Extreme Value Distribution Research Articles

Effects of damage initiation points of depth-damage function on flood risk assessment

The flood depth in a structure is a key factor in flood loss models, influencing the estimation of building and contents losses, as well as overall flood risk. Recent studies have emphasized the importance of determining the damage initiation point (DIP) of depth-damage functions, where the flood damage is assumed to initiate with respect to the first-floor height of the building. Here we investigate the effects of DIP selection on the flood risk assessment of buildings located in Special Flood Hazard Areas. We characterize flood using the Gumbel extreme value distribution’s location (μ) and scale (α) parameters. Results reveal that average annual flood loss (AAL) values do not depend on μ, but instead follow an exponential decay pattern with α when damage initiates below the first-floor height of a building (i.e., negative DIP). A linear increasing pattern of the AAL with α is achieved by changing the DIP to the first-floor height (i.e., DIP = 0). The study also demonstrates that negative DIPs have larger associated AAL, thus contributing substantially to the overall AAL, compared to positive DIPs. The study underscores the significance of proper DIP selection in flood risk assessment.

APPLICATION OF GENERALIZED EXTREME VALUE DISTRIBUTION TO ANNUAL MAXIMUM RAINFALL

Generalized Extreme Value Distributions was used to model annual maximum rainfall data in Akure, Ondo State, Nigeria from 1981-2019. The parameters of the distribution are estimated using the maximum likelihood estimation method. The model fit indicated that the shape parameter is negative this suggests that Fréchet distribution is the appropriate model for describing annual maximum rainfall in Ondo-state Nigeria. The estimated return levels for different return periods revealed an increase in the value over the years.

China's future wind energy considering air density during climate change

To assess the impact of air density on future wind resources under representative concentration pathway (RCP) scenarios (RCP2.6, RCP4.5, and RCP8.5), the Coordinated Regional Downscaling Experiment-East Asia project was utilized to simulate the future air density characteristics of China (2021–2100). Empirical air density distributions were calculated, and fourteen probability density functions were fitted to the empirical air density distributions, determining the optimal fitted distribution functions. In this study, the effect of air density on the annual energy production and wind power density was quantified. The results indicated that only approximately 4 % of regional air density values reaches the standard air density under the three climate scenarios. The seven parameter Generalized Extreme Value-Generalized Extreme Value distribution, six parameter Gamma-Generalized Extreme Value distribution, and six parameter Exponentiated Weibull- Generalized Extreme Value distribution matched the empirical distributions well under RCP2.6, RCP4.5, and RCP8.5, respectively. Annual energy production and wind power density decreased by more than 15 % after considering air density. Under the different RCP scenarios (RCP2.6, RCP4.5, and RCP8.5), the errors of annual energy production and wind power density gradually escalate. In the Tibetan Plateau region, accounting for air density results in an overestimation of annual energy production by over 40 % and wind power density by more than 35 %. The findings of this study offer guidance for future wind energy resource planning, enabling optimal utilization of wind energy resources.

Performance assessment of corroded stiffened steel plates considering non-Gaussian spatial correlated corrosion random field

This paper investigates the effect of corrosion randomness on the compression performance of stiffened steel plates. An anisotropic non-Gaussian random filed model is proposed to characterize the corrosion depth of the corroded steel plate surface. The specimens of corroded steel plate were obtained utilizing the artificial climate environment method. Corrosion characteristics were measured through 3D-scanning and reverse modeling. Statistical methods are utilized to analyze corrosion depth, including probability distribution and correlation coefficient. Two models are proposed for steel plate placing flatly and inclinedly, respectively. It is found that for both models corrosion depth follows truncated GEV distribution, and the correlation coefficient follows a bidirectional exponential function. To investigate the effect of non-Gaussian and correlation characteristics on bearing capacity, the proposed model is used for generating anisotropic non-Gaussian corrosion random fields for stiffened steel plates. Generated samples were used for finite element analysis. It is found the ignorance of non-Gaussian or correlation of the corrosion depth field will underestimate the deterioration of bearing capacity of stiffened steel plates. Finally, a parametric study on the correlation coefficients of the corrosion field indicates that correlation length will affect the residual bearing capacity of corroded steel plate. The proposed random field for corrosion depth of steel plate could be used for potential application on the safety assessment of corroded steel structures.

