© B. Qian et al., Published by EDP Sciences 2025

1 Introduction

The auroral electrojets (AEJ) are important current systems in the ionosphere, flowing horizontally within the auroral oval (Baker, 1986; Newell & Gjerloev, 2011). At E-region altitudes, they primarily comprise Hall and Pedersen currents, whose intensity and spatial configuration are determined by ionospheric conductivity and the electric field imposed on the ionosphere by the ionosphere magnetosphere-coupling (e.g., Richmond & Thayer, 2000). Under conditions where the electric field lacks an inductive (rotational) component and Hall or Pedersen conductance gradients remain parallel to that field, Hall currents, which flow perpendicular to both the electric and magnetic fields, can often be approximated as the divergence-free component of the ionospheric current. In such scenarios, Hall currents predominantly form the eastward electrojet in the dusk sector and the westward electrojet in the dawn sector (Heppner, 1972). By contrast, Pedersen currents, which flow parallel to the electric field, can be treated as the curl-free component under the same conditions and also connect the Region 1 (R1) and Region 2 (R2) field-aligned currents (FACs) in the ionosphere. R1 FACs typically descend into the ionosphere on the poleward side of the auroral oval and ascend on the equatorward side, while R2 FACs exhibit the opposite pattern (Iijima & Potemra, 1976). Divergence in Hall currents may induce charge accumulation, generating a polarization electric field that modifies the overall current structure (Baumjohann, 1982; Amm, 1995). Oriented predominantly meridionally, this field propels Pedersen currents and, in concert with Hall currents and FAC, ensures current continuity throughout the magnetosphere-ionosphere system.

Davis & Sugiura (1966) first defined the auroral electrojet (AE) index by using geomagnetic northward disturbance components measured by 12 ground observatories located within the auroral zone but in different local time sectors, monitoring the variations of ionospheric horizontal currents in the form of a magnetic index. This provided a global, quantitative measure of the magnetic disturbances produced by ionospheric currents flowing within the auroral oval. With increasing development of ground stations, the SuperMAG project (Newell & Gjerloev, 2011) later improved the original AE index by using data from over 100 ground stations. This dense-coverage ground-based data was used to calculate the enhanced auroral electrojet index, so-called SME/SMU/SML, which can address some of the original AE index’s limitations in both latitude and longitude. However, even though the number of SuperMAG stations is rather large, their distribution is not uniformly located e.g., they have rather poor coverage in latitudinal, in the oceanic regions, as well as in the southern hemisphere.

Another disadvantage of using ground-based magnetic field observations is that they can only estimate equivalent currents and cannot accurately determine the central position and peak intensity of AEJ. In contrast, satellite-based magnetic observations at higher altitudes offer a significant advantage. They can detect the full latitudinal profile of AEJ and estimate also the FAC (e.g., Anderson et al., 2000; Ritter et al., 2013; Korth et al., 2014). Additionally, satellites flying in polar orbit can obtain a comprehensive north–south current density profile and cover areas in the Southern Hemisphere where ground-based station data are insufficient, providing a better description of the variation in current position and magnitude with latitude. Therefore, the magnetic measurements from satellites have been used to track and monitor the auroral electrojet. Moretto et al. (2002), using the line current (LC) method proposed by Olsen (1996), developed a polar electrojet index based on magnetic field observations from the CHAMP and Ørsted satellites. This index showed a correlation of 78% or higher with the AE index in the Arctic region. Ritter et al. (2004) expanded on this study and further created a map that can show the location and intensity of auroral electrojet in detail during each satellite pass over the polar regions. Aakjær et al. (2016) evaluated and improved the regularization method proposed by Olsen (1996), for inverting the LC method, achieving the AEJ activity characteristics with a squared coherence of 0.95 with the Auroral Electrojet index. Notably, the LC method has been routinely applied in the Level-2 processing chain to produce the Swarm AEJ data product (Kervalishvili et al., 2020). Furthermore, Juusola et al. (2009) used a one-dimensional version of the 2D spherical elementary current systems (SECS) method developed by Amm (1997) to track auroral electrojet using CHAMP satellite vector data. Workayehu et al. (2019, 2020) applied this method to the Swarm data, providing statistical characteristics of ionospheric currents from hemispheric and seasonal perspectives. For a detailed comparison between the LC and SECS methods, Juusola et al. (2016) explored their applicability under different spatial resolutions and assumptions using Swarm data. Compared to the LC method, which only used magnetic field intensity, the SECS method used the vector data that can introduce computational complexity and potential sources of error.

Vennerstrom & Moretto (2013) proposed a method using the along-track gradient of magnetic field intensity to determine the location and intensity of AEJ. They applied this method to five years of CHAMP data, and found a high correlation between the derived AEJ characteristics in the Northern Hemisphere and the ground-based AE index. In contrast to the LC and SECS methods, the along-track gradient of magnetic field intensity method offers high-resolution meridional coverage, allowing AEJ and latitude to be pinpointed with a precision better than 0.1°. However, it has relatively sparse temporal resolution. Smith et al. (2017) validated the effectiveness of this method and applied it to the Swarm and earlier CHAMP dataset. They examined the response to the IMF clock angle and season, identifying hemispheric differences.

As introduced above, though both the LC and SECS methods theoretically calculate the size and location of AEJ over the entire orbital profile, requiring preset model resolutions and iterative inversion methods, that can result in over-smoothing the peak of AEJ value and positions. In this study, we adopt the along-track gradient of magnetic field intensity method to determine the location and intensity of AEJ. The computed equivalent peak current intensity and position serve as indicators of AE activity. Unlike the conventional AE and SME indices, which are expressed as magnetic indices, our parameter is derived from an equivalent current. Our current calculation method is somewhat similar to that used by Vennerstrom & Moretto (2013), but we apply it to the Swarm data, spanning ten years, which offers a longer statistical time. Unlike the LC method, we do not model line currents across the entire profile but rather assume that a single equivalent peak line current exists beneath the satellite’s orbit, generating the observed magnetic effect. We refer to this approach as the single line current (SLC) method. The SLC method relies basically on the measurements of magnetic field intensity along the satellite orbit. Compared to the full vector magnetic field measurements, these intensity measurements are easier to obtain, more accurate and stable, while also being less prone to data gaps. Our analysis explored the relationship between peak of AEJ calculated using the SLC method and peak of AEJ data from the Swarm-AEBS dataset, as well as the SuperMAG electrojet (SME) index. Based on statistical analysis, we confirm that using satellite data to calculate the local peak of AEJ could serve as an alternative to the AE index. This approach enhances our understanding of the spatial distribution characteristics and formation mechanisms of auroral electrojets.

