Extreme Value Distribution Method Research Articles

Quantifying regional rainfall dynamics in southern India: Unravelling monsoon characteristics and intense precipitation using satellite and observed data records

Rainfall patterns are unpredictable, which has implications for planning irrigation systems, constructing farm ponds and drainage systems, and conserving water and soil. The research findings have been compiled over 36 years, utilizing gridded daily precipitation data from the IMD and PWD (1984–2019). This study investigates the frequency of consecutive rainy days, the yearly rainfall pattern and the precipitation threshold value that triggers the flood. The Mann-Kendall approach is used to analyze trends in the statistical application XLSTAT. According to the trend analysis, rainfall and wet days during the Northeastern Monsoon (NEM) throughout the year show significant and nonsignificant increasing trends at most stations. Statistical or empirical approaches can be used to establish the threshold value of precipitation that causes a flood by examining historical flood episodes and the precipitation that occurred. The Gumbel extreme value distribution method was used to determine the recurrence intervals of days 1, 2, 3, and 4 that are consecutive and equal to or above 5 days. The study's findings will show that rainfall patterns can be used to forecast floods and estimate their return and recurrence intervals. As a result, implementing this research with these precipitation threshold values could help with flood warning systems and the infrastructure required for emergency responses to flooding disasters.

Flood frequency analysis of Asa River, Ilorin, Nigeria

Flooding poses a risk to human lives, livelihoods, infrastructure, and the environment. Therefore, understanding the flood frequency patterns of the Asa River is crucial in developing effective flood management strategies. This study explores the statistical technique to understand the nature and magnitude of high discharge of floods in the Asa River, aiming at relating the magnitude of floods and their frequency of occurrence through probability distribution. The Gumbel Extreme Value Distribution method was used to analyze the 30 years (1991-2020) flood discharge data of River Asa which was collected from Lower Niger River Basin and Development Authority, Ilorin, and flood discharge for the return periods of 5 years, 10 years, 20 years, 30 years, 50 years, 100 years, and 150 years, was predicted. From the observations of Gumbel’s distribution, the R2 value acquired from the trend line equation was 0.9227, indicating that Gumbel's extreme value distribution is suitable for estimating predicted river flood flow. The expected flood discharge for the return periods of the upcoming 5 years, 10 years, 15 years, 20 years, 25 years, 50 years, 100 years, and 150 years, was estimated to be 43.19 m3/s, 51.12 m3/s, 55.60 m3/s, 58.73 m3/s, 63.11 m3/s, 68.58 m3/s, 75.96 m3/s, and 80.27m3/s respectively. The results obtained in this research would adequately serve as a planning guide for the decision makers on the development and flood risk management along Asa River, to achieve sustainable development and management, with a view of protecting lives and properties downstream of the watershed.

A conditional extreme value distribution method for dynamic reliability analysis of stochastic structures

An efficient post-processing simulation method is proposed to estimate small failure probabilities of stochastic dynamic structures involving the inherent randomness of structural physical-geometrical parameters and external excitations. To extract a small failure probability, the proposed method introduces an intermediate event to represent the realizations of extreme structural response in the tail of distribution. With the aid of this intermediate event, structural failure probability is reformulated as a product of the event’s occurrence probability and the conditional exceedance probability of extreme response when the event occurs. The latter corresponds to a distribution of extreme response under the condition of the intermediate event, referred to as the conditional extreme value distribution (CEVD). Accordingly, the proposed method is termed the CEVD method. To reconstruct the CEVD, a truncated shifted generalized lognormal distribution model is employed. Bayesian estimation method is utilized to determine the two shape parameters of this model based on the samples of both original extreme value distribution and CEVD, where the CEVD samples are generated by Markov chain Monte Carlo sampling. The efficiency and accuracy of the proposed method are demonstrated through two numerical examples considering seismic reliability analyses of a 10-story nonlinear frame and a soil-foundation-structure interaction system.

