Automatic selection of Dst storms and their seasonal variations in two versions of Dst in 50 years
© The Author(s) 2017
Received: 14 October 2016
Accepted: 12 April 2017
Published: 26 April 2017
KeywordsGeomagnetic Dst storms Semiannual variation Energy input Ring current Equinoctial hypothesis RM effect
Geomagnetic storms are disturbances in Earth’s magnetic field lasting from several hours to several days, and are produced by enhanced solar wind–magnetosphere coupling (e.g., Svalgaard 1977; Akasofu 1981; Gonzalez et al. 1994; Kamide et al. 1998) and ionosphere–magnetosphere plasma coupling (e.g., Daglis 1997; Khazanov et al. 2003; Ebihara et al. 2005). Geomagnetic indices such as the low-latitude Dst (disturbance storm time) index have been developed to study geomagnetic storms (e.g., Sugiura 1964; Sugiura and Kamei 1991; Love and Gannon 2009); see also Rostoker (1972). The storms have been studied for over 150 years using geomagnetic data, indices and models (e.g., Sabine 1856; Mayaud 1978; Iyemori 1980; Takalo et al. 1995; Siscoe and Crooker 1996; Daglis 1997; Kamide et al. 1998; Gonzalez et al. 1999; Cliver et al. 2000; Fok et al. 2001; Liemohn et al. 2001; O’Brien and McPherron 2002; Vijaya Lekshmi et al. 2011; Yakovchouk et al. 2012; Zhao and Zong 2012; Katus and Liemohn 2013; Kumar et al. 2015; Lakhina and Tsuritani 2016). From these studies, it is known that the occurrence and intensity of the storms vary with solar activity, time of year and time of day.
The storms are frequent and intense at high levels of solar activity (e.g., Ellis 1899; Zhang et al. 2007) due to the frequent occurrence of CMEs and ICMEs (interplanetary CMEs) (e.g., Gopalswamy et al. 2005). During solar minimum, the interaction of co-rotating interaction regions (CIRs) of solar origin with the magnetosphere produces weak recurrent storms (e.g., Richardson et al. 2001; Tulasiram et al. 2010; Cramer et al. 2013). Geomagnetic storms undergo a semiannual variation with equinoctial maxima and solstice minima (e.g., Cortie 1912; Cliver et al. 2000, 2001, 2004; Svalgaard et al. 2002; Svalgaard 2011). The semiannual variation has been interpreted in terms of the (1) axial hypothesis based on the variation of the heliospheric latitude of the Earth with time of year (e.g., Cortie 1912), (2) equinoctial hypothesis based on the variation of the angle between the Earth–Sun line and Earth’s dipole axis (e.g., Bartels 1932) and (3) Russell–Mcpherron (RM) effect based on the varying angle between the GSM (geocentric solar magnetospheric) Z-axis and GSE (geocentric solar ecliptic) Y-axis (Russell and McPherron 1973). Newell et al. (2001) suggested that both auroral ovals going simultaneously to darkness can cause the activity maximizing at equinoxes. Recently, Azpilicueta and Brunini (2012) suggested another version of the equinoctial hypothesis, that is, the deformation during the year of the shape of the magnetospheric cavity within which the ring current flows can cause the activity maximizing at equinoxes.
Recently, Mursula et al. (2011) found the global geomagnetic activity index (Ap) in 15 years in 1993–2008 showing a dominant annual variation, with equinoctial maxima alternating between spring in solar cycle (SC) 22 and fall in SC 23. Consequently they suggested that the overall semiannual variation in geomagnetic activity is due to the solar hemispheric asymmetry in the distribution of solar wind, which varies from one SC to another; and the overall semiannual variation has been seriously over estimated and is largely an artifact of the dominant annual variation with maxima alternating between spring and fall. However, using the inter-hourly variation (IHV) data for over 200 years Svalgaard (2011) contradicted this suggestion and showed that the semiannual variation is not an artifact. Thus, it is worth re-examining the semiannual variation in other indices.
In this paper, we present the seasonal variations of Dst storms in 50 years of Dst data. In addition to the widely used Kyoto Dst, the new (and improved) USGS Dst is used to check and confirm the findings. A brief comparison of the two Dst versions is presented in “Dst data” section. The storms in both versions are identified by developing a computer program (“Storm identification” section). The storms are analyzed for their important characteristics including the mean value of Dst during main phase (MP) (called ⟨DstMP⟩). Wavelet spectra of the storms are used to identify their periodic variations. The results are presented and discussed in “Results” and “Discussion” sections. Similar semiannual variations observed in both Dst versions are interpreted in terms of the equinoctial hypothesis and RM effect.
