Swarm is a three-satellite mission of the European Space Agency to study the Earth's magnetic field . Two of the satellites (Alpha and Charlie) were launched to fly side by side with an initial orbital height of 430 km, whereas the third (Bravo) has an orbital height of 530 km. The Swarm-AEBS product is based on the measurements of the Vector Field Magnetometer . We use the Swarm-AEBS product data for the Northern Hemisphere and for Swarm Alpha and Bravo. The data from Charlie are almost identical to those from Alpha; thus, using both Alpha and Charlie would most likely skew the statistics. Swarm-AEBS data contain the electrojet current density and boundaries derived with both the SECS method and the line current (LC) method as well as estimations of the oval boundaries from FACs . In this study, we use only the SECS-based data to determine the integrated currents for auroral oval crossings and the locations of the maxima as well as the equatorward and poleward borders of the electrojets. The current densities have been derived with the one-dimensional (1-D) SECS method . The 1-D SECS method is used to determine latitude profiles of the divergence-free current density, curl-free current density and field-aligned current density for each crossing of the auroral region. The electrojets are defined from the divergence-free part of the current. The analysis is performed in an orthogonal spherical coordinate system (Semi QD) whose pole is rotated to match the pole in the proper quasi-dipole (QD) coordinates , which are very useful for organizing data but do not provide an orthonormal basis for the analysis. In this set-up, the divergence-free current is orientated zonally in the Semi QD coordinate system. However, when we bin the location of the electrojets, we use the QD latitude of the points in question. The electrojets are identified by locating the sign changes in the current density for each oval crossing profile. The latitude values of the sign changes are then used to integrate the profile in the meridional direction in the Semi QD coordinate system between two consecutive sign changes. Thus, the operation is a line integral along a meridian on the surface of a sphere with a radius of 6481 km, which is the distance from the centre of the Earth, where the currents are assumed to flow. The WEJ limits are then defined as the coordinates of the sign changes between which the integrated value is most negative, and the EEJ limits are the coordinates of the sign changes between which the integrated value is most positive. The peak value is then searched for within both the EEJ and WEJ limits separately. For more details on the detection method, we refer the reader to . Figure  shows an example of the divergence-free current density for an auroral oval crossing with the detected electrojets. The figure also shows other areas of current in addition to the main electrojets. As mentioned earlier, only the sequences with the most positive and most negative integrated current values are defined as electrojets in the context of this study. Figure  also demonstrates that even though the current values are sampled to match the 1 Hz magnetic field measurements used as input data, the 1∘ SECS pole separation provides the scale limit for features in the current.

The SuperMAG substorm list is based on measurements from the SuperMAG ground magnetometer network . The list is based on the SuperMAG AL index (SML), which is an auroral electrojet index derived from the SuperMAG data. It is similar to the AL index with the biggest difference being the much greater number of stations used. The latitude and magnetic local time (MLT) coverage of the stations enable the identification of the time, MLT and latitude of the onsets without visual data. Another advantage of SuperMAG-based substorm identification is that data availability matches well with the lifetime of Swarm. However, even though the number of SuperMAG stations is large, ocean areas are obviously not well covered, and the onset location is naturally dependent on the position of the contributing magnetometers. The onsets in the substorm list have been shown to be highly correlated with a rise in auroral power , and the list gives us a temporal relation between the currents and oval boundaries from Swarm measurements and onset parameters (see Figs.  and ). We note that substorms derived using the SOPHIE (Substorm Onsets and PHases from Indices of the Electrojet) method could also be used .

The QD latitude and MLT were calculated for the SuperMAG substorm onsets to match the data with the Swarm-AEBS data. From the onset list, we selected all substorm onsets that were more than 2.5 h from the previous one and in the MLT sector between 18:00 and 6:00, including the midnight. The 2.5 h limit is close to what obtained for the periodicity of substorms under constant solar wind driving in their minimal substorm model. We believe that this selection gives us the possibility to interpret the times before these onsets as a quieter baseline compared with the times near and after the onsets. Apart from this definition of isolation, we do not have any categorization for different scenarios of substorm occurrence (i.e. globally quiet or disturbed magnetospheric conditions or verification of the type of expansion by visible auroras). Figure  shows an example of a time series of the SML index and the related substorm onsets in relation to the oval crossing in Fig. . We do not distinguish cases where there are no recurrent onsets after the initial one from onsets that are followed by recurrent activity.

