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Relationship between the geomagnetic Dst(min) and the interplanetary Bz(min) during cycle 23
ARTICLE IN PRESS Planetary and Space Science 58 (2010) 392–400
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Relationship between the geomagnetic Dst(min) and the interplanetary Bz(min) during cycle 23 R.P. Kane n ~ Jose´ dos Campos, SP, Brazil Instituto Nacional de Pesquisas Espaciais, C.P. 515, 12245-970 Sao
a r t i c l e in f o
a b s t r a c t
Article history: Received 30 May 2009 Received in revised form 9 November 2009 Accepted 10 November 2009 Available online 26 November 2009
In cycle 23 for geomagnetic storms of Dst(min) 450 nT, the plot of Dst(min) versus Bz(min) for the low Bz(min) range 0–10 nT showed erratic variation in Dst(min), (correlation 0.19). Even for Bz(min) range 10–20 nT, Dst(min) values had considerable scatter (correlation 0.57). For Bz(min). 420 nT, the relationship was good (correlation 0.82). For the whole range Bz(min) 0–50 nT, the correlation was high (0.88). Thus, if Bz(min) is very large ( 20 nT), large Dst(min) occurs but in a wide range of 100–500 nT. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Geomagnetic storms Dst Interplanetary magnetic fields Sun–Earth relationship
1. Introduction For geomagnetic storms to occur, a necessary condition is that either an ICME (Interplanetary coronal mass ejection blob or cloud, a modified form of CMEs of the Sun as it reaches Earth’s orbit at 1 AU) or a shock front (fast stream–slow stream interaction) should engulf the Earth. However, this condition is not sufficient. In addition, the ICME blob or cloud should have a magnetic field B with a significant negative Bz component ( 45 nT, Gonzalez et al., 1994). With Bz negative, geomagnetic disturbances occur by the Dungey (1961) mechanism, where reconnection occurs at the daytime magnetopause between the terrestrial magnetic field and the southward Bz component of the interplanetary field. When the field lines are swept back in the geomagnetic tail, a neutral point is formed, through which the solar wind gets an entry into the magnetosphere. Low-energy particles spiral around the stretched geomagnetic field lines and impinge on the terrestrial atmosphere in the polar regions, causing enhanced aurora. High-energy particles rush towards the Earth but are deflected around the Earth (Fleming’s right-hand rule law) in circular orbits in the equatorial plane, forming a ring current at several earth radii, which causes large geomagnetic field reductions at the ground. These reductions in the terrestrial magnetic field strength in the Earth’s equatorial region are measured by the disturbance storm time index (Dst, Sugiura,
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1964), which can attain values as large as 4500 nT in very severe storms. How good is the relationship of Bz(min) with Dst(min)? In this note, this aspect is examined for all categories of storms (weak, Dst(min) 50–100 nT; moderate, 100–200 nT; severe, 4200 nT), which occurred in cycle 23 (1996–2006) and for which interplanetary data, namely, number density N, velocity V and magnetic field component Bz were available. Data were obtained from the NGDC website http://spidr2.ngdc.noaa.gov/spidr/ and hourly values are used.
2. Dst(min) frequency of occurrence in every year Storms were considered only when hourly ( Dst) was 450 nT. For all storms irrespective of whether interplanetary data were available or not, Fig. 1 shows the occurrence frequency of Dst(min) in different Dst ranges; 50–70 nT, 70–90 nT etc. for each year, for years 1996–1999 (rising phase of the sunspot activity) in the first column, 2000–2002 (peak sunspot activity) in the second (middle) column, and 2003–2006 (declining phase of the sunspot activity) in the third column. In each frame, the year is shown in parenthesis, the circled numbers in the left at the top are the total number of storms in that year, and the numbers in rectangles in the right at the top are the yearly sunspot numbers for that year. The following may be noted: (1) In the rising phase (first column), starting from very few, weak storms in 1996, the number of stronger storms increased gradually up to 1999, parallel to the sunspot activity.
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Fig. 1. Occurrence frequency of Dst(min) in different ranges 50–70 nT, 70–90 nT, etc. for each year, for years 1996–1999 (rising phase of sunspot activity) in the first column, 2000–2002 (peak sunspot activity) in the second (middle) column, and 2003–2006 (declining phase of sunspot activity) in the third column. In each frame, the year is shown in parenthesis, the circled numbers in the left at top are the total number of storms in that year, and the numbers in rectangles in the right at top are the yearly sunspot numbers for that year.
(2) In the peak activity years 2000–2002 (second column), there were many more storms, including severe storms. (3) In the declining phase (third column), the number of storms was much more than in the rising phase. This discrepancy (excess geomagnetic activity in the declining phase of the sunspot activity) is known since long (Kane, 2007a, and references therein) and is attributed to two facts. Firstly, one of the origins of geomagnetic activity is the ICME occurrence frequency, which follows sunspot activity from the sunspot minimum to the sunspot maximum but then lingers around for some time in the declining phase (Kane, 2006 and references therein). Secondly, geomagnetic storms are also caused by the shock waves formed when highspeed solar wind from coronal holes impinges on the ambient slow solar wind in the interplanetary space and produces corotating interplanetary regions (CIR due to solar rotation of 27-day period) and these are copious in the declining phase of the sunspot activity. Incidentally, this excess geomagnetic activity is found to be useful for predicting the sunspot maxima in the ‘‘precursor’’ method evolved by Ohl (1976), where the excess geomagnetic activity (measured by Ap or aa indices) during the declining phase of the sunspot activity was noted to be proportional to the sunspot number Rz(max) of the next cycle. (The precursor methods are considered as more effective than all other methods, Joselyn et al., 1997). Various workers adopting the precursor method have been using geomagnetic indices in different parts in the declining phase. For example, Thompson (1993) uses the middle part, Chopra and Dabas (2006) and Jain (2006) use data an year or two before the sunspot minimum, while Kane (2007b and references therein) and Hathaway and Wilson (2004) use data near sunspot minimum. For cycle 24, all these have given a forecast of Rz(max) of 120 (Kane, 2007b).
3. Dst/Bz relationship In Fig. 1, the total number of storms ( Dst 450 nT) was 345, but the interplanetary data were available only for 232 (67%) events. Even among the severe storms ( Dst 4200 nT), from 19 events, interplanetary data were available for only 12 (63%)
Fig. 2. Plot of -Dst (min) versus Bz(min). Average Dst(min) values are shown as big dots with standard error bars. Correlations for various Bz(min) ranges are indicated. The straight line indicates the regression equation Dst(min)= [24.273.1]+ [6.67 0.2][ Bz(min)] for the whole Bz(min) range 0 to 50 nT. The circled crosses represent events of very high velocities, exceeding 800 km/s. Note that some of these are in the low Bz(min), low Dst(mean) region, indicating that high velocities do not ensure strong events.
events. Fig. 2 shows a plot of Dst(min) versus Bz(min). Following may be noted:
(1) For Bz(min) between 0 and 10 nT, the average Dst(min) values (big dots with standard error bars, values given in Table 1) are almost constant and the scatter (also the standard error) is very large, indicating a very poor relationship (correlation 0.1970.08, see Table 2(a). (2) For Bz(min) between 10 and 20 nT, there is an indication of trend but the scatter is large and correlation is only 0.5770.08.
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Table 1 Average values of -Dst(min) and their standard deviations for different -Bz(min) ranges. Bz(min) nT Number of events Average Dst(min) nT Standard error Limit 1 Limit 2
0–2 5 70 10 60 81
2–4 24 70 18 53 88
4–6 35 65 15 50 81
6–8 44 67 14 53 80
8–10 34 79 23 56 102
10–12 23 81 63 18 144
12–14 19 97 25 72 123
14–20 35 122 34 88 156
20–30 5 203 72 130 275
30–50 8 335 89 245 424
Table 2 Correlations of Dst(min) with Bz(min) for (a) different -Bz(min) ranges and (b) different Dst(min) ranges. (a) Bz(min) nT Number of events Corr. Dst(min)/Bz(min) Standard error
0–10 142 0.19 0.08
10–20 77 0.57 0.08
420 13 0.82 0.09
0–20 219 0.64 0.04
0–50 232 0.88 0.02
(b) Dst(min) nT Number of events Corr. Dst(min)/Bz(min) Standard error
50–100 166 0.38 0.07
101–200 54 0.46 0.11
201–500 12 0.77 0.12
50–200 220 0.64 0.04
50–500 232 0.88 0.02
Table 3 Expected values of Dst(min) for input values 5, 10, 15 y.. 50 nT of –Bz(min) used in the Dst/Bz regression Eq. (1). Bz(min) nT 5 10 15 20 25 30 35 40 45 50 Dst(min) nT 57 91 124 157 190 223 257 290 323 356 Standard error 3.3 3.9 4.8 5.7 6.8 7.8 9.0 10.1 11.2 12.4 % Std. error 5.8 4.3 3.8 3.6 3.5 3.5 3.5 3.5 3.5 3.5
(3) For Bz(min) 420 nT, the correlation is good (0.82 70.09), though there is still some scatter. (4) For Bz(min) from 0 to 20 nT, the correlation is moderate (0.64 70.04) but significant, indicating that there is some contrast between Dst(min) values corresponding to low and high Bz(min) values. (5) When all Bz(min) values 0–50 nT are considered, the correlation is high (0.8870.02), indicating that Dst(min) is related to Bz(min), but only in an overall way. (6) If the range 0–10 of Bz(min) is omitted, the relationship for Bz(min) between 10 and 50 nT is slightly higher (0.91 70.01). (7) If the data are sorted by values of Dst(min), the correlations are as given in Table 2b. Thus, whereas the general dependence of Dst(min) on Bz(min) is indicated qualitatively, the relationship is more secure only for large values. For the whole range Bz(min) 0–50 nT, the regression equation is: DstðminÞ ¼ ½24:2 73:1½6:6 70:2½BzðminÞ
ð1Þ
The regression line is shown in Fig. 2. For values of Bz(min) as 5, 10, y.. 50 nT, the expected Dst(min) would be as given in Table 3. The standard error for low Bz(min) (5–10 nT), is higher (5,8%) as compared to that for higher Bz(min) values ( 410 nT, 3,5%). However, this equation does not reflect fully the very low correlation (0.19) and the very large scatter in the low Bz(min) and the low Dst(min) region (Fig. 2, left bottom). A curious fact about low Dst values (NOAA website catalogue) is that whereas during quiet periods, the Dst values are generally almost zero, there have been quiet intervals when Dst (in the catalogue) is not near zero but above zero or below zero for weeks together. So, when a storm occurs, one wonders whether the Dst(min) should be taken on its face value or whether the pre-
10–50 90 0.91 0.02
storm level should be subtracted. This will make a difference of about 720 nT. A part of the scatter in the -Dst(min) values for the Bz(min) range 0–10 nT may be due to this uncertainty but only partly; because of the scatter there is much larger than 20 nT, almost 50 nT or more. We have avoided events when the Dst base level was more than 20 nT (positive or negative), but among these, we have used data for storm events when -Dst(min) was 4100 nT. The Dst(min) and the Bz(min) rarely occur simultaneously. Gonzalez and Echer (2005) report that the Dst(min) is delayed with respect to the Bz(min) by 1–4 h, with an average values of 2 h, though in less than 5% storms, the Dst(min) occurred before the Bz(min). They suggest that this delay indicates a physical response time of the ring current to the solar wind driver at the peak interval of an intense storm. In our analysis, this aspect is initially ignored, and we consider in Fig. 2 only the magnitudes of the minimum values of Dst and Bz, no matter how and when these occurred with respect to each other.
