Determining the best fitting distribution of annual precipitation data in Serbia using L-moments method

2020 ◽  
Author(s):  
Milan Gocic ◽  
Lazar Velimirovic ◽  
Miomir Stankovic ◽  
Slavisa Trajkovic
Keyword(s):  
Annual Precipitation ◽  
Precipitation Data ◽  
Moments Method ◽  
Best Fitting ◽  
L Moments

Tenderfoot Creek Experimental Forest Annual Precipitation Data: 1993-2010

2011 ◽  
Author(s):  
David K. Wright ◽  
Lance S. Glasgow ◽  
Ward W. McCaughey ◽  
Elaine K. Sutherland
Keyword(s):  
Annual Precipitation ◽  
Precipitation Data

scholarly journals MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2092
Author(s):  
Songbai Song ◽  
Yan Kang ◽  
Xiaoyan Song ◽  
Vijay P. Singh
Keyword(s):  
Parameter Estimation ◽  
Confidence Intervals ◽  
Asymptotic Variance ◽  
Information Matrix ◽  
Estimation Method ◽  
Flood Frequency Analysis ◽  
Annual Precipitation ◽  
Precipitation Data ◽  
Marquardt Algorithm ◽  
Design Values

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values

scholarly journals Changes and contemporary trends in the annual amounts of precipitation in Serbia

2021 ◽  
Vol 44 ◽  
pp. 73-79
Author(s):  
Hristo Popov ◽  
Jelena Svetozarevich
Keyword(s):  
Balkan Peninsula ◽  
Middle Part ◽  
River Valley ◽  
Annual Precipitation ◽  
Precipitation Data ◽  
Southeast Europe ◽  
The Republic ◽  
River Valleys ◽  
Annual Amount ◽  
The Sava River

The Republic of Serbia is а continental country located in the western part of the Balkan Peninsula, in Southeast Europe. In terms of physical characteristics, Serbia is divided into two parts: Pannonian part and mountainous part. The northern part of the country is located in the valley of the Middle Danube, the Sava River valley and the Tisza River valley. In the middle part of the country, the river valleys of the Drina, the Kolubara and the Morava are located. For the purposes of this research, the authors have used the annual precipitation data from 15 meteorological stations distributed throughout the Republic of Serbia. The data from these meteorological stations for the period between 1991 and 2019 has been provided by The Serbian Institute of Meteorology and Hydrology. This data has been used to calculate the annual amount of precipitation, and the trends in annual precipitation.

scholarly journals Effects of record length and resolution on the derived distribution of annual precipitation

2015 ◽  
Vol 12 (12) ◽  
pp. 12987-13018
Author(s):  
C. I. Meier ◽  
J. S. Moraga ◽  
G. Pranzini ◽  
P. Molnar
Keyword(s):  
High Resolution ◽  
Interannual Variability ◽  
Probability Model ◽  
Annual Precipitation ◽  
Annual Rainfall ◽  
Precipitation Data ◽  
Return Periods ◽  
Record Length ◽  
High Return ◽  
Log Normal

Abstract. Traditional frequency analysis of annual precipitation requires the fitting of a probability model to yearly precipitation totals. There are three potential problems with this approach: a long record (at least 25 ~ 30 years) is required in order to fit the model, years with missing data cannot be used, and the data need to be homogeneous. To overcome these limitations, we test an alternative methodology proposed by Eagleson (1978), based on the derived distribution approach (DDA). This allows for better estimation of the probability density function (pdf) of annual rainfall without requiring long records, provided that high-resolution precipitation data are available to derive external storm properties. The DDA combines marginal pdfs for storm depth and inter-arrival time to arrive at an analytical formulation of the distribution of annual precipitation under the assumption of independence between events. We tested the DDA at two temperate locations in different climates (Concepción, Chile, and Lugano, Switzerland), quantifying the effects of record length. Our results show that, as compared to the fitting of a normal or log-normal distribution, the DDA significantly reduces the uncertainty in annual precipitation estimates (especially interannual variability) when only short records are available. The DDA also reduces the bias in annual precipitation quantiles with high return periods. We also show that using precipitation data aggregated every 24 h, as commonly available at most weather stations, introduces a noticeable bias in the DDA. Our results point to the tangible benefits of installing high-resolution (hourly or less) precipitation gauges at previously ungauged locations. We show that the DDA, in combination with high resolution gauging, provides more accurate and less uncertain estimates of long-term precipitation statistics such as interannual variability and quantiles of annual precipitation with high return periods even for records as short as 5 years.

scholarly journals Determining suitable probability distribution models for annual precipitation data (a case study of Mazandaran and Golestan provinces)

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Mohammad Mahdavi ◽  
Khaled Osati ◽  
Sayed Ali Naghi Sadeghi ◽  
Bakhtiar Karimi ◽  
Jalil Mobaraki
Keyword(s):  
Probability Distribution ◽  
Annual Precipitation ◽  
Precipitation Data ◽  
Distribution Models

scholarly journals Use of L-moments Method for Extreme Statistics of Storm Wave Heights

