Preliminary SWOT Orbit Design Study R. Steven Nerem, Ryan Woolley, George Born, James Choe Colorado Center for Astrodynamics Research, University of Colorado Richard Ray NASA/Goddard Space Flight Center Ernesto Rodriguez Jet Propulsion Laboratory

University of Colorado at Boulder Colorado Center for Astrodynamics Research 2 Orbit Design Considerations Latitudinal coverage (orbit inclination) Temporal Sampling Spatial Sampling Tidal Aliasing Starting Point: –15-25 day repeat – km altitude –Near 78° inclination Other Considerations: –Calibration/Validation –Multiple Orbit/Mission Phases –Orbit Maintenance Final Orbit Design Derived from Science Requirements

University of Colorado at Boulder Colorado Center for Astrodynamics Research 3 ~60 km ~10 km km Sensor Swath Pattern ~3.5° ~0.6°

University of Colorado at Boulder Colorado Center for Astrodynamics Research 4 15-Day Orbit Coverage Gaps 3° N 0°0° 3° S 60 km 400 km

University of Colorado at Boulder Colorado Center for Astrodynamics Research 5 22-Day Orbit Coverage 2° N 0°0° 2° S

University of Colorado at Boulder Colorado Center for Astrodynamics Research 6 Repeat Period vs Equatorial Spacing

University of Colorado at Boulder Colorado Center for Astrodynamics Research 7 ~130 km total swath width Repeat Period vs Coverage (i = 78°)

University of Colorado at Boulder Colorado Center for Astrodynamics Research 8 15-Day Repeat, 1-Day Subcycle Base Interval ~25° or ~3000 km Day

University of Colorado at Boulder Colorado Center for Astrodynamics Research 9 14-Day Repeat, 3-Day Subcycle Base Interval ~25° or ~3000 km Day

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, 3-Day Subcycle Base Interval ~25° or ~3000 km Day

University of Colorado at Boulder Colorado Center for Astrodynamics Research 11 3-Day Repeat Base Interval ~25° or ~3000 km Day

University of Colorado at Boulder Colorado Center for Astrodynamics Research 12 1-Day Repeating Ground Track

University of Colorado at Boulder Colorado Center for Astrodynamics Research 13 3-Day Repeating Groundtrack

University of Colorado at Boulder Colorado Center for Astrodynamics Research 14 4-Day Repeating Groundtrack

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat – 3 Day Subcycle

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat – 3 Day Subcycle

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat – 3 Day Subcycle

University of Colorado at Boulder Colorado Center for Astrodynamics Research 18 Possible Orbit Altitudes: i = 78° Repeat Length (days) + Repeat Orbit at Subcycle

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Subcycles Repeat Length (days)

University of Colorado at Boulder Colorado Center for Astrodynamics Research 20 Properties of Repeat Track Orbits Complete exactly N orbits in C days –N is an integer, C is not (except for SS orbits) Altitude precisely determined by i, N, and C Ground track forms a grid on Earth’s surface, one point fixes the whole grid Grid “denser” for increasing C Sub-cycle length is a complex function of N and C

University of Colorado at Boulder Colorado Center for Astrodynamics Research 21 Candidate Orbits Repeat Length # of Orbits to Repeat Equatorial Spacing

University of Colorado at Boulder Colorado Center for Astrodynamics Research 22 Tidal Aliasing This initial analysis does not consider possible benefits of swath coverage (tidal solutions using swath “crossover” measurements) Tidal aliasing frequencies completely determined by orbit repeat period (function of altitude and inclination) Desirable characteristics: –Good separation of major tide constituents aliasing frequencies –Alias frequencies should not be close to one cycle per year –Tides should not alias to very long periods (<< 1 year)

University of Colorado at Boulder Colorado Center for Astrodynamics Research 23 Four main solar diurnal tides are separated in frequency by 1 cpy. The precession rate of the satellite orbit plane determines which frequency is aliased to zero. To avoid unfavorable aliasing generally requires a precession rate ≤ –2°/d (cf. Topex), which limits satellite inclination. We must trade off inclination and aliasing. Aliasing Near Diurnal Solar Tides

University of Colorado at Boulder Colorado Center for Astrodynamics Research 24 Tidal Alias Frequencies: i = 75°

