Extreme Probability Research Articles

Dynamic reliability analysis for non-stationary non-Gaussian response based on the bivariate vector translation process

Calculation of probability of exceedance for nonstationary non-Gaussian responses remains a great challenge to researchers in the field of structural reliability. In this paper, an analytical solution is proposed for calculating the mean upcrossing rate (MCR) of the non-stationary non-Gaussian responses by approximating the displacement and velocity responses with the bivariate vector translation process, in which the unified Hermite polynomial model (UHPM) is selected as the mapping function. The first four moments (i.e., mean value, standard deviation, skewness, and kurtosis) and cross-correlation function of the displacement and velocity responses needed in UHPM are estimated from some representative samples generated by random function-spectral representation method (RFSRM) and time-domain analysis. Under the Poisson assumption of the upcrossing events, the calculation of extreme value distribution or probability of exceedance for structural response can be determined with the proposed method. The proposed method is applicable to a wide range of structural responses, including asymmetric and hardening or softening responses. Three numerical examples are provided to demonstrate the efficiency and accuracy of the proposed method. It can be concluded that the proposed method provides an accurate and useful tool for dynamic reliability assessment in engineering applications.

Likelihood of compound dry and hot extremes increased with stronger dependence during warm seasons

Compound extreme climates may pose disproportionate and serious impacts on humanity and natural ecosystems, and thus it is valuable to explore the patterns and mechanisms of changes in compound climate extremes. However, quantitative analysis of extreme climate tends to be univariate statistics with a lack of focusing on the interactions between multiple climatic variables. In this study, the spatiotemporal changes in the likelihood of compound dry and hot extremes were investigated, using the copula method and the Standardized Precipitation Index (SPI). Our study demonstrated that the probability of compound dry and hot extremes increased with a stronger dependence between the SPI and temperature. The SPI and temperature showed negative correlations with large spatial difference on the global land, and variations in the negative correlation induce changes in the high-risk areas of occurring dry and hot extremes. The Mediterranean region, western United States, Southeast Asia, the Amazon, and southern Africa were typically affected. Moreover, most of the global land experienced an increase in the joint probability of concurrent dry and hot extremes as well as the conditional probability of hot under dry conditions, whereas small proportion of the global land exhibited an increase in the conditional probability of dry under hot conditions. The changes in high-risk hotspots indicate that regions with a strong negative correlation between the SPI and temperature are vulnerable to a warming climate. Our findings have implications in aiding mitigation the impacts of compound dry and hot extremes under global warming.

Can the probability of extreme returns be the basis for profitable portfolios? Evidence from China

Based on the generalized logit predicting model from Jang and Kang (2019), this paper estimates the ex-ante probability of extreme returns and finds that the significantly negative (positive) influence of the predicted crash (jackpot) probability is robust, whether based on the traditional portfolio construction, orthogonalized portfolio construction and Fame-Macbeth cross-section regression. Further analyses show both the behavioral speculators' trading and rational investors' arbitrage limits could be the sources of mispricing caused by extreme returns. Overall, this paper applies a predicting model to estimate the probabilities of the future extreme returns, and figures out the significant influence and possible sources of the crash and jackpot probabilities in China. Portfolios based on extreme return probabilities can be profitable and steady bases for uninformed investors in the Chinese stock market.

