Preliminary SWOT Orbit Design Study R. Steven Nerem, Ryan Woolley, George Born, James Choe Colorado Center for Astrodynamics Research, University of Colorado.

Preliminary SWOT Orbit Design Study

R. Steven Nerem, Ryan Woolley, George Born,

James Choe

Colorado Center for Astrodynamics Research, University of Colorado

Richard RayNASA/Goddard Space Flight Center

Ernesto Rodriguez

Jet Propulsion Laboratory

University of Colorado at BoulderColorado 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

~60 km ~60 km~10 km

800-1000 km

Sensor Swath Pattern

~3.5° ~3.5°

~0.6°


4

15-Day Orbit Coverage Gaps

3° N

0°

3° S

60 km

400 km


5

22-Day Orbit Coverage

2° N

0°

2° S


6

100120140160180200220240260280300

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Repeat Length (days)

Spa

cing

(km

)Repeat Period vs Equatorial Spacing


7

0

10

20

30

40

50

60

70

15 16 17 18 19 20 21 22

Repeat (days)

Equatorial Gap Width (km)

Latitude of Full Coverage(deg)

~130 km total swath width

Repeat Period vs Coverage (i = 78°)


8

15-Day Repeat, 1-Day Subcycle

Base Interval ~25° or ~3000 km

2 5 6 7 8 9 103 4 11Day 1 141312 15


9



6 1 4 7 2139 5Day 3 118 1412 10


10



21 8 11 14 120 4Day 3 107 135 17218159 126 16 19 22


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3-Day Repeat


21 8 11 14 120 4Day 3 107 135 17218159 126 16 19 22


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1-Day Repeating Ground Track


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3-Day Repeating Groundtrack


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4-Day Repeating Groundtrack


15

22 Day Repeat – 3 Day Subcycle


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17



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Possible Orbit Altitudes: i = 78°

700 750 800 850 900 950 10000

2

4

6

8

10

12

14

Altitude (km)

Sub

cycl

e (

da

ys)

i = 78 deg

5

10

15

20

25

30R

epeat Length (days)

+ Repeat Orbit at Subcycle


19

3-5 Day Subcycles

920 930 940 950 960 970 980 990 1000

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Altitude (km)

Sub

cycl

e (

da

ys)

i = 78 deg

15

16

17

18

19

20

21

22

23

24

25

16 19 22 25 23 20 17

17 21 25 23 19 15

18 23

16 21 24 19 R

epeat 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 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


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Candidate Orbits

Repeat Length

# of Orbits to Repeat

Equatorial Spacing


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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 (<< 1

year)


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Four main solar diurnal tides areseparated 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


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Tidal Alias Frequencies: i = 75°


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26



27



28

Average Tidal Frequency Separation


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Average Tidal Frequency Separation


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Tidal Aliasing: i = 78°

X

X

XXX

XX

X

X

X

X

X

X

X

XX

X

X

XXX


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Candidate Orbits

Minimal Tidal Aliasing


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3-5 Day Subcycles

920 930 940 950 960 970 980 990 1000

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Altitude (km)

Sub

cycl

e (

da

ys)

i = 78 deg

15

16

17

18

19

20

21

22

23

24

25

16 19 22 25 23 20 17

17 21 25 23 19 15

18 23

16 21 24 19


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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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21.8635-day repeat

latitude 32.0°

Case 1:One ascending arc per repeat cycle

Example Sampling of Tides by SWOT

Nominal aliasperiod

818 d

111 d

68 d

285 d

160 d

89 d

48 d

80 d

143 d


35

21.8635-day repeat

latitude 32.0°

Case 2:Two ascending arcs per repeat cycle

Added sampling helpslunar tides, but not solar.


Nominal aliasperiod

818 d

111 d

68 d

285 d

160 d

89 d

48 d

80 d

143 d


36

21.8635-day repeat

latitude 32.0°

Case 3:Two ascending arcs +two descending arcs per repeat cycle

Added sampling helpssolar diurnal tides, but not solar semidiurnals.


Nominal aliasperiod

818 d

111 d

68 d

285 d

160 d

89 d

48 d

80 d

143 d


37

21.8635-day repeat

latitude 60.0°

Case 3b:Two ascending arcs +two descending arcs per repeat cycle

Nominal aliasperiod

818 d

111 d

68 d

285 d

160 d

89 d

48 d

80 d

143 d

Added sampling helpssolar tides, depending on latitude.



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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

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


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4-Days of 22-Day Repeat, Aghulas


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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


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22-Day Repeat, Amazon


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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?

Preliminary SWOT Orbit Design Study R. Steven Nerem, Ryan Woolley, George Born, James Choe Colorado Center for Astrodynamics Research, University of Colorado.

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