orbit selection issues for wide-swath altimeter

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


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

3


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

4


Orbits & TidesOrbits & Tides

• Repeat orbits can be found at any inclination that meet this criteria for some tides

5


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)

6


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

7


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

8


• There are orbits near 80° inclination that have better aliasing properties than T/P

9


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

10


• Average f = 0.4 cpy implies mean separation time of 2.5 years, 0.7 cpy = 1.42 years

• 800-1300 km altitude

11


• Inclination = 78°• Altitude ~ 845 km

Exact Repeat Period (days)

12


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

13


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


ExtrasExtras


• 800-1000 km altitude

16


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

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

17


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

orbit selection issues for wide-swath altimeter

Documents