Search Results (16)

This study delved into the analysis of hourly observed as well as future precipitation data in the towns of Willoughby and Buffalo on the Lake Erie Coast to examine the variations in IDF relationships over the 21st century. Several regional climate models (RCMs) and general circulation models (GCMs) from the Coupled Model Intercomparison Project (CMIP) Phases 5 and 6 were used. The study evaluated three RCMs with historical and Representative Concentration Pathway (RCP) 8.5 scenarios for each CMIP5 and three GCMs with historical and Shared Socioeconomic Pathways (SSPs) (126, 245, 370, and 585) scenarios for each CMIP6. The results suggested that the town of Willoughby would experience an increase of 9–46%, whereas Buffalo would experience an upsurge of 6–140% in the hourly precipitation intensity under the worst-case scenarios of RCP8.5 for CMIP5 and SSP585 for CMIP6. This increase is expected to occur in both the near (2020–2059) and far future (2060–2099), with a return period as low as 2 years and as high as 100 years when compared to the baseline period (1980–2019). The analysis indicated an increased range of 9–39% in the near future and 20–55% in the far future for Willoughby, while the Buffalo region may experience an increase of 2–95% in the near future and 3–192% in the far future as compared to the baseline period. In contrast to CMIP6 SSP585 models, CMIP5 RCP8.5 models predicted rainfall with an intensity value that is up to 28% higher in the town of Willoughby, while the reverse was true for the Buffalo region. The findings of this study are expected to be helpful for the design of water resource infrastructures. Full article

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. Full article

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. Full article

Floods are one of the most destructive natural hazards in Pakistan, causing significant damage. During monsoons, when westerly winds and concentrated rainfall occur in rivers’ catchments, floods become unmanageable. Given the limited resources of Pakistan, there has been minimal effort to quantify the amount of rainfall and runoff generated by ungauged catchments. In this study, ten hill torrents in Koh e Suleiman (District Rajanpur and DG Khan), an area affected by flash flooding in 2022 due to extreme precipitation events, were investigated. The Hydrologic Engineering Centre’s Hydrologic Modeling System (HEC-HMS), a semi-distributed event-based hydrological model, was used to delineate streams and quantify runoff. Statistical analysis of the rainfall trends was performed using the non-parametric Gumbel extreme value analysis type I distribution, the Mann–Kendall test, and Sen’s slope. The results of the study show that the total inflow to the river Indus is 0.5, 0.6, 0.7, and 0.8 MAF for 25, 50, 100, and 200 years of return period rainfall, respectively. This study presents appropriate storage options with a retention potential of 0.14, 1.14, and 1.13 MAF based on an analysis of the hydrology of these hill torrents to enhance the spate irrigation potential as flood control in the future. Full article

In order to examine the relationship between rainfall return periods and flood return periods, the design storm approach is compared to the rainfall–runoff continuous simulation and flood frequency analysis approach. The former was based on rainfall frequency analysis and event-based hydrological simulations, while the latter was based on continuous hydrological simulations and flood frequency analysis. All hydrological simulations were undertaken employing the HEC-HMS software. For the rainfall frequency analysis, the Generalized Extreme Value (GEV) probability distribution was used. For the flood frequency analysis, both the Extreme Value Type I (Gumbel) and GEV theoretical distributions were used and compared to each other. Flood hazard (inundation depth, flow velocities and flood extent) was estimated based on hydrodynamic simulations employing the HEC-RAS software. The study area was the Pineios catchment, upstream of Larissa city, Greece. The results revealed that the assumption of equivalent return periods of rainfall and discharge is not valid for the study area. For instance, a 50-year return period flood corresponds to a rainfall return period of about 110 years. Even if flow measurements are not available, continuous simulation based on re-analysis datasets and flood frequency analysis may be alternatively used. Full article

Regional flood frequency analysis (RFFA) is a powerful method for interrogating hydrological series since it combines observational time series from several sites within a region to estimate risk-relevant statistical parameters with higher accuracy than from single-site series. Since RFFA extreme value estimates depend on the shape of the selected distribution of the data-generating stochastic process, there is need for a suitable goodness-of-distributional-fit measure in order to optimally utilize given data. Here we present a novel, least-squares-based measure to select the optimal fit from a set of five distributions, namely Generalized Extreme Value (GEV), Generalized Logistic, Gumbel, Log-Normal Type III and Log-Pearson Type III. The fit metric is applied to annual maximum discharge series from six hydrological stations along the Sava River in South-eastern Europe, spanning the years 1961 to 2020. Results reveal that (1) the Sava River basin can be assessed as hydrologically homogeneous and (2) the GEV distribution provides typically the best fit. We offer hydrological-meteorological insights into the differences among the six stations. For the period studied, almost all stations exhibit statistically insignificant trends, which renders the conclusions about flood risk as relevant for hydrological sciences and the design of regional flood protection infrastructure. Full article

