gumbel distribution
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Atmosphere ◽  
2022 ◽  
Vol 13 (1) ◽  
pp. 131
Author(s):  
Ahmad H. Y. Abu Hammad ◽  
Ala A. M. Salameh ◽  
Riad Qara Fallah

This study aimed at analysis of the general-index change for the mean annual and seasonal precipitation in six stations in Latakia Governorate (Syria). The data of precipitation were collected for 40 consecutive years (1970–2010) in order to figure out the extent of the changes and variability in precipitation rates and the impact of this change on changes in the potential density that might cause extremely high or low precipitation rates according to Gumbel distribution of the extreme precipitation rates. Results revealed a decrease of the annual precipitation rates in all stations, the reduction in precipitation ranged from 46 to 210 mm during the whole period of the study. Spring, however, recorded the highest and statistically significant reduction, which reached 46–210 mm, while winter precipitation increased by 21–82 mm. Spring also has witnessed a decrease of about 3–9% of the total annual precipitation as compared to winter precipitation which increased by 5–8% of the total. The potential density of extremely high winter precipitation rates increased in all stations as indicated from Gumbel distribution in winter, and a greater increase took place in the probabilities of occurrence of the extremely low spring precipitation rates. This shows significant probability of occurrence of drought during spring season. By contrast, probabilities of winter precipitation rates increased more, thus winter is relatively more humid than before and spring is relatively drier than before.


Water ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 112
Author(s):  
Sérgio Lousada ◽  
Leonardo Gonçalves ◽  
Alper Atmaca

This study aims to examine the flood propensity of the main watercourse of São Vicente drainage basin and, if relevant, to propose two methodologies to alleviate the impacts, i.e., detention basin sizing and riverbed roughness coefficient adjustment. Geomorphological data were obtained from the watershed characterization process and used through the SIG ArcGIS software for the flood propensity assessment and then for the calculation of the expected peak flow rate for a return period of 100 years through the Gumbel Distribution. Subsequently, the drainage capacity of the river mouth was verified using the Manning-Strickler equation, in order to establish whether the river mouth of the watershed has the capacity to drain the entire volume of rainwater in a severe flood event. In summary, it was possible to conclude that São Vicente’s watershed river mouth is not able to completely drain the rain flow for the established return period. Thus, its drainage capacity was guaranteed by modifying the walls and streambed roughness coefficient and by sizing the detention basin using the Dutch and the Simplified Triangular Hydrograph methods.


Water ◽  
2021 ◽  
Vol 13 (23) ◽  
pp. 3439
Author(s):  
Iwona Markiewicz

The Upper Vistula Basin is a flood-prone region in the summer season (May–October) due to intensive rainfall. From the point of view of water management, it is particularly important to assess the variability in this main factor of flood risk, as well as to establish the depth–duration–frequency (DDF) relationship for maximum precipitation, this having not yet been derived for the region. The analysis of a 68-year (1951–2018) data series of summer maximum precipitation collected by 11 meteorological stations showed the series’ stationarity, which supports the conclusion that there is no increase in the risk of rainfall floods due to the intensification of extreme precipitation. A new approach is proposed for the determination of the DDF relationship, where the best-fitted distribution for each station is selected from among the set of candidate distributions, instead of adopting one fixed distribution for all stations. This approach increases the accuracy of the DDF relationships for individual stations as compared to the commonly used approach. In particular, the traditionally used Gumbel distribution turns out to be not well fitted to the investigated data series, and the advantage of the recently popular GEV distribution is not significant.


Author(s):  
G.G. Hamedani ◽  
Mahrokh Najaf ◽  
Amin Roshani ◽  
Nadeem Shafique Butt

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.


