High-resolution global storm index: Dst versus SYM-H

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi:10.1029/2005ja011034, 2006 High-resolution global storm index: Dst versus SYM-H James A. Wanliss 1 and Kristin M. Showalter 1 Received 27 January 2005; revised 1 November 2005; accepted 25 November 2005; published 17 February 2006. [1] The classic view is that Dst and SYM-H time series differ mainly due to the dissimilarity in the method to determine the base values. Dst and SYM-H are both indices designed to measure the intensity of the storm time ring current. They are calculated in similar but not identical manners. Since SYM-H has the distinct advantage of having 1-min time resolution compared to the 1-hour time resolution of Dst, it is worth determining if the differences introduced by using different ground stations and slightly different methods of baseline subtraction produce statistically significant differences in the values of the indices. We have examined data from these indices collected over more than 20 years to determine the extent to which Dst and SYM-H are equivalent or different. We found that a simple combination of linear trends with a break at SYM-H = 300 nt provides an excellent comparison with the Dst index. For quiet times and for small storms the deviations are typically no more than 10 nt. Moderate storms feature deviations typically only slightly more than 10 nt, and intense storms have deviations that are usually less than 20 nt. We conclude that the classic view is accurate and recommend that in future studies the SYM-H index be used as a de facto high-resolution Dst index. Citation: Wanliss, J. A., and K. M. Showalter (2006), High-resolution global storm index: Dst versus SYM-H, J. Geophys. Res., 111,, doi:10.1029/2005ja011034. 1. Introduction [2] Space storms are the global geomagnetic disturbances that result from the interaction between magnetized plasma that propagates from the Sun and plasma and magnetic fields in the near-earth space plasma environment. Chapman [1919] placed the global aspect of storms on a firm footing by using ground magnetometers to demonstrate that for some time after a period of great geomagnetic disturbances and associated auroral activity, the horizontal component of the magnetic field around the world is significantly reduced from its average. These studies led to development of the most widely used statistical descriptor of space storm activity, namely, the Dst index; it was designed to reveal the global magnetic field reductions during storms. At the time the extent to which the inner magnetosphere participated in storm activity was not fully appreciated and this led to the classical magnetic storm terminology. Since the start of the age of satellites, we have learned that the main and recovery phases feature complex interactions [Summers et al., 2002; Horne et al., 2003; Horne and Thorne, 2003; Meredith et al., 2003] and large, rapid fluctuations of the energetic particle fluxes, particularly of the high-energy (>1 MeV) killer electrons [Kamide et al., 1998; Reeves, 1998; Reeves et al., 1998, 2003] and protons [Kamide et al., 1998; Lambour et al., 2003; Daglis et al., 2003]. Space storms include a rich variety of complex plasma electromagnetic processes extending from the ionosphere into 1 Department of Physical Sciences, Embry-Riddle Aeronautical University, Daytona Beach, Florida, USA. Copyright 2006 by the American Geophysical Union. 0148-0227/06/2005JA011034$09.00 space, with the primary locus of activity being in the near- Earth geospace environment [e.g., Baker et al., 1997; Li et al., 1997; Reeves et al., 1998]. [3] The Dst index is often considered to reflect variations in the intensity of the symmetric part of the ring current that circles Earth at altitudes ranging from about 3 to 8 Earth radii (R E ), and is proportional to the total energy in the drifting particles that form the ring current [e.g., Dessler and Parker, 1959; Sckopke, 1966]. It is calculated as an hourly index from the horizontal magnetic field component at four observatories, namely, Hermanus (33.3 south, 80.3 in magnetic dipole latitude and longitude), Kakioka (26.0 north, 206.0 ), Honolulu (21.0 north, 266.4 ), and San Juan (29.9 north, 3.2 ). These four observatories were selected because they are close enough to the magnetic equator that they are not strongly influenced by auroral current systems. Second, they are far enough away from the magnetic equator so that they are not significantly influenced by the equatorial electrojet current that flows in the ionosphere. They are also relatively evenly spaced in longitude. The convolution of their magnetic variations forms the Dst index, measured in nt, which is thought to provide a reasonable global estimate of the variation of the horizontal field near the equator. In recent years, a higherresolution version of Dst was created. The SYM-H index uses different magnetometer stations to calculate the symmetric portion of the horizontal component magnetic field near the equator. [4] It is shown by T. Iyemori et al. (available at http:// swdcwww.kugi.kyoto-u.ac.jp/aeasy/asy.pdf) that the difference between Dst and SYM-H stems...from the difference in the method to determine the base values. The base value at each station is more carefully determined for the 1of10

