Do Annual Geopotential Variations Affect IGS Products ?

J. Ray NOAA/NGS

with major help fromS. Bettadpur, J. Ries U. Texas/CSRT.-S. Bae Sejong U.X. Collilieux IGN/LAREGT. van Dam U. LuxembourgK. 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

Annual Geopotential Terms Considered

wk1668

• Pick two extreme weeks 6 months apart for testing: 1668 & 1694– Difference NGS solutions WITH & WITHOUT adding annual terms

wk1694

Compare Test OrbitsWITH wrt WITHOUT Annual Terms – Wk 1668

dX dY dZ RX RY RZ SCL wRMS Medid 0 -0.2 0.6 -1.2 2 9 -2 0.02 4 4

d 1 0.1 -0.2 -0.9 -8 -6 -5 0.01 2 2

d 2 -0.6 -0.1 -1.0 -8 -4 7 0.01 3 3

d 3 0.1 -0.4 -0.6 -4 1 3 0.01 3 3

d 4 0.1 0.0 0.2 2 5 0 0.00 3 3

d 5 -0.2 0.3 -1.3 9 -7 9 0.01 3 3

d 6 -0.6 0.3 -0.5 3 -7 0 0.00 4 4units: mm, mm, mm, µas, µas, µas, mm, mmWITH wrt WITHOUT Annual Terms – Wk 1694

dX dY dZ RX RY RZ SCL wRMS Medid 0 0.2 -0.2 -0.7 2 10 0 0.00 2 2

d 1 0.4 -0.2 -0.9 -4 6 2 0.01 2 2

d 2 -0.1 0.0 -0.9 1 1 -7 0.00 2 2

d 3 -0.2 0.3 -1.0 -2 -1 -2 0.01 2 2

d 4 0.0 0.2 -0.2 0 0 -4 0.00 2 2

d 5 0.1 -0.1 -0.4 0 1 -1 0.01 2 2

d 6 0.0 0.2 -0.9 -2 7 2 0.00 3 3units: mm, mm, mm, µas, µas, µas, ppb, mm, mm

Compare Test Terrestrial Frames

WITH → WITHOUT Differences – Wk 1668dX dY dZ RX RY RZ SCL wRMS

offsets -0.61 -0.17 -1.32 5.2 2.2 -2.4 0.002 0.45

± 0.02 0.02 0.02 0.7 0.7 0.6 0.003units: mm, mm, mm, µas, µas, µas, ppb, mm 228 stations

WITH → WITHOUT Differences – Wk 1694dX dY dZ RX RY RZ SCL wRMS

offsets 0.24 0.10 -0.83 3.4 -3.4 0.5 0.007 0.29

± 0.01 0.01 0.01 0.4 0.5 0.4 0.002units: 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 ERPsWITH wrt WITHOUT Annual Terms – Wk 1668

Xpole Ypole Xprate Yprate LODd 0 2.9 -0.3 42.5 -21.7 -4.14

d 1 -3.0 -6.1 -6.8 34.7 -2.59

d 2 -2.2 -6.2 -3.3 -13.0 -2.22

d 3 -3.3 -1.3 18.3 -9.7 -0.56

d 4 6.4 -3.6 -33.0 -23.3 -1.60

d 5 -12.0 10.0 51.6 -32.8 -3.21

d 6 -10.7 3.5 -18.4 -0.1 -0.50units: µas, µas, µas/d, µas/d, µsWITH wrt WITHOUT Annual Terms – Wk 1694

Xpole Ypole Xprate Yprate LODd 0 11.7 1.7 4.4 -2.1 -1.14

d 1 6.6 -10.0 5.3 0.3 -3.14

d 2 -0.6 3.3 -64.3 14.2 -3.46

d 3 -2.3 -3.2 -47.9 -44.2 -0.60

d 4 -0.2 -0.2 -13.7 19.6 -1.31

d 5 5.1 0.9 -17.5 1.8 -2.29

d 6 8.6 0.5 6.5 -25.7 -1.39units: 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 variabilityAuthor: Srinivas BettadpurDate: June 27, 2012Version: 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)

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 coefficientsDate: Wed, 27 Jun 2012 15:40:36 -0500From: John C. Ries <ries@csr.utexas.edu>

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)