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.

Statistical Study of Geomagnetic Storms during Year 1996-2007

2012 ◽  
Vol 433-440 ◽  
pp. 268-271
Author(s):  
Balveer S. Rathore ◽  
Subhash C. Kaushik ◽  
K.K. Parashar ◽  
Rammohan S. Bhadoria ◽  
Dinesh C. Gupta
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Geomagnetic Storm ◽  
Statistical Study ◽  
Geomagnetic Storms ◽  
Sunspot Cycle ◽  
Solar Wind Plasma ◽  
Strongly Correlated ◽  
Minimum Phase ◽  
Solar Cycle 23

A geomagnetic storm is a global disturbance in Earth’s magnetic field usually occurred due to abnormal conditions in the interplanetary magnetic field (IMF) and solar wind plasma emissions caused by various solar phenomenon. A study of 220 geomagnetic storms associated with disturbance storm time (Dst) decreases of more than -50 nT to -300 nT, observed during 1996-2007, the span of solar cycle 23. We have analyzed and studied them statistically. We find yearly occurrences of geomagnetic storm are strongly correlated with 11-year sunspot cycle, but no significant correlation between the maximum and minimum phase of solar cycle-23 have been found. It is also found that solar cycle-23 is remarkable for occurrence of Intense geomagnetic storm during its declining phase. The detailed results are discussed in this paper.

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.

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.

Extreme value statistics: potential benefits in water quality management

1997 ◽  
Vol 36 (5) ◽  
pp. 133-140 ◽  
Author(s):  
O. Thas ◽  
P. Vanrolleghem ◽  
B. Kops ◽  
L. Van Vooren ◽  
J. P. Ottoy
Keyword(s):  
Water Quality ◽  
Quality Management ◽  
Extreme Values ◽  
Water Quality Management ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Design Stage ◽  
Sea Levels ◽  
Wind Speeds ◽  
Potential Benefits

Recently extreme value statistics have proven useful in environmental applications like the assessment of sea-levels, wind speeds and ozone concentrations. In this paper, after a brief overview of the statistical theory of extreme values, modelling issues are discussed with stress on applications in water quality management. Risk analysis procedures are presented that consider the extremal behaviour of water quality in the design stage of environmental constructions.

scholarly journals Ionospheric storms at geophysically-equivalent sites – Part 1: Storm-time patterns for sub-auroral ionospheres

2009 ◽  
Vol 27 (4) ◽  
pp. 1679-1694 ◽  
Author(s):  
M. Mendillo ◽  
C. Narvaez
Keyword(s):  
Solar Cycle ◽  
Northern Hemisphere ◽  
Electric Fields ◽  
Geomagnetic Storms ◽  
Hemispheric Differences ◽  
Solar Cycles ◽  
Plasma Dynamics ◽  
Storm Effects ◽  
Typical Morphology ◽  
Minimum Solar Activity

Abstract. The systematic study of ionospheric storms has been conducted primarily with groundbased data from the Northern Hemisphere. Significant progress has been made in defining typical morphology patterns at all latitudes; mechanisms have been identified and tested via modeling. At higher mid-latitudes (sites that are typically sub-auroral during non-storm conditions), the processes that change significantly during storms can be of comparable magnitudes, but with different time constants. These include ionospheric plasma dynamics from the penetration of magnetospheric electric fields, enhancements to thermospheric winds due to auroral and Joule heating inputs, disturbance dynamo electrodynamics driven by such winds, and thermospheric composition changes due to the changed circulation patterns. The ~12° tilt of the geomagnetic field axis causes significant longitude effects in all of these processes in the Northern Hemisphere. A complementary series of longitude effects would be expected to occur in the Southern Hemisphere. In this paper we begin a series of studies to investigate the longitudinal-hemispheric similarities and differences in the response of the ionosphere's peak electron density to geomagnetic storms. The ionosonde stations at Wallops Island (VA) and Hobart (Tasmania) have comparable geographic and geomagnetic latitudes for sub-auroral locations, are situated at longitudes close to that of the dipole tilt, and thus serve as our candidate station-pair choice for studies of ionospheric storms at geophysically-comparable locations. They have an excellent record of observations of the ionospheric penetration frequency (foF2) spanning several solar cycles, and thus are suitable for long-term studies. During solar cycle #20 (1964–1976), 206 geomagnetic storms occurred that had Ap≥30 or Kp≥5 for at least one day of the storm. Our analysis of average storm-time perturbations (percent deviations from the monthly means) showed a remarkable agreement at both sites under a variety of conditions. Yet, small differences do appear, and in systematic ways. We attempt to relate these to stresses imposed over a few days of a storm that mimic longer term morphology patterns occurring over seasonal and solar cycle time spans. Storm effects versus season point to possible mechanisms having hemispheric differences (as opposed to simply seasonal differences) in how solar wind energy is transmitted through the magnetosphere into the thermosphere-ionosphere system. Storm effects versus the strength of a geomagnetic storm may, similarly, be related to patterns seen during years of maximum versus minimum solar activity.

