Orbit Selection Issues for WideSwath Altimeter Don P

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 • 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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 2

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 9. 915625 days (“ 10 -days”), or 237. 975 hours » M 2 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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 3

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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 4

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

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 lowfrequency (approaching a bias) D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 6

General 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 K 1 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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 7

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 • K 1 aliased to within 0. 11 cpy of semi-annual » 9 -years to separate D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 8

• There are orbits near 80° inclination that have better aliasing properties than T/P D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 9

Average Frequency Separation • Find minimum separation between each constituent and all others (incl. annual, semiannual): fi f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f 10 • 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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 10

• Average f = 0. 4 cpy implies mean separation time of 2. 5 years, 0. 7 cpy = 1. 42 years • 800 -1300 km altitude D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 11

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

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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 13

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

• 800 -1000 km altitude D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 16

Calculating 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 D. Chambers Wide-Swath Ocean Sciences and Hydrology Meeting 31 October 2006 17

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