1. Preliminary SWOT Orbit Design Study R. Steven Nerem, Ryan Woolley, George Born, James Choe Colorado Center for Astrodynamics Research, University of Colorado Richard Ray NASA/Goddard Space Flight Center Ernesto Rodriguez Jet Propulsion Laboratory

2. University of Colorado at Boulder Colorado Center for Astrodynamics Research 2 Orbit Design Considerations Latitudinal coverage (orbit inclination) Temporal Sampling Spatial Sampling Tidal Aliasing Starting Point: –15-25 day repeat –800-1000 km altitude –Near 78° inclination Other Considerations: –Calibration/Validation –Multiple Orbit/Mission Phases –Orbit Maintenance Final Orbit Design Derived from Science Requirements

3. University of Colorado at Boulder Colorado Center for Astrodynamics Research 3 ~60 km ~10 km 800-1000 km Sensor Swath Pattern ~3.5° ~0.6°

4. University of Colorado at Boulder Colorado Center for Astrodynamics Research 4 15-Day Orbit Coverage Gaps 3° N 0°0° 3° S 60 km 400 km

5. University of Colorado at Boulder Colorado Center for Astrodynamics Research 5 22-Day Orbit Coverage 2° N 0°0° 2° S

6. University of Colorado at Boulder Colorado Center for Astrodynamics Research 6 Repeat Period vs Equatorial Spacing

7. University of Colorado at Boulder Colorado Center for Astrodynamics Research 7 ~130 km total swath width Repeat Period vs Coverage (i = 78°)

8. University of Colorado at Boulder Colorado Center for Astrodynamics Research 8 15-Day Repeat, 1-Day Subcycle Base Interval ~25° or ~3000 km 256789103411Day 114131215

9. University of Colorado at Boulder Colorado Center for Astrodynamics Research 9 14-Day Repeat, 3-Day Subcycle Base Interval ~25° or ~3000 km 614721395Day 3118141210

10. University of Colorado at Boulder Colorado Center for Astrodynamics Research 10 22-Day Repeat, 3-Day Subcycle Base Interval ~25° or ~3000 km 21811141204Day 310713517218159126161922

11. University of Colorado at Boulder Colorado Center for Astrodynamics Research 11 3-Day Repeat Base Interval ~25° or ~3000 km 21811141204Day 310713517218159126161922

12. University of Colorado at Boulder Colorado Center for Astrodynamics Research 12 1-Day Repeating Ground Track

13. University of Colorado at Boulder Colorado Center for Astrodynamics Research 13 3-Day Repeating Groundtrack

14. University of Colorado at Boulder Colorado Center for Astrodynamics Research 14 4-Day Repeating Groundtrack

15. University of Colorado at Boulder Colorado Center for Astrodynamics Research 15 22 Day Repeat – 3 Day Subcycle

16. University of Colorado at Boulder Colorado Center for Astrodynamics Research 16 22 Day Repeat – 3 Day Subcycle

17. University of Colorado at Boulder Colorado Center for Astrodynamics Research 17 22 Day Repeat – 3 Day Subcycle

18. University of Colorado at Boulder Colorado Center for Astrodynamics Research 18 Possible Orbit Altitudes: i = 78° Repeat Length (days) + Repeat Orbit at Subcycle

19. University of Colorado at Boulder Colorado Center for Astrodynamics Research 19 3-5 Day Subcycles 16 19 22 25 23 20 17 17 21 25 23 19 15 18 23 16 21 24 19 Repeat Length (days)

20. University of Colorado at Boulder Colorado Center for Astrodynamics Research 20 Properties of Repeat Track Orbits Complete exactly N orbits in C days –N is an integer, C is not (except for SS orbits) Altitude precisely determined by i, N, and C Ground track forms a grid on Earth’s surface, one point fixes the whole grid Grid “denser” for increasing C Sub-cycle length is a complex function of N and C

21. University of Colorado at Boulder Colorado Center for Astrodynamics Research 21 Candidate Orbits Repeat Length # of Orbits to Repeat Equatorial Spacing

22. University of Colorado at Boulder Colorado Center for Astrodynamics Research 22 Tidal Aliasing This initial analysis does not consider possible benefits of swath coverage (tidal solutions using swath “crossover” measurements) Tidal aliasing frequencies completely determined by orbit repeat period (function of altitude and inclination) Desirable characteristics: –Good separation of major tide constituents aliasing frequencies –Alias frequencies should not be close to one cycle per year –Tides should not alias to very long periods (<< 1 year)

23. University of Colorado at Boulder Colorado Center for Astrodynamics Research 23 Four main solar diurnal tides are separated in frequency by 1 cpy. The precession rate of the satellite orbit plane determines which frequency is aliased to zero. To avoid unfavorable aliasing generally requires a precession rate ≤ –2°/d (cf. Topex), which limits satellite inclination. We must trade off inclination and aliasing. Aliasing Near Diurnal Solar Tides