University of Colorado at Boulder Colorado Center for Astrodynamics Research 25 Tidal Alias Frequencies: i = 77°

University of Colorado at Boulder Colorado Center for Astrodynamics Research 26 Tidal Alias Frequencies: i = 80°

University of Colorado at Boulder Colorado Center for Astrodynamics Research 27 Tidal Alias Frequencies: i = 85°

University of Colorado at Boulder Colorado Center for Astrodynamics Research 28 Average Tidal Frequency Separation

University of Colorado at Boulder Colorado Center for Astrodynamics Research 29 Average Tidal Frequency Separation

University of Colorado at Boulder Colorado Center for Astrodynamics Research 30 Tidal Aliasing: i = 78° X X X X X X X X X X X X X X X X X X X X X

University of Colorado at Boulder Colorado Center for Astrodynamics Research 31 Candidate Orbits Minimal Tidal Aliasing

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Subcycles

University of Colorado at Boulder Colorado Center for Astrodynamics Research 33 How Does This Analysis Change for SWOT? Many measurement locations have 2 or more ascending/descending passes. Most measurement locations are “cross over” points.

University of Colorado at Boulder Colorado Center for Astrodynamics Research day repeat latitude 32.0° Case 1: One ascending arc per repeat cycle Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

University of Colorado at Boulder Colorado Center for Astrodynamics Research day repeat latitude 32.0° Case 2: Two ascending arcs per repeat cycle Added sampling helps lunar tides, but not solar. Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

University of Colorado at Boulder Colorado Center for Astrodynamics Research day repeat latitude 32.0° Case 3: Two ascending arcs + two descending arcs per repeat cycle Added sampling helps solar diurnal tides, but not solar semidiurnals. Example Sampling of Tides by SWOT Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d

University of Colorado at Boulder Colorado Center for Astrodynamics Research day repeat latitude 60.0° Case 3b: Two ascending arcs + two descending arcs per repeat cycle Nominal alias period 818 d 111 d 68 d 285 d 160 d 89 d 48 d 80 d 143 d Added sampling helps solar tides, depending on latitude. Example Sampling of Tides by SWOT

University of Colorado at Boulder Colorado Center for Astrodynamics Research 38 Nadir vs Swath Sampling of the Tides Additional sampling within a repeat period generally solves aliasing issues of lunar tides. At most latitudes, additional sampling of solar tides does not help resolve semidiurnal tides. For some sea level studies, additional sampling will help mitigate solar tide-model errors, depending on data processing strategies. For tide model improvement studies, swath altimetry provides only marginal improvement for the solar tides over what is offered from conventional nadir altimetry. Therefore, Nadir-type aliasing studies generally apply to SWOT - for solar tides. Most lunar tides will not alias to long periods, so we can neglect them during orbit design (but it’s easy to check M2, O1, etc.).

University of Colorado at Boulder Colorado Center for Astrodynamics Research 39 Coverage Analysis 3 Cases studied to get representative coverage for different latitude bands: –Mid-latitude to high-latitude: Aghulas current region (Gulf Stream is similar) –Equatorial: Amazon River –High-latitude: Lena River Plots of number of visits within a cycle, for 10 day and 4 day sampling periods Histograms of temporal revisits within a cycle (i.e., no revisits between cycles considered)

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Aghulas

University of Colorado at Boulder Colorado Center for Astrodynamics Research days of 22-Day Repeat, Aghulas

University of Colorado at Boulder Colorado Center for Astrodynamics Research 42 4-Days of 22-Day Repeat, Aghulas

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Aghulas

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Amazon

University of Colorado at Boulder Colorado Center for Astrodynamics Research Days of 22-Day Repeat, Amazon

University of Colorado at Boulder Colorado Center for Astrodynamics Research 46 4-Days of 22-Day Repeat, Amazon

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Amazon

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Lena

University of Colorado at Boulder Colorado Center for Astrodynamics Research Days of 22-Day Repeat, Lena

University of Colorado at Boulder Colorado Center for Astrodynamics Research 50 4 Days of 22-Day Repeat, Lena

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat, Lena

University of Colorado at Boulder Colorado Center for Astrodynamics Research Day Repeat

University of Colorado at Boulder Colorado Center for Astrodynamics Research 53 1-Day (3-D) Questions?