This section discusses the final GRACE-FO data set and its application. We assess the residuals to CHAOS-7 predictions of all vector components and perform an independent validation by comparison to high-precision observations from the simultaneous Swarm mission, e.g., during orbit conjunctions or close flybys. By discussing selected scientific applications on auroral field-aligned currents and signatures of the magnetospheric ring current, this section aims at further outlining opportunities and limitations of the GRACE-FO data set.
Assessment of final data set
Table 3 provides the mean and the standard deviations of the residuals of the final magnetic field vector of GF1 and GF2 to CHAOS-7 predictions for \(|\text{QDLAT}|<50^\circ\), \({\text{Kp}}\le2\), and \(|\text{Dst}| \le 30\,\text {nT}\). Averaged over the entire period of GRACE-FO, the mean is zero, which is not surprising, since the data have been calibrated against CHAOS-7. The standard deviation is few nanotesla and is in general a bit higher for GF2 than for GF1. For a single day, the standard deviations do not differ significantly from the one of the entire period, but the mean is slightly biased. For comparison, the lower rows in Table 3 provide the values for the raw magnetic data provided in L1b. Both mean and standard deviation have dramatically been reduced after calibration and characterisation. The amplitudes in standard deviation of few nanoteslas are similar to those of the root mean scatter of the CryoSat-2 residuals discussed in Olsen et al. (2020), which varied between 4 and 15 nT depending on local time and geomagnetic activity. This agreement is especially remarkable, because CryoSat-2 carries three identical magnetometers, and Olsen et al. (2020) compares the mean of their calibrated times series, which further reduces the effect of the intrinsic noise from the single instruments.
Table 3 Mean and standard deviation of residuals to CHAOS-7 for GF1 and GF2 for geomagnetic quiet times and for a single quiet day, 30 January 2019 To estimate the impact of the different parameters on the final results, Eq. 5 was applied but omitting single parameters in Table 2 in each application. The standard deviation of the residuals to CHAOS-7 for each of these applications is given in Table 4 for both GF1 and GF2. The minimum and maximum values of the residuals of each respective result are also provided. Largest standard deviation is observed when solar array and battery currents are not considered in the characterisation. Large spikes or jumps can be corrected with knowledge of the magnetorquer currents. For GF2, battery currents and solar arrays have larger impact than for GF1. Also, on GF2, the temperature dependence of the scale factor is an important parameter.
Table 4 Magnetic impact of calibration and characterisation, respectively, for each parameter given in Eq. 13 and the non-linear parameters in Eq. 9 Figure 3 provides residuals between the processed data and CHAOS-7 predictions for January 2019, e.g., their mean of all residuals within each bin of a grid with bin size of \({5}^{\circ }\) geocentric latitude and \({5}^{\circ }\) geocentric longitude. The four columns are for the \(B_\text{N}\), \(B_\text{E}\), and \(B_\text{C}\) component of the NEC frame, respectively, and for the total field F. The first row displays residuals to the core, the crustal and the large-scale magnetospheric field predictions of CHAOS-7 for GF1, and the second row shows the same for GF2. The grey lines indicate the \({0}^{\circ }\) and \(\pm {70}^{\circ }\) magnetic latitude (QDLAT). The third row shows the difference between GF1 and GF2 residuals. The last row gives geomagnetic and solar indices and magnetic local time of the data set of this month. Hence, the mission flew in a 07/19 MLT orbit and the month was geomagnetically very quiet. In both GF1 and GF2, largest deviations occur at auroral regions which result from the auroral electrojet and field-aligned currents. Since the data are collected at 07/19 MLT, no significant low- and mid-latitude ionospheric disturbances are expected, neither significant effects from magnetospheric currents during the quiet times. However, some systematic deviations occur, such as above the northern Atlantic in the \(\Delta B_\text{E}\) and \(\Delta B_\text{C}\) components of GF1 and the ribbon at low latitudes in \(\Delta B_\text{C}\) of GF2. These could not be accounted for through correlation with any known satellite characteristic. However, residuals of 10 nT or less can be seen as an acceptable result for data from a non-dedicated magnetometer where magnetic cleanliness of the satellite