scholarly journals Extreme value theory in the solar wind: the role of current sheets

2019 ◽  
Vol 490 (2) ◽  
pp. 1879-1893
Author(s):  
Tiago F P Gomes ◽  
Erico L Rempel ◽  
Fernando M Ramos ◽  
Suzana S A Silva ◽  
Pablo R Muñoz
Keyword(s):  
Solar Wind ◽  
Power Spectra ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Intermittent Turbulence ◽  
Current Sheets ◽  
Developed Turbulence ◽  
The Right

ABSTRACT This article provides observational evidence for the direct relation between current sheets, multifractality and fully developed turbulence in the solar wind. In order to study the role of current sheets in extreme-value statistics in the solar wind, the use of magnetic volatility is proposed. The statistical fits of extreme events are based on the peaks-over-threshold (POT) modelling of Cluster 1 magnetic field data. The results reveal that current sheets are the main factor responsible for the behaviour of the tail of the magnetic volatility distributions. In the presence of current sheets, the distributions display a positive shape parameter, which means that the distribution is unbounded in the right tail. Thus the appearance of larger current sheets is to be expected and magnetic reconnection events are more likely to occur. The volatility analysis confirms that current sheets are responsible for the −5/3 Kolmogorov power spectra and the increase in multifractality and non-Gaussianity in solar wind statistics. In the absence of current sheets, the power spectra display a −3/2 Iroshnikov–Kraichnan law. The implications of these findings for the understanding of intermittent turbulence in the solar wind are discussed.

scholarly journals Return Period Evaluation of the Largest Possible Earthquake Magnitudes in Mainland China Based on Extreme Value Theory

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3519
Author(s):  
Yanbing Bai ◽  
Ning Ma ◽  
Shengwang Meng
Keyword(s):  
Earthquake Engineering ◽  
Return Period ◽  
Extreme Value Theory ◽  
Threshold Model ◽  
Mainland China ◽  
Value Theory ◽  
Extreme Value ◽  
Geographical Information ◽  
Geographical Regions ◽  
The Right

The largest possible earthquake magnitude based on geographical characteristics for a selected return period is required in earthquake engineering, disaster management, and insurance. Ground-based observations combined with statistical analyses may offer new insights into earthquake prediction. In this study, to investigate the seismic characteristics of different geographical regions in detail, clustering was used to provide earthquake zoning for Mainland China based on the geographical features of earthquake events. In combination with geospatial methods, statistical extreme value models and the right-truncated Gutenberg–Richter model were used to analyze the earthquake magnitudes of Mainland China under both clustering and non-clustering. The results demonstrate that the right-truncated peaks-over-threshold model is the relatively optimal statistical model compared with classical extreme value theory models, the estimated return level of which is very close to that of the geographical-based right-truncated Gutenberg–Richter model. Such statistical models can provide a quantitative analysis of the probability of future earthquake risks in China, and geographical information can be integrated to locate the earthquake risk accurately.

Current sheets, magnetic islands and associated particle acceleration in the solar wind as observed by Ulysses near the ecliptic plane

2020 ◽  
Author(s):  
Olga Malandraki ◽  
Olga Khabarova ◽  
Roberto Bruno ◽  
Gary Zank ◽  
Gang Li and the ISSI-405 team
Keyword(s):  
Solar Wind ◽  
Particle Acceleration ◽  
Magnetic Reconnection ◽  
Energetic Particle ◽  
Particle Flux ◽  
Energetic Particles ◽  
Magnetic Islands ◽  
Intermittent Turbulence ◽  
Current Sheets ◽  
Energetic Particle Flux

<p>Recent studies of particle acceleration in the heliosphere have revealed a new mechanism that can locally energize particles up to several MeV/nuc. Stream-stream interactions as well as the heliospheric current sheet – stream interactions lead to formation of large magnetic cavities, bordered by strong current sheets (CSs), which in turn produce secondary CSs and dynamical small-scale magnetic islands (SMIs) of ~0.01AU or less owing to magnetic reconnection. It has been shown that particle acceleration or re-acceleration occurs via stochastic magnetic reconnection in dynamical SMIs confined inside magnetic cavities observed at 1 AU. The study links the occurrence of CSs and SMIs with characteristics of intermittent turbulence and observations of energetic particles of keV-MeV/nuc energies at ~5.3 AU. We analyze selected samples of different plasmas observed by Ulysses during a widely discussed event, which was characterized by a series of high-speed streams of various origins that interacted beyond the Earth’s orbit in January 2005. The interactions formed complex conglomerates of merged interplanetary coronal mass ejections, stream/corotating interaction regions and magnetic cavities. We study properties of turbulence and associated structures of various scales. We confirm the importance of intermittent turbulence and magnetic reconnection in modulating solar energetic particle flux and even local particle acceleration. Coherent structures, including CSs and SMIs, play a significant role in the development of secondary stochastic particle acceleration, which changes the observed energetic particle flux time-intensity profiles and increases the final energy level to which energetic particles can be accelerated in the solar wind.</p>

The role of resonance in the extreme value statistics of flow-induced response

2020 ◽  
Vol 148 (4) ◽  
pp. 2789-2789
Author(s):  
Connor J. McCluskey ◽  
Manton J. Guers ◽  
Stephen C. Conlon
Keyword(s):  
Extreme Value ◽  
Extreme Value Statistics ◽  
Induced Response

