Corresponding author: S. Vennerstrom, National Space Institute, Technical University of Denmark, Elektrovej 328, 2800 Kgs. Lyngby, Denmark. (firstname.lastname@example.org)
 The strong horizontal ionospheric currents in the auroral oval constitute an important space weather parameter. Here we present a method to estimate the latitude location and intensity of these currents from measurements of variations in the magnetic field magnitude made by low Earth polar orbiting satellites. The method is simple enough to be implemented for real-time monitoring, especially since it does not require the full vector field measurement. We demonstrate the method on 5 years of Challenging Minisatellite Payload (CHAMP) data and show how the monitoring depends on the local time of the satellite orbit and how it varies with local time and season in both hemispheres. Statistically, the strongest currents are observed in the predawn and predusk local time quadrants at latitudes that depend on the general magnetic activity level. We also show how the satellite-derived parameters relate to and complement existing ground-based indices. The CHAMP magnetometer in 350–450km altitude easily measures an electrojet which on the ground would produce an Auroral Electrojet (AE)-type signal as small as 20 nT. Thus, while the signal decreases roughly proportionally to the square of the distance to the current, this does not significantly affect the utility of the method for space weather applications even for satellites at substantially higher altitudes. The results for several individual magnetic storm periods demonstrate that large variability can exist in both the latitude and intensity of the currents during the progression of a storm. In the storms analyzed, the latitude of the strongest observed currents are seen to vary between 52° and 84° magnetic latitude.
 Horizontal currents flowing in the high-latitude ionospheres constitute an important space weather parameter. They are a major contributor to space weather effects such as the generation of geomagnetically induced currents and increased drag on low-altitude spacecraft through atmospheric heating, see, e.g., Pirjola et al.  and Liu and Luhr . The most intense currents in the ionosphere are the auroral electrojets that flow approximately in the auroral oval, predominantly as an eastward current in the dusk side of the oval and a westward current in the dawn side. The westward electrojet is occasionally fed by the closure of the substorm current wedge [Baker, 1986; Newell and Gjerloev, 2011] and, therefore, is where, over all, the most intense currents are found. The ionospheric currents can be determined very reliably from ground-based magnetic measurements. This has been used successfully in a wealth of science investigations of the solar wind-magnetosphere-ionosphere interactions (see, e.g., Moretto et al. ; Weygand and Zesta ; Gjerloev et al.  for some recent examples). It is also the basis for the auroral electrojet indices (AU, AL, and AE) designed by Davis and Sugiura , which have been used since the late 1960s for routine monitoring of the ionospheric currents in the auroral oval region. The indices are based on a ring of stations distributed roughly evenly in longitude around the globe and at magnetic latitudes (MLAT) between 60° and 71°. The limitation in the indices to capture the electrojet currents during very active times when the strongest currents will be located equatorward of the stations, or during quiet times when they will contract poleward of the stations, was recognized early on and has been the subject of many discussions since then [Rostoker, 1972; Kamide and Akasofu, 1983; Ahn et al., 2000; Kauristi et al., 1996]. Similarly, the stations are not distributed densely and evenly enough in longitude to provide equally good coverage in all longitude sectors. Therefore, the measurements, as well as the indices derived from them, may be plagued by local time aliasing as the stations turn with the Earth. Especially, even if all land masses were to be well covered, large gaps would likely remain over the oceans. Finally, by design, the indices are for the Northern Hemisphere only and, thus, cannot measure any differences that may exist between the Southern and Northern Hemispheres. As illustrated in Newell and Gjerloev  utilizing the global network of more than 100 ground stations participating in the SuperMAG project, extended and improved auroral electrojet indices can be derived that overcome some of the shortcomings of the original AE indices, both in their latitudinal and longitudinal coverages. However, significant gaps still exist, making the indices not free from local time biasing. Particularly, only a few local time sectors are covered with dense enough meridional chains of stations to allow for the determination of the latitude of the strongest signal with useful range and precision. In addition, the coverage for the Southern Hemisphere is still very sparse.
