Probability Of Extreme Events Research Articles

A wee exploration of techniques for risk assessments of extreme events

AbstractAssessing the behaviour of extreme events in univariate and multivariate settings entails many challenges, from the need to capture different sources of non-stationarity to adequately extrapolate into the tail of the distribution and compute probabilities of extreme events associated with high-dimensional vectors. Motivated by these common issues, we use a combination of methods from extreme-value theory, dimensionality reduction, non-parametric statistics, copula theory, and bootstrap model averaging to provide estimates of risk measures associated with environmental extremes. The work is tailored to the four data challenges presented in the EVA (2023) Conference Data Challenge competition, and the methods introduced here represent the approach taken by the Wee Extremes group.

Modern extreme value statistics for Utopian extremes. EVA (2023) Conference Data Challenge: Team Yalla

AbstractCapturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a modern toolbox of four methodological frameworks, motivated by classical extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13$$^\text {th}$$ th International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of “Utopia”.

Understanding uncertainty shocks and the role of black swans

Uncertainty shocks can trigger business cycles, bank runs and asset price fluctuations. But how do those shocks translate into changes in beliefs and actions? What makes people suddenly become uncertain? This paper provides an explanation for subjective uncertainty shocks, estimated on real-time GDP data, that fits puzzling features of professional forecasts. The key ingredients are that agents do not know the true model governing the distribution of macroeconomic outcomes, but they believe that distribution to be potentially skewed. When agents estimate higher probabilities of extreme tail events, their uncertainty rises. Our estimates reveal that learning about probabilities of tail events – black swans – explains much of the fluctuations in subjective uncertainty.

Spatial-temporal assessment of future population exposure to compound extreme precipitation-high temperature events across China.

Global warming has increased the probability of extreme climate events, with compound extreme events having more severe impacts on socioeconomics and the environment than individual extremes. Utilizing the Coupled Model Intercomparison Project Phase 6 (CMIP6), we predicted the spatiotemporal variations of compound extreme precipitation-high temperature events in China under three Shared Socioeconomic Pathways (SSPs) across two future periods, and analyzed the changes in exposed populations and identified influencing factors. From the result, we can see that, the CMIP6 effectively reproduces precipitation patterns but exhibits biases. The frequency of compound event rises across SSPs, especially under high radiative forcing, with a stronger long-term upward trend. Furthermore, the economically developed areas, notably China's southeastern coast and North China Plain, will be hotspots for frequent and intense compound extreme events, while other regions will see reduced exposure. Finally, in the long-term future (2070-2100), there is a noteworthy shift in population exposure to compound events, emphasizing the increasing influence of population factors over climate factors. This highlights the growing importance of interactions between population and climate in shaping exposure patterns.

Residual canopy cover provides buffering of near-surface temperatures, but benefits are limited under extreme conditions

Increasing summer temperatures and higher probabilities of extreme heat events have led to concerns about tree damage and mortality. However, insufficient attention has been given to conditions leading to heat-related regeneration failures in temperate forests. To address this, managers need to understand how microclimate varies under a range of overstory conditions. We measured air temperatures at 2 cm above-ground underneath a gradient of canopy cover on south-facing slopes in recently thinned Douglas-fir stands in western Oregon, USA. To expand the ecological relevance of these data to impacts on regeneration, we created the stress degree hours (SDH) metric, representing the amount of time—and by how much—temperatures exceeded biologically relevant stress thresholds. Overall, for every 10% increase in canopy cover, maximum temperatures at 2 cm were 1.3 °C lower, the odds of temperatures exceeding stress thresholds for conifer regeneration declined by a multiplicative factor of 0.26, and the total of SDH decreased by 40%. These reductions are large enough to be worthy of attention when managing for tree regeneration. However, data collected during the Pacific Northwest Heat Dome in June 2021 indicate that with various climate change scenarios and heatwave occurrences, temperatures will be unfavorable for regeneration regardless of overstory cover.

