Systematic Errors in IGS Terrestrial Frame Products

1. Systematic errors inIGS terrestrial frame products Paul Rebischung, Zuheir Altamimi(with contributions from Ralf Schmid, Jim Ray & Wei Chen) IGS Workshop 2017, Paris, 3-7 July 2017

2. Outline • GNSS-derived geocenter motion • GNSS-derived terrestrial scale • GNSS station position time series • Draconitics • Fortnightly signals • Equipment-related biases • Bonus: • ITRF2014 post-seismic deformation models: 2.5 years after • Comparison of I/D/JTRF2014 polar motion serieswith geophysical excitation data

3. GNSS-derived geocenter motion ― Daily IGS repro2 combined geocenter coordinates ― Smoothed repro2 combined geocenter coordinates ― Smoothed geocenter coordinatesderivedfrom the SLR contribution to ITRF2014 Amplitude spectra of the:― IGS repro2 ― SLR-derivedgeocenter time seriesshown in the left plots

4. GNSS-derived geocenter motion • Non-negligible offsets & rates wrt ITRF2008(inter-AC agreement at the level of 3 mm; 0.3 mm/yr) • Annual geocenter motion: • Underestimated along X • Overestimated along Y • Out-of-phase with SLR along Z • Obvious contamination by draconitic signals Results from trend + annual + semi-annual fits to: ― the repro2 combined geocenter time series ― geocenter time seriesderivedfrom the SLR contribution to ITRF2014

5. GNSS-derived geocenter motion • GNSS still far from contributing to the definitionof the ITRF origin • Why? • Nearly perfect correlation between geocenter coordinates andsatellite & station clock offsets + tropospheric parameters + network shapein standard GNSS analyses • Modelling errors (most likely orbit modelling errors) • Prospects • Satellite clock modelling (Galileo?) • Inclusion of LEOs in GNSS analyses • Orbit modelling improvements

6. GNSS-derived terrestrial scale • Mean scale(determined by igsyy.atx satellite z-PCOs): • igs08.atx: –0.3 ppb bias wrt ITRF2008 scaledue to recent orbit modeling changes • igs14.atx: coincides with ITRF2014 scaleat epoch 2010.0 • Scale rate (determined by the use of constant satellite z-PCOs, i.e. ”intrinsic GNSS scale rate”): • closer to ITRF2008 scale rate (–0.004 ppb/yr)than to ITRF2014 scale rate (+0.026 ppb/yr) • Non-linear scale variations: • Similar seasonal variations (i.e. network effect) with IGb08/igs08.atx and IGS14/igs14.atx • Non-linear, non-seasonal variations less scattered with igs14.atx thanks to improved z-PCOs,esp. for recently launched satellites Cyan: Scale factors between IGb08/igs08.atx-(resp. IGS14/igs14.atx-) based daily solutionsand IGb08 (resp. IGS14) Blue: linear trend [+ annual and semi-annual signals]Red: residuals of the fits, shifted by -1.5 ppb

7. GNSS-derived terrestrial scale • The 0.03 ppb/yr scale rate difference between ITRF2014 and ITRF2008 clearly shows up when confronting the IGS daily solutions with both RFs. • The “intrinsic GNSS scale rate” based on constant z-PCO values is closerto the ITRF2008 than to the ITRF2014 scale rate. • The scale of igs14.atx-based GNSS solutions matches the ITRF2014 scaleat epoch 2010.0, but progressively diverges with time. Schematic representation of the scale and scale rate differences between ITRF2008, ITRF2014 and GNSS solutions based on either igs08.atx or igs14.atx

8. GNSS-derived terrestrial scale • Contribution of GNSS to future ITRF mean scale might become possible with the availability of phase center calibrations for the Galileo satellites. • Contribution of GNSS to future ITRF scale rate could be considered, • but requires careful (re-)assessment of satellite z-PCO stability,hence of the precision of the intrinsic GNSS scale rate. • ≈ 5 mm/yr & 0.25 mm/yr, respectively, according to Collilieux & Schmid (2013) • GNSS may also contribute to future ITRF non-linear (e.g. seasonal) scale variations, • once non-linear motion discrepancies at co-location sites are betterunderstood.