4. Other factors It has been reported earlier (e.g., Gonzalez et al., 1994) that not the Bz(min) but its cumulative value over the interval of Bz negative values is important for the Dst storm development. (It is a gradual process, like the charging of an electrical condenser). In the present analysis, we calculated two new parameters, namely, CPBz, which is cumulative partial Bz, i.e., from the beginning of the negative Bz to its climax value Bz(min), and CTBz, which is cumulative total Bz, i.e., from the beginning of the negative Bz to the end of the negative Bz. Thus, now three parameters could be used, Bz(min) as before, and CPBz, CTBz. Another important factor relates to Dst itself. It is often tactically assumed that the Dst is due to the ring current only. This is not true. Some contributions come from other sources also (Gonzalez et al., 1994). For example, there are induced currents in the solid Earth. These are mostly in a constant proportion with the ring current (about one third) and hence will not affect the correlations with Bz(min) (only the regression coefficient will alter). But there are magnetopause currents that depend upon the solar wind ram pressure only (depend on N and V) and not on Bz(min). Their contribution to Dst(min) can be substantial and may differ considerably from event to event, even though Bz(min)
ARTICLE IN PRESS R.P. Kane / Planetary and Space Science 58 (2010) 392–400
may remain the same. For the true ring current effect Dstn after a correction due to magnetopause currents is applied to Dst, according to Burton et al. (1975), the relationship between Dst and Dstn is Dst ¼ DstMst ¼ DstbP1=2 þ c
ð2Þ
where Mst is the magnetopause current contribution, P is the storm time solar wind ram pressure, obtained as Nm + V2 (N and V being the solar wind density and velocity respectively, and m + the proton mass), b is a proportionality factor, and c is the quiet time solar wind ram pressure contribution. Typically, b= 8.74 nT/(nPa)1/2 and c =11.54 nT. (Turner et al., 2001). OBrien and McPherron (2000) have calculated these as b= 7.26 and c= 11.0, but the overall results seem to remain almost the same (Turner et al., 2001) In small samples, the reliability of the correlations is doubtful and it was noticed that including or deleting a single event could sometimes alter the correlation substantially. In the present case where weak and moderate storms were also considered, Dstn is calculated for every storm and the correlations using Dstn(min) are also calculated. A major problem is to ascertain appropriately the hourly values of various parameters. Fig. 3 shows the plots of interplanetary N, V, Bz and geomagnetic Dst during twelve severe storm events that had Dst(min) 4200 nT, in chronological order with events numbered as 1, 2, 3, and 4 in the first row; 5, 6, 7, and 8 in the second row and 9, 10, 11, and 12 in the third row, years 1998 (events 1 and 2), 1999 (event 3), 2001 (events 4 and 5), 2003 (events 6, 7 and 8), 2004 (events 9 and 10) and 2005 (events 11 and 12). The maxima of N and V and the minima of Dst and Bz are marked with big dots. As can be seen, Bz(min) occurred earlier than Dst(min) in the 12 events by 1, 5, 1, 2, 0, 5, 2, 4, 4, 5, 2, and
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2 h, (range 0–5 h, average 33/12= 2.8 h, slightly larger than the 2 h mentioned by Gonzalez et al., 1994). The correlation between Dst(min) and Bz(min) for the Dst(min) range 201–500 (Table 2(b)) was 0.77, if only the magnitudes (irrespective of phase shift) are considered. The correlation is dominated by the two Halloween events of October 30, 2003 and one of November 20, 2003. If these three events are omitted, the correlation reduces to 0.65, indicating some scatter. Here, for the two storms of October 29–30, 2003 (called Halloween events) numbered 6 and 7 in Table 2, an explanation is needed for the values of parameters used by us. These two were the strongest interplanetary storms of cycle 23, with ICME velocity V exceeding 2000 km/s, in contrast to velocities below 1000 km/s in the other 10 storms. Unfortunately, the satellite data for these storms were not fully satisfactory. Skoug et al. (2004) have given complete details of the functioning of the instrumentation and the data records and mention that for several consecutive h, some instruments failed (no data for some parameters). The number density Np was most probably underestimated. In the rest of the data, they mention in their paragraphs 20, 22 and their Fig. 4, values for October 29, 2003 as V= 2240 km/s, Np 10 or less, Bz(min)= 68 nT, Bmax = 68 nT and for October 30, 2003 as V= 1710 km/s, Np 10 or less, Bz(min)= 35 nT, Bmax = 40 nT. However, these are, so to say, instantaneous (1–5 min) values. Their averages over one hour would certainly be lesser, the question is, how much lesser. In their Fig. 6, Skoug et al. (2004) plot hourly values of V as 42000 km/s in event 6 and 1800 km/s in event 7 (numbering of our Table 2). No mention is made of Bz(min). In their Table 3, the values are mentioned for October 30 events as V 2000 km/s, 1 Np 10–20, B as 68 nT, and Bz as –68 nT (obviously the extreme instantaneous values). In their plot in Fig. 4, the Bz values do not
Fig. 3. Plots of interplanetary number density N, solar wind velocity V, magnetic field north–south component Bz, and geomagnetic disturbance index Dst, for individual severe storms (-Dst 4200 nT), 1–4 in the first row, 5–8 in the second row and 9–12 in the third row. The maxima of N, V, Dst(min) and Bz(min) are marked with big dots, and the hours by which Bz(min) occurred before Dst(min) are indicated as negative numbers in parentheses in each of the 12 panels.
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have a steady negative high level; instead, there are violent fluctuations from positive to negative values. It is probably because of these fluctuations in Bz values that the SPIDR NOAA website mentions hourly values of Bz as only –25 and –29 nT for the two events. These are very low values as compared to the –68 and –35 nT instantaneous negative values of Bz. Thus, considerable uncertainties are involved. The low Bz values 25–29 nT are not commensurate with the high Dst values 363 and 401 nT of these events. Hence, keeping in view all these facts and uncertainties, we assigned Bz(min) as –50 nT, V as 2000 km/s, and Np as 15, for both the events, somewhat arbitrarily but helplessly. Another problem was, what values of N and V to choose for calculating Dstn in Eq. (2). In Fig. 3, the N and V values changed rapidly during the storm interval and their maxima rarely coincided between themselves or with the hours of Bz(min) or Dst(min). Thus, choosing the maximum values of N and V during the whole storm interval would be inappropriate. More proper would be to choose the N and V values at the hours of Bz(min) or Dst(min) and here again, there was a doubt as to which hour to choose, as Bz(min) and Dst(min) rarely coincided, and Dst(min) occurred with a delay of 0–5 h. Hence, we chose both, namely, VB and NB as V and N values at the Bz(min) hour, and VD and ND as V and N values at the Dst(min) hour. These VB, NB and VD, ND pairs were used in Eq. (2) and two values of magnetopause effects MstB and MstD were obtained. Subtracting these from the Dst(min) values, two estimates of the true ring current Dstn were obtained, namely DstBn and DstDn. Thus, for correlation analysis, for each storm, the following parameters were used: Dst(min), DstBn, and DstDn to be correlated separately with: Bz(min), two values of cumulative Bz, namely, CPBz (partial) and CTBz (total), VB.Bz(min) and VD.Bz(min). The latter two were used because some workers have reported that the Dst(min) shows a better correlation with the product of Bz(min) and velocity V, namely V.Bz(min), than with Bz(min) alone (Gonzalez et al., 1994 and references therein). Table 4 shows the correlations. The following may be noted: For Dst(min),
(1) Correlations with Bz(min) for increasing ranges 0–10, 10–20 and 20–50 nT are: 0.19, 0.57 and 0.82. In the whole range 0–50, the correlation is larger (0.8870.02) because of the great contrast of low and high values.