hourly Dst index taking into account the geomagnetic secular variation than for this provisional SYM-H index. The main difference between the 1 min SYM-H and the hourly Dst index is the time resolution, and the effects of the solar wind dynamic pressure variations are more clearly seen in the SYM-H than in the hourly Dst index. [5] In this paper we briefly examine the extent to which Dst and SYM-H are equivalent. Our interest in this kind of study is threefold: first, the Dst index has a venerable history and is well utilized by the space physics community; second, Dst is calculated at 1 hour intervals and is therefore not able to resolve higher-frequency variations that may be helpful in understanding space storm triggers. It is well known that coupling of the magnetosphere-ionosphere system produces geospace and ground magnetic variations that depend on both local time and latitude [Boteler et al., 1998; Weigel et al., 2002; Wanliss and Reynolds, 2003] and that storm time geomagnetic variations have considerable temporal structure that is not resolved by Dst [Häkkinen et al., 2002; Campbell, 2004]. For example, Dst is not sensitive to higher-frequency variations that are classified as micropulsations, even though these could play an important role in magnetospheric substorms and space storms [Wanliss and Rankin, 2002]. Substorm effects are clearly observed in these Dst but without significant resolution. This is due to the fact that the substorm timescale is typically about 1 hour, so most of its higher-frequency variations are averaged out when the Dst index is computed. Iyemori and Rao [1996] selected 100 storm-time substorms and superposed the Dst index relative to the substorm expansive phase onset. The average response in Dst during the main phase was to decrease before the onset, and its rate of decrease became less negative after onset. In the storm recovery phase, Dst became less negative, suggesting perhaps that part of the ring current disappeared. [6] Finally, if Dst and SYM-H are truly equivalent, then the community has at its disposal a tool for resolving higher-resolution effects, and SYM-H could be used exclusively in place of Dst, except for historical studies prior to SYM-H existence. Detailed analyses of storm events will thus be facilitated due to the higher temporal and spatial resolution of the system dynamics. Since we are embarking on a comparison of these two indices, in section 2 we examine the details of how Dst and SYM-H time series are formed. Following this, in section 3, we discuss several factors that could make the two indices different. In section 4 we perform an analysis that compares Dst and SYM-H for over 20 years. We also clearly delineate the differences between the indices during times that are considered to be quiet and those which are considered to be storm times. Section 5 closes this paper with conclusions and a discussion of our results. 2. Description of Data [7] The method to calculate Dst, described by Sugiura and Kamei [1991], begins with the removal of the secular variation from the recorded data, followed by removal of the solar quiet daily variation, Sq. The secular variation is estimated through the determination of the annual mean value of the horizontal magnetic field, H, from the 5 quietest days of each month for the year under consideration and for Figure 1. The hourly Dst index from 1981 to 2002. 4 preceding years. The annual mean values are then fitted with a polynomial of second-order, which provides a slowly varying baseline for each day, H bl. The difference dh = H H bl still contains Sq variations which must be removed. The official method to remove Sq considers the overall solar quiet signal to be the sum of harmonic components, calculated as S q ðt; sþ ¼ X6 X 6 m¼1 n¼1 A mn cosðmt þ a n Þcosðns þ b n Þ: This series consists of 48 unknown coefficients A mn, a m, b n, which are determined by computing one Sq curve for each month as an average of the variation curves over the 5 quietest days of the month. The local time and month number are given by t and s, respectively. Linear trends which exist from one local midnight to the next local midnight are subtracted. A total of 288 data points are provided from these Sq curves from which the unknown coefficients can be determined by a least squares fitting. The above equation can be used it compute the Sq(T) variation for any UT time, T, during the year. At every magnetometer station the local horizontal magnetic field variation is obtained from D(T) = dh(t) S q (T). Finally, if one assumes that the disturbance is caused by a symmetric ring current flowing in the magnetic equatorial plane, the average equatorial variation across the Earth can be calculated from the measurement of the horizontal field divided by cos (l), where l is the magnetic latitude of the observatory. The final Dst index is defined as an average of these variations for the four stations, and is considered a rough average for the global horizontal variation, DstðTÞ ¼ X 4 X 4 D n¼1 nðtþ : cos ð l n¼1 nþ Figure 1 shows the Dst index, calculated as described above, for 1981 through 2002. These data exist as a continuous time series from 1963, but here we show the portion that is used in our comparative analysis with the SYM-H index, since 2of10

