An Alternative Method for Identifying Interplanetary Magnetic Cloud Regions

Using the STE method, we analyzed IMF data using a time interval of 10 days, ensuring that a wide interval that contains the occurrence of at least one pre-identified MC will be used. As a criterion for IE index calculation, we select a convenient data interval of 2500 records moving forward by 200 record steps until the end of the time series. For every data segment, the STE is calculated at each step. It allows the analysis of the STE evolution along the series, with an adequate resolution defined by the chosen step. We select 2500 points because this interval represents an interval of $11.11\,\mathrm{hr}$, and the MCs have a smooth magnetic field vector rotation on the order of 1 day, where the field reaches a peak and decreases (Burlaga 1988). With a temporal window size of $11.11\,\mathrm{hr}$ and a resolution of $16\,{\rm{s}}$, it is possible to cover the entire range of the trend in most MCs with time extension larger than $\approx 16\,\mathrm{hr}$. The STE calculation has stable values in time series with data points from 2000 to 4000 records (see Ojeda et al. (2013, Figure 2). Moreover, if this interval is shorter than 2500 points, then the STE value could be close to zero in places that are not cloud regions. Therefore, this methodology may not be applicable in identifying small and weak MCs. The STE values are calculated every $0.89\,\mathrm{hr}$ (time resolution adopted, with 200 records) and represent ∼8% of the size of each temporal window. Thus, the variation of the STE values between two adjacent windows of $11.11\,\mathrm{hr}$ must also be in the order of $\sim \pm 8 \%$.

Zoom In Zoom Out Reset image size

In summary, higher STE value variation (close to 100%) indicates disorganization, i.e., no flux rope structure, while lower value variation (close to zero) indicates that organization has been reached, i.e., a flux rope-like structure.

Based on the MC magnetic structure, not all of the magnetic components are expected to have STE values close to zero simultaneously. We expect to find at least one component with entropy close to zero. However, this value should exist for two hours or longer. This is the reason for creating a standardized interplanetary entropy index (the so-called IE index). This index, joined with the STE, results for the three variables $({B}_{x},{B}_{y},{B}_{z})$, which are affected by the physical process, in an easily interpreted diagnosis. The index is the result of the multiplication of the STE values obtained from the calculation on each of the three variables, using a data set taken at the same time t, and normalized by 10⁴. It is given by

$$\begin{eqnarray}&&\mathrm{IE}=\displaystyle \prod _{i}\displaystyle \frac{{\mathrm{STE}}_{i}}{{10}^{4}}[ \% ],\,\mathrm{where}\,i=[x,y,z].\end{eqnarray} \tag{ 1 }$$

This normalization is convenient for showing the IE index in the same scale as the STE, from 0% to 100%. The IE should be less than ≈1.5% (where zero is the best result) to consider the region an MC candidate. Therefore, the threshold chosen is ≈1.5%. We report the IE index as an approximate value.

Based on the test case of the MC on 1998 January 6–8, (see Table 1), an SW data set of 10 days, from 1998 January 3–12 (see Table 2), is selected. The STE is calculated in a total of 256 time windows, each with 2500 records. In Figure 2, we show the STE values versus date for the time series of the IMF components for this interval. STE values for B_x, B_y, and B_z are plotted with a dotted line, dashed line, and continuous thin line, respectively. In addition, we investigate if ACE detected some other event during those 10 days.

Richardson & Cane (2010) reported two ICMEs in this interval: from January 7, 01:00, to January 8, 22:00, the event has an MC; while from 1998 January 9, 07:00, to January 10, 08:00, no event is classified as an MC. Thus, in Figure 2, we have one MC, one interplanetary disturbance not classified as an MC, and a quiet SW period. The MC was also reported by Huttunen et al. (2005), but with a different size.

In Figure 2 (both panels), the shock, start, and end of the MC are represented by three vertical lines, at the times listed in Table 1. In the top panel, components of the interplanetary magnetic field are plotted. In the bottom panel, the dashed horizontal line is the threshold of $1.5 \%$. The previous line is plotted in other similar figures in this work where the IE is shown. The ${B}_{y},{B}_{z}$ components have zero STE values $(\mathrm{IE}\leqslant 1.5 \% )$ only during the passage of the MC, approximately in its first half. The second minimum value of $\mathrm{STE}=10 \%$ corresponds to the B_z component on January 9. On this date (January 9, 07:00–January 10, 08:00), Richardson & Cane (2010) detected one ICME. It is not classified as an MC. This result is very interesting, because in this interval of 10 days of SW data, only two magnetic components (${B}_{y}{\rm{}}\,{\rm{and}}\,{\rm{}}{B}_{z}$) have STE values of zero, and it is within the MC. Huttunen et al. (2005) first performed a visual inspection of the data to find the cloud candidates. This is always the first step in any work aimed at studying MCs. Although automatic ways of identification exist, the plasma data still need to be used in the usual tools (Lepping et al. 2005). Therefore, the calculation of the STE could be a very useful mathematical tool to help find MC candidates.

