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 = Dec 2011 – 1694 = 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

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

Compare Test Orbits WITH wrt WITHOUT Annual Terms – Wk 1668 dXdYdZRXRYRZSCLwRMSMedi d d d d d d d units: mm, mm, mm, µas, µas, µas, mm, mm WITH wrt WITHOUT Annual Terms – Wk 1694 dXdYdZRXRYRZSCLwRMSMedi d d d d d d d units: mm, mm, mm, µas, µas, µas, ppb, mm, mm

Compare Test Terrestrial Frames WITH → WITHOUT Differences – Wk 1668 dXdYdZRXRYRZSCLwRMS offsets ± units: mm, mm, mm, µas, µas, µas, ppb, mm 228 stations WITH → WITHOUT Differences – Wk 1694 dXdYdZRXRYRZSCLwRMS offsets ± 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

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

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

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

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

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

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

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

Compare Test ERPs WITH wrt WITHOUT Annual Terms – Wk 1668 XpoleYpoleXprateYprateLOD d d d d d d d units: µas, µas, µas/d, µas/d, µs WITH wrt WITHOUT Annual Terms – Wk 1694 XpoleYpoleXprateYprateLOD d d d d d d d units: µas, µas, µas/d, µas/d, µs

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

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/ theta = omega*( t_mjd ) 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)

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 E E E E+00 SLRGAC E E E E+00 ANNUAL E E E E-10 ANNUAL E E E E Subject: Re: degree-2 annual coefficients Date: Wed, 27 Jun :40: 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 E E E E-10 I have to suspect that the higher degrees are not very important. JR Models Used from S. Bettadpur & J. Ries (2/2)