Table 1. List of Stations Used in the Calculation of the SYM-H Index Station Name GG Latitude GG Longitude GM Latitude GM Longitude San Juan 18.4 293.9 29.1 5.2 Fredericksburg 38.2 282.6 49.1 352.2 Boulder 40.1 254.8 48.7 319.0 Tucson 32.3 249.2 40.4 314.6 Honolulu 21.3 202.0 21.5 268.6 Memambetsu 43.9 144.2 34.6 210.2 Alibag 18.6 72.9 9.9 145.8 Martin de Vivies 37.8 77.6 46.9 142.8 Hermanus 34.4 19.2 33.7 82.7 Chambon-la-Foret 48.0 2.3 50.1 85.7 SYM-H only exists from 1981. These data can be downloaded from the World Data Center for Geomagnetism, Kyoto (http://swdcwww.kugi.kyoto-u.ac.jp/). [8] The method to calculate SYM-H is described in detail by Iyemori [1990] and T. Iyemori et al. (available at http:// swdcwww.kugi.kyoto-u.ac.jp/aeasy/asy.pdf) and is essentially equivalent to the calculation for Dst, except that different stations are used. The SYM-H index is calculated from six ground-based magnetic stations, taken from the list indicated in Table 1. Only six of the stations listed there are used for the derivation of each month. Honolulu and Memambetsu are always used. Depending on availability and data quality, the other four stations are chosen one out of each remaining group of two stations, from Boulder or Tucson, Fredericksburg or San Juan, Hermanus or Chambon-la-Foret, Alibag or Martin de Vivies. Just as for Dst, the first step in deriving SYM-H consists of subtraction of the geomagnetic main field and the Sq field. There is a slight difference from the Dst computation in that SYM-H is calculated on a monthly basis. To calculate the monthly background field, data of the 5 international quiet days are used for that month; the original data of the international 5 quiet days of the month that include the Sq and geomagnetic main field are averaged every minute and fitted by spline functions. In unusual cases where some of the 5 quietest days data are not suitable (e.g., data gaps), another day is selected from the international 10 quiet days of the month. The background field is then subtracted to obtain the monthly disturbance field at 1-min intervals. [9] These calculations are followed by a coordinate transformation to a magnetic dipole system, with the tacit assumption that the ring current flows parallel to the dipole equatorial plane [Iyemori, 1990]. After this, the six station average of the longitudinal symmetric magnetic field component is calculated from the averages of the disturbance component at each minute. Finally, SYM-H is computed by making latitudinal corrections, similar to the Dst calculation; the final calculation involves division by the average value of the cosines of the dipole latitude. It is important to note that because the data are processed in increments of 1 month some gap in the magnitude is sometimes seen between successive months. 3. Sources of Index Differences [10] The network of stations used to produce the SYM-H index consists of several different observatories than those used for Dst computation, some of which are at higher latitudes (Table 1). In addition, since SYM-H uses more observatories, more evenly distributed in longitude, it provides a better description of the variations with longitude of the disturbance field. Since different observatories are used numerous differences in the final indices can arise because of different variation fields observed by the several magnetometer stations. As well, the difference in the temporal resolution of the indices can also yield deviations. In this section we will discuss these crucial factors because of their influence on the final value of the Dst and SYM-H indices, and the reader is referred to the papers by Häkkinen et al. [2002] and Campbell [2004] for further insights into factors that influence Dst. [11] 1. At present it is not clear that Dst (or SYM-H) provides a clear representation of the symmetric ring current. Much evidence indicates that the ring current might actually contribute only a very small part to these indices [Campbell, 1996, 2004]. On the basis of the assumption that Dst is produced by a symmetric ring current, and that components of low-latitude fields increase with the increasing latitude, it has been the custom to normalize the variation fields to the equatorial region by a division by the average of geomagnetic latitudes, as indicated by the equations previously introduced (see also Figure 2 from Campbell [2004]). The aforementioned study indicates that this 1/cos (l) adjustment typically fails and can thus introduce small errors into the calculation. [12] 2. Dst is thought to provide some measure to estimate the ring current energy density, although recent studies have indicated that it contains many contributions from several sources other than the azimuthally symmetric ring current. For example, it is estimated that the tail current contributes about one quarter to the total of the horizontal magnetic field [Turner et al., 2000]. Skoug et al. [2003] show that the situation can be far worse; they present a case where Dst is almost completely driven by the tail current. The tail current has plenty of fine structure that contributes to different variation fields at different nightside latitudes and longitudes, thus introducing differences between the Dst and SYM-H indices when different observatories are used. In addition to shielding tail current variations the conductive Earth also results in shielding of the nightside partial ring current at low-latitude dayside observatories. This means that dayside magnetometer observatories will not observe similar variations as those on the nightside and the longitudinal spacing of the stations can strongly influence the final index value. [13] 3. Problems in Sq removal have already been highlighted by Tarpley [1973] and Sugiura and Kamei [1991]. Whereas the Dst and SYM-H indices are calculated via subtraction of the Sq based on five quietest days of each month, the Sq current system is highly dynamic and often changes over time periods of a few hours resulting in larger deviations during more active intervals. As well, small changes in the focus of the current system nearby magnetic observatories could cause changes in the amplitude and phase of the Sq field subtracted to form the indices. Errors in subtraction caused by day-to-day variability of the Sq dynamo current can be on the order of 10 nt [Iyemori, 1990]. [14] 4. Probably the major problem resulting in differences between Dst and SYM-H is related to induced electric currents near the Earth s surface. We contend that these 3of10