The thick curve in Figure 2 represents the IE calculated along the analyzed period. The IE value can only decrease close to zero $(\mathrm{IE}\leqslant 1.5 \% )$ somewhere inside the MC. MCs have simple flux rope-like magnetic fields with enhanced strengths and which rotate slowly through a large angle. The time series of the IMF components show a trend toward more ordered dynamic behavior and a higher degree of correlation with its temporary neighbors (Ojeda et al. 2005, 2013). The aforementioned behavior is found only in the magnetic structures of the MCs or flux rope-like magnetic fields, a necessary condition for the threshold IE value.

The IE methodology is required to validate that the STE is not zero for any other interplanetary disturbance, except for MCs. This is the reason why the term "negative case" is used here. Although it is not a true proof, this empirical test corroborates the results that have been obtained for a large number of SW data. This case, chosen to create a difficult situation for analysis because of its physical similarity with the MC, serves as an example of validation, or initial acceptance, of the method.

In Table 2, an SW data set of 6 days, from 1999 October 20–25, is indicated. The interface between the interplanetary ejecta and high-speed stream on 1999 October 22 is an excellent study case (Dal Lago et al. 2006). High-speed streams, originating in coronal holes, are often observed following ICMEs at 1 au (Klein & Burlaga 1982). Dal Lago et al. (2006) studied the 1999 October 17–22 solar-interplanetary event, which was associated with a very intense magnetic storm (${Dst}=-237\,\mathrm{nT}$).

Figure 3, bottom panel, shows the values of STE as a function of time for the time series of the IMF ${B}_{x},{B}_{y}\ {\rm{and}}\,{\rm{}}{B}_{z}$ components in the SW from 1999 October 20–25. In these SW data intervals, 150 time windows (each with 2500 records) were obtained. STE values of each of the three IMF components are calculated. Using Equation (1), the IE is calculated and plotted (thick curve) over the analyzed period in this figure.

Zoom In Zoom Out Reset image size

Dal Lago et al. (2006) presented an analysis of pressure balance between the ICME observed on October 21–22 and the high-speed streams following it. Close to the Earth, at L1, an interplanetary shock was detected by the ACE magnetic field and plasma instruments on 1999 October 21, 01:34, shown in Figure 3 by the first vertical dotted line. The driver of this shock is an ICME, which can be distinguished from the normal SW by its intense magnetic field, of the order of $20\,\,\mathrm{nT}$ throughout most of October 21, and by its low plasma beta (∼0.1) (Dal Lago et al. 2006). The start of the ejecta was on October 21, 03:58. Toward the end of this ejecta, an increase of the magnetic field intensity was observed, starting on October 22, 02:30, reaching a peak value of $37\,\,\mathrm{nT}$ (Dal Lago et al. 2006). At 06:15 UT on October 22 (the second vertical dotted line in Figure 3), the magnetic field dropped abruptly around $10\,\,\mathrm{nT}$. Dal Lago et al. (2006) defined this point as the end of the ICME. They were not sure whether or not this ICME has an MC according to the criteria of Burlaga et al. (1981), because the direction of the magnetic field does not rotate smoothly. Richardson & Cane (2010) also detected an ICME that was not classified as an MC, from 1999 October 21, 08:00, to October 22, 07:00.

It is clear that during the period of 1999 October 20–25, no event was identified as an MC. In Figure 3, the values of the STE are always different from zero, so the IE index is also different from zero. This result helps validate the use of IE in detecting MCs. The IE index methodology can differentiate when an ICME is not classified as an MC, because the IE index is only close to zero ($\mathrm{IE}\leqslant 1.5 \%$) inside an MC. This capability is related to the correct diagnosis of the intrinsic magnetic field configuration existing in an MC, representing a very high organized plasma structure.

With the idea of trying the method, we randomly selected one MC among the 80 MC events (73 MCs and 7 cloud candidates) identified by Huttunen et al. (2005). It is the second case in Table 1, identified as the MC event of 1999 February 18–19. Table 2 indicates the 10 day interval, 1999 February 14–23, of the collected SW data set to be analyzed. Considering a total of 256 time windows, the STE values are calculated. The result is shown in Figure 4, bottom panel. The STE reaches a value of zero for the B_x component. Thus, there is an IE index presenting a value of zero in the examined period.

