1. Quality indicators for Swarm FAC products and their statistical behavior Maosheng He 1, Joachim Vogt 1, Adrian Blagau 1,2 (1) Jacobs University Bremen gGmbH, Gremany (2) Institute for Space Sciences Bucharest-Magurele, Rumania Paris, 09/09/2015, 5th Swarm Cal/Val Workshop

2. Configuration of FACs Aurora, and FAC system from space. [From internet Link]Link

3. Assumptions: Large planar current Time independent structure Velocity vector is normal to current sheet Swarm Level-2 FAC products: single-satellite method Large planer current Procedures: 1) Transform to local (x,y) coordinates (45° w.r.t. velocity) 2) Ampere law 3) Projection of radial current to magnetic field direction The velocity coordinate [Ritter et al., 2013]

4. [Ritter and Luehr, 2006; Ritter et al., 2013] Procedures: 1) Construct quad configuration 2) Boundary integral, j r as a function of dB and line elements equivalent to the finite di ff erencing 3) Projection of radial current to magnetic field direction Swarm Level-2 FAC products: dual-satellite method Assumptions: Linear spatial variation of dB Time independent structure SwC

5. L2 FAC Products & Assumptions Assumptions: Linear spatial variation Time independent structure Large sheet-like current Sheet normal aligned with velocity vector L2 FAC products: j ||,A : single-satellite from SwA j ||,B : single-satellite from SwB j ||,C : single-satellite from SwC j ||,AC : dual-satellite from SwA and SwC

6. L2 FAC products: j ||,A : single-satellite from SwA j ||,B : single-satellite from SwB j ||,C : single-satellite from SwC j ||,AC : dual-satellite from SwA and SwC How consistent are j ||,A, j ||,C, and j ||,AC ? j ||,A and j ||,C Aurora Centre from MFACE Downward J Upward J L2 FAC Products & Assumptions

7. How well are the underling assumptions satisfied? [MFACE, He et al., 2012, GRL] FAC evolution at moderate levels of geomagnetic activity L2 FAC Products & Assumptions Assumptions: Linear spatial variation Time independent structure Large sheet-like current Sheet normal aligned with velocity vector

8. L2 FAC products: j ||,A : single-satellite from SwA j ||,B : single-satellite from SwB j ||,C : single-satellite from SwC j ||,AC : dual-satellite from SwA and SwC L2 FAC Products & Assumptions Assumptions: Linear spatial variation Time independent structure Large sheet-like current Sheet normal aligned with velocity vector Questions How consistent are j ||,A, j ||,C, and j ||,AC ? —Definition of consistency measures for Level-2 FAC products —Statistics of the consistency measures How well are the underling assumptions satisfied? —Definition of quality indicators using only magnetic field data —Statistics of the quality indicators

9. L2 FAC products: j ||,A : single-satellite from SwA j ||,B : single-satellite from SwB j ||,C : single-satellite from SwC j ||,AC : dual-satellite from SwA and SwC Questions How consistent are j ||,A, j ||,C, and j ||,AC ? —Definition of consistency measures for Level-2 FAC products —Statistics of the consistency measures How well are the underling assumptions satisfied? —Definition of quality indicators using only magnetic field data —Statistics of the quality indicators How well do the quality indicators predict FAC consistency measures? L2 FAC Products & Assumptions Assumptions: Linear spatial variation Time independent structure Large sheet-like current Sheet normal aligned with velocity vector

10. Outline How consistent are j ||,A, j ||,C, and j ||,AC ? —Definition of consistency measures for Level-2 FAC products —Statistics of the consistency measures How well are the underling assumptions satisfied? How well do the quality indicators predict FAC consistency measures?

11. Level-2 FAC Consistency ： Definitions Three L2 products: single-satellite FAC product from SwA: j ||,A single-satellite FAC product from SwC: j ||,C dual-satellite FAC product from SwA and SwC: j ||,AC As a measure of L2 FAC consistency we use the maximum of the cross-correlation function (correlation coe ffi cient R as a function of lag τ): ConsL2 X&Y = Max R {j ||,X (t), j ||,Y (t + τ) } The consistency measures range from zero (no consistency) to one (perfect consistency). dual sat. single sat.

12. Level-2 FAC Consistency ： Low-pass Filtering ESA L2 j ||,A and j ||,C ESA L2 j ||,AC MFACE approach: j ||,A and j ||,C, and ESA L2 j ||,AC ESA L2 j ||,A and j ||,C is produced at 1Hz, whereas j ||,AC is low pass filtered. For a comparison, we produce j ||,A and j ||,C using low pass filtered Level-1b data with the approach and filter employed MFACE [He et al., 2012].