scholarly journals Predicting the occurrence of super-storms

2005 ◽  
Vol 23 (9) ◽  
pp. 2989-2995 ◽  
Author(s):  
N. Srivastava
Keyword(s):  
Solar Cycle ◽  
Geomagnetic Storm ◽  
High Speed ◽  
Geomagnetic Storms ◽  
Active Regions ◽  
Initial Speed ◽  
Reliable Prediction ◽  
Intense Storm ◽  
Ram Pressure ◽  
Class Flare

Abstract. A comparative study of five super-storms (Dst<-300 nT) of the current solar cycle after the launch of SoHO, to identify solar and interplanetary variables that influence the magnitude of resulting geomagnetic storms, is described. Amongst solar variables, the initial speed of a CME is considered the most reliable predictor of the strength of the associated geomagnetic storm because fast mass ejections are responsible for building up the ram pressure at the Earth's magnetosphere. However, although most of the super-storms studied were associated with high speed CMEs, the Dst index of the resulting geomagnetic storms varied between -300 to -472 nT. The most intense storm of 20 November 2003, (Dst ~ -472 nT) had its source in a comparatively smaller active region and was associated with a relatively weaker, M-class flare while all other super-storms had their origins in large active regions and were associated with strong X-class flares. However, this superstorm did not show any associated extraordinary solar and interplanetary characteristics. The study also reveals the challenge in the reliable prediction of the magnitude of a geomagnetic storm from solar and interplanetary variables.

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 Topics in data analysis using R in extreme value theory

2013 ◽  
Vol 10 (1) ◽  
Author(s):  
Helena Penalva ◽  
Manuela Neves
Keyword(s):  
Applied Sciences ◽  
Data Analysis ◽  
Open Source Software ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Data Sets ◽  
Statistics Of Extremes

The statistical Extreme Value Theory has grown gradually from the beginning of the 20th century. Its unquestionable importance in applications was definitely recognized after Gumbel's book in 1958, Statistics of Extremes. Nowadays there is a wide number of applied sciences where extreme value statistics are largely used. So, accurately modeling extreme events has become more and more important and the analysis requires tools that must be simple to use but also should consider complex statistical models in order to produce valid inferences. To deal with accurate, friendly, free and open-source software is of great value for practitioners and researchers. This paper presents a review of the main steps for initializing a data analysis of extreme values in R environment. Some well documented packages are briefly described and two data sets will be considered for illustrating the use of some functions.

scholarly journals Climate change impact on groundwater levels: ensemble modelling of extreme values

2012 ◽  
Vol 9 (6) ◽  
pp. 7835-7875 ◽  
Author(s):  
J. Kidmose ◽  
J. C. Refsgaard ◽  
L. Troldborg ◽  
L. P. Seaby ◽  
M. M. Escrivà
Keyword(s):  
Climate Models ◽  
Extreme Values ◽  
Control Period ◽  
Extreme Value ◽  
Global Climate Models ◽  
Extreme Value Statistics ◽  
Return Periods ◽  
Future Period ◽  
Groundwater Levels ◽  
The Future

Abstract. This paper presents a first attempt to estimate future groundwater levels by applying extreme value statistics on predictions from a hydrological model. Climate for the future period, 2081–2100, are represented by projections from nine combinations of three global climate models and six regional climate models, and downscaled with two different methods. An integrated surface water/groundwater model is forced with precipitation, temperature, and evapotranspiration from the 18 model – and downscaling combinations. Extreme value analyses are performed on the hydraulic head changes from a control period (1991–2010) to the future period for the 18 combinations. Hydraulic heads for return periods of 21, 50 and 100 yr (T21–100) are estimated. Three uncertainty sources are evaluated; climate models, downscaling and extreme value statistics. Of these sources, downscaling dominates for the higher return periods of 50 and 100 yr, whereas uncertainty from climate models and downscaling are similar for lower return periods. Uncertainty from the extreme value statistics only contribute up to around 10% of the uncertainty from the three sources.

scholarly journals GLOBAL FLUCTUATIONS IN PHYSICAL SYSTEMS: A SUBTLE INTERPLAY BETWEEN SUM AND EXTREME VALUE STATISTICS

2008 ◽  
Vol 22 (20) ◽  
pp. 3311-3368 ◽  
Author(s):  
MAXIME CLUSEL ◽  
ERIC BERTIN
Keyword(s):  
Extreme Values ◽  
Random Variables ◽  
Extreme Value ◽  
Physical Models ◽  
Extreme Value Statistics ◽  
Specific Class ◽  
Qualitative Properties ◽  
Rigorous Results ◽  
General Mapping ◽  
Global Fluctuations

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses different connections that may appear between problems of sums and of extreme values of random variables, and emphasizes physical situations in which such connections are relevant. Along this line of thought, standard convergence theorems for sums and extreme values of independent and identically distributed random variables are recalled, and some rigorous results as well as more heuristic reasonings are presented for correlated or non-identically distributed random variables. More specifically, the role of extreme values within sums of broadly distributed variables is addressed, and a general mapping between extreme values and sums is presented, allowing us to identify a class of correlated random variables whose sum follows (generalized) extreme value distributions. Possible applications of this specific class of random variables are illustrated on the example of two simple physical models. A few extensions to other related classes of random variables sharing similar qualitative properties are also briefly discussed, in connection with the so-called BHP distribution.

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