(2) With cumulative Bz, the correlations are not better (in fact, these are poorer). (3) With the product V.Bz, the correlation is low in the smaller Bz(min) range 0–10 nT, but in the 10–20 nT range, correlation improves from 0.57 to 0.70. However, in the bigger range 20–50 nT, there is a decrease from 0.82 to 0.55. In the total range 0–50 nT also, there is a decrease from 0.8870.02 to 0.7770.02. Thus, the product of velocity and Bz(min) in the middle ranges does show improvement over Bz(min) alone, but in the higher ranges, the effect is not obvious. There is virtually no difference between the correlations using VB and VD, because during the few hours of difference (0–5 h) between Bz(min) and Dst(min), the V does not change much (the correlation between VB and VD is 0.96). So, using VB alone may be enough. For DstBn, all correlations are in general only very slightly higher than the corresponding ones for Dst(min). Thus, the improvement by correcting for magnetopause current effects has proved to be insignificant. It may be noted, however, that the magnitudes of the magnetopause effects are rather small, mostly less than 25 nT and were high only for the Halloween events ( 75 nT). Other characteristics like correlations with CTBz slightly larger than for CPBz are similar to those of Dst(min). For DstDn, correlations are similar to those for DstBn. This is because, since VB and VD were similar, DstBn and DstDn were also similar (correlation 0.99). Table 5 shows correlations for different ranges of –Dst(min). The following may be noted: For Dst(min), (1) Correlations with Bz(min) for increasing –Dst(min) ranges 50–100, 101–200, and 200–500 nT are: 0.38, 0.46, and 0.77. In the whole range 50–500 nT, the correlation is large (0.88 70.02, same as in Table 4), because of the great contrast of low and high values. (2) With cumulative Bz, the correlations are not better, in fact, these are smaller. (3) With the product V.Bz, the correlation is the same in the smaller -Dst(min) range 50–100 nT, higher in the100–200 nT range, and lower in higher ranges. There is virtually no difference between the correlations using VB and VD, because during the few hours of difference (0–5 h) between Bz(min) and Dst(min), the V does not change much (the correlation between VB and VD is 0.96). So, using VB alone may be enough.
Table 4 Correlations of Dst(min), DstBn. DstDn with Bz(min), cumulative Bz, namely, CPBz (partial) and CTBz (total), and the products VB.Bz(min) and VD.Bz(min) for negative Bz(min) ranges, 0–10, 10–20, 20–50, and 0–50 nT. Bz(min) nT
0–10
Number of events
142
Std. error
77
Std. error
13
Std. error
232
Std. Error
Dst/ Dst/ Dst/ Dst/ Dst/ DstBn/ DstBn/ DstBn/ DstBn/ DstBn/ DstDn/ DstDn/ DstDn/ DstDn/ DstDn/
0.19 0.16 0.17 0.26 0.28 0.19 0.13 0.13 0.27 0.28 0.20 0.14 0.15 0.27 0.29
0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
0.57 0.22 0.40 0.71 0.70 0.59 0.14 0.32 0.75 0.74 0.58 0.19 0.32 0.72 0.72
0.08 0.11 0.10 0.06 0.06 0.10 0.10 0.08 0.08 0.08 0.09 0.11 0.08 0.08 0.08
0.82 0.56 0.59 0.55 0.55 0.86 0.63 0.59 0.69 0.69 0.86 0.63 0.58 0.69 0.68
0.09 0.25 0.25 0.13 0.13 0.09 0.24 0.24 0.13 0.13 0.09 0.25 0.24 0.13 0.13
0.88 0.65 0.66 0.77 0.76 0.89 0.64 0.64 0.81 0.81 0.89 0.65 0.64 0.81 0.81
0.02 0.05 0.05 0.02 0.02 0.02 0.05 0.04 0.02 0.02 0.03 0.05 0.05 0.02 0.02
Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min)
10–20
20–50
0–50
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Table 5 Correlations of Dst(min), DstBn. DstDn with Bz(min), cumulative Bz, namely, CPBz (partial) and CTBz (total), and the products VB.Bz(min) and VD.Bz(min) for negative Dst(min) ranges, 50–100, 101–200, 201–500, and 50–500 nT. Dst(min) nT
50–100
Number of events
166
Std. error
54
Std. error
12
Std. error
232
Std. Error
Dst/ Dst/ Dst/ Dst/ Dst/ DstBn/ DstBn/ DstBn/ DstBn/ DstBn/ DstDn/ DstDn/ DstDn/ DstDn/ DstDn/
0.38 0.26 0.27 0.38 0.40 0.43 0.23 0.25 0.44 0.46 0.41 0.25 0.24 0.42 0.44
0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
0.46 0.26 0.35 0.58 0.61 0.42 0.13 0.18 0.61 0.62 0.48 0.23 0.23 0.62 0.66
0.08 0.11 0.10 0.06 0.06 0.10 0.10 0.08 0.08 0.08 0.09 0.11 0.08 0.08 0.08
0.77 0.69 0.83 0.50 0.49 0.82 0.77 0.84 0.68 0.68 0.83 0.78 0.84 0.67 0.67
0.18 0.25 0.25 0.13 0.13 0.18 0.24 0.24 0.13 0.13 0.21 0.25 0.24 0.13 0.13
0.88 0.65 0.66 0.77 0.76 0.89 0.64 0.64 0.81 0.81 0.89 0.65 0.64 0.81 0.81
0.02 0.05 0.05 0.02 0.02 0.02 0.05 0.04 0.02 0.02 0.03 0.05 0.05 0.02 0.02
Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min)
100–200
200–500
50–500
Table 6 Correlation between Dst(min) and Bz(min) for (a) different thresholds and (b) different ranges of the velocity VB at the hour of Bz(min). (a) VB (km/s) Number of events Corr. Dst(min)/Bz(min) Standard error (b) VB (km/s) Number of events Corr., Dst(min)/Bz(min) Standard error
All 232 0.88 0.02
4400 195 0.90 0.01 Upto 400 37 0.24 0.16
4450 151 0.92 0.01
4500 118 0.93 0.01
401–500 77 0.71 0.06
For DstBn, all correlations are almost similar to the ones for Dst(min). For DstDn, correlations are similar to those for DstBn.
5. Correlation Dst(min)/V It is generally expected that a very fast interplanetary blob would result in very intense storms. However, as described in detail in Kane (2005), the Dst(min) is poorly correlated with the interplanetary velocity. In the present case, the overall correlation Dst(min)/VB was only 0.50, the overall correlation Dst(min)/ Bz(min) was 0.88, and the overall correlation Dst(min)/ VB.Bz(min) was 0.80 (see the last columns in Tables 4 and 5). Thus, the role of V is only through the VB relationship. A glaring example of poor relationship between Dst(min) and V directly was that of the August 4, 1972 event, when the velocity was enormous ( 2800 km/s) but the Dst(min) was only about 125 nT, mainly because the Bz component fluctuated between 0 and a few nT negative (Tsurutani et al., 1992, 2003). In cycle 23, some events in Fig. 2 are marked with encircled crosses. All these had high velocities (exceeding 800 km/s), but the points are spread all over, low as well as large Dst(min) and Bz(min), indicating that a high velocity does not ensure high Dst. Recently, Wu and Lepping (2002a, b) reported an interesting feature, namely that for the subset of interplanetary blobs called ‘‘magnetic clouds‘‘ (these have organized internal magnetic fields), the Dst(min)/Bz(min) correlation increased dramatically, when the solar wind speed exceeds 600 km/s. To examine this aspect, our data were sorted on VB values. Table 6 shows the
4550 83 0.94 0.01 501–600 59 0.91 0.02
4600 59 0.94 0.01 601–700 37 0.93 0.02
4 650 31 0.96 0.01
4 700 22 0.96 0.01 701–800 10 0.97 0.01
4800 12 0.97 0.01 4800 12 0.97 0.01
Dst(min)/Bz(min) correlations for VB of different thresholds, 4400, 4450 etc. and of different ranges. The following may be noted: (1) In Table 6(a), for all velocities, the correlation Dst(min)/ Bz(min) was 0.8870.02, but for higher velocity ranges 4400, 4450 etc., the correlation increased to 0.9670.01 for VB 4650 km/s, a significant increase. (2) In Table 6(b), the correlations were low (0.24) for low velocities, moderately high (0.71) for velocities up to 500 km/s, but were very high for velocities between 500 and 800 km/s.
6. Conclusions and discussion For cycle 23, geomagnetic storms with Dst(min) 450 nT were compared with the minimum value Bz(min) of the negative Bz component of the interplanetary magnetic field. (1) It was noticed that in the plot of Dst(min) versus Bz(min) for Bz(min) in the low range 0–10 nT, the Dst(min) varied erratically, indicating very poor relationship (correlation 0.19). Any value of Bz(min) could be associated with any value of Dst(min) (2) Even for Bz(min) between 10 and 20 nT, Dst(min) values had a considerable scatter (correlation 0.57). (3) For Bz(min) 420 nT, severe storms occurred, and the relationship was good (correlation 0.82). (4) When the whole range Bz(min) 0–50 nT was considered together, the correlation was high (0.88), because of the great contrast of Dst(min) values from 50 to 500 nT.
