Extreme Value Type Research Articles

Flood frequency analysis in the lower Burhi Dehing River in Assam, India using Gumbel Extreme Value and log Pearson Type III methods

Flood is a widespread climate-related hazard with the potential to occur in almost any geographical location where fluvial processes are active and can occur due to the involvement of multiple factors. Flood frequency analysis (FFA) is considered a valuable hydrologic tool to know the magnitude and frequency of the recurrence of floods. In this research, we have examined the Lower Burhi Dehing River (LBDR) in Assam, India, which frequently experiences severe flooding due to its meandering course induced by heavy monsoon rainfall. Therefore, the present research aims to analyze past flood events and current trends and predict future flood frequencies using Gumbel’s extreme value distribution and Log Pearson Type III Method. In this particular investigation, 25 years of annual maximum peak discharge data from 1972 to 1997 was employed to examine the discharge records of LBDR. This research estimated the return periods of different flood magnitudes, quantifying the likelihood of future floods with varying degrees of severity. In this regard, the return periods are estimated at 2, 5, 10, 20, 50, 100, and 200 years. The study reveals that the largest flood event occurred in 1972, with a discharge of 1134.4 m3/s, and the smallest flood event occurred in 1997, with a discharge of 214.65 m3/s. The 2-year flood is a relatively common event with a 50% probability of occurring in any given year, characterized by a moderate discharge of 1384.90 m3/s and minor impacts of 0.3665. The 5-year flood, occurring with a 20% chance annually, brings a significantly higher water level of 2008.81 m3/s and moderate-to-severe impacts of 1.4999, potentially causing widespread flooding. In the 10-year and 50-year return period, which has a probability of returning 10% and 2% chance annually, the discharge will reach 2421.89 m3/s and 3331.01 m3/s, respectively. The outcome of this research will sustainably guide policymakers and environmental planners to mitigate flood hazards.

Forecasting the design maxima water discharges of floods on the Latorica river according to the data of the Mukachevo gauging station using plotting position formulas

This article presents the results of forecasting design maxima discharges on the Latorica River within Mukachevo town based on hydrological observation data at the “Mukachevo” gauging station using plotting position formulas. While solving the task, a novel non-parametric method of forecasting using observation data is applied. The method includes extrapolating the discrepancy (divergence, disagreement) between the estimates of the statistical annual probabilities of exceedance obtained by different plotting position formulas. The task is considered in the frame of the stationarity hypothesis of the maximum river flow employing a time series of maximal discharges of the Latorica River observed at the “Mukachevo” gauging station from 1947 to 1999.We involved the thirteen plotting position formulas. There was no specific criterion for choosing them to solve the task. All applied formulas were considered admissible options, and results obtained after using them – expert judgments reflecting decision-makers’ predisposition to more cautious or less expensive decision options in flood management strategies.The epistemic uncertainty of the different plotting positions was reduced by employing the Fishburn rule. According to this rule, the significance of various plotting positions was given by arranging their estimates in descending order of importance of their values under decision-making. Depending on the selected significance option assignment of the different plotting position formulas, such rank-weighted estimates of the design peak discharges (each of them for annual exceedance probability 1%, 0.5%, and 0.2%) were computed: (1) the rank-weighted upper bound estimate (sup-estimate) corresponding to the predisposition to more cautious decision options; (2) the rank-weighted lower bound estimate (inf-estimate) corresponding to the predisposition to less expensive decision options. As possible control theoretical alternatives for forecasting design maximal discharges considered were five parametric probability distributions: 1) the Kritskyi-Menkel three-parameter gamma distribution; 2) Pearson’s type III distribution; 3) the Extreme value type I distribution (Gumbell’s type I distribution); 4) the Logarithmic Pearson type III distribution; and 5) the Two-parameters logarithmic-normal distribution. The population statistical parameters for these parametric probability distributions were estimated from the sample statistics by the method of moments.