Tale About Inflation Tails

We study probabilities of extreme inflation events in the Unites States and the euro area. Using a state-space model that incorporates information from a large set of professional forecasters, we generate the term structure of inflation forecasts as well as probabilities of future inflation for any range of inflation outcomes in closed form at any horizon. Since the onset of the COVID-19 pandemic, inflation expectations increased materially amid heightened uncertainty about future inflation. Likelihood of significant departures of inflation targets in the longer term reached about 15 percent in the middle of 2022, increasing from near zero levels in 2020. Such an increase in the right tail of the probability distribution over future inflation outcomes drives an increase in inflation expectations and inflation risk premiums. Several popular external uncertainty measures are associated with variation in tail probabilities.

Future projections of meteorological, agricultural and hydrological droughts in China using the emergent constraint

Study regionChina. Study focusIn the context of global warming, droughts occur more frequently and have caused great losses to human society. Therefore, understanding the potential changes in future droughts under climate change is of great scientific significance for disaster prevention and mitigation. In this paper, combining with climate models from CMIP6, the emergent constraint and the skill scoring methods are used to analyze the characteristics of meteorological, agricultural and hydrological droughts in China under four socioeconomic scenarios in the mid and late 21st century. New hydrological insights for the regionIn the mid-21st century, there are more frequent meteorological, agricultural and hydrological droughts in northern China. In the late 21st century, sustained and more intense droughts are more likely to occur in China than in the mid-21st century. Additionally, the relationship between meteorological drought and agricultural/hydrological drought is strengthened to varying degrees in the future. From the perspective of extreme drought events, the probabilities of extreme drought events with long duration and high severity increase significantly in Northwest and Central China under each scenarios. In a higher socioeconomic scenario, drought is suppressed in the mid 21st century, but is intensified in the late 21st century. These findings are of great significance for drought monitoring under climate change and can provide a basis for developing measures to respond to drought.

Generative emulation of weather forecast ensembles with diffusion models.

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts by running physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While we focus on weather forecasting, this methodology may enable creating large climate projection ensembles for climate risk assessment.

Visualisation of Mahalanobis Distances for Trivariate JOINT Distributions

The Mahalanobis distance is a statistical measure used to quantify the distance between elliptic distributions with distinct locations and shared shapes, while accounting for the variables' covariance structure. It is applicable to both estimative and predictive estimation approaches, where variations are limited to location, and it assesses the similarity or dissimilarity between data and the mean (centroid) of a multivariate distribution, within the family of multivariate elliptic distributions. It is thus useful for outlier identification. The aim of the study is to provide, for the first time, a three-dimensional visualisation of the Mahalanobis distance when the underlying framework comprises three jointly connected variables (rather than the standard two variables presented in textbooks). Data with Mahalanobis distances exceeding a predefined threshold, determined using a distribution, are considered outliers. This approach is analogous to identifying outliers for univariate distributions based on critical values derived from confidence levels. While the literature mainly discusses the Mahalanobis distance formulation for bivariate distributions, we extend the discussion to include one additional variable and provide a visualisation of the resulting Mahalanobis distance for a trivariate distribution. An empirical example is presented to illustrate a practical application of a trivariate Mahalanobis distance. Visualising outliers alongside other historical events within three-factor systems can offer valuable insights into the risk profile of the current environment and assess the probability of future extreme events.

Investigating climate change effects on bridges and tunnels

The earth's climate is changing, partly from continued natural warming since the last ice age and partly man made. The changing climate with resulting more extreme weather events is likely to impact bridges and other long-life infrastructure assets. This research considers the broad effects of climate change on load effects, load combinations and material properties of bridges and tunnels. Effects such as temperature, fire, storminess, precipitation, snow, ice, wind, sea levels and acidity as they affect bridges are discussed. The uncertainty of the data in its probability and the magnitude of extreme events on these climate effects is noted and discussed in relation to resilience. Specific examples of where climate change may affect bridges and tunnels are considered, and where further research is required. A risk assessment of the likelihood and impact of climate change is presented to quantify the effects on bridges and tunnels, to support design or asset management decisions. The work is primarily based on British and north European data, but data from other parts of the world are also considered. Current code and standard provisions for design and assessment are reviewed in relation to climate change and resilience, and recommendations are outlined. Conducting asset- or region-specific risk assessments using the methods of this research is recommended.