2 Method and data

2.1 Data

The Swarm mission was launched on 22 November 2013 into a near-polar orbit with an inclination of 87.5°. Initially, the three satellites orbited in a string-of-pearls configuration at an altitude of 500 km. On 17 April 2014, they achieved their dedicated orbital constellation. In this arrangement, Swarm A and C fly side-by-side at approximately 460 km altitude, separated by 1.4° in geographic longitude in the east–west direction. Swarm B orbits at about 520 km with a higher inclination, causing the angle between the orbital planes of Swarm A/C and Swarm B to increase by about 20° per year (Xiong & Lühr, 2023).

In this study, to estimate the peak of AEJ, we used data from the scalar field magnetometer (ASM) on the Swarm satellites, with a data resolution of 1 Hz, obtained from SW_MAGx_LR_1B version 0602/0603 (https://swarmhandbook.earth.esa.int/catalogue/SW_MAGx_LR_1B). To filter out high-frequency noise and variations caused by small-scale currents, we applied a smoothing technique using a running average over a 20-second window. To isolate the ionospheric field from the measured magnetic field, we subtracted the contributions from the core, crust, and other large-scale magnetospheric sources. We use the combination of CHAOS-7.16 core field model up to degree 20, a static lithospheric magnetic field from degrees 21–110 of CHAOS-7.16, and the large-scale magnetospheric magnetic field corrected with the ring current (RC) index (Finlay et al., 2016).

To evaluate the results from our SLC approach, the Swarm-AEBS product of Swarm has been used for comparison. Swarm-AEBS data contain the electrojet current density and boundaries derived using both the SECS method (Juusola et al., 2016) and the LC method (Olsen, 1996), as well as estimations of the oval boundaries from the small scale FAC (Xiong et al., 2014). In this study, we use the LC-based data to determine the peak currents for AEJ (https://swarmhandbook.earth.esa.int/catalogue/SW_AEJxLPL_2F). In addition, the SME auroral electrojet index was also used for comparison, which was obtained on 18 April 2017 and is produced from the SuperMAG ground magnetometer network (Gjerloev, 2012). SME is similar to the AE index (Davis & Sugiura, 1966), with the main difference being the much greater number of stations used.

2.2 Method

The LC method, originally developed by Olsen (1996), determines well the latitudinal profiles of AEJ. It assumes that only the horizontal ionospheric currents contribute to the parallel component of the magnetic field as measured by satellites. The horizontal ionospheric sheet current density is approximated by a series of line currents placed at an altitude of 110 km in the ionospheric E-layer. These line currents are directed parallel to equal latitudes in quasi-dipole (QD) coordinates (Laundal & Richmond, 2017) and are separated in the horizontal (along-track) direction by 113 km (equivalent to 1° in latitude). The QD coordinate system can accurately reflect the magnetic effects of currents at ionospheric altitudes. Similarly, our SLC method also assumes that only horizontal ionospheric currents contribute to the parallel component of the magnetic field as measured by the satellite. Perturbations of the magnetic field strength along the satellite track are used to estimate perturbations in the field-aligned component. This allows for the determination of the maximum gradients that indicate the latitude location and strength of the most intense auroral currents.

The assumptions of both the LC and SLC methods are based on the following principle: the magnetic field generated by currents is always perpendicular to the current direction. The ionospheric E-layer primarily consists of horizontal and vertical currents. The magnetic field generated by FAC is perpendicular to the Earth’s main magnetic field lines. Therefore, the magnetic field data observed by satellites, in the direction parallel to the Earth’s main magnetic field lines, do not include the magnetic field generated by FAC. However, these data are sensitive to contributions from horizontal currents in the ionospheric E-layer, which constitute the AEJ. As a result, the magnetic field intensity measured by satellites, denoted as F = |B|, represents the Earth’s magnetic field. By examining F observations from satellites, it is possible to accurately estimate these currents.

The SLC algorithm requires only the magnetic field intensity, making it independent of any potential issues with attitude data or vector data processing. The total magnetic field at a point is a combination of internal and external sources, B = B_int + B_ext, where B_int is approximately 40,000 nT (including the geomagnetic core field and lithospheric magnetic field) and B_ext is approximately 100 nT (including the ionospheric and magnetospheric fields) at altitudes of satellites in low Earth orbit when above 50° latitude (Smith et al., 2017). By separating the total field, B, into components parallel (B_∥) and perpendicular (B_⊥) to the internal field, we can approximate B_∥ with the magnetic field total intensity (scalar) F, as B_⊥ is much smaller than B_∥. As follows:

$$F=\left|\mathit{B}\right|={\left({\mathit{B}}_{\parallel }^2+{\mathit{B}}_{\perp }^2\right)}^{\frac{1}{2}}=\left|{\mathit{B}}_{\parallel }\right|{\left(1+\frac{{\mathit{B}}_{\perp }^2}{{\mathit{B}}_{\parallel }^2}\right)}^{\frac{1}{2}}=\left|{\mathit{B}}_{\parallel }\right|{\left(1+O\left({10}^{-5}\right)\right)}^{\frac{1}{2}}.$$(1)

To isolate the ionospheric field from the core and crustal fields, an internal field model, B_int must be subtracted. Additionally, it is necessary to eliminate the contributions from the magnetospheric external sources included in B_ext. Therefore, δF ≈ |B_ion| = |B| – |B_core| – |B_lithosphere| – |B_{magnetosphere}|. In the context of the satellite measurements near the poles, |B| represents the magnetic field magnitude along the satellite’s orbit, |B_core|, |B_lithosphere| and |B_{magnetosphere}| are the magnetic fields from the core, lithosphere, and magnetosphere, respectively, as modeled by the CHAOS-7.16 model, detailed in Section 2.1.

The electrojet can be effectively represented as a horizontal line current perpendicular to the satellite track, aligning with magnetic latitude (MLAT) contours due to the north-south flying of Swarm. The time derivative of the magnetic field perturbation, δF, expressed as dδF/dt, corresponds to the along-track gradient, dδF/ds, where ds denote the satellite’s shift during the time interval dt. Assuming the electrojet remains stationary throughout the satellite pass, the peak observed in dδF/ds indicates the latitudinal position of the current, with its polarity determined by the current’s direction. The magnitude of the peak is used to determine the strength of an equivalent infinite line current placed perpendicularly to the satellite track at an altitude of 110 km.

Following Olsen (1996), the contribution of a single line current to the magnetic field strength δB is given by

$$\begin{array}{c}\delta {\mathit{B}}_{\left|\right|}=\delta {\mathit{B}}_r\mathrm{sinI}+\delta {\mathit{B}}_H\cos I\\ \delta {\mathit{B}}_H=\frac{{\mu }_{0}J}{2\pi }\frac{\xi }{{\xi }^2+{\eta }^2}\\ \delta {\mathit{B}}_r=\frac{{\mu }_{0}J}{2\pi }\frac{\eta }{{\xi }^2+{\eta }^2}\end{array}$$(2)

Where δB_H represents the horizontal component of the geomagnetic field, δB_r represents the radial component of the geomagnetic field, I is the magnetic inclination of the main field model, η and ξ measure the radial and horizontal distance between the satellite and the line current, respectively. Here, η = r_ksin(β_n – β_k) and ξ = r_n − r_kcos(β_n – β_k), r_n and r_k represent the satellite location and the line current at that location, respectively. The parameters β_n and β_k describe the distance from the Satellite locations and line current locations closest to the magnetic north or south geomagnetic pole. These parameters are shown in Figure 1.