Effect of springing and whipping on exceedance probability of vertical bending moment of a ship

An extreme value distribution method for the vertical bending moment (VBM) is developed using a reduced order model (ROM) based on CFD-FEM coupling. A post-Panamax containership is considered to be a subject model and for which experiment was performed in our previous study. In ROM, VBM for all the components, i.e., wave-induced, whipping, and springing components, are calculated separately and superimposed. The vessel motions and wave-induced components are estimated from transfer functions derived from nonlinear strip theory and later corrected using CFD-FEM coupling. The whipping component is evaluated using von Karman's momentum theory with proper adjustment to specific hull parameters and additionally corrected using CFD-FEM coupling. A new semi-empirical springing ROM is developed based on CFD-FEM coupled analysis and experimental results. A numerous number of irregular waves are generated for a severe short-term sea state using random numbers, for which VBM time series is compared between ROM and coupled CFD-FEM analysis. The effect of springing and whipping in calculating the extreme value distribution of VBM is described for different probability levels. The effect of consecutive bow-stern slamming is also discussed. The development of this method will aid to attain real-time shipload prediction without expensive computational costs due to coupled CFD-FEM.

Flood Frequency Analysis of Araniar Medium Irrigation Project in Chittoor District by using Gumbel's Distribution

Flood frequency analysis is one of the most important statistical technique to understand the nature and magnitude of high discharge of floods in the river. The objective of flood frequency analysis was to relate the magnitude of floods and their frequency of occurrence through probability distribution. Flood frequency analysis is essential to reduce the impact of flood damage by predicting the floods by adopting the suitable flood prediction model. The Araniar reservoir was constructed across the Araniar river in the Chittoor district of Andhra Pradesh. The flood frequency analysis was conducted on the Araniar reservoir using Gumbel’s extreme value distribution method in the year 2019-2020. Daily maximum inflow data from the Department of Water Resources, Andhra Pradesh, were collected for the period 1990-2019 and used for flood frequency analysis of Araniar Reservoir using Gumbel's extreme value distribution method. From the observations of Gumbel’s distribution, the R2 value acquired from the trend line equation was 0.9803, indicating that Gumbel's extreme value distribution was suitable for estimating predicted reservoir flood flow. The estimated flood flow for upcoming years of 2 years, 10 years, 50 years, 100 years,150 years, 200 years, 300 years and 400 years were found to be 38.29 Mm3/year, 66.96 Mm3/year, 92.08 Mm3/year, 102.71 Mm3/year, 108.90 Mm3/year, 113.29 Mm3/year, 119.47 Mm3/year and 123.85 Mm3/year respectively. The mean instantaneous flow in the reservoir was 40.88149 Mm3/year which was nearly equal to a return period of about 2 years. The estimated flood flows of the Araniar reservoir was useful for constructing important dam hydraulic structures, advising agricultural patterns in the command area, and protecting lives and property downstream of the catchment region.

Analysis of construction parameters of outriggers in the mega column-core tube-outrigger structure based on seismic reliability

The design of outriggers is one of the hot issues in mega column-core tube-outrigger structures (MCCTOS). Therefore, the analysis of the parameters of the outriggers is of great practical significance. In this paper, based on the generalized probability density evolution theory, the reliabilities of MCCTOS with different outrigger parameters are investigated by absorbing boundary condition method and extreme-value distribution method, respectively. Based on the consideration of the randomness of the structural parameters and earthquake, the influence of the linear bending stiffness ratio of the outrigger-to-core tube, the number and position of the outriggers on the MCCTOS are analyzed by quantitative reliability. By comparing the results, it is found that for one-outrigger structure and two-outrigger structure, the reliability of the structure will reach a stable stage when the linear bending stiffness ratio of the outrigger-to-core tube is taken as 0.5 and 0.7 respectively. It indicates that the difference in the number of outriggers leads to the different reasonable values of the linear bending stiffness ratio of the outrigger-to-core tube. In addition, the reasonable locations of the outriggers can maximize the overall reliability of the structure and make the distribution of the reliability of each storey more uniform. The analysis of construction parameters of outriggers from the perspective of reliability can more comprehensively describe the influence of outriggers on the seismic capacity of the structure. The investigation on the seismic reliability of MCCTOS can more objectively evaluate the safety of structure. Moreover, the analysis of different construction parameters of outriggers in the MCCTOS based on seismic reliability can provide more objective suggestions for the design of outriggers.

