Don P. Chambers Center for Space Research The University of Texas at Austin Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Orbit Selection Issues for Wide-Swath Altimeter

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Overview 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 S 1 »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 Period Alias period depends on the satellite’s exact repeat period and the period of the tide »TOPEX/Poseidon exact repeat period is days (“10-days”), or hours »M2 period is 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

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Minimum 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

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Orbits & Tides Repeat orbits can be found at any inclination that meet this criteria for some tides 5

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Orbits & Tides (cont) Other tides have a problem as satellite inclination goes above 80° Especially a problem for S 1, S 2 as orbit approaches sun-synchronous inclination where alias is very low- frequency (approaching a bias) 6

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 General Observations Only orbits with an inclination 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

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Frequency 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

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 9

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Average Frequency Separation Find minimum separation between each constituent and all others (incl. annual, semiannual):  f i First requirement is the smallest be larger than some minimum value »For T/P, this was cpy (~ 6- year separation time) From these, calculate average »Higher numbers mean separation of all constituents in shorter time f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 f9f9 f8f8  f 10 10

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 km altitude 11

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Inclination = 78° Altitude ~ 845 km Exact Repeat Period (days) 12

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Conclusions 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 K 1 in the minimum frequency calculation Suggest that these orbits be studied in more detail for the Wide-Swath Altimeter 13

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 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 S 1 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 Extras

km altitude 16

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Calculating Tide Alias Period Alias period (  ) depends only on the satellite’s exact repeat period (P repeat ) and the period of the tide constituent (P Tide ) P repeat is the precise repeat period, not the nearest integer repeat period »e.g., TOPEX/Poseidon exact repeat period is days (“10-days”), or seconds 17

D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 Orbit Period & Repeat Period Although the tidal constituent periods are known, the exact repeat period (P repeat ) is a non-linear function of semi-major axis (a) and inclination (i)