Modeling Crossing Random Seas by Fully Non-Linear Numerical Simulations

Bimodal spectrum wave conditions, known as crossing seas, can produce extreme waves which are hostile to humans during oceanic activities. This study reports some new findings of the probability of extreme waves in deep crossing random seas in response to the variation of spectral bandwidth through fully non-linear numerical simulations. Two issues are addressed, namely (i) the impacts of the spectral bandwidth on the changes of extreme wave statistics, i.e., the kurtosis and crest exceedance probability, and (ii) the suitability of theoretical distribution models for accurately describing the wave crest height exceedance probability in crossing seas. The numerical results obtained by simulating a large number of crossing sea conditions on large spatial-temporal scale with a variety of spectral bandwidth indicate that the kurtosis and crest height exceedance probability will be enhanced when the bandwidth of each wave train becomes narrower, suggesting a higher probability of encountering extreme waves in narrowband crossing seas. Meanwhile, a novel empirical formula is suggested to predict the kurtosis in crossing seas provided the bandwidth is known in advance. In addition, the Rayleigh and second-order Tayfun distribution underestimate the crest height exceedance probability, while the third-order Tayfun distribution only yields satisfactory predictions for cases with relatively broader bandwidth regarding the wave conditions considered in this study. For crossing seas with narrower bandwidth, all the theoretical distribution models failed to accurately describe the crest height exceedance probability of extreme waves.

Probabilistic Modeling of Information Dynamics in Networked Cyber–Physical–Social Systems

Cyber–physical–social systems (CPSS) are physical devices with highly integrated functions of sensing, computing, communication, and control, and are seamlessly embedded in human society. The levels of intelligence and functions that CPSS can perform rely on their extensive collaboration and information sharing through networks. In this article, information diffusion within CPSS networks is studied. Information dynamic models are proposed to characterize the evolution of information processing and decision-making capabilities of individual CPSS nodes. The data-driven statistical models are based on a mesoscale probabilistic graph model, where the individual nodes’ sensing and computing functions are represented as the probabilities of correct predictions; whereas the communication functions are represented as the probabilities of mutual influences between nodes. A copula dynamics model is proposed to explicitly capture the information dependency among individuals with joint prediction probabilities and estimated from extremal probabilities. A topology-informed vector autoregression model is proposed to represent the mutual influence of prediction capabilities. A spatial–temporal hybrid Gaussian process regression model is also proposed to simultaneously capture correlations between nodes and temporal correlation in the time series.

Analysis of Dangerous Sea States in the Northwestern Mediterranean Area

Extreme sea waves, although rare, can be notably dangerous when associated with energetic sea states and can generate risks for the navigation. In the last few years, they have been the object of extensive research from the scientific community that helped with understanding the main physical aspects; however, the estimate of extreme waves probability in operational forecasts is still debated. In this study, we analyzed a number of sea-states that occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. For this purpose, we performed phase-resolving simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We produced statistics of the sea-surface elevation field, calculating crest distributions and the probability of extreme events from the analysis of a long time-series of the surface elevation. We found a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, in contrast with a significant underestimate given by the Rayleigh distribution. We then related spectral quantities like angular spreading and wave steepness to the probability of occurrence of extreme events finding an enhanced probability for high mean steepness seas and narrow spectra, in accordance with literature results, finding also that the case study of the reported accident was not amongst the most dangerous. Finally, we related the skewness and kurtosis of the surface elevation to the wave steepness to explain the discrepancy between theoretical and numerical distributions.

Improvements to Flood Frequency Analysis on Alluvial Rivers Using Paleoflood Data

AbstractHydrologists and engineers routinely use flood frequency analyses to compute flood probabilities for mitigation, infrastructure planning, and emergency management. Conventional flood frequency analyses—in which annual discharge maxima from a stream gage are fit to a statistical probability distribution—often encounter large uncertainties when estimating extreme flood levels. Most gage records span relatively short periods of time (<100 years), and thus the most extreme and infrequently occurring flood events tend to be poorly represented in instrumental data sets. Here, we demonstrate how a new generation of paleoflood records derived from floodplain sediments can be used to improve the accuracy and precision of extreme flood probability estimates along alluvial rivers. We use a series of simulation experiments to show that incorporating large numbers of paleoflood events in flood frequency analyses can significantly reduce the uncertainty of extreme flood estimates when the paleoflood data are sufficiently accurate and precise. Our results illustrate that robust paleoflood records can improve the shape parameter of flood frequency distributions, which determine the thickness of distribution tails, when as many as 50 paleoflood events are incorporated. We conclude by demonstrating how an alluvial paleoflood data set reduces uncertainty in a flood frequency analysis for a gage on the lower Mississippi River. Finally, we provide recommendations for how to incorporate paleoflood information into flood frequency analysis to improve the accuracy of extreme flood probabilities.

