Challenging the Use of Ring Current Indices During Geomagnetic Storms

The ring current experiences dramatic enhancements during geomagnetic storms; however, understanding the global distribution of ring current energy content is restricted by spacecraft coverage. Many studies use ring current indices as a proxy for energy content, but these indices average over spatial variations and include additional contributions. We have conducted an analysis of Van Allen Probes' data, identifying the spatial distribution and storm‐time variations of energy content. Ion observations from the HOPE and RBSPICE instruments were used to estimate energy content in L‐MLT bins. The results show large enhancements particularly in the premidnight sector during the main phase, alongside reductions in local time asymmetry and intensity during the recovery phase. A comparison with estimated energy content using the Sym‐H index was conducted. In agreement with previous results, the Sym‐H index significantly overestimates (by up to ∼4 times) the energy content, and we attribute the difference to contributions from additional current systems. A new finding is an observed temporal discrepancy, where energy content estimates from the Sym‐H index maximize 3–9 h earlier than in‐situ observations. Case studies reveal a complex relationship, where variable degrees of agreement between the Sym‐H index and in‐situ measurements are observed. The results highlight the drawbacks of ring current indices and emphasize the variability of the storm time ring current.

Ground magnetometers whose locations map to the inner magnetosphere can observe north-south magnetic field perturbations induced by the ring current, and fluctuations in this perturbation are often inferred as corresponding to changes in the ring current strength. Ring current indices (such as the Dst index (Sugiura & Poros, 1964), the Sym-H index (Iyemori, 1990), and the SMR index (Newell & Gjerloev, 2012)) are derived from magnetometers that map to this region and cover a range of local times. Furthermore, the magnitude of the indices can be directly related to the total energy content of the ring current population, E T , using the Dessler-Parker-Sckopke (DPS) equation (Dessler & Parker, 1959;Sckopke, 1966): In Equation 1, μ 0 is the permeability constant (4π × 10 −7 H m −1 ), B 0 is the magnetic field strength at the surface of the Earth (3.12 × 10 −5 T), and R E is the radius of Earth (1R E = 6,372 km). The global magnetic field perturbation, ΔB, can be considered equivalent to the value of a ring current index. Equation 1 provides a relatively simple means to indirectly infer the total energy content of the ring current from the indices and monitor the storm-time variations.
However, Liemohn (2003) reported that the DPS relation makes several key assumptions, such as linear field distortions and a symmetric ring current. In addition, other magnetospheric current systems, notably the tail current and the magnetopause current, can contribute significantly to the observed magnetic field perturbations (e.g., Burton et al., 1975;Turner et al., 2000). Attempts to account for these contributions led to the development of corrected ring current indices, known as the Dst* index and the Sym-H* index (Burton et al., 1975). Furthermore, Gkioulidou et al. (2016) demonstrated that the Sym-H index poorly describes long time scale variations that are driven by the radial diffusion of the high energy ring current ions. Gkioulidou et al. (2016) showed that the high energy ion contribution to the ring current is not well correlated with the absolute value of the Sym-H index and the fluctuations in the Sym-H index are instead dominated by variations in the low energy ion population that occur on much shorter convective time scales.
To assess the accuracy of the ring current indices and the use of the DPS relation, the estimates can be compared to direct in-situ observations of the ring current population. Previous work has shown that in-situ energy density and plasma pressure measurements are typically ∼2 times less than the values predicted from the ring current indices (e.g., Ebihara & Ejiri, 2000;Hamilton et al., 1988;Roeder et al., 1996;Turner et al., 2001Turner et al., , 2000Zhao et al., 2015). However, these studies were often based on single storm events, presenting difficulties in understanding the typical storm-time variations, and made several assumptions regarding energy ranges (neglected low energy populations) and ring current symmetry.
This study aims to identify how the ring current varies temporally during a storm. A statistical analysis of direct in-situ observations was conducted to avoid the assumptions made by the ring current indices and the DPS relation, and also to allow for spatial variations to be explored. The results provide information on where energy is deposited and how ion transport distributes that energy across the inner magnetosphere during storms. We also challenge the use of the ring current indices with the DPS relation by conducting a direct comparison to the in-situ observations.