Will Climate Change Exacerbate the Economic Damage of Flood to Agricultural Production? A Case Study of Rice in Ha Tinh Province, Vietnam

In developing countries in general and in Vietnam in particular, flood induced economic loss of agriculture is a serious concern since the livelihood of large populations depends on agricultural production. The objective of this study was to examine if climate change would exacerbate flood damage to agricultural production with a case study of rice production in Huong Son District of Ha Tinh Province, North-central Vietnam. The study applied a modeling approach for the prediction. Extreme precipitation and its return periods were calculated by the Generalized Extreme Value distribution method using historical daily observations and output of the MRI-CGCM3 climate model. The projected extreme precipitation data was then employed as an input of the Mike Flood model for flood modeling. Finally, an integrated approach employing flood depth and duration and crop calendar was used for the prediction of potential economic loss of rice production. Results of the study show that in comparison with the baseline period, an increase of 49.14% in the intensity of extreme precipitation was expected, while the frequency would increase 5 times by 2050s. As a result, the seriousness of floods would increase under climate change impacts as they would become more intensified, deeper and longer, and consequently the economic loss of rice production would increase significantly. While the level of peak flow was projected to rise nearly 1 m, leading the area of rice inundated to increase by 12.61%, the value of damage would rise by over 21% by 2050s compared to the baseline period. The findings of the present study are useful for long-term agricultural and infrastructural planning in order to tackle potential flooding threats to agricultural production under climate change impacts.

Prediction of the Variability of Changes in the Intensity and Frequency of Climate Change Reinforced Multi-Day Extreme Precipitation in the North-Central Vietnam Using General Circulation Models and Generalized Extreme Value Distribution Method

Flooding of downstream agricultural fields and cities is normally caused by consecutive days of extreme precipitation in upstream areas. As climate change is widely projected to accelerate the hydrological cycle, concerns about the increase in frequency and intensity of extreme precipitation arise. The present study used Pattern Scaling coupled with Generalized Extreme Value (GEV) distribution to calculate changes in multi-day extreme precipitation in the North Central Vietnam in 2050, 2070, and 2090 under three AR5’s Representative Concentration Pathways RCP2.6, RCP6.0 and RCP8.5. Twenty long-term historical observation stations in the study area with daily data mostly date back to more than 50 years were employed and 5-day maximum total precipitation was analyzed. The results reveal an agreement among the employed GCMs on an increase in the intensity and a shortening of the return periods of extreme precipitation, with the most reinforced trend occurring under RCP8.5, followed by RCP6.0 and then RCP2.6. This indicates that the risk of associated floods is likely to increase, especially under higher RCPs. Therefore, planning and decision making of durable infrastructure along with flood mitigation strategies to cope with such events are recommended.

A study on b-value and investigation of seismic hazard in Sylhet seismic region, Bangladesh using Gumbel’s extreme value distribution method

In Gutenberg–Richter (GR) earthquake frequency magnitude relationship the b-value plays an important role and is required for the seismic hazard analysis of any region. In this study, both the Gumbel’s extreme distribution and the GR methods are used to estimate the b-value for Sylhet region of Bangladesh. Due to the geological location this region is the most seismically vulnerable area of the country. Sylhet region is situated on the south eastern part of the Dauki fault. The frequency of seismic activity at the Dauki fault zone has lessened after the great Indian earthquake that occurred in 1897. Therefore, energy may be stored in this fault region, which leaves possibilities that Sylhet may encounter an earthquake. The Sylhet region has experienced nearly 184 earthquakes of magnitude ranging from 4 to 7.2 during the last 101 years. In this study, the probability of recurrence of earthquakes of various magnitude has also been investigated using USGS catalogue which has been prepared by taking moment magnitude (Mw) as a homogenous magnitude. The least square regression method has been applied to compute the b-value by the GR relationship, which resulted in the b-value to be 0.75. Nevertheless, the regression analysis through Gumbel’s extreme value displays a satisfactory result. Further the regression analysis through Gumbel’s method estimated the b-value to be 0.91 and using this the earthquake recurrence probability and the return period for different magnitudes have been calculated. From the probabilistic analysis it has been found that the probability of recurrence of an earthquake (R) of Mw ≥ 6.5 in 100 years is 85% and its return period (Tr) is 53 years in this region. The earthquake recurrence probability of significant damaging earthquakes affecting Sylhet and their return periods have also been investigated. It has been observed that the probability of recurrence of an earthquake equal or greater than 1885 Bengal earthquake (Mw ≥ 7.0) in 100 years is 48.5% in this region and its return period (Tr) is 151 years.