In order to relate the onset parameters to the Swarm-AEBS data, we associate timestamps and MLT values with the integrated current values and latitudinal extents for each auroral oval crossing in the Swarm-AEBS data. To do this, we use the mean time and MLT sector of the observations which cover the detected electrojets. Because the satellites can cover a large MLT sector close to the poles, the parameters were determined separately for the WEJ and the EEJ. The MLT range covered by a single oval crossing can exceed 2 h in some cases. We have used all oval crossings for the time period from 25 November 2013 to 31 December 2019 in the Northern Hemisphere where both the EEJ and WEJ are identified well, i.e. corresponding to the best possible quality flag . In practice, this means that both the boundaries and the peaks of the electrojets are well defined between the expected auroral electrojet latitude range from 50 to 85∘ QD latitude and that the satellite path covers the QD latitudes from 50 to 85∘. Altogether, the statistics are calculated from roughly 8430 oval crossings that fulfil our selection criteria. The crossings cover 2976 onsets from the SuperMAG onset list. For each onset, we calculated the MLT and QD latitude so that we could compare the oval crossing parameters to the onsets. The mean MLT and QD latitude of the onsets were 0.15 decimal hours and 67.3∘ respectively. The integrated WEJ and EEJ values as well as the locations of the maxima and latitudinal extents (see Fig. ) were then binned in 2 h bins of MLT difference from the onset MLT and 15 min bins with respect to the time difference from the relevant substorm onset. The evolution of the parameters of interest are then inferred from the median and percentiles in each bin. We also further separate the pre-midnight and post-midnight onsets to study the dependence of the data on the MLT of the onset around the onset time.

The binning was chosen to be reasonable with the fact that the SECS method assumes temporally stationary conditions for the duration of the oval crossing (about 10 min) and that divergence-free currents are calculated from measurements of the whole oval crossing. We acknowledge that this limits the interpretation of the results to these specific scales. In doing this, we also assume that the integrated currents and the averaged timestamp and MLT sector assigned to it are consistent with each other. Figure  shows the number of data points in each bin.

Figure shows the general development of the median integrated WEJ (panel a) and EEJ (panel b) with respect to the MLT difference and temporal offset to the substorm onset. Panels c and d show the ratio of each median compared to the last median before the onset of the same ΔMLT bin (panel c for the WEJ and panel d for the EEJ). For the sake of clearer presentation, we have highlighted two MLT sectors in both panels: W1 and W2 in Fig. 4a and c for the WEJ and E1 and E2 in Fig. 4b and d for the EEJ. Sector W1 stands for 1 h west (towards smaller ΔMLT values) to 5 h east (towards larger ΔMLT values) of the onset, sector W2 stands for 1 to 5 h west, sector E1 stands for 11 to 3 h west and sector E2 stands for 3 h west to 3 h east. Figure 4a and b show that the binning organizes the WEJ data better than the EEJ data. As the substorm onset MLT locations in the SuperMAG list are focused heavily around the nightside, we observe traces of the dawn and dusk electrojets in sectors W1 and E1 respectively before the onset (i.e. the negative temporal difference portion of the plot). A strengthening in amplitude of the WEJ median (corresponding to more negative values) after the onset is clearly visible in sectors W1 and W2. The maximum absolute values of the WEJ are observed 30 to 90 min after onset. The medians reach values of about 2 to 3 times the values before the onset, and the absolute values of the integrated current in sector W1 can be seen to be about 2 to 2.5 times greater in amplitude than the values in sector W2. The greatest relative increase in the eastward current in Fig. 4b and d can be seen in sector E2 after the onset, but the current also increases in sector E1. The intensification in E2 seems to reach the maximum eastward extent only after 15 to 30 min following the onset, and the values mostly reach 2 to 2.5 times the values before the onset. We will return to the difficulty of interpreting the EEJ results in Sect. .

