Probability Of Extreme Events Research Articles

Regime-Switching Models for Estimating Inflation Uncertainty

This paper constructs regime-switching models for estimating the probability of inflation returning to its relatively high levels of variability and persistence in the 1970s and 1980s. Forecasts and probabilities of extreme events from the models are evaluated against comparable estimates from other statistical models, from surveys, and from financial markets. The paper then uses the models to construct prediction intervals around Federal Reserve Board staff forecasts of PCE price inflation, combining the recent non-parametric forecast error distribution with parametric information from the model. The outer tails of the prediction intervals depend importantly on the probability inflation is in its high-variance, high-persistence regime.

Regime-Switching Models for Estimating Inflation Uncertainty

This paper constructs regime-switching models for estimating the probability of inflation returning to its relatively high levels of variability and persistence in the 1970s and 1980s. Forecasts and probabilities of extreme events from the models are evaluated against comparable estimates from other statistical models, from surveys, and from financial markets. The paper then uses the models to construct prediction intervals around Federal Reserve Board staff forecasts of PCE price inflation, combining the recent non-parametric forecast error distribution with parametric information from the model. The outer tails of the prediction intervals depend importantly on the probability inflation is in its high-variance, high-persistence regime.

<b>Is the Conditional Density Network more suitable than the Maximum likelihood for fitting the Generalized Extreme Value Distribution?

The Generalized Extreme value Distribution (GEV) has been widely used to assess the probability of extreme weather events and the parameter estimation method is a key factor for improving its quantile estimates. On such background, this study aimed to indicate under which conditions (sample size and tail behavior) the Conditional Density Network (CDN) leads to better GEV quantile estimates than the widely used Maximum likelihood method (MLE) does. With Monte Carlo simulations and rainfall series of several Brazilians regions, we highlight the following results: the return period and the tail behavior of the GEV (specified by the shape parameter) are two of the main factors affecting the quantile estimates. For -0.1 ≤ shape ≤ 0.1 and sample size ≤ 50, the CDN outperformed the MLE. For shape ≥ 0.20 the CDN outperformed the MLE for all sample sizes (30-90). The results also suggested that the CDN is more suitable than the MLE for fitting the GEV parameter to the Brazilian extreme rainfall series. We conclude that when the shape parameter are equal to or greater than -0.1 the CDN should be preferred over the MLE.

Modeling Variability and Uncertainty of Photovoltaic Generation: A Hidden State Spatial Statistical Approach

In this paper, we construct, fit, and validate a hidden Markov model for predicting variability and uncertainty in generation from distributed (PV) systems. The model is unique in that it: 1) predicts metrics that are directly related to operational reserves, 2) accounts for the effects of stochastic volatility and geographic autocorrelation, and 3) conditions on latent variables referred to as “volatility states.” We fit and validate the model using 1-min resolution generation data from approximately 100 PV systems in the California Central Valley or the Los Angeles coastal area, and condition the volatility state of each system at each time on 15-min resolution generation data from nearby PV systems (which are available from over 6000 PV systems in our data set). We find that PV variability distributions are roughly Gaussian after conditioning on hidden states. We also propose a method for simulating hidden states that results in a very good upper bound for the probability of extreme events. Therefore, the model can be used as a tool for planning additional reserve capacity requirements to balance solar variability over large and small spatial areas.

Influence of boreal summer intraseasonal oscillation on rainfall extremes in southern China

ABSTRACTHow boreal summer intraseasonal oscillation (BSISO) modulates the probability and spatial distributions of extreme rainfall occurrence over populous southern China was examined, using the newly proposed BSISO indices and two high‐resolution rain‐gauge‐based rainfall datasets in China. The probability density function of May–August rainfall in southern China is skewed towards large values in phases 2–4 of the first component and in phases 5–7 of the second component of BSISO life cycle, during which the probability of extreme rainfall events at the 75th (90th) percentile increases by 30–50% (over 60%) relative to the non‐BSISO period. The devastating floods with prolonged extreme rainfall in southern China over the three past decades occurred coincidently with these BSISO phases. The first component of BSISO, associated with 30–60‐day eastward/northeastward‐propagating ISO, is more favourable for the rainfall extreme over in‐land China. In contrast, the second component of BSISO, related to the 10–30‐day northwestward propagating ISO, tends to link with the rainfall extreme along the southeast coast of South China. Moisture budget indicates that the favourable environment for rainfall extreme is associated with southwesterly moisture convergence over southern China, while the moisture advection contributes insignificantly. This study suggests a potential for monitoring and probabilistic prediction of extreme rainfall events in southern China based on the real‐time BSISO indices.

