They are often called ‘Quantal Variables’ or ‘Stimulus and Response Models’ in Biological Literature. The conventional R2 measure of goodness-of-fit is problematic in logit models. This has therefore led to the proposal of several alternative goodness-of-fit measures. But researchers in this area have identified the base rate problem in using these several alternative goodness-of-fit measures. This research is an extension of work done by people in this area. Specifically, this research is aimed at investigating the goodness-of-fit performances of eight statistics using the Bernoulli and Binomial distributions as explanatory variables under various scenarios. The study will draw conclusions on the “best” fit. The data for the study was generated through simulation and analysed using the multiple correlation analysis. The findings clearly show that for the Bernoulli Distribution, the goodness-of-fit statistics to use are: RO2, RC2, RM2 and λp; and for the Binomial Distribution, the goodness-of-fit statistics to use are: and RN2 and λp. RO2 stood out as the “best” goodness-of-fit statistics.

scholarly journals Probability Distribution of Philippine Daily Rainfall Data

2017 ◽  
Author(s):  
Vanessa Althea B. Bermudez ◽  
Ariel Bettina B. Abilgos ◽  
Diane Carmeliza N. Cuaresma ◽  
Jomar F. Rabajante
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Economic Systems ◽  
Tropical Country ◽  
Data Set ◽  
Cumulative Rainfall ◽  
The Pacific ◽  
The Pacific Ocean

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

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 Uncertainty of Intensity-Duration-Frequency Curves Due to Adoption or Otherwise of the Temperature Climate Variable in Rainfall Disaggregation

Water ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2337
Author(s):  
Sherien Fadhel ◽  
Mustafa Al Aukidy ◽  
May Samir Saleh
Keyword(s):  
Daily Rainfall ◽  
Rainfall Data ◽  
The United Kingdom ◽  
Daily Rainfall Data ◽  
Daily Data ◽  
Idf Curves ◽  
The Difference ◽  
Intensity Duration Frequency ◽  
Historical Temperature ◽  
Temperature Climate

Most areas around the world lack fine rainfall records which are needed to derive Intensity-Duration-Frequency (IDF) curves, and those that are available are in the form of daily data. Thus, the disaggregation of rainfall data from coarse to fine temporal resolution may offer a solution to that problem. Most of the previous studies have adopted only historical rainfall data as the predictor to disaggregate daily rainfall data to hourly resolution, while only a few studies have adopted other historical climate variables besides rainfall for such a purpose. Therefore, this study adopts and assesses the performance of two methods of rainfall disaggregation one uses for historical temperature and rainfall variables while the other uses only historical rainfall data for disaggregation. The two methods are applied to disaggregate the current observed and projected modeled daily rainfall data to an hourly scale for a small urban area in the United Kingdom. Then, the IDF curves for the current and future climates are derived for each case of disaggregation and compared. After which, the uncertainties associated with the difference between the two cases are assessed. The constructed IDF curves (for the two cases of disaggregation) agree in the sense that they both show that there is a big difference between the current and future climates for all durations and frequencies. However, the uncertainty related to the difference between the results of the constructed IDF curves (for the two cases of disaggregation) for each climate is considerable, especially for short durations and long return periods. In addition, the projected and current rainfall values based on disaggregation case which adopts historical temperature and rainfall variables were higher than the corresponding projections and current values based on only rainfall data for the disaggregation.

scholarly journals ESTIMATE OF THE INTENSITY-DURATION-FREQUENCY PARAMETERS OF INTENSE RAINFALL FOR THE STATE OF ALAGOAS, BRAZIL

2020 ◽  
Vol 28 ◽  
pp. 314-325
Author(s):  
João Batista Lopes da Silva ◽  
Nicole Lopes Bento ◽  
Gabriel Soares Lopes Gomes ◽  
Alcinei Ribeiro Campos ◽  
Danilo Paulúcio da Silva
Keyword(s):  
Return Period ◽  
Probabilistic Models ◽  
Daily Rainfall ◽  
The State ◽  
Data Series ◽  
Intense Rainfall ◽  
Maximum Rainfall ◽  
Rain Gauges ◽  
Intensity Duration Frequency ◽  
Using Data

The study of the rainfall characteristics is of fundamental importance since the frequency of floods has increased in several parts of Brazil due to anthropic impacts of climatic changes. Thus, this study aimed to determine the parameters of the intense rainfall equation (K, a, b, c) for 52 municipalities in the State of Alagoas using data from 164 rain gauges ta available from the National Water Agency (ANA). The data series were subjected to consistency analysis and further desegregation of maximum daily rainfall to durations of the 5; 10; 15; 20; 25; 30; 60; 360; 480; 600; 720 and 1,440 minutes and return period of 5; 10; 25; 50 and 100 years according to different probabilistic models. The adjustment of the parameters was carried out by means of non-linear regression, with R² greater than 0.949 for all the stations, considering for this purpose one station per municipality, totaling 51 municipalities of study. It was obtained that the maximum rainfall intensity predicted increases with the increase in the return period and decreases with the increase of the duration of the rain. The greater intensities were detected in the mesoregion of Eastern Alagoano and the lowest intensities in the mesoregion of Sertão Alagoano.

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