The Dependence of Solar Wind Burst Size on Burst Duration and Its Invariance Across Solar Cycles 23 and 24

Abstract

Time series of solar wind variables are bursty in nature. Bursts, or excursions, in the time series of solar wind parameters are associated with various transient structures in the solar wind plasma and are often the drivers of increased space weather activity in Earth's magnetosphere. We define bursts by setting a threshold value of the time series and identifying how often, and for how long, it is exceeded. This allows us to study how the statistical distributions and scaling properties of burst parameters vary over solar cycles 23 and 24. We find that the distributions of burst duration and integrated burst size vary over the solar cycle and between the equivalent phases of consecutive cycles. However, there exists a single power law scaling relation between burst size and duration, with a joint area‐duration scaling exponent α that is independent of the solar cycle. This provides a solar cycle invariant constraint between possible sizes and durations of solar wind bursts that can occur.

Network community structure of substorms using SuperMAG magnetometers

“…For each event, the time series from each magnetometer are Fourier-transformed, the phase spectrum is randomized whilst preserving the amplitude spectrum and this is then inverse Fourier-transformed to give a surrogate time series with the same power spectrum as the original signals, but with no time correlation (for an example see ref. 56 ). We used an iterated amplitude-adjusted Fourier transform 57 method with the Matlab code supplied by ref.…”

The Development of a Space Climatology: 3. Models of the Evolution of Distributions of Space Weather Variables With Timescale

“…Hence, developing a climatology giving the probability of space weather events of a given geoeffectiveness that covers both these extremes of the long‐term solar variation requires us to develop an understanding of relationships between these annual means and the distributions of event amplitudes, quantified over the relevant timescales. Because space weather events come in bursts, the integrated value of any activity index X over the most relevant timescale τ , I X , is a useful metric (Borovsky, ; Echer et al, ; Lockwood et al, ; Tindale et al, ), and this equals the arithmetic mean value times τ (i.e., I X = ∫ τ X d t = τ < X > τ ). Hence, it is important to study how < X > τ varies with τ and how it relates to the annual arithmetic mean value < X > τ =1year .…”

Variation of Geomagnetic Index Empirical Distribution and Burst Statistics Across Successive Solar Cycles

“…We have considered the burst return period, R, and burst duration, τ, which are both commonly studied; τ is also an important factor in terms of burst size (Tindale et al, 2018;Uritsky et al, 2001) Note. Exceedences are defined above the quantile threshold, q E .…”

“…We have considered the burst return period, R , and burst duration, τ , which are both commonly studied; τ is also an important factor in terms of burst size (Tindale et al., 2018; Uritsky et al., 2001) and burst time‐integrated effects (Haines et al., 2019; Mourenas et al., 2018). LC theory stipulates that for a given time series sample, the burst distribution averages $$\bar{\tau }$$ and $$\bar{R}$$ are not independent quantities; their ratio, $$\bar{\tau }$$/$$\bar{R}$$, can be determined wholly from the quantiles of the underlying empirical distribution of the observations from which the bursts were constructed.…”

“…Counting events in order to construct empirical distributions can be problematic as geomagnetic storms can have multiple onsets and substorms are generally not isolated (Kamide et al., 1998). One approach is to define a threshold and investigate bursts, or excursions of the variable, above this threshold (e.g., Consolini, 1997; Freeman et al., 2000; Hush et al., 2015; Moloney & Davidsen, 2011, 2014; Tindale et al., 2018; Uritsky et al., 2001). In order to construct bursts from geomagnetic index time series, we will therefore exploit the 1‐min resolution AE index and the recently constructed high‐time resolution equatorial index, SMR , for the years 1975–2017.…”