Preliminary SWOT Orbit Design Study

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
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
Sensor Swath Pattern
3.5
3.5
0.6
800-1000 km
60 km
60 km
10 km
4
15-Day Orbit Coverage Gaps
3 N
0
400 km
60 km
3 S
5
22-Day Orbit Coverage
2 N
0
2 S
6
Repeat Period vs Equatorial Spacing
7
Repeat Period vs Coverage (i 78)
130 km total swath width
8
15-Day Repeat, 1-Day Subcycle
9
14-Day Repeat, 3-Day Subcycle
10
22-Day Repeat, 3-Day Subcycle
21
8
11
14
20
4
Day 3
10
7
13
5
17
18
15
9
12
6
16
19
22
11
3-Day Repeat
21
8
11
14
20
4
Day 3
10
7
13
5
17
18
15
9
12
6
16
19
22
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1-Day Repeating Ground Track
13
3-Day Repeating Groundtrack
14
4-Day Repeating Groundtrack
15
22 Day Repeat 3 Day Subcycle
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22 Day Repeat 3 Day Subcycle
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22 Day Repeat 3 Day Subcycle
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Possible Orbit Altitudes i 78
Repeat Length (days)
Repeat Orbit at Subcycle
19
3-5 Day Subcycles
Repeat Length (days)
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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 Earths surface, one
  point fixes the whole grid
• Grid denser for increasing C
• Sub-cycle length is a complex function of N and C

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Candidate Orbits
Repeat Length
Equatorial Spacing
of Orbits to Repeat
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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 (ltlt 1
  year)

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Aliasing Near Diurnal Solar Tides
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.
Four main solar diurnal tides are separated in
frequency by 1 cpy.
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Tidal Alias Frequencies i 75
25
Tidal Alias Frequencies i 77
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Tidal Alias Frequencies i 80
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Tidal Alias Frequencies i 85
28
Average Tidal Frequency Separation
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Average Tidal Frequency Separation
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Tidal Aliasing i 78
X
X
X
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Candidate Orbits
Minimal Tidal Aliasing
32
3-5 Day Subcycles
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.

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Example Sampling of Tides by SWOT
818 d
21.8635-day repeat latitude 32.0
68 d
111 d
160 d
285 d
Case 1 One ascending arc per repeat cycle
48 d
89 d
80 d
143 d
Nominal alias period
35
Example Sampling of Tides by SWOT
21.8635-day repeat latitude 32.0
818 d
68 d
111 d
160 d
285 d
Case 2 Two ascending arcs per repeat cycle
48 d
89 d
80 d
Added sampling helps lunar tides, but not solar.
143 d
Nominal alias period
36
Example Sampling of Tides by SWOT
21.8635-day repeat latitude 32.0
818 d
68 d
111 d
160 d
285 d
Case 3 Two ascending arcs two descending arcs
per repeat cycle
48 d
89 d
80 d
Added sampling helps solar diurnal tides, but not
solar semidiurnals.
143 d
Nominal alias period
37
Example Sampling of Tides by SWOT
21.8635-day repeat latitude 60.0
818 d
68 d
111 d
160 d
285 d
Case 3b Two ascending arcs two descending arcs
per repeat cycle
48 d
89 d
80 d
Added sampling helps solar tides, depending on
latitude.
143 d
Nominal alias period
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 its easy to check
  M2, O1, etc.).

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)

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22-Day Repeat, Aghulas
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10 days of 22-Day Repeat, Aghulas
42
4-Days of 22-Day Repeat, Aghulas
43
22-Day Repeat, Aghulas
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22-Day Repeat, Amazon
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10 Days of 22-Day Repeat, Amazon
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4-Days of 22-Day Repeat, Amazon
47
22-Day Repeat, Amazon
48
22-Day Repeat, Lena
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10 Days of 22-Day Repeat, Lena
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4 Days of 22-Day Repeat, Lena
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22-Day Repeat, Lena
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22-Day Repeat
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1-Day (3-D)
Questions?