Zoom In Zoom Out Reset image size

Richardson & Cane (2010) detected an ICME that is not classified as an MC, from 1999 February 13, 19:00 to February 14, 15:00. Figure 4 shows the results of the calculation of the STE on 1999 February 14, 15:00, where the IE has a small, but non-zero, value. During 1999 February 18–21, the ACE spacecraft detected an ICME (that has an MC) (Richardson & Cane 2010). Inside the MC, which is delimited by the vertical lines in Figure 4, $\mathrm{STE}=0 \%$ only for one IMF component (in this case, for B_x). It generates an IE index with a value of zero only inside the MC region. Therefore, the IE index indeed shows the occurrence of one MC event in this data interval. So far, we often see MCs with STE values of zero only in one of the IMF components. However, the IE has always detected the existence of MCs through the threshold value. Thus, using the IE index, we can find the MC occurrence but not its boundaries (or time extension). The consistent results from other aleatory cases are not shown in this work.

Thirty-three near-Earth ICMEs in 1999 have been chosen from the catalog of Richardson & Cane (2010, their Table 3). In the previous manuscript, a "2" in Column 15 indicates that the ICME includes an MC reported on the WIND MCs list (Wu et al. 2003) or by Huttunen et al. (2005). A "1" indicates that there is evidence of rotation in the magnetic field direction, but overall, the magnetic field characteristics do not meet those of an MC. Events with no MC-like magnetic field features are indicated by "0." Thirteen near-Earth ICME included MCs, of which seven are indicated with "1" and six with "2." In Table 3 from rows 1 to 3, the three previous cases are shown. Column 2 shows the total number of MCs. Column 3 shows the total number of MCs $({N}_{\mathrm{IE}})$ in column 2 that were identified with the IE methodology, i.e., where the IE is less than 1.5%. A success rate of 100% is the best result. The successfulness of the IE index methodology is calculated using the equation (${N}_{\mathrm{IE}}$/Total) × 100%. The IE index analysis versus another identifier of MCs (Richardson & Cane 2010, Table 3) has an average successfulness of ≈70%. The unsuccessful cases (≈30%) are caused by small and weak MCs.

The same study explained in the above paragraph was performed with two other identifiers of MCs (see Huttunen et al. 2005, their Table 2, and Wu et al. 2003, /WIND list). In Table 3, the results are shown in the last two columns. The low successfulness (55.5%) with Huttunen et al. (2005) has an explanation. The IE methodology was unsuccessful in four events: one event was identified as a cloud candidate (cl) with a time extension of eight hours; two events were classified as MCs, however, on that date ICMEs were not reported; and the last MC was also identified by Wu et al. (2003, /WIND list, event 42 (September 21) with poor quality (3) and with a time extension of seven hours.

Furthermore, we saw false alarm cases. False alarm cases are grouped into three categories: (1) non-MC ICMEs according to the catalog of Richardson & Cane (2010, Table 3) (20 of these cases were identified); (2) stream interaction regions (SIRs) according to the catalog of Jian et al. (2006, p. 367–371), where 36 SIRs were identified; (3) other cases (non-MC ICMEs and non-SIRs). In Table 4, the previous categories are shown. In the first category, 15% of false alarms are reported. This is important and can save time, e.g., when a specialist wants to identify new MCs in a large data period. These three cases could be MC-ICME; however, they are not studied in this work.

Table 4.  Summary of Events That Are Not MCs Reported in 1999 and False Alarm Cases in the IE Analysis

False Alarm Cases	Total	NIEa	Pb
Non-MC ICMEs	20c	3	15%
SIRs	36d	1	2.8%
Other cases (non-ICMEs and non-SIRs)	⋯	5	⋯

Notes.

^aNumber of false alarm cases, i.e., where $\mathrm{IE}\leqslant 1.5 \%$. ^bPercent of false alarm cases $(({N}_{\mathrm{IE}}$/Total) × 100%). ^cAdapted from Richardson & Cane (2010, Table 3), from 33 ICMEs: 13 were MCs-ICMEs and 20 were non-MC ICMEs. ^dJian et al. (2006, p. 367–371).

Download table as:  ASCIITypeset image

In the second category, there is only one false positive case. In summary, the IE methodology is not useful to identify SIRs. Finally, five cases are in the third category. These cases are interesting because disturbances in the IMF can be observed. In addition, we are left with two open questions. What really are these events? Why do they have low IE values, similar to an MC? We think that these cases could be flux ropes. However, further study should be done to investigate the above cases.

