Relationships Among Geomagnetic Storms, Interplanetary Shocks, Magnetic Clouds, and Sunspot Number During 1995 – 2012

Abstract

During 1995 – 2012, the Wind spacecraft has recorded 168 magnetic clouds (MCs), 197 magnetic cloud-like structures (MCLs), and 358 interplanetary (IP) shocks. Ninety-four MCs and 56 MCLs had upstream shock waves. The following features are found: i) The averages of the solar wind speed, interplanetary magnetic field (IMF), duration ($\langle \Delta t \rangle$), the minimum of $B_{\min}$, and intensity of the associated geomagnetic storm/activity ($\mbox{Dst}_{\min}$) for MCs with upstream shock waves ($\mbox{MC}_{\mathrm{shock}}$) are higher (or stronger) than those averages for the MCs without upstream shock waves ($\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$). ii) The average $\langle \Delta t \rangle$ of $\mbox{MC}_{\mathrm{shock}}$ events (${\approx}\,19.8~\mbox{h}$) is 9 % longer than that for $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events (${\approx}\,17.6~\mbox{h}$). iii) For the $\mbox{MC}_{\mathrm{shock}}$ events, the average duration of the sheath ($\langle\Delta t_{\mathrm{sheath}}\rangle$) is 12.1 h. These findings could be very useful for space weather predictions, i.e. IP shocks driven by MCs are expected to arrive at Wind (or at 1 AU) about 12 h ahead of the front of the MCs on average. iv) The occurrence frequency of IP shocks is well associated with sunspot number (SSN). The average intensity of geomagnetic storms measured by $\langle \mbox{Dst}_{\min}\rangle$ for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events is −102 and $-31~\mbox{nT}$, respectively. The average values $\langle \mbox{Dst}_{\min} \rangle$ are −78, −70, and $-35~\mbox{nT}$ for the 358 IP shocks, 168 MCs, and 197 MCLs, respectively. These results imply that IP shocks, when they occur with MCs/MCLs, must play an important role in the strength of geomagnetic storms. We speculate about the reason for this. Yearly occurrence frequencies of $\mbox{MC}_{\mathrm{shock}}$ and IP shocks are well correlated with solar activity (e.g., SSN). Choosing the correct $\mbox{Dst}_{\min}$ estimating formula for predicting the intensity of MC-associated geomagnetic storms is crucial for space weather predictions.

1 Introduction

A geomagnetic storm is one of the most important space weather events; it could damage operating space vehicles, interrupt radio communications, damage power plants, etc. The presence of a southward oriented interplanetary magnetic field (IMF) is one of the major solar wind features to affect the strength of geomagnetic activity. It is well known that a geomagnetic storm depends on the strength and duration of the solar wind IMF $B_{z}$ component (in the Geocentric Solar Magnetospheric (GSM) coordinate system) and the speed of the associated impacting plasma parcel in which the field is imbedded (Tsurutani and Gonzalez 1997), but likewise important is the size of the magnetosphere at the time of this interaction (e.g., Shue et al. 1998). The size of the magnetosphere is known to depend on the instantaneous solar wind dynamic (or ram) pressure: a strong ram pressure causes the magnetosphere to significantly decrease on the front-side (and elsewhere) and, in turn, result in a strong northern internal magnetic field at the front-side magnetopause. If a relatively strong increase in ram pressure occurs just before the interaction of an intense and long-lasting IMF $B_{z}$ component, the expected magnetic merging at the magnetopause will be unusually strong because the magnetic field is intense on both sides of the front-side magnetopause for any fixed IP speed.

A geomagnetic storm can be caused by a southward IMF associated with an interplanetary (IP) shock wave (sheath), a magnetic cloud (MC), heliospheric current sheet sector boundary crossing, and combinations of these interplanetary structures (e.g., Echer and Gonzalez 2004). A strong geomagnetic storm can be produced by the interaction between an IP shock and an MC (e.g., Wang et al. 2003) or the interaction among multiple MC events (including upstream shock) (e.g., Wang et al. 2003). The largest geomagnetic storm of Solar Cycle 23, which occurred on 20 November 2003 (Dst dropped to $-472~\mbox{nT}$), was caused by the combination of a southward IMF behind the IP shock wave (a sheath region) and an MC itself (Gopalswamy et al. 2005). Tsurutani and Gonzalez (1997) reviewed the interplanetary (IP) cause of magnetic storms. They discussed the various IP magnetic field configurations that can trigger geomagnetic storms, including magnetic clouds and various sheath field configurations (Figure 6).

An MC is defined as a region of high magnetic field strength, low proton temperature, low proton beta, and smoothly changing (rotating) magnetic field (e.g., Burlaga et al. 1981). Inside of an MC there typically is a long-lasting relatively strong southward IMF. Therefore, MCs are one of the most geoeffective IP structures typically causing $\mbox{Dst}_{\min} \leq -30~\mbox{nT}$ (e.g., Wu and Lepping 2002a, 2011, 2015). On average, most MC events (${\approx}\,90~\%$ MCs) induce geomagnetic storms, and ${\approx}39~\%$ of MCs generate intense geomagnetic storms (e.g., Wu, Lepping, and Gopalswamy 2006; Wu and Lepping 2015). Magnetic clouds interacting with the geomagnetosphere usually have all of the ingredients to produce strong geomagnetic storms because they mostly move fast and have strong and long-lasting southward $B_{z}$ components. Immediately upstream of many MCs, either a driven shock wave exists, which increases the ram pressure well above the typical value of 2.2 nPa, or a pressure pulse heading toward becoming a shock wave beyond 1 AU. The MC upstream-driven shock wave or pressure pulse, when they occur, are expected to significantly increase the solar wind ram pressure (sometimes to values as high as 25 nPa or higher), which usually remains elevated during the passage of the sheath-interval, that is, between the shock and the MC front.