Figure 1 Sketch of the geometry used in the Line Current method. The auroral electrojets are represented by a series of line currents located at an altitude of 110 km. δB denotes the total magnetic residual, where δB∥ is the component parallel to the main magnetic field and δB⊥ is the perpendicular component. The triangle represents the satellite’s flight path, and the circles mark the positions of the line currents. (rn, βn) and (rk, βk) indicate the satellite and the line current at a given location, respectively. Δβ signifies a systematic shift toward lower latitudes in the location of the current maximum. Modified from Aakjær et al. (2016).

By substituting equation (2) from equation (1), we get:

$${\delta F}_n\approx {\delta \mathit{B}}_{\parallel }=\frac{{\mu }_0}{2\pi }\frac{\xi \cos I+\eta \sin I}{{\xi }^2+{\eta }^2}\cdot J,$$(3)

where μ₀ = 4π × 10⁻⁷ T m/A is vacuum magnetic permeability, J represents the intensity of the line current. By taking the derivative of the magnetic field latitude along the satellite’s flight path, β_n, we obtain:

$$\frac{\mathrm{d}{\delta F}_n}{\mathrm{d}\beta }=\frac{{\mu }_0{r}_k}{2\pi {\left({\xi }^2+{\eta }^2\right)}^2}·j\left[\left({\xi }^2\sin I-{\eta }^2\sin I-2\xi \eta \cos I\right)\cos \left({\beta }_n-{\beta }_k\right)+\left({\eta }^2\cos I-{\xi }^2\cos I-2\xi \eta \sin I\right)\sin \left({\beta }_n-{\beta }_k\right)\right].$$(4)

The orbital parameter β for each data point of the selected orbit arc can be determined by using the spherical trigonometry:

$$\cos \beta =\cos {\theta }_0\cos \theta +\sin {\theta }_0\sin \theta \cos \left(\varphi -{\varphi }_0\right),$$(5)

where the θ₀ and ϕ₀ represent the geographic co-latitude and longitude of the satellite measurements.

As we focus on a single line current and assume it is directly beneath the satellite on a single orbit, we get β_n = β_k, which means the satellite flight trajectory and the line current are at the same sub-satellite measuring point. The final expression of the current is derived as:

$$J=\frac{2\pi {\left(r_n-r_k\right)}^2}{r_k{\mu }_0\sin I}\frac{\mathrm{d}\delta F_n}{\mathrm{d}\beta }$$(6)

To much more details clarifying our SLC algorithm, we established a basic physical model. This model assumes the Earth’s radius is 6371.2 km, with a satellite orbiting at 400 km above the surface towards the North Pole. Line currents are located at an altitude of 110 km in the ionospheric E layer, with a strength of 1 MA. We place the line current at 60° in QD coordinate system, where the local inclination of the main magnetic field is approximately 74°. A schematic of the satellite track, the field geometry, as well as the maximum gradient in the magnetic field strength over an oval crossing of the satellite is shown Figure 2. In the simulated satellite orbit, when the satellite’s trajectory aligns directly above the line current placed at the height of the ionosphere, a notable peak in dδF/ds is observed. The application of this method to Swarm allows for orbit-by-orbit tracking and calculation of the anticipated position and strength of the prevailing ionospheric electrojet.

Figure 2 The parallel magnetic perturbation components (blue line) with respect to the main magnetic field at 60° MLAT. The green dotted line is the derivative along the track of the magnetic perturbation components, the red vertical line indicates the location of peak green dotted line. The gray vertical line indicates the position of the placed current line.

The dδF/ds contribution is identified by its characteristic peak near the electrojet latitude. The electrojet latitude is determined by selecting the maximum (either negative or positive) over each auroral region pass. The magnitude of this peak is used to estimate the electrojet current, which is modeled as an infinite line current at that latitude. We assign the position and intensity values of the infinite line current, flowing along the MLAT circle, to each estimated maximum gradient.

When there is more than one peaks in dδF/ds, indicating multiple currents at different latitudes, it can lead to a wide range of latitude and current estimates. If we convert the magnetic disturbance caused by a long, straight current in a vacuum, assuming the current is located at an altitude of 110 km, a 20 nT AE signal observed on the ground corresponds to a line current amplitude of 11 kA. Following the suggestion by Vennerstrom & Moretto (2013), by excluding signals below 11 kA can effectively eliminate the non-auroral electrojet influences.

Thus, to exclude other contributions unrelated to the electrojet at very low current strengths, only electrojet detections above a minimum threshold of 11 kA for Swarm measurements are accepted. On this basis, all peaks are counted, and only those within 75% of the maximum absolute value are retained. Additionally, only the peak and location of the electrical current closest to the low latitude side should be considered. When multiple current peaks appear in the latitude profile, the high-latitude side may include more complex local currents, whereas the low-latitude peak is more representative of the dominant AEJ current overall. Nonetheless, it is important to note that a single detection alone does not fully represent the complexity of the electrojet.

It is important to note that the peak in dδF/ds may be negative or positive depending on the direction of the current. For the analysis in this study, we do not differentiate between eastward and westward currents and consider only the current magnitude. The data is divided into passes over the northern and southern auroral regions, specifically above 50° QD latitude. Due to the satellite crossing the polar cap, the calculated peak of AEJ often shows two peaks when approaching and departing the polar cap. To facilitate statistical analysis, we independently calculate the peak of AEJ for the ascending and descending orbits and eventually include them in our dataset.

It is worth noting that measuring the gradient in a magnetic field component aligned with the Earth’s internal magnetic field, rather than in the strictly vertical component, results in a systematic latitudinal shift of the estimated peak of AEJ towards lower latitudes, as also illustrated by the Δβ in Figure 1. This slight offset can also be seen from the misfit of red and grey vertical lines as illustrated in Figure 2. To correct this systematic error, we calculated the systematic biases at different MLAT and altitudes. As the satellite moves closer to lower latitude points along its orbit, the estimated MLAT shift of the line current increases as shown in Figure 3a. Additionally, the higher the satellite flies, the greater the deviation at the corresponding points as shown in Figure 3b. Although the observed deviation is below 0.6°, our results require the peak of AEJ position to be more precise compared to the LC method, which typically constructs line currents with a resolution of approximately 1°. Therefore, we use regression fitting from model experiments as a correction.