In summary, the IE methodology identified 9 from 13 MCs, and nine false alarm cases are emitted. In a year (1999), a total of 788 windows of 2500 values exist, which means that the percent of false alarms was 1.14%, which is a good result. However, we prefer to propose it as a preliminary result because one year is considered poor statistics to accept the result as a robust identifier of MCs. Despite the difficulties, we can conclude that the IE methodology is useful for studying MCs, and in the next section, the IE methodology is used to identify two MCs.

Using the same procedure applied to the earlier cases, a study is done on the period including the 2000 October 12–14 event (presented in Table 1). The extended 10 day interval is shown in Table 2. In Figure 5 (bottom panel), the STE values for each component as a function of time are plotted with different line types. The thick black curve represents the IE calculated along the analyzed period. The MC around October 14 is plotted with three vertical dashed lines (the shock and cloud boundaries). The properties of this cloud are described by Huttunen et al. (2005). During the passage of this MC, the ${B}_{y},{B}_{z}$ components have $\mathrm{STE}=0 \%$ approximately in its first half, and the IE identifies this MC $(\mathrm{IE}\leqslant 1.5 \% )$. As expected, the STE method was once again demonstrated to be useful and capable of producing valid results.

Zoom In Zoom Out Reset image size

However, on October 8, the ${B}_{x},{B}_{y}$ components have STE values of almost zero (${\mathrm{STE}}_{x}^{\min }=12 \%$ and ${\mathrm{STE}}_{y}^{\min }=4 \%$), with $\mathrm{IE}\leqslant 1.5 \%$. On this date, the presence of an ICME was not reported, but a small magnetic structure where the field had a smooth variation is noticeable.

To identify MC boundaries, a combination of analyses of plasma data with the MVA method is usually applied. The data was measured by ACE from 2000 October 7 to 9, with a 1 hr time resolution. Figure 6 is composed of six panels: (top panels) magnetic field strength and polar (B_lat) angles of the magnetic field vector in the GSE coordinate system; (middle panels) azimuthal (B_long) angle and plasma beta; (bottom panels) maximum and minimum variance planes, respectively. The plasma beta minimum value was ${\beta }_{p}=2.7\times {10}^{-3}$ on October 7 at 23:00 UT. We used the magnetic field rotation confined to one plane and the plane of the maximum variance $({B}_{x}^{* }{B}_{y}^{* })$ to find the boundaries of the cloud; the dates are written in Table 5. In all panels of Figure 6, the first vertical line indicates the shock and the other two vertical lines indicate the MC interval. The MVA method gives the eigenvalue ratio ${\lambda }_{2}{\lambda }_{3}^{-1}=47.5$, the angle between the first and the last magnetic field vectors $\chi =148\buildrel{\circ}\over{.} 4$, the orientation of the axis $({\phi }_{C},{\theta }_{C})=(113\buildrel{\circ}\over{.} 8,7^\circ )$, the direction of minimum variance $({\phi }_{\min },{\theta }_{\min })=(22^\circ ,-10^\circ )$, and eigenvalues $[{\lambda }_{1},{\lambda }_{2},{\lambda }_{3}]=[124.6,41.8,0.9]$. This MC has a flux rope-type SEN as can be seen in Figure 6, right top panel and left middle panel, respectively. The observed angular variation of the magnetic field is left-handed. An MC event has been characterized. The STE method demonstrates not only its usefulness, but also its capability to produce new results (or, at least, interesting cases for studies). However, a question remains: how is it possible to identify a cloud in a region without ICMEs? Therefore, we think that this event is caused by the partial-halo CME on 2000 October 4, 06:26:05, which leaves the Sun with a linear speed of 237 km s⁻¹ (see the CME catalog, http://cdaw.gsfc.nasa.gov/CME_list/).

Zoom In Zoom Out Reset image size

On 2010 April 3, the Sun launched a cloud of material, known as a coronal mass ejection (CME), in a direction that reached the Earth. This CME was very fast, with a speed of at least $800\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The bulk of the CME passed south of the Earth, but a piece of it hit the Earth's magnetosphere on April 5, causing a geomagnetic storm (${{Dst}}_{\mathrm{minutes}}=-73\,\,\mathrm{nT}$ on April 6 at $15:00$ UT).

The ACE Magnetic Field Experiment data in level 2 (verified) were not available in 2010 April when the data were processed (2010 April–May). It was only possible to obtain such data for 16 s average IMF in RTN or GSE coordinates via anonymous ftp, from Caltech.⁷ For this reason, in Figure 7 (bottom panel), the STE values are calculated using data in GSE coordinates. This is not a problem, because the choice of the coordinate system, i.e, GSE, GSM, or RTN, does not affect the methodology for this study.