Rainfall Frequency Analysis of Some Cities in Niger Delta Region of Nigeria

Rainfall frequency analyses for four cities namely Benin City, Port Harcourt, Calabar and Uyo in Nigeria's Niger Delta area were carried out utilizing daily rainfall data from the yearly maxima series for 48 years (1965 – 2012) at each location. The study's goal was to identify the probability distribution model that fit the data the best and applicable to each location from among six candidate probability distribution models namely: Pearson Type III (PIII), log Normal (LN), log Pearson Type III, Generalized Extreme value (GEV), Extreme value type I (EVI), and Generalized Pareto (GPA). The method of moments (MOM) was used to estimate the distributions' parameters applying the outcomes of seven goodness of fit tests, the most optimal fit distribution model was chosen for each site namely Root Mean Squared Error (RMSE), Relative Root Mean Square Error (RRMSE), Maximum Absolute Derivation Index (MADI), Chi–Square etc. The best distribution model at each location was utilized to predict rainfall of desired return periods. Based on our findings, PIII for Benin City, GEV for Port Harcourt, GEV for Calabar and EVI and LN for Uyo are the distribution models that suit the data the best., The Best Fit Probability Distribution Model predicted rainfall return values (RT) at 200 years return period ranging from192.92mm at Uyo, 185mm at Port Harcourt; 218mm for Benin City; and 245 mm at Calabar.. The study's findings are helpful in the planning, designing, and maintaining of hydraulic structures for preventing flood damage and mitigating floods at the locations

Statistical analysis of wind load probabilistic models considering wind direction and calculation of reference wind pressure values in Liaoning Province, China

Wind pressure serves as the fundamental base for architectural design, particularly the reference wind pressure value, which affects the reliability and economy of high-rise, towering, and large-span structures. To facilitate the calculation of reference wind pressure values for design reference periods, load codes from various countries offer probabilistic distribution models for wind speed or reference wind pressure. However, the application of a uniform load probabilistic distribution model for calculating the reference wind pressure for the reference period often results in overestimation or underestimation of the reference wind pressure. To this end, this study collected annual maximum wind speed data from 34 meteorological stations in Liaoning Province, a region in Northeast China, and established extreme value type I, extreme value type III, lognormal, and generalized extreme value distribution models for the annual maximum wind speeds using the maximum likelihood method and method of moment, respectively. The goodness-of-fit test was conducted utilizing the Kolmogorov–Smirnov method. The results showed that the extreme value type III model and the method of moment achieved the best goodness-of-fit for the probabilistic distribution of annual maximum wind speeds. Based on the measured wind direction data corresponding to the annual maximum wind speed, joint probability density functions and cumulative probability density functions of wind speed and wind direction were established. Finally, the influence of different load statistical periods on the reference wind pressure was analyzed.

Gumbel (EVI)-Based Minimum Cross-Entropy Thresholding for the Segmentation of Images with Skewed Histograms

In this study, we delve into the realm of image segmentation, a field characterized by a multitude of approaches; one frequently used technique is thresholding-based image segmentation. This process divides intensity levels into different regions based on a specified threshold value. Minimum Cross-Entropy Thresholding (MCET) stands out as an independent objective function that can be applied with any distribution and is regarded as a mean-based thresholding method. In certain cases, images exhibit diverse structures that result in different histogram distributions. Some images possess symmetric histograms, while others feature asymmetric ones. Traditional mean-based thresholding methods are well-suited for symmetric image histograms, relying on Gaussian distribution definitions for mean estimations. However, in situations involving asymmetric distributions, such as left and right-skewed histograms, a different approach is required. In this paper, we propose the utilization of a Maximum Likelihood Estimation (MLE) of Gumbel’s distribution or Extreme Value Type I (EVI) distribution for the objective function of an MCET. Our goal is to introduce a dedicated image-thresholding model designed to enhance the accuracy and efficiency of image-segmentation tasks. This model determines optimal thresholds for image segmentation, facilitating precise data analysis for specific image types and yielding improved segmentation results by considering the impact of mean values on thresholding objective functions. We compare our proposed model with original methods and related studies in the literature. Our model demonstrates better performance in terms of segmentation accuracy, as assessed through both unsupervised and supervised evaluations for image segmentation.