A magnetic cloud-like (MCL) structure is found (initially as a candidate MC) by an automatic identification scheme (Lepping, Wu, and Berdichevsky 2005) that uses the same criteria as for an MC, but the MCL structure in this case is apparently not a simple force-free flux rope after further examination. That is, strictly speaking, an MCL structure cannot be shown to be a flux rope by using the MC-fitting model developed by Lepping, Burlaga, and Jones (1990), although it qualitatively appears to be an MC according to the original definition of Burlaga et al. (1981) (see also Burlaga 1988, 1995). We consider this to be an operational definition of an MCL. This lack of accommodation by this MC model with regard to MCLs may be due to one or more of many possibilities. For example, the attempted model fitting may not properly converge (usually the main reason), or the estimated closest approach may show a value of close to, or greater than, 1.0, or the $\chi^{2}$ of the fit may be excessively large, or the estimated asymmetry may be unacceptably large, etc.; the details of a scheme for assessing quality of an MC fitting using the Lepping, Burlaga, and Jones (1990) fitting scheme are given by Lepping et al. (2006).

A so-called sudden storm commencement (SSC) is usually caused by either an IP shock or a strong pressure pulse colliding with Earth’s magnetosphere. An SSC might be followed by a geomagnetic storm, if the IMF is strong enough and remains southward for a long enough period of time, and if is fast enough. An IP shock or pressure pulse may be driven by an MC, a corotating interaction region (CIR), or other IP structures. Previous study shows that more than approximately half of the MCs observed by Wind have upstream shocks (Lepping et al., 2002, 2015). The average intensity of $\mbox{Dst}_{\min}$ associated with IP shocks is $\langle \mbox{Dst}_{\min} \rangle = -74.6~\mbox{nT}$ (Wu and Lepping 2008). This does not mean that IP shocks directly cause geomagnetic storms. It may be that the $\mbox{Dst}_{\min}$ is indirectly related to the shock through the creation of a sheath – if $B_{z}$ is southward in that sheath. A possible southward $B_{z}$ field in the sheath probably is a condition itself for a geomagnetic storm, possibly in combination with the MC, causing a dual storm (or a two-step storm). The average storm intensity associated with MCs is $-70~\mbox{nT}$ (e.g., Wu and Lepping 2015), which is relatively high, and it is believed that the very largest $\mbox{Dst}_{\min}\mbox{s}$ are usually caused by MCs; an example is the storm of 13 – 14 March 1989, which had a $\mbox{Dst}_{\min} = -589~\mbox{nT}$, and was caused by an MC. All of this motivates us to statistically examine MCs and MCLs, along with their possible driven upstream shock waves, in their role as generators of geomagnetic storms.

The Wind spacecraft has collected solar wind in situ data for more than 20 years (1995 – mid-2015). The data set (1995 – 2012) used in this work provides a good opportunity for statistically studying the long-term effects of MCs/MCLs and IP shocks on geomagnetic storms, and in relation to the sunspot number (SSN). Data analysis and results are given in Section 2, and the summary is given in Section 3.

2 Data Analysis and Results

Five data sets were used in this study. The first data set, Wind solar wind plasma and magnetic field data, was obtain from the NASA (USA) Wind Solar Wind Experiment (SWE) and Magnetic Field Investigation (MFI) teams ( http://cdaweb.gsfc.nasa.gov/pub/data/wind ). The second data set, MCs for January 1995 to December 2009, is listed on the Wind/MFI web-site ( http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_pub1.html ), and the 2010 – 2012 MCs are listed in Lepping et al. (2012, 2015). MCLs can be found in Wu and Lepping (2015). The third data set, the geomagnetic activity index, Dst is obtained from both the National Geophysical data Center, Boulder, Colorado, USA and Kyoto University, Kyoto, Japan. The fourth data set, a list of Wind IP shocks, is obtained from Harvard–Smithsonian Center for Astrophysics Interplanetary Shock Database ( https://www.cfa.harvard.edu/shocks/wi_data/ ). The fifth data set, solar activity or the SSN, was obtained from the National Geophysical data Center, Boulder, Colorado, USA.

2.1 Occurrence Frequency of MCs with Upstream Shock Waves

We identified 168 MCs in Wind in situ solar wind and magnetic field data during 1995 – 2012 (e.g., Lepping et al. 2015). Viewing upstream (up to 30 h) of each of the 168 MCs, 94 MCs were seen to have upstream shock waves, and 74 MCs did not have upstream shock waves; we justify the reasonableness of the 30 h-limit on $\Delta t_{\mathrm{sheath}}$ below. This means that 56 % of the Wind-observed MCs had upstream shock waves when the full interval of 1995 – 2012 is considered, which is consistent with past findings using a smaller data set (Lepping et al. 2002).