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(5) If Bz(min) is very large ( 420 nT), large Dst(min) would occur in a wide range 100–500 nT, and the proportionality of the magnitudes of Dst(min) and Bz(min) was loose, far from one-to-one. (6) The correlations of Dst(min) with the product V.Bz(min) were better as compared to those of Dst(min) with Bz(min) alone in the intermediate ranges (Bz 10–20 nT and Dst 100–200 nT), but for higher ranges, V.Bz was not superior. (7) Replacing Bz(min) with cumulative Bz (sum of hourly values from the beginning to the end of the negative Bz values) did not improve the correlations. (8) Using Dstn (the true ring current after subtracting magnetopause current effects from the observed Dst(min)) did not improve the correlations appreciably; because the magnetopause effects were small (less than 25 nT), except for the Halloween events of October 30, 2003) when the effects were 75 nT. Thus, the correlation between Dst(min) and Bz(min) is rather loose, particularly in the middle ranges of Dst(min) around 200 nT and Bz(min) around 20 nT, indicating that the geomagnetic effects due to the entry of solar wind at the neutral point in the geomagnetic tail region are not a straightforward affair. Several complications are involved. The main problem is to establish an energy function to quantify the solar wind–magnetosphere energy transfer. Several functions have been studied (Gonzalez et al., 1989, 1990; De Lucas et al., 2007, and references therein). One of these functions considers the reconnection process as the main phenomenon for energy injection into the magnetosphere (Perreault and Akasofu, 1978). After being injected in the dayside magnetosphere, the solar wind energy is finally dissipated into different regions of the magnetosphere. Based on the functions for energy injection and dissipation assumed by Feldstein et al. (2003), the result is that one-half of the energy is injected into the magneto-tail and dissipated there. After the reconnection at the magnetotail, a part of this energy is accelerated earthward in the equatorial region. Another part of the solar wind energy is deposited in the auroral ionosphere as heat energy, which arises partly from Joule heating and partly from the impact of auroral particles. Therefore, the total energy dissipation can be estimated through the sum of these contributions (Akasofu, 1981). Monreal-MacMahon and Gonzalez (1997) took into account the magnetopause position as a function of the solar wind ram pressure. The energy transfer from the solar wind to the magnetosphere was then estimated through a corrected version of the Perreault and Akasofu ‘e’ parameter based on the dayside magnetopause ram pressure. In their recent paper, De Lucas et al. (2007) discussed this problem in detail and suggested modifications to this function. Their aim was to evaluate the interplanetary characteristics (interplanetary dawn–dusk electric field and interplanetary magnetic field component BS), the ‘e’ parameter, and the total energy input into the magnetosphere for two classes of magnetic storms, namely, intense storms and super-intense storms. (see also Vichare et al., 2005). However, in Fig. 3 of De Lucas et al. (2007), where the estimated values of the energies injected and dissipated during the main phase of intense storms are plotted versus the absolute values of the Dst index, the scatter is large. They mention a correlation of 0.88 for 8 events, but if the one point of very high Dst(min) is omitted, the correlations are lower, almost like our plot of Dst(min) versus Bz(min) (our Fig. 2). Earlier, Turner (2000) studied the solar wind– magnetosphere coupling and the global energy budgets in the Earth’s magnetosphere and reported that in the energy flow, there is a clear domination of ionospheric energy deposition in the polar region, with the Joule heating alone accounting for around half of the total energy; and the ring current energy deposition was
10–15% of the total energy. Later, Turner et al. (2001) showed that ring current ions contributed on the average, half of the Dst depression, but with a large variation among individual events. Vichare et al. (2005) computed for nine intense geomagnetic storms, the solar wind energies, magnetospheric coupling energies, auroral and Joule heating energies, and the ring current energies. They found that only about 3.5% of the total solar wind kinetic energy was available for redistribution in the magnetosphere, and around 20% of this goes into the inner magnetosphere and in the auroral ionosphere of both the hemispheres. However, in all these works, a curious feature is seen. In figures showing dependence on Bz(min) or Dst(min), good correlations ( 0.8) are reported when the whole range is considered, but these good correlations get reduced considerably if some events with very high Bz(min) and/or Dst(min) are omitted, more so when very intense storms are considered. Also, the middle range of Bz(min) near 20–30 nT or Dst(min) near 250 nT shows considerable scatter, no matter how sophisticated the methodology of calculating the energies is. This is important because it is above 250 nT of the Dst depression that electrical damages in high latitudes commence. So, if Bz(min) near 20 nT gives unreliable estimates of Dst(min) (could be anything between 100 and 350 nT), considerable quantitative prediction potential is lost. Turner et al. (2001) mention that some of the discrepancies could be due to ring current asymmetry. The fact remains that for a medium size Bz(min), the percentage going to cause equatorial Dst(min) as compared to polar region effects varies considerably from event to event, even if Dst is corrected for magnetopause effects. It seems, therefore that there are some factors still missing from consideration. Further work may resolve this discrepancy. Recently, Alex et al. (2006) studied the geomagnetic signatures of the intense storms of October 29 and November 20, 2003. Using ground magnetic field measurements from equatorial and lowlatitude locations in the Indian longitude zone in conjunction with interplanetary solar wind and magnetic field parameters, they estimated the maximum magnitudes of the total magnetospheric energy injected into the magnetosphere during the main phase of the three major storms as (2.8–3.5) 1013 W. They also reported a close correspondence between Bz(min) and Dst(min) and low-latitude digital magnetic records. Rawat et al. (2006) illustrated another aspect, namely the low-latitude geomagnetic signatures during major ‘‘solar energetic particle (SEP) events of cycle 23, two in 2000 and two in 2001. They showed a close correspondence between the persistence of a high level of proton flux after the interplanetary shock in some events and the ensuing intense magnetic storms and the role of southward Bz duration generation of a strong main phase. Incidentally, all such analyses have only an academic value and hardly any prediction potential, for the following reason. Severe geomagnetic storms (-Dst 4300 nT) can cause severe damages to electrical installations (including burnout of transformers) in high latitudes. As such, the engineers would like to have as much accurate information of the commencement and maximum extent of the storm, as possible. Long ago, Chapman and Bartels (1940) mentioned that after the occurrence of a solar flare, a geomagnetic storm may occur after about 20–100 h. This is still true today, but this range of uncertainty is very large. Later, solar wind theory was formulated (Parker 1959) and the presence of a perpetual solar wind was confirmed by observations (Gringauz et al., 1960 and others). Soon after, Tousey (1973) discovered the coronal mass ejections (CME) phenomenon and now, with the SOHO LASCO setup where the main solar disc is artifically occulted, CMEs can be detected on the sky background as emissions coming out of the Sun on the limbs. The lateral expansion speed can be calculated and regression equations are available for the relation
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of this velocity with the velocity of the ICMEs near Earth. Thus, having seen a CME, it is possible to calculate its arrival time near the Earth (Manoharan et al., 2003; Dal Lago et al., 2004; Schwenn et al., 2005). However, there is an uncertainty of about 20% and estimates of 20 h can be wrong by 4 h (details given in Kane 2008). Still, this is a much better estimate than that suggested by Chapman and Bartels (1940). Having had this preliminary warning, cosmic ray directional muon telescopes can give another preliminary warning of the incoming interplanetary cloud, probably a few hours before the cloud reaches the Earth (Space Weather Prediction with Cosmic Rays, website http://neutronm. bartol.udel.edu/spaceweather/). The next warning comes when the cloud reaches the ACE satellite situated between the Sun and the Earth (much nearer to Earth), with a ICME cloud transit time antecedance of about half an hour. Finally, when the cloud engulfs the Earth, a magnetogram shows an storm sudden commencement (SSC) and the storm is supposed to start. More uncertainties start here. Firstly, there is no way to tell whether a storm will follow an SSC at all. It will depend upon how the negative Bz component evolves and whether it will be substantial and if so, when. The Dst storm may start within a few hours (0–4) and there is no way to tell when exactly Dst(min) will occur and of what magnitude. These factors are very important for the electrical engineers to know as early as possible. Indices like Kp and Dst are calculated from data of various stations, but this takes time and information will not be available before the storm, unless one uses model predictions as in Temerin and Li (2006); but these have their own limitations and uncertainties. Also, Dst is a global storm index, while what the transformers would respond to is the local magnetic field in that vicinity, which has a Dst component and a DS component (dependent on the local time LT), which may not be negligible. Thus, the sure way for the engineer would be to have a magnetometer available for watching the evolution of the magnetic field depression and switch off the transformer as soon as the field decreases below say, o 250 nT. This is still a gamble, because the magnetic field may not drop further and the switching off may cost billions of dollars of revenue. If the field does decrease further, the transformers should be restarted when the recovery starts and the field recoups within 0 to 250 nT. Beland (2004) mentions that ‘‘for Hydro-Quebec (HQ) in the province of Quebec in Canada, there are now two measurement systems (one primary and one backup) monitoring groundinduced current (GIC) effects on the grid in real time. To be informed in advance of a probable GIC occurrence, HQ now relies on a specialized organization providing geomagnetic activity alert and forecast. Following an alert or the detection of GIC effects on the network exceeding a minimal threshold, special operation rules become in effect for ensuring maximum stability and safety margin. Also, series capacitors are introduced on several 735 kV lines, which increase network stability and also block GIC circulation’’. Other installations might be using other methods. In some cases, operations are stopped (if possible) during the storm interval. Obviously, statistical correlation and regression analyses do not have much role to play in this scenario.
Acknowledgements This work was partially supported by FNDCT, Brazil, under contract FINEP-537/CT. References Akasofu, S.-I., 1981. Energy coupling between the solar wind and the magnetosphere. Space Science Reviews 28, 121–190.