Figure 3 Systematic deviation in estimated peak of AEJ corresponding to different altitudes and MLAT.

3 Results

3.1 Statistical distribution

The MLAT versus magnetic local time (MLT) distribution of the peak of AEJ dataset, calculated from Swarm A, is shown in Figure 4. Results are presented separately for the Northern and Southern Hemispheres under different SME conditions. The results of Swarm B are provided in Appendix Figure A1.

Figure 4 All detections collected from Swarm A data have been assigned based on the inferred current strength using the SLC method at QD coordinate system. The detections are shown for both the Northern and Southern Hemispheres, with 95,462 in the Northern Hemisphere and 87,349 in the Southern Hemisphere. An approximate 90-minute interval is allocated each hemisphere for collecting each peak dataset, while each detection phase takes about 20 min to analyze data points above 50° QD latitude. Negative values represent westward electrojets, while positive values represent eastward electrojets.

The occurrence of maximum current characteristics depends on both magnetic latitude and local times. Statistical analysis of the 10-year dataset, which includes 182,811 orbital arcs (95,462 in the Northern Hemisphere and 87,349 in the Southern Hemisphere), reveals that between 04:00–14:00 MLT, the peak of AEJ is typically located between 70° and 85° MLAT, while between 19:00–04:00 MLT, it is usually found between 60° and 80° MLAT. There is a noticeable local time asymmetry. This asymmetry is similar in both hemispheres, although there are fewer data points within the 80° polar cap in the Southern Hemisphere. This may be due to the larger displacement of the southern magnetic pole from the geographic pole, which, combined with satellite inclination limitations, affects observations of the oval closest to the South Pole. Consequently, there is a greater detection loss in the southern polar region compared to the northern polar region.

When the SME index ranges from 0 to 300 nT, the AEJ peak is distributed between 62° and 84° MLAT during 00:00–06:00 MLT, shifting poleward in the 06:00–14:00 MLT range and toward lower latitudes in the 22:00–02:00 MLT range. This distribution pattern agrees well with earlier studies by Iijima & Potemra (1976, 1978), who found that current ovals expand with increasing geomagnetic activity, reflecting the Expanding-Contracting Polar Cap (ECPC) paradigm as described by Siscoe & Huang (1985) and Cowley & Lockwood (1992). Recent researches, including work by Clausen et al. (2012, 2013) using AMPERE and DMSP data, confirm this feature, showing a correlation between oval expansion and geomagnetic activity, as well as a direct relationship between the open/closed field line boundary and auroral oval dynamics. In the Southern Hemisphere, larger AEJs are concentrated around 00:00–10:00 MLT, while the Northern Hemisphere exhibits more dispersion. As geomagnetic activity increases (300 < SME < 500 nT), the AEJ peak shifts equatorward, typically located between 62° and 72° MLAT during 00:00–06:00 MLT, with stronger electrojets appearing closer to the equator. The observed AEJ peak positions align with the auroral ovals described by Juusola et al. (2009) and empirical models by Xiong & Lühr (2014). At higher geomagnetic activity levels (SME > 1000 nT), the AEJ peaks concentrate between 60° and 67° MLAT, although data scarcity limits further analysis in this range. The amplitude of the AEJ peak systematically increases with geomagnetic activity, shifting from 00:00–04:00 MLT under magnetically quiet condition to 02:00–06:00 MLT during moderate activity, and extending to 00:00–08:00 MLT during higher activity. This observation of shifting AEJ peak positions is consistent with the expansion and contraction of auroral ovals linked to magnetic reconnection, as reported by Coxon et al. (2014).

Figures 5–8 illustrate the evolution of the AEJ under different SME conditions and across various seasons, calculated from Swarm A. The results of Swarm B are provided in the Figures A2–A5 of Appendix A. When 0 < SME < 300 nT (Fig. 5), the auroral electrojet (AEJ) peak distribution exhibits an approximate symmetry between the hemispheres during local spring/fall. However, more pronounced hemispheric differences emerge in local summer and winter, where the northern hemisphere detects a higher number of AEJ peaks in summer than in that in winter, while the southern hemisphere shows a similar increase in its local summer season. In both hemispheres, stronger AEJ peaks cluster near 12 MLT during local summer; however, the southern hemisphere features an additional set of westward AEJ peaks at 04:00–08:00 MLT at lower MLAT. During the equinoxes, the AEJ peak distributions become more similar in both hemispheres. When 300 < SME < 500 nT (Fig. 6), the overall count of AEJ peaks does not vary significantly by season. Nevertheless, during local spring/fall, the northern hemisphere records higher AEJ peak values at 14:00–18:00 MLT compared to the southern hemisphere. Under 500 < SME < 1000 nT (Fig. 7), the southern hemisphere exhibits a broader, oval-shaped distribution of AEJ peaks during local summer than the northern hemisphere. Finally, when SME > 1000 nT (Fig. 8), both hemispheres show a relatively larger number of AEJ peaks around the September equinox, although limited data constrain further detailed analysis. Overall, regardless of season or hemisphere, the oval-shaped AEJ peak distribution expands with increasing geomagnetic activity.

Figure 5 Same as Figure 4, using Swarm A data, divided by season under the condition 0 < SME < 300. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure 6 Same as Figure 4, using Swarm A data, divided by season under the condition 300 < SME < 500. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure 7 Same as Figure 4, using Swarm A data, divided by season under the condition 500 < SME < 1000. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure 8 Same as Figure 4, using Swarm A data, divided by season under the condition 1000 < SME. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

3.2 Comparison with the Swarm AEBS products

In the following, we compare further the differences in peak current magnitudes estimated by the SLC and LC methods at different local times in both the Northern and Southern Hemispheres. Figure 9 illustrates the statistical results from nearly 10 years of data from Swarm A, spanning from 25 November 2013 to 30 November 2023. Figure 9a shows that globally, it can be seen that the relationship between the two methods is linear and there is a strong correlation in amplitude estimation. The correlation value between the peak currents estimated by SLC and LC is above 0.96. From Figure 9c to Figure 9e, the Northern Hemisphere displays slightly higher correlation results than the Southern Hemisphere. Additional results for Swarm B are available in Appendix Figure B1. Figure 9b shows that the global average estimation error between the LC and SLC methods is within 0.5°, with a standard deviation of around 5°. The relative estimation error is larger during 12:00–14:00 MLT. From Figure 9d to Figure 9f, there are also some differences between the results in the Northern and Southern Hemispheres. For example, the standard deviation of the estimates in the Northern Hemisphere is smaller than in the Southern Hemisphere, especially in 07:00–09:00 MLT and 16:00–18:00 MLT.