Figure 1a shows the time profile of $\mbox{MC}_{\mathrm{shock}}$ (as a black solid line) and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ (as a red dashed line) events for the yearly occurrence frequency $N_{\mathrm{MC}}$ and sunspot number (as an orange dot-dashed line). Figure 1b shows the duration of the sheaths ($\Delta t_{\mathrm{sheath}}$), and Figure 1c shows the duration of the MCs ($\Delta t_{\mathrm{MC}}$), during 1995 – 2012. We note that “sheath”, as used above, means the region between the IP-driven shock and the front boundary of the MC. The black solid lines and red dashed lines represent yearly averaged values. The yearly occurrence rate of $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ is 5.2 and 4.1, respectively. The average of $\Delta t_{\mathrm{sheath}}$ ($\langle \Delta t_{\mathrm{sheath}}\rangle$) is 12.0 h (black diamond solid line), and $\sigma_{\Delta t}$ is 6.5 h, but values as low as 1.1 h and as high as ${\approx}\,30~\mbox{h}$ have been observed. The average of $\Delta t_{\mathrm{MC}}$ for the $\mbox{MC}_{\mathrm{shock}}$ events ($\langle \Delta t_{\mathrm{MC}}\rangle = 19.8~\mbox{h}$ and $\sigma_{\Delta t} =11.0~\mbox{h}$) is ${\approx}\,11~\%$ longer than that for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events ($\langle \Delta t_{\mathrm{MC}} \rangle = 17.6~\mbox{h}$). We note that [$\langle \Delta t_{\mathrm{sheath}} \rangle + 2 \times \sigma(\Delta t)$] for MCs is $(12.0 + 13.0)~\mbox{h} = 25.0~\mbox{h}$. This means that our choice of 30 h for the limit of $\Delta t_{\mathrm{sheath}}$ values, when examining the data, further ensures that very few IP shocks are missed.

Figure 1

(a) The occurrence frequency of $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, (b) duration of the sheath ($\Delta t_{\mathrm{sheath}}$) for $\mbox{MC}_{\mathrm{shock}}$ (middle panel), and (c) duration of MCs for both $\mbox{MC}_{\mathrm{shock}}$ (red diamond, black solid diamond line is the yearly average) and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ (red dashed and triangles) events (bottom panel) during 1995 – 2012. The small black diamonds and red triangles represent $\Delta t$ for the $\mbox{MC}_{\mathrm{shock}}$ events and for $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, respectively. Black solid diamond and red dashed triangle lines represent yearly averages for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, respectively.

Figure 1a shows that the occurrence frequency of $\mbox{MC}_{\mathrm{shock}}$ is associated with solar activity. The correlation coefficient (CC) for SSN vs. $N_{\mathrm{MC}}$ (for shocks) is 0.7. For example, the peak of $N_{\mathrm{MC}}$ (for shocks) occurred in 2000, no $\mbox{MC}_{\mathrm{shock}}$ in 2006 and 2008, and only one $\mbox{MC}_{\mathrm{shock}}$ in 1996 and in 2007. In addition, $\langle \Delta t_{\mathrm{sheath}} \rangle$ is also associated with solar activity (see Figure 1b): i) $\langle \Delta t_{\mathrm{sheath}}\rangle$ is much longer in the solar active period, e.g., $\langle \Delta t_{\mathrm{sheath}} \rangle > 10~\mbox{h}$ in 2011 and during 1999 – 2002. ii) $\langle \Delta t_{\mathrm{sheath}} \rangle$ is shorter in the quiet period, e.g., $\langle \Delta t_{\mathrm{sheath}}\rangle \approx5~\mbox{h}$ in 1996 and in 2008. In contrast (see Figure 1c), $\langle \Delta t_{\mathrm{MC}}\rangle$ is not well associated with solar activity.

2.2 Solar Wind Variation of MCs and Sheath Parameters

Figure 2 shows the averages of solar wind parameters in the sheath for the 94 $\mbox{MC}_{\mathrm{shock}}$ events. Over the long-term period (1995 – 2012), the average density $\langle N_{\mathrm{p}} \rangle$ is $15.8~\mbox{cm}^{-3}$, the velocity $\langle V \rangle$ is $513~\mbox{km}\,\mbox{s}^{-1}$, the magnetic field $\langle B \rangle$ is 13.2 nT, the thermal speed $\langle V_{\mathrm{th}}\rangle$ (or temperature) is $49.2~\mbox{km}\,\mbox{s}^{-1}$, the minimum $B_{z} \langle B_{z,\min}\rangle$ is $-15.3~\mbox{nT}$, and the associated geomagnetic storm intensity $\langle\mbox{Dst}_{\min}\rangle$ is $-102~\mbox{nT}$. We point out that $\langle V_{\mathrm{th}}\rangle$, $\langle V \rangle$, and $\langle B \rangle$ are higher in the solar active period than they are in the quiet period. For example, $\langle V_{\mathrm{th}}\rangle$ was $20~\mbox{km}\,\mbox{s}^{-1}$ in 1996, but was $80~\mbox{km}\,\mbox{s}^{-1}$ in 2003 (see Figure 2c).