has not explicitly been taken care of. The differences between the GF1 and GF2 residuals show similar amplitudes in mid and low latitudes, which indicates that artificial disturbances from the satellite are not identical between the two spacecraft. It is interesting to note that the statistics for calibrated CryoSat-2 magnetic data provided by Olsen et al. (2020) (not shown) reveal a similar behaviour. CryoSat-2 satellite carries three active magnetometers from the same type of Billingsley (Billingsley 2020) as does GRACE-FO, and, e.g., only \(B_\text{C}\) from one magnetometer (magnetometer 2) show a disturbance at the magnetic equator with similar amplitude than for \(B_\text{C}\) of GF2, but this effect is reduced or absent for the other two data sets of \(B_\text{C}\) of CryoSat-2. In contrast, high amplitudes due to auroral electric currents are largely reduced in the third row of Fig. 3, but did not vanish as could be expected from a natural signal. This fact hints to small-scale structures in the magnetic field at high latitudes that have shorter wavelengths than 20 s (Gjerloev et al. 2011), being the mean separation time between GF1 and GF2. These observations need detailed investigations, e.g., sorted for MLT or geomagnetic activity, to allow discrimination between natural and satellite intrinsic variability, which is currently beyond the scope of this paper. A first analysis, however, revealed that the positive differences at around \({30}^{\circ } \, \text {E}\) at the daylight Southern polar region accumulates around magnetic noon, which is the typical region of the polar cusp and known for small-scale structures. As the reader shall note, Fig. 3 represents one of the geomagnetic quietest months of the processed period of GRACE-FO data. The pattern changes from month to month and mean residuals up to 15 nT also at mid and low latitudes occur at other months.
Figure 4 provides orbit-wise residual vectors in the NEC frame for a period in September 2019 for ascending (\(\sim\) 12 MLT) and descending (\(\sim\) 00 MLT) orbits around noon and midnight, respectively. Top panel red lines show GF1 results and bottom panel blue lines GF2 results. Black lines provide mean values at each QDLAT. The geomagnetic activity was low with Kp \(\le\) 4 (median Kp = 1.3) and Dst > − 30 nT (mean Dst = − 5.5 nT). The significant variability of the single orbits indicates the day-to-day variability of ionospheric currents, and the statistical mean hints to typical ionospheric features. As expected, largest deviations occur at auroral latitudes. The negative excursion of \(B_{\text{N}}\) and the flip of sign towards negative towards North in \(B_{\text{C}}\) reflect signatures of the eastward equatorial electrojet. The amplitudes in both components of about 10 nT are consistent with signatures detected earlier in CHAMP (Lühr and Maus 2006). The flip of sign towards positive towards north in \(B_{\text{E}}\) with a few nanotesla amplitude during noon is also consistent with the earlier CHAMP results and reflects inter-hemispheric field-aligned currents. These signatures relate to a statistical analysis for inter-hemispheric field-aligned currents and F-region dynamo currents conducted by Park et al. (2020) based on GRACE-FO data. GF2 observations are less clear for these low-latitude ionospheric signatures, a fact which is also supported by Park et al. (2020). On the night side, the GF1 residuals are very low which is expected due to the absence of strong ionospheric currents. However, an inconsistency is visible in GF2 \(B_{\text{C}}\) at the magnetic equator, as already noted in Fig. 3. This disturbance seems being artificial and is in opposite direction to the equatorial electrojet signatures on the dayside. Assuming that this artificial disturbance is not only confined to the night side, it might be the reason why the dayside equatorial GF2 \(B_{\text{C}}\) shows lower amplitudes than the expected 10 nT from the natural signal. Similar consideration seems true for all three components, which are in general more disturbed during nighttime at GF2 than at GF1 and appear artificial.
Comparison to magnetic data of Swarm
Figure 5 shows the MLT and altitude evolution of the GRACE-FO, Swarm, and CryoSat-2 missions, as well as the daily (grey) and monthly averaged (black) solar flux index F10.7. GRACE-FO and Swarm B fly at similar altitudes and a conjunction in MLT between GRACE-FO and Swarm B occurred early November 2019. At this time, the solar flux index has been low with approximately \({F10.7} = 70\,\text {sfu} \; (1\,\text {sfu} = 10^{22}\,\text {W} \,\text {m}^{-2}\,\text {Hz}^{-1})\).
