In order to exclude storm time effects in the magnetic data, we identified days between December 2013 and December 2014 with the following selection criteria based on geomagnetic indices: Dst > −20 nT and AE < 100 nT during 00–24 UT of the respective day and Kp ≤ 1 during 00–24 UT of the respective day and of the two preceding days. We also looked for local times for which we either can expect pronounced features of typical ionospheric currents, or periods for which ionospheric currents are very small or absent. Therefore, we concentrated on periods when satellite Swarm A was in a noon–midnight orbit. At noon, the EEJ and the Sq currents are largest and their signatures are clearly expected in the magnetic field. At midnight, E region currents at mid- and low latitudes are absent, and we expect reduced F region currents, such as diamagnetic and gravity-driven currents, e.g., compared with post-sunset hours where these currents can reach several nanoteslas in the magnetic field at low Earth orbit altitude (e.g., Alken 2015). Between December 2013 and December 2014, we identified orbits from 21 days that meet these criteria. Out of these days, we choose December 12, 2013, for which the Dst index varied between 2 and −11 nT, and the auroral electrojet index (AE index) did never exceed 89 nT.
In order to be able to discuss representative examples, we further identified orbits where the lithospheric field is pronounced (i.e., above the African continent) and another orbit where it is weak (i.e., above the Pacific). The two dayside orbits have been selected since those show clear signatures of the Sq currents at the Southern Hemisphere. We believe that this selection is representative for a broad range of typical scenarios.
Figure 1 shows differences of the magnetic field magnitude, ∆F, between observations and IGRF and CHAOS-5 model predictions for the three selected orbits on December 12, 2013, for Swarm spacecraft A, plotted over quasi-dipole (QD) latitude. The QD magnetic coordinate system is described in Emmert et al. (2010). The lower panels show the magnetic local time of the respective orbital segments. The left panel represents a descending orbital part located around local midnight and the middle and right panel ascending orbits around local noon. The black line shows ∆F
Io time series and includes signatures from ionospheric currents. As expected for mid- and low latitudes (<60° QD latitude) at the nightside, the ionospheric signals are very weak (<1 nT) and can be attributed to remaining gravity-driven currents, plasma pressure gradient-driven currents, or currents produced by the F region dynamo, or might include other unmodeled sources. For this example orbit, the residual at the magnetic equator vanishes (∆F
Io = 0 nT); thus, the predictions of the magnetospheric field from the CHAOS-5 model did match the observed magnetospheric signature at this time and location very well. The left panel of Fig. 2 shows equatorial segments of all (92) orbits between December 2013 and December 2014 and 23–01 LT for days with Kp ≤ 1 and Dst ≥ −20 nT. The mean of large-scale equatorial ∆F
Io is about +2 nT and in a few cases reaches up to ±10 nT. This implies that the recent models of the magnetospheric field in certain cases slightly under- or overestimates the magnetospheric effects. One reason could be that the RC index, although derived from observatories located at different longitudes, provides a global mean value that cannot reflect potential local time and/or longitudinal variations of the magnetospheric ring current. However, we did not investigate this issue in more detail here.