2021 ◽  
Vol 11 (23) ◽  
pp. 11385
Author(s):  
Pengfei Wang ◽  
Weiqiang Wang ◽  
Sanlong Zheng ◽  
Zengliang Gao

The testing of KMN steel bending fatigue with different cycles was carried out using a nonlinear ultrasonic detector to obtain its nonlinear coefficient. The experimental results show that the nonlinear coefficient first increases and then decreases with an increase in fatigue cycles. The relationship between the propagation of the micro-cracks inside the material and the nonlinear coefficient was researched by microscopic analysis in the dangerous position of the specimens. As the fatigue cycles increase, the microstructure of the specimen gradually deteriorates and cracks occur, which proves that nonlinear ultrasonic detection can be used to characterize the initiation of micro-cracks in the early fatigue stages of the material and that the nonlinear coefficient β of the material can be used to reflect the fatigue damage degree and fatigue life of the interior of the material. An analysis of the numerical statistics of the fatigue cracks inside the specimens was carried out, and the extreme value of fatigue cracks was calculated using the Gumbel distribution. An empirical formula for the nonlinear coefficient and crack growth size of KMN steel was established and then a method for estimating the fatigue life of KMN steel based on nonlinear ultrasonic testing was proposed.


Author(s):  
Djigbo Félicien Badou ◽  
Audrey Adango ◽  
Jean Hounkpè ◽  
Aymar Bossa ◽  
Yacouba Yira ◽  
...  

Abstract. West African populations are increasingly exposed to heavy rainfall events which cause devastating floods. For the design of rainwater drainage facilities (to protect populations), practitioners systematically use the Gumbel distribution regardless of rainfall statistical behaviour. The objective of this study is twofold. The first is to update existing knowledge on heavy rainfall frequency analysis in West Africa to check whether the systematic preference for Gumbel's distribution is not misleading, and subsequently to quantify biases induced by the use of the Gumbel distribution on stations fitting other distributions. Annual maximum daily rainfall of 12 stations located in the Benin sections of the Niger and Volta Rivers' basins covering a period of 96 years (1921–2016) were used. Five statistical distributions (Gumbel, GEV, Lognormal, Pearson type III, and Log-Pearson type III) were used for the frequency analysis and the most appropriate distribution was selected based on the Akaike (AIC) and Bayesian (BIC) criteria. The study shows that the Gumbel's distribution best represents the data of 2/3 of the stations studied, while the remaining 1/3 of the stations fit better GEV, Lognormal, and Pearson type III distributions. The systematic application of Gumbel's distribution for the frequency analysis of extreme rainfall is therefore misleading. For stations whose data best fit the other distributions, annual daily rainfall maxima were estimated both using these distributions and the Gumbel's distribution for different return periods. Depending on the return period, results demonstrate that the use of the Gumbel distribution instead of these distributions leads to an overestimation (of up to +6.1 %) and an underestimation (of up to −45.9 %) of the annual daily rainfall maxima and therefore to an uncertain design of flood protection facilities. For better validity, the findings presented here should be tested on larger datasets.


2021 ◽  
Vol 21 (2) ◽  
pp. 159-165
Author(s):  
A.ROSHAN ◽  
H. SEDGHI ◽  
R.A.SHARIFAN ◽  
J.PORHEMMAT

Intensity-duration-frequency (IDF) curves are among the standard design tools for many engineering applications such as urban drainage management. Since climate change may considerably affect precipitation, updating of IDF curves is highly necessary. The present study aims to examine the impacts of climate change on IDF curves of Shiraz synoptic station using downscaled outputs of Hadcm3 AOGCM under various emission scenarios (A1B, A2,B1) applying larswg-5 model for the period of 2046 to 2065. The fitted Gumbel distribution was used to estimate the maximum short-term precipitation quantiles in the base period (1968-2000) and the verified empirical Bell type equation was used for the future period. The results show that the mean of maximum daily precipitation and annual precipitation will decrease in the future. Also, the maximum precipitation intensities up to 60 min duration will reducefrom 0.15 mm hr-1 to about 10.79 mm hr-1 compared to the observed period in all returns periods and various scenarios. Overall, there were no tangible changes in intensities for durations higher than 60 min. The highest reduction in precipitation intensity would be at the 20 min duration with 100-year return period in the A2 scenario.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sergej Rempel ◽  
Marcus Ricker ◽  
Tânia Feiri