Figure 6 compares the magnetic data between the two missions during their conjunction interval between November 2 and November 14. Geomagnetic activity was low with Kp \(\le 2^{+}\) and Dst \(\ge\) − 20 nT. The two missions were counter-rotating, e.g., the MLT at their respective equator crossings was \(\sim\) 10 MLT for the ascending node of GRACE-FO and for the descending node of Swarm B, and it was \(\sim\) 22 MLT for the descending/ascending nodes, respectively. We define a ’conjunction’ when the distance between the GF1 or GF2 satellites and Swarm B were less than 400 km. Since the conjunctions occurred during counter-rotating orbital segments, they only lasted few seconds each. Panels 3 give the intra-satellite distance for each conjunction and panels 4 provide the mean QDLAT at which the conjunction happened. Panels 5–7 plot the differences between the residuals of the calibrated magnetic data to the respective CHAOS-7 predictions for GF1 or GF2 and Swarm B for each conjunction and for each magnetic component. The majority (> 80%) of the differences of the single conjunctions are within ± 10 nT for all 3 components. The smallest scatter occurs for \(B_\text{C}\), followed by that of \(B_\text{N}\) and then of \(B_\text{E}\). This can have several reasons, such that different ionospheric currents affect different components at different latitudes. Another aspect is that \(|B_\text{C}|\) includes the widest range of values with up to 65,000 nT, followed by \(|B_\text{N}|\) up to 30,000 nT, and \(|B_\text{E}|\) up to 15,000 nT. Variables with wider ranges can be estimated with lower uncertainty. The mean difference to Swarm B over all conjunctions is slightly larger for day time than for night time orbits, e.g., GF1 day time \(\Delta (B_\text{N}, B_\text{E}, B_\text{C})\) = (−1.02, −2.56, 0.73) nT, GF1 night time \(\Delta (B_\text{N}, B_\text{E}, B_\text{C})\) = (0.12, −0.41, 0.95) nT, GF2 day time \(\Delta (B_\text{N}, B_\text{E}, B_\text{C})\) = (−0.20, −3.72, 1.44) nT, and GF2 night time \(\Delta (B_N, B_E, B_C)\) = (−1.18, −0.07, 1.47) nT. The less good agreement during day may result from dayside ionospheric currents which introduce stronger spatial and temporal variability of the magnetic field. The overall small differences between the GRACE-FO and the Swarm observations further support the high quality of the calibrated magnetic data set of the GRACE-FO mission.
The magnetic effect of the magnetospheric ring current during the August 26, 2018 storm
A geomagnetic storm with values of Dst < −150 nT occurred on August 26, 2018. During this time, all Swarm spacecraft, CryoSat-2, and GF1 were in orbit, and calibrated magnetic data are available for each of these missions. Unfortunately, GF2 does not provide magnetic data for August 2018. Figure 7 shows the evolution of the magnetic effects of the magnetospheric ring current, as well as the Dst index. The squares, triangles, and circles represent medians of residuals of the horizontal component of the magnetic field (\(\sqrt{B_{\text{N}}^2+B_{\text{E}}^2}\)) within \(\pm\, {20}^{\circ }\) QDLAT and projected to \({0}^{\circ }\) QDLAT for each low-latitude orbital segment of the respective satellite. The residuals are with respect to the CHAOS-7 core and crustal field predictions. The large-scale magnetospheric field was not subtracted, and signatures from magnetospheric currents (including its induced counterpart in Earth) remain included in the data. The point populations of all missions follow in generally well each other and the Dst index, despite the different retrieval technique for magnetospheric signatures in ground and satellite data. It is known from earlier studies that ground-based derived ring current signatures (such as for deriving the Dst index) show systematic differences to those derived in space (Maus and Lühr 2005; Olsen et al. 2005; Lühr et al. 2017), e.g., the ring current signal at LEO is generally more negative than at ground, which is also here reflected in an offset between the Dst index and the satellite-derived residuals. In addition, different groups of missions categorised in ascending and descending nodes appear to cluster and show an apparent offset to each other. This apparent offset between the categories represent local time differences of the magnetospheric ring current signature. Figure 8 shows the SuperMAG Magnetospheric Ring current indices (SMR, Newell and Gjerloev 2012) for the four local time sectors at midnight, dawn, noon, and dusk (00 MLT, 06 MLT, 12 MLT, and 18 MLT) together with the Dst index. Also here, a few differences between the two index groups may occur due to different retrieval techniques, such as in baseline determination or selection of observatories (e.g., Love and Gannon 2009; Gjerloev 2012; Newell and Gjerloev 2012). While the values for the four MLT sectors of the SMR are close to each other before the storm onset around 18 UTC on August 25, as well as during the recovery phase after about 18 UTC on August 27, they significantly deviate during the main phase of the storm, with highest values at 06 MLT and lowest at 18 MLT. The values at 12 MLT and 00 MLT are similar to each other and in-between the values at dawn and dusk.
