Extreme Probability Research Articles

A learning-based optimal uncertainty quantification method and its application to ballistic impact problems

This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse topology) rather than fully specified. Such partial knowledge provides constraints on the input probability measures. The theory of Optimal Uncertainty Quantification allows us to convert the task into a constraint optimization problem where one seeks to compute the least upper/greatest lower bound of the system’s output uncertainties by finding the extremal probability measure of the input. Such optimization requires repeated evaluation of the system’s performance indicator (input to performance map) and is high-dimensional and non-convex by nature. Therefore, it is difficult to find the optimal uncertainty bounds in practice. In this paper, we examine the use of machine learning, especially deep neural networks, to address the challenge. We achieve this by introducing a neural network classifier to approximate the performance indicator combined with the stochastic gradient descent method to solve the optimization problem. We demonstrate the learning-based framework on the uncertainty quantification of the impact of magnesium alloys, which are promising light-weight structural and protective materials. Finally, we show that the approach can be used to construct maps for the performance certificate and safety design in engineering practice.

Rapidly increasing likelihood of exceeding 50 °C in parts of the Mediterranean and the Middle East due to human influence

As the world warms, extremely hot days are becoming more frequent and intense, reaching unprecedented temperatures associated with excess mortality. Here, we assess how anthropogenic forcings affect the likelihood of maximum daily temperatures above 50 °C at 12 selected locations around the Mediterranean and the Middle East. We adopt a risk-based attribution methodology that utilises climate model simulations with and without human influence to estimate the probability of extremes. We find that at all locations, temperatures above 50 °C would have been extremely rare or impossible in the pre-industrial world, but under human-induced climate change their likelihood is rapidly increasing. At the hottest locations we estimate the likelihood has increased by a factor of 10–103, whereas by the end of the century such extremes could occur every year. All selected locations may see 1–2 additional months with excess thermal deaths by 2100, which stresses the need for effective adaptation planning.

Gaidai reliability method for long-term coronavirus modelling.

Novel coronavirus disease has been recently a concern for worldwide public health. To determine epidemic rate probability at any time in any region of interest, one needs efficient bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of novel coronavirus infection rate. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the multi-dimensionality advantage, that suggested methodology offers, namely dealing efficiently with multiple regions at the same time and accounting for cross-correlations between different regional observations. Modern multi-dimensional novel statistical method was directly applied to raw clinical data, able to deal with territorial mapping. Novel reliability method based on statistical extreme value theory has been suggested to deal with challenging epidemic forecast. Authors used MATLAB optimization software. This paper described a novel bio-system reliability approach, particularly suitable for multi-country environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of extreme novel coronavirus death rate probability. Namely, accurate maximum recorded patient numbers are predicted for the years to come for the analyzed provinces. The suggested method performed well by supplying not only an estimate but 95% confidence interval as well. Note that suggested methodology is not limited to any specific epidemics or any specific terrain, namely its truly general. The only assumption and limitation is bio-system stationarity, alternatively trend analysis should be performed first. The suggested methodology can be used in various public health applications, based on their clinical survey data.

Probabilistic and deductive reasoning in the human brain

Reasoning is a process of inference from given premises to new conclusions. Deductive reasoning is truth-preserving and conclusions can only be either true or false. Probabilistic reasoning is based on degrees of belief and conclusions can be more or less likely. While deductive reasoning requires people to focus on the logical structure of the inference and ignore its content, probabilistic reasoning requires the retrieval of prior knowledge from memory. Recently, however, some researchers have denied that deductive reasoning is a faculty of the human mind. What looks like deductive inference might actually also be probabilistic inference, only with extreme probabilities. We tested this assumption in an fMRI experiment with two groups of participants: one group was instructed to reason deductively, the other received probabilistic instructions. They could freely choose between a binary and a graded response to each problem. The conditional probability and the logical validity of the inferences were systematically varied. Results show that prior knowledge was only used in the probabilistic reasoning group. These participants gave graded responses more often than those in the deductive reasoning group and their reasoning was accompanied by activations in the hippocampus. Participants in the deductive group mostly gave binary responses and their reasoning was accompanied by activations in the anterior cingulate cortex, inferior frontal cortex, and parietal regions. These findings show that (1) deductive and probabilistic reasoning rely on different neurocognitive processes, (2) people can suppress their prior knowledge to reason deductively, and (3) not all inferences can be reduced to probabilistic reasoning.