Figure 2

Averages of various solar wind parameters of the sheath for the 94 $\mbox{MC}_{\mathrm{shock}}$ events. Bottom to top: averages of density ($N_{\mathrm{p}}$), velocity ($V$), magnetic field ($B$), thermal speed ($V_{\mathrm{th}}$), minimum $B_{z}$ ($B_{z,\min}$), $\Delta t_{\mathrm{sheath}}$, and associated geomagnetic activity ($\mbox{Dst}_{\min}$).

Figure 3 shows the time profile of various solar wind parameters inside an MC for both $\mbox{MC}_{\mathrm{shock}}$ (black diamonds) and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ (red triangles) events. Black solid diamond curves and red dashed triangle curves represent yearly averages for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, respectively. The averages of the solar wind speed ($V$), magnitude of IMF ($B_{\mathrm{MC}}$), strength of $B_{z,\min}$, and the associated intensity of the geomagnetic activity ($\mbox{Dst}_{\min}$) for $\mbox{MC}_{\mathrm{shock}}$ events are higher or stronger than those for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. Comparing data for the sheaths (Figure 2) and for the MCs (Figure 3), we found the following, on average. i) The solar wind density in the sheath ($N_{\mathrm{p}, \mathrm{sheath}}$) is about 90 % higher than inside the MCs. ii) The solar wind velocity in the sheath is 5 % faster than in the MC. iii) The solar wind temperature is higher in the sheath than in the MC by 98.4 % [${=}\,(49.2-24.8)/24.8$]. Finally, iv) the magnitude of the magnetic field and strength of $B_{z, \min}$ are stronger for the MC than for the sheath.

Figure 3

Time profile of various solar wind parameters inside MCs for both $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. Small black diamonds and small red triangles represent events for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$, respectively. Black diamond curves and red triangle curves represent yearly averages for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$, respectively.

2.3 Some Relationships Among MCs/MCLs, IP Shocks, Geomagnetic Activity, and SSN

Figure 3 shows an interesting result: the $\langle\mbox{Dst}_{\min}\rangle$ for $\mbox{MC}_{\mathrm{shock}}$ events ($-102~\mbox{nT}$) is ${\approx}\,3.3$ times stronger than for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events ($\langle\mbox{Dst}_{\min}\rangle = -31~\mbox{nT}$). This is mainly due to the following two features: i) the difference in the strengths of the southward IMFs inside of the MCs (or in the sheath regions) for these two conditions, viz., $\langle B_{z,\min}\rangle$ is $-17.4~\mbox{nT}$ for $\mbox{MC}_{\mathrm{shock}}$, but is $-6.0~\mbox{nT}$ for $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$; and ii) the dynamic pressure operating on the magnetosphere for the shock cases: the increased strength of the Earth’s field just inside the magnetopause due to the increased dynamic pressure of the impinging shock or sheath. For example, $\langle B_{z,\min}\rangle$ inside the MCs is −9.2, −12.8, and $-6.0~\mbox{nT}$ for all MCs, $\mbox{MC}_{\mathrm{shock}}$, and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, respectively (see the last column of Table 1). These findings should be useful for space weather prediction, i.e. MC-driven IP shocks typically arrive at Wind (or 1 AU) about 12 h ahead of the MCs. The arrival of an MC-driven IP shock could be used as a pre-cursor of the MC. Therefore, knowledge of such IP shocks could play an important role in estimating the timing and intensity of geomagnetic storms.

Table 1 Averages of solar wind parameters of MCs and MCLs observed by Wind during 1995 – 2012.

IP shocks are not only important for MC-magnetosphere interactions, they are also important for MCL – magnetosphere interactions. For example, $\langle\mbox{Dst}_{\min}\rangle$ are −35, −51, and $-29~\mbox{nT}$ for all MCLs, $\mbox{MCL}_{\mathrm{shock}}$, and $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events, respectively (see Table 1, last column); these are significant values, although they are expected to be lower (in absolute value) than those for the MC events, as shown in the upper part of Table 1. $\langle\mbox{Dst}_{\min}\rangle$ for the $\mbox{MCL}_{\mathrm{shock}}$ events is 1.8 times stronger than that for the $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. Again, $B_{z,\min}$ is one of the major factors that affects the strength of $\mbox{Dst}_{\min}$ for the events associated with MCLs. Solar wind density, temperature (thermal speed, $V_{\mathrm{th}}$), speed, and magnetic field for $\mbox{MCL}_{\mathrm{shock}}$ events are all higher for the shock-related MCs than for $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. Out of 197 MCLs, only 56 have upstream shock waves. Only 28 % of MCL events are $\mbox{MCL}_{\mathrm{shock}}$ types. The IP shock occurrence rate for MCs is twice that for the MCLs.

As stated above, IP shocks can play an important role in affecting the strength of geomagnetic storms (e.g., Wu and Lepping 2008). An SSC is an indication of an IP shock arrival at Earth, just before the storm. Table 1 confirms (for MC cases) that IP shocks play an important role in affecting geomagnetic activity. For MCLs, $\langle\mbox{Dst}_{\min} \rangle$ for $\mbox{MCL}_{\mathrm{shock}}$ events is 1.8 times stronger than that for the $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. These results are consistent with previous studies that showed that MCs are among the most important interplanetary structures in causing strong geomagnetic storms (e.g., Wu and Lepping 2002a, 2002b, 2005, 2007; Wu, Lepping, and Gopalswamy 2003); on average, the geomagnetic activity is more strongly affected by MCs than by MCLs or IP shocks alone (e.g., Wu and Lepping 2008).