9. Station position time series: spectra Averaged Lomb-Scargleperiodograms of the station position residual time series from the long-term stackings of the AC repro2 contributions ― results from white + power-law noise (i.e., a + b/fα) fits • crossover frequencies between white & power-law noises

10. Station position time series: draconitics • Strong spatial correlations for low harmonics → Main orbit-related source • Maps generally similar amongst ACs up to the 4th harmonic → Possibly common modeling errors

11. Station position time series: 14d signals 14.76 days (M2 alias): • Spectral peaks visible in the horizontal residuals of all ACs  consistent with a rotational origin (e.g. error in the IERS subdaily EOP tide model) • More pronounced for GFZ/GTZ (?) and MIT/ULR (absence of ocean tide geopotential corrections in GAMIT orbit integrator?) Square-root of the averaged Lomb-Scargleperiodogramsshown in slide 9: zoom on the fortnightly band

12. Station position time series: 14d signals 14.19 days (O1 alias): • Small spectral peaks discernable in the horizontal residuals of some ACs  consistent with a rotational origin (e.g. error in the IERS subdaily EOP tide model) • More pronounced for MIT/ULR (absence of ocean tide geopotential corrections in GAMIT orbit integrator?) Square-root of the averaged Lomb-Scargleperiodogramsshown in slide 9: zoom on the fortnightly band

13. Station position time series: 14d signals 13.66 days (Mf tide) / 13.63 days (75,565 tide): • Both lines visible in (almost) all 3 components of all ACs • 13.63 day lines generally larger, although they correspond to a minor tide!? • Much lower peaks for JPL: low-frequency error absorbed by JPL’s stochastic orbit parameters? • Vertical peaks larger for MIT/ULR Square-root of the averaged Lomb-Scargleperiodogramsshown in slide 9: zoom on the fortnightly band

14. Equipment-related biases antenna change receiver changes antenna changes • Biases in IGS station positions are evidenced by equipment-related discontinuities: • Whatis the magnitude of equipment-relateddiscontinuities in the IGS repro2 station position time series? • Whatdoesit tell about the accuracy of IGS station positions? • Do antenna change discontinuitiesgetsmallerwith igs14.atx? Distribution of identified discontinuity causes in IGS repro2 station position time series MAS1 (Maspalomas, Spain)Cyan: Detrended repro2 station position time seriesBlue: piecewise linear + annual + semi-annual fit

15. Equipment-related biases • What is the magnitude of equipment-related discontinuities in the IGS repro2 station position time series? Histograms and empirical cumulative distribution functions (CDF) of 985 equipment-related discontinuities estimated during the long-term stacking of the daily IGS repro2 solutions

16. Equipment-related biases • What is the magnitude of equipment-related discontinuities in the IGS repro2 station position time series? Histograms and empirical cumulative distribution functions (CDF) of 985 equipment-related discontinuities estimated during the long-term stacking of the daily IGS repro2 solutions • Best fitting Student’s t-distributions: • East: ν = 2.02; σ = 2.85 mm • North: ν = 2.10; σ = 2.74 mm • Up: ν = 1.88; σ = 7.45 mm • → Discontinuity sizes aren’t normally distributed, but show "heavy tails". Tried to identifydifferentsub-categories: • antenna changes / receiver changes, • uncalibrated radomes, • problematicantenna types…but withoutsuccess.

17. Equipment-related biases • What does it tell about the accuracy of IGS station positions? Discontinuity sizes = station position biases – station position biases ? ? = * ? ? = * ? ? = *

18. Equipment-related biases • What does it tell about the accuracy of IGS station positions? Student’s t≈Student’s t * Student’s t ≈ * ≈ * ≈ *

19. Equipment-related biases • Whatdoesit tell about the accuracy of IGS station positions? • Equipment-relatedbiases in IGS station positions followheavy-tailed distributions (modelledhere as Student’st-distributions). → Confidence intervalsgrow « fast » with confidence levels.

