1. Do Annual Geopotential Variations Affect IGS Products ? J. Ray NOAA/NGS with major help from S. Bettadpur, J. Ries U. Texas/CSR T.-S. Bae Sejong U. X. Collilieux IGN/LAREG T. van Dam U. Luxembourg K. Choi, J. Griffiths NOAA/NGS Test effect of GRACE RL05 annual model fits from CSR – consider terms (2,0), (2,1), (2,2), & (3,1) Compare GPS results for two extreme weeks – 1668 = 25 - 31 Dec 2011 – 1694 = 24 -30 Jun 2012 Impacts at levels up to several mm Other ACs should test & consider using in Repro2 IGS Workshop 2012, AC Splinter Meeting, Olsztyn, Poland, 26 July 2012

2. Annual Geopotential Terms Considered wk 1668 Pick two extreme weeks 6 months apart for testing: 1668 & 1694 –Difference NGS solutions WITH & WITHOUT adding annual terms wk 1694

3. Compare Test Orbits WITH wrt WITHOUT Annual Terms – Wk 1668 dXdYdZRXRYRZSCLwRMSMedi d 0 -0.20.6-1.229-20.0244 d 1 0.1-0.2-0.9-8-6-50.0122 d 2 -0.6-0.1-8-470.0133 d 3 0.1-0.4-0.6-4130.0133 d 4 0.10.00.22500.0033 d 5 -0.20.3-1.39-790.0133 d 6 -0.60.3-0.53-700.0044 units: mm, mm, mm, µas, µas, µas, mm, mm WITH wrt WITHOUT Annual Terms – Wk 1694 dXdYdZRXRYRZSCLwRMSMedi d 0 0.2-0.2-0.721000.0022 d 1 0.4-0.2-0.9-4620.0122 d 2 -0.10.0-0.911-70.0022 d 3 -0.20.3-2-20.0122 d 4 0.00.2-0.200-40.0022 d 5 0.1-0.1-0.4010.0122 d 6 0.00.2-0.9-2720.0033 units: mm, mm, mm, µas, µas, µas, ppb, mm, mm

4. Compare Test Terrestrial Frames WITH → WITHOUT Differences – Wk 1668 dXdYdZRXRYRZSCLwRMS offsets -0.61-0.17-1.325.22.2-2.40.0020.45 ± 0.02 0.7 0.60.003 units: mm, mm, mm, µas, µas, µas, ppb, mm 228 stations WITH → WITHOUT Differences – Wk 1694 dXdYdZRXRYRZSCLwRMS offsets 0.240.10-0.833.4-3.40.50.0070.29 ± 0.01 0.40.50.40.002 units: mm, mm, mm, µas, µas, µas, ppb, mm 253 stations Orbit & TRF frames both shift by about -1 mm in Z component –probably due to N/S network asymmetry –recall that current IGS Z bias wrt SLR origin is ~10 larger –global WRMS impact on stations positions at level of ~0.5 mm

5. Week 1668 (25-31 Dec 2011) - (IGS-load) Distribution of dU Shifts TASH

6. IGS Repro1 Residuals (TASH – Loads) TASH heights are too low each December –annual geopotential effect might partially compensate ?

7. Week 1694 (24-30 Jun 2012) - (IGS-load) Distribution of dU Shifts Sometimes regions of good correlation

8. Week 1668 (25-31 Dec 2011) - (IGS-load) Distribution of dN Shifts

9. Week 1694 (24-30 Jun 2012) - (IGS-load) Distribution of dN Shifts

10. Week 1668 (25-31 Dec 2011) - (IGS-load) Distribution of dE Shifts

11. Week 1694 (24-30 Jun 2012) - (IGS-load) Distribution of dE Shifts But also sometimes areas of poor correlation

12. Compare Test ERPs WITH wrt WITHOUT Annual Terms – Wk 1668 XpoleYpoleXprateYprateLOD d 0 2.9-0.342.5-21.7-4.14 d 1 -3.0-6.1-6.834.7-2.59 d 2 -2.2-6.2-3.3-13.0-2.22 d 3 -3.3-1.318.3-9.7-0.56 d 4 6.4-3.6-33.0-23.3-1.60 d 5 -12.010.051.6-32.8-3.21 d 6 -10.73.5-18.4-0.1-0.50 units: µas, µas, µas/d, µas/d, µs WITH wrt WITHOUT Annual Terms – Wk 1694 XpoleYpoleXprateYprateLOD d 0 11.71.74.4-2.1-1.14 d 1 6.6-10.05.30.3-3.14 d 2 -0.63.3-64.314.2-3.46 d 3 -2.3-3.2-47.9-44.2-0.60 d 4 -0.2 -13.719.6-1.31 d 5 5.10.9-17.51.8-2.29 d 6 8.60.56.5-25.7-1.39 units: µas, µas, µas/d, µas/d, µs