It is also well known that most IP shocks recorded at 1 AU are driven by solar ejecta (e.g., MCs, IP coronal mass ejections). The Wind spacecraft has recorded 358 IP shocks during 1995 – 2012 (see the blue dot-dashed line in Figure 4 for the yearly occurrence rate, $N_{\mathrm{shock}}$). The yearly occurrence frequency of IP shocks is $\langle N_{\mathrm{shock}}\rangle_{\mathrm{year}}=19.8$. The Dst index was checked two days after an IP shock arrived at L1 during 1995 – 2012. The average of $\mbox{Dst}_{\min}$ for these 358 IP shocks is $\langle\mbox{Dst}_{\min}\rangle_{\mathrm{shock}} = -78~\mbox{nT}$. The combined effects of both the southward IMF in the sheath and in the MC could cause a strong or even a severe geomagnetic storm, which is the so-called two-step storm (e.g., Kamide et al. 1998; Tsurutani et al. 1997; Wu and Lepping 2002a). The $\mbox{MC}_{\mathrm{shock}}$ events are usually associated with the strongest geomagnetic storms, i.e., $\langle\mbox{Dst}_{\min}\rangle = -102~\mbox{nT}$ (see Table 1).

Figure 4

(a) Yearly occurrence frequency of MCs (black solid line), MCs with upstream shock wave (blue dotted line), MCs without upstream shock (red dashed line), and IP shock waves (dark blue dash-dot-dot-dotted line), and sunspot numbers (orange dot-dashed line). (b) Yearly occurrence frequency of MCLs (black solid line), MCLs with upstream shock wave (blue dotted line), MCLs without upstream shock (red dashed line), IP shock waves (dark blue dash-dot-dot-dotted line), and sunspot numbers (orange dot-dashed line). Total numbers (1995 – 2012) of MCs/MCLs are marked in the top left corner. The correlation coefficient (CC) between yearly sunspot number (SSN) and yearly occurrence frequency of MCs/MCLs are marked in the top-right corner.

The CCs for SSN vs. occurrence rates for MCs, $\mbox{MC}_{\mathrm{shock}}$, and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events are 0.27, 0.70, and −0.29, respectively (see the designations in Figure 4a). The CCs for SSN vs. occurrence rates for MCLs, $\mbox{MCL}_{\mathrm{shock}}$, and $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events are 0.85, 0.87, and 0.79, respectively (see the designations in Figure 4b). The CCs for SSN vs. $N_{\mathrm{MC}}$ for both $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MCL}_{\mathrm{shock}}$ are greater than 0.70. Therefore, $\langle N_{\mathrm{shock}}\rangle$ is reasonably well associated with SSN. This result is consistent with our previous study (Wu and Lepping 2008): the occurrence frequency of sudden storm commencements ($N_{\mathrm{SSC}}$) is reasonably well correlated with SSN, where CC for $N_{\mathrm{SSC}}$ vs. SSN is 0.77. We note that from mid-2003, Wind moved behind the Earth’s bow shock and remained there for approximately nine months. Without using data for 2003 and 2004, the CC for SSN vs. occurrence rate for $\mbox{MC}_{\mathrm{shock}}$ increases to 0.79. Figure 4 shows that there is a well-correlated trend between IP shocks (dash-dot-dotted line) and SSN (dash-dotted lines), where the CC is 0.79 between them.

This study shows that 56 % of the total observed MCs have upstream shock waves when the full interval of 1995 – 2012 is considered, but only 28 % (or 56 out of 197) of MCLs have shock waves over the same period (see Table 1). The values of $\langle\mbox{Dst}_{\min}\rangle$ for MCLs, $\mbox{MCL}_{\mathrm{shock}}$, and $\mbox{MCL}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events are −35, −51, and $-29~\mbox{nT}$, respectively. For MC events, the yearly occurrence frequency of MC-driven shocks is associated with sunspots ($\mbox{CC}=0.70$). The duration of the sheath ($\Delta t_{\mathrm{sheath}}$) is also correlated with SSN: on average, $\Delta t_{\mathrm{sheath}}$ in the solar active period was longer than that in the quiet solar period (see Figure 1a). The yearly occurrence rate of $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ is 5.2 and 4.1, respectively.

For MCs events, the IP $B_{z,\min}$ is a good indicator for estimating $\mbox{Dst}_{\min}$ because $\mbox{Dst}_{\min}$ is well correlated with $B_{z,\min}$ (e.g., Wu and Lepping 2008, 2011, 2015). The intensity of a geomagnetic storm ($\mbox{Dst}_{\min}$) is predictable if $B_{z,\min}$ is known in advance, provided $V_{\mathrm{SW}}$ is known. However, the correlation coefficient (CC) of $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ varies somewhat with different data types, but the spread is small. For example, the CCs are 0.75, 0.85, 0.69, 0.82, 0.68, and 0.68 for $B_{z,\min}$ obtained in the (a) MC, (b) MC or sheath, (c) $\mbox{MC}_{\mathrm{shock}}$, (d) $\mbox{MC}_{\mathrm{shock}}$ or sheath, (e) sheath, (f) $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$, respectively (see column 5 in Table 2). The CC is higher for $\mbox{MC}_{\mathrm{shock}}$ events than that for $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events.