We use the Kyoto Dst of 1 nT resolution available at http://wdc.kugi.kyoto-u.ac.jp/dstdir/ and USGS Dst of 0.1 nT resolution available at http://geomag.usgs.gov/data for 50 years from 1958 to 2007. Both versions of the low-latitude hourly index (Dst) are obtained from the horizontal H component measured at four low-latitude stations (3 in north and 1 in south) outside the equatorial electrojet belt. The method of calculating Kyoto Dst (Sugiura 1964; Sugiura and Kamei 1991) involves (1) defining the baseline magnetic perturbation by a power series in time, (2) determining the solar quiet (Sq) variation for each observatory by selecting five quietest days for each month and using a double Fourier series as a function of local time and month, (3) obtaining the disturbance time variation [D(t)] for each observatory by removing the signals in (1) and (2) from the observed H component and (4) calculating Dst as the average of the four D(t) values normalized to the dipole equator. Karinen and Mursula (2005; and references therein) reconstructed the Kyoto Dst for 1932–2002 using the H component data from Cape Town for 1932–1940, which is not available for the closest Dst station (Hermanus). They also pointed out some obvious errors in Kyoto Dst.
Following the same calculation algorithm of Sugiura (1964), Love and Gannon (2009) produced the USGS Dst, first introduced as Dst5807-4SH. The two versions of Dst differ primarily in the removal of secular and Sq variations. While Kyoto Dst partially removes these variations, USGS Dst more fully removes them by using both time- and frequency-domain band-stop filtering that selectively removes the specific Fourier terms approximating periodic variations driven by Earth’s rotation, Moon’s orbit, Earth’s orbit around the Sun, and their mutual coupling. The resulting four disturbance time series are weighted by the observatory geomagnetic latitude and then averaged to get the USGS Dst. Love et al. (2015) used the Dst data for forecasting extreme geomagnetic storms. The Kyoto Dst data do not seem to be corrected for the excessive, seasonally varying quiet-time level, or the “non-storm component” which is unrelated to magnetic storms (Cliver et al. 2001; Karinen and Mursula 2006).
A comparison of the two Dst indices shows significant offset (or difference) between them, which is found to depend on short and long time scales (time of day, year and solar cycles) and level of Dst. The offset of Kyoto Dst compared to USGS Dst on the whole is −8.50 nT in all data together and −5.00 nT in quiet-time data (Dst > −25 nT) alone. The offset is mainly due to the different methods of removal of the secular and Sq variations (Sugiura and Kamei 1991; Love and Gannon 2009); detailed studies of the offset are beyond the scope of the present paper.
The identified storms are analyzed for their important characteristics. Main phase duration T MP is the time interval between main phase onset (MPO) when Dst starts decreasing and DstMin. ∫TMP |Dst|dt is the integral (or sum) of the modulus of Dst from MPO to DstMin. Since energy input takes place during MP, the mean value of Dst during MP is calculated as ⟨DstMP⟩ = (−1/T MP)∫TMP |Dst|dt. It represents the impulsive strength (or strength in short) of Dst storms while DstMin represents their intensity (Balan et al. 2014). It (⟨DstMP⟩) has been shown to be a unique parameter that can indicate the severity of space weather while the conventional parameter DstMin is insufficient (Balan et al. 2016). Average DstMin (=ΣDstMin/number of storms) and average ⟨DstMP⟩ = (Σ⟨DstMP⟩/number of storms) represent the average intensity and average strength of a certain number of storms during a specific period. Energy input in the ring current is estimated as E = ((dDst/dt)MP + αDstMP) where α = 0.13 is the ring current decay constant and DstMP in the second term is the mean of the two Dst values used for the first term (Burton et al. 1975; Stern 1984). Mean energy input during MP (⟨E MP⟩ = ∫E MP/T MP) is computed.
The seasonal variations of the storm characteristics studied separately for super storms, intense storms and all storms together are found similar. So we consider all storms together in the rest of the paper for statistics.