Figure 2. Power spectrum of SYM-H (top curve) and Dst (bottom curve) for 1981 2002. The SYM-H curve has been shifted up so that it can be compared easily to the Dst spectral density. Several peaks in power are evident at 6 months, 1 month, and 24 hours, which are indicated by arrows. problems are larger than that produced by the tail current contribution mentioned above (point 2), primarily because the time variation of the tail current is likely to produce similar artifacts in both Dst and SYM-H. Induced electric currents are formed by magnetic perturbations that are timedependent, primarily from sources external to the Earth. These electric currents in turn create an induced magnetic field that contributes to the final overall magnetometer measurement at the surface of the Earth. The magnitude of the induced magnetic field is strongly dependent on the frequency of the external source magnetic field and can contribute a substantial fraction to the total measured field [Wanliss and Antoine, 1995]. The main geomagnetic field with its secular variations contributes negligibly to the induced fields because the time dependence is so weak. Thus it is the external fields, attributed primarily to ring current variations, magnetic field-aligned currents, and ionospheric currents that produce significant induced currents and induced magnetic fields. The most significant induction effects result from electric current systems that vary rapidly with time such as are usually associated with storm main phase. That induced currents can contribute so much, over 25%, to the horizontal component magnetic field [Price, 1967, p. 286; Häkkinen et al., 2002] suggests that differences between SYM-H and Dst might actually be quite noteworthy at times. If the conductivity structures beneath the stations were identical, then the induced magnetic field would be similar at different stations, assuming that the incoming external magnetic field was uniform spatially. In this case, one would expect close correlation between SYM-H and Dst. In reality the external magnetic fields are not spatially uniform even over small distances at low latitudes [Wanliss and Antoine, 1995], and geologic conductivity structures beneath the stations used to compute the indices are also decidedly variable. For example, stations near the highly conductive ocean, e.g., Hermanus and Honolulu, will have induced fields that are quite different from stations that are significantly inland [Häkkinen et al., 2002]. Induced fields also result in phase shifts [Wanliss and Antoine, 1995] and some induced electromagnetic anomalies change sign, and some do not, depending on the interaction between the induced electric currents at a given period and the geometry of the electrical conductivity contrasts [Tarits and Grammatica, 2000]. [15] 5. Transients with time scales less than one hour will be smoothed out by Dst but will be observed by SYM-H. These high-frequency variations highlight the role of localized, strong current systems that are in abundance during storm main phase. For example, geomagnetic micropulsations with periods less than 1 hour can often have amplitudes on the order of 10 nt [Wanliss and Antoine, 1995]. Other transients are formed from compression of the magnetopause during, for example, magnetic cloud events. This drives the magnetopause currents much closer to the surface of the Earth resulting in fluctuations from dayside magnetometers that vary on timescales less than 1 hour. 4. Analysis and Results [16] We will do a long-term comparison of Dst and SYM- H data for 1981 2002. These data are characterized by long-range dependence and intermittent behavior [Wanliss, 2004, 2005] (Figure 1). Figure 2 shows the power spectrum of Dst (lower curve), with the corresponding power spectrum for SYM-H (upper curve) for comparison. Several peaks in power are observed at interesting periodicities, and we point out peaks at 6 months, 1 month, and 24 hours. The 6-month peak indicates differences arising between solstice and equinox and may also include a contribution from the influence of seasonal magnetotail positions [Campbell, 4of10

Figure 3. Probability density function of Dst for 1963 2002. The PDF for raw data is shown by the dots, and the best-fit sum of two lognormal distributions is shown as the solid line. The individual lognormal distributions are shown as the dashed and dashed-dotted curves. 