Analysis of snow load probabilistic models and calculation of reference snow pressure using maximum likelihood method for multiple cities in Liaoning Province, China

The accurate determination of snow loads is crucial for structural design, and determining the reference snow pressure is particularly important for structures vulnerable to snow. The Load Code for the Design of Building Structures (GB50009–2012) provides a standard probabilistic model and fitting method to facilitate the calculation of reference snow pressure during the design reference period. However, using a unified load probabilistic distribution model across different provinces in China may result in overestimation or underestimation of reference snow pressure due to variations in geographic locations. Therefore, this study takes Liaoning Province, including all its cities as an example, which is the only province in northeast China that is both coastal and inland. Measured data from the Global Land Data Assimilation System (GLDAS) were used to establish the extreme value type I distribution, extreme value type III distribution, lognormal distribution, and generalized extreme value distribution models for snow depth using maximum likelihood and moment methods. The Kolmogorov–Smirnov test was used to evaluate the goodness-of-fit of the established models, and the maximum likelihood method was compared with the fitting method (moment method) recommended by the Load Code for the Design of Building Structures. The results showed that the lognormal distribution model and the maximum likelihood method achieved the best goodness-of-fit for the probabilistic distribution of snow depth. Additionally, the influence of snow density uncertainty on reference snow pressure was analyzed using measured data for snow pressure and snow depth.

Alibeyköy Havzası İçin En Uygun Taşkın Olasılık Dağılımı

Determination of peak flow rates is crucial in reducing the economic and social impact of flood. Therefore, the investigation of various methods for estimating flood is of paramount importance. Flood frequency analysis can be used as a practical method in predicting the peak flow values as the flood peaks have return periods that are typically much larger than the recording length. In this study, 7 different probability distributions (normal (N), two-parameter lognormal (LN2), three-parameter lognormal (LN3), extreme value type I (Gumbel), generalized extreme value (GEV), Pearson Type III (P3) and Log-Pearson Type III (LP3)) are employed for flood frequency analysis of Alibeyköy Watershed using 44-years of measured annual maximum flow. K-S and PPCC tests are applied to determine the most suitable distributions to estimate the flood flow rate. Based on these tests, GEV and Gumbel distributions appear to be the most preferable distributions in flood flow estimation.

A new alpha logarithmic-generated class to model precipitation data with theory and inference

Precipitation, or rainfall, is a central feature of the weather cycle and plays a vital role in sustaining life on Earth. However, existing models such as the Poisson, exponential, normal, log-normal, generalized Pareto, gamma, generalized extreme value, lognormal, beta, Gumbel, Weibull, and Pearson type III distributions used for predicting precipitation are often inadequate for precisely representing the complex pattern of rainfall. This study proposes a novel and innovative approach to address these limitations through the new alpha logarithmic-generated (NAL-G) class of distributions. The study authors thoroughly examine the NAL-G class and a unique model, the NAL-Exponential (NAL-Exp) distribution, with a focus on analyzing mathematical properties such as moments, quantile function, entropy, order statistics, and more. Six recognized classical estimation methods are employed, and extensive simulations are conducted to determine the best one. The NAL-Exp distribution demonstrates its high adaptability and value through its superior performance in modeling four distinct rainfall data sets. The results show that the NAL-Exp distribution outperforms other commonly used distribution models, highlighting its potential as a valuable tool in hydrological modeling and analysis. The increased versatility and flexibility of this new approach hold great potential for enhancing the accuracy and reliability of future rainfall predictions.