13. Level-2 FAC consistency: ESA L2 FAC VS. MFACE Approch All of j ||,A, j ||,C, j ||,AC ESA L2 Product j ||,A, j ||,C : MFACE approach j ||,AC : ESA L2 Product Large number of auroral zone crossings All consistencies have a median less than 0.1, rather low Significant improvement

14. Level-2 FAC Consistency: Geographic/Geomagnetic Distribution Near the geographic poles: higher values for single-single consistency lower values for dual-single consistency Higher values at lower MLat for dual-single consistency

15. Level-2 FAC Consistency: Geographic/Geomagnetic Distribution Low values Near the geographic poles: higher values for single-single consistency lower values for dual-single consistency Higher values at lower MLat for dual-single consistency

16. Level-2 FAC consistency: Geographic Distribution Dual-single consistency decreases with increasing latitude. Single-single consistency increases with increasing latitude. Latitude(°) NorthernSouthern Dual-Single Single-Single

17. Level-2 FAC consistency: Geographic Distribution Latitude(°) Dual-Single Single-Single NorthernSouthern A sudden drop at latitude about 80° Dual-single consistency decreases with increasing latitude. Single-single consistency increases with increasing latitude.

18. The quality of j ||,AC suffers from the exclusion zone. Level-2 FAC Consistency: Dual-single Value Near to the Exclusion Zone

19. Pla.>0.9 Sta.>0.9 Level-2 FAC Consistency: Dual-single Value Near to the Exclusion Zone The quality of j ||,AC suffers from the exclusion zone.

20. Outline How consistent are j ||,A, j ||,C, and j ||,AC ? How well are the underling assumptions satisfied? —Definition of quality indicators using only magnetic field data —Statistics of the geometry indicators How well do the quality indicators predict FAC consistency measures?

21. Quality Indicators AssumptionsIndicators Linear spatial variation-missing Time independent structureStationarity Large sheet-like currentPlanarity Velocity vector is normal to current sheetInclination

22. Quality Indicators: Definitions All indicators are derived from dB, the measurement after subtracting the model All indicators range between zero for the worst quality and one or the best quality

23. Quality Indicators: Constructed from Magnetic Profiles Procedural details: Compute one set of quality indicators for each auroral zone crossing (four crossings per orbit). Combine MVA and wavelet analysis to find Auroral Current Center (ACC) as in the construction of MFACE [He et al., 2012]. For the lag correlation analysis, use a time window of 180 seconds around the ACC. An example for MVA

24. Quality Indicators: Histogram Meaningful quality indicators were obtained for a large number of auroral zone crossings in the time range from 15 April to 05 November 2014.

25. Quality Indicators: Geographic/Geomagnetic Distribution Geographic distributions: variability near the geographic poles probably due to orbit geometry and smaller distance between satellites A and C. Geomagnetic distributions: higher values of planarity and stationarity inthe evening and morning sectors due to reduced auroral dynamics.

26. Outline How consistent are j ||,A, j ||,C, and j ||,AC ? How well are the underling assumptions satisfied? How well do the quality indicators predict FAC consistency measures? —Regression and correlation analysis

27. Correlation Analysis between the Consistency and Indicators Dual-Single Single-Single Dual-Single Single-Single Dual-single - Low correlation Dual-Single Single-Single Single-single - Good correlation for Stationarity

28. Dual-single - Low correlation - Latitude control on the distribution Correlation Analysis between the Consistency and Indicators Dual-Single Single-Single Single-single - Good correlation for Stationarity - Less latitude control on the distribution except on the Inclination

29. Dual-single - Low correlation - Latitude control on the distribution - Latitude control on cc. 1) High cc. for Planarity and Stationarity at low latitude 2) Low cc. for Inclination Correlation Analysis between the Consistency and Indicators Dual-Single Single-Single Single-single - Good correlation for Stationarity - Less latitude control on the distribution except on the Inclination - Less latitude control on cc.

30. Dual-single - Low correlation - Latitude control on the distribution - Latitude control on cc. 1) High cc. for Planarity and Stationarity at low latitude 2) Low cc. for Inclination Correlation Analysis between the Consistency and Indicators Dual-Single Single-Single Single-single - Good correlation for Stationarity - Less latitude control on the distribution except on the Inclination - Less latitude control on cc.

31. How consistent are j ||,A, j ||,C, and j ||,AC ? –Consistency of L2 FAC products is defined using maximum of cross- correlation function. –The consistency between the ESA L2 FAC product of dual satellite approach and the single satellite product is significantly dependent on the geographic latitude, because the ESA L2 dual satellite approach suffers badly from the exclusion zone. How well are the underling assumptions satisfied? –Quality indicators are defined for individual auroral zone crossings: planarity, inclination, stationarity. –Geographic and geomagnetic distribution are controlled by the orbit geometry. How well do the quality indicators predict FAC consistency measures? –At low latitude, the consistency is significantly correlated with the indicators. Summary

32. Thanks