Semiannual maxima and minima of storm parameters
Number of storms
Average DstMin (nT)
Average ⟨DstMP⟩ (nT)
The important results are discussed. A computer program is developed to identify the geomagnetic storms in Dst data (“Storm identification” section). Using four selection criteria, the program identified about 24 and 35% of the storms in 50 years (1958–2007) in Kyoto Dst and USGS Dst, respectively, compared to those (3187 and 1870) that would have been identified if the usual procedure based on criterion 1 (DstMin ≤ −50 nT and MP duration >2 h) alone were used. The new selection procedure largely minimized the non-storm-like fluctuations in both versions of Dst. These are major advantages of the automated storm selection procedure. Recently, Katus and Liemohn (2013) reported another automated storm selection procedure. It involves searching for negative peaks in Dst (DstMin < −50 nT), finding the maximum Dst within 24 h prior to DstMin for MPO and 96 h after DstMin for the end of recovery phase, and looking for a sharp increase in Dst within 8 h prior to MPO for storm sudden commencement (SSC). Using this procedure Katus and Liemohn (2013) identified 697 storms in Kyoto Dst in 24 years (1985–2009) while the present procedure identified nearly the same number of storms (761) but in 50 years (1958–2007).
The identified storms are 30% more in Kyoto Dst (761) than in USGS Dst (587) mainly due to the baseline offset (or difference) between the two indices that arises from the different methods of removal of the secular and Sq variations calculated in different ways in the two indices (e.g., Sugiura and Kamei 1991; Love and Gannon 2009), which also leads to storm time differences (Fig. 2). A constant shift of one of the Dst versions by their average offset (8.5 nT) cannot give equal number of storms (Fig. 3) because the offset varies with short and long times scales and level of Dst. Detailed studies of the offset are beyond the scope of the present paper. Katus and Liemohn (2013) also found large differences between the storms in Kyoto Dst, USGS Dst and SYM-H indices especially at DstMin, on average up to 20% of the peak DstMin, though the storms in the indices are highly correlated.
Irrespective of the offset, the overall seasonal variation of occurrence of the storms in both versions of Dst in 50 years exhibits nearly equal (~±28%) semiannual patterns (Fig. 4) with maxima at equinoxes and minima in solstices. Unlike in earlier studies, the average intensity and average strength of the storms (average DstMin and average ⟨DstMP⟩) used in the present study also exhibit clear semiannual variations though with reduced maxima and minima (~±17%). The monthly occurrence of the storms in the five 11-year SCs 19–23 considered separately also show clear semiannual variation in all four SCs 20–24 (Fig. 6). Wavelet spectra of these data reveal the presence of weak longer- and shorter-period components in some SCs in addition to the clear and distinct semiannual component (Fig. 7). However, the long-period components (around annual period, 9–15 months) are not found to alternate between spring and fall in successive SCs as was observed in Ap index in 1993–2008 (Mursula et al. 2011), maybe because the ring current index Dst and global geomagnetic activity index Ap have somewhat different properties and drivers.
Of the different possibilities introduced in “Background” section, the equinoctial hypothesis (Bartels 1932) and RM effect (Russell and McPherron 1973) are usually used to explain the semiannual variation. Both mechanisms involve solar wind–magnetosphere coupling through the connection (and reconnection) mechanism between IMF Bz and magnetopause magnetic field (e.g., Dungey 1961), though the mechanism was not known at the time of proposal of the equinoctial hypothesis. Cliver et al. (2000) argued that while the RM effect causes stronger maxima at equinoxes (such as mountain building) the equinoctial hypothesis can cause deeper minima in solstices (such as valley digging). O’Brien and McPherron (2002) showed that the RM effect is present though the enhancements in the Dst index exhibit a seasonal pattern that is significantly different from the RM effect.
We attempt to connect the observed semiannual variation with equinoctial hypothesis and RM effect. Equinoctial hypothesis involves the variation of Earth’s dipole tilt angle μ with respect to the GSM Z-axis in X–Z plane where X points toward Sun from Earth. The tilt angle (μ) varies (i) between ±23.5° with time of year due to the tilt of Earth’s axis of rotation with respect to solar ecliptic plane and (ii) between ±11.2° with time of day due to the tilt of Earth’s dipole axis from its rotation axis. The total tilt μ of the dipole axis is therefore the sum of (i) and (ii), which varies between ±34.7° within a year with positive sign toward the Sun (in northern hemisphere) and negative sign away from the Sun. The RM effect involves the varying angle θ of the Earth’s dipole axis with respect to GSE (geocentric solar ecliptic) Y-axis in the plane perpendicular to the Earth–Sun line. The angle θ varies between 53° and 90° within a year. The variations of μ and θ with time of the day (UT hours) and year (days) were presented by O’Brien and McPherron (2002).