Reliability of Ensemble Climatological Forecasts

AbstractEnsemble climatological forecasts play a critical part in benchmarking the predictive performance of hydroclimatic forecasts. Accounting for the skewness and censoring characteristics of hydroclimatic variables, ensemble climatological forecasts can be generated by the log, Box‐Cox and log‐sinh transformations, by the combinations of the Bernoulli distribution with the Gaussian, Gamma, log‐normal, generalized extreme value, generalized logistic and Pearson type III distributions and by the non‐parametric resampling, empirical cumulative distribution function and kernel density estimation methods. This paper is concentrated on the reliability of the 12 types of ensemble climatological forecasts. Specifically, mathematical formulations are presented and large‐sample tests are devised to verify the forecast reliability for the Multi‐Source Weighted‐Ensemble Precipitation version 2 across the globe. Climatological forecasts of monthly precipitation over 18,425 grid cells are generated for 30 years under leave‐one‐year‐out cross validation, leading to 6,633,000 (12 × 18425 × 30) sets of ensemble climatological forecasts. The results point out that the reliability of climatological forecasts considerably varies across the 12 methods, particularly in regions with high hydroclimatic variability. One observation is that climatological forecasts tend to deviate from the distributions of observations when there is inadequate flexibility to fit precipitation data. Another observation is that ensemble spreads can be overly wide when there exist overfits of sample‐specific noises in cross validation. Through the tests of global precipitation, the robustness of the log‐sinh transformation and the Bernoulli‐Gamma distribution is highlighted. Overall, the investigations can serve as a guidance on the uses of transformations, distributions and non‐parametric methods in generating climatological forecasts.

Pipelines reliability assessment considering corrosion-related failure modes and probability distributions characteristic using subset simulation

A methodology using the subset simulation and the modified Metropolis-Hastings algorithm with delayed rejection (SS-MMHDR) is developed to evaluate the time-dependent reliability of corroded pipelines under multiple failure modes. This methodology considers the competition between the small leak and burst failures and the correlated non-normal distribution of the defect variables, and characterizes the defect geometric probability distribution from extensive inspection data. Results demonstrate that SS-MMHDR has high accuracy and low variability in evaluating the pipeline failures, outperforming the SS-MMH and Monte Carlo simulation algorithms, especially under low probability levels, but with slightly increased computation time. The Generalized Extreme Value Type II (GEVII) distribution is the optimal distribution for internal corrosion defect lengths from the Kolmogorov-Smirnov test. Lognormal, Weibull and Normal distributions provide more conservative estimates on burst and composite failure probabilities and limiting maintenance times than GEVII. Effects of operating pressure and its variability, corrosion rate on failure probability, and pipeline limiting maintenance time are also revealed through numerical cases.

Frequency Analysis of Flood Flow in Markanda Basin of Ghaggar River System in North Western India

Abstract This study aims to estimate the probabilities of occurrence and return periods of peak flood discharges over the Markanda basin of Ghaggar river system in north western India. For this purpose, two most frequently employed probability distribution models, namely Gumbel Extreme Value (GEV) and Log-Pearson Type III (LP-III) have been used to estimate the future flood discharges by means of annual extreme flood series (Qmax) data from 1990 to 2013, available at eight gauge and discharge sites. Two goodness-of-fit tests, i.e., Kolmogorov-Smirnov and Anderson-Darling have been applied to the fitted probability distributions to identify the best-fit model. The Qmax for several return periods, for example 2, 5, 10, 25, 50, 100, and 200 years have been estimated and compared. The return period for the highest Qmax recorded at Jhansa (2670 m3/s) gauge and discharge site has been computed as 9.5 and 8.2 years using the GEV and LP-III distribution model, respectively. The analyses have shown that GEV distribution model has produced the overestimated results in comparison to LP-III distribution model. Also, flood index has been computed for flood regionalization. The flood index values have been found variable at different gauge and discharge sites with an increase in return periods. Finally, the finding of this study will be valuable for water resource engineers in designing the hydraulic structures for the management of recurrent floods.

The Reliability Analysis of a Jacket Platform under Ice Loads Based on Respond Surface Method