Testing the number of common factors by bootstrapped sample covariance matrix in high-dimensional factor models

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions.

A study on wave climate variability along the nearshore regions of Bohai Sea based on long term observation data

The Bohai Sea off the coast of northern China plays important economic and ecological roles. No studies have been conducted on wave characteristics in the Bohai Sea nearshore area using ocean station data in the past. Observational data (1998–2022) from eight ocean-stations in the Bohai Sea were used in the present study. Overall, wave height (Hs) was small; winter seasons had higher Hs than summer seasons, and the maximum Hs occurred in the Bohai Strait. Joint distribution analysis indicated that waves with Hs ranging from 0.2 to 0.4 m, and mean wave periods (Tm) ranging from 3 to 3.5 s, were most common. Hs in the Bohai Sea nearshore area showed a weak response to climate variability and was moderately correlated with the Ocean Niño Index (ONI) and the North Pacific Index (NPI) in winter, and with the Arctic Oscillation (AO) in summer. Under extreme conditions, Hs was best described by a Generalized Pareto distribution, Tm was best described by a GEV distribution, and wave directions mainly followed a t location-scale distribution. The maximum wave height (Hmax)/Hs was 1.51, and the ratio varied with location. Machine learning methods were used to calculate Hmax more precisely, and they yielded better results than statistical methods.

Modelling multidecadal variability in flood frequency using the Two-Component Extreme Value distribution

The Two-Component Extreme Value (TCEV) distribution is traditionally known as the exact distribution of extremes arising from Poissonian occurrence of a mixture of two exponential exceedances. In some regions, flood frequency is affected by low-frequency (decadal) climate fluctuations resulting in wet and dry epochs. We extend the exact distribution of extremes approach to such regions to show that the TCEV arises as the distribution of annual maximum floods for Poissonian occurrences and (at least two) exponential exceedances. A case study using coastal basins in Queensland and New South Wales (Australia) affected by low-frequency climate variability, shows that the TCEV produces good fits to the marginal distribution over the entire range of observed values without the explicit need to resort to climate covariates and removal of potentially influential low values. Moreover, the TCEV reproduces the observed dog-leg, a key signature of different flood generation processes. A literature review shows that the assumptions underpinning the TCEV are conceptually consistent with available evidence on climate and flood mechanisms in these basins. We provide an extended domain of the TCEV distribution in the L-moment ratio diagram to account for the wider range of parameter values encountered in the case study and show that for all basins, L-skew and L-kurtosis fall within the extended domain of the TCEV.

Impact of Climate Change on Extreme Rainfall Events and Pluvial Flooding Risk in the Vojvodina Region (North Serbia)

Extreme precipitation events, which are common natural hazards, are expected to increase in frequency due to global warming, leading to various types of floods, including pluvial floods. In this study, we investigated the probabilities of maximum 3-day precipitation amount (Rx3day) occurrences during spring in the Vojvodina region, covering both past (1971–2019) and future (2020–2100) periods. We utilized an ensemble of eight downscaled, bias-corrected regional climate models from the EURO-CORDEX project database, selecting the RCP8.5 scenario to examine future Rx3day amounts. The probabilities of occurrences of Rx3day were modeled using the GEV distribution, while the number of events where Rx3day in spring exceeds specific thresholds was modeled using the Poisson distribution. The results indicate that Rx3day with a ten-year return period during the spring months is expected to increase by 19% to 33%. Additionally, the probabilities of having more than one event where Rx3day exceeds thresholds are projected to rise by 105.6% to 200.0% in the future compared to the historical period. The analysis comparing the design values of Rx3day with future projections for the period 2020–2100 revealed that 51 drainage systems are likely to function without difficulties under future climate conditions. However, for the remaining 235 drainage systems, an increased risk of pluvial flooding was identified, as their design precipitation amounts are lower than the future projections. This study reveals that analyzing extreme rainfall events in the context of climate change yields crucial information that facilitates effective planning and policy making in water management, particularly flood protection.