Using Van Allen Probes Data
Direct in-situ observations of the ring current population were obtained from the Van Allen Probes (Mauk et al., 2013), consisting of two identically instrumented spacecraft (Probe A and Probe B). The orbit has a perigee of ∼600 km altitude, an apogee of 5.8R E geocentric radial distance, and an inclination of 10°. The orbital period is 9 h and the orbital apogee precesses in local time, such that sampling over all local times is achieved in <2 years. Overall, the Van Allen Probes provide highly suitable coverage of the ring current region, and with data availability from 2012 onwards, the spatial and temporal coverage allows for statistical analysis.
This study employed observations from the Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) (Mitchell et al., 2013)  instruments. The RBSPICE data sets include: H + ions in the energy range of 50-660 keV; O + ions in the energy range of 120-990 keV; He + ions in the energy range of 60-980 keV. Observations of lower energy ions were provided by the HOPE instrument and these data sets include: H + ions in the energy range of 1 eV-50 keV; O + ions in the energy range of 1 eV-50 keV. These data sets cover the bulk population of H + ions with energies of a few hundred keV (e.g., Krimigis et al., 1985;. Previous work clearly demonstrates that heavy ions and low energy ions can contribute significantly during geomagnetically active times, and in some cases dominate the ring current population (e.g., Keika et al., 2018;Kistler et al., 2016;Stepanova et al., 2019;Zhao et al., 2015). Therefore, the contribution of these ions was also covered in the data sets used.
The data sets provided observations of the omnidirectional ion energy flux and we employed the method of  and Sandhu et al. (2019) to estimate the energy content in L-MLT bins. The L-MLT coordinate system uses the L value (radial distance of where the given field line crosses the equatorial plane in Earth Radii) as a radial coordinate and the Magnetic Local Time (MLT) value as the azimuthal coordinate. We refer the reader to  for full details of the methodology and briefly summarize here. The following steps were taken: 1. For each data set, the mean partial ion energy density was estimated from the omnidirectional energy flux, for a spacecraft pass through an L-MLT bin of width ΔL and ΔMLT. The time taken for the spacecraft to traverse the L-MLT is recorded as the uncertainty in the time of measurement (typically 6 min for ΔL = 0.5). The partial ion energy density from each data set (corresponding to a given ion species and energy range) was summed to estimate the total ring current energy density. 2. The volume of the L-MLT bin was then estimated using a dipole magnetic field model scaled for the local magnetic field strength as observed by the Electric and Magnetic Field Instrument Suite and Integrated Science instrument (Kletzing et al., 2013) onboard the Van Allen Probes. 3. The ion energy density was integrated over the volume of the bin to obtain an estimate of the total energy content for the L-MLT bin, E.
This method was applied to all Van Allen Probe A and B data between October 2012 to June 2019 to provide a data set of E values.
It is noted that this approach uses coincident observations from two separate instruments (HOPE and RB-SPICE). Significant efforts by the HOPE instrument team have minimized any intercalibration issues in the latest data release (Release 04), such the 87% of ion fluxes agree to within a factor of 2 (see https://www. rbsp-ect.lanl.gov/rbsp_ect.php).

Using Ring Current Indices
Although there are a range of ring current indices available, the most common being the Dst index, the Sym-H index, and the SMR index, we opted to present a detailed comparison for the Sym-H index. All are derived using a similar method, but key differences relate to the subtraction of baselines, the number of stations used in the calculation, and the cadences of the indices. Our findings are consistent across all indices.
A detailed description of how the Sym-H index is derived is provided by Iyemori (1990) and briefly summarized here. The Sym-H index is calculated with a 1 min temporal resolution from a range of ground magnetometers spanning magnetic latitudes from −47° to 50°. The data are processed in units of one month, and for each month only six stations that are approximately evenly spaced in longitude are used. First, the disturbance component of the measured H (north-south) component is obtained by subtracting the background geomagnetic field and the solar quiet daily variation. Next, a coordinate transformation to the dipole coordinate system is applied. Finally, for each minute, the disturbance component over the six stations is averaged to provide the Sym-H index.
As mentioned previously, attempts to remove contributions from other current systems to the observed Sym-H index have been made, resulting in the corrected Sym-H index. This is termed as Sym-H*. Although there are many different versions of Sym-H*, they generally follow the formulation of Burton et al. (1975): SANDHU ET AL.

10.1029/2020JA028423
3 of 19 where the parameters b and c are empirically determined and P dyn is the solar wind dynamic pressure. In this study, we use the values of b and c determined by O'Brien and McPherron (2000): b = 7.26 nT nPa 1/2 and c = 11 nT. The Sym-H* index endeavors to correct for the contribution of magnetopause currents and the quiet day currents.
The calculation of the Sym-H index relies on using observations from magnetometer stations mapping to different MLT sectors of the ring current population and taking an average of those measurements. Therefore, this average perturbation can be considered as describing the symmetric component of the ring current. Alternatively, the Asy-H index can be used to describe the asymmetric component of the ring current (Iyemori et al., 1992). The Asy-H index is derived similarly to the Sym-H index but, instead of averaging the perturbations, the difference between the smallest perturbation and the largest perturbation over the six stations is taken for each minute sample.
For each sample of the energy content provided by the Van Allen Probes, we also took the Sym-H, Sym-H*, and Asy-H indices at the given time.
From the data set of Sym-H and Sym-H* values, we estimated the corresponding total ring current energy content for each sample according to the DPS relation (Equation 1).