Heterogeneity of probability weighting in investment decisions

This study examines how the heterogeneity of elevation or curvature in probability weighting affects investors’ market participation and the equity premium. We analyze the rank-dependent utility with the generalized Wang transform (GWT) as an inverse S-shaped weighting function. The two parameters of GWT elicit pessimism (elevation) and likelihood insensitivity to less extreme probability (curvature). There is non-participation when the heterogeneity of elevation or curvature is significant. The mean of elevation does not affect market participation, but that of curvature does. With elevation dispersion, a GWT weighting function with a single prior is compatible with a maxmin model with multiple priors.

Increasing likelihood of global compound hot-dry extremes from temperature and runoff during the past 120 years

Compound hot-dry extremes pose great threats to human health, ecosystems, and food production. A lot of attention has been paid to compound meteorological hot-dry extremes (based on high near-surface air temperature and low precipitation); however, there is a gap on the compound hydrological hot-dry extremes (based on high near-surface air temperature and low surface runoff) which is more directly related to damages on social and natural systems. Here, using the ensemble empirical mode decomposition method and Copula function based on multiple global gridded datasets during 1902–2019, we find that the globe is dominated by accumulated increases in zonal average of warm-season (i.e., May-September in the Northern Hemisphere and November-March in the Southern Hemisphere) mean precipitation (WMP), while zonal average of warm-season mean runoff (WMR) mainly shows accumulated decreases. This discrepancy is possibly due to the modulation effect of zonally accelerated warming trends in warm-season mean temperature (WMT). Despite of the discrepancy in changes of individual WMP and WMR, compound meteorological hot-dry extremes (from WMT and WMP) show increased occurrence probability, expanded affected area, and enlarged spatial homogeneity (i.e., connectedness), and these features are worse for compound hydrological extremes (from WMT and WMR). Both high WMT and low WMP can lead to negative anomalies of WMR; however, the negative anomalies of WMR can be largely amplified by additional low WMP under high WMT conditions. The increased occurrence probability of compound hydrological hot-dry extremes is directly related to WMT, WMR, and their dependence. Although a strong dependence is found between WMT and WMR especially at mid-latitudes in the Northern Hemisphere, attribution results show that increased WMT plays a dominant role in reducing return periods of compound hydrological hot-dry extremes at the global scale. Our results provide a deeper understanding of changes in compound hydrological hot-dry extremes at the global scale from a longer-term period.

Shape investigation and probabilistic representation of coastal storms. Applications to Mykonos and Barcelona

The main objective of the present work is the probabilistic representation of coastal storms’ parameters through non-parametric probability distributions that can give satisfactory estimates in the whole range of the variables’ values. Their proper probabilistic representation can provide crucial information for many applications including the probabilistic design of marine and coastal structures. Different non-parametric univariate distributions in combination with different copula types or the conditional model are applied, to check the closeness of their fit to the available bivariate coastal storm data (e.g., the storms’ maximum wave height and the associated peak wave period). Moreover, except for the classical kernel distribution, a new, recently developed Box-Cox transformed kernel method is also examined and applied. The latter has been already evaluated so far to sea states data but not to storm data. Therefore, the adopted methodology is implemented to real coastal storms in two different locations, derived from wave recordings from Mykonos (Greece) and Barcelona (Spain). Furthermore, some of the significant statistical properties of the observed coastal storms, such as the calm period, the duration, and the shape (triangular or trapezoid) are also detected. From the present analysis, the derived methodology for representing accurately coastal storms is clarified, giving thus a useful tool to engineers and researchers to consider extreme events probability of occurrence, which is essential for the design of coastal structures and consequently for the protection of coastal communities.

Forecasting extreme negative returns in gold and silver: A discrete‐duration approach to POT models

AbstractSudden and massive drops in precious metal prices severely impact the investment risk on these commodity markets. In this study, we examine the dynamics of extreme negative returns on gold and silver, as well as propose the discrete‐duration version of the autoregressive conditional duration peaks‐over‐threshold (ACD‐POT) model for measuring market risk. The model is tailored for the dynamics of extreme events in precious metal markets; this is because it can exhibit both the strong clustering of extreme‐event days, and the serial correlation in the magnitudes of extreme losses. From an econometric perspective, our approach complements the existing dynamic versions of POT models; this is so that the time interval (i.e., duration) between the extreme negative returns is treated not as a continuous variable, but as a discrete one. The discrete hazard function in our model represents the daily extreme loss event probability and it can be used to derive one‐day‐ahead forecasts of both the value at risk and expected shortfall for investments in gold and silver. Formal backtesting methods show that the discretized version of the POT model has a superior in‐sample fit and forecasting performance than the continuous‐duration POT models.