Real estate risk: heavy tail modelling using Excel

Purpose– The purpose of this paper is to present a practice briefing in the form of a user’s manual for Excel-based simulation of real estate risk. Based on a generic discounted cash flow model, the simulation incorporates the often ignored heavy tail behaviour of real estate investments, and consolidates Jensen’s inequality. The briefing attempts to explain a model that permits the user to decide whether to include extreme events in real estate risk modelling and how extreme these events may be. Practitioners can generate a variety of modelling outcomes and then choose risk comfort zones in which to contemplate a range of returns.Design/methodology/approach– The paper provides an overview of the underlying mathematical concepts and challenges, as well as on the perspectives on their application from the current academic literature. It offers a step-by-step walk-through of the Excel model (the model being downloadable at:www.mathestate.com).Findings– Existing models for real estate risk modelling fall short with respect to realistic simulation of the probability of extreme events due to challenges in the implementation of stable laws. These former barriers to the implementation of stable laws have been overcome by providing a unique combination of Excel-resident functionalities with a stable pseudo random number generator.Research limitations/implications– Investment advisers no longer need expensive add-ins to estimate risk. The presented Excel model is more robust than common approaches as it considers distribution shapes that are not otherwise easily available. The only apparent limitation is that users need to be familiar with the most basic functionality of Excel.Practical implications– Practitioners are provided with an easy-to-use Excel model that does not require further software add-ins. The model simulates real estate investment returns, based on a more realistic inclusion of risk behaviour. It allows specifying how much extreme value behaviour characterizes the volatility in future projections modelled to guide investment decisions.Social implications– Risk is a cost to society. Many recent news events demonstrate the importance of including extreme values in modelling. The paper attempts to contribute to more realistic risk estimation in real estate investment.Originality/value– This briefing introduces a real estate risk simulation model that includes using stable laws, using Excel, a familiar and widely used platform. Such a model has not previously been reported in the academic or practitioners’ literature.

Analyzing streamflow extremes in the upper Ürümqi River with the generalized Pareto distribution

The generalized Pareto distribution (GPD), as one of the most important distributions in statistical theory of extreme value, is often used to explain the probability of extreme events in nature, through setting up a model with the observation points exceeding the threshold. This paper uses GPD model to fit the distributions of the relatively large and small monthly average discharge of Urumqi River in Northwest China and gives the detailed steps of this method. Firstly, the Mean Excess, shape parameter and modified scale parameter plots are applied to determine the thresholds; then the parameters of GPD are estimated by the maximum likelihood method; next the models are diagnosed by the probability and quantile plots; finally the return levels and the corresponding 95 % confidence intervals of the discharge are calculated by the maximum likelihood and profile likelihood methods, respectively. The results show that the return levels of the maximum monthly average discharge with the return periods 10, 25, 50 and 100 years are 35.4, 39.9, 43.2 and 46.3 m3 s−1, respectively, and the return levels of the minimum monthly average discharge with the return periods 10, 25, 50 and 100 years are 0.60, 0.43, 0.30 and 0.18 m3 s−1, respectively. Some comparisons are also made between the generalized extreme value (GEV) and GPD models. The results of these two models are close to each other while the GPD model should be more reliable because it can make use of more information than the GEV model. This paper proposes a complete framework for modeling hydrological data by GPD model.

Contribution of changes in atmospheric circulation patterns to extreme temperature trends.