20. Equipment-related biases • Do antenna change discontinuities get smaller with igs14.atx ? • Subset of 346 antenna change discontinuities involving at least one antenna with updated calibration from igs08 to igs14.atx • Apply PPP-derived position corrections to compute expected discontinuity sizes with igs14.atx → « igs08.atx to igs14.atx » position corrections have marginal impact on discontinuity sizes. → Errors in type-mean antenna calibrations do not seem to be a major contributor to current IGS station position biases. igs08.atx (before correction) igs14.atx (after correction)

21. ITRF2014 PSD models: 2.5 years after • Compare IGS daily station position time series with propagated ITRF2014 coordinates: two examples — daily IGS station position time series — propagated ITRF2014 coordinates — ± 3σ confidenceintervalsend of ITRF2014 input data

22. ITRF2014 PSD models: 2.5 years after end of ITRF2014 input data • PSD model prediction errors • depend on each individual case,but generally on: • age of the last earthquake, • amplitude of the post-seismic deformations, • (presence of other non-linear deformations) • are mostly comparable with prediction errors of classicallinear ITRF2014 coordinates: Differences between IGS daily station position time series and propagated ITRF2014 coordinates — Stations without PSD model — Stations with PSD model

23. ITRF2014 PSD models: 2.5 years after end of ITRF2014 input data • PSD model prediction errors • depend on each individual case,but generally on: • age of the last earthquake, • amplitude of the post-seismic deformations, • (presence of other non-linear deformations) • are mostly comparable with prediction errors of classicallinear ITRF2014 coordinates, • especially for IGS14 stations(whose selection took the PSD model formal errors into account): Differences between IGS daily station position time series and propagated ITRF2014 coordinates — IGS14 stations without PSD model — IGS14 stations with PSD model

24. Inter-comparison of I/D/JTRF2014polar motion series Detrended polar motion differences Power spectra of polar motion differences

25. Inter-comparison of I/D/JTRF2014polar motion series • Background noise in PM differences approximately flicker • JTRF ypseries shows spectral peaks at 52.18 cpy (7d) and harmonics, due to using weekly ig2 solutions as input • JTRF yp[semi-]annual signals different from both others, due to filter approach used • JTRF different from both other series at low frequencies (<5 cpy), due to filter approach used • DTRF slightly different from both other series at mid frequencies (5-70 cpy) • ITRF slightly different from both other series at high frequencies (> 70 cpy) RMS of the total pairwise polar motion difference series,of the periodic signals fitted to each difference series,and of their low-, mid- and high-frequency residuals

26. I/D/JTRF2014 polar motion seriesvs. geophysical excitation data • Convert polar motion series into “geodetic excitation” series by the “gain adjustment” method of Chen et al. (2013) • Compare geodetic excitation series with geophysical (LDC) excitation series derived from GRACE, SLR, plus atmospheric, oceanic and hydrological models (Chen et al., 2013) • Differences between “X – LDC” and “ITRF – LDC” excitation difference power spectra, offset by multiples of 50 mas²/d² for clarity • Negative values mean: closer to LDC than ITRF • Positive values mean: further from LDC than ITRF

27. I/D/JTRF2014 polar motion seriesvs. geophysical excitation data • Total RMS significantly larger for DTRF (χ2) and JTRF • ITRF & IG2_s globally show best agreement with LDC at [semi-]annual periods;JTRF globally worst • ITRF shows better agreement with LDC than DTRF & JTRF at high frequencies Correlation coefficients between geodetic and LDC excitation series;RMS of the “geodetic – LDC” excitation difference series, of the periodic signals fitted to eachdifference series, and of their low-, mid- and high-frequency residuals

28. Thankyou for your attention!