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Orbit Selection Issues for Wide-Swath Altimeter. Don P. Chambers Center for Space Research The University of Texas at Austin Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006. Overview. Consider orbits that are not sun-synchronous - PowerPoint PPT Presentation
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Don P. ChambersCenter for Space Research
The University of Texas at Austin
Wide-Swath Ocean Sciences and Hydrology Meeting
31 October 2006
Orbit Selection Issues Orbit Selection Issues forfor
Wide-Swath AltimeterWide-Swath Altimeter
D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
OverviewOverview
• Consider orbits that are not sun-synchronous
• Examine orbits at higher inclination and lower altitude than T/P-Jason
• Use tidal aliasing frequencies to evaluate orbits
» 8 largest constituents and S1
» Examine min. frequency and frequency separation
• Discuss how these characteristics change in general vs. inclination, altitude, groundtrack repeat period
2
D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Calculating Tide Alias PeriodCalculating Tide Alias Period• Alias period depends on the satellite’s exact repeat
period and the period of the tide
» TOPEX/Poseidon exact repeat period is 9.915625 days (“10-days”), or 237.975 hours
» M2 period is 12.420601 hours
• Although the tidal periods are known, the exact repeat period is a non-linear function of semi-major axis and inclination
• Hundreds of orbits exist within a reasonable range of inclination and semi-major axis, each with very different aliasing frequencies
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Minimum Aliasing FrequencyMinimum Aliasing Frequency
• Want to examine a few parameters related to alias frequencies to eliminate certain orbits from consideration
• One parameter is minimum of all aliasing frequencies
• Greater than 2 cycles-per year (period less than half-year)
• This ensures multiple cycles of the any alias period within a few years so the tide can be estimated from the data
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Orbits & TidesOrbits & Tides
• Repeat orbits can be found at any inclination that meet this criteria for some tides
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Orbits & Tides (cont)Orbits & Tides (cont)
• Other tides have a problem as satellite inclination goes above 80°
• Especially a problem for S1, S2 as orbit approaches sun-synchronous inclination where alias is very low-frequency (approaching a bias)
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
General ObservationsGeneral Observations
• Only orbits with an inclination < 66° alias all major constituents to frequencies > 2 cpy
• Retrograde orbits have poor aliasing of solar tides
• If we do not require that the K1 alias > 2 cpy
» Orbits that meet the requirement for all other constituents exist up to 80° inclination
» This covers more of the Arctic Ocean, all of the Antarctic boundary, and most rivers in Siberia
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Frequency SeparationFrequency Separation
• Another important factor to consider is the separation between alias frequencies and between the alias and annual/semi-annual frequency (f)
• Determines time needed to separate two tides in altimeter observations for an estimation
» Time to separate ~ 1/f
• T/P did not have optimal separation for some constituents
• K1 aliased to within 0.11 cpy of semi-annual
» 9-years to separate
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
• There are orbits near 80° inclination that have better aliasing properties than T/P
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Average Frequency SeparationAverage Frequency Separation• Find minimum separation between
each constituent and all others (incl. annual, semiannual): fi
• First requirement is the smallest be larger than some minimum value
» For T/P, this was 0.167 cpy (~ 6-year separation time)
• From these, calculate average
» Higher numbers mean separation of all constituents in shorter time
f1
f2
f3
f4
f5
f6f7
f9
f8
f10
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
• Average f = 0.4 cpy implies mean separation time of 2.5 years, 0.7 cpy = 1.42 years
• 800-1300 km altitude
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
• Inclination = 78°• Altitude ~ 845 km
Exact Repeat Period (days)
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
ConclusionsConclusions
• There are quite a few orbits at high inclinations that have excellent tidal aliasing properties
» Inclinations as high as 78°
» Altitudes ~ 800 to 900 km
» Repeat periods cluster around 10- to 11-days and 20 to 22-days
• Properties are even better than T/P-Jason if we ignore K1 in the minimum frequency calculation
• Suggest that these orbits be studied in more detail for the Wide-Swath Altimeter
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Conclusions (cont)Conclusions (cont)
• Current “compromise” orbit being used in studies is based on a report I wrote 5 years ago
» At that point, I was ignoring all orbits significantly lower than 1000 km because of orbit determination concerns
» Also, was not considering S1 tide
• We need to be careful not to hardcode this “compromise” orbit into any mission documents (as was done with NPOESS) until more studies are done
D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
ExtrasExtras
D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
• 800-1000 km altitude
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Calculating Tide Alias PeriodCalculating Tide Alias Period
• Alias period () depends only on the satellite’s exact repeat period (Prepeat) and the period of the tide constituent (PTide)
• Prepeat is the precise repeat period, not the nearest integer repeat period
» e.g., TOPEX/Poseidon exact repeat period is 9.915625 days (“10-days”), or 856710 seconds
€
φ=2πPrepeatTTide
−π to π( )
€
=abs2πPrepeat
Δφ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
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D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006
Orbit Period & Repeat PeriodOrbit Period & Repeat Period
• Although the tidal constituent periods are known, the exact repeat period (Prepeat) is a non-linear function of semi-major axis (a) and inclination (i)
€
Psat = 2πa3
μE
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2
1−3
2J2
REa
⎛
⎝ ⎜
⎞
⎠ ⎟2
4cos2 i −1( ) ⎡
⎣ ⎢
⎤
⎦ ⎥
€
N = NINT2πD
Psat (ωE − ˙ Ω )
⎛
⎝ ⎜
⎞
⎠ ⎟
€
˙ Ω = −3
2J2
μEa3
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2RE
a(1− e2)
⎡
⎣ ⎢ ⎤
⎦ ⎥
2
cosi
€
Prepeat = N × Psat