Storm Identification
To extract storm time periods for analysis, storms were identified using the algorithm described by Walach and Grocott (2019). The reader is referred to Walach and Grocott (2019) for full details, and we summarize the key aspects here. The algorithm identifies storms from variations in the Sym-H index, and a typical Sym-H index trace is shown in Figure 1. Figure 1 demonstrates the typical features of a geomagnetic storm, which can generally be split into three distinct phases: the initial phase, the main phase, and the recovery phase. The initial phase is present for most storms and is characterized by an enhancement in the Sym-H index driven by enhancements in the magnetopause currents. The initial phase typically lasts ∼20 h (Walach & Grocott, 2019). The main phase is identified from a sharp and rapid negative excursion in the Sym-H index, driven by significant energization of the ring current, and has a typical duration of ∼8 h (Walach & Grocott, 2019). Finally, the recovery phase, where the Sym-H index gradually increases to quiet time values as the ring current decays, generally lasts several days (Walach & Grocott, 2019). Geomagnetic storms typically exhibit important structure within the recovery phase, namely a two-step decay. In the early recovery phase, the decay of the ring current and consequent increase of the Sym-H index is rapid. This is followed by a lower rate of change in the late recovery phase. The two-step characteristic of the ring current recovery indicates that there are multiple process in operation that occur on different time scales (e.g., Daglis et al., 2003;Hamilton et al., 1988;Jorgensen et al., 2001;. As well as identifying the storm time periods, the algorithm of Walach and Grocott (2019) also determines the timings of each storm phase. First, a storm is identified as a period where the Sym-H index crosses below a storm time threshold of −80 nT. The storm peak, or alternatively the start of the recovery phase, is marked as the point where the Sym-H index is at its lowest level. The start of the main phase and the end of the recovery phase are then marked as the times immediately prior to and after the storm peak where the Sym-H index is at the quiet time level (here defined as −15 nT). To bound the initial phase, we identify where the Sym-H index reaches a maximum value and then record the time immediately prior to this that the Sym-H index is at the quiet time level. The quiet time threshold of −15 nT and the storm time threshold of −80 nT are taken from Hutchinson et al. (2011).
We note that the Walach and Grocott (2019) algorithm does not distinguish between the early and late recovery phase for storms with a two-step recovery phase, and hence the substructure of ring current variations within the recovery phase will not be the focus of this study. It is hoped that further developments of the algorithm will allow for a detailed analysis of the recovery phase dynamics in a future study.
The Walach and Grocott (2019) algorithm identified 52 storms occurring between 2012 and 2019, and the storm list is included in the Supplementary Information (Data Set S1). Using the storm times, we binned the in-situ measurements, the Sym-H index, and the Sym-H* index for storm phase. The following sections explore how the measurements vary during storm times. Figures 2a and 2c also includes the mean energy profiles, E(L), for the storm initial phases (yellow circles), main phases (orange squares), and recovery phases (light blue triangles). Nonstorm times are labeled as quiet and the mean energy profile is shown by the blue diamonds. The bars on each profile indicate the standard deviations. The profiles show that the energy values during quiet times and the initial phase are similar (∼0.8 × 10 13 J at L = 5). The energy values in the premidnight sector are ∼0.1 × 10 13 J larger during quiet times compared to during the initial phase, which is attributed to the quiet time intervals containing periods of nonstorm time activity associated with substorm-related enhancements Sandhu et al., 2019) or residual poststorm enhancements of the ring current for example. Furthermore, during the initial phase the increase in solar wind coupling increases the number of ions on open drift paths through an increase in the convection electric field and the earthward displacement of the magnetopause (Ozeke & Mann, 2001;Staples et al., 2020). These ions are then lost through the dayside magnetopause and the average ring current energy content experiences a decrease compared to the quiet time level.

Variations with Storm Phase
During the main phase, Figures 2a and 2c demonstrate the substantial increases relative to the main phase are observed in the premidnight sector, with values exceeding 2 × 10 13 J at 4 ≥ L < 5. In contrast, in the prenoon sector the main phase values are only slightly elevated by ∼0.1 × 10 13 J compared to the initial phase profile. During the recovery phase, the values remain elevated in the premidnight sector and the profile is very close to the main phase profile (Figure 2c). In the prenoon sector, the values increase substantially compared to the main phase and peaks at ∼1.8 × 10 13 J. Overall, Figures 2a and 2c shows that large storm SANDHU ET AL.  However, based on the Sym-H trace the ring current undergoes dramatic changes throughout each storm phase, which cannot be assessed by averaging over each phase. Instead, a superposed epoch analysis was used to explore the variations in energy content during a storm and variations within a storm phase.  Figures S1 and S2). In general, each bin contains ∼10-100 samples. Overall, Figure 3 demonstrates average ring current energy variations during a storm, considering changes in the spatial distribution as well as the magnitude. It is noted that the storm main phases were normalized to a length of 12 h (the mean duration of main phases across the storm studied here), which avoided averaging initial and main phases together and accounted for the large variation in main phase durations.
Figures 3a-3c encapsulate both the initial phase and the main phase, describing variations leading up to the storm peak. We observe that the energy values increase with time. The largest enhancements are observed in the premidnight sector where energy values increase from ∼1 × 10 13 to ∼2.5 × 10 13 J, representing an increase of ∼150%. The energy distribution at the storm peak ( Figure 3c) is highly asymmetric with energy values peaking in the premidnight sector. Following the storm peak, the start of the recovery phase shows that the ring current remains at an elevated state ( Figure 3d). However, the energy values are high (∼2 × 10 13 J) across all MLT sectors and the energy distribution is more symmetric. Throughout the rest of the recovery phase (Figures 3e-3l) the energy distribution remains very symmetric and the magnitude of the energy content values gradually reduce with time.
In order to further analyze temporal variations, Figure 4 shows the energy values relative to the values at the storm peak. Using the same format as Figure 3, each L-MLT bin shows the difference in energy ΔE (J), comparing the mean energy value at that time to the mean energy value at the storm peak in the same spatial bin. In addition, the distribution of energy values is compared using the Kolmogorov-Smirnov test, which allows for an identification of whether the energy distributions have changed significantly. Using a p value threshold of 0.01, distributions that are not significantly different have the corresponding L-MLT bin plotted as gray. If the distributions are different, the ΔE value is plotted, where red corresponds to an increase in energy and blue corresponds to a decrease in energy relative to t = t 0 . Note that the L-MLT map shown in Figure 4c shows no changes in energy because the values are being compared are identical.
Figures 4a and 4b clearly show that the energy values are lower prior to the storm peak, and that the largest differences are mostly observed in the dusk MLT sector. An interesting feature arises in Figure 4d. The majority of the L-MLT bins show an increase in energy relative to the storm peak. The increases are generally localized to 21 ≤ MLT ≤ 00 and the morning sector with ΔE exceeding ∼1 × 10 13 J. The morning sector enhancement is sustained throughout the recovery phase (Figures 4d-4l), although the magnitude and spatial extent reduces. Elsewhere, the bins show a decrease in energy content with time throughout the recovery phase.
Figures 3 and 4 show interesting local time dependent variations occurring close to the storm peak and in the early recovery phase. To attempt to extract further temporal information, Figure 5 shows the data in the same L-MLT format plots, but using a smaller time binsize of 6 h and focusing on the period from 9 h prior to the storm peak to 15 h after the storm peak. Following the same formats and color scale as   Figure 5 shows similar features as previously highlighted. The energy values increase from the main phase to the storm peak, resulting in a highly asymmetric ring current, where values peak in the premidnight sector. Following the storm peak, the energy values remain sustained at high levels in the premidnight sector. The ring current also becomes comparatively more symmetric with values increasing in the prenoon MLT sector.