Objective: The jacket platform is made of various types of steel pipes and beams welded, mainly used in shallow water areas, such as Bohai oilfield in China. In winter, the sea area where the platform is located will freeze, and the influence of ice load on the platform can not be ignored. So the influence of ice load on the reliability of jacket platform is studied in this paper. Methods: In this research, the finite element model of the jacket platform was established in the form of beam element, and the loads were applied from different directions to find the load direction with the greatest influence on the platform state. When calculating the ultimate load of the platform structure, it is necessary to carry out nonlinear analysis. Selecting the ice load condition, increasing the ice load step by step on the platform structure. As the applied load gradually increases, the platform will appear nonlinear, then the ultimate load of the jacket platform will be obtain. The pile radius and pile thickness are uncertain components in the reliability study of the jacket platform due to manufacture, processing, and other factors, therefore the values of the pile's parameters are all random. Consider the deviation of geometric parameters with the extreme value type I distribution of ice load, the limit state equation for the strength failure of the platform under ice loads is obtained using Response Surface Method, then the reliability of the platform is calculated by the Monte Carlo method and First Order Second Moment Reliability method. Results: By nonlinear analysis, the ultimate bearing capacity of the platform studied in this paper is about 8000kN. The reliability probability of the platform calculated by Monte Carlo method is 0.9999993, and the reliability index is 4.813. The reliability probability of the platform calculated by the first order second moment method is 0.9999994, and the reliability index is 4.852. Conclusion: The results obtained by the two methods are almost the same, and the reliability index is very large, indicating that the platform can operate safely and reliably under the ice load.

Frequency analysis of rainfall events in Karbala city, Iraq, by creating a proposed formula with eight probability distribution theories

ABSTRACT Due to its impact on the derivation of hydrological models and the safe design of sewer and storm networks, the anticipation of rainfall events should be intensively studied. In this regard, studying the rainfall events in Karbala, Iraq, has specific importance after the rapid increase in population in this city and the impact of climate change beyond 2003. Herein, the maximum daily rainfall depth of Karbala city has been analyzed to investigate and extract its probability of future occurrence using frequency analysis. Eight theoretical probability distributions, which are Weibull, Gamma, Gumbel, Log normal, Generalized Extreme Value, Normal, Exponential, and Log-Pearson Type III, were fitted using Hyfran Plus software to simulate the characteristics of the observed probability of rainfall depth. Based on the results of four statistical indicators, the exponential distribution revealed the best performance as compared with other distributions. Accordingly, ‎the synthetic storms of 24 hr were derived‎ for cumulative and incremental distribution of rainfall depth using the Soil Conservation Service method type ΙΙ for the arid and semiarid region to recurrence periods ‎‎(T = 2, 5, 10, 15, 25, 50, 100, 200, and 500), also the rainfall intensity duration frequency curves were developed. As an essential finding, new validated empirical formula has been proposed to optimize the coefficients of the location of Karbala city which may fill the gap for predicting the rainfall intensity and improving storm management strategies in Iraq.

Evaluating the Efficacy of Different DEMs for Application in Flood Frequency and Risk Mapping of the Indian Coastal River Basin

Floods are among the most occurring natural hazards that cause severe damage to infrastructure and loss of life. In India, southern Gujarat is affected during the monsoon season, facing multiple flood events in the Damanganga basin. As the basin is one of the data-scarce regions, evaluating the globally available dataset for flood risk mitigation studies in the Damanganga basin is crucial. In the present study, we compared four open-source digital elevation models (DEMs) (SRTM, Cartosat-1, ALOS-PALSAR, and TanDEMX) for hydrodynamic (HD) modeling and flood risk mapping. The simulated HD models for multiple flood events using HEC-RAS v6.3 were calibrated by adopting different roughness coefficients based on land-use land cover, observed water levels at gauge sites, and peak flood depths in the flood plain. In contrast to the previous studies on the Purna river basin (the neighboring basin of Damanganga), the present study shows that Cartosat-1 DEM provides reliable results with the observed flood depth. Furthermore, the calibrated HD model was used to determine the flood risk corresponding to 10, 25, 50, and 100-year return period floods calculated using Gumbel’s extreme value (GEV) and log-Pearson type III (LP-III) distribution techniques. Comparing the obtained peak floods corresponding to different return periods with the observed peak floods revealed that the LP-III method gives more reliable estimates of flood peaks for lower return periods, while the GEV method gives comparatively more reliable estimates for higher return period floods. The study shows that evaluating different open-source data and techniques is crucial for developing reliable flood mitigation plans with practical implications.