Figure 9a–d shows four snapshots of magnetic residuals equatorward of \(\pm\, {20}^{\circ }\) QDLAT and collected within 2 h time windows from each of the satellite missions, before the storm onset (16 UTC, August 25), shortly after the storm onset (23 UTC, August 25), during the main phase of the storm (06 UTC, August 26), and during the recovery phase (04 UTC, August 27). After the storm onset, a clear expansion of the magnetospheric field develops at the dusk side and the signal is least at dawn. This is in agreement with the SuperMAG indices, and the values are comparable with about − 25 nT/− 75 nT and − 100 nT/− 200 nT in panels b and c at dawn/dusk, respectively. The selected constellation of satellite missions did not cover midnight and noon, and less information is available from these MLT sectors. The described scenario is a typical storm behaviour and has been identified and discussed by statistical studies from LEO satellite observations or extended ground-based magnetic networks (e.g., Le et al. 2011; Pick et al. 2019). It has been attributed to either an asymmetric ring current component, to addition ionospheric currents, or to effects of enhanced high-latitude R2 field-aligned currents during geomagnetic storms.
Auroral field-aligned currents
The calibrated magnetometer data from GF1 and GF2 were used to derive magnetic field-aligned currents. Therefore, we applied the processing algorithm, which is based on Ampères law and is similar to that used to derive Swarm single satellite field-aligned current (FAC) products available as the Swarm Level-2 product FACxTMS_2F (with x = A, B, C) from ESA and described in Ritter et al. (2013) and Kervalishvili (2017). We refer the reader to these documents for a detailed description of the algorithm. The method has also successfully been applied to magnetic observations from earlier missions, like CHAMP (e.g., Wang et al. 2005) and to DMSP (Xiong et al. 2020).
Figure 10 shows FACs derived from GF1 and GF2 data for an event on 31 October 2019 when they crossed the northern auroral latitudes. At this time, Kp = \(4^{-}\), AE \(\sim\) 100 nT (Auroral Electrojet index), and Dst \(\sim\) − 7 nT. The event was chosen due to co-located data by Swarm B, which will be discussed in the next paragraph. The data of the two GRACE-FO satellites show similar FAC variations along their orbits, but with a time delay of about 24 s, the time difference when GF1 and GF2 reached the highest magnetic latitude of their orbits (upper panel).
The middle panel shows the time-series plotted along Apex latitude (MLAT, Richmond 1995; Emmert et al. 2010). FAC signatures derived from the two satellites compare well to each other in location of occurrence and in amplitude. Enhanced FAC events are observed between \({65}^{\circ }\) and \({72}^{\circ }\) and \({70}^{\circ }\) and \({83}^{\circ }\) MLAT on the dusk and dawn sides, respectively. At other latitudes, GRACE-FO FACs show a noise level less than 0.5 \({\upmu } \text {A}/\text{m}^{2}\). After applying a low-pass filter with cut-off frequency of 20 s, the FAC profiles from the two satellites are nearly identical. This cut-off frequency ensures a cut-off for kinetic Alfvén waves that is observed to be at periods between 4 and 10 s depending on ionospheric conductivity (Ishii et al. 1992). The cross-correlation between the two time-series over MLAT maximises with \(R_{\text{max}}\) = 0.86/0.73 for the 1 s-series and with \(R_{\text{max}}\) = 0.98/0.93 when the 20 s filter was applied. This maximum correlation was found for zero time-shift for both the 1 s and 20 s-filtered FAC series. This result indicates that large-scale structures in the FAC event dominated and are persistent and almost stationary within 24 s, the time both satellites crossed the same area. This result is in agreement with Gjerloev et al. (2011) who applied magnetic data of the ST 5 constellation mission of 3 spacecraft following each other with varying separation between few seconds and 10 min. The mission was operational for 3 months within May and June 2006 and was launched in dawn–dusk orbit. They correlated the magnetic signatures of field-aligned currents of different scale sizes and concluded that FAC systems with scale sizes larger than 200 km (corresponding to 26 s for an average satellite velocity of 7.5 km/s) appear to be stable on time scales of about 1 min. When several years of GRACE-FO data will be available in future, similar studies can be conducted across all local times and seasons, with the only caveat of a fixed inter-spacecraft separation.