Table 2 Estimating $\mbox{Dst}_{\min}$ formulae obtained from a linear fit of $B_{z,\min}$.

2.4 Effect of an IP Shock on the Intensity of a Geomagnetic Storm

An upstream shock wave of an $\mbox{MC}_{\mathrm{shock}}$ event typically arrives at Earth about 12 h ahead of the front boundary of the MC. An IP shock may be used as a precursor of a geomagnetic storm occasionally because 56 % of the MCs have upstream shock waves. Table 2 shows that $\mbox{MC}_{\mathrm{shock}}$ events generally associated with severe geomagnetic storms since $\langle\mbox{Dst}_{\min}\rangle$ is $-102~\mbox{nT}$ for $\mbox{MC}_{\mathrm{shock}}$ events.

The value of $\langle\mbox{Dst}_{\min}\rangle$ for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events is $-31~\mbox{nT}$. This means that most $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events are not associated with strong geomagnetic storms, although many are, if $|B_{z,\min}|$ and $V_{\mathrm{SW}}$ are large, of course. This value is close to the value for MCLs ($\langle\mbox{Dst}_{\min}\rangle_{\mathrm{MCLs}} = -35~\mbox{nT}$). Therefore, an IP shock may be a main contributor to the strength of a geomagnetic storm, even if indirect. About 90 % of the MCs are associated with geomagnetic storms ($\mbox{Dst}_{\min} < -30~\mbox{nT}$). IP shocks play an important role in geomagnetic activity because $\langle\mbox{Dst}_{\min}\rangle$ for $\mbox{MC}_{\mathrm{shock}}$ is 3.25 times stronger than for $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events (see the top panel of Figure 3). But again this does not mean that an IP shock alone can cause a geomagnetic storm.

2.5 Formulae for Estimating $\mbox{Dst}_{\min}$

Figure 5 shows a distribution of geomagnetic $\mbox{Dst}_{\min}$ and IP $B_{z,\min}$ for 168 MCs (Figures 5a and 5b), 94 $\mbox{MC}_{\mathrm{shock}}$ (Figures 5c, 5d, and 5e), and 74 $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ (Figure 4f) during 1995 – 2012. The CCs for $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ are marked in the third line in the top-left corner of each panel. $B_{z,\min}$ is obtained from the inside of the MCs (in Figures 5a, 5c, and 5f), the sheath region (for Figure 5e), and either the sheath or the MC (Figures 5b and 5d). The red straight lines are the linear fitting functions for the estimates of $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$. The actual fitted function for the $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ linear estimation is shown in the bottom of each panel, and the CC for $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ is denoted below the fitting function. This detailed information is also listed in Table 2. The largest two CCs ($=0.85$ and 0.82) are obtained from either the sheath or the MC for the 168 MCs and 94 $\mbox{MC}_{\mathrm{shock}}$ events because $\mbox{Dst}_{\min}$ would occur in the sheath region or inside the MC. This shows that $B_{z,\min}$ statistically plays a major role in affecting the intensity of geomagnetic storms, as expected. It is crucial to use the correct estimator of $B_{z,\min}$ for predicting the storm intensity (i.e. $\mbox{Dst}_{\min}$).

Figure 5

Distribution of geomagnetic storm intensity ($\mbox{Dst}_{\min}$) and minimum $B_{z}$ ($B_{z,\min}$) for all MCs (panels a, b), MCs with upstream shock waves (panels c, d, e), and MCs without upstream shock (panel f) during 1995 – 2012. $\mbox{Dst}_{\min}$ linear fitting function and the correlation coefficients (CCs) are denoted at the top (the third line) and bottom of each panel, respectively. The averages of $\langle N_{\mathrm{MC}}\rangle$ and $\langle\mbox{Dst}_{\min}\rangle$ are denoted at the first and fourth lines at the top of each panel in respective order.

2.6 Evaluating the Formulae for Estimating $\mbox{Dst}_{\min}$

Figure 6a shows an example of an MC that induced a severe geomagnetic storm. The value of $\mbox{Dst}_{\min}$ is $-90~\mbox{nT}$, which is caused by a $B_{z,\min}$ of $-10~\mbox{nT}$ in the MC. Figure 1a clearly shows that the MC is an isolated solar disturbance (or event) that did not interact with any other kind of interplanetary structure [e.g., heliosphere current sheet (HCS), co-rotating interaction region (CIR), another MC, or interplanetary coronal mass ejection (ICME)]. The direction of the IMF was changing smoothly from the front boundary to the end boundary of the MC, and an obvious driven shock was about 0.5 day ahead of the MC front boundary.

Figure 6

Examples of two MCs that were observed on 4 March 1995 (a) and on 17 September 2011 (b). From top to bottom: $\chi^{2}$ of quadratic fit to latitude of the field ($\theta_{B}$), running average of proton plasma beta ($\beta$) and dotted curve representing its running average, Dst, magnetic field ($B$) in terms of magnitude, latitude ($\theta_{B}$) and longitude ($\phi_{B}$) in GSE coordinates, induced electric field ($VB_{\mathrm{s}}$), $B_{z}$ of the field in GSE, $\varepsilon$ (see Akasofu 1981), proton plasma thermal speed ($V_{\mathrm{th}}$), bulk speed ($V$), and number density ($N_{\mathrm{p}}$). The red horizontal bar in the top panel represents the scheme identification of the extent of this MC candidate (Lepping, Wu, and Berdichevsky 2005). The vertical yellow dashed line and blue dotted line represent front and rear boundaries identified by the MC automatic identifying model. The averages of $N_{\mathrm{p}}$, $V$, $V_{\mathrm{th}}$, and $B$ for MC/MCL are provided in red in each panel.