 Just as on the ground, the magnetic effect of the horizontal ionospheric currents in the auroral electrojets can be observed by low-altitude, near-polar orbiting satellites. The utility of this was first demonstrated with data from the MAGSAT satellite by Olsen  and was further explored with data from the Oersted, Challenging Minisatellite Payload (CHAMP), and SAC-C satellite missions by Moretto et al. . More recently, Juusola et al.  presented a method to estimate both the horizontal and field-aligned currents in the auroral ionosphere from the full vector magnetic field measurements from the CHAMP satellite. They used this to investigate the statistical behavior of these currents based on 5 years of CHAMP measurements. In this paper we pursue a different approach based on the much simpler measurement of perturbations only in magnetic field strength. Specifically, we show how these measurements can be used to estimate the latitude location and also provide a rough measure of the intensity of the strongest ionospheric current observed for each auroral crossing of the satellite. By using only the magnetic field strength measurements, we avoid any problems of obtaining continually high precision attitude information for the field measurements. While this is not a big problem for the CHAMP satellite, it greatly simplifies the requirements imposed on any other current or future missions for which one might want to adopt the method. In turn, this also greatly improves the accuracy and easy, near-real-time availability of measurements from such missions. We illustrate the results from this method on the same 5 years of CHAMP data that was used in Juusola et al. . The satellite-based measure proposed here would complement the ground-based electrojet indices as a monitoring tool for auroral electrojet currents: one which does not have the local time aliasing problem (staying in fairly fixed local time zones throughout events), that has full, high-resolution meridional coverage (ability to locate the latitude of the strongest signal with better than 1° accuracy), and that covers both hemispheres equally.
2 Method and Data
 An extended horizontal line current in the ionosphere will produce a distinct magnetic signature in a near-vertical magnetic field component measured by a crossing satellite some few hundred kilometers above it. This is the premise of the measure we propose here and is illustrated in Figure 1. The maximum of the gradient in a near-vertical component of the magnetic field measured along the satellite track across the current provides an estimate for the location and strength of the current. Measuring the gradient in a magnetic field component aligned with the internal Earth magnetic field, rather than in the strictly vertical component, introduces a systematic shift toward lower latitude in the location of the maximum, as demonstrated in the figure, that can easily be calculated and corrected for.
 The Challenging Minisatellite Payload (CHAMP) was launched in July 2000 [Reigber et al., 2002] into a near-circular polar orbit (87° inclination) with an initial altitude of 454 km that had decreased to roughly 350 km by the end of 2005. The orbital period is about 1.5 h, resulting in more than 15 revolutions per day and as many crossings of the auroral region in two local time sectors and in both the Southern and Northern Hemispheres. The orbit plane drifts roughly 3 h in local time every month to cover all local time sectors in 131 days.
 In this study we use the high-accuracy magnetic field measurements from CHAMP. However, as stated above, we do not use the full vector magnetic field measurements but, rather, only the field strength. Estimates of magnetic field strength perturbations are obtained by subtracting from the measured field strength value the contribution from the Earth's internal magnetic field, using an advanced updated model [Olsen et al., 2006] that also accounts for contributions from a symmetric ring current as well as some other large-scale magnetospheric contributions.
 Following Olsen , we assume that only horizontal ionospheric currents (not field-aligned currents flowing into and out of the ionosphere) contribute to the parallel component of the magnetic field as measured by the satellite. Furthermore, as demonstrated in Olsen  and Moretto et al. , in the strong Earth magnetic field, to a very good approximation, only the field-aligned (parallel) component contributes to the absolute value of the field. Consequently, perturbations in magnetic field strength measurements along the satellite track can be used to estimate perturbations in the field-aligned component and, thus, to determine the maximum gradients that signal the latitude location and strength of the most intense auroral currents. As illustrated in Figure 2, the maximum gradient in the magnetic field strength over an oval crossing of the satellite is a consistent, clear signal in the data that tracks very well, orbit by orbit, the expected location and strength of the dominating ionospheric electrojet current. A dynamic succession of intensifications and equatorward progressions followed by poleward retractions and reweakenings is readily apparent in the gradient maxima and matches the behavior expected for the electrojet during varying geomagnetic activity.