Assessing the impact of reaction time on the crossing and merging conflicts and identifying suitable reaction time to detect the critical conflict

ABSTRACT Due to the increased vehicular traffic in developing countries, safety in mixed traffic conditions has become a concern. When critical speed was used with surrogate safety measures to identify critical conflicts, studies assumed some driver reaction time without any analysis. This study aims to assess the impact of different reaction times on the Percentage of Critical Conflicts (PCC) and identify the suitable reaction time for critical conflict identification. Post Encroachment Time was used in this study to assess the safety of crossing and merging traffic at unsignalized T-intersections. It was observed that an increase of 1 s reaction time increases 26.92% of PCC. PET extremes of different reaction times were modelled using Generalized Extreme Value distribution. The 1-second reaction time was found suitable as the estimated crash frequencies were similar to the actual field crashes. This approach could also be employed in the homogenous traffic conditions for critical conflict identification.

Event-based rainfall analysis in Sinai, Egypt

ABSTRACT This study investigates event-based rainfall characteristics in Sinai (Egypt) using hourly precipitation data from the Global Satellite Mapping of Precipitation (GSMaP). A hierarchical cluster analysis of a 19-year dataset (2003–2021) identified five regions in Sinai. Distinct storms were identified using a minimum inter-event time of 5 h. The analysis of storm characteristics revealed that rainfall events in Sinai last from 1.7 to 3.6 h, with a mean storm volume of 6.4 mm. Rainfall intensity ranges from 1.7 to 4 mm/h, and the average dry period duration is 34 days. The northern region has the highest frequency of storms (25 events/year). The Weibull distribution was found to fit the best for all rainfall characteristics except for intensity, which was best represented by the generalized extreme value distribution. This study provides valuable insights about rainfall events in Sinai that can be applied to improve flood mitigation strategies and water resources management.

Interannual variations in the seasonal cycle of extreme precipitation in Germany and the response to climate change

Abstract. Annual maxima of daily precipitation sums can be typically described well with a stationary generalized extreme value (GEV) distribution. In many regions of the world, such a description does also work well for monthly maxima for a given month of the year. However, the description of seasonal and interannual variations requires the use of non-stationary models. Therefore, in this paper we propose a non-stationary modeling strategy applied to long time series from rain gauges in Germany. Seasonal variations in the GEV parameters are modeled with a series of harmonic functions and interannual variations with higher-order orthogonal polynomials. By including interactions between the terms, we allow for the seasonal cycle to change with time. Frequently, the shape parameter ξ of the GEV is estimated as a constant value also in otherwise instationary models. Here, we allow for seasonal–interannual variations and find that this is beneficial. A suitable model for each time series is selected with a stepwise forward regression method using the Bayesian information criterion (BIC). A cross-validated verification with the quantile skill score (QSS) and its decomposition reveals a performance gain of seasonally–interannually varying return levels with respect to a model allowing for seasonal variations only. Some evidence can be found that the impact of climate change on extreme precipitation in Germany can be detected, whereas changes are regionally very different. In general, an increase in return levels is more prevalent than a decrease. The median of the extreme precipitation distribution (2-year return level) generally increases during spring and autumn and is shifted to later times in the year; heavy precipitation (100-year return level) rises mainly in summer and occurs earlier in the year.

Areal reduction factors from gridded data products

Areal reduction factors (ARFs) convert a point estimate of extreme precipitation to an estimate of extreme precipitation over a spatial domain, and are commonly used in flood risk estimation. The fixed-area approach to ARF estimation considers an area of a certain size and constructs the ratio of extremes with the same exceedance probability for areal average precipitation and point precipitation at a representative location. In regions with sparse observation networks, estimates of areal average precipitation are highly uncertain if based on rain gauge data only. We construct and compare regional and seasonal ARF estimates for Norway using different gridded data products, both observation-based products (SURFdat, seNorge) and reanalysis products (NORA3). For data products that cover a sufficiently long time period, the extremes are estimated using the generalised extreme value (GEV) distribution, while the metastatistical extreme value (MEV) formulation is applied to data products with short records. The results indicate that the NORA3 reanalysis, available at a temporal resolution of 1 h and a spatial resolution of 3km, provides a good overall adequacy for the purpose of obtaining robust and reliable ARF estimates.