2009 ◽  
Vol 65 (1) ◽  
pp. 161-165
Author(s):  
Yoshimi GODA ◽  
Masanobu KUDAKA ◽  
Hiroyasu KAWAI
Keyword(s):  
Extreme Statistics ◽  
Moments Method ◽  
Storm Wave ◽  
Wave Heights ◽  
L Moments

Regional frequency analyses of successive-duration annual maximum rainfalls by L-moments method

2016 ◽  
Vol 61 (4) ◽  
pp. 647-668 ◽  
Author(s):  
Tefaruk Haktanir ◽  
Hatice Citakoglu ◽  
Neslihan Seckin
Keyword(s):  
Annual Maximum ◽  
Moments Method ◽  
L Moments ◽  
Regional Frequency

scholarly journals Gender Wise Distribution of Income Using L-Moments Method

2019 ◽  
Vol 2 (1) ◽  
pp. 29
Author(s):  
Muhammad Alam ◽  
Saeed Ullah Jan ◽  
Alam Zeb
Keyword(s):  
Income Distribution ◽  
Sample Size ◽  
Small Sample Size ◽  
Small Sample ◽  
Parameters Estimation ◽  
Large Sample Size ◽  
Unknown Parameters ◽  
Moments Method ◽  
L Moments ◽  
Distribution Of Income

<em>The main purpose of this work is to explore the income distribution of both male and female in Pakistan over the period of 2010-2011. For this purpose, the lognormal distribution with known parameters is used as a model and its unknown parameters are estimated by three methods that are likelihood, moments and L-moments. The results show that citizens of Pakistan are not equal in income and the probability plot suggested that the income of the male is greater than that of a female in Pakistan. Moreover, for small sample size, the best method of parameters estimation is the L-moments, while, for large sample size the best method is a maximum likelihood. Findings of the study suggest that suitable policy is required to maintain equality in income distribution in the country. It will consequently reduce the gap among rich and poor and will certainly improve social welfare.</em>

scholarly journals Describing the interannual variability of precipitation with the derived distribution approach: effects of record length and resolution

2016 ◽  
Vol 20 (10) ◽  
pp. 4177-4190 ◽  
Author(s):  
Claudio I. Meier ◽  
Jorge Sebastián Moraga ◽  
Geri Pranzini ◽  
Peter Molnar
Keyword(s):  
Time Series ◽  
Interannual Variability ◽  
Lognormal Distribution ◽  
Traditional Approach ◽  
Probability Model ◽  
Extreme Rainfall ◽  
Annual Precipitation ◽  
Annual Rainfall ◽  
Precipitation Data ◽  
Record Length

Abstract. Interannual variability of precipitation is traditionally described by fitting a probability model to yearly precipitation totals. There are three potential problems with this approach: a long record (at least 25–30 years) is required in order to fit the model, years with missing rainfall data cannot be used, and the data need to be homogeneous, i.e., one has to assume stationarity. To overcome some of these limitations, we test an alternative methodology proposed by Eagleson (1978), based on the derived distribution (DD) approach. It allows estimation of the probability density function (pdf) of annual rainfall without requiring long records, provided that continuously gauged precipitation data are available to derive external storm properties. The DD approach combines marginal pdfs for storm depths and inter-arrival times to obtain an analytical formulation of the distribution of annual precipitation, under the simplifying assumptions of independence between events and independence between storm depth and time to the next storm. Because it is based on information about storms and not on annual totals, the DD can make use of information from years with incomplete data; more importantly, only a few years of rainfall measurements should suffice to estimate the parameters of the marginal pdfs, at least at locations where it rains with some regularity. For two temperate locations in different climates (Concepción, Chile, and Lugano, Switzerland), we randomly resample shortened time series to evaluate in detail the effects of record length on the DD, comparing the results with the traditional approach of fitting a normal (or lognormal) distribution. Then, at the same two stations, we assess the biases introduced in the DD when using daily totalized rainfall, instead of continuously gauged data. Finally, for randomly selected periods between 3 and 15 years in length, we conduct full blind tests at 52 high-quality gauging stations in Switzerland, analyzing the ability of the DD to estimate the long-term standard deviation of annual rainfall, as compared to direct computation from the sample of annual totals. Our results show that, as compared to the fitting of a normal or lognormal distribution (or equivalently, direct estimation of the sample moments), the DD approach reduces the uncertainty in annual precipitation estimates (especially interannual variability) when only short records (below 6–8 years) are available. In such cases, it also reduces the bias in annual precipitation quantiles with high return periods. We demonstrate that using precipitation data aggregated every 24 h, as commonly available at most weather stations, introduces a noticeable bias in the DD. These results point to the tangible benefits of installing high-resolution (hourly, at least) precipitation gauges, next to the customary, manual rain-measuring instrument, at previously ungauged locations. We propose that the DD approach is a suitable tool for the statistical description and study of annual rainfall, not only when short records are available, but also when dealing with nonstationary time series of precipitation. Finally, to avert any misinterpretation of the presented method, we should like to emphasize that it only applies for climatic analyses of annual precipitation totals; even though storm data are used, there is no relation to the study of extreme rainfall intensities needed for engineering design.

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