Orbit Selection for the WATER HM Mission R. S. Nerem CCAR, CIRES, University of Colorado D. P. Chambers Center for Space Research, University of Texas at Austin (with input from Gregg Jacobs, Richard Ray, and John Ries)

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 General Constraints on Search l No sun-synchronous orbits l Altitudes lower than 1000 km to avoid radiation exposure l Inclinations greater than 75° in order to sample most rivers in Siberia l Repeat period ~ 20-days in order to meet groundtrack spacing requests of mesoscale oceanography and hydrology (~10 days was also considered to meet a request for higher temporal resolution studies)

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Sun Synchronous Orbits

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Why not Sun-Synchronous Orbits? l Prevents Serious Tidal Studies l Tides poleward of 66° l Tides in shallow water and estuaries l Wavelengths shorter than 300 km l Maps Diurnal Errors to Undesirable Periods l Into long-period “climate-like” signals l Into seasonal variations (annual, semi-annual) l Into the mean sea surface

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Calculating Tidal Aliasing P is satellite repeat period T is tide period  p is tide alias period

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Aliasing Considerations l For applications in oceans and estuaries, we desire a satellite orbit that aliases all tides to frequencies greater than 2 cycles-per year l The alias period is shorter than the semi-annual (half-year) signal l Can observe multiple cycles of the alias period within a few years Another important factor to consider is the separation between alias frequencies and between the aliases and annual/semi-annual (  f) l Determines time needed to separate two tides in altimeter observations Time to separate ~ 1/  f l T/P did not have optimal separation for some constituents l K1 aliased to within 0.11 cpy of semi-annual l 9-years to separate

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Tidal Aliasing ~10 Day Repeat

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Tidal Aliasing ~20 Day Repeat

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Tidal Aliasing ~20 Day Repeat

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Orbit 1 Altitude = km Inclination = 78° Repeat Period = days Orbit 2 Altitude = km Inclination = 78° Repeat Period = days Except for K1, these two orbits have very good aliasing properties for 9 major constituents

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 General Observations l Only orbits with an inclination 2 cpy l Retrograde orbits have poor aliasing of solar tides l If we do not require that the K1 alias > 2 cpy l Good orbits do exist up to 80° inclination l This covers more of the Arctic Ocean, all of the Antarctic boundary, and most rivers in Siberia

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Shallow Water Tides l In shallow water (including estuaries) tides are nonlinear and have much smaller wavelength than in the deep ocean l In 40 m, tide wavelength is 10x smaller than in 4000m l Shallow water tides are poorly observed by current altimeter systems l Examine aliasing of select nonlinear tides for potential orbits

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Orbit 1 Altitude = km Inclination = 78° Repeat Period = days Orbit 2 Altitude = km Inclination = 78° Repeat Period = days Some close aliases between nonlinear and primary tides Aliasing of Nonlinear Tides

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Comments on the Orbit “ ….. many coastal locations at mid to high latitudes would be sampled twice in each 10-day orbit, for a repeat of about 5 days. Those interested in coastal applications prefer that this repeat time not be increased. Five days will still not resolve the rapid coastal ocean response to synoptic forcing (periods of 1-5 days), relying on models to assimilate the SSH data and provide the higher temporal resolution needed.” T. Strub “The basic recommendation on orbits for mesoscale is for full coverage. So I would lean toward the longer repeat (~ 20 days) if the swath were 60 km to each side. Tidal aliasing should be considered for mesoscale.” G. Jacobs “Inclination greater than 74°, temporal sampling not critical, but more frequent overpasses desirable.”, D. Alsdorf

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Orbit Repeat Period 11-Day Repeat15-Day Repeat 21-Day Repeat

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 WaTER HM Swath

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 HM sampling (9.95 days) Nadir sampling (9.95 days) Sampling with 200 km Swath

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Groundtrack Separation 140 km 200 km

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Precision Orbit Determination l Availability of GRACE gravity models has significantly reduced gravity-driven orbit error. l GPS has made precise continuous tracking routinely available. l For orbit altitudes in the km range, 2 cm orbit accuracy should be easily obtainable. l Extended antennas and solar arrays may complicate the orbit determination. l Thought should be given to monitoring motion of antenna phase centers with respect to s/c center-of-mass, attitude determination, GPS multipath issues.

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Radial Orbit Errors due to Gravity Predicted using difference between GGM02C-GFZ04C Proposed Wide-Swath OrbitJason Orbit Mean Portion RMS about Mean

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Conclusions l For a 120 km swath, a ~20 day repeat is desired to obtain near global coverage. l A variety of orbits exist with altitudes near 800 km, inclinations of ~ 78°, and repeat periods near 21 days that have good tidal aliasing properties for deep ocean tides and meet other mission requirements l Care must be given to the precision orbit determination, but 2 cm radial accuracy should be possible. l Preliminary Recommendation (Altitude = km, Inclination = 78°, Repeat Period = days) l Will be able to additionally observe the M 4 tide as well as 2MN 2, 2MS 6, and 2MS 2, will not be able to separate MS 4 and M 6 tides l More effort might find an orbit that can sample both MS 4 and M 4 well

The University of Colorado Colorado Center for Astrodynamics Research Nerem 10/29/07 Shallow Water Tides