Nils Olsen DNSC Copenhagen

1. Study of an Improved Comprehensive Magnetic Field Inversion Analysis for SwarmKick-off E2Eplus Study Nils Olsen DNSC Copenhagen

2. Draft Agenda • 09:00 Welcome • 09:05 Presentation of proposed activity • Relation to Phase E2E Mission Performance Simulator • Discussion of Assessment criteria • "Quick response" issues • Draft list of failure cases to be studied • General discussion • 12:30 lunch • 13:30 AOB • 14:45 Adjourn 27. January 2006 | Kick-off, E2Eplus | page 2

3. Questions addressed by ESA 1 • What subset of all Swarm mission objectives are subject of the study? • “Crustal field” and “core field dynamics” are the main mission objectives that will be assessed in this study. However, since we are using a comprehensive approach, a beneficial impact on other objectives (like mantle conductivity) can not be ruled out (and is likely), but will not be considered in this study. • The anticipated improvements of the method shall be explained in relation to the phase A results for the relevant mission objectives. • Our aim is to obtain (and perhaps improve) the Phase A high-degree crustal field recovery (obtained using the gradient approach) by using the CI approach. This concerns the SH coefficients beyond degree n=80. We aim at a crustal field recovery beyond degree n=133, and on a more realistic recovery of all coefficients (alignment issue). • What is expected from the multi-satellite Euler angle estimation method compared to the method in phase A where an a priori model was used? • All Phase A activities have been obtained assuming perfectly aligned vector data (i.e. perfectly known Euler angles). The present study aims at considering a more realistic case. • All objectives shall be addressed. • Only crustal field and core field dynamics will be addressed. 27. January 2006 | Kick-off, E2Eplus | page 3

4. Questions addressed by ESA 2 A presentation shall be given on the phase A method and procedures and the relation to the current study in terms of: • Communalities and differences in approach (including algorithms), • Communalities and differences in synthetic data generation (including orbits, undisturbed signals, the error part (contributors to and characteristics of “level 0” and/or “level 1b” errors, and unmodelled signal), • Explanation of the analysed satellite options ABCD, ABC, AB, A and link to new ones • Examples of assessment tools and link to previous points • Necessary delta developments (also block diagram of full simulator and data flow), • Explanation of the whole “system” of data generation (measurements), building up the relation with the parameters and the solution of parameters. This needs to improve the understanding of the quick response mechanism and options to be analysed. • Other relevant points of the study to address. Answers to most of these questions can be found in the Phase A E2E Final Report (SWE2E/DSRI/MIS/TN/0003(1), available at http://esamultimedia.esa.int/docs/EarthObservation/Swarm/E2E-Simulator_FR.pdf) and in the proposal. 27. January 2006 | Kick-off, E2Eplus | page 4

5. Phase A E2E Simulator: Study Logic • Task 1: Industrial Module • Task 2+3: Swarm mission simulation • Determination and evaluation of scientific benefit of different mission scenarios • Task 3: including s/c and payload errors 27. January 2006 | Kick-off, E2Eplus | page 5

6. alignment Phase A E2E: Outline of Simulator 27. January 2006 | Kick-off, E2Eplus | page 6

7. Phase A Constellation #2 • Pool of 6 (7) satellites • Analysis of data from different combinations of up to 4 satellites • Final name convention • Swarm A (= 4) • Swarm B (= 5) • Swarm C (= 1) • Swarm D (= 2) • Cf. Swarm MRD, SW-MD-ESA-SY-001, page 25. 27. January 2006 | Kick-off, E2Eplus | page 7

8. Magnetic Field Generation 27. January 2006 | Kick-off, E2Eplus | page 8

9. Various Approaches for Field Recovery • Comprehensive Inversion • Core Field and Secular Variation - Method 1 • Core Field and Secular Variation - Method 2 • Lithospheric Field Recovery - Method 1 (Gradient Method) • Lithospheric Field Recovery - Method 2 • 3-D Mantle conductivity - Method 1 • 3-D Mantle conductivity - Method 2 27. January 2006 | Kick-off, E2Eplus | page 9

10. Questions addressed by ESA 3 • In relation to this (anticipated improvements of the method), pass/fail criteria could be defined using the assessment tools to indicate the success/failure of the new developments. • The assessment will be based on the criteria that were developed for and used in the Phase A E2E mission simulation. • For the Euler angles, the estimated angles will be compared with the true Euler angles (for instance by looking at angular difference between original and recovered angles). • The assessment in 3.4 should also allow an analysis of the estimated Euler angles versus the true Euler angles to quantify and characterise the difference. An assessment with respect to ground calibration shall be reviewed and discussed. • Assessment of true vs estimated Euler angles will be performed. However, an assessment wrt the ground calibration is not part of this study. 27. January 2006 | Kick-off, E2Eplus | page 10