Comparison to Ring Current Indices
Figures 3-5 demonstrate significant changes in energy content during storms. These results are now compared to the energy content predicted by the Sym-H and Sym-H* indices using the DPS relation.
For context, Figure 6a shows the Sym-H traces of all storms included in the analysis in gray. The mean Sym-H profile as a function of time is shown in blue. Vertical bars indicate the size of the standard deviation. Figure 6a provides insight into the variability across the storms in the range of Sym-H index values.
For a given L-MLT map shown in Figure 5, the mean energy values displayed were summed together to estimate the total ring current energy content, E T , for the time bin. The time range was also extended from Figure 5 to cover the full storm period. The pink circles in Figure 6b show the total energy, E T , for each 6 h time bin, plotted relative to the storm peak (noting that the energy axis is reversed here). Using error propagation of the standard deviation values for each L-MLT bin, vertical bars are also included to show the extent of the standard deviation for each time bin. However, due to the standard deviation being relatively small compared to the mean (∼10 13 and <7% of the mean value), they cannot easily be seen in Figure 6b. Horizontal bars show the uncertainty in the mean time for each bin, using the same error propagation techniques. The extent of the bars is again visually small in Figure 6b Figure 6b shows that the in-situ measurements of E T vary from ∼0.4 × 10 15 to ∼1.0 × 10 15 J, maximizing between 3 and 9 h following the storm peak on a statistical basis. In contrast, the DPS-derived energy content values from the Sym-H index vary from ∼0.2 × 10 15 up to ∼3.3 × 10 15 J at the storm peak. The peak in energy occurs at t = t 0 by definition of the storm peak. It is also noted that the peak is substantially more defined than the peak in the in-situ energy values. Figure 6b shows that the range in these energy values (see blue bars) is largest at the storm peak, suggesting a large variability in the energy content at this time across different storms. The energy content values predicted from the corrected ring current index, Sym-H*, show a largely similar temporal dependence to the values using Sym-H. The magnitudes using Sym-H are also very similar to Sym-H*, differing by <∼0.1 × 10 15 J.
Although the peak in E T appears comparatively slight, partly due to the large y axis range, we emphasize that the result is underpinned by statistical testing (see Figure 4). Furthermore, comparisons of sample distributions for adjacent temporal bins around the E T peak show significant differences according to the Kolmogorov-Smirnov test with a confidence level of >99.99% (not shown for brevity).
It is noted here that the time binsize of 6 h is chosen, although we find that the minimum in observed E T remains at t = t 0 + 6 h when smaller time binsizes are used (not shown). However, binsizes smaller than 6 h have significantly reduced statistical significance. Furthermore, for binsizes smaller than the duration of a full spacecraft pass through the ring current region (4.5 h) leads to inconsistent spatial sampling between time bins.
Previous work has identified that the tail current systems can contribute significantly to the observed ring current indices during substorms (e.g., Belova & Maltskv, 1994;Kalegaev et al., 2005;Ohtani et al., 2001;Siscoe & Petschek, 1997;Turner et al., 2000). Turner et al. (2000) shows that the tail current contributes ∼25% to the observed ring current index value during both storm time and nonstorm time substorms. To identify whether there was substorm activity during the storms analyzed here, and hence important tail contributions to the Sym-H and Sym-H* indices, we include the average SML index trace in Figure 6c. The SML index can be considered as equivalent to the AL index in terms of construction, and describes the strength of the high latitude nightside westward auroral electrojets (Gjerloev, 2012;Newell & Gjerloev, 2011). In contrast to the AL index, the coverage of ground magnetometers used for the SML index extends over a larger range of latitudes (40-80° magnetic latitude) and will provide reliable measurements of the storm time westward auroral electrojet (Ahn et al., 2005;Feldstein et al., 1999). Reductions in the SML index are signatures of substorm activity and the magnitude of the reduction over the substorm expansion phase is an indicator of the substorm size. Figure 6c shows a decrease in the SML index during the storm, centered around the storm peak (t = t 0 ).
In order to investigate the role of substorm activity, the SOPHIE (Substorm Onsets and Phases from Indices of the Electrojet) identification technique is employed to identify the occurrence and properties of substorms during each storm (Forsyth et al., 2015). In this study, the SOPHIE technique identifies substorm expansion phases based on percentiles of the rate of change of the SML index (using an expansion percen- enhanced magnetospheric convection the SML index will exhibit substorm-like reductions and these fluctuations are also reflected in the SMU index (the upper component of the SuperMAG auroral electrojet index), whereas during substorms the SML and SMU index vary relatively independently (Rostoker, 1972). In order to identify whether an expansion phase identification corresponds to a period of enhanced convection (a false identification), the SOPHIE technique also consults variations in the SMU index and removes identifications where the SML and SMU indices are varying in a similar way. For full details on the SOPHIE technique, the reader is referred to Forsyth et al. (2015). Using the SOPHIE identifications, Figure 6d shows the average number of substorms in a given time bin, indicated by the height of the filled bars. The number of substorms maximize at the storm peak with an average of 3-4 substorms occurring for a typical storm. The circles in Figure 6d show the average size of the substorm, where the size was inferred from the change in the SML index over the substorm expansion phase. We also identify that substorms are, on average, largest at the storm peak.
Although the energy content of the ring current is estimated by summing over all local time sectors and accounts for any local time dependences in energy content, the Sym-H index is constructed by averaging over local time asymmetries. In order to more accurately compare the E values observed with the Sym-H indices, an alternative approach can be adopted that aims to replicate the Sym-H generation technique. At a given time and for a given MLT sector shown in Figures 5a-5d, the values were summed over L bins to provide the energy content for the MLT sector. The value was then integrated to cover 24 h of MLT, and from a single MLT sector estimate the total ring current energy content, E T . This echoes the Sym-H technique, where each magnetometer measures perturbations that would correspond to a hypothetical symmetric ring current across all MLTs. The construction of the Sym-H index then averages the measurements from six magnetometer stations to describe the average ring current over all local times. Essentially, the resultant E T values can be interpreted as what a single magnetometer would measure as the total ring current energy. Figure 7a shows the E T values binned for MLT and time relative to the storm peak. The color of the bin shows the E T value. Figure 7a demonstrates the key storm time features that have been previously identified. Specifically, we observe increases in energy content during the main phase that maximize close to the storm peak and gradually decay throughout the recovery phase. The ring current is also highly asymmetric around the storm peak, with values maximizing in the premidnight MLT sector, and increasingly symmetric following the storm peak.
The Sym-H index is generated by averaging perturbations from a range of local times. Figure 7b shows the result of averaging values shown in Figure 7a across all MLT sectors, considering each time bin separately. The pink open circles show the mean E T value, and the error-propagated standard deviation is shown by pink bars. (As before the bars are considerably smaller than the range of the axes and are not easily visible). The corresponding mean Sym-H and Sym-H* values as a function of time are shown by the blue solid and light blue dashed profiles, respectively. The bars show the width of the standard deviation. The y axes are scaled according to the DPS relation (similarly to Figure 6b). Overall, the profiles show the same features as discussed from Figure 6b. The estimates of total energy content are extremely similar in both magnitude and temporal variation, and it appears that the alternative technique has little impact on the estimations.
An advantage of the technique is the ability to conduct a comparison to the Asy-H index. As described in Section 2.2, the Sym-H index is the average over the perturbations measured across stations whereas the Asy-H index is the difference between the maximum and minimum perturbations across stations.  shows the mean Asy-H index as a function of time in green, where the bars indicate the standard deviation across values. Using the E T values shown in Figure 7a, the maximum and minimum E T value across the range of MLT sectors can be taken for each time bin. The pink profile in Figure 7c shows the difference between the maximum and minimum values for each time bin, the vertical bars shows the error-propagated standard deviation, and the horizontal bars show the uncertainty in time. Note that the y axes are scaled according to the DPS relation. Both the energy values and the Asy-H profiles show similar temporal variation. The values increase during the main phase and maximize at the storm peak (within ±3 h). The values then reduce throughout the recovery phase, with a rapid recovery in the early recovery phase and a comparatively gradual recovery in the late recovery phase. The variability in values is largest at the storm peak. These trends arise as the ring current is highly asymmetric at the storm peak and gradually becomes increasingly symmetric during the recovery phase (Figures 3 and 7a). Interestingly, we note that the peaks in observed asymmetry and intensity occur at different times during the storm, on average. Whereas the observed energy content (shaped by the magnitudes of ion source and loss processes) maximizes at 3 ≤ t 0 < 9 h, the asymmetry (dominated by drift path configurations that control the ratio of open and closed drift paths) maximizes at −3 ≤ t 0 < 3. Figure 7c also shows that there are significant differences in magnitude between the observed energy values and the Asy-H index especially at the storm peak, similarly to the comparison to the Sym-H index. The source of the discrepancy is expected to be the same as the discrepancies with the Sym-H index, and will be discussed in the following section.