The dark northern auroral latitudes show signatures of some +20 nT caused by the auroral electrojet, and this is consistent with regular activity even during very quiet geomagnetic times (Ritter and Lühr 2006). Auroral field-aligned currents connecting the ionospheric and magnetospheric current systems strongly affect satellite magnetic data since the spacecraft is directly crossing, or in close proximity to, these currents. However, field-aligned currents have no signatures in the component along the field line and therefore a negligible effect in ∆F. The sunlit southern auroral region is electrically more conductive and carries E region ionospheric currents with a signature of several tens of nanotesla in the satellite data. The red curve shows ∆F
IoLi and thus includes ionospheric and lithospheric signals. Here, the satellite crosses the African continent, which exhibits significant crustal magnetization anomalies. The residuals ∆F
IoLi have amplitudes up to ± 10nT in mid- and low latitudes. The amplitudes and spatial extensions are comparable to that of the signal from ionospheric sources like the (nighttime) auroral and equatorial electrojets and the midlatitude Sq currents. The blue curve shows ∆F
IoMa and includes the field of the large-scale magnetospheric ring current plus the ionospheric signal. The magnetospheric signal clearly dominates in amplitude, and its magnetic field in first approximation is globally southward directed at the Earth, thus reducing the magnetic field strengths at low latitudes and increasing it at high latitudes. The magnetospheric field has its largest impact in leveling magnetic signals from other, e.g., ionospheric sources. As an example, the start and peak points of a magnetic signature caused by an auroral electrojet in the Northern Hemisphere are indicated by thick bullets on the black and blue lines in the left panel of Fig. 1. Taking this example, the difference between the northern polar end of the orbit and the peak in ∆F
Io at 73°N QD latitude is reduced from 10.7 nT in ∆F
IoLi to 9.1 nT in ∆F
IoMa, while the difference between the equatorward edge of the current signature and the peak in ∆F at 73°N QD latitude are enlarged from 16.2 to 17.8 nT, respectively (differences relate to the thick points on the black and blue lines). Both, compression and stretching, amount to a deformation of this ionospheric signal by about 10 % on each side. The large-scale trend that is introduced by missing magnetospheric corrections distorts the apparent shape of ionospheric and lithospheric signals and depends on the strength of the magnetospheric signal that is time varying and has longitudinal dependence (e.g., Newell and Gjerloev 2012). The residuals between the observations and the IGRF predictions, \(\Delta F_{\text{IGRF}}\), are shown by the green line. It includes signatures from the magnetosphere and lithosphere. Residuals to IGRF are not suitable to investigate quiet-time currents on the nightside. Without the high-resolution crustal magnetic field model, it would not be possible to identify and interpret the ionospheric signals in the magnetic data except of those from strong electric currents which occur in the sunlit auroral and polar cap region or during substorms.
The middle panel in Fig. 1 shows residuals of a dayside orbit from Swarm A, where E region currents are prominent and dominate the ionospheric magnetic signatures in the low- and midlatitudes. The equatorial electrojet (EEJ) flows along the geomagnetic equator and depresses the magnetic field at satellite altitudes by about 8 nT in this example. Another prominent depression of ∆F is visible at about −28° QD latitude which results from the midlatitude Sq currents that are strong on the local summer hemisphere. This orbit is located over the Pacific Ocean, where the lithospheric magnetization is weak. Its contribution causes only minor modulations of the ionospheric signals at low- and midlatitudes (red and black lines). As mentioned earlier, it is mainly the large-scale magnetospheric field that influences the leveling and thus the shape of other signals. For example, the peak of the southern Sq current signal in the middle panel is shifted from −29.3 to −33.9 nT and from −8.2° QD latitude to −26.8° QD latitude (from black to blue curve). At the north polar region, a lithospheric anomaly is present at the same place where auroral currents can be expected with similar amplitudes (compare with the left panel of Fig. 1). This orbital segment is located above Alaska, where the crustal magnetization is again enhanced compared with the oceanic crust. Here, the lithospheric model predicts a magnetization anomaly. Reduced by also the lithospheric predictions, only a very weak, if any, ionospheric signal remains in ∆F
Io.
A dayside orbit with significant ionospheric and lithospheric signals is given in the right panel of Fig. 1, showing an orbit above the African continent. Both amplitudes from the EEJ and the Sq currents are significantly disturbed, if predictions of the lithospheric field are not considered. As for the example of the EEJ, the amplitude between ∆F
Io and ∆F
IoLi is reduced by 15 % from −13.8 to −11.6 nT. The peak of the Sq current signal is reduced from −19.6 to −22.8 nT in the southern midlatitudes. The residuals between the observations and the IGRF predictions, \(\Delta F_{\text{IGRF}}\), are not suitable to describe properly quiet-time currents in the dayside E region.