Tropical cyclone contribution to extreme rainfall over southwest Pacific Island nations

Southwest Pacific nations are among some of the worst impacted and most vulnerable globally in terms of tropical cyclone (TC)-induced flooding and accompanying risks. This study objectively quantifies the fractional contribution of TCs to extreme rainfall (hereafter, TC contributions) in the context of climate variability and change. We show that TC contributions to extreme rainfall are substantially enhanced during active phases of the Madden–Julian Oscillation and by El Niño conditions (particularly over the eastern southwest Pacific region); this enhancement is primarily attributed to increased TC activity during these event periods. There are also indications of increasing intensities of TC-induced extreme rainfall events over the past few decades. A key part of this work involves development of sophisticated Bayesian regression models for individual island nations in order to better understand the synergistic relationships between TC-induced extreme rainfall and combinations of various climatic drivers that modulate the relationship. Such models are found to be very useful for not only assessing probabilities of TC- and non-TC induced extreme rainfall events but also evaluating probabilities of extreme rainfall for cases with different underlying climatic conditions. For example, TC-induced extreme rainfall probability over Samoa can vary from ~ 95 to ~ 75% during a La Niña period, if it coincides with an active or inactive phase of the MJO, and can be reduced to ~ 30% during a combination of El Niño period and inactive phase of the MJO. Several other such cases have been assessed for different island nations, providing information that have potentially important implications for planning and preparing for TC risks in vulnerable Pacific Island nations.

Numerical Analysis of Storm Surges on Canada’s Western Arctic Coastline

A numerical study was conducted to characterize the probability and intensity of storm surge hazards in Canada’s western Arctic. The utility of the European Centre for Medium-Range Weather Forecasts Reanalysis 5th Generation (ERA5) dataset to force numerical simulations of storm surges was explored. Fifty historical storm surge events that were captured on a tide gauge near Tuktoyaktuk, Northwest Territories, were simulated using a two-dimensional (depth-averaged) hydrodynamic model accounting for the influence of sea ice on air-sea momentum transfer. The extent of sea ice and the duration of the ice season has been reducing in the Arctic region, which may contribute to increasing risk from storm surge-driven hazards. Comparisons between winter storm events under present-day ice concentrations and future open-water scenarios revealed that the decline in ice cover has potential to result in storm surges that are up to three times higher. The numerical model was also used to hindcast a significant surge event that was not recorded by the tide gauge, but for which driftwood lines along the coast provided insights to the high-water marks. Compared to measurements at proximate meteorological stations, the ERA5 reanalysis dataset provided reasonable estimates of atmospheric pressure but did not accurately capture peak wind speeds during storm surge events. By adjusting the wind drag coefficients to compensate, reasonably accurate predictions of storm surges were attained for most of the simulated events. The extreme value probability distributions (i.e., return periods and values) of the storm surges were significantly altered when events absent from the tide gauge record were included in the frequency analysis, demonstrating the value of non-conventional data sources, such as driftwood line surveys, in supporting coastal hazard assessments in remote regions.

Record‐breaking daily rainfall in the United Kingdom and the role of anthropogenic forcings

AbstractThe breaking of the United Kingdom's daily rainfall record in October 2020 made a striking addition to the list of recent heavy precipitation events in the country. Mounting evidence from attribution research suggests that such extremes become more frequent and intense in a warming climate. Although most studies consider extreme events in specific months or seasons, here we investigate for the first time how extremes of the wettest day of the year may be influenced by anthropogenic forcings. Data from large multimodel ensembles indicate that the moderate historical trend towards wetter conditions will emerge more strongly in coming decades, while a notable anthropogenic influence on the variability of the wettest day may be identified as early as the 1900s. Experiments with different forcings are employed to estimate the changing probability of extremes due to anthropogenic climate change in a risk‐based attribution framework. We introduce a new methodology of estimating probabilities of extremes in the present and future that calibrates data from long simulations of the preindustrial climate to the mean state and variability of the reference climatic period. The new approach utilises larger samples of rainfall data than alternative methods, which is a major advantage when analysing extremely rare events. The record rainfall of the wettest day in year 2020 is estimated to have become about 2.5 times more likely because of human influence, while its return time, currently about 100 years, will decrease to only about 30 years by 2100. Compared to a hypothetical natural climate, we estimate a 10‐fold increase in the chances of such extreme rainfall events in the United Kingdom by the end of this century, which underlines the need for effective adaptation planning.