Case Studies
Figures 6b and 7b demonstrate that there is a statistical difference in the temporal profile of the energy content estimated using ring current indices with the DPS relation and of the in-situ estimates, such that the in-situ values peak ∼6 h later. Is this a feature consistent across all storms or is it a result of averaging storms with different temporal trends? In order to shed light on this question, we present a selection of case studies, shown in Figures 8 and 9.
As before, the time series are plotted relative to the storm peak, defined using the Sym-H index. The Sym-H (blue) and Sym-H* (light blue) indices (nT) are shown in panel (a) and the SML (orange) and SMU (light orange) indices (nT) are shown in panel (b). The enhanced level of magnetospheric convection during the storm main phase is apparent from the simultaneous increase in the SMU index with the decrease in the SML index. Superimposed deviations in the SML index, with no corresponding changes in the SMU index, are also evident throughout both events and indicate the occurrence of substorms. Panel (c) shows the number of substorms in each time bin (filled bars), as identified using the SO-PHIE technique, as well as the average change in SML index over the substorm expansion phases (circles). The   Figures 8g and 9g show variations in the energy content during the storm period, with the values increasing across almost all L values then decreasing. However, the duration of the enhancement differs between the case studies. In order to extract changes in energy content relative to the time of the storm peak, panel (h) shows the difference in mean energy content relative to t = t 0 , ΔE (J), for the same spatial bin. Prior to the storm peak, the energy values are reduced by ∼10 13 J. Following the storm peak, Figure 8 shows a general decrease in energy whereas Figure 9 shows initial enhancements in the early recovery phase followed by a decrease after a few days. The variation is further explored in panel (i), which shows the estimated total energy content, E T (J), obtained by summing over the spatial bins for each time bin. As some time periods have L bins with no sampling, the L dependence shown in Figure 2b is used to extrapolate over the 3 ≤ L ≤ 7 region. Figures 8h and  8i show that the energy content increases prior to the storm peak, over the main phase, and then maximizes at the storm peak, following a gradual reduction in the energy content over the recovery phase. This closely follows the temporal trends of the ring current indices. Figures 9h and  9i similarly show that the energy content increases over the main phase. However, following the storm peak (t > t 0 ) there is continued enhancement and the energy content peaks ∼12 h afterward. This is in agreement with the statistical trends shown in Figure 4.
It is noted here that larger time bins are used compared to Figure 6. This was to avoid differences between inbound and outbound spacecraft passes (which sample different MLT sectors) being interpreted as temporal variations. Using a time bin of 12 h ensures that a full orbit is sampled.

