1. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Ideas for improving the disturbance model or Welcome to the Null-Space! Nils Olsen, Lars Tøffner-Clausen, Chris C. Finlay, Jonas Nielsen DTU Space

2. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Vector Disturbance Maps These results (LTC model) are obtained by describing the dependence of the disturbance field on sun position using spherical harmonics, and using TSVD to regularize the model Use of localized basis functions instead ? Other regularisation method?

3. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Disturbance field modeled by point-sources (monopoles) 1280 point sources distributed on icosahedron grid at depth 0.9 Mean horizontal separation: 0.056

4. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Model Parametrisation Data set: 0403 data set without disturbance field correction (fully calibrated, but uncorrected data) Preliminary data screening: removal of 0.5% outliers (> 5  wrt to preliminary disturbance field model) Data subsampling: 10 minute values (615 000 vector triplets)

5. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Disturbance field modeled by point-sources (monopoles) Model regularisation: minimizing ||m|| (quadratic regularisation) = 5 x 10 5 larger  (smoother model) smaller 

6. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Vector Disturbance Maps LTC model (spherical harmonics) point sources

7. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Why modeling using point sources instead of spherical harmonics? Disturbance model is overparameterized d/o 25 in case of LTC model, corresponding to 3 x 25*27 = 3 x 675 = 2025 coefficients 3 x 1280 point sources Model regularisation is needed Quadratic regularisation (Tikhonov, TSVD, …) minimizes the mean energy ”smoothed peaks”, possible spurious features in ”weak field” regions Maximim Entropy Regularisation Sharp(er) boundaries

8. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Experience with crustal field modeling Kother et al (GJI, in review)

9. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Experience with crustal field modeling Kother et al (GJI, in review)

10. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) First results Quadratic regularisation Maximum Entropy regularisation rms misfit: 169 pT

11. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Preliminary Conclusion Disturbance field modeling using localized basis function (point sources) results in almost identical ruesults compared to use of spherical harmonics Maximum Entropy instead of quadratic regularisation leads to minimal changes … difference to crustal field situation because disturbance field is basically large-scale?

12. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Assumption: disturbance depends on Sun position ( ,  ) wrt S/C First challenge: VFM disturbance Swarm Alpha nT

13. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Second Challenge: Calibration of VFM on Charlie ”Mapping” of F ASM (A)  F(C) Use of F(C) (instead of missing F ASM (C)) to calibrate B VFM (C) Assessment of these two approaches: Difference  F ASM (A) –  |B VFM (C)| no ASM available 230 pT rms 410 pT rms This value includes contributions from remaining VFM disturbance field Ionospheric contributions (dawn-dusk orbit) Data from night side regions

14. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) Assessment of VFM disturbance correction, VFM calibration and alignment Difference of vector components  B(A) –  B(C) Difference in vector components between Alpha and Charlie provides independent check of VFM calibration VFM disturbance correction VFM – STR alignment (Euler angle determination) for both satellites … … and of the geomagnetic field model that has been used for the mapping A  C 1 nT noise spec on field measurements appears to be met with margins - as far as one can tell 440 pT rms 380 pT rms 360 pT rms

15. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) SIFM+: Model using Vector Gradient Data SIFM no gradient : no gradient data SIFM: with scalar gradient data no vector gradient data SIFM+: with scalar gradient data with vector gradient data Model from 2 years of CHAMP satellite data at 320 km altitude (10 x more crustal field power at n=70) Degree correlation  n

16. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) SIFM+: Model using Vector Gradient Data Difference to MF7 B r at surface, n = 16 - 65 SIFM: no vector gradient data SIFM+: with vector gradient data Inclusion of vector gradient data alleviates Backus effect

17. Swarm ASM-VFM meeting 9-10 Apr 2015ESTEC (NL) SIFM+: Model using Vector Gradient Data B r at surface, n = 16 - 75