Method of Evaluation of Extreme Wave Probability

Method of evaluation of cumulative probability of appearance of wind waves with any given height is described. The method is based on direct modeling of wind wave fields and uses long-term dataset of significant wave height. The application of the method using wave forecast model data is presented. The disadvantages of the analyses of annually and seasonally average fields of extreme wave height probability obtained by the method are considered. Another application of evaluating of extreme wave height field based on the method is proposed.

Existence Conditions for Extremal Probability Measures on Polish Spaces and Some of Their Properties

Existence Conditions for Extremal Probability Measures on Polish Spaces and Some of Their Properties

Modeling Time-Varying Tail Dependence, with Application to Systemic Risk Forecasting

Abstract Empirical evidence for multivariate stock suggests that there are changes from asymptotic independence to asymptotic dependence and vice versa. Under asymptotic independence, the probability of joint extremes vanishes, whereas under asymptotic dependence, this probability remains positive. In this paper, we propose a dynamic model for bivariate extremes that allows for smooth transitions between regimes of asymptotic independence and asymptotic dependence. In doing so, we ignore the bulk of the distribution and only model the joint tail of interest. We propose a maximum-likelihood estimator for the model parameters and demonstrate its accuracy in simulations. An empirical application to losses on the CAC 40 and DAX 30 illustrates that our model provides a detailed description of changes in the extremal dependence structure. Furthermore, we show that our model issues adequate forecasts of systemic risk, as measured by CoVaR. Finally, we find some evidence that our CoVaR forecasts outperform those of a benchmark dynamic t-copula model.returns

A new statistical model for extreme rainfall: POT-KumGP

The accurate prediction of the extreme rainfall is of great interest in geology to make provision for nature events such as landslide. The extreme value theory is widely used to predict the daily extreme rainfall probability. In this study, we introduce a new extreme value model based on the Kumaraswamy generalized-Pareto distribution by applying it to peaks-over-threshold method. This method is shortly denoted as POT-KumGP. The extreme rainfall modeling accuracy of the POT-KumGP model is compared with a POT-GP model by means of a real data modeling on the daily rainfall data of Hopa region located in Artvin province of Turkey. The empirical results show that the POT-KumGP model produces more accurate results than POT-GP model based on the model selection criteria and result of goodness-of-fit test.

Global positive gross primary productivity extremes and climate contributions during 1982–2016

Gross primary production (GPP) quantifies the photosynthetic uptake of carbon by the terrestrial ecosystem. Positive GPP extremes represent the potential capacity of the terrestrial ecosystem to uptake carbon dioxide. Studying the positive GPP extreme is vital for the global carbon cycle and mitigation of global warming. With increasing climate extreme events, many kinds of research focus on studying negative GPP and the negative impact of climatic extremes on GPP. There is still a lack of research on positive GPP extremes and whether climatic extremes could be beneficial to global carbon uptake. In this study, we used daily Boreal Ecosystem Productivity Simulator (BEPS) to simulate GPP of the global terrestrial ecosystem during 1982–2016 and combined TRENDY models to detect positive GPP extremes and investigate the effects of climate extremes on GPP. We found the results of the TRENDY models have large differences in some areas of the globe, and the BEPS model driven by remote sensing data could be more suitable for simulating the long-term time series of global terrestrial GPP. Compared to other plant functional types, grasslands contributed the most to positive GPP extremes, accounting for approximately 41.6% (TRENDY) and 34.8% (BEPS) of the global positive GPP extremes. The probabilities of positive GPP extremes caused by positive precipitation extremes were significantly higher than those caused by temperature and radiation in most areas of the globe, indicating that sufficient precipitation (not a flood) would boost the carbon uptake ability of the global terrestrial ecosystem to form positive GPP extremes. On the contrary, the partial correlation coefficients between temperature and GPP were negative in most areas of globe, suggesting that global warming will not be conducive to carbon uptake of the terrestrial ecosystem. This study may provide new knowledge on the global positive GPP extremes.