Discussion and Interpretation
The results demonstrate clear and statistically significant changes in the energy content, both in magnitude as well as local time distribution. Prior to the storm peak and during the main phase, the ring current undergoes large global enhancements with the energy content more than doubling in some regions. Interestingly, the L shell dependence is observed to be relatively independent of storm phase, where the L profile shown in Figure 2b is similar for both storm times and quiet times. The peak in energy content does not demonstrate any observable change in L location. Although some previous work suggests that the peak moves Earthwards during storm times (e.g., Hamilton et al., 1988;Roeder et al., 1996), Zhao et al. (2015) observes that the energy density peak does not exhibit substantial changes in L position. Zhao et al. (2015) asserts that although the low energy ion contribution is significant during storm times and moves to lower L values, the higher energy (more than few hundred keV) H + contribution that is neglected in some studies does not change significantly in L location. Therefore, the higher energy ions continue to control the location of the ring current energy peak and, especially for small and moderate storms, are critical in determining the L distribution of energy content. The results shown here support the conclusions of Zhao et al. (2015), and suggests that the higher energy ions are dominant in shaping the L profile on a statistical basis.
In terms of the MLT distribution, Figures 5 and 7 demonstrate that during the main phase, the energy content is highly asymmetric and the values peak in the premidnight sector. This feature is well documented and attributed to the enhanced supply of plasma from the nightside plasma sheet via injection and convection (e.g., Antonova & Ganushkina, 1997;Buzulukova et al., 2010;Ebihara & Ejiri, 2000;Ebihara et al., 2002;Fok et al., 1996;Katus et al., 2013;Li et al., 2011;Lui, 2003;Perez et al., 2012). Due to strongly enhanced electric fields in the inner magnetosphere, the ring current is dominated by ions on open drift SANDHU ET AL.  paths. Ions enter the inner magnetosphere on the nightside, experience westward drift, and are lost to the duskside magnetopause, thus generating the local time asymmetry (Liemohn et al., 2001(Liemohn et al., , 2015Milillo et al., 2003;Mouikis et al., 2019;Takahashi et al., 1990).
Closely following the storm peak (3 ≤ t 0 < 9 h), the ring current becomes more symmetric. Figure 5 shows enhancements on the nightside corresponding to continued and increased transport of plasma from the nightside plasma sheet. Relative enhancements on the dayside arise from a subsidizing of the convection electric field, allowing ions to be trapped on closed drift paths and access all local time sectors (e.g., Daglis et al., 2003;Liemohn et al., 2001). The drift of ions from the duskside on closed drift paths acts to reduce the local time asymmetry (Antonova et al., 2014;Ebihara & Ejiri, 2000). Throughout the recovery phase, the ring current asymmetry continues to decrease as the ions drift and populate all local time sectors (Ebihara & Ejiri, 2000). The energy content gradually reduces due to a multitude of ring current loss process, namely charge exchange (Antonova, 2006;Dessler & Parker, 1959;Hamilton et al., 1988;Welling et al., 2015).