Evolution of Turbulence in the Kelvin–Helmholtz Instability mediated by the Magnetopause and its Boundary Layer

2020 ◽  
Author(s):  
Francesca Di Mare ◽  
Luca Sorriso-Valvo ◽  
Alessandro Retino' ◽  
Francesco Malara ◽  
Hiroshi Hasegawa
Keyword(s):  
Boundary Layer ◽  
Solar Wind ◽  
Large Scale ◽  
Velocity Shear ◽  
Helmholtz Instability ◽  
Intermittent Turbulence ◽  
Large Scale Structures ◽  
Developed Turbulence ◽  
Spacecraft Data ◽  
Efficient Transfer

<p>The turbulence at the interface between the solar wind and the Earth’s magnetosphere, mediated by the magnetopause and its boundary layer are investigated by using Geotail and THEMIS spacecraft data during ongoing Kelvin-Helmholtz instability (KHI). The efficient transfer of energy across scales for which the turbulence is responsible, achieves the connection between the macroscopic flow and the microscopic dissipation of this energy. This boundary layer is thought to be the result of the observed plasma transfer, driven by the development of the KHI, originating from the velocity shear between the solar wind and the almost static near-Earth plasma. A collection of 20 events spatially located on the tail-flank magnetopause, selected from previously studied by Hasegawa et al. 2006 and Lin et al. 2014, have been tested against standard diagnostics for intermittent turbulence. In light of the results obtained, we have investigated the behaviour of several parameters as a function of the progressive departure along the Geocentric Solar Magnetosphere coordinates, which roughly represent the direction in which we expect the KHI vortices to evolve towards fully developed turbulence. It appears that a fluctuating behaviour of the parameters exist, visible as a decreasing, quasi-periodic modulation with an associated periodicity, estimated to correspond to approximately 6.4 Earth Radii. Such observed wavelength is consistent with the estimated vortices roll-up wavelength reported in the literature for these events. If the turbulence is pre-existent, it is possible that the KHI modulates its properties along the magnetosheath, as we observed. On the other hand, if we assume that the KHI has been initiated near the magnetospheric nose and develops along the flanks, then the different intervals we study may be sampling the plasma at different stages of evolution of the KH-generated turbulence, after the instability has injected energy in a cascading process as large-scale structures.</p>

scholarly journals Weather regime dependence of extreme value statistics for summer temperature and precipitation

2008 ◽  
Vol 15 (3) ◽  
pp. 365-378 ◽  
Author(s):  
P. Yiou ◽  
K. Goubanova ◽  
Z. X. Li ◽  
M. Nogaj
Keyword(s):  
North Atlantic ◽  
Clustering Algorithm ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Climate Data ◽  
Atmospheric Variability ◽  
Weather Patterns ◽  
The North ◽  
Temperature And Precipitation

Abstract. Extreme Value Theory (EVT) is a useful tool to describe the statistical properties of extreme events. Its underlying assumptions include some form of temporal stationarity in the data. Previous studies have been able to treat long-term trends in datasets, to obtain the time dependence of EVT parameters in a parametric form. Since there is also a dependence of surface temperature and precipitation to weather patterns obtained from pressure data, we determine the EVT parameters of those meteorological variables over France conditional to the occurrence of North Atlantic weather patterns in the summer. We use a clustering algorithm on geopotential height data over the North Atlantic to obtain those patterns. This approach refines the straightforward application of EVT on climate data by allowing us to assess the role of atmospheric variability on temperature and precipitation extreme parameters. This study also investigates the statistical robustness of this relation. Our results show how weather regimes can modulate the different behavior of mean climate variables and their extremes. Such a modulation can be very different for the mean and extreme precipitation.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Accurate Estimate ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.

scholarly journals Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps

2011 ◽  
Vol 31 (5) ◽  
pp. 1363-1390 ◽  
Author(s):  
CHINMAYA GUPTA ◽  
MARK HOLLAND ◽  
MATTHEW NICOL
Keyword(s):  
Time Series ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Distributed Processes ◽  
Return Time Statistics ◽  
Generic Points ◽  
Lozi Maps

AbstractIn this paper we establish extreme value statistics for observations on a class of hyperbolic systems: planar dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. In particular, we show that for time series arising from Hölder observations on these systems which are maximized at generic points the successive maxima of the time series are distributed according to the corresponding extreme value distributions for independent identically distributed processes. These results imply an exponential law for the hitting and return time statistics of these dynamical systems.

scholarly journals The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)

2017 ◽  
Vol 10 (11) ◽  
pp. 88
Author(s):  
Sonia Benito Muela ◽  
Carmen López-Martín ◽  
Mª Ángeles Navarro
Keyword(s):  
Extreme Value Theory ◽  
Market Risk ◽  
Heavy Tail ◽  
Capital Requirements ◽  
Value Theory ◽  
Extreme Value ◽  
Skewed Distribution ◽  
Symmetric Distribution ◽  
Volatility Model

In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Value at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm’s loss function. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.

scholarly journals An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails

2021 ◽  
Author(s):  
M. de Carvalho ◽  
S. Pereira ◽  
P. Pereira ◽  
P. de Zea Bermudez
Keyword(s):  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Finite Sample ◽  
Bayesian Lasso ◽  
Proposed Model ◽  
Left And Right ◽  
Heavy Tailed ◽  
The Right ◽  
Type Specification

AbstractWe introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

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