1. Comparison of Field-Aligned Currents calculated by single spacecraft and dual spacecraft methods. Yulia V. Bogdanova, Malcolm W. Dunlop RAL Space, STFC, UK

2. Field-Aligned Currents Large-scale statistical R1/R2 current density distribution. In addition, smaller-scale and more variable current systems: - cusp and FTE-associated currents, - NBz currents, - R0 current system, - substorm current wedge, - BBFs-associated current systems, - aurora. 1. Single-SC method Slavin et al., 2008 2. Dual-SC method Ritter and Luhr, 2006: ~ Luhr et al., 1996: Assumptions: - Stable current sheet. - Indefinite current sheet. - SC crosses the current sheet at 90º. Assumptions: - Static system. - Constant current within the area. - 1Hz data are filtered.

3. Aim and outline The aim was to find: - How reliable the currents estimates are. - How well currents’ estimated by two methods agree with each other. - Have a statistical picture of currents’ agreement/disagreement. Agreement depends on: - Calibration of the magnetic field data. - Cross-calibration between two SC, A and C. - Quality of methods of current estimates and validity of the assumptions made. Outline: - Discussion of few events. - Results of statistical study.

4. FAC data from one orbit ~14 LT ~2 LT Single SC currents show small-scale variations and higher amplitudes than currents estimated by dual-SC method.

5. Small-scale current systems estimated by single SC method are not visible in 2- SC method – as that data set was averaged over ~ 20 sec. Can compare only large scale behaviour. For comparison, averaged single SC data over 20 sec using 2 methods: (i) moving box average with window of 20 sec; (ii) low-pass filter to remove high frequency fluctuations above 0.05 Hz (corresponds to t = 20 sec). Field-aligned currents, dusk-side (~14 LT), south

6. SC-AC vs SC-A SC-AC vs SC-C Both averaging methods agree quite well, remove high frequency fluctuations, and give averaged, lower amplitude, current density.

7. SC-AC, SC-A, and SC-C comparison Only averaged & filtered values are shown from SC- A and SC-C. Good agreement between two methods of filtering high-frequency signal from single SC data, although there are some differences. Relatively good agreement with dual-SC data – fluctuations of the current density. Dual-SC method gives larger peaks. Close to pole: large disagreement between the data – seen in many events. SC-A vs SC-AC SC-C vs SC-AC

8. SC-AC, SC-A, and SC-C comparison, dayside (11/12 LT), southern hemisphere Can see the similar fluctuations, but absolute values do not agree at the centre of the interval.

9. Active interval, high Kp index. Very good agreement for the strong current system Less so for smaller currents. Off-set in the data? SC-AC,SC-A, and SC-C comparison, nightside (1- 2 LT), northern hemisphere

10. Used all available data: dates 18/04/2014 – 05/11/2014 Version: V01_01. Only high-latitude regions have been used, Abs(LAT): 55-85º. Estimated averages of single-SC current density by two methods as discussed above. Resampled dual-SC data to the same timeline. Split the data set into 4 different sectors: dayside, 10-14 LT; dusk, 14-20 LT; dawn, 4-10 LT; nightside, 20-4 LT. Estimated: (i) ratio of the current density strengths estimated by dual- SC (SC-AC) and single spacecraft methods. (ii) difference between the current densities. Looked at ratios/differences as function of local time, LAT and strength of the current density estimated by dual-SC method. Method for statistical study

11. Dayside, 10-14 LT ~965,000 data points Field-aligned current density distribution from dual-SC method vs LT: Majority of measurements in ± 2 µA/m^2 range. There are some erroneous data points.

12. Ratio of currents’ strength vs LAT J AC /J A-averaged J AC /J A-filtered J AC /J C-averaged J AC /J C-filtered 1000 -1000 Large spread in the data points; negative points indicate opposite polarity if the currents, asymmetry between southern and northern hemisphere, both methods give similar picture, both SC also produce similar results.

13. Ratio of currents’ strength vs LAT J AC /J A-averaged south north Most data points are in ± 20 range. Colour: log10(# of points in the bin) Large number of events with opposite polarity. The most populated bins are with ratio between 0 and 1, and 1 and 2. Reasonably good agreement on a statistical level.

14. Ratio of currents’ strength vs LAT J AC /J A-filtered south north Low-pass filter method gives very similar statistical results, but with less spread in the distribution.

15. Ratio of currents’ strength vs LT J AC /J A-averaged J AC /J A-filtered J AC /J C-averaged J AC /J C-filtered 1000 -1000 Some spread in the data, two methods give similar results, two SC, A and C, give similar results.

