scholarly journals Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part II: Trend Detection and Assessment

2007 ◽  
Vol 64 (7) ◽  
pp. 2159-2175 ◽  
Author(s):  
Mara Felici ◽  
Valerio Lucarini ◽  
Antonio Speranza ◽  
Renato Vitolo
Keyword(s):  
Time Series ◽  
Total Energy ◽  
Extreme Values ◽  
Linear Time ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Trend Detection ◽  
Ratio Test ◽  
Scale Parameters ◽  
Baroclinic Model

Abstract A baroclinic model for the atmospheric jet at middle latitudes is used as a stochastic generator of nonstationary time series of the total energy of the system. A linear time trend is imposed on the parameter TE, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent generalized extreme value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location μ and scale parameters σ depend quadratically and linearly on time, respectively, while the shape parameter ξ is kept constant. From this family, a GEV model is selected with Akaike’s information criterion, complemented by the likelihood ratio test and by assessment through standard graphical diagnostics. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on TE. In particular, power-law dependences of μ and σ on TE are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of TE spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

scholarly journals Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

2007 ◽  
Vol 64 (7) ◽  
pp. 2137-2158 ◽  
Author(s):  
Mara Felici ◽  
Valerio Lucarini ◽  
Antonio Speranza ◽  
Renato Vitolo
Keyword(s):  
Time Series ◽  
Total Energy ◽  
Goodness Of Fit ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Stationary Time Series ◽  
Return Level ◽  
Extreme Value Statistics ◽  
Intermediate Complexity

Abstract A baroclinic model of intermediate complexity for the atmospheric jet at middle latitudes is used as a stochastic generator of atmosphere-like time series. In this case, time series of the total energy of the system are considered. Statistical inference of extreme values is applied to sequences of yearly maxima extracted from the time series in the rigorous setting provided by extreme value theory. The generalized extreme value (GEV) family of distributions is used here as a basic model, both for its qualities of simplicity and its generality. Several physically plausible values of the parameter TE, which represents the forced equator-to-pole temperature gradient and is responsible for setting the average baroclinicity in the atmospheric model, are used to generate stationary time series of the total energy. Estimates of the three GEV parameters—location, scale, and shape—are inferred by maximum likelihood methods. Standard statistical diagnostics, such as return level and quantile–quantile plots, are systematically applied to assess goodness-of-fit. The GEV parameters of location and scale are found to have a piecewise smooth, monotonically increasing dependence on TE. The shape parameter also increases with TE but is always negative, as is required a priori by the boundedness of the total energy. The sensitivity of the statistical inferences is studied with respect to the selection procedure of the maxima: the roles occupied by the length of the sequences of maxima and by the length of data blocks over which the maxima are computed are critically analyzed. Issues related to model sensitivity are also explored by varying the resolution of the system. The method used in this paper is put forward as a rigorous framework for the statistical analysis of extremes of observed data, to study the past and present climate and to characterize its variations.

scholarly journals Statistics of the largest geomagnetic storms per solar cycle (1844-1993)

1997 ◽  
Vol 15 (6) ◽  
pp. 719-728 ◽  
Author(s):  
D. M. Willis ◽  
P. R. Stevens ◽  
S. R. Crothers
Keyword(s):  
Statistical Analysis ◽  
Solar Cycle ◽  
Geomagnetic Storm ◽  
Extreme Values ◽  
Geomagnetic Storms ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Relative Dispersion ◽  
Solar Cycles ◽  
Aa Index

Abstract. A previous application of extreme-value statistics to the first, second and third largest geomagnetic storms per solar cycle for nine solar cycles is extended to fourteen solar cycles (1844–1993). The intensity of a geomagnetic storm is measured by the magnitude of the daily aa index, rather than the half-daily aa index used previously. Values of the conventional aa index (1868–1993), supplemented by the Helsinki Ak index (1844–1880), provide an almost continuous, and largely homogeneous, daily measure of geomagnetic activity over an interval of 150 years. As in the earlier investigation, analytic expressions giving the probabilities of the three greatest storms (extreme values) per solar cycle, as continuous functions of storm magnitude (aa), are obtained by least-squares fitting of the observations to the appropriate theoretical extreme-value probability functions. These expressions are used to obtain the statistical characteristics of the extreme values; namely, the mode, median, mean, standard deviation and relative dispersion. Since the Ak index may not provide an entirely homogeneous extension of the aa index, the statistical analysis is performed separately for twelve solar cycles (1868–1993), as well as nine solar cycles (1868–1967). The results are utilized to determine the expected ranges of the extreme values as a function of the number of solar cycles. For fourteen solar cycles, the expected ranges of the daily aa index for the first, second and third largest geomagnetic storms per solar cycle decrease monotonically in magnitude, contrary to the situation for the half-daily aa index over nine solar cycles. The observed range of the first extreme daily aa index for fourteen solar cycles is 159–352 nT and for twelve solar cycles is 215–352 nT. In a group of 100 solar cycles the expected ranges are expanded to 137–539 and 177–511 nT, which represent increases of 108% and 144% in the respective ranges. Thus there is at least a 99% probability that the daily aa index will satisfy the condition aa < 550 for the largest geomagnetic storm in the next 100 solar cycles. The statistical analysis is used to infer that remarkable conjugate auroral observations on the night of 16 September 1770, which were recorded during the first voyage of Captain Cook to Australia, occurred during an intense geomagnetic storm.

