Transcript Repeating Ground Track Coverage

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
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
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
2
Sensor Swath Pattern
~3.5°
~3.5°
~0.6°
800-1000
km
~60 km
~60 km
~10 km
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
3
15-Day Orbit Coverage Gaps
3°
N
0°
400 km
60 km
3°
S
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
4
22-Day Orbit Coverage
2° N
0°
2° S
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
5
Spacing (km)
Repeat Period
vs Equatorial
Spacing
Equatorial
Spacing
300
280
260
240
220
200
180
160
140
120
100
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Repeat Length (days)
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
6
Repeat Period vs Coverage (i = 78°)
Repeat Ground Coverage
70
~130 km total swath width
Equatorial Gap Width (km)
60
Latitude of Full Coverage(deg)
50
40
30
20
10
0
15
16
17
18
19
Repeat (days)
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
20
21
22
7
15-Day Repeat, 1-Day Subcycle
Day 1 2
3
4
5
6
7
8
9 10 11 12 13 14 15
Base Interval
~25° or ~3000
Colorado Center for Astrodynamics Research
km
University of Colorado at Boulder
8
14-Day Repeat, 3-Day Subcycle
Day 3
6
9 12 1
4
7 10 13
2
5
8
11 14
Base Interval
~25° or ~3000
Colorado Center for Astrodynamics Research
km
University of Colorado at Boulder
9
22-Day Repeat, 3-Day Subcycle
Day 3 6 9 12 15 18 21 2
5
8 11 14 17 20 1
4
7 10 13 16 19 22
Base Interval
~25° or ~3000
Colorado Center for Astrodynamics Research
km
University of Colorado at Boulder
10
3-Day Repeat
Day 3 6 9 12 15 18 21 2 5
8 11 14 17 20 1
4
7 10 13 16 19 22
Base Interval
~25° or ~3000
Colorado Center for Astrodynamics Research
km
University of Colorado at Boulder
11
1-Day Repeating Ground Track
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
12
3-Day Repeating Groundtrack
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
13
4-Day Repeating Groundtrack
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
14
22 Day Repeat – 3 Day Subcycle
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
15
22 Day Repeat – 3 Day Subcycle
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
16
22 Day Repeat – 3 Day Subcycle
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
17
Possible Orbit Altitudes: i = 78°
i = 78 deg
14
30
12
25
Subcycle (days)
20
8
6
15
Repeat Length (days)
10
4
10
2
0
700
750
800
850
900
Altitude (km)
950
1000
Colorado Center for Astrodynamics Research + Repeat Orbit at Subcycle
University of Colorado at Boulder
5
18
3-5 Day Subcycles
16 21 24 19
i = 78 deg
25
5
24
4.8
18 23
23
4.6
Subcycle (days)
4.2
21
4
20
3.8
19
3.6
18
3.4
16 19 22 25 23 20 17
Repeat Length (days)
22
17 21 25 23 19 15
4.4
17
3.2
16
3
920
930
940
950
960
Altitude (km)
970
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
980
990
1000
15
19
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
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
20
Candidate Orbits
Repeat Length
Equatorial Spacing
# of Orbits to Repeat
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
21
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)
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
22
Aliasing Near Diurnal Solar Tides
Four main solar diurnal tides are
separated in frequency by 1 cpy.
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
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.
23
Tidal Alias Frequencies: i = 75°
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
24
Tidal Alias Frequencies: i = 77°
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
25
Tidal Alias Frequencies: i = 80°
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University of Colorado at Boulder
26
Tidal Alias Frequencies: i = 85°
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University of Colorado at Boulder
27
Average Tidal Frequency Separation
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University of Colorado at Boulder
28
Average Tidal Frequency Separation
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
29
Tidal Aliasing: i = 78°
X
X
X
X
X X
X X X X X
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
X
X
X X
X X
X
X X X
30
Candidate Orbits
Minimal Tidal Aliasing
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
31
3-5 Day Subcycles
16 21 24 19
i = 78 deg
25
5
24
4.8
18 23
23
4.6
Subcycle (days)
22
17 21 25 23 19 15
4.4
4.2
21
4
20
3.8
19
3.6
18
3.4
16 19 22 25 23 20 17
17
3.2
16
3
920
930
940
950
960
Altitude (km)
970
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
980
990
1000
15
32
How Does This Analysis Change for SWOT?
• Many measurement locations have 2 or more
ascending/descending passes.
• Most measurement locations are “cross over” points.
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
33
Example Sampling of Tides by SWOT
818 d
21.8635-day repeat
68 d
latitude 32.0°
111 d
160 d
285 d
Case 1:
One ascending arc
per repeat cycle
48 d
89 d
80 d
143 d
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
Nominal alias
period
34
Example Sampling of Tides by SWOT
21.8635-day repeat
818 d
latitude 32.0°
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.
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
143 d
Nominal alias
period
35
Example Sampling of Tides by SWOT
21.8635-day repeat
818 d
latitude 32.0°
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.
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
143 d
Nominal alias
period
36
Example Sampling of Tides by SWOT
21.8635-day repeat
818 d
latitude 60.0°
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.
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
143 d
Nominal alias
period
37
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.).
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
38
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)
Colorado Center for Astrodynamics Research
University of Colorado at Boulder
39
22-Day Repeat, Aghulas
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University of Colorado at Boulder
40
10 days of 22-Day Repeat, Aghulas
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University of Colorado at Boulder
41
4-Days of 22-Day Repeat, Aghulas
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University of Colorado at Boulder
42
22-Day Repeat, Aghulas
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University of Colorado at Boulder
43
22-Day Repeat, Amazon
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University of Colorado at Boulder
44
10 Days of 22-Day Repeat, Amazon
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University of Colorado at Boulder
45
4-Days of 22-Day Repeat, Amazon
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University of Colorado at Boulder
46
22-Day Repeat, Amazon
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University of Colorado at Boulder
47
22-Day Repeat, Lena
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University of Colorado at Boulder
48
10 Days of 22-Day Repeat, Lena
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University of Colorado at Boulder
49
4 Days of 22-Day Repeat, Lena
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University of Colorado at Boulder
50
22-Day Repeat, Lena
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University of Colorado at Boulder
51
22-Day Repeat
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University of Colorado at Boulder
52
1-Day (3-D)
Questions?
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University of Colorado at Boulder
53