In order to have a more robust view of the binned electrojet currents, we also present figures of the medians and the ranges containing the second and third quartiles (when we refer to the range from here onward, we specifically mean the range defined like this) of the data overlapped with the plots of the previous time step for the period from 30 min before the onset to 75 min after the onset in Figs.  and . Fig. a shows that the distributions of the consecutive time steps are very similar. Comparing the last and first time bins before and after the onset in Fig. 5b, we observe a clear increase of approximately 50–150 kA in the magnitude of the WEJ median and both the upper and lower quartiles, mostly in the W1 and W2 sectors. Figure 5c shows that the median continues to strengthen in the eastern part of sector W1 (i.e. 1 to 3 h east of the onset) from 15 to 30 min after the onset, but the effect is wider in the lower quartile, extending completely through both sectors W1 and W2. After 30 min, there is a well-defined sector of strong westward current in the W1 sector, with the integrated current median values reaching between -200 and -250 kA. The median values and ranges in sector W2 never drop below -125 kA. From 30 min following the onset (panels d, e and f) there is very little change in the medians, but the quartiles show the large variability in the data, with the lower quartile reaching values of roughly -360 kA.

The statistics of the EEJ in Fig. a show no clearly interpretable development of the distribution. Figure 6b shows the development of a second maximum of the EEJ near the onset location in sector E2 in addition to the initial peak in sector E1 which is formed dominantly from the signature of the dusk-side EEJ. The magnitude of this peak is rather small, as the median reaches only 75 kA. This double-peak structure in the median persists in Fig. 6c, but the peak in sector E2 is more concentrated around the middle of the sector, as the integrated values rise mostly in the middle and eastern parts of the sector. In Fig. d, e and f, the double-peak structure is still present, but the level of large-scale organization seems to be decreasing with positive and negative changes both in the medians and ranges in multiple ΔMLT sectors. The largest EEJ values are located in sector E1, with the upper quartile reaching maximum values of a little over 200 kA.

Figures and show the medians and ranges for the location of the electrojet with respect to the onset latitude. The shape of the WEJ latitudinal extent as a function of ΔMLT in Fig.  is unsurprisingly reminiscent of the shape of the auroral oval of the westward-flowing current. The shape of the oval of the eastward current can be seen west of the onset in Fig. . Looking at Fig. , we see that the location of the WEJ in sector W1 is quite well centred near the onset latitude at the onset location and around 1∘ poleward of the onset location after the onset time. Figure c, d and e show that the peak currents seen in sector W2 are located approximately 2 to 4∘ poleward of the onset sector currents, whereas the W1 sector currents are located consistently closer to the onset latitude. The equatorward and poleward extent indicate a poleward movement of the order of 1 to 2∘ in the WEJ position after the onset just west of the onset in sector W2. However, keeping in mind that the SECS method resolution is at most 1∘ in either direction, there is uncertainty in the significance of the observation. Figure a shows how the EEJ in sector E1 is located poleward of the onset latitude but is clearly located more equatorward close to the onset location. It is also evident that the enhanced EEJ values in the eastern part of sector E2 in Fig.  are mostly located poleward of the onset location and the WEJ. In sector E2, the median values of the maximum as well as the poleward and equatorward extents of the EEJ location move sharply around 5∘ poleward at the western end of the sector after the onset in Fig. b. However, the medians are located 5∘ equatorward of the pre-onset position on the extreme western edge of the sector in panels c, d, e and f. While the ranges reveal that the data in these panels include EEJ structures similar to the medians in panel b and vice versa, the sharp jump in the median location persists but is now located in the middle of sector E2. This sharp edge of over 5∘ is in contrast with the smoother poleward transition of the medians in panel a. This is most likely caused by the enhanced WEJ dominating the E2 sector so that the EEJ is found either poleward or equatorward of the WEJ, which naturally leads to this splitting of the distribution into two populations.

To sum up the median behaviour of the WEJ data, we present the combined temporal development of the current and the location of the WEJ in Fig. , which illustrates that the W1 sector currents are greater than the W2 currents and that the jet in sector W1 is positioned around the onset location in contrast to the poleward position of the jet in sector W2. The apparent poleward displacement of the median WEJ location after the onset on the eastern edge of sector W2 is also visible.