An investigation of traffic speed distributions for uninterrupted flow at blackspot locations in a mixed traffic environment

Modelling traffic characteristics is the foundation for resolving various traffic and transportation issues. Among them, traffic speed has a significant impact on roadway crashes at blackspot (BS) locations. Speed is a random variable; several studies have recommended normal distribution to characterize the distribution of traffic speed for uninterrupted flow. However, a mixed-traffic situation causes heterogeneity, and the distribution of speeds deviates from the normal distribution. The present study investigates the distributions of traffic speeds for uninterrupted flow at 18 blackspot locations and individual vehicle types in mixed-traffic environments. Seven distribution models, namely Normal, Lognormal, Gamma, Logistic, Weibull, Burr, and Generalized Extreme Value (GEV), are considered to determine the speed characteristics. Different parametric distribution models are fitted to the vehicular speeds using maximum likelihood estimation (MLE) methods. Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and two penalized criteria, i.e., Akaike and Bayesian Information Criteria (AIC and BIC), are used as goodness-of-fit (GoF) measures to find the best-fitting distribution. The overall suitability of each predicted distribution is also determined using a novel ranking method. The test findings suggest that GEV and Burr are the most suitable empirical speed distributions, with GEV fitting best above 96%. When the heavy vehicle composition (truck, bus, and tractor) is below 10%, 10–14%, 15–20%, and above 20%, it follows the Weibull, Gamma, GEV, and Burr distributions, respectively, in a mixed traffic environment.

Advanced floodplain mapping: HEC-RAS and ArcGIS pro application on Swat River

AbstractFloods stand out as one of the most devastating environmental threats worldwide resulting in the tragic loss of human lives and significant damage to our essential infrastructure. This study focuses on creating floodplain maps for the two important reaches of Swat River in the Khyber Pakhtunkhwa Province of Pakistan, namely, Kalam–Khwazakhela and Khwazakhela–Chakdara reaches. The Advanced Land Observing Satellite Phased Array Type L-band Synthetic Aperture Radar (ALOS PALSAR) 12.5 m Digital Elevation Model (DEM) data has been used for this purpose. Furthermore, the sensitivity of the flood model was assessed for the Flood 2022 event, considering simulated flood depth, extent, and velocity in relation to various terrains derived from the 12.5-m ALOS PALSAR data. To estimate extreme flows for different return periods (2, 5, 10, 25, 50, and 100 years), the Log Normal (LN), Log Pearson III (LP3), and Generalized Extreme Value (GEV) distributions were employed for the frequency analysis. The GEV distribution turned out to be the best fit for modeling the Swat River for both the Chakdara and Khwazakhela gauge stations. To predict flood levels for the peak floods identified through frequency analysis and for the specific return periods the Hydrologic Engineering Center's River Analysis System (HEC-RAS) 2D simulations were performed. Subsequently the outcomes of this model were used to create floodplain maps using Geographic Information System Professional (ArcGIS Pro) software customized for various return periods. The analysis revealed a linear increase in flood inundation area with longer return periods. The floodplain maps developed hold significant importance for the governing authorities of the Swat region. These maps serve as essential tools for implementing proactive measures against potential infrastructure damage, thereby protecting against economic losses and enhancing public safety. This research effectively combines hydrological modeling and geospatial technology offering practical solutions for managing flood risks. It serves as a valuable guide for making well-informed decisions and promoting sustainable development in flood-prone areas.

Bivariate q- generalized extreme value distribution: A comparative approach with applications to climate related data

The premise of extreme value theory focuses on the stochastic behaviour and occurrence of extreme observations in an event that is random. Traditionally for univariate case, the behaviour of the maxima is described either by the types-I, types-II or types-III extreme value distributions, primarily known as the Gumbel, Fréchet or reversed Weibull models. These are all particular cases of the generalized extreme value (GEV) model. However, in real-world scenario, these incidents take place as a consequence of concurrent dependent random events, where the relationship between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the q− generalized extreme value (q−GEV) distribution, as well as the q− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bi-variate (EV) data, arising naturally from independent q−GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model interdependent bivariate observations consisting of extreme values in terms of q−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate q−GEV. Additionally, conventional method to propose the newly defined bivariate (q−GEV) distribution with bivariate q− Gumbel distribution (a special case for ξ→0) has also been established with related inferences and application to climate data.