11. Assessment criteria, E2E • Focus on field contributions that are main Swarm objectives • Core field and secular variation • Lithospheric field • Test quantities: Difference between recovered and original model • Power spectrum of the model SH coefficients • Degree correlation rn of coefficients • Sensitivity matrix • Global Maps (e.g., of Br) of the model difference • Same criteria will be used for E2Eplus 27. January 2006 | Kick-off, E2Eplus | page 11

12. Comparison of Filter Method and CI, E2E • CI superior at n<80, especially for terms m close to 0 • Filter method is superior for n > 80 Gradient Method Sensitivity matrix CI 27. January 2006 | Kick-off, E2Eplus | page 12

13. Assessment, lithospheric field, E2E 27. January 2006 | Kick-off, E2Eplus | page 13

14. Assessment: Lithospheric Field • A: 4-5 times more accurate than CHAMP • Lower pair A+B (gradient) for detail • Higher C separates external sources • Combination A+B+C: optimal recovery up to n=130 27. January 2006 | Kick-off, E2Eplus | page 14

15. Shortcomings of E2E Study and need for E2Eplus • The Phase A E2E results were obtained assuming perfectly aligned vector data (i.e. perfectly known Euler angles). The present study aims at considering a more realistic case using two approaches: • How well can the Euler angles be determined using multi-satellite approach? In other words: what is the expected accuracy of the Level 1b-NEC data product, using multi-satellite in-flight alignment methods? • Is it possible to obtain ”good” models of crustal and core field even if Euler angles are ”wrong”? Use og Level 1b-FGM rather than 1b-NEC for data analysis. • Phase A CI crustal field recovery was degraded for n>80, where Gradient method was superior. Incorporation of Gradient method in CI because • Phase A Gradient method requires fully aligned data. • Possible to improve Phase A results for n > 130 (especially for near-zonal terms)? 27. January 2006 | Kick-off, E2Eplus | page 15

16. E2Eplus Study Logic 27. January 2006 | Kick-off, E2Eplus | page 16

17. alignment E2E vs. E2EplusNew developments • Orbit determination • Completely new approach • Expected gain in speed: hours instead of weeks • Forward Module • Strong heritage from E2E • Perhaps modification of induced part due to ionospheric sources • to make this more consistent with magnetospheric part) • Change is expected to have only minor influence on results • Calibration (alignment) • Will be part of CI inversion • Inversion • Modification of CI code to account for • Non-linearity (alignment / scalar data) • Euler angles • Gradient stuff • Assessment • Strong heritage from E2E 27. January 2006 | Kick-off, E2Eplus | page 17

18. Questions addressed by ESA • A proposal for representation of the quick response mechanism is requested, like a distinction between the data generation, the build up of the relation matrices between observations and parameters, and the parameter estimation with as a guideline the examples of the various scenario options. • A table with these numbers will be produced during the study and a draft will be presented at PM1. These numbers are unknown at KO, but we are aiming at a significant improvement (factor 5-10?) compared to Phase A activities. • For the “quick response” all anticipated improvements shall be bundled and discussed, also addressing the corresponding work package tasks. • First draft will be included in the presentation at KO. ”Quick Response” means ”quicker response” (compared to E2E) 27. January 2006 | Kick-off, E2Eplus | page 18

19. Timing Issues • Production of synthetic data: • 190 million satellite positions per constellation • 10,950 data files, 26.5 GB of data • Production of synthetic data for one constellation takes a couple of weeks • Bottleneck: Calculation of synthetic orbits • integration of equations of motion, pieces of 3 months length, merging by hand • Inversion: Computer resources for one CI model (linear, i.e., one iteration) • 4 separate accumulation runs using 64 processors …about 2 hr wall-clock time each • 1 Echelon reduction/Back-substitution run on 16 processors…about 1 hr wall-clock time • Presently done at NASA/GSFC HPC cluster ”Halem” • About 520 CPU hours (22 CPU days) in total for one run. 27. January 2006 | Kick-off, E2Eplus | page 19