Figure shows the WEJ latitude location and MLT data from the 2 h MLT bin centred on the onset MLT (i.e. the ΔMLT=0 bin) and the time step corresponding to the period between 0 and 15 min after the onset. We see that although the onset MLT distribution is spread out, the point distribution is consistently such that the ΔQD=0 is close to the peak values and between the equatorward and poleward borders for onsets between 21:00 and 6:00. However, for onsets between 18:00 and 21:00, the peak location moves poleward of the onset MLT, and the furthest duskward jets are located nearly completely poleward of the onset, although the number of cases is low in this sector. It is possible that the poleward displacement is a signature arising from the Harang discontinuity . Figure also shows that the latitudinal extent of the WEJ is larger on the dawn side compared with the dusk side. We believe this is because the WEJ is generally better established on the dawn side. The Harang discontinuity could also be an explanation for the equatorward extent of the WEJ moving poleward in the dusk sector. For comparison with the substorm time results, we also checked 1797 oval crossings that were within 1 h west and 1 h east of the SML value with any temporal distance to any substorm. For this check, we also required that the SML MLT was between 18:00 and 6:00. The latitudinal position distribution of the WEJ maximum was found to be centred around the SML QD latitude. The median difference between the WEJ maximum and the SML QD was 0.5∘ poleward. However, unlike in the substorm time crossings shown in Fig. , there were several outliers far away from the SML QD latitude.

To study the amplitude evolution, we divided the data into pre-midnight onsets and post-midnight onsets. Of the 2976 onsets, 1411 are located post-midnight and 1565 are located pre-midnight. Figure  shows the median WEJ data covering sectors W1 and W2 but now separately for the two sets of onsets covering the time period between 15 min before and 30 min after the onset time. The three time steps together contain 1260 oval crossings in the pre-midnight onset group and 1087 oval crossings in the post-midnight onset group. The basic statistical nature of the MLT distribution of the oval WEJ underlies the changes in time, as the pre-midnight values are clearly smaller, and the pattern formed by the pre-midnight data is similar to the post-midnight data but shifted eastward. Figure a shows the same data as Fig. b. The 90 % confidence intervals shown in the figure were calculated using the bias-corrected and accelerated bootstrap method (BCa) (, pp. 178–188; , pp. 85–88). The pre-midnight curve has a minimum east of the onset sector. By contrast, the post-midnight curve has a minimum within the onset sector. Figure b shows the bootstrap estimated difference in the medians, which were again calculated with the BCa method, between the last bin before and the first bin after the onset (i.e. the difference between Fig. b and a). The absolute value of the difference in the medians is greatest at the onset sector and the centre of sector W1 for both the pre-midnight and the post-midnight curves, with values of roughly 80 kA for pre-midnight onsets and 100 kA for post-midnight onsets. The pre-midnight values catch and take over the post-midnight values at the eastern edge of sector W1.

To interpret the temporal development of our results, we must note that it would be beneficial to use a normalized timescale in a similar fashion to , in order to avoid mixing the expansion and recovery phases of substorms in a statistical study. For example, also used the same normalized timescales. However, as the Swarm oval crossings provide only snapshots of substorms from certain MLT sectors, it is not possible to avoid this mixing when working with Swarm data alone, and we have to keep this in mind when looking at the MLT distribution of the currents at different times. obtained approximately 30 min as the mean duration on the expansion phase, and we can use this information to roughly assume that on average the bins from 0 to 15 and from 15 to 30 min are mostly samples of the expansion phase of the substorms, whereas the bins after the 30 min mark are a mix of samples from the expansion and recovery phases as well as recurrent substorm activity after the initial onset. This is supported by the large-scale organization of the temporal behaviour in Fig. b and c, which show general strengthening of the medians as well as the lower and upper quartiles. By contrast, the medians are stable, but the ranges between quartiles are large from the 30 min mark onward in Fig. d, e and f, showing the mixing of different phases in observations.

Our observation of the median and the ranges of the WEJ reaching values close to their maximum values at 15–30 min after the onset is consistent with the observations of , who found maximum values for Region 1 and Region 2 FACs and their ratio. also observed similar timescales for the average Region 1 and Region 2 FACs to reach their maximum values. We conclude that the timescales for WEJ intensification coincide quite well with the FAC timing obtained from the global AMPERE observations.