Discrepancies Between the Ring Current Energy Content and the Ring Current Indices
Although both the in-situ observations and energy values derived using the DPS relation with ring current indices show the same general trends, where the energy content increases during the main phase then gradually reduces in the recovery phase, there are also significant discrepancies in the magnitude and temporal variations. These are clearly apparent from Figure 6a. We find that during the storm period, the in-situ estimates are ∼50% smaller than the estimates using Sym-H and Sym-H*, and are almost 4 times smaller at the storm peak.
The observed discrepancy may initially appear to contradict some previous results. For example, Greenspan and Hamilton (2000) show that, on average, during geomagnetic storms the DPS relation is upheld with no significant discrepancy between the Dst index and in-situ measurements. However, a key factor relating to the Greenspan and Hamilton (2000) study and others is that the statistical analyses consider the full storm interval and instead order observations using ring current indices (whereas in this study we separate samples according to storm phase). Due to the comparatively longer duration of the recovery phase compared to the main phase, the statistical storm time analysis will be mostly represented by recovery phase samples. The results shown here suggest that the statistically significant discrepancy with the DPS relation predominantly occurs in a relatively small period of time compared to the storm length and compared to the recovery phase duration. Therefore, we suggest that time periods where the DPS relation is not a good description is not statistically significant when Greenspan and Hamilton (2000) and others consider the full storm period. On this basis, it is justified that these results do not necessarily contradict previous work, but instead highlights the capabilities of different analysis techniques to understand the temporal evolution during geomagnetic storms. Furthermore, previous studies also report a difference in magnitude between observed ring current energy content and values derived from ring current indices with the DPS relation. For example, Hamilton et al. (1988) observes that ring current energy content ranges from 1 to 4 times smaller than the estimates using the DPS relation applied to the Dst index. Previous work attributes discrepancies in the magnitude to a variety of factors, which will now be discussed in the context of this study.

Unrepresentative in-Situ Estimates
The in-situ estimates of ring current energy content assume that the total energy is contributed by ions within an L range from 3 to 7. If these assumptions disregard a population or region that contributes a substantial amount of energy to the ring current, then the approach will underestimate the total ring current energy content. Although it is assumed that the ring current is carried solely by ions and neglects electron contributions, results from Zhao et al. (2016) show that this is a reasonable premise. Zhao et al. (2016) demonstrated the electrons contribute ∼12% of the energy content for a moderate storm, and even less for intense storms. The electron contribution is clearly insufficient to be dominating the observed discrepancy.
In terms of the L range considered, Zhao et al. (2015) identified that ring current ions at radial distances outside the Van Allen Probe coverage have a very small contribution due to the steep radial gradient in energy density. Therefore, we conclude that the L range is not excluding a substantial portion of the ring current energy density.

Contributions From Other Current Systems
A breadth of the published literature demonstrates that the Sym-H index includes significant contributions from additional magnetospheric current systems: 1. Internal magnetic fields: Dessler and Parker (1959) showed that for a perfectly diamagnetic Earth, the magnetic field perturbation is multiplied by ∼50% at the equator. Langel and Estes (1985) suggested that the observed ring current indices should be multiplied by 0.3-0.5 in order to mitigate for this contribution. 2. The magnetopause: Enhancements in the magnetopause current contribute positively to the measured magnetic field perturbation, as demonstrated by strong correlations between the solar wind dynamic pressure and ring current indices (Stepanova et al., 2019). In order to account for this contribution, Burton et al. (1975) suggested the use of a corrected ring current index. However, Figure 6a shows that the discrepancy persists. 3. The substorm current wedge: When a substorm current wedge is present, ground magnetometer stations located outside the wedge experience an additional negative perturbation and stations located inside the wedge experience a positive perturbation. If the station coverage is uniform, then this effect is averaged out. If station coverage is limited, then the contribution from the substorm current wedge can be significant, with reports that the perturbation is comparable to the tail current effects (Friedrich et al., 1999;Munsami, 2000). The Sym-H index is derived from only six magnetometer stations, suggesting that the substorm current wedge effects could be important. However, the large similarity in results when the SMR index is used instead (derived from ∼100 stations (Newell & Gjerloev, 2012)), indicates that this is unlikely to be the dominant driver of the discrepancy with in-situ estimates. 4. The tail current: As previously mentioned, preceding work shows that the tail current is a significant contributor to the observed ring current indices, representing ∼25% of the measured perturbation (e.g., Turner et al., 2000). Dubyagin et al. (2014) observed a nearly linear relationship between the ring current index and the tail current contribution, and concluded that the tail current is a dominant factor compared to the other additional current systems. Furthermore, Kalegaev et al. (2005) establishes that during moderate storm times, the tail current and ring current contributions to ring current indices are comparable, although the tail current contribution is less important for intense storms. Figure 6a shows a temporal discrepancy, where the in-situ energy content estimation peaks, on average, at a later time (3 ≤ t 0 < 9 h) than estimates using the Sym-H index. From an examination of in-situ tail current observations, Ohtani et al. (2001) found that there is a tendency for a substorm onset to occur at the storm peak. The authors suggest that the associated reduction of the tail current following substorm onset drives a corresponding reduction in the magnitude of the observed Sym-H index (see also Friedrich et al., 1999;Iyemori & Rao, 1996). Therefore, Ohtani et al. (2001) concluded that the start of the recovery phase (or equivalently the time of the storm peak), where the Sym-H index begins to increase, is due to the tail current dynamics and independent of the ring current intensity. Furthermore, Ohtani et al. (2001) suggest that a substorm onset would act to increase the ring current enhancement following the storm peak through substorm-associated ion injections. They also noted that the estimates of the tail current contribution are restricted by spacecraft coverage. The contribution to the Sym-H index is likely to be even larger as they cannot measure how widely and completely the tail current is disrupted. This effect is also supported by modeling results, where Kalegaev et al. (2005) showed that the tail current begins to decay while the ring current continues intensifying during a storm. The substorm-related recovery of the tail current was estimated to cause an increase in the Dst index by ∼50 nT for a moderate storm.