Precipitation Characteristics and Future Changes Over the Southern Slope of Tibetan Plateau Simulated by a High‐Resolution Global Nonhydrostatic Model

AbstractCurrent climate model resolution cannot accurately describe the complex topography over the Tibetan Plateau, which limits our understanding of past and future precipitation over this region. This study investigates the daily precipitation characteristics and its future changes over the Tibetan Plateau, especially for the southern slope of Tibetan Plateau (SSTP), by 14‐km Nonhydrostatic ICosahedral Atmospheric Model (NICAM) with explicitly calculated convection for historical and future 30‐years period. By comparing with the satellite Global Precipitation Measurement (GPM), NICAM well reproduces the historical precipitation spatial pattern, seasonal cycle, and the extreme precipitation belt over SSTP, but overestimates precipitation amount by ∼35%. It is found that heavy precipitation probability decreases as elevation becomes higher while the light precipitation generally shows the opposite. For the precipitation changes during June to September from 1979–2008 to 2075–2104, NICAM predicts that mean precipitation will decrease over low‐level SSTP but increase over high‐level SSTP. Nonprecipitation and heavy precipitation probability will increase while light precipitation probability will decrease in the future over SSTP. The extreme precipitation probability and intensity will increase ∼50%/°C and ∼8%/°C over SSTP, and this increase is more obvious as elevation becomes higher. The robust increase of extreme precipitation along the SSTP topography is unique and has not been identified by the climate model simulations before. The strong meridional gradient of specific humidity over SSTP is found to be further enhanced under global warming, and this gradient enhancement is suggested to be responsible for the increase in the extreme precipitation over SSTP.

Are Kenya Meteorological Department heavy rainfall advisories useful for forecast-based early action and early preparedness for flooding?

Abstract. Preparedness saves lives. Forecasts can help improve preparedness by triggering early actions as part of pre-defined protocols under the Forecast-based Financing (FbF) approach; however it is essential to understand the skill of a forecast before using it as a trigger. In order to support the development of early-action protocols over Kenya, we evaluate the 33 heavy rainfall advisories (HRAs) issued by the Kenya Meteorological Department (KMD) during 2015–2019. The majority of HRAs warn counties which subsequently receive heavy rainfall within the forecast window. We also find a significant improvement in the advisory ability to anticipate flood events over time, with particularly high levels of skill in recent years. For instance actions with a 2-week lifetime based on advisories issued in 2015 and 2016 would have failed to anticipate nearly all recorded flood events in that period, whilst actions in 2019 would have anticipated over 70 % of the instances of flooding at the county level. When compared against the most significant flood events over the period which led to significant loss of life, all three such periods during 2018 and 2019 were preceded by HRAs, and in these cases the advisories accurately warned the specific counties for which significant impacts were recorded. By contrast none of the four significant flooding events in 2015–2017 were preceded by advisories. This step change in skill may be due to developing forecaster experience with synoptic patterns associated with extremes as well as access to new dynamical prediction tools that specifically address extreme event probability; for example, KMD access to the UK Met Office Global Hazard Map was introduced at the end of 2017. Overall we find that KMD HRAs effectively warn of heavy rainfall and flooding and can be a vital source of information for early preparedness. However a lack of spatial detail on flood impacts and broad probability ranges limit their utility for systematic FbF approaches. We conclude with suggestions for making the HRAs more useful for FbF and outline the developing approach to flood forecasting in Kenya.