With the estimating $\mbox{Dst}_{\min}$ formulae (a) through (f) in Table 2, the estimated $\mbox{Dst}_{\min}$ are −71.5, −55.36, −84.09, −53.68, −73.78, and $-54.12~\mbox{nT}$, and the errors of prediction ($|\mbox{Dst}_{\mathrm{prediction}} - \mbox{Dst}_{\mathrm{observation}}| / |\mbox{Dst}_{\mathrm{observation}}| \times 100~\%$) are 20.6 %, 38.5 %, 7.6 %, 40.4 %, 18.0 %, and 39.9 %, respectively (see also the details in Table 3). Formula (c) gives the best estimate; it is based on the events that have upstream shock waves, and where $B_{z,\min}$ inside the MC was used.

Table 3 Estimated $\mbox{Dst}_{\min}$ for the geomagnetic storm caused by an MC event that occurred on 4 March 1995.

Figure 6b shows another example: an MC (that occurred on 18 September 2011) has an upstream shock (on 17 September) that induced a sheath geomagnetic storm ($\mbox{Dst}_{\min} = -70~\mbox{nT}$). For this event, the $B_{z,\min}$ were −10 and $-5~\mbox{nT}$ in the sheath and MC, respectively. Using the estimated $\mbox{Dst}_{\min}$ formulae (a), (b), (c), (d), (e), and (f) for the MC on 17 September 2011, the estimated $\mbox{Dst}_{\min}$ are −37.4, −55.36, −53.49, −53.69, −73.78, and $-24.97~\mbox{nT}$, and the errors of prediction are 46.5 %, 20.9 %, 23.6 %, 23.3 %, 5.4 %, and 64.3 %, respectively. Details can be found in Table 4. Formula (e) gave the best estimated $\mbox{Dst}_{\min}$. Formula (e) was based on the events that had upstream shock waves and on using the sheath $B_{z,\min}$ to obtain $\mbox{Dst}_{\min}$ in this case.

Table 4 Estimating $\mbox{Dst}_{\min}$ by using $B_{z,\min}$ for an MC event on 18 September 2011.

$\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ has a higher correlation for the MCs associated with higher speed than those with lower speed (e.g., Wu and Lepping 2002b). To understand the effects of solar wind velocity on geomagnetic storms, we cataloged MC events into different ranges of velocity. Figure 7 shows the relations between storm intensity ($\mbox{Dst}_{\min}$) for various solar wind parameters for various $\langle V_{\mathrm{MC}} \rangle$ ranges (correlation coefficients are also calculated and given in each panel). The distribution of the geomagnetic storm intensity ($\mbox{Dst}_{\min}$) and minimum $B_{z}$ ($B_{z,\min}$) for all MCs is (left panel: A) and for MCs with upstream shock waves (right panel: B) during 1995 – 2012. $\mbox{Dst}_{\min}$ linear fitting function and the associated CCs are denoted at the top (the third line) and bottom of each panel, respectively. The averages of $\langle N_{\mathrm{MC}}\rangle$ and $\langle \mbox{Dst}_{\min}\rangle$ are denoted in the first and fourth lines at the top of each panel in respective order.

Figure 7

Distribution of geomagnetic storm intensity ($\mbox{Dst}_{\min}$) and minimum $B_{z}$ ($B_{z,\min}$) for all MCs (A, top panel) and for MCs with upstream shock waves (B, bottom panel) during 1995 – 2012. $\mbox{Dst}_{\min}$ linear fitting function and the correlation coefficients (CCs) are denoted at the top (the third line) and bottom of each panel, respectively. The averages of $\langle N_{\mathrm{MC}}\rangle$ and $\langle\mbox{Dst}_{\min}\rangle$ are denoted at the first and fourth lines at the top of each panel in respective order.

Tables 5 and 8 show the CCs between $\mbox{Dst}_{\min}$ and $B_{z,\min}$ for various $\langle V_{\mathrm{MC}}\rangle$ ranges. Figure 7 and Tables 5, 6, 7, 8 clearly show that the higher speed of MCs is associated with stronger geomagnetic storms (see the second column of Tables 5 – 8). Tables 5 – 8 also show that all MC events with speeds higher than $600~\mbox{km}\,\mbox{s}^{-1}$ have driven an IP shock. The CCs for $\mbox{Dst}_{\min}$ vs. $B_{z,\min}$ (in MC or sheath) are higher for events with higher speeds. For events with speeds higher than $600~\mbox{km}\,\mbox{s}^{-1}$, the CCs are higher than 0.8. This means that its $\mbox{Dst}_{\min}$ estimating function is reliable for performing space weather prediction.

Table 5 Correlation coefficients between $\mbox{Dst}_{\min}$ and $B_{z,\min}$ for various $\langle V_{\mathrm{MC}}\rangle$ ranges.

Table 6 Estimating $\mbox{Dst}_{\min}$ formulae obtained from linear fit of $B_{z,\min}$ for various $\langle V_{\mathrm{MC}}\rangle$ ranges for 168 MCs observed during 1995 – 2012.