Max-sum test based on Spearman's footrule for high-dimensional independence tests

Testing high-dimensional data independence is an essential task of multivariate data analysis in many fields. Typically, the quadratic and extreme value type statistics based on the Pearson correlation coefficient are designed to test dense and sparse alternatives for evaluating high-dimensional independence. However, the two existing popular test methods are sensitive to outliers and are invalid for heavy-tailed error distributions. To overcome these problems, two test statistics, a Spearman's footrule rank-based quadratic scheme and an extreme value type test for dense and sparse alternatives, are proposed, respectively. Under mild conditions, the large sample properties of the resulting test methods are established. Furthermore, the proposed two test statistics are proved to be asymptotically independent. The max-sum test based on Spearman's footrule statistic is developed by combining the proposed quadratic with extreme value statistics, and the asymptotic distribution of the resulting statistical test is established. The simulation results demonstrate that the proposed max-sum test performs well in empirical power and robustness, regardless of whether the data is sparse dependence or not. Finally, to illustrate the use of the proposed test method, two empirical examples of Leaf and Parkinson's disease datasets are provided.

Determining optimal probability distributions for gridded precipitation data based on L-moments

Understanding the probability distributions of precipitation is crucial for predicting climatic events and constructing hydraulic facilities. To overcome the inadequacy of precipitation data, regional frequency analysis was commonly used by “trading space for time”. However, with the increasing availability of gridded precipitation datasets with high spatial and temporal resolutions, the probability distributions of precipitation for these datasets have been less explored. We used L-moments and goodness-of-fit criteria to identify the probability distributions of annual, seasonal, and monthly precipitation for a 0.5° × 0.5° dataset across the Loess Plateau (LP). We examined five 3-parameter distributions, namely General Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO), and Pearson type III (PE3), and evaluated the accuracy of estimated rainfall using the leave-one-out method. We also presented pixel-wise fit-parameters and quantiles of precipitation as supplements. Our findings indicated that precipitation probability distributions vary by location and time scale, and the fitted probability distribution functions are reliable for estimating precipitation under various return periods. Specifically, for annual precipitation, GLO was prevalent in humid and semi-humid areas, GEV in semi-arid and arid areas, and PE3 in cold-arid areas. For seasonal precipitation, spring precipitation mainly conforms to GLO distribution, summer precipitation around the 400 mm isohyet prevalently follows GEV distribution, autumn precipitation primarily meets GPA and PE3 distributions, and winter precipitation in the northwest, south, and east of the LP mainly conforms to GPA, PE3 and GEV distributions, respectively. Regarding monthly precipitation, the common distribution functions are PE3 and GPA for the less-precipitation months, whereas the distribution functions of precipitation for more-precipitation months vary substantially across different regions of the LP. Our study contributes to a better understanding of precipitation probability distributions in the LP and provides insights for future studies on gridded precipitation datasets using robust statistical methods.

Statistical Modeling of Rainfall Distribution in Jos, Plateau State, Nigeria


 
 
 
 Rainfall is a form of precipitation that occurs when water vapor in the atmosphere condenses into droplets which can no longer be suspended in the air. Flood is as a result of rainfall overflowing onto land. Flood is associated with a lot of negative consequences on the activities of man and animals in general and even threatens their existences. In this study, rainfall data obtained on rainfall occurrence in Jos, Plateau State were described. Five theoretical distributions; Weibull, Log-normal, Gamma, Extreme value type 1 and Log-Pearson type III distributions were fitted to the data. Kolmogorov-Smirnov and Anderson-Darling tests of goodness of fit were used to identify the most appropriate distribution. The Maximum likelihood estimator, Bayesian estimator and Principle of maximum entropy were used to estimate the parameters of the identified distribution. Alkaike information criterion (AIC) was used to compare the estimates of the parameters from the different estimators. The probability of the returning periods and the future amount of rainfall were then predicted. The results obtained show that the distribution is skewed to the left, with median annual rainfall of 2383.5mm and inter-quartile range of 432.4mm.The results obtained also show that the Log-Pearson Type III distribution best fitted the rainfall data with the Bayesian method as the best estimator of the parameters of the distribution. Results on the probability of the returning period show that it decreases as the number of years increases while the amount of rainfall increases as the number of year’s increases.
 