Zoom In Zoom Out Reset image size

In Figure 7 (bottom panel), we find minimum values of $\mathrm{STE}=1 \%$ in the B_z component on April 5 at 21:33:20 and 22:26:40 UT. The B_x and B_y components had STE values less than 10% on April 5 from 18:00:00 to 18:53:20 UT, respectively. Then, the IE has a minimum value of less than 1.5% on day 5, from 18:00:00 to 23:20:00 UT. Thus the IE detects a structure with characteristics of a MC candidate.

We think that an MC exists inside of these ICMEs. The methodology implemented in this work identifies a region characteristic of an MC in the magnetic field data. Using the earlier treatments, the boundaries found for the MC candidate is delimited in the data shown in Figure 8.

Zoom In Zoom Out Reset image size

In Figure 8, the data are measured by ACE from 2010 April 1–11, with a $1\,\mathrm{hr}$ time resolution. The figure is composed of six panels: (top panels) magnetic field strength and polar (B_lat) angles of the magnetic field vector in the GSE coordinate system, (middle panels) azimuthal angle (B_long) and plasma beta, (bottom panels) planes of maximum and minimum variance, respectively. On 2010 April 5, at 07:00 UT, the proton density was ${N}_{p}=2.8\,\,{\mathrm{cm}}^{-3}$, proton temperature ${T}_{p}=2.4\ast {10}^{5}\,\,{\rm{K}}$, ratio of alphas/protons = 7 × 10^–2, proton speed ${V}_{p}=564.5\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, magnetic field magnitude $B=5.2\,\,\mathrm{nT}$, and plasma beta ${\beta }_{p}=0.9$. One hour later, some parameters had changed: ${N}_{p}=7.98\,\,{\mathrm{cm}}^{-3}$, ${T}_{p}=5.5\,\times {10}^{5}\,\,{\rm{K}}$, alphas/protons = 1.7 × 10^–2, ${V}_{p}=724.8\,\,\mathrm{km}\,{{\rm{s}}}^{-1}$, $B=10.9\,\,\mathrm{nT}$, and ${\beta }_{p}=1.3$. It is easy to identify a shock because the velocity, density, and magnetic field magnitude increase abruptly, and we believe that it is related to the arrival of an event at ACE. Eight hours after the time of the shock, at $16:00$ UT, the plasma beta decreases to ${\beta }_{p}=3.2\ast {10}^{-2}$, and it is the start of the MC.

The plasma beta minimum value was ${\beta }_{p}=8.8\times {10}^{-3}$ on April 6 at 12:00 UT. We used the magnetic field rotation confined to one plane, the maximum variance plane $({B}_{x}^{* }{B}_{y}^{* })$, to find the boundaries of the MC. The dates are shown in Table 6. The minimum variance plane $({B}_{y}^{* }{B}_{z}^{* })$ has a problem, because the plot is not in ${B}_{z}^{* }=0$ (there is an offset), and we report this MC to be of medium quality in the identification. Thus, in all panels of Figure 8, the first vertical line indicates the shock and the other two vertical lines show the MC interval. The MVA method gives the eigenvalue ratio ${\lambda }_{2}{\lambda }_{3}^{-1}=16$, the angle between the first and the last magnetic field vectors $\chi =48^\circ$, the orientation of the axis $({\phi }_{C},{\theta }_{C})=(33^\circ ,-32\buildrel{\circ}\over{.} 6)$, the direction of minimum variance $({\phi }_{\min },{\theta }_{\min })=(129^\circ ,9^\circ )$, and eigenvalues $[{\lambda }_{1},{\lambda }_{2},{\lambda }_{3}]=[16.8,3.6,0.2]$. This MC has the flux rope-type NWS, as can be seen in Figure 8, right top panel and left middle panel, respectively. The observed angular variation of the magnetic field is left-handed. With the proposed methodology, we were able to identify a new MC.

By calculating the STE of the magnetic structures, evaluated by an IE index, the methodology proposed here allows MC candidates to be identified, as well as revealing some of them that present interesting features for further studies. The use of computational techniques to identify MC candidates seems better than performing an exhausting visual inspection of the data set to find the MC candidates, as done in other studies. Although there are other identification methodologies, another advantage of the IE index methodology is that it deals only with the IMF data. Finally, we should emphasize that this methodology is only an auxiliary identification tool, to be added to the others.