Realistic runoff estimates are crucial for the accurate design of stormwater drainage systems, particularly in developing urban catchments which are prone to overland flow and street inundation following extreme rainstorms. This paper derives new intensity–duration–frequency (IDF) curves for the Yalamlam area in the Kingdom of Saudi Arabia. These curves were obtained based on daily rainfall measurements and, in some short durations, across the entire study area over 30 years. The study is based on applying two distributions—the Log-Pearson type III and Gumbel—to estimate the average rainfall for the different return periods. The results show that there are slight differences between the Log-Pearson type III distribution and the Gumbel distribution, so the average parameters were used to construct the IDF curve in the Yalamlam area. The maximum daily rainfall was converted into sub-daily intervals using two methods and compared with the observed value. The new ratios were calculated using the converting rainfall from daily to sub-daily. These ratios are recommended for application in the Yalamlam area if there are no short-time-interval data available. The following ratios for 1-day rainfall were proposed: 0.37, 0.40, 0.46, 0.53, 0.61, 0.66, 0.70, 0.76, 0.80, and 0.87 for 10 min, 15 min, 30 min, 1 h, 2 h, 3 h, 4 h, 6 h, 8 h, and 12 h rainfall, respectively. The developed IDF curve for the Yalamlam district was built based on the daily and sub-daily observed data. Full article

Water-injection, oil production and water-supply pipelines are prone to pitting corrosion that may have a serious effect on their longer-term serviceability and sustainability. Typically, observed pit-depth data are handled for a reliability analysis using an extreme value distribution such as Gumbel. Available data do not always fit such monomodal probability distributions well, particularly in the most extreme pit-depth region, irrespective of the type of pipeline. Examples of this are presented, the reasons for this phenomenon are discussed and a rationale is presented for the otherwise entirely empirical use of the ‘domain of attraction’ in extreme value applications. This permits a more rational estimation of the probability of pipe-wall perforation, which is necessary for asset management and for system-sustainability decisions. Full article

Data with a multimodal pattern can be analyzed using a mixture model. In a mixture model, the most important step is the determination of the number of mixture components, because finding the correct number of mixture components will reduce the error of the resulting model. In a Bayesian analysis, one method that can be used to determine the number of mixture components is the reversible jump Markov chain Monte Carlo (RJMCMC). The RJMCMC is used for distributions that have location and scale parameters or location-scale distribution, such as the Gaussian distribution family. In this research, we added an important step before beginning to use the RJMCMC method, namely the modification of the analyzed distribution into location-scale distribution. We called this the non-Gaussian RJMCMC (NG-RJMCMC) algorithm. The following steps are the same as for the RJMCMC. In this study, we applied it to the Weibull distribution. This will help many researchers in the field of survival analysis since most of the survival time distribution is Weibull. We transformed the Weibull distribution into a location-scale distribution, which is the extreme value (EV) type 1 (Gumbel-type for minima) distribution. Thus, for the mixture analysis, we call this EV-I mixture distribution. Based on the simulation results, we can conclude that the accuracy level is at minimum 95%. We also applied the EV-I mixture distribution and compared it with the Gaussian mixture distribution for enzyme, acidity, and galaxy datasets. Based on the Kullback–Leibler divergence (KLD) and visual observation, the EV-I mixture distribution has higher coverage than the Gaussian mixture distribution. We also applied it to our dengue hemorrhagic fever (DHF) data from eastern Surabaya, East Java, Indonesia. The estimation results show that the number of mixture components in the data is four; we also obtained the estimation results of the other parameters and labels for each observation. Based on the Kullback–Leibler divergence (KLD) and visual observation, for our data, the EV-I mixture distribution offers better coverage than the Gaussian mixture distribution. Full article

In the design of offshore platforms, the height of the bottom deck directly affects the safety and engineering cost of the entire platform. It is a very important scale parameter in platform planning. The American Petroleum Institute (API) specification shows that the key to determining the height of the bottom deck lies in the wave height and calculation of the return level of the water increase. Based on the perspective of stochastic processes, this paper constructs a new distribution function model for joint parameter estimation of the marine environment. The new model uses a family of random variables to show the statistical characteristics of design wave height and water increase in both time and space, with extreme value expanded EED-I type distribution used as marginal distribution. The new model performs statistical analysis on the measured hydrological data of the Naozhou Station during the flood period from 1990 to 2016. The Gumbel–Copula structure function is used as the connection function, and the compound distribution model of the wave height and the water increase is used to obtain the joint return level of the wave height and the water increase and through which the bottom deck height of the area is calculated. The results show that the stochastic compound distribution improves the issue of the high design value caused by simple superposition of univariate return levels. The EED-I type distribution still has good stability under the condition of less measured data. Thus, under the premise of ensuring the safety of the offshore platform, less measured data can still be used to calculate the height of the bottom deck more accurately. Full article