The Role of Substorms
However, the analysis conducted by Ohtani et al. (2001) considered the effect of a single substorm and showed that the storm peak in Sym-H would be shifted by ∼1 h earlier (time scale for a substorm). To support the observations shown in Figure 6a, where the storm peak is shifted by several hours, we require a sustained and continued period of substorm activity. This is confirmed by Figures 6b and 6c. We observe substorm activity throughout storms, but the frequency and substorm size clearly maximizes at the storm peak. The high level of substorm activity not only reduces the tail current contribution, but also enhances the supply of plasma to the ring current region. Substorms are associated with long lived and substantial enhancements in ring current ion fluxes through enhanced convection and injection events (e.g., Sandhu et al., 2019;Yue et al., 2018). For example, Gkioulidou et al. (2014) demonstrates that substorms play a crucial role in contributing to and building up ring current energy content during geomagnetic storms. The continued transport of plasma from the nightside plasma sheet is evident from the nightside enhancements following the storm peak (Figure 4d). Figure 9i provides an example of continued ring current energization following the storm peak. Figure 9b shows both enhanced convection as well as intensified levels of substorm activity throughout the main phase and around the storm peak. The substorm identifications shown in Figure 9c demonstrate that as well as heightened substorm occurrence (eight substorms occurring close to the storm peak), the average size of these substorms is slightly increased with an average ΔSML ∼ −300 nT. The magnetic field observations at geosynchronous orbit, provided by the GOES 15 spacecraft and shown in Figure 9c, indicate coincident dipolarization signatures on the nightside and provides support for the enhanced level of substorm activity during the main phase. The frequency and size of substorms then subsides during the recovery phase (Figures 9b-9d).
In contrast, Figure 8i shows that the ring current energy content peak is coincident with the storm peak. For this storm, there is significant substorm activity during the early main phase (five substorms with an average size of ∼800 nT) which is reflected in slight positive perturbations in the Sym-H trace (Figures 8a-8d). However, at the storm peak, the level of substorm activity is considerably decreased. Comparing Figure 8c to Figure 9c reveals that the average substorm size is approximately halved. However, during the recovery phase the number of substorms is markedly elevated. High numbers of substorms are observed with coincident dipolarization signatures (Figures 8c and 8d). For this storm, we suggest that the low level of substorm activity during the end of the main phase did not significantly change the tail current. The start of the recovery phase in the Sym-H index is not thought to be driven by tail current dynamics, and instead is driven by the ring current. Although there is observed substorm activity during the recovery phase and the early main phase, the dynamics at the storm peak would be the key factor for causing an early recovery in the Sym-H index and generating a temporal discrepancy between the Sym-H index and the in-situ energy values.
Overall, Figures 8 and 9 show that although the Sym-H trace tends to show similar temporal trends, the ring current energy content variation with time is more variable. This variability in the level of agreement between the in-situ observations and Sym-H trace is further supported by additional case studies (not shown here for brevity). We suggest that the varying timing discrepancy between the storm peak and the maximum in ring current energy content may be dominated by varying levels of substorm activity during a storm. A comparison between Figures 8b and 8c and 9b and 9c shows that the level of substorm activity varies significantly between individual storm events, so the dominance of the tail current dynamics close to the storm peak is expected to also vary substantially between events.
As the energy content maxima occurs at varying times relative to the storm peak, the superposed epoch analysis approach has averaged over peaks occurring at different points. This leads to the very broad peak in energy content shown in Figure 6a. In order to further investigate when the ring current energy content peaks, without applying assumptions of local time asymmetries on a spacecraft sampling a single MLT sector, we require global, multipoint measurements of the inner magnetosphere. Future work will focus on multispacecraft analysis of the ring current during storm times to investigate the temporal profiles further.

Conclusions
Spatial variations in energy content during geomagnetic storms were explored using observations from the HOPE and RBSPICE instruments onboard the Van Allen Probes. The presence of an asymmetric ring current, with significant energy enhancements in the premidnight MLT sector, agrees with previous work and provide information on ion trajectories in the inner magnetosphere. The distribution of energy content with L shows little change with storm phase, supporting previous results that the high energy population dominates the peak location.
A superposed epoch analysis revealed important discrepancies between in-situ energy content measurements and estimated values using ring current indices. In agreement with previous results, the Sym-H index combined with the DPS relation severely overestimates the ring current energy content. Statistically, there are substantial temporal discrepancies, such that energies estimated using the Sym-H index peak at an earlier time than the ring current energy content. The magnitude of this discrepancy is on average between 3 and 9 h, and a suggested cause is intense substorm activity occurring at the end of the main phase. The discrepancies in magnitude and timing persist for the Sym-H* index, the Dst index, the SMR index, and the partial SMR indices. An analysis of case studies shows that level of agreement between the ring current indices and the ring current energy content is highly variable. We emphasize that the substorm-ring current relationship is complicated. Although previous studies (e.g., Ohtani et al., 2001) provides some basis for the proposed mechanisms, further quantitative analysis of the tail current contribution to the Sym-H index is essential for validating the suggested role of substorm activity.
Overall, this work highlights the level of variability across storms, and proposes the importance of substorms in inner magnetospheric dynamics. We challenge the use of the Sym-H index to directly infer temporal variations in the ring current intensity and highlight potential issues with using ring current indices to organize storm time behavior (Borovsky & Shprits, 2017; "Exploration of a Composite Index to Describe Magnetospheric Activity: Reduction of the Magnetospheric State Vector to a Single Scalar," 2018). In order to fully understand the drivers of the Sym-H index and the cause of these reported discrepancies, future work will involve a corresponding investigation into the role of the tail current during storm times, as well as focusing on how the Sym-H index may be corrected to account for nonring current contributions.