Figure 9 Swarm A based quantitative relationship study of the estimated intensities using the LC and SLC methods (a–b is the global result, c–d is the northern hemisphere result, e–f is the southern hemisphere result). The left panels present the peak current amplitude of the SLC method is shown on the bottom x-axis, and the peak current amplitude of the LC method is shown on the left y-axis. The color indicates the occurrence distribution of the collected data points. The line of fit is shown in solid blue. The right panels present the variation in estimated AEJ peak positions with local time for both the SLC and LC methods. ΔQD latitude represents the difference in estimated AEJ peak magnetic latitude between the SLC and LC methods in the QD coordinate system. The blue dots indicate the average relative error, while the red vertical lines represent the standard deviation, with an averaging window of 1 h.

Figure 10 shows the statistical distribution of deviations over latitude difference for Swarm A. In both hemispheres, the distribution is quite consistent, indicating a high degree of agreement between the two estimation methods. The difference distribution around 0° and ±1° exhibits an approximately Gaussian distribution, with the error centered at 0° accounts for 80% of the data. Additionally, there is a second peak around ±5° but with very low occurrence rate, which is presumed to be caused by high AEJ activity. This high activity leads to discrepancies between the physical model and the actual current morphology, causing misjudgments. Very similar results from Swarm B are provided in Appendix Figure B2.

Figure 10 Swarm A based study on the positional bias in peak of AEJ estimates using the LC and SLC methods (top is global results; bottom displays Northern Hemisphere results on the left and Southern Hemisphere results on the right).

3.3 Indicator of local auroral electrojet peak intensity and latitude from SLC method during the substorm

To evaluate the capability of the SLC method in observing AEJ activity, we selected a month that includes substorm events. Figure 11 shows the variation of AEJ peak intensities calculated using the LC and SLC methods compared to the SME index during 7 March 2015 to 1 April 2015. Results the Northern and Southern Hemisphere, as well as combined two hemispheres are shown separately. The correlation coefficients are calculated by correlating the AEJ peak index of SLC method, the AEJ peak index of LC method, and the interpolated ground-based SME index.

Figure 11 Examples of data from Swarm A, where the time series of the sheet current amplitude is compared to the SME index. The time series of the SME index and the current estimated by the LC method or SLC method are shown for a period of 768 orbits from 7 March to 31 March 2015.

When calculating the peak of AEJ, we converted the current density data from the Swarm AEBS product into the total current at the corresponding resolution. We want to note that the data product provided in AEBS is current density, with a resolution of 1° along the track, approximately 110 km.

To convert the AEBS results into current strength, they are multiplied by 110, which corresponds to integrating the current density data over a 1° gap. This ensures unit consistency between the SLC and LC methods for numerical comparison. The satellite provides two latitude locations and an amplitude for the maximum current signature for roughly every 90 min. These results indicate a good correlation between the peak AEJ intensities calculated by the LC and SLC methods and the SME index, with similar patterns in the auroral electrojet intensities calculated by both methods.

During the St. Patrick’s Day storm on 17–18 March 2015, both the LC and SLC methods detected strong AEJ intensities. Relative smaller active features were also detected during the pre- and post-storm days, e.g., on 13–14 March and 21–22 March. The correlation with the SME index is higher for the SLC method than for the LC method, suggesting that the local auroral electrojet peak intensity and latitude calculated by the SLC method may serve as a more effective indicator of AEJ activity. Compared the results in two hemispheres, the correlation with the SME index is higher in the Northern Hemisphere than that in the Southern Hemisphere. This difference may be due to the greater deviation of the geomagnetic pole from the geographic pole in the Southern Hemisphere compared to the Northern Hemisphere. This larger deviation can cause a more significant misalignment of polar-orbiting satellite trajectories with the direction perpendicular to the AEJ in the Southern Hemisphere. Consequently, the measured current in the Southern Hemisphere may not fully represent the complete current. In addition, it may also be related to the fact that most of the geomagnetic stations calculating the SME index are located in the Northern Hemisphere. From the later perspective, the lower correlation in the Southern Hemisphere does not indicate poor representation of AEJ activity using satellite data. Instead, it suggests that satellite data could complement the ground-based data for monitoring the Southern Hemisphere auroral electrojet.

As the density profile data retrieved from the Swarm AEBS product is sparse, similar to the data calculated using the SLC method for the peak of AEJ, it is necessary to unify them to calculate the time series correlation. As shown in Figure 11, the AE intensities calculated using the SLC and LC methods show consistent trends, while obvious differences in amplitude are also observed. Therefore, in Figure 12, we focus on comparing the differences in AEJ intensity determined by the two methods and explore their differences of AEJ peak positions. Data of Swarm A from the Northern Hemisphere over four days from 13 to 16 May 2019 have been considered, as there was a strong substorm.

Figure 12 Using Swarm A data, the figure illustrates the estimated peak of AEJ positions using the SLC and LC methods for the Northern Hemisphere over four days starting from 13 March 2019. The second and third rows show the peak of AEJ positions for ascending and descending orbits, respectively. The first row represents the time variations of SME, SMU, and SML. The fourth row displays the time series of AEJ calculated using the SLC method compared to SME.

During this period, the ascending orbit of Swarm A corresponds to approximately 03:30 MLT, and the descending orbit corresponds to approximately 15:30 MLT. During the geomagnetically quiet period from 0 to 8 h, the AEJ on the dayside is located at higher latitudes, while the AEJ on the nightside is at lower latitudes. Around 06:00 UTC on the 14th, of the SME index reached approximately 1500 nT, suggesting a strong substorm occurred. Both the LC and SLC methods show that the estimated PEJ peak positions shifted to lower latitudes during the substorm and returned to higher latitudes later. This result is consistent with the finding of Vennerstrom & Moretto (2013), indicating that the AEJ estimate tracks well over consecutive orbits, showing latitudinal expansion and contraction patterns associated with strengthening and weakening current strength during geomagnetic activity, and a strong correlation with the AE index.

However, the significant changes of AEJ peak position cannot be captured by the ground-based SME index. Between 64 h and 72 h after 13th of May 2019, the SME values were below 100 nT, indicating minimal geomagnetic disturbance as measured by ground-based data. However, SME represents an average of geomagnetic disturbances measured by ground stations covering multiple local times, and these stations may not always be located within the peak AEJ region. Consequently, there is a significant deviation between the SME index and Swarm A’s measurements.

Nevertheless, despite this discrepancy, both the SLC and LC algorithms maintain a statistically strong correlation with the SME index, achieving correlation coefficients of 0.7 or higher (see Fig. 11). Because satellites measure the AEJ along the satellite orbit, the observed values vary with MLT and MLAT, as illustrated in Figure 13 for Swarm A (with corresponding results for Swarm B shown in Fig. C1). The correlation is lower during pre-noon (10:00–12:00 MLT) and pre-midnight (21:00–23:00 MLT) sectors. Regarding the MLAT dependences, the highest correlation is observed in the between 62° and 78° MLAT, where AEJ peaks occur. Below 62° MLAT, there is a noticeable jump in correlation in both hemispheres. In addition, the correlation starts to decrease beyond 76° MLAT, likely to be caused by less SME monitoring stations at higher MLAT.