DEVELOPMENT OF INTENSITY DURATION FREQUENCY CURVES FOR NARSAPUR MANDAL, TELANGANA STATE, INDIA

Abstract The government of Telengana State, India, has taken up restoration of minor irrigation tanks to store its maximum capacity under a massive programme called Mission Kakatiya. For estimation of runoff into these tanks, intensity of rainfall for shorter duration is required. Hence, an attempt is made in this study to generate intensity of rainfall for durations from 1-hour to 12-hour using an empirical formula from Indian Meteorological Department (IMD). Frequency analysis using Gumbel’s Extreme Value Distribution method is considered to establish Intensity-Duration-Frequency curves. Daily rainfall data for the years 2009-14 of Narsapur Mandal, Medak District, Telengana State, India, is taken for the analysis considering various return periods of 5 Year, 10 Year, 25 Year, 50 Year and 100 Years.

Combined Cycle Fatigue of Ni-Base Superalloy

Fatigue life of a cast Ni-base superalloy IN 713LC under combined cycle loading consisting of a superposition of low- and high-cycle fatigue at 800 °C was experimentally determined. No measurable effect of combined cycle was found for studied loading conditions. High scatter of fatigue life related to the initiation of cracks on casting defects was observed. Size of the largest defect in a specimen was predicted by the largest extreme value distribution method. The predicted size was compared with fractographic observation of defects resulting in final fatigue failure.

Development of Extreme Value Distribution Method for Estimation of Expressway Capacity

Although the concept of road capacity remains open to debate, randomness is a well-known feature of capacity. Previous attempts to estimate capacity have met difficulties in validation and application. A new empiric capacity estimation method that uses extreme value distribution (EVD) was developed. The EVD method has been widely applied to meteorological science for many years, especially to precipitation and flood prediction. Results of this study show that the EVD method can provide a clear and intuitive approach to capacity estimation with empirical data.

Frequency analysis for predicting 1% annual maximum water levels along Florida coast, US

AbstractIn the Coastal Flood Insurance Study by the Federal Emergency Management Agency (FEMA, 2005), 1% annual maximum coastal water levels are used in coastal flood hazard mitigation and engineering design in coastal areas of USA. In this study, a frequency analysis method has been developed to provide more accurate predictions of 1% annual maximum water levels for the Florida coast waters. Using 82 and 94 years of annual maximum water level data at Pensacola and Fernandina, performances of traditional frequency analysis methods, including advanced method of Generalized Extreme Value distribution method, have been evaluated. Comparison with observations of annual maximum water levels with 83 and 95 years of return periods indicate that traditional methods are unable to provide satisfactory predictions of 1% annual maximum water levels to account for hurricane‐induced extreme water levels. Based on the characteristics of annual maximum water level distribution of Pensacola and Fernandina stations, a new probability distribution method has been developed in this study. Comparison with observations indicates that the method presented in this study significantly improves the accuracy of predictions of 1% annual maximum water levels. For Fernandina station, predictions of extreme water level match well with the general trend of observations. With a correlation coefficient of 0·98, the error for the maximum observed extreme water level of 3·11 m (National Geodetic Vertical Datum) with 95 years of return period is 0·92%. For Pensacola station, the prediction error for the maximum observed extreme water level with a return period of 83 years is 5·5%, with a correlation value of 0·98. The frequency analysis has also been reasonably compared to the more costly Monte Carlo simulation method. Copyright © 2008 John Wiley & Sons, Ltd.