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given. Full article

We conducted a study on climate-driven flash flood risk in the Boise River Watershed using flood frequency analysis and climate-driven hydrological simulations over the next few decades. Three different distribution families, including the Gumbel Extreme Value Type I (GEV), the 3-parameter log-normal (LN3) and log-Pearson type III (LP3) are used to explore the likelihood of potential flash flood based on the 3-day running total streamflow sequences (3D flows). Climate-driven ensemble streamflows are also generated to evaluate how future climate variability affects local hydrology associated with potential flash flood risks. The result indicates that future climate change and variability may contribute to potential flash floods in the study area, but incorporating embedded-uncertainties inherited from climate models into water resource planning would be still challenging because grand investments are necessary to mitigate such risks within institutional and community consensus. Nonetheless, this study will provide useful insights for water managers to plan out sustainable water resources management under an uncertain and changing climate. Full article

Hydrological studies are useful in designing, planning, and managing water resources, infrastructure, and ecosystems. Probability distribution models are applied in extreme flood analysis, drought investigations, reservoir volumes studies, and time-series modelling, among other various hydrological studies. However, the selection of the most suitable probability distribution and associated parameter estimation procedure, as a fundamental step in flood frequency analysis, has remained the most difficult task for many researchers and water practitioners. This paper explains the current approaches that are used to identify the probability distribution functions that are best suited for the estimation of maximum, minimum, and mean streamflows. Then, it compares the performance of six probability distributions, and illustrates four fitting tests, evaluation procedures, and selection procedures through using a river basin as a case study. An assemblage of the latest computer statistical packages in an integrated development environment for the R programming language was applied. Maximum likelihood estimation (MLE), goodness-of-fit (GoF) tests-based analysis, and information criteria-based selection procedures were used to identify the most suitable distribution models. The results showed that the gamma (Pearson type 3) and lognormal distribution models were the best-fit functions for maximum streamflows, since they had the lowest Akaike Information Criterion values of 1083 and 1081, and Bayesian Information Criterion (BIC) values corresponding to 1087 and 1086, respectively. The Weibull, GEV, and Gumbel functions were the best-fit functions for the annual minimum flows of the Tana River, while the lognormal and GEV distribution functions the best-fit functions for the annual mean flows of the Tana River. The choices of the selected distribution functions may be used for forecasting hydrologic events and detecting the inherent stochastic characteristics of the hydrologic variables for predictions in the Tana River Basin. This paper also provides a significant contribution to the current understanding of predicting extreme hydrological events for various purposes. It indicates a direction for hydro-meteorological scientists within the current debate surrounding whether to use historical data and trend estimation techniques for predicting future events with issues of non-stationarity and underlying stochastic processes. Full article

It is of vital importance in statistical distributions to fit rainfall data to determine the maximum amount of rainfall expected for a specific hydraulic work. Otherwise, the hydraulic capacity study could be erroneous, with the tragic consequences that this would entail. This study aims to present the Dagum distribution as a new statistical tool to calculate rainfall in front of frequent statistical distributions such as Gumbel, Log-Pearson Type III, Gen Extreme Value (GEV) and SQRT-ET max. The study was performed by collecting annual rainfall data from 52 meteorological stations in the province of Badajoz (Spain), using the statistical goodness-of-fit tests of Anderson–Darling and Kolmogorov–Smirnov to establish the degree of fitness of the Dagum distribution, applied to the maximum annual rainfall series. The results show that this distribution obtained a flow 21.92% greater than that with the traditional distributions. Therefore, in the Southwest of Spain, the Dagum distribution fits better to the observed rainfall data than other common statistical distributions, with respect to precision and calculus of hydraulics works and river flood plains. Full article

The aim of this study was to determine the best probability distributions for calculating the maximum annual daily precipitation with the specific probability of exceedance (P_maxp%). The novelty of this study lies in using the peak-weighted root mean square error (PWRMSE), the root mean square error (RMSE), and the coefficient of determination (R²) for assessing the fit of empirical and theoretical distributions. The input data included maximum daily precipitation records collected in the years 1971–2014 at 51 rainfall stations from the Upper Vistula Basin, Southern Poland. The value of P_maxp% was determined based on the following probability distributions of random variables: Pearson’s type III (PIII), Weibull’s (W), log-normal, generalized extreme value (GEV), and Gumbel’s (G). Our outcomes showed a lack of significant trends in the observation series of the investigated random variables for a majority of the rainfall stations in the Upper Vistula Basin. We found that the peak-weighted root mean square error (PWRMSE) method, a commonly used metric for quality assessment of rainfall-runoff models, is useful for identifying the statistical distributions of the best fit. In fact, our findings demonstrated the consistency of this approach with the RMSE goodness-of-fit metrics. We also identified the GEV distribution as recommended for calculating the maximum daily precipitation with the specific probability of exceedance in the catchments of the Upper Vistula Basin. Full article