Surface weather conditions are closely governed by the large-scale circulation of the Earth's atmosphere. Recent increases in the occurrence of some extreme weather phenomena have led to multiple mechanistic hypotheses linking changes in atmospheric circulation to increasing probability of extreme events. However, observed evidence of long-term change in atmospheric circulation remains inconclusive. Here we identify statistically significant trends in the occurrence of atmospheric circulation patterns, which partially explain observed trends in surface temperature extremes over seven mid-latitude regions of the Northern Hemisphere. Using self-organizing map cluster analysis, we detect robust circulation pattern trends in a subset of these regions during both the satellite observation era (1979-2013) and the recent period of rapid Arctic sea-ice decline (1990-2013). Particularly substantial influences include the contribution of increasing trends in anticyclonic circulations to summer and autumn hot extremes over portions of Eurasia and North America, and the contribution of increasing trends in northerly flow to winter cold extremes over central Asia. Our results indicate that although a substantial portion of the observed change in extreme temperature occurrence has resulted from regional- and global-scale thermodynamic changes, the risk of extreme temperatures over some regions has also been altered by recent changes in the frequency, persistence and maximum duration of regional circulation patterns.

Effect of noise on extreme events probability in a one-dimensional nonlinear Schrödinger equation

We report a numerical observation that multiplicative random forcing (noise) significantly increases the probability of formation of extreme events in the one-dimensional, focusing nonlinear Schrödinger equation. Furthermore, this phenomenon is sensitive to the noise's spatial correlation length. Highly correlated multiplicative noise may increase the probability of extreme events even when the average nonlinearity of the system is weak. On the contrary, noise with short spatial correlations substantially increases the probability of extreme events only for sufficiently strong average nonlinearity.

Spatial Characterization and Bivariate Frequency Analysis of Precipitation and Runoff in the Upper Huai River Basin, China

The variability of the relationship between precipitation and runoff is of vital importance to study the characteristics of regional water cycle and water resource management and planning. In this study, in order to explore the relationship between precipitation and runoff of the different hydrological patterns, the analysis of bivariate precipitation and runoff distributions and the simultaneous occurrence probability was analyzed by employing the Archimedean copula, based on the monthly runoff and precipitation data during 1960 ~ 2000 in the upper Huai river basin, China. The results indicated that: (I) the study region could be classified into four hydrological patterns, namely the Huai river valley zone, Huaibei plain zone, Huainan mountain zone and Huaibei mountain zone, with Xixian, Zhuanqiao, Meishan and Zhaopingtai as the maximal loading subbasin respectively. (II) There were positive dependence structure between precipitation and runoff in the study area, and the bivariate frequency distributions could be fitted best by the Gumbel-Hougaard copula. (III) The simultaneous occurrence probability of bivariate drought events was remarkable higher than that of corresponding classification of bivariate flood events; besides, the simultaneous occurrence probability of bivariate extreme events was maximum in the Huainan mountain zone, followed by the Huai river valley zone and Huaibei mountain zone, while that was minimum in the Huaibei plain zone. These results would be of essential guiding significance for water resource management and planning, flood and drought control and layout optimization of water conservancy projects in the study region.

Anomalous Weather Patterns in Relation to Heavy Precipitation Events in Japan during the Baiu Season

Abstract Anomalous weather patterns (WPs) in relation to heavy precipitation events during the baiu season in Japan are investigated using a nonlinear classification technique known as the self-organizing map (SOM). The analysis is performed on daily time scales using the Japanese 55-year Reanalysis Project (JRA-55) to determine the role of circulation and atmospheric moisture on extreme events and to investigate interannual and interdecadal variations for possible linkages with global-scale climate variability. SOM is simultaneously employed on four atmospheric variables over East Asia that are related to baiu front variability, whereby anomalous WPs that dominated during the 1958–2011 period are obtained. Our analysis extracts seven typical WPs, which are linked to frequent occurrences of heavy precipitation events. Each WP is associated with regional variations in the probability of extreme precipitation events. On interannual time scales, El Niño–Southern Oscillation (ENSO) affects the frequency of the WPs in relation to the heavy rainfall events. The warm phase of ENSO results in an increased frequency of a WP that provides a southwesterly intrusion of high equivalent potential temperature at low levels, while the cold phase provides southeastern intrusion. In addition, the results of this analysis suggest that interdecadal variability of frequency for heavy rainfall events corresponds to changes in frequency distributions of WPs and are not due to one particular WP.