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A study on the peak Dst and peak negative Bz relationship during intense geomagnetic storms. Geophysical Research Letters 32, L18103, doi:10.1029/2005GL023486. Gonzalez, W.D., Tsurutani, B.T., Clua de Gonzalez, A.L.C., Smith, E.J., Tang, F., Akasofu, S.-I., 1989. Solar wind–magnetosphere coupling during intense magnetic storms (1978–1979). Journal of Geophysical Research–Space Physics 94, 8835–8851. Gonzalez, W.D., Clua de Gonzalez, A.L.C., Lee, L.C., Tsurutani, B.T., 1990. Role of the lifetime of ring current particles on the solar wind–magnetosphere power transfer during the intense geomagnetic storm of 28 August 1978. Planetary and Space Science 38 (36), 765–769. Gonzalez, W.D., Joselyn, J.A., Kamide, Y., Kroehl, H.W., Rostoker, G., Tsurutani, B.T., Vasyliunas, V., 1994. What is a geomagnetic storm? Journal of Geophysical Research-Space Physics 99, 5771–5792. Gringauz, K.I., Bezrukikh, V.V., Ozerov, V.D., Rybchinskii, R.E., 1960. A study of the interplanetary ionized gas, high-energy electrons, and corpuscular radiation from the Sun by means of the three-electrode trap for charged particles on the second Soviet cosmic rocket, (in Russian). Doklady Akademii Nauk SSSR 131 (6), 1301–1304 1960. (English translation, Sov. Phys. Dokl. 5, 1960, pp. 361–364). Hathaway, D.H., Wilson, R.M., 2004. What the sunspot record tells us about space climate. Solar Physics 224, 5–19. Jain, R.: 2006, Prediction of the amplitude in sunspot cycle 24 In: 36th COSPAR Scientific Assembly, 16–23 July 2006, Beijing, China, 642 (TC1-0229;C4.20053-06, Program p. 178). Joselyn, J.A., Anderson, J.B., Coffey, H., Harvey, K., Hathaway, D., Heckman, G., Hildner, E., Mende, W., Schatten, K., Thompson, R., Thomson, A.W.P., White, O.R., 1997. Panel achieves consensus prediction of solar cycle 23. Eos, Transactions American Geophysical Union 78, 205. Kane, R.P., 2005. How good is the relationship of solar and interplanetary plasma parameters with geomagnetic storms? Journal of Geophysical Research-Space Physics 110, A02213, doi:10.1029/2004JA010799. Kane, R.P., 2006. Comparison of the variations of CMEs and ICMEs with those of other solar and interplanetary parameters, during solar cycle 23. Solar Physics 233, 107–115. Kane, R.P., 2007a. Solar terrestrial effects of two distinct types. Advances in Space Research 39, 1890–1897. Kane., R.P., 2007b. A preliminary estimate of the size of the coming solar cycle 24, based on Ohl’s Precursor method. Solar Physics 243, 205–217. Kane, R.P., 2008. Limitations of the utility of CMEs for forecasting timings and magnitudes of geomagnetic Dst storms. Indian Journal of Radio and Space Physics 37, 303–311. Manoharan, P K, Gopalswamy, N, Yashiro, S, Lara, A, Michalek, G, Howard, R A, 2003. Influence of coronal mass ejection interaction on propagation of interplanetary shocks. 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Perreault, P., Akasofu, S.-I., 1978. A study of geomagnetic storm. Geophysics Journal of the Royal Astronomical Society 54, 547–573. Rawat, R., Alex, S., Lakhina, G.S., 2006. Low-latitude geomagnetic signatures during major solar energetic particle events of solar cycle-23. Annales. Geophysique 24, 3569–3583. Schwenn, R, Dal Lago, A, Huttunen, E., Gonzalez, W D, 2005. The association of coronal mass ejections with their effects near the Earth. Annales Geophysicae 23, 1033–1059. Skoug, R.M., Gosling, J., Steinberg, J., McComas, D.J., Smith, C.W.,.Ness, N.F., Hu, Q., Burlaga, L.F., 2004, Extremely high speed solar wind: October 29–30, 2003, Journal of Geophysical Research–Space Physics 109, A09102, 10.1029/2004JA010494. Sugiura, M., 1964. Hourly Values of the Equatorial Dst for IGY. Annals of the International Geophysical Year, vol. 35. Pergamon Press, Oxford, pp. 945–948. Temerin, M., Li, X., 2006. Dst model for 1995–2002. Journal of Geophysical Research–Space Physics 111 (A4), A04221, doi:10.1029/2005JA011257. Thompson, R.J., 1993. A technique for predicting the amplitude of the solar cycle. Solar Physics 148, 383–388. Tousey R, 1973, The Solar Corona, (eds. M.J. Rycroft and S.K. Runcom), SpringerVerlag, New York, 173pp. Tsurutani, B.T., Gonzalez, W.D., Tang, F., Lee, Y.T., Okada, M., Park, D., 1992. Reply to L. J. Lanzerotti: solar wind ram pressure corrections and an estimation
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Relationship between the geomagnetic Dst(min) and the interplanetary Bz(min) during cycle 23 R.P. Kane n ~ Jose´ dos Campos, SP, Brazil Instituto Nacional de Pesquisas Espaciais, C.P. 515, 12245-970 Sao
a r t i c l e in f o
a b s t r a c t
Article history: Received 30 May 2009 Received in revised form 9 November 2009 Accepted 10 November 2009 Available online 26 November 2009
In cycle 23 for geomagnetic storms of Dst(min) 450 nT, the plot of Dst(min) versus Bz(min) for the low Bz(min) range 0–10 nT showed erratic variation in Dst(min), (correlation 0.19). Even for Bz(min) range 10–20 nT, Dst(min) values had considerable scatter (correlation 0.57). For Bz(min). 420 nT, the relationship was good (correlation 0.82). For the whole range Bz(min) 0–50 nT, the correlation was high (0.88). Thus, if Bz(min) is very large ( 20 nT), large Dst(min) occurs but in a wide range of 100–500 nT. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Geomagnetic storms Dst Interplanetary magnetic fields Sun–Earth relationship
1. Introduction For geomagnetic storms to occur, a necessary condition is that either an ICME (Interplanetary coronal mass ejection blob or cloud, a modified form of CMEs of the Sun as it reaches Earth’s orbit at 1 AU) or a shock front (fast stream–slow stream interaction) should engulf the Earth. However, this condition is not sufficient. In addition, the ICME blob or cloud should have a magnetic field B with a significant negative Bz component ( 45 nT, Gonzalez et al., 1994). With Bz negative, geomagnetic disturbances occur by the Dungey (1961) mechanism, where reconnection occurs at the daytime magnetopause between the terrestrial magnetic field and the southward Bz component of the interplanetary field. When the field lines are swept back in the geomagnetic tail, a neutral point is formed, through which the solar wind gets an entry into the magnetosphere. Low-energy particles spiral around the stretched geomagnetic field lines and impinge on the terrestrial atmosphere in the polar regions, causing enhanced aurora. High-energy particles rush towards the Earth but are deflected around the Earth (Fleming’s right-hand rule law) in circular orbits in the equatorial plane, forming a ring current at several earth radii, which causes large geomagnetic field reductions at the ground. These reductions in the terrestrial magnetic field strength in the Earth’s equatorial region are measured by the disturbance storm time index (Dst, Sugiura,
n
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1964), which can attain values as large as 4500 nT in very severe storms. How good is the relationship of Bz(min) with Dst(min)? In this note, this aspect is examined for all categories of storms (weak, Dst(min) 50–100 nT; moderate, 100–200 nT; severe, 4200 nT), which occurred in cycle 23 (1996–2006) and for which interplanetary data, namely, number density N, velocity V and magnetic field component Bz were available. Data were obtained from the NGDC website http://spidr2.ngdc.noaa.gov/spidr/ and hourly values are used.
2. Dst(min) frequency of occurrence in every year Storms were considered only when hourly ( Dst) was 450 nT. For all storms irrespective of whether interplanetary data were available or not, Fig. 1 shows the occurrence frequency of Dst(min) in different Dst ranges; 50–70 nT, 70–90 nT etc. for each year, for years 1996–1999 (rising phase of the sunspot activity) in the first column, 2000–2002 (peak sunspot activity) in the second (middle) column, and 2003–2006 (declining phase of the sunspot activity) in the third column. In each frame, the year is shown in parenthesis, the circled numbers in the left at the top are the total number of storms in that year, and the numbers in rectangles in the right at the top are the yearly sunspot numbers for that year. The following may be noted: (1) In the rising phase (first column), starting from very few, weak storms in 1996, the number of stronger storms increased gradually up to 1999, parallel to the sunspot activity.
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Fig. 1. Occurrence frequency of Dst(min) in different ranges 50–70 nT, 70–90 nT, etc. for each year, for years 1996–1999 (rising phase of sunspot activity) in the first column, 2000–2002 (peak sunspot activity) in the second (middle) column, and 2003–2006 (declining phase of sunspot activity) in the third column. In each frame, the year is shown in parenthesis, the circled numbers in the left at top are the total number of storms in that year, and the numbers in rectangles in the right at top are the yearly sunspot numbers for that year.
(2) In the peak activity years 2000–2002 (second column), there were many more storms, including severe storms. (3) In the declining phase (third column), the number of storms was much more than in the rising phase. This discrepancy (excess geomagnetic activity in the declining phase of the sunspot activity) is known since long (Kane, 2007a, and references therein) and is attributed to two facts. Firstly, one of the origins of geomagnetic activity is the ICME occurrence frequency, which follows sunspot activity from the sunspot minimum to the sunspot maximum but then lingers around for some time in the declining phase (Kane, 2006 and references therein). Secondly, geomagnetic storms are also caused by the shock waves formed when highspeed solar wind from coronal holes impinges on the ambient slow solar wind in the interplanetary space and produces corotating interplanetary regions (CIR due to solar rotation of 27-day period) and these are copious in the declining phase of the sunspot activity. Incidentally, this excess geomagnetic activity is found to be useful for predicting the sunspot maxima in the ‘‘precursor’’ method evolved by Ohl (1976), where the excess geomagnetic activity (measured by Ap or aa indices) during the declining phase of the sunspot activity was noted to be proportional to the sunspot number Rz(max) of the next cycle. (The precursor methods are considered as more effective than all other methods, Joselyn et al., 1997). Various workers adopting the precursor method have been using geomagnetic indices in different parts in the declining phase. For example, Thompson (1993) uses the middle part, Chopra and Dabas (2006) and Jain (2006) use data an year or two before the sunspot minimum, while Kane (2007b and references therein) and Hathaway and Wilson (2004) use data near sunspot minimum. For cycle 24, all these have given a forecast of Rz(max) of 120 (Kane, 2007b).
3. Dst/Bz relationship In Fig. 1, the total number of storms ( Dst 450 nT) was 345, but the interplanetary data were available only for 232 (67%) events. Even among the severe storms ( Dst 4200 nT), from 19 events, interplanetary data were available for only 12 (63%)
Fig. 2. Plot of -Dst (min) versus Bz(min). Average Dst(min) values are shown as big dots with standard error bars. Correlations for various Bz(min) ranges are indicated. The straight line indicates the regression equation Dst(min)= [24.273.1]+ [6.67 0.2][ Bz(min)] for the whole Bz(min) range 0 to 50 nT. The circled crosses represent events of very high velocities, exceeding 800 km/s. Note that some of these are in the low Bz(min), low Dst(mean) region, indicating that high velocities do not ensure strong events.
events. Fig. 2 shows a plot of Dst(min) versus Bz(min). Following may be noted:
(1) For Bz(min) between 0 and 10 nT, the average Dst(min) values (big dots with standard error bars, values given in Table 1) are almost constant and the scatter (also the standard error) is very large, indicating a very poor relationship (correlation 0.1970.08, see Table 2(a). (2) For Bz(min) between 10 and 20 nT, there is an indication of trend but the scatter is large and correlation is only 0.5770.08.