 The amplitude of the signal in the gradient as well as the latitude correction indicated in Figure 1 depends on the satellite altitude. To derive a consistent quantitative measure, therefore, these must be normalized. We do this simply by assigning to each estimated gradient maximum the location and strength values for the infinite line current flowing along magnetic latitude circles that reproduce the observed maximum (location and amplitude) for that particular satellite track. In this way, each identified maximum gradient gets assigned consistent magnetic latitude and normalized amplitude (in units of Amp) measures that can be combined and analyzed statistically over all satellite orbits. It is important to note that while a line current amplitude is calculated to normalize the maximum gradient signal in the measured magnetic field, it does not follow that this line current amplitude is a good estimate for the total current in the ionosphere that causes the measured field signal. As is evident when comparing the signals in Figures 1 and 2, the measured magnetic signal is typically wider than the signal from a single line current, implying that the amplitude measure from this method will underestimate the total current.
 The application of this method to CHAMP observations is demonstrated in Figure 3. The top example illustrates the sensitivity of the measurements and the method with a very low amplitude signal. The normalized amplitude for this event is 11 kA, which is just above the threshold of 10 kA that we apply as the minimum amplitude to include in the large statistical study. To put this in perspective, an infinite line current of 10 kA flowing in the ionosphere at a height of 100 km would cause a horizontal deflection (AE-type signal) of about 20 nT in a magnetometer on the ground. Examining the 1 min AE data for the last two solar cycles (1990–2012), values of AE less than or equal to 20 nT count for only 5.5% of this entire data set. Thus, the application of this threshold does not limit the effectiveness of the method for space weather applications in any significant way. Further, this example illustrates that the threshold of 10 kA is not at the limit of the sensitivity of the method as applied to CHAMP measurements. The successful detection of this low amplitude signal requires the capability to measure a gradient in the magnetic field magnitude of roughly 20 nT over about 1000 km along the orbit. However, it is clear from the figure that even a signal of much smaller magnitude would be easily measurable in the data. Sensitivity of the measurement is not what determines the threshold. Rather, the threshold is required to ensure that the maximum gradient that gets identified is likely to be from an auroral electrojet current. Below this threshold, other sources, especially at lower latitudes, produce comparable signals that can potentially lead to erroneously low latitudes for our electrojet measure. The middle example is of a typical pass. Two gradient extrema of opposite polarity are present: a larger amplitude one at auroral latitudes together with a weaker amplitude one at higher latitudes. The normalized amplitude of the maximum gradient is 93 kA. The final example at the bottom illustrates a situation when two opposite gradient signals of comparable strength are observed. The primary maximum (marked with a black dot as for the previous events) has a normalized amplitude of 58 kA. The secondary maximum is marked with a triangle in the figure. In cases like this, when the amplitude of the secondary maximum is greater than 75% of the amplitude of the primary, we mark up the primary maximum and record also the information for the secondary maximum.
 In general, mark-ups result whenever a single maximum gradient in B is not clearly identified. Most of the time, this happens because a secondary maximum of almost the same amplitude but of the opposite polarity as the primary maximum is observed, as is the case for the example in Figure 3. This could result, for example, by the eastward and westward electrojects overlapping, or a cusp current developing at higher latitudes at the same time as an electroject exists at lower latitude. Other times, it is caused by more than one maximum of the same polarity being identified, which would correspond to two separate currents flowing in the same direction being present at the same time. When monitoring orbit by orbit in these situations, the maximum can jump between two or more concurrent local maxima, leading to jumps in the overall maximum latitude and corresponding amplitude. It is important to note that this does not mean that the method provides a wrong location or amplitude but only that in these situations, other significant maxima exist, presumably indicating additional significant currents at other latitudes.
 We apply the method to 5 years of CHAMP data. This provides nearly 100.000 individual current estimates, roughly equally divided between the Northern and Southern Hemispheres and each corresponding to an individual oval crossing. Roughly 20% of the estimates are marked up as having significant secondary maxima as described above.
3 Results of Statistical Analysis
 The resulting distribution from the entire data set of the latitudes at which the maximum current signature is observed is displayed in Figure 4. The maps illustrate that the satellite measurements provide maximum current signatures at all longitudes in both hemispheres. Similar to the auroral oval, the latitudes at which the maximum current signatures appear depend on the magnetic activity level but also on the geographic longitude sector and are significantly different in the two hemispheres. During quiet times, the maximum current, as determined with the method used here, is observed at latitudes close to the poles, between 60° and 80° in the north and correspondingly in the south, with the lowest median latitudes located in the North American sector in the north and the Australian sector in the south The same general pattern is observed for higher activity levels. During strong activity, the most likely locations of the maximum current generally move equatorward, down to 55°, again moving more equatorward in the North American and Indian/Australian longitude sectors. The width of the oval in the south appears more asymmetric than in the north, presumably due to the larger displacement of the magnetic pole from the geographic pole in the south. Closeness to the geographic pole is limited by the satellite inclination (87° means 3° from the pole). This may affect the observations of the oval in the south closest to the pole.