Experimental investigation on statistical properties of wave heights and crests in crossing sea conditions

Some theoretical and numerical studies highlighted that the occurrence of rogue waves could increase in the presence of crossing sea. This sea state is characterized by the coexistence of two wave systems with different directions of propagations and is considered one of the most common causes of ship accidents in bad weather conditions. In particular, the angle between the two interacting wavetrains, Δθ, was found to be an important parameter that could lead to an enhanced probability of extreme events. We present an experimental investigation on wave heights and crest for surface elevation mechanically generated in different crossing sea conditions (10° < Δθ < 40°). The results of statistical analysis confirm that the probability of extreme events increases with the angle between the two systems, but does not exceed the values of the unidirectional case, which also presents waves with greater heights. Moreover, the correlation between the heights, crests, and troughs of consecutive waves assumes higher values for the case of 40°, when compared to the unidirectional case: this could mean that it is easier to find waves of the same height within a packet in the conditions Δθ = 40° with respect to the unidirectional or other Δθ conditions considered.

Soil moisture trends in the Czech Republic between 1961 and 2012

ABSTRACTCentral Europe is generally not considered a drought‐prone region compared with, for example, the Mediterranean. However, Central Europe, including the Czech Republic, recently experienced a series of drought events with substantial impacts, especially on crop production. Because agriculture systems, and vegetation in general, have adapted to evenly distributed precipitation, the region is susceptible to even short‐term droughts. The recent drought events may be the result of multi‐decadal climate variability or a more general trend, with some studies showing a link to a more frequent occurrence of atmospheric circulation patterns that are conducive to drought. This study introduces an innovation to the standard methodological approaches in evaluating drought climatology by analysing soil moisture conditions over more than 50 years. This approach relies on state‐of‐the‐art observed weather data and state‐of‐the‐art soil moisture model data, and focuses on the dynamic simulation of soil moisture content with high temporal (daily) and spatial (500 m) resolution in a diverse landscape. Statistically significant trends of decreasing soil moisture content were found, notably during May and June between 1961 and 2012. In contrast, trends towards higher soil moisture content were noted during the October–March time period. When the periods of 2001–2012 and 1961–1980 were compared, the probability of drought between April and June was found to increase by 50%. This indicates a loading of the ‘climate dice’ towards drier conditions. The probability of extreme drought events has also been found to increase. These results support concerns about the potentially increased severity of drought events in Central Europe under projected climate change.

Use of Landsat TM/ETM+ to monitor the spatial and temporal extent of spring breakup floods in the Lena River, Siberia

A warmer-than-normal air temperature enhances the probability of extreme hydrologic events. A spring breakup flood is among the most serious hydrologic events in high-latitude regions. This study examined the use of Landsat Thematic Mapper/Enhanced Thematic Mapper Plus (TM/ETM+) to monitor the spatial and temporal extent of spring breakup floods in the Lena River, Siberia. Although the 30 m spatial resolution of Landsat produced a detailed mapping of the floodplain, acquisition of Landsat images at short-term intervals was difficult because of the long revisit time of Landsat (16 days) and the frequent cloud cover over Siberia. However, information from two sensors (i.e. TM and ETM+) was combined to essentially halve the revisit time. Moreover, frequent Landsat images were acquired at higher latitudes by using information from overlap areas between neighbouring path images. Therefore, the average revisit time was determined to be 2.6 (= 16/3/2) days in the triple overlap area using two sensors. Updated data sets with a high temporal frequency enhanced the ability to monitor the spatial and temporal extent of the spring breakup floods, although the area was small. In addition, the neighbouring Landsat images themselves were used for large-scale monitoring of breakup floods, given that Landsat overpasses from west to east operating in a near-polar sun-synchronous orbit with a progression speed that is almost the same as the speed of a spring breakup flood. In 2007, spring breakup floods were successively monitored from Solyanka to Yakutsk. Reliable and timely information for large-area monitoring of floods was crucial to understand better the influence on regional hydrology and climate. The images from Landsat TM/ETM+ sensors were regarded as a suitable data source for operational use in flood monitoring due to the wide geographic coverage, high temporal resolution, adequate spatial resolution, and minimal cost.