1984; McPherron, 2000]. Since it is likely that the asymmetry part of the SYM index is produced by a field-aligned current system, its strength should depend on season. In winter, more current should close through the summer auroral ionosphere. Similarly, the SYM-H index will also depend on season, since it is impossible to perfectly decouple the symmetric and asymmetric part of the SYM index. Another peak in the power spectrum is observed at 1 month; it is much broader than the first peak but not so clearly resolved. The 24 hour peak, and subsequent harmonics, gives evidence that removal of the Sq is not ideal. Lunar tidal variations of ionospheric origin have also been identified in Dst [Stening, 1990]. [17] The probability density of the Dst index from 1963 to 2002 is shown in Figure 3 (dots) and displays a heavy tail for large negative values. We attempted several different fits of common distribution functions, such as those of Gauss, Rayleigh, Maxwell, as well as the normal and lognormal distribution functions. All these distributions (apart from lognormal) have Gaussian asymptotes and so are immediately unsuitable as stable heavy tailed candidates, but we nonetheless applied the fits for completeness to verify that they were unsatisfactory. The best fit we obtained was from the convolution of two lognormal distributions such that there is a long tail for large negative values of Dst. The form of the double lognormal distribution used for the fits is h i Px ðþ¼ A 1 exp ðlogðþ b x 1 Þ 2 =c 2 1 h i þ A 2 exp ðlogðþ b x 2 Þ 2 =c 2 2 : The variables A are a gauge of the area under each curve, b indicates the locations of the peaks, and c represents scale parameters that act to reduce or extend the median. The best fit it is shown as the solid line, with the component lognormal distributions as dashed and dot-dashed curves. The prospect of a multifractal Dst time series is immediately suggested by the heavy tail of the distribution and also by the possible long-range dependence behavior [Wanliss, 2004; Wanliss et al., 2005]. It is reasonable to suspect that one scaling exponent is not sufficient to describe the high variability of the signal, and this suspicion has been borne out by recent analysis and simulations [Wanliss et al., 2005]. This is also consistent with the suggestion by Campbell [1996] that Dst is produced by a superposition of many independent processes, rather than by a single monolithic ring current. [18] According to classical statistical theory for a system in an equilibrium state, we might expect to observe Gaussian statistics for measurable physical quantities. On the contrary, systems that cannot reach an equilibrium state might have probability distributions that are significantly different from normal ones. This is particularly true for nonlinear systems that feature inhomogeneous dissipation in time. In this picture our results suggest that the physical processes that produce the Dst index (typically associated mainly with the ring current) result in nonequilibrium dynamical configurations. Even if we consider the small values of Dst around zero, we find that the distribution function is significantly different from a Gaussian. Our results, including those from a recent multifractal analysis [Wanliss et al., 2005], suggest that the ring current (or 5of10

Figure 4. Probability density function of SYM-H for 1981 2002. The PDF for raw data is shown by the dots, and the best-fit sum of two lognormal distributions is shown as the solid line. The individual lognormal distributions are shown as the dashed and dashed-dotted curves. whatever the processes are that produce Dst) is out of equilibrium. [19] The fit is only shown for Dst > 150 nt since only 0.3 percent of these data have values smaller than this. The peak of the quiet distribution, indicated by the dashed line, occurs at 9 nt. For the active distribution, indicated by the dashed-dot line, the peak occurs at 38 nt. These two distributions cross at 46 nt. We consider the overall bimodality of the distribution to be reflective of quiet and active behaviors. These terms are suggested by the location of the crossing at 46 nt; magnetic storms are frequently classified based on Dst [Gonzalez et al., 1994], with storms having Dst < 50 nt classified as moderate or intense and those with larger values (less negative) classified as small storms. In fact, it has been noted that the small storms are actually more representative of magnetospheric substorms [Gonzalez et al., 1994]. Dst is therefore affected by highlatitude substorms, even though it is not able to fully resolve that effect due to its low resolution. We do not slavishly hold to the above space storm designation, as it is quite reasonable to note that both distributions include active intervals but that one is simply more active than the other. Another possible interpretation, as suggested by the lognormal form of the distribution functions and the results from multifractal analysis [Wanliss et al., 2005], is that these two distributions are produced by processes that are significantly different, perhaps indicative of different magnetospheric responses to a variable solar wind. [20] For completeness, in Figure 4 we show the probability density of the SYM-H index for 1981 through 2002 (dots). Not surprisingly, this probability density function is also fit by a combination of two lognormal distributions. The raw distribution is shown by the dots, the fit by the solid curve, and the individual lognormal contributions to the fit are shown as the dashed-dot and dashed curves. The raw distribution has a slightly higher probability at small values of SYM-H than for Dst (0.20 compared to 0.18). Although well fit by these distribution functions, the shapes of the individual lognormal distributions are slightly different than those found for Dst. When we produced a distribution function of a decimated SYM-H, reduced to one averaged value per hour, the distribution more closely matches that of Dst (not shown). We believe the differences between Figures 3 and 4 thus reflect the effect of the higher temporal resolution of SYM-H compared to Dst. [21] In Figure 5, results comparing the indices for just 1 year are presented. In the top panel, SYM-H (red dots) and