 To present an overview of the amplitude of the maximum current signature, we order the data by magnetic latitude and local time (MLT). This makes most differences between the two hemispheres disappear in the statistics and, therefore, the whole data set is plotted together. The resulting MLAT, MLT maps for each of the three activity levels are displayed in Figure 5. As observed in the geographic plots, the maximum current signatures are observed in an oval that expands with magnetic activity level. During quiet conditions, the median MLAT of the maximum current signature is located between 69 and 79 as a function of MLT. During moderately active periods, the median latitudes are between 66° and 76°, and during magnetic storm conditions, the median latitudes are between 63° and 73°. These results are consistent with the locations of the oval based on the field-aligned currents that are quoted in Juusola et al.  and also with the results of Ahn et al. . As indicated by the width of the displayed oval, there is quite a large spread in the observed latitudes and individual signatures can be observed far further poleward or equatorward than the median location. This will be demonstrated in the event studies that we present in the following section.
 Similarly to the latitudes, amplitude levels for the maximum current signatures vary systematically with magnetic activity level and with MLT sector. During quiet conditions, the median amplitude is between 22 and 30 kA, with the highest values found around 02–08 MLT, a second local maximum around 14–16 MLT, and the lowest values found around 19–22 MLT. During moderately active periods, the median amplitude is between 35 and 70 kA, with the highest values around 01–06 MLT and a second local maximum at 14–19 MLT, and with the lowest values around 09–12 MLT. During magnetic storm conditions, the median amplitude varies between 60 and 160 kA, with the same variations in local time as for the moderately active periods. Averaging over all local times, the median intensity increases by a factor of 4 from the low to the high activity bin. Correspondingly, for the field-aligned currents, Juusola et al.  report a factor 7 increase between Kp=0 and Kp>=5.
 While the overall differences between the Northern and Southern Hemispheres disappear in the statistics when ordering the data in magnetic coordinates, large differences between the hemispheres can still exist at any individual time. One obvious component of this is a seasonal effect. This is illustrated in Figure 6. The nightside currents increase only slightly (by a factor of 1.1) between winter and summer. In contrast, a large increase (by a factor of 1.9) is observed for the dayside (cusp) currents between winter and summer conditions. This is in agreement with the results of Juusola et al.  for the field-aligned currents.
 As one might expect, the maximum current signature for the Northern Hemisphere is fairly well correlated with the traditional auroral electrojet measure, the AE index. This is illustrated in Figure 7. Given the features of the AE index discussed in the introduction, the correlation is expected to depend both on MLT and on the latitude where the maximum current signature is observed. The results in Figure 7 confirm this. The best correlation is found with satellite measurements in the 00–06 MLT quadrant, consistent with this being the local time sector that most often provides the AE measurement [Kauristi et al., 1996; Gjerloev et al., 2004; Ahn et al., 2005]. Similarly, when the satellite observes maximum current signatures at latitudes that correspond to the location of the AE stations, that is between 60° and 70° MLAT, the correlation is better than when the satellite maximum current signature is observed at higher latitudes. These results show that in the appropriate local time sector and at appropriate latitudes of the current, the satellite maximum current measure captures the activity as well as the AE index. However, in addition, the satellite current measure can provide estimates also in other local time sectors, at all latitudes, and in the Southern Hemisphere. In these ways, it complements AE.
4 Results of Event Studies
 For a specific local time sector and hemisphere, the satellite provides a latitude location and an amplitude for the maximum current signature roughly every 90 min. One satellite monitors two separate local time sectors in each hemisphere in this way. We illustrate this capability through a selection of four individual magnetic storm periods.