Figure 13 The correlation between the peak of AEJ calculated using the LC algorithm and the SME index, as well as the correlation between the peak of AEJ calculated using the SLC algorithm and the SME index, across different MLT and MLAT values. (Using 2s bin window based on Swarm A, data from Swarm A spanning the period from December 2013 to November 2023 were analyzed. A total of 182,811 detections were recorded, with 95,462 in the Northern Hemisphere and 87,349 in the Southern Hemisphere).

4 Discussion

In this study, we introduce the SLC method to derive the AEJ peak latitude, which is basically based on the magnetic field intensity along the satellite orbit. Compared to the magnetic field vector measurements, magnetic intensity is easier to obtain, and also less prone to data gaps. Based on the magnetic intensity, the latitude and magnitude of the strongest AEJ encountered can be determined during each auroral crossing. This demonstrates the utility of this approach for studying AEJ behavior in response to various drivers.

4.1 Monitoring AEJ activity

In Figure 4, we show the distribution of AEJ peaks for different MLT sectors in both hemispheres, under different auroral activity indicated by the SME index. Similar to the auroral oval spreading to lower latitudes with increasing geomagnetic activity, the magnetic latitude of the maximum current also depends on the level of auroral activity. As the SME index increases, AEJ peak shifts towards lower latitudes, transitioning from predominantly located between 60° and 80° MLAT to a narrower range concentrated between 65° and 67° MLAT. Compared to the Northern Hemisphere, there are fewer valid AEJ peaks found in the Southern Hemisphere, which likely due to hemispheric asymmetry in current strength and the detection threshold excluding currents below 11 kA. The complexities of this hemispheric asymmetry of AEJ, as well as FAC remains a topic of debate. Figure 4 shows that, at lower SME levels, AEJ peaks in the Northern Hemisphere are more numerous, compared to that in the Southern Hemisphere. Specifically, when SME is less 300 nT, there are significantly more AEJ peaks found in the Northern Hemisphere. However, for SME is larger than 300 nT, the difference between hemispheres is minimal, as also evident in Figures 5–8 and Figures A2–A5, which present the seasonal comparisons. This suggesting that the hemispheric asymmetry of valid AEJ counts differ under varying geomagnetic conditions. Recent studies by Workayehu et al. (2019–2021) revealed substantial seasonal variations of FACs, with stronger values in the Northern Hemisphere, particularly in local winter season. This suggests a complex interaction between solar wind conditions and magnetospheric processes that warrants further investigation. Coxon et al. (2016) highlighted the role of seasonal and diurnal cycles in current dynamics, noting that discrepancies often arise from methodological differences, underscoring the need for standardized measurement techniques and analytical frameworks to ensure consistency.

The SLC method for calculating AEJ peak characteristics shows potential for observing auroral electrojet activity. As shown in Figure 12, with the rapid increase of auroral activity, the positions of AEJ peaks vary accordingly. During periods of high geomagnetic activity period, the peaks are located towards lower latitudes, while during quiet periods the peaks are located at higher latitudes. Such AEJ peak variation agrees well with the expansion and contraction of the auroral oval during geomagnetically active and quiet conditions.

Based on the magnetic measurements of CHAMP satellite, Vennerstrom & Moretto (2013) calculated the correlation of the local AEJ peak intensity calculated derived from the along-track gradient of magnetic field intensity with the AE index derived from ground. The correlation is better when the satellite observes the maximum current feature at latitudes corresponding to ground station to derive AE (i.e., between 60° and 70° MLAT) than when it observes the maximum current feature at higher or lower latitudes. In addition, they also found a MLT influence on the correlation, e.g., the correlation reduces to lower than 0.6 for the 08:00–14:00 MLT. In our study, the correlation between the SME and Swarm derived AE-index is generally higher than 0.8 as shown in Figure 13a, which is possibly due to much more ground stations have been used to derive the SME index compared to the AE index. The high correlation also illustrates the potential and complementarity of combining ground and satellite-based observations for monitoring the auroral activity.

4.2 Comparison with LC method

As mentioned, one of the Swarm Level-2 products, AEBS, remains an excellent source of AEJ product data. Although the SLC method is much simpler than the methods (such as SECS and LC) applied to AEBS, its simplicity facilitates the integration of multiple satellites for joint observations. By analyzing Swarm A and Swarm B data over 10 years, we examined the correlation and difference between the SLC and LC methods in estimating the peaks of AEJ. Our results show a strong correlation in both amplitude and estimated position of AEJ peaks, indicating that even when simplifying the model currents from 81 (LC method) to just one, the SLC method can still effectively characterize the peaks and amplitudes of AEJ. Additionally, the strong correlation with the SME index derived from ground stations suggests that the SLC method can also be severed as a promising tool for auroral electrojet monitoring.

In the calculations, the SLC method estimates the current intensity at a specific point, while the LC method estimates the current value over the entire auroral crossing. Although there is a difference in AEJ peak amplitude between the two methods, their morphologies are very consistent, as shown in Figure 14a. This suggests that when the AEJ morphology is assumed to be relatively simple, the SLC method can be used in place of the LC method for deriving the local AEJ peak intensity and latitude. However, during periods of intense geomagnetic activity, the current may exhibit complex structures, such as the appearance of two closely spaced peaks, as shown in Figure 14b. The maximum can jump between two or more concurrent local maxima, leading to jumps in the overall maximum latitude and corresponding amplitude. It is worth to note that this does not mean our SLC method provides a wrong location or amplitude of AEJ, but could suggests that the AEJ sometimes may have shorter scale length, which needs further investigation.

Figure 14 Peak of AEJ position and intensity estimated using SLC and LC methods on satellite orbit (the left side corresponds to the ascending orbit, and the right side to the descending orbit).

We want to note that the SLC method provides only the location of AEJ peak. This approach more accurately represents the true current when the flow is concentrated in a narrow range of latitude. The actual magnetic signal is wider than the signal generated by an infinite line current, so the results may underestimate the true current (Vennerstrom & Moretto, 2013). However, in cases where the current system is complex, there may introduce deviations in our results. For instance, when the magnetic characteristics do not conform to the idealized “single line current” form, false positives and ambiguities can occur. For example, Figure 4 shows statistically that most AEJ peaks appear at low latitudes during the night and at high latitudes during the morning side. However, the specific examples in Figure 12 reveal that during the magnetic storm recovery phase, AEJ peak jumps can anomalously appear, indicating that the AEJ are highly dynamic being disturbed by the solar wind, and the current morphology is far from the simple line current flowing along magnetic latitudes.