Dst (solid blue) indices for 1984 are shown. Numerous excursions to large negative values are observed through the year, representing intense magnetic storms. With the exception of these times, it is difficult to see large differences, and for the most part, it appears that the time series are very closely matched with no systematic trends. The middle panel of Figure 5 is more illustrative of the dissimilarity, and represents a simple difference between the 1984 Dst and SYM-H time series as plotted versus time of year. The SYM-H values used for comparison with Dst are from a reduced version calculated from hourly averages. The mean is close to zero and the largest differences appear to have occurred during large magnetic storms. Abrupt shifts occur just after 5100 hours and near 7300 and 8000 hours. The shifts are likely to be due to the different methods of baseline removal. As mentioned previously, the baseline removal method for Dst applies a second-order polynomial for the data for the entire year. This is a slowly varying, smooth function. On the other hand, SYM-H baselines are 6of10

Figure 5. (top) Plot of Dst (blue solid curve) and SYM-H (red dotted curve) versus time in hours for 1984. (middle) Plot of the difference (Dst - SYM-H) versus time. (bottom) Plot of the difference (Dst - SYM-H) versus Dst. determined monthly from the 5 quietest days of the month. Shifts could occur if the 5 quietest days for one month are actually much more active than for that of the successive month, resulting in abrupt changes in the baseline. This hypothesis appears reasonable, considering that a closer look reveals that clear abrupt shifts occur at the transition between July/August (5112 hours), October/November (7320 hours), and November/December (8040 hours). [22] In the lowest panel of Figure 5 we plot the difference between the 1984 series as a function of Dst. Although the statistics are not as good for large negative Dst values, the overall variance becomes larger when the Dst value is more negative. As well, we note that for positive values of Dst the variance is smallest. [23] We perform a linear regression of Dst versus SYM- H, but there is some question as to which SYM-H value to use. Since SYM-H is computed once a minute and Dst is computed only once per hour, there are 60 values of SYM- H for every value of Dst. Each Dst value is really an average calculated from magnetic field measurements over the preceding hour. For the purposes of the comparison, for each Dst value given at time t (UT hours), we used three different values for SYM-H. In the first case, the value of SYM-H chosen is that at the start of the hour for which Dst is defined. In the second, the value of SYM-H chosen is halfway through the hour for which Dst is defined. In the third, the value used is the average of the 60 values of SYM-H for the entire hour. Symbolically, we compare Dst(t) with (1) SYM-H! SYM-H(t), (2) SYM-H! SYM-H(t 1/2 hour), and (3) SYM-H! [ X t i¼t 1 hour SYM H(i)]/60. [24] In Figure 6 we show the plot of Dst versus SYM-H for case 1 mentioned above for the entire data set from 1981 to 2002. Results for cases 2 and 3 are not shown because they are indistinguishable from this plot. Polynomial fits up to order six were applied through least-squares regression. These time series have long tails in their distributions that can skew the results. We have seen that less than 1% of the time series have values below 150 nt and these outliers can have a large influence on the fit because squaring the residuals magnifies the effects of these extreme data points. A disadvantage of least squares regression is its sensitivity to outliers. Accordingly, we used robust least-squares regression with a bisquare weighting scheme [Draper and Smith, 1998] that fits the bulk of the data and minimizes the effect of outliers. The minimization uses a weighted sum of squares, where the weight given to each data point depends on the distance from the fitted line. Points close to the line get full weight and those further from the line get reduced weight. [25] The best fit was determined on the basis of (1) visual examination of the residuals, (2) goodness-of-fit statistics, and (3) confidence bounds. With the exception of the thirdorder polynomial model the regression coefficient was very high and similar for all orders, making it difficult to discriminate between the different fits. The linear and fourth-order fits have the smallest residuals, but a visual examination indicated that the fourth-order polynomial fit 7of10

Figure 6. Plot of Dst against SYM-H. Since there are 60 values of SYM-H for every Dst value, here we replace individual SYM-H by SYM-H! SYM-H(t). The best linear fits in the regions below and above 300 nt are shown as the solid lines in the upper plot. To indicate which data are being fitted, we use different symbols in the two regions (crosses and dots). The 95% confidence bounds are shown as the dashed lines. The lower plot shows that for the most part the residuals appear to be randomly distributed, indicating that the major trends are modeled accurately. the outliers significantly better. Visual inspection of the residuals from all three comparisons indicated that for values of SYM-H > 300 nt the residuals from fourthand first-order polynomials were very close except for positive values of SYM-H. Only 0.02% of the dataset had values smaller than 300 nt, and the apparent break in the data at 300 nt led us to attempt two linear fits on either side of this value. Our preference was to fit the simplest