 The first event, shown in Figure 8, is a fairly short-lived, well-defined magnetic storm on 15 May 2005. The Dst index for the storm period is displayed in the bottom panel. It reaches a minimum value of −260 nT, which would characterize this as a major storm. This storm exhibited striking and unique substorm behavior and auroral features that are discussed in Lyons et al.  and Lazutin and Kuznetsov . Latitude and amplitude estimates for the maximum current signature are shown (top two panels) for the Southern Hemisphere in a local time sector that spans the interval 08–12 MLT. The gaps in data during the first part of the plots result because no signal of amplitude greater than the threshold of 10 kA were found for those crossings. It is observed that the amplitude starts to build at high latitudes and the latitudes migrate equatorward before the main drop in Dst that indicates the start of the main phase. There is a strong and prolonged compression signature in Dst ahead of the main phase. This is associated with the first observed spike in amplitude and equatorward progression of the latitude signal. The second amplitude intensification and further equatorward progression of the latitudes are associated with the main phase of the storm. This amplitude spike is larger, reaching values of around 400 kA. The equatorward progression of latitudes continues into the recovery phase of the storm, even beyond the peak in amplitude, reaching a minimum latitude just below 60° (southern) MLAT. Storm recovery is observed as a relocation of the latitude back to higher latitudes. However, it starts with the only “marked” signature observed in the event. This results because two comparable maximum signatures are present, a primary at very low latitudes (shown as a dot with circle) and a secondary at very high latitudes (shown as a star), respectively. This evolution indicates the appearance of a new separate current system at high latitudes that gradually increases in intensity at the same time as the storm-related current system at lower latitude is fading. The latitude and amplitude variations observed toward the end of the period illustrate how typical nonstorm related auroral activity is captured in the maximum current signature.
 The results from another major storm event on 4–7 November 2001 are displayed in Figure 9. Minimum Dst for this storm is −290 nT. This time, we show results from monitoring the Northern Hemisphere in a local time sector spanning 05–10 MLT. Again, gaps in the latitude and amplitude data result from the sensitivity threshold of 10 kA that we apply for the amplitude. General auroral activity and dynamics before and after the main phase of the storm are also illustrated in this event. As for the previous storm, the main phase of the storm is associated with an equatorward progression of the latitude, again reaching a minimum latitude of just below 60° MLAT, and an increase in amplitude of the maximum current signature. An outstanding feature of this storm, however, is the very large amplitude peak, reaching 600 kA, that is observed during the main phase. Another very interesting feature is the abrupt poleward relocations of the current signature that occurs early in the recovery phase of the storm, reaching latitudes above 80° MLAT. This dynamic is the result of sharp and strong variations in the north-south component of the interplanetary magnetic field that also cause interesting auroral features as described in lyons et al., . We note that the dramatic variations in the latitude location of the maximum current signature are not at all reflected in the Dst index and also would not be possible to capture with the traditional AE index.
 Our third example event is a weaker storm during 21–25 June 2005, for which we show in Figure 10 the results of monitoring the Northern Hemisphere in the local time sector spanning 03–07 MLT. Minimum Dst for this storm is only −90 nT. Correspondingly, the extremes in the latitude and amplitude signatures are smaller than observed in the previous two events, reaching a minimum latitude of 63° MLAT and a maximum amplitude just below 200 kA. The general evolution of the signatures through the storm as well as the dynamic features observed throughout the event, however, are very similar in nature to the previous examples.
 The last example we show is for the so-called Halloween storm from 29 October to 3 November 2003. This storm has been heralded as the most powerful storm of the last solar cycle as well as one of the most interesting episodes of solar activity observed during the space age and has been the subject of intense reporting [Tretkoff, 2010] and scientific investigation. For an overview of the event, see, for example, Toth et al.  and Pulkkinen et al. , and references therein. The results from the Southern Hemisphere in a local time sector spanning 10–14 MLT are displayed in Figure 11. Even though this is a very powerful storm, with Dst reaching a minimum of −380 nT, the maximum amplitude observed is only slightly above 400 kA. This is significantly lower than what was observed for the storm of November 2001 in Figure 9. The likely explanation for this is that the results in Figure 11 are recorded near noon local time as opposed to the dawn sector results shown in Figure 9. In fact, maximum current signature amplitudes for the Halloween storm recorded by the satellite near midnight local time do reach 600 kA (not shown). A striking feature of the signature during this storm is that it migrates to very low latitudes, reaching a minimum southern latitude of 52° MLAT. The fact that this is observed near noon local time makes this result even more remarkable [Feldstein, 1997 and Ahn et al., 2000]. It is perfectly consistent, though, with the results for a March, 2001 storm reported by Wang et al. . They also used the CHAMP magnetic field data to locate the auroral electrojet centers and saw them expand to below 55 MLAT during this intense storm. In addition, they report that the times when the largest current densities are observed do not always coincide with the times when the electrojet is furthest equatorward. The same is true for all four events presented here. None of them has the minimum latitude and maximum amplitude in the signatures coincide. Finally, we note the many occurrences of close secondary maxima for this event. As before, this is an indication of the complex dynamic nature of the current systems that are typically observed during active times and, especially, in this local time sector (cusp region).