Climate models capture key features of extreme precipitation probabilities across regions

Quantitative simulation of precipitation in current climate has been an ongoing challenge for global climate models. Despite serious biases in correctly simulating probabilities of extreme rainfall events, model simulations under global warming scenarios are routinely used to provide estimates of future changes in these probabilities. To minimize the impact of model biases, past literature tends to evaluate fractional (instead of absolute) changes in probabilities of precipitation extremes under the assumption that fractional changes would be more reliable. However, formal tests for the validity of this assumption have been lacking. Here we evaluate two measures that address properties important to the correct simulation of future fractional probability changes of precipitation extremes, and that can be assessed with current climate data. The first measure tests climate model performance in simulating the characteristic shape of the probability of occurrence of daily precipitation extremes and the second measure tests whether the key parameter governing the scaling of this shape is well reproduced across regions and seasons in current climate. Contrary to concerns regarding the reliability of global models for extreme precipitation assessment, our results show most models lying within the current range of observational uncertainty in these measures. Thus, most models in the Coupled Model Intercomparison Project Phase 6 ensemble pass two key tests in current climate that support the usefulness of fractional measures to evaluate future changes in the probability of precipitation extremes.

Efficient Computation of Extreme Excursion Probabilities for Dynamical Systems through Rice's Formula

We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses a Markov chain Monte Carlo or a Laplace approximation approach to construct a biasing distribution that in turn is used in an importance sampling procedure to estimate the extreme excursion probabilities. The prior and likelihood of the biasing distribution are obtained by using Rice's formula from excursion probability theory. We use Gaussian mixture biasing distributions and approximate the non-Gaussian initial state distribution by the method of moments to circumvent the linearity and Gaussianity assumptions needed by excursion probability theory. The method requires the tangent linear model of the nonlinear dynamical system to be bounded. Additionally, our method works best when the uncertainty-induced trajectories of the nonlinear dynamical system are small perturbations around a mean linear trajectory and thus when the target system exhibits only mild nonlinearity. We demonstrate the effectiveness of this computational framework for nonlinear dynamical systems of up to 100 dimensions.

Climate Extremes along the Mining Chain over the Eastern Amazon: Projections to 2050

The mineral industry is of great importance for the economy and for the development of Brazil. However, climate change further accentuates the impacts caused by extreme weather and climate events on the logistics and operation processes of the mineral production chain (from the mine to the port). In order to reduce these effects, it is essential to have information about the future climate that will help this economic sector to carry out better long-term planning of its activities. However, the current scientific literature still lacks studies with this approach applied to the mineral industry. Therefore, the purpose of this study was to evaluate the future seasonal patterns of climate extremes in eastern Amazonia, exploring their impacts on the mineral production chain in the near future (2019-2050). To categorize the dry and rainy climate extremes, the Standard Precipitation Index (SPI) was calculated for the precipitation data series of Climate Prediction Center (CPC) observations and the PRECIS regional modeling system, considering the IPCC RCP4.5. The 1981-2005 period was defined as the present climate and used to assess the performance of the modeling system in reproducing the extremes. The analyses were based on the relative frequency of the categories of dry and rainy extremes. The performance evaluation of PRECIS showed that it had better accuracy in representing seasonal extremes of drought than extremes of rain. Along the mineral chain in eastern Amazonia, its accuracy was better over the port region, except for the dry extremes experienced from June to August (JJA), and from December to February (DJF) and March to May (MAM) for rainy extremes. The analysis of the frequency of occurrence of these events for the future indicates a greater probability of rain extremes along the mineral chain compared to another category of extremes. In addition, JJA will be the most suitable period to optimize operational processes in eastern Amazonia, as extremes are less likely to occur. On the other hand, the greater probability of extreme rain events from September through to November (SON) and MAM make these two periods less suitable for activity in the mining regions and areas north of the railway. The results of this study suggest an increasing risk to the processes of the mineral chain until 2050 associated with the occurrence of climate extremes, since it is susceptible to adverse weather conditions.