1. GNSS Observations of Earth Orientation Jim Ray, NOAA/NGS 1. Polar motion observability using GNSS – concepts, complications, & error sources – subdaily considerations 2. Performance of IGS polar motion series – compare Ultra-rapid, Rapid, & Final products – assess random & systematic errors 3. Utility of IGS length-of-day (LOD) – assess value for combinations with VLBI UT1 4. Impact of errors in subdaily EOP tide model – effects on orbits, EOPs, & other IGS products Wuhan University, May 2013

2. IGS Core Product Lines (2012) Series ID code Latency Issue times (UTC) Data spans (UTC) Remarks Ultra-Rapid (predicted half) IGUreal-time @ 03, 09, 15, 21 +24 hr @ 00, 06, 12, 18 ● for real-time apps ● GPS & GLONASS ● issued with prior IGA Ultra-Rapid (observed half) IGA3 - 9 hr @ 03, 09, 15, 21 -24 hr @ 00, 06, 12, 18 ● for near real-time apps ● GPS & GLONASS ● issued with following IGU Rapid IGR17 - 41 hr @ 17 daily ±12 hr @ 12 ● for near-definitive, rapid apps ● GPS only Final IGS12 - 18 d weekly each Thursday or Friday ±12 hr @ 12 for 7 d ● for definitive apps ● GPS & GLONASS 02

3. IGS Core Product Accuracies (2011) SeriesIDProduct TypesAccuraciesOutput Intervals Ultra-Rapid (predicted half) IGU ● GPS orbits~ 5 cm (1D) 15 min ● GLONASS orbits~10 cm (1D) 15 min ● GPS SV clocks~3 ns RMS / ~1.5 ns Sdev 15 min ● EOPs: PM + dLOD~250 µas / ~50 µs 6 hr Ultra-Rapid (observed half) IGA ● GPS orbits~ 3 cm (1D) 15 min ● GLONASS orbits~5 cm (1D) 15 min ● GPS SV clocks~150 ps RMS / ~50 ps Sdev 15 min ● EOPs: PM + dLOD<50 µas / ~10 µs 6 hr Rapid IGR ● GPS orbits~2.5 cm (1D) 15 min ● GPS SV & station clocks~75 ps RMS / ~25 ps Sdev 5 min ● EOPs: PM + dLOD<40 µas / ~10 µs daily Final IGS ● GPS orbits<2.5 cm (1D) 15 min ● GLONASS orbits<5 cm (1D) 15 min ● GPS SV & station clocks~75 ps RMS / ~20 ps SDev 30 s (SVs) + 5 min ● EOPs: PM + dLOD<30 µas / ~10 µs daily ● Terrestrial frames~2 mm N&E / ~5 mm U weekly IGS aims for ~1 cm orbit & ~1 mm terrestrial accuracies –to satisfy most demanding mm-level user application requirements 03

4. Ultra-Rapid Products 04

5. IGS Ultra-Rapid Update Cycle day 1day 2day 3 ●● ●● ●● ●● ●● ● ● ● ● 00h06h12h18h00h06h12h18h00h06h = 24 hr of Observations●= Observed ERPs = 24 hr of Predictions●= Predicted ERPs IGU updates every 6 hr are always 3 hr after the beginning of each prediction interval 05

6. Ultra-Rapid AC Orbit Comparisons (over 48 hr) Performance among ACs is bimodal & widely dispersed –SIO & USN have been rejected for ~5 years; NGS & WHU added recently –AC quality is more uniform over first 6 hr of predictions –biggest differences come from 6 – 24 hr predictions 06

7. Some IGU AC Orbits Have Large Rotations SIO, USN, & NGS have had large Z rotations –NGS recently improved –CODE sometimes has moderately large Z rotations 0.5 mas = 64 mm error @ GPS hgt 07

8. Ultra-Rapid Orbit Diffs (mm) wrt IGR (2009) DXDYDZRXRYRZSCLRMSWRMS MEDI TOTAL ERR IGU 6-hr predictions: mean3.5-0.60.3 0.8 3.1-0.728.921.315.6 41.7 std dev4.7 4.93.413.816.327.2 2.619.7 8.0 2.6 IGU 24-hr predictions: mean1.10.3-0.1-0.5-0.6-0.9-1.364.747.330.2 80.2 std dev1.82.0 3.821.931.252.0 1.933.316.3 6.0 IGA observations: mean1.20.30.1-0.20.9 2.6-1.29.08.07.2 16.3 std dev0.80.91.3 3.4 12.7 1.51.61.31.2 Orbit errors double when prediction interval increases by x4 IGA total err only ~40% worse than IGRs (but 175% worse for RZ) 08

9. Ultra-Rapid Orbit Diffs (mm) wrt IGR (2009) DXDYDZRXRYRZSCLRMSWRMS MEDI TOTAL ERR IGU 6-hr predictions: mean3.5-0.60.3 0.8 3.1-0.728.921.315.6 41.7 std dev4.7 4.93.413.816.327.2 2.619.7 8.0 2.6 IGU 24-hr predictions: mean1.10.3-0.1-0.5-0.6-0.9-1.364.747.330.2 80.2 std dev1.82.0 3.821.931.252.0 1.933.316.3 6.0 IGA observations: mean1.20.30.1-0.20.9 2.6-1.29.08.07.2 16.3 std dev0.80.91.3 3.4 12.7 1.51.61.31.2 Largest RT orbit prediction error comes from UT1 predictions IGA accuracy also limited by RZ rotations Z rotation errors are largest RT error – from UT1 prediction errors 09