24. University of Colorado at Boulder Colorado Center for Astrodynamics Research 24 Tidal Alias Frequencies: i = 75°

25. University of Colorado at Boulder Colorado Center for Astrodynamics Research 25 Tidal Alias Frequencies: i = 77°

26. University of Colorado at Boulder Colorado Center for Astrodynamics Research 26 Tidal Alias Frequencies: i = 80°

27. University of Colorado at Boulder Colorado Center for Astrodynamics Research 27 Tidal Alias Frequencies: i = 85°

28. University of Colorado at Boulder Colorado Center for Astrodynamics Research 28 Average Tidal Frequency Separation

29. University of Colorado at Boulder Colorado Center for Astrodynamics Research 29 Average Tidal Frequency Separation

30. University of Colorado at Boulder Colorado Center for Astrodynamics Research 30 Tidal Aliasing: i = 78° X X X X X X X X X X X X X X X X X X X X X

31. University of Colorado at Boulder Colorado Center for Astrodynamics Research 31 Candidate Orbits Minimal Tidal Aliasing

32. University of Colorado at Boulder Colorado Center for Astrodynamics Research 32 3-5 Day Subcycles 16 19 22 25 23 20 17 17 21 25 23 19 15 18 23 16 21 24 19

33. University of Colorado at Boulder Colorado Center for Astrodynamics Research 33 How Does This Analysis Change for SWOT? Many measurement locations have 2 or more ascending/descending passes. Most measurement locations are “cross over” points.

34. University of Colorado at Boulder Colorado Center for Astrodynamics Research 34 21.8635-day repeat latitude 32.0° Case 1: One ascending arc per repeat cycle Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

35. University of Colorado at Boulder Colorado Center for Astrodynamics Research 35 21.8635-day repeat latitude 32.0° Case 2: Two ascending arcs per repeat cycle Added sampling helps lunar tides, but not solar. Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

36. University of Colorado at Boulder Colorado Center for Astrodynamics Research 36 21.8635-day repeat latitude 32.0° Case 3: Two ascending arcs + two descending arcs per repeat cycle Added sampling helps solar diurnal tides, but not solar semidiurnals. Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

37. University of Colorado at Boulder Colorado Center for Astrodynamics Research 37 21.8635-day repeat latitude 60.0° Case 3b: Two ascending arcs + two descending arcs per repeat cycle Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d Added sampling helps solar tides, depending on latitude. Example Sampling of Tides by SWOT

38. University of Colorado at Boulder Colorado Center for Astrodynamics Research 38 Nadir vs Swath Sampling of the Tides Additional sampling within a repeat period generally solves aliasing issues of lunar tides. At most latitudes, additional sampling of solar tides does not help resolve semidiurnal tides. For some sea level studies, additional sampling will help mitigate solar tide-model errors, depending on data processing strategies. For tide model improvement studies, swath altimetry provides only marginal improvement for the solar tides over what is offered from conventional nadir altimetry. Therefore, Nadir-type aliasing studies generally apply to SWOT - for solar tides. Most lunar tides will not alias to long periods, so we can neglect them during orbit design (but it’s easy to check M2, O1, etc.).

39. University of Colorado at Boulder Colorado Center for Astrodynamics Research 39 Coverage Analysis 3 Cases studied to get representative coverage for different latitude bands: –Mid-latitude to high-latitude: Aghulas current region (Gulf Stream is similar) –Equatorial: Amazon River –High-latitude: Lena River Plots of number of visits within a cycle, for 10 day and 4 day sampling periods Histograms of temporal revisits within a cycle (i.e., no revisits between cycles considered)

40. University of Colorado at Boulder Colorado Center for Astrodynamics Research 40 22-Day Repeat, Aghulas

41. University of Colorado at Boulder Colorado Center for Astrodynamics Research 41 10 days of 22-Day Repeat, Aghulas

42. University of Colorado at Boulder Colorado Center for Astrodynamics Research 42 4-Days of 22-Day Repeat, Aghulas

43. University of Colorado at Boulder Colorado Center for Astrodynamics Research 43 22-Day Repeat, Aghulas

44. University of Colorado at Boulder Colorado Center for Astrodynamics Research 44 22-Day Repeat, Amazon

45. University of Colorado at Boulder Colorado Center for Astrodynamics Research 45 10 Days of 22-Day Repeat, Amazon

46. University of Colorado at Boulder Colorado Center for Astrodynamics Research 46 4-Days of 22-Day Repeat, Amazon

47. University of Colorado at Boulder Colorado Center for Astrodynamics Research 47 22-Day Repeat, Amazon

48. University of Colorado at Boulder Colorado Center for Astrodynamics Research 48 22-Day Repeat, Lena

49. University of Colorado at Boulder Colorado Center for Astrodynamics Research 49 10 Days of 22-Day Repeat, Lena

50. University of Colorado at Boulder Colorado Center for Astrodynamics Research 50 4 Days of 22-Day Repeat, Lena

51. University of Colorado at Boulder Colorado Center for Astrodynamics Research 51 22-Day Repeat, Lena

52. University of Colorado at Boulder Colorado Center for Astrodynamics Research 52 22-Day Repeat

53. University of Colorado at Boulder Colorado Center for Astrodynamics Research 53 1-Day (3-D) Questions?