Non-storm-related studies using the magnetic field are often concentrated on atmosphere–ionosphere coupling. Investigating the effect of residuals for single orbits is relevant when one is interested in uncertainties of magnetic field residuals during single events. This is the case, e.g., when investigating the effect of stratospheric warming events on the EEJ in satellite data, as such effects are expected to last only a few days (e.g., Park et al. 2012). For climatological investigations based on longer data sets, such as the longitudinal or latitudinal variation of quiet-time ionospheric currents, neglecting the static lithospheric field can add uncertainties in the results, for the example for EEJ studies. The middle panel in Fig. 2 shows results for all (49) orbits between December 2013 and December 2014 over the African continent between −10° and 50° geographic longitude during days with Kp ≤ 1 and Dst ≥ −20 nT and between 11 and 13 LT, when the EEJ is well developed. The thin black lines show ∆F
Io for each selected orbit, and the thin red lines show corresponding ∆F
IoLi. The thick lines show the respective means. The seasonal variability and the day-to-day variability of the EEJ are reflected by the large scatter of the profiles. The mean relative difference at the EEJ peak (at the magnetic equator 21–20 nT) is 5 %, and it is often higher for single passes. Alken and Maus (2007) published climatological model of the EEJ for 7 years of magnetic satellite observations from the CHAMP, Ørsted and SAC-C missions. Converting EEJ model estimates at the equator to eastward electric field (considering a conductivity model for conversion), they compared these estimates with electric field observations by the JULIA radar at the Jicamarca observatory located at about −78° longitude in Peru. They give an average uncertainty of their model predictions of 55.8 μV/m. A typical strength of the dayside equatorial electric field is 0.5 mV/m (see their Figure 7), which, in this case, corresponds to an uncertainty of about 10 %. Alken et al. (2015) compared direct outputs of electric field predictions derived from EEJ observations by CHAMP and Swarm, and similar deviations between the model prediction and JULIA observations of about 5–10 % occur for a typical value of 0.5 mV/m (their Table 1). The discussed climatological models analyzed magnetic observations with corrected lithospheric field, so the estimated error probably reflects other model uncertainties. However, they are in a similar range as the uncertainties that are introduced through missing lithospheric contributions in regions where the lithospheric field is significant, such as above the African continent. We therefore conclude that correcting for the lithospheric field in satellite magnetic data is significant when climatological models for longitudinal variations of ionospheric currents during quiet times are derived. For comparison, the right panel in Fig. 2 shows results for all (38) orbits between December 2013 and December 2014 over the Pacific ocean between −150° and −90° geographic longitude during days with Kp ≤ 1 and Dst ≥ −20 nT and between 11 and 13 LT. The lithospheric signatures are low above the Pacific, and as expected, the ionospheric residuals are almost not affected by them.
The Sq current is a dayside current that is flowing anticlockwise at the Northern Hemisphere and clockwise at the Southern Hemisphere. The current flow is around a focus that is located at midlatitudes approximately around noon but can shift by about ±1 LT hour depending on season, longitude or lunar age (e.g., Yamazaki et al. 2011; Stening and Winch 2013). At the focus, the horizontal magnetic signature from the E region current minimizes in amplitude, while the vertical component, Z, peaks. Therefore, Sq current circuits are better investigated from the magnetic field components than from the total field. Figure 2 shows \(\Delta B\) time series for the \(B_{X}\), \(B_{Y}\) and \(B_{Z}\) components for the orbit from the middle panel in Fig. 1. In Fig. 3, the Sq signature shows a zero crossing of \(\Delta B_{{X ,\,{\text{Io}}}}\) (upper left panel) collocated with the maximum of \(\Delta B_{{Z,\,{\text{Io}}}}\) (lower left panel). Hence, with reductions in core, lithosphere and magnetospheric predictions from a high-resolution magnetic field model, the focus of Sq is estimated at −30° QD latitude for this example. The identification of the Sq focus here would not have been possible without the reduction by a quiet-time magnetospheric model, as is shown by the blue and green lines. Note, however, that we did not take into account interhemispheric field-aligned currents that flow between the southern and the northern foci due to electric potential differences, mainly driven