possible model that provides reasonable fits. When we used two linear fits we found smaller residuals than for the single polynomial fits. The linear fits for case 1 are shown as the solid curves in Figure 6, and are fitted with the equation Dst =A (SYM-H) + B. Table 2 summarizes the results for the linear regression analysis for the different cases above. The differences between the fits for the three different cases are negligible (the smallest mean squared error occurs for Case 3). The fits for SYM-H > 300 nt have much smaller confidence bounds (cf. Figure 6 and uncertainties in Table 2), indicating a better fit for this portion of the distribution. For smaller values during hyperactive times the data are very sparse resulting in large error bars. [26] We have also compared the extent to which Dst and SYM-H are equivalent during different levels of magnetospheric activity. In the classification system of Gonzalez et al. [1994] four levels of activity are delineated, as indicated in Table 3. On the basis of the Dst value, each point in the data set was classified according to these activity levels. Next, the mean jdj of the absolute differences of Dst and modified SYM-H (for each of the three cases defined above), the mean D, and standard deviation of the mean s D, were computed. For all the cases calculated below the mean of the residual is close to zero, indicating a rather good fit. We also computed the mean of the absolute values of the residual because this will give a maximum error bound. It is clear from Table 3 that in every case increased activity resulted in larger differences between Dst and SYM-H. The difference between cases 1 through 3 are only a few nt, so it appears that there is no particular advantage in choosing one case over another. However, we note that the best fit (smallest statistical errors) is obtained for case 3. Table 3 also provides the percentage variation, calculated as the variation divided by the mean SYM-H for the different activity categories. Variations are largest for the quietest times and smallest for the stronger storms when Dst is very large negative. Even a large absolute difference results in a small percentage difference. However, even with much smaller absolute differences, the percentage differences are larger during quiet times when Dst is small. Finally, because of the apparent problem of baseline shifts between months we have compared the differences in the indices at the interface between all months for 1981 2002. We find shifts with residuals of jdj = 8.4 nt, D ± s D = 1.9 ± 11.0 nt. These should be compared to the All Values column of Table 3, namely, jdj = 7.2 nt, D ± s D = 0.4 ± 9.5 nt. It is clear that the residuals for the monthly interface values are larger than for the same calculated over the entire data set. This result suggests that if one uses SYM-H as a high- Table 2. Linear Regression Coefficients A and B for the Fit of Dst =A (SYM-H) + B a Case A 1 B 1 A 2 B 2 1 0.959 ± 0.002 2.5 ± 0.1 0.727 ± 0.095 62.2 ± 37.1 2 0.967 ± 0.002 2.4 ± 0.1 0.808 ± 0.105 36.4 ± 41.7 3 0.979 ± 0.002 2.2 ± 0.1 0.792 ± 0.100 46.9 ± 39.8 a The subscript for the regression coefficients are 1 for values of SYM-H 300 nt, and 2 for all other values. Three different values of SYM-H are used to compare with Dst, namely cases (1) SYM-H! SYM-H(t), 1 X t (2) SYM-H! SYM-H(t 1/2 hour), and (3) SYM-H! SYM-H(i). 60 i¼t 1 hour 8of10

Table 3. Various Statistics Calculated From the Residual for Each of the Three Cases Defined in Table 2 a Case 1 Case 2 Case 3 jdj D s D jdj D s D jdj D s D All values 7.2 0.4 9.5 7.0 0.4 9.1 6.8 0.4 8.9 Percents 38.9 2.3 51.6 37.6 2.2 49.4 36.7 2.2 48.1 SYM-H > 30 6.9 0.2 9.0 6.7 0.2 8.7 6.5 0.2 8.5 Percents 69.3 2.0 90.7 67.3 2.1 87.5 65.3 2.2 84.6 50 < SYM-H 30 7.6 0.6 10.0 7.3 0.6 9.6 7.1 0.6 9.3 Percents 19.4 1.5 25.6 18.6 1.6 24.4 17.6 1.5 23.2 100 < SYM-H 50 9.2 2.3 12.3 8.9 2.2 11.5 8.6 2.1 11.1 Percents 13.7 3.5 18.2 13.2 3.2 17.0 12.5 3.1 16.1 100 SYM-H 14.3 4.1 18.7 13.6 3.2 17.7 12.8 2.8 16.4 Percents 10.0 2.8 13.1 9.5 2.2 12.4 8.9 2.0 11.3 a The residual is defined as D = Dst (model Dst). The statistics are the mean of the absolute values, jdj, the mean, D, and the standard deviation of the mean s D. All units are in nt. resolution proxy for Dst that one should be cautious if the data of interest envelop a monthly interface since the actual differences here can be slightly larger than average. 5. Summary and Discussion [27] Because the SYM-H and Dst indices are calculated from different magnetometer stations and because of the effects of induced and other fluctuation magnetic fields, there is a priori reason to expect differences between them, differences that in certain cases might be quite significant. In a worst-case scenario induced electric currents, for example, could contribute up to 50% to the horizontal component magnetic field [Häkkinen et al., 2002]. These problems notwithstanding, it is generally held that SYM-H is the de facto high-resolution version of the Dst index (http://swdcwww.kugi.kyoto-u.ac.jp/aeasy/asy.pdf), and it is frequently used in that role [e.g., Reeves et al., 2003]. To our knowledge, this paper presents the first systematic study of long-term interdecadal data to determine the real extent to which Dst and SYM-H are equivalent. We have compared Dst and SYM-H from 1981 to 2002 and also as a function of magnetic activity. [28] Because of the different time resolution of the indices, the comparison required a decimation of the original SYM-H series. We selected three methods to decimate the