Rare Event Simulation of Extreme European Winter Rainfall in an Intermediate Complexity Climate Model

AbstractWe test the application of a rare event simulation (RES) algorithm to accelerate the sampling of extreme winter rainfall over Europe in a climate model. The genealogical particle analysis algorithm, an ensemble method that interrupts the simulation at intermediate times to clone realizations in which an extreme event is developing, is applied to the intermediate complexity general circulation model PlaSim. We show that the algorithm strongly reduces the numerical effort required to estimate probabilities of extremes, demonstrating the potential of RES of seasonal precipitation extremes.

Increased impact of heat domes on 2021-like heat extremes in North America under global warming

During summer 2021, Western North America (WNA) experienced an unprecedented heatwave with record-breaking high temperatures associated with a strong anomalous high-pressure system, i.e., a heat dome. Here, we use a flow analog method and find that the heat dome over the WNA can explain half of the magnitude of the anomalous temperature. The intensities of hot extremes associated with similar heat dome-like atmospheric circulations increase faster than background global warming in both historical change and future projection. Such relationship between hot extremes and mean temperature can be partly explained by soil moisture-atmosphere feedback. The probability of 2021-like heat extremes is projected to increase due to the background warming, the enhanced soil moisture-atmosphere feedback and the weak but still significantly increased probability of the heat dome-like circulation. The population exposure to such heat extremes will also increase. Limiting global warming to 1.5 °C instead of 2 °C (3 °C) would lead to an avoided impact of 53% (89%) of the increase in population exposure to 2021-like heat extremes under the RCP8.5-SSP5 scenario.

Offloading operation bivariate extreme response statistics for FPSO vessel

The Floating Production Storage and Offloading unit (FPSO) is an offshore unit producing and storing crude oil prior to tanker transport. An important design concern is an accurate prediction of risky dynamic hawser tensions during FPSO offloading operations. Bivariate extreme hawser tension contours are important for selecting proper design values. This paper employed the AQWA hydrodynamic software to analyze vessel hydrodynamic wave loads dynamic response, acting on FPSO vessels under realistic sea state conditions. This paper presents an efficient method for estimating FPSO bivariate response statistics based on numerical simulations validated by various experiments. The bivariate Average Conditional Exceedance Rate (ACER2D) method offers an accurate bivariate extreme value probability distribution and return period contours estimation, utilizing available data efficiently. The two-dimensional probability contours, corresponding to low probability return periods, are easily obtained by the ACER2D method. The performance of the presented method has shown that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The suggested approach may be used for FPSO vessel design, minimizing potential FPSO hawser damage. Bivariate contours yield bivariate design points, as opposed to a pair of uncoupled univariate design points with the same return period as currently adopted in the industry.

Simulating hydrological extremes for different warming levels–combining large scale climate ensembles with local observation based machine learning models

Climate change has a large influence on the occurrence of extreme hydrological events. However, reliable estimates of future extreme event probabilities, especially when needed locally, require very long time series with hydrological models, which is often not possible due to computational constraints. In this study we take advantage of two recent developments that allow for more detailed and local estimates of future hydrological extremes. New large climate ensembles (LE) now provide more insight on the occurrence of hydrological extremes as they offer order of magnitude more realizations of future weather. At the same time recent developments in Machine Learning (ML) in hydrology create great opportunities to study current and upcoming problems in a new way, including and combining large amounts of data. In this study, we combined LE together with a local, observation based ML model framework with the goal to see if and how these aspects can be combined and to simulate, assess and produce estimates of hydrological extremes under different warming levels for local scales. For this, first a new post-processing approach was developed that allowed us to use LE simulation data for local applications. The simulation results of discharge extreme events under different warming levels were assessed in terms of frequency, duration and intensity and number of events at national, regional and local scales. Clear seasonal cycles with increased low flow frequency were observed for summer and autumn months as well as increased high flow periods for early spring. For both extreme events, the 3C warmer climate scenario showed the highest percentages. Regional differences were seen in terms of shifts and range. These trends were further refined into location specific results. The shifts and trends observed between the different scenarios were due to a change in climate variability. In this study we show that by combining the wealth of information from LE and the speed and local relevance of ML models we can advance the state-of-the-art when it comes to modeling hydrological extremes under different climate change scenarios for national, regional and local scale assessments providing relevant information for water management in terms of long term planning.