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Table 1 Average values of -Dst(min) and their standard deviations for different -Bz(min) ranges. Bz(min) nT Number of events Average Dst(min) nT Standard error Limit 1 Limit 2
0–2 5 70 10 60 81
2–4 24 70 18 53 88
4–6 35 65 15 50 81
6–8 44 67 14 53 80
8–10 34 79 23 56 102
10–12 23 81 63 18 144
12–14 19 97 25 72 123
14–20 35 122 34 88 156
20–30 5 203 72 130 275
30–50 8 335 89 245 424
Table 2 Correlations of Dst(min) with Bz(min) for (a) different -Bz(min) ranges and (b) different Dst(min) ranges. (a) Bz(min) nT Number of events Corr. Dst(min)/Bz(min) Standard error
0–10 142 0.19 0.08
10–20 77 0.57 0.08
420 13 0.82 0.09
0–20 219 0.64 0.04
0–50 232 0.88 0.02
(b) Dst(min) nT Number of events Corr. Dst(min)/Bz(min) Standard error
50–100 166 0.38 0.07
101–200 54 0.46 0.11
201–500 12 0.77 0.12
50–200 220 0.64 0.04
50–500 232 0.88 0.02
Table 3 Expected values of Dst(min) for input values 5, 10, 15 y.. 50 nT of –Bz(min) used in the Dst/Bz regression Eq. (1). Bz(min) nT 5 10 15 20 25 30 35 40 45 50 Dst(min) nT 57 91 124 157 190 223 257 290 323 356 Standard error 3.3 3.9 4.8 5.7 6.8 7.8 9.0 10.1 11.2 12.4 % Std. error 5.8 4.3 3.8 3.6 3.5 3.5 3.5 3.5 3.5 3.5
(3) For Bz(min) 420 nT, the correlation is good (0.82 70.09), though there is still some scatter. (4) For Bz(min) from 0 to 20 nT, the correlation is moderate (0.64 70.04) but significant, indicating that there is some contrast between Dst(min) values corresponding to low and high Bz(min) values. (5) When all Bz(min) values 0–50 nT are considered, the correlation is high (0.8870.02), indicating that Dst(min) is related to Bz(min), but only in an overall way. (6) If the range 0–10 of Bz(min) is omitted, the relationship for Bz(min) between 10 and 50 nT is slightly higher (0.91 70.01). (7) If the data are sorted by values of Dst(min), the correlations are as given in Table 2b. Thus, whereas the general dependence of Dst(min) on Bz(min) is indicated qualitatively, the relationship is more secure only for large values. For the whole range Bz(min) 0–50 nT, the regression equation is: DstðminÞ ¼ ½24:2 73:1½6:6 70:2½BzðminÞ
ð1Þ
The regression line is shown in Fig. 2. For values of Bz(min) as 5, 10, y.. 50 nT, the expected Dst(min) would be as given in Table 3. The standard error for low Bz(min) (5–10 nT), is higher (5,8%) as compared to that for higher Bz(min) values ( 410 nT, 3,5%). However, this equation does not reflect fully the very low correlation (0.19) and the very large scatter in the low Bz(min) and the low Dst(min) region (Fig. 2, left bottom). A curious fact about low Dst values (NOAA website catalogue) is that whereas during quiet periods, the Dst values are generally almost zero, there have been quiet intervals when Dst (in the catalogue) is not near zero but above zero or below zero for weeks together. So, when a storm occurs, one wonders whether the Dst(min) should be taken on its face value or whether the pre-
10–50 90 0.91 0.02
storm level should be subtracted. This will make a difference of about 720 nT. A part of the scatter in the -Dst(min) values for the Bz(min) range 0–10 nT may be due to this uncertainty but only partly; because of the scatter there is much larger than 20 nT, almost 50 nT or more. We have avoided events when the Dst base level was more than 20 nT (positive or negative), but among these, we have used data for storm events when -Dst(min) was 4100 nT. The Dst(min) and the Bz(min) rarely occur simultaneously. Gonzalez and Echer (2005) report that the Dst(min) is delayed with respect to the Bz(min) by 1–4 h, with an average values of 2 h, though in less than 5% storms, the Dst(min) occurred before the Bz(min). They suggest that this delay indicates a physical response time of the ring current to the solar wind driver at the peak interval of an intense storm. In our analysis, this aspect is initially ignored, and we consider in Fig. 2 only the magnitudes of the minimum values of Dst and Bz, no matter how and when these occurred with respect to each other.
4. Other factors It has been reported earlier (e.g., Gonzalez et al., 1994) that not the Bz(min) but its cumulative value over the interval of Bz negative values is important for the Dst storm development. (It is a gradual process, like the charging of an electrical condenser). In the present analysis, we calculated two new parameters, namely, CPBz, which is cumulative partial Bz, i.e., from the beginning of the negative Bz to its climax value Bz(min), and CTBz, which is cumulative total Bz, i.e., from the beginning of the negative Bz to the end of the negative Bz. Thus, now three parameters could be used, Bz(min) as before, and CPBz, CTBz. Another important factor relates to Dst itself. It is often tactically assumed that the Dst is due to the ring current only. This is not true. Some contributions come from other sources also (Gonzalez et al., 1994). For example, there are induced currents in the solid Earth. These are mostly in a constant proportion with the ring current (about one third) and hence will not affect the correlations with Bz(min) (only the regression coefficient will alter). But there are magnetopause currents that depend upon the solar wind ram pressure only (depend on N and V) and not on Bz(min). Their contribution to Dst(min) can be substantial and may differ considerably from event to event, even though Bz(min)
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may remain the same. For the true ring current effect Dstn after a correction due to magnetopause currents is applied to Dst, according to Burton et al. (1975), the relationship between Dst and Dstn is Dst ¼ DstMst ¼ DstbP1=2 þ c
ð2Þ
where Mst is the magnetopause current contribution, P is the storm time solar wind ram pressure, obtained as Nm + V2 (N and V being the solar wind density and velocity respectively, and m + the proton mass), b is a proportionality factor, and c is the quiet time solar wind ram pressure contribution. Typically, b= 8.74 nT/(nPa)1/2 and c =11.54 nT. (Turner et al., 2001). OBrien and McPherron (2000) have calculated these as b= 7.26 and c= 11.0, but the overall results seem to remain almost the same (Turner et al., 2001) In small samples, the reliability of the correlations is doubtful and it was noticed that including or deleting a single event could sometimes alter the correlation substantially. In the present case where weak and moderate storms were also considered, Dstn is calculated for every storm and the correlations using Dstn(min) are also calculated. A major problem is to ascertain appropriately the hourly values of various parameters. Fig. 3 shows the plots of interplanetary N, V, Bz and geomagnetic Dst during twelve severe storm events that had Dst(min) 4200 nT, in chronological order with events numbered as 1, 2, 3, and 4 in the first row; 5, 6, 7, and 8 in the second row and 9, 10, 11, and 12 in the third row, years 1998 (events 1 and 2), 1999 (event 3), 2001 (events 4 and 5), 2003 (events 6, 7 and 8), 2004 (events 9 and 10) and 2005 (events 11 and 12). The maxima of N and V and the minima of Dst and Bz are marked with big dots. As can be seen, Bz(min) occurred earlier than Dst(min) in the 12 events by 1, 5, 1, 2, 0, 5, 2, 4, 4, 5, 2, and
395
2 h, (range 0–5 h, average 33/12= 2.8 h, slightly larger than the 2 h mentioned by Gonzalez et al., 1994). The correlation between Dst(min) and Bz(min) for the Dst(min) range 201–500 (Table 2(b)) was 0.77, if only the magnitudes (irrespective of phase shift) are considered. The correlation is dominated by the two Halloween events of October 30, 2003 and one of November 20, 2003. If these three events are omitted, the correlation reduces to 0.65, indicating some scatter. Here, for the two storms of October 29–30, 2003 (called Halloween events) numbered 6 and 7 in Table 2, an explanation is needed for the values of parameters used by us. These two were the strongest interplanetary storms of cycle 23, with ICME velocity V exceeding 2000 km/s, in contrast to velocities below 1000 km/s in the other 10 storms. Unfortunately, the satellite data for these storms were not fully satisfactory. Skoug et al. (2004) have given complete details of the functioning of the instrumentation and the data records and mention that for several consecutive h, some instruments failed (no data for some parameters). The number density Np was most probably underestimated. In the rest of the data, they mention in their paragraphs 20, 22 and their Fig. 4, values for October 29, 2003 as V= 2240 km/s, Np 10 or less, Bz(min)= 68 nT, Bmax = 68 nT and for October 30, 2003 as V= 1710 km/s, Np 10 or less, Bz(min)= 35 nT, Bmax = 40 nT. However, these are, so to say, instantaneous (1–5 min) values. Their averages over one hour would certainly be lesser, the question is, how much lesser. In their Fig. 6, Skoug et al. (2004) plot hourly values of V as 42000 km/s in event 6 and 1800 km/s in event 7 (numbering of our Table 2). No mention is made of Bz(min). In their Table 3, the values are mentioned for October 30 events as V 2000 km/s, 1 Np 10–20, B as 68 nT, and Bz as –68 nT (obviously the extreme instantaneous values). In their plot in Fig. 4, the Bz values do not
Fig. 3. Plots of interplanetary number density N, solar wind velocity V, magnetic field north–south component Bz, and geomagnetic disturbance index Dst, for individual severe storms (-Dst 4200 nT), 1–4 in the first row, 5–8 in the second row and 9–12 in the third row. The maxima of N, V, Dst(min) and Bz(min) are marked with big dots, and the hours by which Bz(min) occurred before Dst(min) are indicated as negative numbers in parentheses in each of the 12 panels.