4.3 Improvement and development

One of the most serious issue affecting the accuracy of geomagnetic field models comes from rapidly changing, high-amplitude signals due to polar and auroral current systems driven by magnetosphere-ionosphere coupling, particularly during geomagnetic storms or substorms. As described in Section 2, ideally, we need to remove uncoupled geomagnetic field effects to obtain reasonable results from our method. This means we need a geomagnetic field model that accurately represents all sources without mutual contamination. At present, no geomagnetic field model can adequately represent these signals, which means their signatures can inadvertently be mapped in the estimated internal field due to their internal origin to the satellites. Therefore, geomagnetic field modeling is also a crucial topic. It requires careful consideration of factors such as mantle conductivity separation, long-term solar wind conditions, and solar cycle variations (Smith et al., 2017). Using satellite-based indices is helpful for the data selection for the core and lithosphere fields modeling (e.g., Kauristie et al., 2017). The appearance of these trends in the polar along-track gradient is particularly important, as it is one of the largest noise sources in internal field modeling (Olsen & Stolle, 2017). Additionally, assuming the selected geomagnetic field model is completely accurate, the SLC method is better able to detect some small-scale equivalent current structures.

Although there is a strong linear relationship between the peak of the AEJ calculated using the SLC method and the SME index, further study is required to refine the classification of polar electrojet activity levels based on satellite-derived AE indices. When applying the SLC method across different satellites, several factors must be considered. For example, variations in satellite orbits and altitudes can introduce biases that affect the consistency of measurements across different spacecraft. Satellites in different orbits may cover distinct local time sectors, and altitude differences can influence how currents are detected due to changes in magnetic field strength and current geometry. These potential biases must be carefully addressed when combining data from multiple satellites to ensure consistent AE index estimations. Moreover, orbit segment selection should consider geographic and magnetic pole offsets, as well as the differing shapes of the auroral oval between hemispheres, since these factors can lead to discrepancies in comparing AEJ activity between the Northern and Southern Hemispheres. Another important consideration is the applicability limits regarding satellite orbits, particularly concerning maximum inclination and altitude. Since the SLC method assumes that the current is perpendicular to the satellite track, deviations from this assumption-especially in the Southern Hemisphere, where geometry is less favorable-could result in errors in current estimation. The lower temporal resolution of satellite measurements compared to ground-based SME data also poses a challenge. Combining satellite indices with ground-based measurements can provide a more comprehensive and accurate picture of auroral electrojet activity by covering more local time sectors and enhancing temporal resolution. Future refinements to the SLC method should focus on addressing these challenges to improve the accuracy and reliability of AE index classification for operational purposes.

5 Summary

Based on 10-year scalar magnetic field data from Swarm, we utilized the SLC method to calculate and analyze the global distribution of AEJ peak strength and location. The main findings are summarized as:

1. Compared to the LC method, which uses multiple line currents to estimate the auroral electrojet profile, the SLC method estimates the AEJ from the magnetic field intensity measured along the satellite trajectory. This simplified approach facilitates continuous, long-term assimilation of satellite observations, thereby producing equivalent current intensity and positional indicators that are well suited for monitoring AEJ activity.

2. We compared the peaks of AEJ derived from SLC method with that from the Swarm AEBS products based on LC method. The results indicate that the AEJ peak positions estimated by both methods agree quite well. In terms of AEJ peak amplitude estimation, the two methods exhibit a close linear relationship.

3. The AEJ peaks calculated using the SLC method effectively capture the level of AEJ activity. The results align well with the expansion and contraction of the auroral oval in response to variations in geomagnetic activity.

4. The SLC-derived AEJ peaks were compared further with the ground-based SME index, and both indices show high correlation in the MLAT range of 62°–76°, with stronger correlation in the Northern Hemisphere than in the Southern Hemisphere. The comparison confirms the reliability of our proposed SLC method for monitoring the auroral activity.

5. Despite being different types of data, both the SME index and the SLC method’s AEJ peak consistently depict the main characteristics of the AEJ system. This encourages the future use of combined ground-based and satellite datasets, which can improve spatial coverage, resolution, and uncertainty estimates compared to using a single data source, promising more accurate diagnoses of space weather conditions.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (42174191) and the Dragon-6 Cooperation 2024-2028 (Project No. 95437). The authors thank the European Space Agency for the magnetic field data and for making the Swarm data publicly available. We gratefully acknowledge the SME/SMU/SML indices, using the Newell and Gjerloev technique (Newell & Gjerloev, 2011), and special thanks to the “Macau Science Satellite-1” team for their guidance on this paper. We thank the anonymous referees and the editor for their helpful comments and suggestions. The editor thanks Ashley Smith and John Coxon for their assistance in evaluating this paper.

Data Availability Statement

Swarm Level 1b products are available from http://earth.esa.int/eogateway/missions/swarm/data.

The Swarm LC sourced from the Swarm AEBS products AEJxLPL_2F (Kervalishvili et al., 2020), are available from the https://swarmhandbook.earth.esa.int/catalogue/SW_AEJxLPL_2F.

The CHAOS 7-16 model can be accessed at the https://www.spacecenter.dk/files/magnetic-models/CHAOS-7/.

The Newell & Gjerloev (2011) SME indices are available from the https://supermag.jhuapl.edu/substorms/. The editor thanks Ashley Smith and John Coxon for their assistance in evaluating this paper.

Appendix A

Statistical Distribution Derived from Swarm B

In the Appendix A, we present the MLAT versus MLT distribution of the peak of AEJ dataset, derived from Swarm B, under different SME conditions as an indicator of geomagnetic activity and across various seasonal effects. With a large dataset coverage, the results from Swarm B show a high degree of similarity to those from Swarm A.

Figure A1 All detections collected from Swarm B data have been assigned based on the inferred current strength using the SLC method at QD coordinate system. The detections are shown for both the Northern and Southern Hemispheres, with 96,164 in the Northern Hemisphere and 89,320 in the Southern Hemisphere. Format matches Figure 4.

Figure A2 Same as Figure 4, using Swarm B data, divided by season under the condition 0 < SME < 300. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure A3 Same as Figure 4, but using Swarm B data, divided by season under the condition 300 < SME < 500. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure A4 Same as Figure 4, using Swarm B data, divided by season under the condition 500 < SME < 1000. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Figure A5 Same as Figure 4, using Swarm B data, divided by season under the condition 1000 < SME. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.

Appendix B

Comparison with the Swarm AEBS Products Using the Swarm B Dataset

In Appendix B, we present a comparison between the Swarm AEBS products and the results derived from the Swarm B dataset. Similar to the findings from Swarm A, our results exhibit a strong correlation with the AEBS estimates, with a high degree of consistency in the AEJ peak location estimations.