Seasonal Dependence and Variability of Rainfall Extremes in a Tropical River Basin, South Asia

In recent years, rainfall extremes have increased significantly and have threatened the socio-economic development in Sri Lanka. This study investigates the rainfall extremes in the Mahaweli River Basin (MRB) of Sri Lanka with daily station datasets from 1985 to 2015. The extreme rainfall indices recommended by the Expert Team on Climate Change Detection Monitoring Indices (ETCCDMI) have been used in this study. Results showed a strong seasonal variation of rainfall extreme events over the MRB and a significant interdecadal change of extreme rainfall indices between 1985–1999 and 2000–2015 in the wet region of MRB, which is coherent with the decadal shift of southwest monsoon (SWM) rainfall from wet to dry situations since the year 2000. Based on the General Extreme Value distributions, the long-term mean of SWM rainfall in the wet region (814 mm) moved leftward for the 2000–2015 period (704 mm) and rightward for the 1985–2000 period, suggesting that SWM rainfall is decreased in the late period. The observed above-average (below-average) rainfall and associated rainfall extremes during the SWM can be ascribed to strengthening (weakening) moisture flux from the Arabian Sea direction and strong (weak) convergence over the study domain. The results further identified the negative correlation between Dipole Mode Index and SWM rainfall and associated rainfall extremes in the wet region, signifying that the negative Indian Ocean Dipole phase can enhance the SWM rainfall over the MRB. The negative correlation between Nino3.4 and SWM rain and extreme indices suggested that high probability of wet rainfall extremes in the La Nina phase. The findings of this study can be used to understand precipitation extremes in the context of climate change at the river basin scale and benefit policymakers in building local adaptation strategies in response to long-term climate change.

Increased probability of hot and dry weather extremes during the growing season threatens global crop yields

Although extreme weather events recur periodically everywhere, the impacts of their simultaneous occurrence on crop yields are globally unknown. In this study, we estimate the impacts of combined hot and dry extremes as well as cold and wet extremes on maize, rice, soybean, and wheat yields using gridded weather data and reported crop yield data at the global scale for 1980–2009. Our results show that co-occurring extremely hot and dry events have globally consistent negative effects on the yields of all inspected crop types. Extremely cold and wet conditions were observed to reduce crop yields globally too, although to a lesser extent and the impacts being more uncertain and inconsistent. Critically, we found that over the study period, the probability of co-occurring extreme hot and dry events during the growing season increased across all inspected crop types; wheat showing the largest, up to a six-fold, increase. Hence, our study highlights the potentially detrimental impacts that increasing climate variability can have on global food production.

Environmental Condition Boundary Design for Direct-Drive Permanent Magnet (DDPM) Wind Generators by Using Extreme Joint Probability Distribution

In future engineering applications, it is important for a direct-drive permanent magnet (DDPM) wind generator to be designed with optimized environmental condition boundary. This paper presents a novel extreme joint probability distribution method of boundary design to formulate the evaluation model and correlation between component design and environmental conditions. With this method, the joint probability distributions of multidimensional parameters for typical wind resource areas in China are studied. A 3.3-MW DDPM wind generator is involved in the case study to validate the superiority of the method. Furthermore, to improve the generalizability of the method, some typical wind resource data platforms are calibrated regarding the measured data. It is shown that the ERA5 dataset can be used as a supplement to enhance the representativeness of the measured data for the joint probability distributions. Therefore, the proposed method can be potentially used to optimize the system design of future DDPM wind generators.

Subseasonal Predictability of the July 2021 Extreme Rainfall Event Over Henan China in S2S Operational Models

AbstractA record‐breaking flooding event occurred in Zhengzhou, Henan Province of China during 17–23 July 2021, causing hundreds of deaths and vast economic losses. Here, we evaluated the predictability of this extreme rainfall event and the impacts of tropical cyclones (TCs) using subseasonal‐to‐seasonal (S2S) operational models. On the monthly timescale, most models initialized in late June reasonably predicted the wet‐in‐north and dry‐in‐south patterns of anomalous rainfall over China in July, accompanied by the well‐predicted westward extension of the western North Pacific subtropical high (WNPSH) and eastward stretching of the South Asian High. On the weekly timescale, only four models captured the location, probability, and sudden intensification of the rainfall extremes in advance of 1 week, largely due to their reasonable prediction of WNPSH variability in mid‐latitudes. However, the S2S models still underestimated the super extremeness of this event. The prediction discrepancies came from the poor predictability of Typhoon IN‐FA and its impact on the daily evolution of the extreme rainfall event, even within a few days forecast lead. Compared with the observation, the prediction bias of tropical disturbance changed the environmental monsoon airflow to induce the earlier warning of rainfall extremes prior to the formation of IN‐FA. After the formation of IN‐FA, the prediction bias of the typhoon's moving speed distorted the typhoon location, which incorrectly predicted the moisture convergence center and underestimated their remote impacts on this heavy rainfall event.