 We have presented a simple way to utilize geomagnetic measurements from low-altitude polar orbiting satellites for monitoring of the auroral electrojet currents. Our method utilizes the very basic measurement of magnetic field intensity along the orbit track. Typically, such measurements are more readily available, are accurate and stable, and have much fewer problems with data gaps than data sets of the full magnetic field vector measurements. This is true in particular for real-time or near-real-time application. A simple signature for the latitude location and amplitude of the most intense ionospheric current encountered in each auroral crossing was derived from these measurements. It was demonstrated that this maximum current signature constitutes a promising electrojet monitoring tool.
 In contrast to ground-based magnetic measurements, including from meridional chains, the satellite monitor stays in the same local time sectors throughout an event. This means that it can capture the large-scale dynamics in specific important local time sectors and it avoids the ambiguity of local time variations in the observations of this dynamic behavior. It also monitors the Southern Hemisphere equally with the Northern, something which cannot be done by ground-based measurements. Our results confirm that this is necessary as significant differences can exist between the electrojets in the two hemispheres at any given time. In contrast to other more advanced satellite-based methods, as explored, for example, in Moretto et al. , Wang et al. , and Juusola et al. , our method has the advantage of being simple enough to be easily implemented for real-time operations. Our results illustrate that large amplitudes and highly dynamic latitude displacements of the current signatures occur over a wide range of local times and latitudes.
 The statistical properties of the signature were examined using 5 years of CHAMP measurements that included some of the largest magnetic storm periods of the last solar cycle. This verified that the signature provides consistent monitoring of the electrojet over all geographic locations, at all latitudes, and at all local times. The existing database of CHAMP measurements, now covering more than 10 years, can be used to develop a statistical model for the signature. Such a model would provide the probability of encountering maximum current signatures of a certain intensity at a given location depending on solar wind or geomagnetic activity parameters. If based on upstream solar wind parameters, it could be used as a predictive tool. This is something that we will explore in future work.
 The CHAMP satellite at 350–450 km altitude is orbiting at lower altitude than most other current and recent polar orbiting satellites. In considering the applicability of the method we propose here to other satellite measurements, it is necessary to examine the effect of altitude on the signal. A satellite orbiting at 700 km altitude is twice the distance from the current source, at roughly 100 km, as compared to CHAMP at 400km and would observe a signal (maximum gradient) from the same infinite line current of a fifth of the amplitude. Our results for CHAMP indicate that this is still possible but is at the limit of the instrument sensitivity with the threshold of 10 kA for the lowest signal that we have applied in this study. However, as we have shown, this threshold corresponds to extremely weak electrojet currents (associated with roughly a 20 nT ground signal). For space weather applications, it is not important to measure the intensity and location of these very weakest electrojet currents. The mere knowledge that currents are very weak (below a certain threshold) is sufficient. Thus, even a significantly higher threshold would be equally useful in this context. Consequently, we feel safe in concluding that the method would work for space weather monitoring with a CHAMP instrument flying at higher altitude. However, for other instruments and satellites, no matter whether in lower or higher orbits, there may be other error sources that need to be accounted for. The application of the method to other satellite magnetometer data sets is something we plan for the future. In fact, preparation for the upcoming Swarm mission (which will fly CHAMP-grade instruments at similar and slightly higher altitudes) is a main motivator for this work.
 The operational support of the CHAMP mission by the German Aerospace Center (DLR) and the financial support for the CHAMP data processing by the German Federal Ministry of Education and Research (BMBF) are gratefully acknowledged, as is also the support of GeoForshungsZentrum Potsdam (GFZ). The research leading to the results presented in this paper has received funding from European Community Seventh Framework Programme (FP7:2007–2013) under grant agreement 218816. This material is based upon work supported by the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.