Table 7 Estimating $\mbox{Dst}_{\min}$ formulae obtained from linear fit of $B_{z,\min}$ for various $\langle V_{\mathrm{MC}}\rangle$ ranges for 94 MC driven shock events observed during 1995 – 2012.

Table 8 Correlation coefficients between $\mbox{Dst}_{\min}$ and $B_{z,\min}$ for various $\langle V_{\mathrm{MC}}\rangle$ ranges for MCs without upstream shock wave.

From the $\mbox{Dst}_{\min}$ estimating formulae listed in Tables 5 and 8, the estimated $\mbox{Dst}_{\min}$ are $-78~\mbox{nT}$ for the MC on 4 March 1995, and $-75.9~\mbox{nT}$ for the MC on 17 September, 2011. The errors of the predictions are 13.3 % and 8.4 % for the MC events that occurred in 1995 and 2011, respectively. It is interesting that the errors are larger than the best value by using Dst formulae that do not depend on velocity. Therefore, the Dst estimating-formulae listed in Table 2 are good for general use, at least on average. This may not hold for individual cases.

3 Summary

From in situ solar wind observations by the Wind spacecraft during 1995 – 2012, the main results of this study are as follows:

• i) We identified 168 MCs and 197 MCLs, of which 94 $\mbox{MC}_{\mathrm{shock}}$ and 56 $\mbox{MCL}_{\mathrm{shock}}$ events had upstream shock waves.

• ii) The average yearly occurrence rates for MCs, MCLs, $\mbox{MC}_{\mathrm{shock}}$, and $\mbox{MCL}_{\mathrm{shock}}$ events are 9.3, 10.9, 5.2, and 3.1, respectively. The relative occurrence rate of $\mbox{MC}_{\mathrm{shock}}$ events (56 %) is about twice that for the $\mbox{MCL}_{\mathrm{shock}}$ events (28 %). The occurrence rate of automatically determined (Lepping, Wu, and Berdichevsky 2005) MCs (and visually confirmed) is not related to the SSN, but the occurrence rate of $\mbox{MC}_{\mathrm{shock}}$ is well correlated with SSN during 1995 – 2012. The yearly occurrence rate of IP shocks is well correlated with SSN.

• iii) The arrival time of an IP shock may be a good indicator for the initiation of a significant geomagnetic storm for space weather prediction because most MC-driven shock events cause strong geomagnetic storms (e.g., $\langle\mbox{Dst}_{\min}\rangle_{\mathrm{shock}} = -102$ and $-51~\mbox{nT}$ for $\mbox{MC}_{\mathrm{shock}}$ and $\mbox{MCL}_{\mathrm{shock}}$ events, respectively). An interplanetary shock can play an important role for the strength of a geomagnetic storm, as shown by the average intensity of geomagnetic storms associated with $\mbox{MC}_{\mathrm{shock}}$ which is ${\approx}\,3.3$ times higher than for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$.

• iv) The averages of solar wind density, speed, thermal speed, and magnetic field for $\mbox{MC}_{\mathrm{shock}}$ events are higher than those for the $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events. The average solar wind speed is ${\approx}\,25~\%$ faster within $\mbox{MC}_{\mathrm{shock}}$ than within $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$. The average absolute value of $B_{z,\min}$ is higher (> two times) within $\mbox{MC}_{\mathrm{shock}}$ than within $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ events.

• v) The average duration during 1995 – 2012 of an $\mbox{MC}_{\mathrm{shock}}$ event (19.8 h) is (${\approx}\,11~\%$) longer than that of an $\mbox{MC}_{\mathrm{no}\mbox{-}\mathrm{shock}}$ event (17.6 h).

• vi) Stronger MC storms follow a solar maximum, but MCLs do not show this trend.

• vii) Choosing the correct $\mbox{Dst}_{\min}$ estimation-formula is very important for space weather predictions.

• viii) Dynamic (or ram) pressure upstream of an MC/MCL event usually plays an important role in the intensity of a possible related geomagnetic storm.

The solar wind velocity plays an important role in affecting the intensity of a geomagnetic storm because the induced electric field at the magnetopause depends on $V_{\mathrm{SW}}$ through $B_{z} V_{\mathrm{SW}}$, but also because a significant increase of velocity could cause a strong increase in the external ram pressure ($\rho V^{2}$). Increased dynamic pressure, as caused by an ejecta-driven shock wave, would compress the Earth’s front-side magnetopause toward Earth. This is due to the decreased size of the magnetosphere (according to $R_{\mathrm{MP}} = R_{\mathrm{o}}(B_{\mathrm{o}}/B_{\mathrm{MP}})^{1/3}$, where $R_{\mathrm{o}}$ is $R_{\mathrm{Earth}} =6378~km$; $B_{\mathrm{o}}$ is the magnetic field on the Earth’s surface), concomitant with the increased northern field of the front-side magnetosphere ($B_{\mathrm{MP}}$), both caused by the increased external ram pressure on the magnetosphere resulting from the IP shock wave and density-enhanced sheath plasma. We speculate that the combination of a possible long-lasting southward field in fast-moving plasma in either the sheath or the MC/MCL structure and the ram pressure effect might cause enhanced storm intensities. Our statistical results seem to give relatively strong evidence of this expected effect.