scholarly journals Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity

Atmosphere ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1273
Author(s):  
Tosiyuki Nakaegawa ◽  
Takuro Kobashi ◽  
Hirotaka Kamahori
Keyword(s):  
Time Series ◽  
Extreme Precipitation ◽  
Extreme Value ◽  
Nonstationary Time Series ◽  
Return Level ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Monthly Precipitation ◽  
Annual Maximum ◽  
Value Analysis

Extreme precipitation is no longer stationary under a changing climate due to the increase in greenhouse gas emissions. Nonstationarity must be considered when realistically estimating the amount of extreme precipitation for future prevention and mitigation. Extreme precipitation with a certain return level is usually estimated using extreme value analysis under a stationary climate assumption without evidence. In this study, the characteristics of extreme value statistics of annual maximum monthly precipitation in East Asia were evaluated using a nonstationary historical climate simulation with an Earth system model of intermediate complexity, capable of long-term integration over 12,000 years (i.e., the Holocene). The climatological means of the annual maximum monthly precipitation for each 100-year interval had nonstationary time series, and the ratios of the largest annual maximum monthly precipitation to the climatological mean had nonstationary time series with large spike variations. The extreme value analysis revealed that the annual maximum monthly precipitation with a return level of 100 years estimated for each 100-year interval also presented a nonstationary time series which was normally distributed and not autocorrelated, even with the preceding and following 100-year interval (lag 1). Wavelet analysis of this time series showed that significant periodicity was only detected in confined areas of the time–frequency space.

scholarly journals Freezing transitions and extreme values: random matrix theory, and disordered landscapes

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120503 ◽  
Author(s):  
Yan V. Fyodorov ◽  
Jonathan P. Keating
Keyword(s):  
Matrix Theory ◽  
Extreme Values ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Constant Length ◽  
Energy Models ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Transition Scenario ◽  
Unitary Ensemble

We argue that the freezing transition scenario , previously conjectured to occur in the statistical mechanics of 1/ f -noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials p N ( θ ) of large N × N random unitary (circular unitary ensemble) matrices U N ; i.e. the extreme value statistics of p N ( θ ) when . In addition, we argue that it leads to multi-fractal-like behaviour in the total length μ N ( x ) of the intervals in which | p N ( θ )|> N x , x >0, in the same limit. We speculate that our results extend to the large values taken by the Riemann zeta function ζ ( s ) over stretches of the critical line of given constant length and present the results of numerical computations of the large values of ). Our main purpose is to draw attention to the unexpected connections between these different extreme value problems.

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.

Prediction of Airgap Statistics for Fixed Offshore Platforms

2011 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai
Keyword(s):  
Time Series ◽  
Random Field ◽  
Wave Field ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Air Gap ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Offshore Platforms ◽  
Spatial Extremes

Air gap statistics for offshore platforms is directly related to the extreme value statistics of the random ocean wave field. The present paper describes a new method for predicting the extreme values of a random wave field in both space and time. The method relies on the use of data provided by measurements or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, a time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using recently developed techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This procedure is applied to the prediction of air gap statistics for a jacket structure.

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.

Electro-Mechanical Admittance-Based Damage Detection Using Extreme Value Statistics

2008 ◽  
Vol 385-387 ◽  
pp. 561-564 ◽  
Author(s):  
Costas P. Providakis
Keyword(s):  
Health Monitoring ◽  
Extreme Values ◽  
Simulated Data ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Engineering Structures ◽  
Value Analysis ◽  
Electromechanical Impedance ◽  
Tail Distribution

This paper presents the use of statistically rigorous algorithms combined with electromechanical (E/M) impedance approach for health monitoring of engineering structures. In particular, a statistical pattern recognition procedure is developed, based on frequency domain data of electromechanical impedance, to establish a decision boundary for damage identification. In order to diagnose damage with statistical confidence, health monitoring is cast in the context of outlier detection framework. Inappropriate modeling of tail distribution of outliers imposes potentially misleading behavior associated with damage. The present paper attempts to address the problem of establishing decision boundaries based on extreme value statistics so that the extreme values of outliers associated with tail distribution can be properly modeled. The validity of the proposed method is demonstrated using finite element method (FEM) simulated data while a comparison is performed for the extreme value analysis results contrasted with the standard approach where it is assumed that the damage-sensitive features are normally distributed.

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