by conductivity differences between both hemispheres. These interhemispheric field-aligned currents are expected to contribute a few nanoteslas in the horizontal components at LEO satellites (Pedatella et al. 2011; Park et al. 2011). We also did not take into account induction currents in the crust, mantle and ocean that can have effects of few nanoteslas (e.g., Kuvshinov et al. 2007). Thus, the amplitudes of the determined Sq system may further change when considering all these aspects as well. However, our example demonstrates that neglecting the quiet-time magnetospheric signature predicted by a geomagnetic model can impact the leveling of the zero crossing of the northward component \(\Delta B_{X}\) locally by 20 nT, even during very quiet times. Also, the magnetospheric ring current reduces the downward magnetic component, \(\Delta B_{Z}\), in the Northern Hemisphere and enhances it in the Southern hemisphere since it is southward directed at the Earth. This behavior is well reflected comparing \(\Delta B_{{Z ,\, {\text{Io}}}}\) (black line) and \(\Delta B_{{Z,\,{\text{IoMa}}}}\) (blue line) in the lower left panel of Fig. 3 and hence results in a depression of the peak magnitude of the vertical component in the apparent focus of the Sq in the Southern Hemisphere. Interestingly, \(\Delta B_{{Z ,\,{\text{IGRF}}}}\) (green line) shows consistently lower values than \(\Delta B_{{Z ,\,{\text{IoMa}}}}\) (blue line) between −50° QD and +50° QD latitude. Such deviations may result from the short wavelengths (degree > 13) due to the difference in highest spherical harmonic degree of the core field description by IGRF and CHAOS-5, or from a difference in the representation of the secular variation. The evaluation of the different models of the core field is not subject to this study. For more details of model comparison, the reader is referred to Thébault et al. 2015b. Here, we want to reveal that considering quiet-time ring current signatures improves the interpretation of ionospheric signals. The magnetospheric ring current has least effects in the y component at Earth’s surface and in low Earth orbit. Therefore, ionospheric signatures are almost not modified by ignoring it, as is visible from the similarities in, \(\Delta B_{{Y , \,{\text{IoMa}}}}\) (blue line) and \(\Delta B_{{Y ,\,{\text{IoLi}}}}\) (red line) at mid- and low latitudes.
Auroral field-aligned currents have strong magnetic signatures in the components perpendicular to the magnetic field, which is reflected in \(\Delta B_{\text{X}}\) and \(\Delta B_{Y}\) compared with much lower fluctuations in \(\Delta B_{Z}\) being in close direction to the magnetic field lines of high inclination at high latitudes. For the horizontal components reflecting field-aligned currents with several tens of nanotesla, the corrections for the lithospheric and magnetospheric predictions get less important in this example.
The lower right panel in Fig. 3 shows another orbital segment at low latitudes and during local evening hours at 20.27 LT on January 21, 2014, with Dst ≥ −11 nT, AE ≤ 57 nT and Kp = 0 throughout the day and Kp ≤ 2 on the preceding two days. After sunset, the equatorial ionosphere is regularly affected by equatorial plasma irregularities that may exhibit strong plasma density gradients and create diamagnetic currents with signatures of up to a few nanoteslas in the magnetic field strengths. The scale and amplitude are overlapping with those of the lithospheric field, and their detection is affected when the satellite crosses regions of significant crustal anomalies. Figure 3 shows such an example with diamagnetic currents that are reflected in the magnetic field strength, F. The close correlation and the colocation of the magnetic variations with plasma depletions detected in situ by the spacecraft’s Langmuir probe confirm their ionospheric origin. On the Southern Hemisphere, the crustal anomalies are very small here and do not influence the detection of ionospheric signals. On the Northern Hemisphere, a crustal anomaly exists at the position of the plasma irregularity. This example shows that neglected lithospheric signals can introduce systematic magnetic signatures in ionospheric studies, e.g., by frequent false detections of ionospheric currents at locations with strong lithospheric magnetic anomalies. On the other hand, the diamagnetic currents can disturb lithospheric modeling. Diamagnetic currents show a typical seasonal and longitudinal distribution, they increase considerably with increasing solar flux, and they are enhanced with proximity to the F region, where the background electron density is increased (Stolle et al. 2008). These criteria are useful when selecting data for global lithospheric magnetic field modeling from LEO satellite observations.