Stochastic simulation of storm surge extremes along the contiguous United States coastlines using the max-stable process

Extreme sea levels impact coastal society, property, and the environment. Various mitigation measures are engineered to reduce these impacts, which require extreme event probabilities typically estimated site-by-site. The site-by-site estimates usually have high uncertainty, are conditionally independent, and do not provide estimates for ungauged locations. In contrast, the max-stable process explicitly incorporates the spatial dependence structure and produces more realistic event probabilities and spatial surfaces. We leverage the max-stable process to compute extreme event probabilities at gridded locations (gauged and ungauged) and derive their spatial surfaces along the contiguous United States coastlines by pooling annual maximum (AM) surges from selected long-record tide gauges. We also generate synthetic AM surges at the grid locations using the predicted distribution parameters and reordering them in the rank space to integrate the spatiotemporal variability. The results will support coastal planners, engineers, and stakeholders to make the most precise and confident decisions for coastal flood risk reduction.

Quantifying the availability of seasonal surface water and identifying the drivers of change within tropical forests in Cambodia.

Surface freshwater is a vital resource that is declining globally, predominantly due to climate and land use changes. Cambodia is no exception and the loss threatens many species, such as the giant ibis a Critically Endangered waterbird. We aimed to quantify the spatial and temporal (2000-2020) change of surface water availability across northern and eastern Cambodia and to assess the impact of this on the giant ibis. We used a Random Forest Classifier to determine the changes and we tested the impact of land use and geographical covariates using spatially explicit regression models. We found an overall reduction of surface water availability of 4.16%. This was predominantly driven by the presence of Economic Land Concessions and roads which increased the probability of extreme drying and flooding events. The presence of protected areas reduced these probabilities. We found changes in precipitation patterns over the wider landscape did not correlate with changes in surface water availability, supporting the overriding influence of land use change. 98% of giant ibis nests recorded during the time period were found within 25m of surface water during the dry season, highlighting their dependency on surface water. The overall surface water decline resulted in a 25% reduction in dry season suitable habitat for the giant ibis. Although absolute changes in surface water over the whole area were relatively small, the impact on the highest quality habitat for ibis is disproportionate and therefore threatens its populations. Defining the threats to such an endangered species is crucial for effective management.

Impacts of coal use phase-out in China on the atmospheric environment: (2) public health and global radiative forcing

In the second of two companion papers, we quantify the potential ultimate benefits for public health and radiative forcing from the phase-out of coal use in China. With the baseline year of 2015, we estimate that the premature deaths and disability-adjusted life years (DALYs) in China will be reduced by 375,000 persons and 8.90 × 106 years (GEMM model), which is 41.7% and 54.5% of the total number of premature deaths and DALYs caused by PM2.5 from anthropogenic sources, effectively improving the health of the population. The provinces with the most significant decreases in fatalities and disabilities are concentrated in large coal-consuming provinces. Regarding age distribution, the phase-out of coal use will effectively extend the life expectancy of the elderly, especially in the age group of 65–89 years. Health benefits’ growth rate upsurges notably once more than half of coal is phased out. Based on the Parallel Offline Radiative Transfer (PORT) model, the global annual average radiative forcing due to changes in short-lived climate pollutants (SLCPs), including sulfate, black carbon, organic carbon, and O3 associated with the phase-out of coal use, is 0.34 W m−2, -0.048 W m−2, 0.00064 W m−2, and 0.00055 W m−2, respectively. The complete phase-out of coal use in China also reduces the emission of long-lived climate pollutants (LLCPs) and causes negative radiative forcing. Among them, the global annual average radiative forcing of CO2, CH4, and N2O is −0.0073 W m−2, -5.48 × 10−5 W m−2, -1.60 × 10−5 W m−2. If the lifetimes of pollutants are considered, the total global reduction in heat uptake is −2.29 × 107 J m−2 over 100 years, dominated by the decrease of CO2, which will slow the rate of global warming and thus may reduce the probability of extreme weather events. This report will incentivize relevant policymakers to remove coal significantly to achieve carbon neutrality.

Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their efficiency does not degrade upon temporal and possibly spatial refinement. For that purpose, we extend algorithms based on the Laplace method for estimating the probability of an extreme event to infinite dimensional path space. The method estimates the limiting exponential scaling using a single realization of the random variable, the large deviation minimizer. Finding this minimizer amounts to solving an optimization problem governed by a differential equation. The probability estimate becomes sharp when it additionally includes prefactor information, which necessitates computing the determinant of a second derivative operator to evaluate a Gaussian integral around the minimizer. We present an approach in infinite dimensions based on Fredholm determinants, and develop numerical algorithms to compute these determinants efficiently for the high-dimensional systems that arise upon discretization. We also give an interpretation of this approach using Gaussian process covariances and transition tubes. An example model problem, for which we provide an open-source python implementation, is used throughout the paper to illustrate all methods discussed. To study the performance of the methods, we consider examples of stochastic differential and stochastic partial differential equations, including the randomly forced incompressible three-dimensional Navier–Stokes equations.

A New Statistical Distribution Derived from a Clayton Copula for Modeling Bivariate Processes

Abstract Rainfall and temperature extremes have become more frequent and severe in recent times due to changing climate. Since these catastrophic occurrences directly affect a region’s hydrology, it is imperative to develop models that can project and explain the joint behavior of climate variables. Copula functions have been used relatively successfully to capture multivariate processes. With climate being a multifaceted process, there is interdependence between variables, making copula use desirable since traditional bivariate distributions do not account for the dependent structure. In this study, we introduced a bivariate exponentiated Teissier distribution based on a Clayton copula. For parameter estimation, the maximum likelihood and inference functions for margin approaches are used. A simulation study that considered various sets of parameters is also conducted in order to select the most efficient parameter estimation method. Last, the applicability of the proposed model is demonstrated using real-world data from flood and temperature processes. After fitting, the log-likelihood, Akaike information criteria (AIC), and Bayesian information criteria (BIC) values of the proposed model are −145.00, 300.00, and 311.71 for flood data, respectively, and −128.71, 267.42, and 275.98 for temperature data, respectively. Estimated parameters are for flood data and for temperature data. It is concluded that this model may be effectively used for modeling the hydrological processes for calculating the probabilities of flood and extreme temperature events.

Wall heat flux in supersonic turbulent expansion flow with shock impingement

We perform direct numerical simulations to investigate the characteristics of wall heat flux (WHF) in the interaction of an oblique shock wave at an angle of 33.2° and free-stream Mach number M ∞ = 2.25 impinging on supersonic turbulent expansion corners with deflection angles of 0o (flat plate), 6o and 12o. The effect of the expansion on the WHF characteristics is analysed by comparing it to the interaction with the flat plate under the same flow conditions and a fixed shock impingement point. In the post-expansion region, the decreased mean WHF is found to collapse onto the flat plate case when scaled with the mean wall pressure. The statistical properties of the WHF fluctuations, including probability density function, frequency spectra, and space–time correlations, are comparatively analysed. The expansion causes an increase in the occurrence probability of negative extreme events, an enhancement of high-frequency energy, and an inhibition of intermediate-frequency energy. The increased expansion angle also results in a faster recovery of characteristic spanwise length scales and an increase in convection velocity. We use the mean WHF decomposition method in conjunction with bidimensional empirical mode decomposition to quantitatively analyse the impact of expansion on scale contributions. It is demonstrated that the presence of the expansion corner has no significant impact on the decomposed results, but it significantly reduces the contribution associated with outer large-scale structures.

