A note on the statistics of the largest geomagnetic storms per solar cycle

Solow, Andrew R.; Beet, Andrew R.

doi:10.1016/j.jastp.2003.12.010

Cited by 2 publications

(7 citation statements)

References 4 publications

(12 reference statements)

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“…In this study, we apply the newly developed BMM and POT methods in the EVT with suitable fitting methods to the most completed daily Aa index to estimate the possibility of the extreme geomagnetic storms. Being consistent with the Solow and Beet (), the probabilities of extreme geomagnetic storms in our results are smaller than the previous studies (Siscoe, ; Willis et al, ). In our study, both methods obtain negative shape parameters, which indicate that the Aa index has an upper bound.…”

Section: Discussionsupporting

confidence: 88%

“…Previous studies applied Gumbel method (one of EVT models) to the Aa index to estimate the probability of the extreme geomagnetic storm occurrence (Siscoe, 1976;Willis et al, 1997). However, as pointed out by Solow & Beet (2004), the fitting methods in these previous studies are problematic, which led to higher probabilities of extreme geomagnetic storms. In this study, we apply the newly developed BMM and POT methods in the EVT with suitable fitting methods to the most completed daily Aa index to estimate the possibility of the extreme geomagnetic storms.…”

Section: Discussionmentioning

confidence: 99%

“…Willis et al (1997) updated the study by Siscoe (1976) with the more extended daily Aa index. Later, Solow and Beet (2004) pointed out that there was a problem in the fitting methods of Siscoe (1976) and Willis et al (1997) that led to higher probabilities of extreme geomagnetic storms. According to Solow and Beet (2004), the maximum likelihood (ML) is a more accurate method for parameter fitting.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Solow and Beet (2004) pointed out that there was a problem in the fitting methods of Siscoe (1976) and Willis et al (1997) that led to higher probabilities of extreme geomagnetic storms. According to Solow and Beet (2004), the maximum likelihood (ML) is a more accurate method for parameter fitting. Recently, two more generalized EVT models, block maxima method (BMM) and peak over threshold (POT), with more accurate fitting models, L moment, and ML fitting, respectively, have been developed (Coles, 2001;Gilleland & Katz, 2016a, 2016b.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Occurrence Probability of Extreme Geomagnetic Storms by Applying Extreme Value Theory to Aa Index

Chen

Chai

et al. 2019

JGR Space Physics

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In this work, the occurrence probability of extreme geomagnetic storms is estimated by applying extreme value theory to the geomagnetic activity Aa index. The Aa index has 172 years observation time span, which is much longer than other geomagnetic indices, and thus is more suitable for analysis for rarely occurred extreme geomagnetic storms. We use two newly developed extreme value theory methods, block maxima method and peak over threshold, and find that the extreme geomagnetic storm that happened in March 1989 may happen once per century. This result implies that we should pay more attention to such extreme geomagnetic storms that can cause space weather hazards.

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Section: Discussionsupporting

confidence: 88%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of the Occurrence Probability of Extreme Geomagnetic Storms by Applying Extreme Value Theory to Aa Index

Chen

Chai

et al. 2019

JGR Space Physics

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“…For our statistical analysis, we need to develop a framework for ranked data. For pairs of samples { x 1 > x 2 }, each taken from blocks of data, the conditional GEV probability density function for x 2 given x 1 is

γ_{2 false| 1} false(x_{2} false| x_{1} false) = \frac{γ false(x_{2} false)}{normalΓ false(x_{1} false)},

and the joint density function for x 1 and x 2 is

γ_{1, 2} false(x_{1}, x_{2} false) = γ_{2 false| 1} false(x_{2} false| x_{1} false) \cdot γ false(x_{1} false) = \frac{γ false(x_{1} false) γ false(x_{2} false)}{normalΓ false(x_{1} false)}

(e.g., Chandler, 1952; Nagaraja, 1982; Solow & Beet, 2004). The marginal density and cumulative functions for x 1 are just those of the GEV distribution,

γ_{1} false(x_{1} false) = \int_{- \infty}^{x_{1}} γ_{1, 2} false(x_{1}, ϕ_{2} false) d ϕ_{2} = γ false(x_{1} false),

and

Γ_{1} false(x_{1} false) = normalΓ false(x_{1} false) .

…”

Section: Framework For Ranked Samplesmentioning

confidence: 99%

Extreme‐Event Magnetic Storm Probabilities Derived From Rank Statistics of Historical Dst Intensities for Solar Cycles 14–24

Love

2021

Space Weather

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A compilation is made of the largest and second‐largest magnetic‐storm‐maximum intensities, −Dst1 and −Dst2, for solar cycles 14–24 (1902–2016) by sampling Oulu Dcx for cycles 19–24, using published −Dstm values for 4 intense storms in cycles 14, 15, and 18 (1903, 1909, 1921, 1946), and calculating 15 new storm‐maximum −Dstm values (reported here) for cycles 14–18. Three different models are fitted to the cycle‐ranked −Dst1 and −Dst2 values using a maximum‐likelihood algorithm: A Gumbel model, an unconstrained Generalized‐Extreme‐Value model, and a Weibull model constrained to have a physically justified maximum storm intensity of −Dstm = 2500 nT. All three models are good descriptions of the data. Since the best model is not clearly revealed with standard statistical tests, inference is precluded of the source process giving rise to storm‐maximum −Dstm values. Of the three candidate models, the constrained Weibull gives the lowest superstorm occurrence probabilities. Using the compiled data and the constrained Weibull model, a once‐per‐century storm intensity is estimated to be −Dst1 = 663 nT, with a bootstrap 68% confidence interval of [497, 694] nT. Similarly, the probability that a future storm will have an intensity exceeding that of the March 1989 superstorm, −Dstm > 565 nT, is 0.246 per cycle with a 68% confidence interval of [0.140, 0.311] per cycle. Noting (possibly slight) ambiguity in the rankings of storm intensities, using the same methods, but storms more intense than those identified for cycles 14–16, would yield a higher once‐per‐century intensity and a higher probability for a −Dstm > 565 nT storm.

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A note on the statistics of the largest geomagnetic storms per solar cycle

Cited by 2 publications

References 4 publications

Estimation of the Occurrence Probability of Extreme Geomagnetic Storms by Applying Extreme Value Theory to Aa Index

Estimation of the Occurrence Probability of Extreme Geomagnetic Storms by Applying Extreme Value Theory to Aa Index

Extreme‐Event Magnetic Storm Probabilities Derived From Rank Statistics of Historical Dst Intensities for Solar Cycles 14–24

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