The Risk of Geomagnetic Storms to the Grid: A Preliminary Review

Life on earth evolved to exploit the flow of energy from the sun — and to withstand its extremes. But if life writ large has adapted to its home star, perhaps civilization has not. Some worry that a cataclysm on the sun could trigger a “geomagnetic storm” on Earth that would knock out so many satellites and high-voltage transformers that advanced societies would lose electricity for months or years while waiting for replacements, creating a humanitarian disaster. This paper critically reviews the evidence while explaining many of the technical ideas. It concludes that some researchers have overestimated the risk, at least as manifested in their data, and perhaps as a result have received disproportionate public attention. Most measures suggest that what appears to have been the largest storm since the industrial revolution, the 1859 Carrington event, was less than two times as strong as recent storms, which civilization has shrugged off. I estimate the probability of catastrophe is well under 1%/decade. Yet the evidence on the probability of extreme events is thin, almost by definition, so the risk cannot be dismissed; and it has historically received little attention. We should not be complacent about the threat.

Statistical Characterization of Wind Power Ramps Via Extreme Value Analysis

Extreme power fluctuations in wind farms are rare but high-impact events, so proper characterization of these extreme fluctuations would assist with power systems operations planning in a power system with a high penetration of wind power. This work applies extreme value analysis methods to the statistical characterization of wind power ramps with 10-min resolution. The annual maxima series (AMS) method and peaks over threshold (POT) method are used to determine the probability of extreme wind power ramp events in a wind farm.

Extreme fluctuations of the relative velocities between droplets in turbulent airflow

We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St &amp;lt; 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, which suggests that the Stokes drag model misses important dynamics. Nevertheless, the scaling behavior of the extreme events in both the experiments and the simulations can be captured by the same multi-fractal model.

Lake level fluctuations boost toxic cyanobacterial "oligotrophic blooms".

Global warming has been shown to strongly influence inland water systems, producing noticeable increases in water temperatures. Rising temperatures, especially when combined with widespread nutrient pollution, directly favour the growth of toxic cyanobacteria. Climate changes have also altered natural water level fluctuations increasing the probability of extreme events as dry periods followed by heavy rains. The massive appearance of Dolichospermum lemmermannii ( = planktonic Anabaena), a toxic species absent from the pelagic zone of the subalpine oligotrophic Lake Maggiore before 2005, could be a consequence of the unusual fluctuations of lake level in recent years. We hypothesized that these fluctuations may favour the cyanobacterium as result of nutrient pulses from the biofilms formed in the littoral zone when the lake level is high. To help verify this, we exposed artificial substrates in the lake, and evaluated their nutrient enrichment and release after desiccation, together with measurements of fluctuations in lake level, precipitation and D.lemmermannii population. The highest percentage of P release and the lowest C∶P molar ratio of released nutrients coincided with the summer appearance of the D.lemmermannii bloom. The P pulse indicates that fluctuations in level counteract nutrient limitation in this lake and it is suggested that this may apply more widely to other oligotrophic lakes. In view of the predicted increase in water level fluctuations due to climate change, it is important to try to minimize such fluctuations in order to mitigate the occurrence of cyanobacterial blooms.

Extreme slowdowns for one-dimensional excited random walks

We study the asymptotics of the probabilities of extreme slowdown events for transient one-dimensional excited random walks. That is, if {Xn}n≥0 is a transient one-dimensional excited random walk and Tn=min{k:Xk=n}, we study the asymptotics of probabilities of the form P(Xn≤nγ) and P(Tnγ≥n) with γ<1. We show that there is an interesting change in the rate of decay of these extreme slowdown probabilities when γ<1/2.

Controlling extreme events on complex networks.

Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.