original SYM-H series so that the new series comprised one value for every single Dst value. We initially modeled the data with polynomials up to the sixth order. For each order polynomial we found a very high correlation coefficient between SYM-H and Dst (above 0.9), and no significant differences in other best-fit statistics. Visual examination of the fits and the residuals was more illuminating and indicated that the fourth-order polynomial fitted the data very well, followed by the first-order polynomial fit. For values above 300 nt the first- and fourth-order polynomials were virtually identical, except for positive values of the magnetic disturbance, where the linear fit is better. The apparent break at 300 nanotesla suggested to us a model based on two first-order polynomial fits on either side of the break (Table 2). [29] Comparisons based on activity levels showed that the differences between the indices were larger during high activity levels; as activity increases the differences between the indices rises, although the relative percentage uncertainty decreases due to the larger average fields (Table 3). Differences may be due to several effects. For example, during periods of high activity, magnetospheric activity is very dynamic and a range of induced magnetic fields with different frequencies and phases can contribute to the overall deviations. This is especially important in the light of the different stations used for the SYM-H and Dst index calculations. In cases when SYM-H uses an inland station rather than one close to the coast induction effects can be quite different, resulting in shifts in the magnetic fields [Gilbert, 2005]. For example, if during a storm a station change is made from Fredericksburg to San Juan, or Martin de Vivies to Alibag and vice versa, there can be significant changes due to the different geology at the different locations, as much as 30%. Häkkinen et al. [2002] noted significant differences in the induced magnetic fields produced during storms at Kakioka and Hermanus; both stations are located near the coast, but Hermanus is wedged between the ocean and the Cape fold belt mountain range with deep roots resulting in a more complicated induction process. The station at Honolulu is also anomalous in its inductive response because of its location at the plume of highly conductive volcanic magma. Second, during high activity, field-aligned currents contribute significantly to the asymmetry of the overall ring current and it is more difficult to accurately separate the symmetric and (more complicated) asymmetric components [Iyemori, 1990]; the more intense the geomagnetic activity the lower the geomagnetic latitude of the auroral oval and thus the more corrupted the signal of the higher-latitude stations that are closest to it. This is more of a problem for SYM-H since four of its stations are in subauroral zones. [30] Other systems such as the magnetopause currents are also typically closer to the Earth during high magnetic activity and can also contribute to the ground-based indices. Notwithstanding these difficulties, the differences between the indices at differing activity levels are on average only a few nt. This suggests that the induced magnetic field and other effects are generally not a serious problem when comparing the indices. For quiet times and for small storms the deviations are typically no more than 10 nt. Moderate storms feature deviations normally only slightly more than 10 nt, and intense storms have deviations that are usually less than 20 nt. [31] A simple combination of linear trends (Table 2) can be used, for all intents and purposes, to create a highresolution (1 min) Dst index. On the basis of this analysis we are able to agree with T. Iyemori et al. (available at http://swdcwww.kugi.kyoto-u.ac.jp/aeasy/asy.pdf) that the main difference between the 1 min SYM-H and the hourly Dst index is in the time resolution. The differences that we have found are not so large that SYM-H could not be used as an alternative high-resolution version of Dst. The use of SYM-H could be helpful in isolating storm triggers since the higher time resolution emphasizes the role of localized electric current systems. Future work will consider the more complex effects of the solar wind dynamic pressure variation on the indices. Because of its high-resolution, we expect that these effects will be more clearly seen in the SYM-H than in the hourly Dst index. [32] While space storms are nearly always accompanied by substorms [Reeves et al., 2003], the storm-substorm relationship remains unresolved; substorms may occur con- 9of10

currently with the development of the storm main phase with no causal relationship at play but with both processes drawing on the same source of energy. The traditional view has been that substorms serve to build up the storm-time ring current through a series of high-energy particle injections. However, recent work suggests that substorm expansive phase does not inject the ring current. For example, Iyemori and Rao [1996] studied 100 substorm onsets that occurred during the main and recovery phases of space storms. When they superposed the Dst index relative to the onset they found that the average response in Dst was to decrease before the onset, and that its rate of decrease became less (not more) negative after substorm onset. During the recovery phase of the storm, they found that Dst actually becomes less negative. This could be interpreted as a reduction in the ring current. 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