AbstractTextile-reinforced concrete has emerged in recent years as a new and valuable construction material. The design of textile-reinforced concrete requires knowledge on the mechanical properties of different textile types as well as their reinforcing behaviour under different loading conditions. Conventional load-bearing tests tend to be complex, time-consuming, costly and can even lack consistent specifications. To mitigate such drawbacks, a standardised tensile test for fibre strands was used to characterise the material properties needed for the design of a textile-reinforced concrete member. The standardised tensile test uses a fibre strand with 160 mm length, which is cut out of a textile grid. For the sake of this study, an epoxy resin-soaked AR-glass reinforcement was considered. The results show that the textile reinforcement has a linear-elastic behaviour, and the ultimate tensile strength can be statistically modelled by a Gumbel distribution. Furthermore, the results indicate that the modulus of elasticity is not influenced by the length or the number of fibre strands. Therefore, the mean value attained from the standardised test can be used for design purposes. These findings are essential to derive an appropriate partial safety factor for the calculation of the design values of the tensile strength and can be used to determine the failure probability of textile-reinforced concrete members.


CERUCUK ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Ahdianoor Fahraini ◽  
Achmad Rusdiansyah

According to the World Meteorological Organization that 2014 was the hottest year in which the hot weather alternated with high rainfall and floods which destroyed the people's economy. Banjarbaru, as one of the central cities of the government of South Kalimantan Province, has a topographic condition that is at an altitude of 0-500 m above sea level, causing rainfall, which is enough frequent. Banjarbaru itself is one of the cities affected by climate change in 2014. Disasters that occurred in the form of flooding at several points of residents and also crippled traffic at that time. Thus, it is important to know the pattern of maximum rainfall changes that occur. By knowing the pattern of maximum rainfall changes, the impact of the high rainfall that can occur will be minimized and can even be anticipated as early as possible.            Data processing is performed with maximum daily rainfall data of 30 years and divided into a database before and after climate change that is 25 years old data and 5 years of new data. Each database calculates the planned rainfall for the return period of 2-1000 years with the distribution obtained from the analyzed database. Next, analyze the deviation of the two data. The purpose of analyzing the deviation of old data and new data is to determine changes in the planned rainfall from both data. Deviation analysis uses the Peak-Weight Root Mean Square Error function.            The conclusion of the analysis is that based on the Statistical Parameters test, the Chi-Square test, and the Smirnov-Kolmogorov test on the old database using the Gumbel distribution and the new data using the Pearson Log Type III distribution for the calculation of the planned rain. Based on the analysis of the rain plan to get new data 5 years has the results of the rain plan is greater than the old data of 25 years and the analysis of the deviation to get the results of the new data 5 years has a greater value of deviation each time when revisiting the old data of 25 years. So it can be suggested that rainfall data with the same characteristics, can use 5 years of new data for the analysis of water building planning.


MAUSAM ◽  
2021 ◽  
Vol 72 (3) ◽  
pp. 607-618
Author(s):  
CHERAITIA HASSEN

The annual maximum temperature was modeled using the Generalized Extreme Value (GEV) distribution to Jijel weather station. The Mann-Kendall (MK) and Kwiatkowski Phillips, Schmidt and Shin (KPSS) tests suggest a stationary model without linear trend in the location parameter. The Kurtosis and the Skewness statistics indicated that the normality assumption was rejected. The Likelihood Ratio test was used to determine the best model and the goodness-of-fit tests showed that our data is suitable with a stationary Gumbel distribution. The Maximum Likelihood estimation method and the Bayesian approach using the Monte Carlo method by Markov Chains (MCMC) were used to find the parameters of the Gumbel distribution and the return levels were obtained for different periods. JEL Classification: C1, C13, C46, C490.


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