20. Plans for Speed-up of Data Production • Phase A: numerical integration of equations of motion, considering a lot of (tiny) effects • Some of the small effects are rather uncertain (e.g., air-drag), and therefore the position prediction error increases tremendously with time • Due to this uncertainty, a ”precise” orbit prediction (extrapolating several months/years in future) is not more precise than an approach that focuses on time-averaged effects (plus short-term effects due to change of air-drag) • For the E2Eplus study we therefore plan to use a much simpler approach, considering what is needed for the simulation : • circular near-polar orbits • realistic drift in local time • realistic altitude decay (solar activity effects …) • realistic maintenance of constellation • We expect that this approach allows us to calculate orbits (3 sat, 4 years) within one hour per constellation (rather than several weeks) 27. January 2006 | Kick-off, E2Eplus | page 20

21. ”Quick Response” 27. January 2006 | Kick-off, E2Eplus | page 21

22. Questions addressed by ESA • The sequence and options of scenarios for the analysis shall be discussed during KO and fixed at MTR. • A first proposal related to the options mentioned in the proposal shall be presented with the classification lost/failure case, change in errors characteristics case, and simulation ranges case (orbit selection, maintaining altitude for lower pair, and inclination range for example). • next slide • It is important to identify the cases that allow comparison with phase A results or add scenarios to it, and those based upon the newly generated data. • A possible link to Phase A: • Phase A results • redo of Phase A inversion using higher sampling rate (e.g., 15 secs rather than 1 min) • same inversion approach, same (high) sampling rate but new constellation • same data, new inversion approach (e.g. gradient analysis ...) 27. January 2006 | Kick-off, E2Eplus | page 22

23. Classification of Failure Cases A lost/failure case B change in error characteristics C change in simulation range 27. January 2006 | Kick-off, E2Eplus | page 23

24. Work Breakdown Structure 27. January 2006 | Kick-off, E2Eplus | page 24

25. Questions addressed by ESA • The software development (MATLAB) and implementation (FORTRAN) steps shall be clarified in more detail with respect to the schedule. The link between the various activities shall be explained: development, testing, implementation etc. What can be done in parallel and what sequential? • Much of the development can be done in parallel. Some examples: • E2E CI problem was a linear problem, E2Eplus deals with a non-linear problem. Modification of the CI code to account for non-linearity is independent of the specific parameterisation (i.e. can partly be done in parallel) • Implementation of Euler angle estimation is (almost) independent of specific parameterization (1-2-3 or 3-2-3 parameterization, or ... ?). Hence can partly be done in parallel, and finally use of ”best” parameterization-subroutine. 27. January 2006 | Kick-off, E2Eplus | page 25

26. Questions addressed by ESA • What tests are planned for the analysis of data in the magnetometer frame and the NEC frame in WP2110 and WP2210? • Assessment of field recovery using NEC data vs. instrument data. • The link/relation between WP3100 and WP3200 needs to be clarified. • WP 3100 is paid by ESA, whereas WP 3200 is paid by NASA. Apart of that, there is hardly any difference; both cover the same topic. • What is the sampling rate of the synthetic magnetic field measurements? • TBD. In Phase A we worked with 1 min sampling rate when using the CI approach (and 5 secs sampling rate when using the gradient approach); for the present study we plan to work with 30 sec or 15 sec sampling rates. 27. January 2006 | Kick-off, E2Eplus | page 26

27. Concerning managerial aspects • Management of the NASA work is not clearly addressed. Please clarify. • Daily e-mail contact with the NASA scientists, weekly telecon. The NASA scientist have access to the DNSC computer network and use it for part of the calculations. • Drafting relevant parts of the report shall follow the work packages, and be presented at the relevant meetings adequately scheduled. • PM1, for example, shall be held after finishing WP1100, WP1200, WP2110, WP2210 with a draft report containing activities within these WP’s and the status of the relevant ongoing work packages. The other meetings and reports shall be organised in the same way. Please propose a corresponding deliverable items list and meeting plan. • We propose that PM1 will be held 2 months after KO (i.e., end of March 2006) at DNSC. We expect to be able to present first results on fast orbit determination and field recovery. We no not think that it is necessary to wait until 3 months after KO for PM1 to present results concerning the algorithms and procedures to be developed in WP1100. • Status reports shall be provided on monthly basis. • According to the SOW (section 4): “During intervals between Progress Meetings that exceed 2 months, bimonthly progress reports shall be prepared …” 27. January 2006 | Kick-off, E2Eplus | page 27

28. Updated list of proposed Meetings and Deliverables 27. January 2006 | Kick-off, E2Eplus | page 28

29. Schedule (from Proposal) 27. January 2006 | Kick-off, E2Eplus | page 29

30. 300 667 aeromagnetic and marine surveys 133 60 Goal: Bridge the gap in resolution between present satellite and aeromagnetic surveys Requirement: lithospheric field model to less than 300 km scales 27. January 2006 | Kick-off, E2Eplus | page 30