Figure B1 Swarm-B based quantitative relationship study of the estimated intensities using the LC and SLC methods. Format matches Figure 9.

Figure B2 Swarm B-based study on the positional bias in peak of AEJ estimates using the LC and SLC methods. Format matches Figure 10.

Appendix C

Correlation Between AEJ Indicator Derived from the SLC Method and SME based on Swarm B Data

In Appendix C, we present the correlation between AEJ peak and location derived using the SLC method and the SME index, evaluated across various MLT and MLAT ranges. These results are based on Swarm B observations, which show slight differences compared to Swarm A. Specifically, at 23:00 MLT in the Southern Hemisphere, the results from Swarm B exhibit a slightly higher correlation with SME than those from Swarm A. However, the overall trend observed in both datasets remains consistent.

Figure C1 The correlation between the peak of AEJ calculated using the LC algorithm and the SME index, as well as the correlation between the peak of AEJ calculated using the SLC algorithm and the SME index, across different MLT and MLAT values (Calculated from Swarm B, total of 182,811 detections were recorded, with 96,164 in the Northern Hemisphere and 89,320 in the Southern Hemisphere). Format matches Figure 13.

References

All Figures

Figure 1 Sketch of the geometry used in the Line Current method. The auroral electrojets are represented by a series of line currents located at an altitude of 110 km. δB denotes the total magnetic residual, where δB∥ is the component parallel to the main magnetic field and δB⊥ is the perpendicular component. The triangle represents the satellite’s flight path, and the circles mark the positions of the line currents. (rn, βn) and (rk, βk) indicate the satellite and the line current at a given location, respectively. Δβ signifies a systematic shift toward lower latitudes in the location of the current maximum. Modified from Aakjær et al. (2016).

In the text

	Figure 2 The parallel magnetic perturbation components (blue line) with respect to the main magnetic field at 60° MLAT. The green dotted line is the derivative along the track of the magnetic perturbation components, the red vertical line indicates the location of peak green dotted line. The gray vertical line indicates the position of the placed current line.
In the text

	Figure 3 Systematic deviation in estimated peak of AEJ corresponding to different altitudes and MLAT.
In the text

Figure 4 All detections collected from Swarm A data have been assigned based on the inferred current strength using the SLC method at QD coordinate system. The detections are shown for both the Northern and Southern Hemispheres, with 95,462 in the Northern Hemisphere and 87,349 in the Southern Hemisphere. An approximate 90-minute interval is allocated each hemisphere for collecting each peak dataset, while each detection phase takes about 20 min to analyze data points above 50° QD latitude. Negative values represent westward electrojets, while positive values represent eastward electrojets.

In the text

	Figure 5 Same as Figure 4, using Swarm A data, divided by season under the condition 0 < SME < 300. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure 6 Same as Figure 4, using Swarm A data, divided by season under the condition 300 < SME < 500. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure 7 Same as Figure 4, using Swarm A data, divided by season under the condition 500 < SME < 1000. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure 8 Same as Figure 4, using Swarm A data, divided by season under the condition 1000 < SME. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

Figure 9 Swarm A based quantitative relationship study of the estimated intensities using the LC and SLC methods (a–b is the global result, c–d is the northern hemisphere result, e–f is the southern hemisphere result). The left panels present the peak current amplitude of the SLC method is shown on the bottom x-axis, and the peak current amplitude of the LC method is shown on the left y-axis. The color indicates the occurrence distribution of the collected data points. The line of fit is shown in solid blue. The right panels present the variation in estimated AEJ peak positions with local time for both the SLC and LC methods. ΔQD latitude represents the difference in estimated AEJ peak magnetic latitude between the SLC and LC methods in the QD coordinate system. The blue dots indicate the average relative error, while the red vertical lines represent the standard deviation, with an averaging window of 1 h.

In the text

	Figure 10 Swarm A based study on the positional bias in peak of AEJ estimates using the LC and SLC methods (top is global results; bottom displays Northern Hemisphere results on the left and Southern Hemisphere results on the right).
In the text

	Figure 11 Examples of data from Swarm A, where the time series of the sheet current amplitude is compared to the SME index. The time series of the SME index and the current estimated by the LC method or SLC method are shown for a period of 768 orbits from 7 March to 31 March 2015.
In the text

Figure 12 Using Swarm A data, the figure illustrates the estimated peak of AEJ positions using the SLC and LC methods for the Northern Hemisphere over four days starting from 13 March 2019. The second and third rows show the peak of AEJ positions for ascending and descending orbits, respectively. The first row represents the time variations of SME, SMU, and SML. The fourth row displays the time series of AEJ calculated using the SLC method compared to SME.

In the text

Figure 13 The correlation between the peak of AEJ calculated using the LC algorithm and the SME index, as well as the correlation between the peak of AEJ calculated using the SLC algorithm and the SME index, across different MLT and MLAT values. (Using 2s bin window based on Swarm A, data from Swarm A spanning the period from December 2013 to November 2023 were analyzed. A total of 182,811 detections were recorded, with 95,462 in the Northern Hemisphere and 87,349 in the Southern Hemisphere).

In the text

	Figure 14 Peak of AEJ position and intensity estimated using SLC and LC methods on satellite orbit (the left side corresponds to the ascending orbit, and the right side to the descending orbit).
In the text

	Figure A1 All detections collected from Swarm B data have been assigned based on the inferred current strength using the SLC method at QD coordinate system. The detections are shown for both the Northern and Southern Hemispheres, with 96,164 in the Northern Hemisphere and 89,320 in the Southern Hemisphere. Format matches Figure 4.
In the text

	Figure A2 Same as Figure 4, using Swarm B data, divided by season under the condition 0 < SME < 300. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure A3 Same as Figure 4, but using Swarm B data, divided by season under the condition 300 < SME < 500. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure A4 Same as Figure 4, using Swarm B data, divided by season under the condition 500 < SME < 1000. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure A5 Same as Figure 4, using Swarm B data, divided by season under the condition 1000 < SME. Each seasonal dataset is composed from observations taken within ±45 days of each solstice/equinox.
In the text

	Figure B1 Swarm-B based quantitative relationship study of the estimated intensities using the LC and SLC methods. Format matches Figure 9.
In the text

	Figure B2 Swarm B-based study on the positional bias in peak of AEJ estimates using the LC and SLC methods. Format matches Figure 10.
In the text

Figure C1 The correlation between the peak of AEJ calculated using the LC algorithm and the SME index, as well as the correlation between the peak of AEJ calculated using the SLC algorithm and the SME index, across different MLT and MLAT values (Calculated from Swarm B, total of 182,811 detections were recorded, with 96,164 in the Northern Hemisphere and 89,320 in the Southern Hemisphere). Format matches Figure 13.

In the text