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have a steady negative high level; instead, there are violent fluctuations from positive to negative values. It is probably because of these fluctuations in Bz values that the SPIDR NOAA website mentions hourly values of Bz as only –25 and –29 nT for the two events. These are very low values as compared to the –68 and –35 nT instantaneous negative values of Bz. Thus, considerable uncertainties are involved. The low Bz values 25–29 nT are not commensurate with the high Dst values 363 and 401 nT of these events. Hence, keeping in view all these facts and uncertainties, we assigned Bz(min) as –50 nT, V as 2000 km/s, and Np as 15, for both the events, somewhat arbitrarily but helplessly. Another problem was, what values of N and V to choose for calculating Dstn in Eq. (2). In Fig. 3, the N and V values changed rapidly during the storm interval and their maxima rarely coincided between themselves or with the hours of Bz(min) or Dst(min). Thus, choosing the maximum values of N and V during the whole storm interval would be inappropriate. More proper would be to choose the N and V values at the hours of Bz(min) or Dst(min) and here again, there was a doubt as to which hour to choose, as Bz(min) and Dst(min) rarely coincided, and Dst(min) occurred with a delay of 0–5 h. Hence, we chose both, namely, VB and NB as V and N values at the Bz(min) hour, and VD and ND as V and N values at the Dst(min) hour. These VB, NB and VD, ND pairs were used in Eq. (2) and two values of magnetopause effects MstB and MstD were obtained. Subtracting these from the Dst(min) values, two estimates of the true ring current Dstn were obtained, namely DstBn and DstDn. Thus, for correlation analysis, for each storm, the following parameters were used: Dst(min), DstBn, and DstDn to be correlated separately with: Bz(min), two values of cumulative Bz, namely, CPBz (partial) and CTBz (total), VB.Bz(min) and VD.Bz(min). The latter two were used because some workers have reported that the Dst(min) shows a better correlation with the product of Bz(min) and velocity V, namely V.Bz(min), than with Bz(min) alone (Gonzalez et al., 1994 and references therein). Table 4 shows the correlations. The following may be noted: For Dst(min),
(1) Correlations with Bz(min) for increasing ranges 0–10, 10–20 and 20–50 nT are: 0.19, 0.57 and 0.82. In the whole range 0–50, the correlation is larger (0.8870.02) because of the great contrast of low and high values.
(2) With cumulative Bz, the correlations are not better (in fact, these are poorer). (3) With the product V.Bz, the correlation is low in the smaller Bz(min) range 0–10 nT, but in the 10–20 nT range, correlation improves from 0.57 to 0.70. However, in the bigger range 20–50 nT, there is a decrease from 0.82 to 0.55. In the total range 0–50 nT also, there is a decrease from 0.8870.02 to 0.7770.02. Thus, the product of velocity and Bz(min) in the middle ranges does show improvement over Bz(min) alone, but in the higher ranges, the effect is not obvious. There is virtually no difference between the correlations using VB and VD, because during the few hours of difference (0–5 h) between Bz(min) and Dst(min), the V does not change much (the correlation between VB and VD is 0.96). So, using VB alone may be enough. For DstBn, all correlations are in general only very slightly higher than the corresponding ones for Dst(min). Thus, the improvement by correcting for magnetopause current effects has proved to be insignificant. It may be noted, however, that the magnitudes of the magnetopause effects are rather small, mostly less than 25 nT and were high only for the Halloween events ( 75 nT). Other characteristics like correlations with CTBz slightly larger than for CPBz are similar to those of Dst(min). For DstDn, correlations are similar to those for DstBn. This is because, since VB and VD were similar, DstBn and DstDn were also similar (correlation 0.99). Table 5 shows correlations for different ranges of –Dst(min). The following may be noted: For Dst(min), (1) Correlations with Bz(min) for increasing –Dst(min) ranges 50–100, 101–200, and 200–500 nT are: 0.38, 0.46, and 0.77. In the whole range 50–500 nT, the correlation is large (0.88 70.02, same as in Table 4), because of the great contrast of low and high values. (2) With cumulative Bz, the correlations are not better, in fact, these are smaller. (3) With the product V.Bz, the correlation is the same in the smaller -Dst(min) range 50–100 nT, higher in the100–200 nT range, and lower in higher ranges. There is virtually no difference between the correlations using VB and VD, because during the few hours of difference (0–5 h) between Bz(min) and Dst(min), the V does not change much (the correlation between VB and VD is 0.96). So, using VB alone may be enough.
Table 4 Correlations of Dst(min), DstBn. DstDn with Bz(min), cumulative Bz, namely, CPBz (partial) and CTBz (total), and the products VB.Bz(min) and VD.Bz(min) for negative Bz(min) ranges, 0–10, 10–20, 20–50, and 0–50 nT. Bz(min) nT
0–10
Number of events
142
Std. error
77
Std. error
13
Std. error
232
Std. Error
Dst/ Dst/ Dst/ Dst/ Dst/ DstBn/ DstBn/ DstBn/ DstBn/ DstBn/ DstDn/ DstDn/ DstDn/ DstDn/ DstDn/
0.19 0.16 0.17 0.26 0.28 0.19 0.13 0.13 0.27 0.28 0.20 0.14 0.15 0.27 0.29
0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
0.57 0.22 0.40 0.71 0.70 0.59 0.14 0.32 0.75 0.74 0.58 0.19 0.32 0.72 0.72
0.08 0.11 0.10 0.06 0.06 0.10 0.10 0.08 0.08 0.08 0.09 0.11 0.08 0.08 0.08
0.82 0.56 0.59 0.55 0.55 0.86 0.63 0.59 0.69 0.69 0.86 0.63 0.58 0.69 0.68
0.09 0.25 0.25 0.13 0.13 0.09 0.24 0.24 0.13 0.13 0.09 0.25 0.24 0.13 0.13
0.88 0.65 0.66 0.77 0.76 0.89 0.64 0.64 0.81 0.81 0.89 0.65 0.64 0.81 0.81
0.02 0.05 0.05 0.02 0.02 0.02 0.05 0.04 0.02 0.02 0.03 0.05 0.05 0.02 0.02
Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min)
10–20
20–50
0–50
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Table 5 Correlations of Dst(min), DstBn. DstDn with Bz(min), cumulative Bz, namely, CPBz (partial) and CTBz (total), and the products VB.Bz(min) and VD.Bz(min) for negative Dst(min) ranges, 50–100, 101–200, 201–500, and 50–500 nT. Dst(min) nT
50–100
Number of events
166
Std. error
54
Std. error
12
Std. error
232
Std. Error
Dst/ Dst/ Dst/ Dst/ Dst/ DstBn/ DstBn/ DstBn/ DstBn/ DstBn/ DstDn/ DstDn/ DstDn/ DstDn/ DstDn/
0.38 0.26 0.27 0.38 0.40 0.43 0.23 0.25 0.44 0.46 0.41 0.25 0.24 0.42 0.44
0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
0.46 0.26 0.35 0.58 0.61 0.42 0.13 0.18 0.61 0.62 0.48 0.23 0.23 0.62 0.66
0.08 0.11 0.10 0.06 0.06 0.10 0.10 0.08 0.08 0.08 0.09 0.11 0.08 0.08 0.08
0.77 0.69 0.83 0.50 0.49 0.82 0.77 0.84 0.68 0.68 0.83 0.78 0.84 0.67 0.67
0.18 0.25 0.25 0.13 0.13 0.18 0.24 0.24 0.13 0.13 0.21 0.25 0.24 0.13 0.13
0.88 0.65 0.66 0.77 0.76 0.89 0.64 0.64 0.81 0.81 0.89 0.65 0.64 0.81 0.81
0.02 0.05 0.05 0.02 0.02 0.02 0.05 0.04 0.02 0.02 0.03 0.05 0.05 0.02 0.02
Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min) Bz(min) CPBz CTBz VB.Bz(min) VDBz(min)
100–200
200–500
50–500
Table 6 Correlation between Dst(min) and Bz(min) for (a) different thresholds and (b) different ranges of the velocity VB at the hour of Bz(min). (a) VB (km/s) Number of events Corr. Dst(min)/Bz(min) Standard error (b) VB (km/s) Number of events Corr., Dst(min)/Bz(min) Standard error
All 232 0.88 0.02
4400 195 0.90 0.01 Upto 400 37 0.24 0.16
4450 151 0.92 0.01
4500 118 0.93 0.01
401–500 77 0.71 0.06
For DstBn, all correlations are almost similar to the ones for Dst(min). For DstDn, correlations are similar to those for DstBn.
5. Correlation Dst(min)/V It is generally expected that a very fast interplanetary blob would result in very intense storms. However, as described in detail in Kane (2005), the Dst(min) is poorly correlated with the interplanetary velocity. In the present case, the overall correlation Dst(min)/VB was only 0.50, the overall correlation Dst(min)/ Bz(min) was 0.88, and the overall correlation Dst(min)/ VB.Bz(min) was 0.80 (see the last columns in Tables 4 and 5). Thus, the role of V is only through the VB relationship. A glaring example of poor relationship between Dst(min) and V directly was that of the August 4, 1972 event, when the velocity was enormous ( 2800 km/s) but the Dst(min) was only about 125 nT, mainly because the Bz component fluctuated between 0 and a few nT negative (Tsurutani et al., 1992, 2003). In cycle 23, some events in Fig. 2 are marked with encircled crosses. All these had high velocities (exceeding 800 km/s), but the points are spread all over, low as well as large Dst(min) and Bz(min), indicating that a high velocity does not ensure high Dst. Recently, Wu and Lepping (2002a, b) reported an interesting feature, namely that for the subset of interplanetary blobs called ‘‘magnetic clouds‘‘ (these have organized internal magnetic fields), the Dst(min)/Bz(min) correlation increased dramatically, when the solar wind speed exceeds 600 km/s. To examine this aspect, our data were sorted on VB values. Table 6 shows the
4550 83 0.94 0.01 501–600 59 0.91 0.02
4600 59 0.94 0.01 601–700 37 0.93 0.02
4 650 31 0.96 0.01
4 700 22 0.96 0.01 701–800 10 0.97 0.01
4800 12 0.97 0.01 4800 12 0.97 0.01
Dst(min)/Bz(min) correlations for VB of different thresholds, 4400, 4450 etc. and of different ranges. The following may be noted: (1) In Table 6(a), for all velocities, the correlation Dst(min)/ Bz(min) was 0.8870.02, but for higher velocity ranges 4400, 4450 etc., the correlation increased to 0.9670.01 for VB 4650 km/s, a significant increase. (2) In Table 6(b), the correlations were low (0.24) for low velocities, moderately high (0.71) for velocities up to 500 km/s, but were very high for velocities between 500 and 800 km/s.