The larger possible control of equinoctial hypothesis than RM effect was in fact suggested earlier by Cliver et al. (2000, 2001) and O’Brien and McPherron (2002). Cliver et al. (2000) showed that while RM effect accounts for the observed higher geomagnetic activity in March and September bulk of the semiannual variation (~65%) results from the equinoctial hypothesis that causes lower geomagnetic activity in solstices. In another paper using 40 years of Kyoto Dst (1957–1997), Cliver et al. (2001) estimated that the amplitude of the storm component of semiannual variation is only ~30–50% while the remaining ~50–70% results from non-storm component. They also showed that the equinoctial hypothesis appears to dominate the storm component by 20–40% while only ~10% accounts for the combined axial/RM effect. They also suggested candidate mechanisms for the non-storm component including the Malin–Isikara effect (the seasonal displacement of ring/tail currents by solar wind compression) (Malin and Isikara 1976) and a semiannual variation of magnetopause currents. O’Brien and McPherron (2002) showed that the enhancements in the Dst exhibit seasonal and diurnal patterns that are significantly different from the RM effect.
In addition to the CME–magnetosphere coupling, ionosphere–ring current coupling (e.g., Fok et al. 2001; Liemohn et al. 2001; Ebihara et al. 2005) can also contribute to the observed semiannual variation as the ionosphere exhibits strong semiannual variation under both magnetically quiet and active conditions (e.g., Balan et al. 1998, 2011). It is important to carry out modeling studies to evaluate the relative importance of the equinoctial hypothesis, RM effect and ionosphere–ring current coupling on the observed semiannual variation of Dst storms. However, such modeling studies are beyond the scope of the present paper.
Seasonal variation of geomagnetic storm parameters in Kyoto Dst and USGS Dst is studied using 50 years (1958–2007) of data. The storms are identified by a computer program that minimizes non-storm-like fluctuations by applying four selection criteria. The program identified 761/585 storms in Kyoto Dst/USGS Dst, which include 34/33 super storms (DstMin ≤ −250 nT), 296/210 intense stroms (−250 < DstMin ≤ −100 nT) and 431/342 moderate storms (−100 < DstMin ≤ −50 nT). The storms are 30% more in Kyoto Dst mainly due to its varying baseline offset (or difference) compared to USGS Dst due to the different methods of removal of the secular and Sq variations in the two indices. The offset that varies with short and long time scales (time of day, year and solar cycles) and level of Dst on the average is −8.50 nT in all data and −5.00 nT in quiet-time (Dst > −25 nT) data.
The storms are analyzed for their important characteristics including the mean value of Dst during the main phase (⟨DstMP⟩). Irrespective of the difference between the two Dst indices, the overall seasonal variation of the storms in both indices show clear semiannual variations not only in occurrence but also in average intensity (average DstMin) and average strength (average ⟨DstMP⟩) with equinoctial maxima and solstice minima though the maxima and minima in intensity and strength (~±17% each) are less than those in occurrence (~±28%). Wavelet spectra of the storms reveal the existence of distinct semiannual component in four solar cycles (SCs 20–23) and weak longer- and shorter-period components in some SCs. The semiannual variations observed also in the mean energy input during MP obtained from Dst are consistent with the variations of the daily mean Earth’s dipole tilt angle µ involved in the equinoctial hypothesis and θ involved in the RM effect. Though both mechanisms can account for the observed semiannual variations, the yearly range of µ (23.2°, from 0.2° to 23.4°) is larger than that of θ (16.3°, from 66.6° to 82.9°). Both versions of Dst seem to confirm that the semiannual variation of Dst storms is real.
NB initiated the study and prepared the paper. ST developed the computer program, did most of the data analysis and participated in the preparation of the paper. PKR, NJV and JRS are also involved in data analysis. YK, ISB and KS are involved in the discussions and preparation of the paper. All authors read and approved the final manuscript.
We thank Kyoto WDC (http://wdc.kugi.kyoto-u.ac.jp/dstdir/) and USGS (http://geomag.usgs.gov/data) for the Dst data. N. Balan thanks CNPq of Brazil (Grants 400373/2014-9 and 303461/2014-4) and ISEE of Nagoya University Japan (Grants JSPS KEKENHI (JP 15H05815 and JP 1606286) for invitation fellowships.
The authors declare that they have no competing interests.
N Balan thanks CNPq of Brazil (Grants 400373/2014-9 and 303461/2014-4) and ISEE of Nagoya University Japan (Grants JSPS KEKENHI (JP 15H05815 and JP 1606286) for invitation fellowships.
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