Figure 11 shows the same event, but comparing GF1 (black line) with Swarm B data (red line) during a conjunction event. GF1 and Swarm B were counter-rotating at similar magnetic local times (top panel), and the UTC difference was about 14 min at the highest magnetic latitude of \({88.8}^{\circ }\) and \({85.8}^{\circ }\) of their respective orbits. Enhanced FAC signatures display at similar magnetic latitudes. The 1 Hz FAC time-series of Swarm B shows larger amplitudes than for GF1 at some locations (middle panel) which may hint to a possibly higher sensitivity of the Swarm science magnetometers, but may also represent differences in FAC structures at the slightly different locations and times. Away from the FAC event, Swarm shows a significantly lower noise level than GRACE-FO. After applying a low-pass filter with a cut-off frequency of 20 s to the 1 Hz data (lower panel) for both satellites, the large-scale structures show consistent features with similar amplitudes between the two missions. This example shows that large-scale FACs derived from GF1 and GF2 compare well with observations from high-precision magnetic data, e.g., from the Swarm mission, and thus can be considered reliable. However, due the enhanced noise level of nearly 0.5 \({\upmu } \text {A}/\text{m}^{2}\), only case studies with event magnitudes well above this noise level can be investigated.
While the GRACE-FO magnetometers sample at a rate of 1 s without on-board filtering of higher sampled data, the Swarm 1 Hz observations are the result of a filtering based on 50 Hz samples. The comparison above shows that spot sampling at 1 Hz (such as for GRACE-FO) does not seem to significantly affect the results for FACs and especially is suitable to reliably derive signatures of FAC structures with scale lengths of 180 km or longer (corresponds to 24 s inter-spacecraft separation).
Figure 12 shows a statistical view of the MLAT versus MLT distributions of FACs derived from GF1. The data from the full data set available have been sorted into MLAT (\({1}^{\circ }\)) and MLT (1 h) for northward (IMF \({B_\text{z}}>\) 0) and southward (IMF \({B_\text{z}}<\) 0) interplanetary magnetic field (IMF) conditions, as well as separately for the two hemispheres. The FAC show clear Region 1 (R1) and Region 2 (R2) patterns, with higher intensity and expanding to lower latitudes for southward IMF \({B_\text{z}}\). For northward IMF \({B_\text{z}}\) (NBZ), the known current pair NBZ appears poleward of the R1 sheet around local noon. The IMF \({B_\text{z}}\) dependence of FAC derived from GF1 compares well to those of previous publications (e.g., Wang et al. 2008; Korth et al. 2010; Milan et al. 2017). Furthermore, the intensity of the FACs in the northern hemisphere is slightly higher than that in the southern hemisphere, which is consistent with the finding of Coxon et al. (2016) derived from AMPERE data, Laundal et al. (2018) and Workayehu et al. (2019) derived from Swarm observations, and with Xiong et al. (2020) derived from DMSP observations. These plots show that also small amplitudes near the noise level of GRACE-FO data are well accessible when they are applied in a statistical approach. This capability was also demonstrated by Park et al. (2020) who used CryoSat-2 and GRACE-FO data and successfully characterised interhemispheric field-aligned currents which have statistical amplitudes of as low as few \({\text{nA}/{\text{m}}^2}\).