Global Soil Moisture–Climate Interactions during the Peak Growing Season

Abstract Soil moisture (SM) during the vegetation growing season largely affects plant transpiration and photosynthesis, and further alters the land energy and water balance through its impact on the energy partition into latent and sensible heat fluxes. To highlight the impact of strong vegetation activity, we investigate global SM–climate interactions over the peak growing season (PGS) during 1982–2015 based on multisource datasets. Results suggest widespread positive SM–precipitation (P), SM–evapotranspiration (ET), and negative SM–temperature (T) interactions with non-negligible negative SM–P, SM–ET, and positive SM–T interactions over PGS. Relative to the influence of individual climate factors on SM, the compounding effect of climate factors strengthens SM–climate interactions. Simultaneously, variations of SM are dominated by precipitation from 50°N toward the south, by evapotranspiration from 50°N toward the north, and by temperature over the Sahara, western and central Asia, and the Tibetan Plateau. Importantly, the higher probability of concurrent SM wetness and climate extremes indicates the instant response of SM wetness to extreme climate. In contrast, the resistance of vegetation partially contributes to a consequent slower response of SM dryness to extreme climate. We highlight the significance of the compounding effects of climate factors in understanding SM–climate interaction in the context of strong vegetation activity, and the response of SM wetness and dryness to climate extremes.

COVID-19 multi-state epidemic forecast in India

Novel coronavirus disease is spread worldwide with considerable morbidity and mortality and presents an enormous burden on worldwide public health. Due to the non-stationarity and complicated nature of novel coronavirus waves, it is challenging to model such a phenomenon. Few mathematical models can be used because novel coronavirus data are generally not normally distributed. This paper describes a novel bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of novel coronavirus infection rate. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the advantage of dealing efficiently with extensive regional dimensionality and cross-correlation between infection rate and mortality. To determine extreme novel coronavirus death rate probability at any time in any region of interest. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the advantage of dealing efficiently with extensive regional dimensionality and cross-correlation between different regional observations. Apply modern novel statistical methods directly to raw clinical data. Multicenter, population-based, medical survey data based bio statistical approach. Due to the non-stationarity and complicated nature of novel coronavirus, it is challenging to model such a phenomenon. Few mathematical models can be used because novel coronavirus data are generally not normally distributed. This paper describes a novel bio-system reliability approach, particularly suitable for multi-country environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of extreme novel coronavirus death rate probability. The suggested methodology can be used in various public health applications, based on their clinical survey data.

Penilaian Risiko Kegagalan Bendungan Dan Tindakan Pengurangan Risiko Pada Bendungan Nglangon

The dam failure that has been operating has a great potential to occur if the administrator does not carry out proper maintenance. Dams require proper and correct maintenance and operation which will greatly affect the safety of the dam itself. Especially for dams that have been operating for a long time, major maintenance activities including repairs and rehabilitation are urgently needed to avoid the worst conditions such as facing natural disasters. Because a dam can cause a large impact if it fails, it is necessary to have a risk assessment to analyze and evaluate the hazard of the dam. Risk research conducted at the Nglangon Dam uses the event tree method, traditional and modified ICOLD. Based on the results of individual and group extreme probability analysis, both traditional and event tree methods, the risk probability value is above the acceptable risk value threshold of 1.00E-05, which means that the Nglangon Dam requires further action. This is in line with the results of the ICOLD modified risk assessment method with classification III (high) which means that the Nglangon Dam is included in a dam that requires special attention and corrective actions to reduce the level of risk in the Nglangon Dam

Estimation of Extreme Daily Rainfall Probabilities: A Case Study in Kyushu Region, Japan

Extreme rainfall causes floods and landslides, and so damages humans and socioeconomics; for instance, floods and landslides have been triggered by repeated torrential precipitation and have caused severe damage in the Kyushu region, Japan. Therefore, evaluating extreme rainfall in Kyushu is necessary to provide basic information for measures of rainfall-induced disasters. In this study, we estimated the probability of daily rainfall in Kyushu. The annual maximum values for daily rainfall at 23 long-record stations were normalized using return values at each station, corresponding to 2 and 10 years, and were combined by the station-year method. Additionally, the return period (RP) was calculated by fitting them to the generalized extreme value distribution. Based on the relationship between the normalized values of annual maximum daily rainfall and the RP, we obtained a regression equation to accurately estimate the RP up to 300 years by using data at given stations, considering outliers. In addition, we verified this equation using data from short-record stations where extreme rainfall events triggering floods and landslides were observed, and thereby elucidated that our method was consistent with previous techniques. Thus, this study develops strategies of measures for floods and landslides.