 
 

Intercomparison of Rainfall Estimates of Three Distributions for Computation of PFD using Rational Formula and SUH Approach

Peak flood discharge (PFD) for a given return period is considered as one of the most important parameters for planning and design of hydraulic structures, river protection works, and development of integrated water resources management projects. This can be achieved by adopting various methods such as flood frequency analysis, rational formula, envelope curves and Synthetic Unit Hydrograph (SUH) approach. Out of which, rational formula is applied for estimation of PFD for ungauged catchments with catchment area less than 25 km2 while SUH approach is adopted for ungauged catchments with catchment area more than 25 km2. This paper aims to investigate the study on intercomparison of probability distributions for estimation of extreme (i.e., 1-day maximum) rainfall for computation of PFD by adopting rational formula and SUH approach for the Vadhavan Port Project (VPP). The annual 1-day maximum rainfall series is extracted from the daily rainfall data observed at Dahanu site during the period 1969 to 2019 and also used for estimation of rainfall. The probability distributions viz., Extreme Value Type-1, 2-parameter Log Normal and Log Pearson Type-3 (LP3) adopted in extreme value analysis of rainfall is evaluated through diagnostic test using root mean square error and accordingly LP3 is adjudged as the best fit for estimation of rainfall. The 1-day maximum rainfall obtained from LP3 is considered to compute the rainfall intensity by applying one-third rule of IMD (India Meteorological Department) and also used for computation of PFD through rational formula. In SUH approach, the areal rainfall, physiographic and SUH parameters of the ungauged catchments are considered for computation of PFD. The study suggests the 25-year, 50-year and 100-year return period PFDs at six locations within the study area using rational formula and SUH approach could be considered for design purposes while designing any civil and hydraulic structures in the VPP.

Horizontal Bearing Capacity and Reliability of Piles in Coastal Soft Soil Considering the Time-Varying Characteristics

In order to study the influence of the creep of soft soil and the corrosion damage of reinforced concrete on the horizontal bearing behavior of piles, the novel p-y curve model was established considering the time-varying characteristics of soil parameters. The attenuation law of the bending stiffness of reinforced concrete piles under chloride erosion was analyzed by introducing the bending stiffness reduction factor. The limit state function of pile reliability analysis was then established considering the time-varying characteristics. The reliability index of a pile under horizontal displacement failure mode was obtained using the quadratic response surface method. Finally, the sensitivity analysis of random variables (cohesion, internal friction angle, concrete cover, and chloride concentration) on the time-varying reliability of a pile under horizontal displacement failure mode was carried out. The influence of the distribution types of soil parameters on the time-varying reliability was considered. The results show that the load-bearing characteristics of the horizontally loaded pile are impacted significantly by the time-varying characteristics of the soil. The maximum horizontal displacement of the pile increases nonlinearly with the increase in service time. When the horizontal displacement failure mode occurs, the variability in the internal friction angle has a significant impact on the reliability of the pile. The reliability index decreases nonlinearly with an increase in service time. When the soil parameters obey the extreme value type I distribution, the corresponding reliability index is greater than that of log-normal distribution and normal distribution.

An Assessment of Uncertainties in Flood Frequency Estimation Using Bootstrapping and Monte Carlo Simulation

Reducing uncertainty in design flood estimates is an essential part of flood risk planning and management. This study presents results from flood frequency estimates and associated uncertainties for five commonly used probability distribution functions, extreme value type 1 (EV1), generalized extreme value (GEV), generalized pareto distribution (GPD), log normal (LN) and log Pearson type 3 (LP3). The study was conducted using Monte Carlo simulation (MCS) and bootstrapping (BS) methods for the 10 river catchments in eastern Australia. The parameters were estimated by applying the method of moments (for LP3, LN, and EV1) and L-moments (for GEV and GPD). Three-parameter distributions (e.g., LP3, GEV, and GPD) demonstrate a consistent estimation of confidence interval (CI), whereas two-parameter distributions show biased estimation. The results of this study also highlight the difficulty in flood frequency analysis, e.g., different probability distributions perform quite differently even in a smaller geographical area.