Structural reliability analysis under stochastic seismic excitations and multidimensional limit state based on gamma mixture model and copula function

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

Hydrological Evaluation Using the Generalized Extreme Value (GEV) Distribution Method at Tamblang Dam, Bali

The purpose of a dam is to control the water flow in a river, stream, sea, or lake. However, the water storage capacity of the dam can decrease over time due to the sediment that settles in the reservoir. Therefore, it is important to manage the water resources well and prevent problems like floods. The frequency analysis shows that the Pearson III and Gumbel Log probability distributions are the best methods to analyze the data because they have the smallest deviation values. The Generalized Extreme Value (GEV) probability distribution is the second-best method and can also be used. The GEV distribution method gives higher results for the maximum discharge in 50-, 00- and 1000-year return periods with percentages of 0.10%, 3.04% and 12.35%.

Enhancing flood risk assessment in the Johor River Basin through trivariate copula

ABSTRACT Copulas are a vital statistical tool, particularly in hydrology, for understanding complex relationships among flood characteristics. This study focuses on three key flood features: peak discharge, flood volume, and flood duration, using trivariate copulas to capture their interdependencies. This is crucial because bivariate and univariate analyses fall short in considering all three factors simultaneously. To handle extreme flood values, L-moment is proposed over maximum likelihood estimation and inference function margin due to its enhanced reliability and susceptibility to outliers and extreme values. Akaike information criterion was employed to identify the best-fit marginal distribution and copula. The Lognormal distribution effectively models peak discharge, while Weibull and generalized extreme value distributions fit flood volume and duration best, respectively. Various copula families, including elliptical and Archimedean, are assessed, where Clayton copula emerge as the most suitable. This analysis demonstrates that when more flood features are considered together, the return period increases, indicating the reduced likelihood of occurrence. The trivariate case of the AND-joint return period surpasses the trivariate case of the OR-joint return period where the TP, V, DAND=5, 405.93 years, while TP, V, DOR=500.46 years. This comprehensive approach enhances hydrological modeling and decision-making for water resource management and flood mitigation projects.

Developing Rainfall Intensity- Frequency- Duration Curves for Three Selected Sites in the Kurdistan Region, Iraq

Developing Rainfall Intensity- Frequency- Duration Curves for Three Selected Sites in the Kurdistan Region, Iraq

Sensitivity of Standardized Precipitation and Evapotranspiration Index (SPEI) to the choice of SPEI probability distribution and evapotranspiration method

Study regionThe state of Oklahoma located in the Southern Plains region of the United States. Study focusThe standardized precipitation evapotranspiration index (SPEI) is a widely used meteorological drought index that incorporates potential evapotranspiration (PET) into a precipitation-based index. However, the understanding of the appropriate PET method for SPEI across different temporal scales in non-arid climate conditions remains limited. We compared Thornthwaite (TW), Hargreaves (HG), and Penman-Monteith (PM) equations for SPEI at various accumulations, considering three temporal scales: 1) long-term (25 years), 2) event-based, and 3) monthly. Also, we examined the log-logistic and generalized extreme value distributions to test the normality of SPEI computed from the three PET methods. To do this, we utilized high-quality climate datasets measured at 107 stations across the state of Oklahoma, United States, which has a diverse climate ranging from semi-arid to humid subtropical. New hydrological insights for the regionThe log-logistic distribution was found to be suitable for SPEI. The SPEI-HG showed better agreement with SPEI-PM than SPEI-TW in this region for the analyses of three temporal scales. However, for accumulations of SPEI longer than one year, both TW and HG equations showed no significant differences with SPEI-PM. The findings provide practical guidance for selecting an appropriate PET equation in the Southern Plains region depending on the purpose of study without resorting to data-intensive methods for PET estimation.