Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study Work performed by Nils Olsen, Terence J. Sabaka, Luis R. Gaya-Pique, Lars Tøffner-Clausen, and Alexei Kuvshinov, Presented by: Nils Olsen

26. June 2006 | MTR E2Eplus | page 2 Draft Agenda Swarm E2Eplus Mid Term Review, June , at ESTEC, Noordwijk 11:00 Welcome 11:05 Presentation of activities done so far (NIO) Summary of activities already presented at PM1 Forward calculation, Constellations #3 and #4 Results of Gradient Approach First results of multi-satellite in-flight alignment List of failure and imperfection cases Plans for the near future 13:00 lunch 14:00 General discussion Telecon with Terence J. Sabaka and L. R. Gaya-Pique, GSFC 17:00 Adjourn

26. June 2006 | MTR E2Eplus | page 3 E2Eplus Study Logic Status of June 2006: New, fast orbit generation scheme Gradient approach Multi-satellite alignment (tests partly concluded)

26. June 2006 | MTR E2Eplus | page 4 Forward calculation Constellation #3 and #4

26. June 2006 | MTR E2Eplus | page 5 Fast Orbit Prediction –circular near-polar orbits –realistic drift in local time –realistic altitude decay (solar activity effects …) –realistic maintenance of constellation Validation of method with CHAMP orbits

26. June 2006 | MTR E2Eplus | page 6 Constellation #3 and #4 Constellation #3 –Essentially similar to constellation #2, but using new orbit propagation method –Data only used for test purposes. This constellation will not be considered further Constellation #4 –Launch on July 1, 1998 (1.5 years later than in Phase A, to account for launch delay) –InclinationSwarm A+B: 87.4º Swarm C: 88.0º –Initial altitude:450 km (A+B) and 530 km (C) –Longitudinal difference between Swarm A and B: 1.4º

26. June 2006 | MTR E2Eplus | page 7 Solar and geomagnetic activity

26. June 2006 | MTR E2Eplus | page 8 Orbit decay for Swarm A, for various launch times

26. June 2006 | MTR E2Eplus | page 9 Local Time and altitude evolution, constellation #4

26. June 2006 | MTR E2Eplus | page 10 Impact of higher sampling rate on lithospheric field recovery

26. June 2006 | MTR E2Eplus | page 11 Re-analysis of Constellation #2 data

26. June 2006 | MTR E2Eplus | page 12 The Gradient Method in the Comprehensive Inversion Approach

26. June 2006 | MTR E2Eplus | page 13 “Selective Infinite Variance Weighting” Development of an approach that produces/identifies data subsets that are particularly sensitive to certain parameter subsets and applying appropriate weighting such that these data strongly influence the determination of such parameters –Example: high-order crustal field is resolved by gradient information (data difference) low-order field is resolved by all data d 1, d 2, d 3 are data of Swarm 1,2,3 d s, d d, are sum and difference of Swarm 1,2 x is all model parameters but crustal field (sensed by all satellites ) y l is low-order crustal field (sensed by d s, d d, d 3 ) y h is high-order crustal field (sensed by d d )

26. June 2006 | MTR E2Eplus | page 14 Results: Gradient approach Difference data contribute only to lithospheric field coefficients of order m > 20 All data (sums and differences) contribute to all other coefficients

26. June 2006 | MTR E2Eplus | page 15 Results: Gradient approach

26. June 2006 | MTR E2Eplus | page 16 Multi-Satellite In-flight Alignment

26. June 2006 | MTR E2Eplus | page 17 The principle of in-flight alignment Model parameters: SHA expansion coefficients g n m, h n m Euler angles  New: CI approach B NEC includes all relevant contributions to Earth’s magnetic field: internal and external potential fields plus toroidal fields Simultaneous estimation of the Euler angles for all Swarm satellites

26. June 2006 | MTR E2Eplus | page 18 Tests Data from all 3 satellites (constellation #4) Solved for 3 x 3 Euler angles plus magnetic field model Only solved for the contributions that are included in the synthetic data Test 1: core field only (up to n=13, temporal variation described by splines) Test 2: lithospheric field (up to n=150) added Test 3: magnetospheric (primary and induced field) added  Test 4: ionospheric (primary and induced field) added  Test 5: toroidal field added Tests 1 – 3 successfully completed (near perfect recovery of core and lithospheric field and Euler angles) Test 4 partly completed (good recovery of core and lithospheric field, but retrieved Euler angles are different from the true ones)

26. June 2006 | MTR E2Eplus | page 19 Result of Test 3 Input data contain core, lithospheric and magnetospheric (primary and induced) field Difference between true and retrieved Euler angles < 1 arcsec

26. June 2006 | MTR E2Eplus | page 20 Result of Test 4 Input data contain static internal field (n = 1-150, no SV!) and ionospheric plus magnetospheric (primary and induced) field Difference between true and retrieved Euler angles:  Swarm A Swarm B Swarm C

26. June 2006 | MTR E2Eplus | page 21 Result of Test 4 Spectra of model differences

26. June 2006 | MTR E2Eplus | page 22 Plans for the near Future Further tests of the multi-satellite alignment –Inclusion of ionospheric field: what went wrong, if anything? –Inclusion of toroidal fields (first tests completed) The Great Unified Code: Combination of gradient and multi-satellite approach –Tests Application to various imperfection and failure scenarii

26. June 2006 | MTR E2Eplus | page 23 Failure and Imperfection Cases 1.Failure of VFM and/or STR on a single satellite a)Only scalar (no vector) data available for Swarm A b)Only scalar (no vector) data available for Swarm C 2.Impact of a S/C magnetic field on a single satellite (Swarm A) a)Constant S/C dipole moment (hard magnetization), corresponding to 2 nT at the location of the ASM b)Induced S/C dipole moment (soft magnetization), corresponding to 3 nT at the location of the ASM over the poles (i.e. the area of maximum Earth’s magnetic field strength) 3.Noise in the CRF attitude of a single satellite (Swarm A) a)Time dependent attitude noise (all components) 2 sin(  t) arcsecs + 10 sin(2  T/24) arcsecs where t is UT,  is orbital frequency, and T is Local Time in hours. 4.Failure of one or more satellite (extension of Phase A analysis) a)Magnetic data from all 3 satellites (Swarm A, B and C) b)Magnetic data from (Swarm A and C) only c)Magnetic data from (Swarm A and B) only d)Magnetic data from (Swarm A) only

26. June 2006 | MTR E2Eplus | page 24

26. June 2006 | MTR E2Eplus | page 25 Work Breakdown Structure

26. June 2006 | MTR E2Eplus | page 26 Updated list of proposed Meetings and Deliverables Meeting PlaceParticipantsPlanned DateDeliverables Kick-Off Meeting (KO)DNSCAllJanuary 27, Progress Meeting 1DNSC2March 29, Midterm Review (MTR)ESTEC2June 26, 2006Draft report Progress Meeting 2DNSC2October Final Presentation (FP)ESTEC4December 2006Final report