13. Conclusions & Recommendations Annual geopotential variations have small but non-negligible impacts for IGS products –DZ component of orbit & terrestrial frames shifted by ~1 mm –LOD is biased by few µs –subdaily orbit residuals differ up to ~4 mm WRMS –station positions shift by up to ~0.7 mm horizontal, ~3 mm vertical, probably seasonally –systematic geographic shifts may significantly alias inferred GPS load signatures –however, annual geopotential effect generally appears to be smaller than annual (GPS – load) residuals, esp for dN & dE Recommend further testing by other ACs –need longer spans of results & further comparisons Recommend possible adoption for Repro2 –if preliminary NGS results confirmed, IGS should consider adopting a conventional model for annual geopotential variations for Repro2 –must coordinate with GRACE, SLR, & IERS groups –Srinivas Bettadpur working on GRACE fit to degree 15

14. Subject: Estimates of non-tidal degree-2 annual geopotential variability Author: Srinivas Bettadpur Date: June 27, 2012 Version: v 0.0 The total variability at the annual frequency is a sum of many processes. Not all of these are included in the estimates here. Total_Annual = 3rd Body Pert (relevant only for orbits) <<-- This is NOT included below + All tides (solid, ocean, solid+ocean pole tide) <<-- This is NOT included below + Atmosphere + non-tidal oceans (AOD1B contents) <<-- This is included below + Everything else left over (GSM contents) <<-- This is included below The estimates for "Everything else left over" depends on what was modeled for the parts labeled "NOT included below". This list is included below: 3rd Body Pert: DE405 for luni-solar positions Solid Tide: Eq. 6.xx from IERS2010, with anelastic earth klm Ocean Tide: Self-consistent equilibrium Solid Earth pole tide: IERS C04 pole series with an-elastic earth klm Ocean pole tide: IERS C04 pole series with self-consistent equilibrium model of Desai To calculate the contributions to the Clm/Slm, in the same normalization as in the Conventions: omega = 2*pi/365.2426 theta = omega*( t_mjd - 54101.0 ) dClm( t_mjd ) = CBAR_cos * cos(theta) + CBAR_sin * sin(theta) dSlm( t_mjd ) = SBAR_cos * cos(theta) + SBAR_sin * sin(theta) Models Used from S. Bettadpur & J. Ries (1/2)

15. Table below gives the values of the annual amplitudes for all the degree-2 harmonics. The GRACE+GAC values are labeled as "ANNUAL". For the (2,0) harmonic, the SLR+GAC based estimates are also provided. name N M CBAR_cos CBAR_sin SBAR_cos SBAR_sin ========== ========== ========== ========== ========== ANNUAL 2 0 0.1103E-09 0.8033E-10 0.0000E+00 0.0000E+00 SLRGAC 2 0 9.9868E-10 1.1105E-10 0.0000E+00 0.0000E+00 ANNUAL 2 1 0.7377E-11 -.2024E-10 0.7651E-10 -.2273E-10 ANNUAL 2 2 -.1394E-10 -.7749E-11 0.5471E-10 -.4229E-10 ------------------------------------------------------------------------------------------------- Subject: Re: degree-2 annual coefficients Date: Wed, 27 Jun 2012 15:40:36 -0500 From: John C. Ries Hi Jim, I imagine that degree 2 is the 'tall pole' for GPS, but I'm curious about the effect of an odd- degree order 1 term. I think it will be too small for GPS, but it has shown to be important for lower satellites. A quick fit to RL05 gets, in the same convention as Srinivas: name N M CBAR_cos CBAR_sin SBAR_cos SBAR_sin ========== ========== ========== ========== ========== ANNUAL 3 1 0.22E-10 -0.08E-10 0.31E-10 0.39E-10 I have to suspect that the higher degrees are not very important. JR Models Used from S. Bettadpur & J. Ries (2/2)