16. Ratio of currents’ strength vs LT J AC /J A-averaged J AC /J A-filtered More broad distribution around at 11.5- 12.5 LT: expected from the cusp small- scale currents variability

17. Ratio of currents’ strength vs SC-AC FAC strength J AC /J A-averaged J AC /J A-filtered J AC /J C-averaged J AC /J C-filtered 1000 -1000 -55 Majority of the FAC SC-AC current density measurements are in ±1 µA/m 2

18. Ratio of currents’ strength vs SC-AC FAC strength J AC /J A-averaged J AC /J A-filtered Most of the data points are with the current values close to zero and with ratios in ± 1 bin. Large spread in ratios at low current values – not surprising. Better agreement at higher current values.

19. Magnitude of difference in currents’ strength vs LAT Abs(J AC -J A-averaged ) 6 0 Abs(J AC -J C-averaged ) Abs(J AC -J A-filtered ) Abs(J AC -J C-filtered ) 10 0 Majority of events are in range < 2 µA/m 2. Spread increases towards the poles – more noticeable in the northern hemisphere.

20. Magnitude of difference in currents’ strength vs LAT Abs(J AC -J A-averaged ) Abs(J AC -J A-filtered ) Majority of events have small differences between current estimates by two methods. Spread of events increases towards the poles. Systematic difference in the southern hemisphere.

21. Magnitude of difference in currents’ strength vs LT Abs(J AC -J A-averaged )Abs(J AC -J C-averaged ) Abs(J AC -J A-filtered ) Abs(J AC -J C-filtered ) Similar results are produced by different averaging methods and on SC-C and SC-A 6 0 10 0

22. Magnitude of difference of currents’ strength vs LT Most events have difference in the current estimates less than 0.1 µA/m 2. Possibly slighter larger spread at around mid-day.

23. Difference in averaged values Magnitude of difference in currents’ strength vs SC- AC strength Abs(J AC -J A-averaged ) Abs(J AC -J C-averaged ) Abs(J AC -J A-filtered )Abs(J AC -J C-filtered ) 6 0 -1010 Most of events are in the centre, with low current and low difference. Large current estimates have larger differences. Low-pass filter gives better results.

24. Magnitude of difference in currents’ strength vs SC- AC strength Abs(J AC -J A-averaged ) Zero-centred distribution, almost symmetrical for positive and negative currents. Disagreement between the current densities increases with the current’s value. Low-pass filter produces slightly better results.

25. Dusk, 14-20 LT, ~775,000 data points Other sectors showed very similar results: -Quick look at dusk sector. -Spread in the data points is smaller at dusk/dawn than at other sectors – as expected.

26. Ratio of currents’ strength vs LAT J AC /J A-averaged J AC /J A-filtered Similar to the dayside sector: differences between hemispheres. Most events are in the ratio range of 0-2.

27. Ratio of currents’ strength vs LT J AC /J A-averaged J AC /J A-filtered Better agreement between the currents’ estimates at ~ 17 LT: less disturbed and larger scale currents are expected.

28. Ratio of current strength vs LT J AC /J A-averaged J AC /J A-filtered More points with the same polarity than in the dayside sector.

29. SC-A Magnitude of difference in currents’ strength vs LAT Abs(J AC -J A-averaged ) Abs(J AC -J A-filtered ) Similar to the dayside sector.

30. Magnitude of difference of current strength vs LT Abs(J AC -J A-averaged )Abs(J AC -J A-filtered ) Better agreement between the currents’ estimates at ~ 17 LT: less disturbed and larger scale currents are expected.

31. Magnitude of difference of current strength vs SC- AC FAC strength Abs(J AC -J A-averaged ) Abs(J AC -J A-filtered ) Similar to the dayside sector.

32. Conclusions Statistical comparison of the L2 data product with single (filtered) and dual-SC estimates of the FAC current densities shows: There is a large spread in the data points, including the currents of opposite polarity as calculated by two methods. However, statistically the currents’ estimates agree very well => confidence in the data products. Both SC-A and SC-C give very similar results statistically. Both averaging methods give similar results, possibly low-pass filter is slightly better. Disagreement between the current estimates increases towards the polar regions. Near southern pole: systematic disagreement between the estimates (off-set). Dusk/dawn estimates agree better than dayside/nightside – in agreement with more stable and large-scale current systems expected at dusk/dawn. Such statistics can be used for production of a ‘quality flag’ for both data sets. Possible improvement: different averaging time, removing data point with current estimates very close to zero.