Recent Increase in a Recurrent Pan-Atlantic Wave Pattern Driving Concurrent Wintertime Extremes

Abstract Wintertime extremes such as cold spells and heavy precipitation can have severe socioeconomic impacts, disrupting critical infrastructures and affecting human well-being. Here, we relate the occurrence of local and concurrent cold or wet wintertime extremes in North America and Europe to a recurrent, quasi-hemispheric wave-4 Rossby wave pattern. We identify this pattern as a fundamental mode of the Northern Hemisphere (NH) winter circulation, since wave 4 exhibits phase-locking behavior. Thus, the associated atmospheric circulation and surface anomalies reoccur over the same locations when the pattern’s wave amplitude is high. The wave pattern is most pronounced over the pan-Atlantic region, and increases the probability of extreme cold or wet events by up to 300% in certain areas of North America and Europe, as well as favoring their concurrence at different locations. High-amplitude wave-4 events have increased significantly in frequency over the past four decades (1979–2021), although no clear evidence is found relating this to modes or patterns of climate variability. The identified wave pattern may provide pathways for early prediction of local and concurrent cold or wet wintertime extremes in North America and Europe.

Future Projections of Extreme Integrated Water Vapor Transport and Population Exposure Over the Asian Monsoon Region

AbstractGlobal warming leads to an intensification of the water cycle and an increase in extreme climate events. Most previous researchers have used precipitation to project extreme hydrological changes. However, compared with precipitation, global climate models (GCMs) have a better performance in simulating the integrated vapor transport (IVT). IVT is thus a reliable tool for understanding how hydrological extremes may change in the future. In this study, we first discuss the relationship between IVT and precipitation over the Asian monsoon (AM) region during 1979–2014. We then assess the climatology, variability and extremes of IVT over the AM region and subregions using 16 GCMs from CMIP6. We further apply GCMs to project changes in the magnitude and probability of dangerous extreme IVT events (e.g., 20‐, 50‐ and 100‐year events) in the future. Finally, we quantify the population exposure to extreme IVT events, and explain change in exposure and its uncertainty. Results show that CMIP6 GCMs capture the spatial distribution of IVT well; the intensity of simulated IVT is lower than the ERA5 IVT. Under global warming of 1.5, 2, and 3°C, the magnitude of extreme events, which is independent of the return period (RP), increases over the AM region with relative changes of about 7%, 12%, and 21%, respectively. The probability increases consistently with global warming and the RP. The increase in exposure for the South Asian monsoon (East Asian monsoon) region is both contributed by more extreme IVT events and higher (fewer) population counts; the former has a larger proportion.

Projections of rainfall erosivity in climate change scenarios for mainland China

This study focuses on improving the accuracy of projections for future rainfall erosivity by selecting five CMIP6-based and bias-adjusted Global Climate Models (GCMs) in China. These models provide more precise estimations of rainfall erosivity under two future periods (2041–2065 and 2076–2100) and two emission scenarios (SSP1-RCP2.6 and SSP5-RCP8.5). The evaluation of the models' performance involved comparing their estimations of two erosivity indices, namely the annual average rainfall erosivity (R-factor) and the extreme storm EI30 with a 10-year return period (10-year storm EI), with reference erosivity maps of China interpolated from hourly observations at 2381 stations. The results indicate that three models, GFDL-ESM4, IPSL-CM6A-LR, and UKESM1-0-LL, outperform the others in terms of higher Nash-Sutcliffe efficiencies and better spatial correlation, especially in regions prone to water erosion. However, it was observed that the R-factor and 10-year storm EI estimated using Multi-Model Ensembles (MMEs) were significantly underestimated for the historical period due to scaling differences. To address this issue, bias-correction factors were determined for each grid cell to improve future projections. The medians of these correction factors were found to be 0.80 for the R-factor and 0.66 for the 10-year storm EI. Overall, the study projects an increase in rainfall erosivity for most regions in China. Under the SSP1-RCP2.6 and SSP5-RCP8.5 scenarios, the R-factor is expected to rise by 18.9% and 19.8% for the near-term and 26.0% and 46.5% for the long-term, respectively. Similarly, the 10-year storm EI is projected to increase by 14.2% and 17.4% for the near-term and 14.9% and 45.0% for the long-term, respectively. These projected increases are primarily attributed to the elevated probability of extreme precipitation events, highlighting the need for enhanced soil and water conservation measures in China to mitigate the challenges posed by global warming.

Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.