6. Conclusions and discussion For cycle 23, geomagnetic storms with Dst(min) 450 nT were compared with the minimum value Bz(min) of the negative Bz component of the interplanetary magnetic field. (1) It was noticed that in the plot of Dst(min) versus Bz(min) for Bz(min) in the low range 0–10 nT, the Dst(min) varied erratically, indicating very poor relationship (correlation 0.19). Any value of Bz(min) could be associated with any value of Dst(min) (2) Even for Bz(min) between 10 and 20 nT, Dst(min) values had a considerable scatter (correlation 0.57). (3) For Bz(min) 420 nT, severe storms occurred, and the relationship was good (correlation 0.82). (4) When the whole range Bz(min) 0–50 nT was considered together, the correlation was high (0.88), because of the great contrast of Dst(min) values from 50 to 500 nT.
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(5) If Bz(min) is very large ( 420 nT), large Dst(min) would occur in a wide range 100–500 nT, and the proportionality of the magnitudes of Dst(min) and Bz(min) was loose, far from one-to-one. (6) The correlations of Dst(min) with the product V.Bz(min) were better as compared to those of Dst(min) with Bz(min) alone in the intermediate ranges (Bz 10–20 nT and Dst 100–200 nT), but for higher ranges, V.Bz was not superior. (7) Replacing Bz(min) with cumulative Bz (sum of hourly values from the beginning to the end of the negative Bz values) did not improve the correlations. (8) Using Dstn (the true ring current after subtracting magnetopause current effects from the observed Dst(min)) did not improve the correlations appreciably; because the magnetopause effects were small (less than 25 nT), except for the Halloween events of October 30, 2003) when the effects were 75 nT. Thus, the correlation between Dst(min) and Bz(min) is rather loose, particularly in the middle ranges of Dst(min) around 200 nT and Bz(min) around 20 nT, indicating that the geomagnetic effects due to the entry of solar wind at the neutral point in the geomagnetic tail region are not a straightforward affair. Several complications are involved. The main problem is to establish an energy function to quantify the solar wind–magnetosphere energy transfer. Several functions have been studied (Gonzalez et al., 1989, 1990; De Lucas et al., 2007, and references therein). One of these functions considers the reconnection process as the main phenomenon for energy injection into the magnetosphere (Perreault and Akasofu, 1978). After being injected in the dayside magnetosphere, the solar wind energy is finally dissipated into different regions of the magnetosphere. Based on the functions for energy injection and dissipation assumed by Feldstein et al. (2003), the result is that one-half of the energy is injected into the magneto-tail and dissipated there. After the reconnection at the magnetotail, a part of this energy is accelerated earthward in the equatorial region. Another part of the solar wind energy is deposited in the auroral ionosphere as heat energy, which arises partly from Joule heating and partly from the impact of auroral particles. Therefore, the total energy dissipation can be estimated through the sum of these contributions (Akasofu, 1981). Monreal-MacMahon and Gonzalez (1997) took into account the magnetopause position as a function of the solar wind ram pressure. The energy transfer from the solar wind to the magnetosphere was then estimated through a corrected version of the Perreault and Akasofu ‘e’ parameter based on the dayside magnetopause ram pressure. In their recent paper, De Lucas et al. (2007) discussed this problem in detail and suggested modifications to this function. Their aim was to evaluate the interplanetary characteristics (interplanetary dawn–dusk electric field and interplanetary magnetic field component BS), the ‘e’ parameter, and the total energy input into the magnetosphere for two classes of magnetic storms, namely, intense storms and super-intense storms. (see also Vichare et al., 2005). However, in Fig. 3 of De Lucas et al. (2007), where the estimated values of the energies injected and dissipated during the main phase of intense storms are plotted versus the absolute values of the Dst index, the scatter is large. They mention a correlation of 0.88 for 8 events, but if the one point of very high Dst(min) is omitted, the correlations are lower, almost like our plot of Dst(min) versus Bz(min) (our Fig. 2). Earlier, Turner (2000) studied the solar wind– magnetosphere coupling and the global energy budgets in the Earth’s magnetosphere and reported that in the energy flow, there is a clear domination of ionospheric energy deposition in the polar region, with the Joule heating alone accounting for around half of the total energy; and the ring current energy deposition was
10–15% of the total energy. Later, Turner et al. (2001) showed that ring current ions contributed on the average, half of the Dst depression, but with a large variation among individual events. Vichare et al. (2005) computed for nine intense geomagnetic storms, the solar wind energies, magnetospheric coupling energies, auroral and Joule heating energies, and the ring current energies. They found that only about 3.5% of the total solar wind kinetic energy was available for redistribution in the magnetosphere, and around 20% of this goes into the inner magnetosphere and in the auroral ionosphere of both the hemispheres. However, in all these works, a curious feature is seen. In figures showing dependence on Bz(min) or Dst(min), good correlations ( 0.8) are reported when the whole range is considered, but these good correlations get reduced considerably if some events with very high Bz(min) and/or Dst(min) are omitted, more so when very intense storms are considered. Also, the middle range of Bz(min) near 20–30 nT or Dst(min) near 250 nT shows considerable scatter, no matter how sophisticated the methodology of calculating the energies is. This is important because it is above 250 nT of the Dst depression that electrical damages in high latitudes commence. So, if Bz(min) near 20 nT gives unreliable estimates of Dst(min) (could be anything between 100 and 350 nT), considerable quantitative prediction potential is lost. Turner et al. (2001) mention that some of the discrepancies could be due to ring current asymmetry. The fact remains that for a medium size Bz(min), the percentage going to cause equatorial Dst(min) as compared to polar region effects varies considerably from event to event, even if Dst is corrected for magnetopause effects. It seems, therefore that there are some factors still missing from consideration. Further work may resolve this discrepancy. Recently, Alex et al. (2006) studied the geomagnetic signatures of the intense storms of October 29 and November 20, 2003. Using ground magnetic field measurements from equatorial and lowlatitude locations in the Indian longitude zone in conjunction with interplanetary solar wind and magnetic field parameters, they estimated the maximum magnitudes of the total magnetospheric energy injected into the magnetosphere during the main phase of the three major storms as (2.8–3.5) 1013 W. They also reported a close correspondence between Bz(min) and Dst(min) and low-latitude digital magnetic records. Rawat et al. (2006) illustrated another aspect, namely the low-latitude geomagnetic signatures during major ‘‘solar energetic particle (SEP) events of cycle 23, two in 2000 and two in 2001. They showed a close correspondence between the persistence of a high level of proton flux after the interplanetary shock in some events and the ensuing intense magnetic storms and the role of southward Bz duration generation of a strong main phase. Incidentally, all such analyses have only an academic value and hardly any prediction potential, for the following reason. Severe geomagnetic storms (-Dst 4300 nT) can cause severe damages to electrical installations (including burnout of transformers) in high latitudes. As such, the engineers would like to have as much accurate information of the commencement and maximum extent of the storm, as possible. Long ago, Chapman and Bartels (1940) mentioned that after the occurrence of a solar flare, a geomagnetic storm may occur after about 20–100 h. This is still true today, but this range of uncertainty is very large. Later, solar wind theory was formulated (Parker 1959) and the presence of a perpetual solar wind was confirmed by observations (Gringauz et al., 1960 and others). Soon after, Tousey (1973) discovered the coronal mass ejections (CME) phenomenon and now, with the SOHO LASCO setup where the main solar disc is artifically occulted, CMEs can be detected on the sky background as emissions coming out of the Sun on the limbs. The lateral expansion speed can be calculated and regression equations are available for the relation
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of this velocity with the velocity of the ICMEs near Earth. Thus, having seen a CME, it is possible to calculate its arrival time near the Earth (Manoharan et al., 2003; Dal Lago et al., 2004; Schwenn et al., 2005). However, there is an uncertainty of about 20% and estimates of 20 h can be wrong by 4 h (details given in Kane 2008). Still, this is a much better estimate than that suggested by Chapman and Bartels (1940). Having had this preliminary warning, cosmic ray directional muon telescopes can give another preliminary warning of the incoming interplanetary cloud, probably a few hours before the cloud reaches the Earth (Space Weather Prediction with Cosmic Rays, website http://neutronm. bartol.udel.edu/spaceweather/). The next warning comes when the cloud reaches the ACE satellite situated between the Sun and the Earth (much nearer to Earth), with a ICME cloud transit time antecedance of about half an hour. Finally, when the cloud engulfs the Earth, a magnetogram shows an storm sudden commencement (SSC) and the storm is supposed to start. More uncertainties start here. Firstly, there is no way to tell whether a storm will follow an SSC at all. It will depend upon how the negative Bz component evolves and whether it will be substantial and if so, when. The Dst storm may start within a few hours (0–4) and there is no way to tell when exactly Dst(min) will occur and of what magnitude. These factors are very important for the electrical engineers to know as early as possible. Indices like Kp and Dst are calculated from data of various stations, but this takes time and information will not be available before the storm, unless one uses model predictions as in Temerin and Li (2006); but these have their own limitations and uncertainties. Also, Dst is a global storm index, while what the transformers would respond to is the local magnetic field in that vicinity, which has a Dst component and a DS component (dependent on the local time LT), which may not be negligible. Thus, the sure way for the engineer would be to have a magnetometer available for watching the evolution of the magnetic field depression and switch off the transformer as soon as the field decreases below say, o 250 nT. This is still a gamble, because the magnetic field may not drop further and the switching off may cost billions of dollars of revenue. If the field does decrease further, the transformers should be restarted when the recovery starts and the field recoups within 0 to 250 nT. Beland (2004) mentions that ‘‘for Hydro-Quebec (HQ) in the province of Quebec in Canada, there are now two measurement systems (one primary and one backup) monitoring groundinduced current (GIC) effects on the grid in real time. To be informed in advance of a probable GIC occurrence, HQ now relies on a specialized organization providing geomagnetic activity alert and forecast. Following an alert or the detection of GIC effects on the network exceeding a minimal threshold, special operation rules become in effect for ensuring maximum stability and safety margin. Also, series capacitors are introduced on several 735 kV lines, which increase network stability and also block GIC circulation’’. Other installations might be using other methods. In some cases, operations are stopped (if possible) during the storm interval. Obviously, statistical correlation and regression analyses do not have much role to play in this scenario.
Acknowledgements This work was partially supported by FNDCT, Brazil, under contract FINEP-537/CT. References Akasofu, S.-I., 1981. Energy coupling between the solar wind and the magnetosphere. Space Science Reviews 28, 121–190.
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