Figures and show that the enhancement of the WEJ after the onset in sector W1 is located near or slightly equatorward of the onset latitude. In sector W2, the westward current is smaller in amplitude and is located 2 to 4∘ poleward. The MLT sectors here are, of course, the edges of our bins and are not to be taken as precise limits for any physical phenomena. In light of the SCW theory and observations of the expansion of bulge-type substorms, it is likely that the distribution in sector W2 is formed mostly of Swarm passes through the substorm bulge and the westward-travelling surge. The W1 sector data, on the other hand, are formed of passes over the part of the SCW that flows along the auroral oval or the eastern part of the bulge. Previous studies supporting this interpretation include, for example, , , , and . We also note that the top currents in sector W1 and W2, especially in Fig. d, are similar to values obtained by for the respective bulge and surge in their model derived from Dynamics Explorer 2 satellite data (see , their Fig. 5). The latitudinal location of the observed WEJ in sectors W1 and W2 is qualitatively consistent with what could be expected from observations of satellite passes over a system depicted in (their Fig. 9), which is based on observations from and . observed similar displacement and amplitude differences of the WEJ from SuperMAG data for the pre-midnight and post-midnight components of the electrojet determined from ground-based data of the SuperMAG network.

Figures and also provide a way to characterize the variability of the jet in a statistical sense. We can interpret the non-overlapping ranges of the locations of the poleward boundary, the peak and the equatorward boundary as a sign of a spatially and temporally stable jet in the chosen coordinate system, and we can interpret overlapping ranges as a sign of temporal and/or spatial variability in the system. Keeping this in mind, we see not only that the WEJ is very clearly defined in sector W1 throughout the studied period but also that the level of organization increases after the onset in sector W2. The lower level of organization in the duskward sectors with overlapping locations and large variability in the amplitudes may arise from the satellite observing variable substructures or structures moving in time instead of a more statically positioned large-scale jet as anticipated.

The onset location is very well located inside the WEJ part of the oval and seems to always be quite close to the peak location, which can be seen clearly in Fig. . The distribution of the points shows the strong correlation between substorm onsets determined from the SuperMAG SML index and the WEJ profiles defined from Swarm data. This not surprising because the magnetic disturbances measured by the SuperMAG network should correspond to the ionospheric equivalent current which, in turn, should correspond quite well to the divergence-free current derived from Swarm; nevertheless, it is an indication that the SML index-based substorm detection does correlate with the enhanced westward divergence-free current with an electrojet-like profile centred on the location. concluded that the substorm onset is co-located with the boundary of the Region 1 and Region 2 FACs which implies that the WEJ peak is also located close this boundary. Figure  shows that it is more likely to reach large currents if the onset location is in the post-midnight sector. This feature is the effect of the substorm enhancement being added to the pre-substorm WEJ which tends to be greater in the post-midnight sector. The actual median current value is clearly greatest at the onset location for the post-midnight onsets, whereas the WEJ intensities tend to peak eastward of the onset in the cases of pre-midnight onsets. We note that the statistical observation of the WEJ peak location differing from the onset location for pre-midnight onsets very likely arises from mixing different substorms and pre-substorm conditions and does not mean that the SML index would not probe the maximum of the WEJ. By contrast, the difference in the median before and after the onset shows the maximum enhancement occurring at the onset location for both pre-midnight and post-midnight onsets. It is likely that the differencing reduces the statistical effect of the underlying oval conditions and more successfully reveals the substorm enhancement.

Looking at Fig. , it is obvious that the number of oval crossings per bin is far from ideal for statistical analysis, ranging from about 40 to 125. The distribution of points is not very uniform across the bins. It is also possible that our quality flag selection – allowing only cases where both the EEJ and WEJ are entirely between QD latitudes of 50 and 85 – causes systematic bias, as certain current systems are not represented in the data set. We also recognize that estimating currents from single-satellite magnetic field measurements with the SECS method involves solving an ill-posed inverse problem. Although SECS has been shown to give reasonable results in a statistical sense and in case studies , some features in its output are affected by adjustments made in the inversion methodology for enhanced robustness in massive data analyses.

As mentioned in Sect. , the statistics show an enhancement of the EEJ in sector E2 after the onset, which seems to propagate eastwards. The enhancement is located mostly poleward of the WEJ, as can be seen from Figs.  and , and also coincides partly with the well-defined WEJ sector. However, it is not clear if this a physical phenomenon or an artefact arising from the limiting 1-D approximation (ignorance of longitudinal gradients) used in current single-satellite products. In Fig. , we see the current profile with quite symmetrical eastward bumps on either side of the westward current. We also note that because the SML index is associated with westward-flowing currents, the WEJ statistics are naturally more organized in our chosen coordinate system in general compared with the EEJ.