10. Ultra-Rapid Orbit Diffs (mm) wrt IGR (2009) DXDYDZRXRYRZSCLRMSWRMS MEDI TOTAL ERR IGU 6-hr predictions: mean3.5-0.60.3 0.8 3.1-0.728.921.315.6 41.7 std dev4.7 4.93.413.816.327.2 2.619.7 8.0 2.6 IGU 24-hr predictions: mean1.10.3-0.1-0.5-0.6-0.9-1.364.747.330.2 80.2 std dev1.82.0 3.821.931.252.0 1.933.316.3 6.0 IGA observations: mean1.20.30.1-0.20.9 2.6-1.29.08.07.2 16.3 std dev0.80.91.3 3.4 12.7 1.51.61.31.2 Next largest RT limits from orbit modelling & PM prediction errors large X, Y rotation errors – from PM prediction errors due to modelling of orbit dynamics 10

11. Ultra-rapid Observed Polar Motion Accuracy dPM-x dPM-y (Ultra Observed – Final) PM Differences (25 Mar 2000 – 31 Dec 2011: daily noon epochs only) Annual mean & std dev of (IGU-IGS) dPM dPM-x dPM-y Polar Motion Differences (µas) Mean & Std Dev (µas) Final PM-x sigma Final PM-y -sigma IGU accuracy improved greatly after ~2003 IGU dPM RMS errors <40 µas in recent years errors in IGS Final PM reference no longer negligible IGS PM errors have low- frequency systematic components improved...  even more...  11

12. Spectra of (Ultra Observed-Final) PM Differences Subdaily tide model alias errors seen at 7.0 & 14.19 d periods –7 th GPS draconitic peak also strong in polar motion rates –3 rd GPS draconitic peak also prominent in IGS orbit discontinuities –note that differencing should remove common-mode errors! (1461 d from 1 Jan 2008 – 31 Dec 2011) dPM-x dPM-y inter-annual power is largest 12

13. Ultra-rapid Predicted Polar Motion Accuracy dPM-x dPM-y (Ultra Predicted – Final) PM Differences (8 Nov 2006 – 31 Dec 2011: daily noon epochs only) Annual mean & std dev of (IGU-IGS) dPM dPM-x dPM-y Polar Motion Differences (µas) Mean & Std Dev (µas) Final PM-x sigma Final PM-y -sigma IGU PM prediction accuracy unchanged since ~2006 recent IGU 1-d RMS prediction errors: ~270 µas for PM-x ~210 µas for PM-y PM prediction errors appear more random than systematic 13

14. Spectra of (Ultra Predicted-Final) PM Differences Subdaily tide model alias errors probably dominate sub-monthly band & perhaps annual, but no distinct lines –draconitic errors probably important in between dPM-x dPM-y (1880 d from 8 Nov 2006 – 31 Dec 2011) 14

15. Ultra-rapid Observed dLOD Accuracy (Ultra Observed – Final) dLOD Differences (25 Mar 2000 – 31 Dec 2011: daily noon epochs only) Annual mean & std dev of (IGU-IGS) dLOD Length-of-Day Differences (µs) Mean & Std Dev (µs) Final dLOD sigma IGU accuracy improved steadily after ~2002 IGU dLOD RMS errors <12 µs in most recent years errors in IGS Final dLOD reference not negligible IGS dLOD errors have high- frequency systematic components 15 improved... 

16. Spectra of (Ultra Observed-Final) dLOD Differences Subdaily tide model alias errors seen at ~7, ~9, & ~14 d bands –long-period errors muted by “calibration” of AC LOD biases via comparison with IERS Bulletin A over sliding window of recent past results (1461 d from 1 Jan 2008 – 31 Dec 2011) 16

17. Ultra-rapid Predicted dLOD Accuracy (Ultra Predicted – Final) dLOD Differences (8 Nov 2006 – 31 Dec 2011: daily noon epochs only) Annual mean & std dev of (IGU-IGS) dPM Length-of-Day Differences (µs) Mean & Std Dev (µas) Final dLODsigma IGU dLOD prediction accuracy slightly improved since ~2006 recent IGU 1-d dLOD prediction error ~50 µs dLOD prediction errors have evident systematic signatures 17

18. Spectra of (Ultra Predicted-Final) dLOD Differences Subdaily tide model alias errors seen at ~9 & ~14 d bands –plus strong 8 th GPS draconitic & semi-annual peaks (1880 d from 8 Nov 2006 – 31 Dec 2011) 18

19. IGS ERP Predictions Compared to Other Services IGS Ultra ERP predictions for 1 d after last observations compared to operational EOP services –IGU ERPs issued 9 hr before prediction epoch –predictions benefit from access to latest high-accuracy observations Compare to IERS (USNO & Paris Obs) & JPL EOP services –results from IERS EOP Combination of Predictions Pilot Project (18.03.2012) –IGU PM predictions better than any others –IGU comparable to UT1/dLOD services due to their use of AAM predictions EOP prediction services should consider assimilating IGU predictions, as well as most recent IGU observations Prediction Service RMS(PM-x) (μas) RMS(PM-y) (μas) RMS(dLOD) (μs) Ultra (Pred) 27021148 (dLOD) USNO/Bull A 44229055 (UT1) Paris Obs 522 - 609337 - 438334 – 414 (UT1) JPL 56242355 (UT1) 19

20. Recent Ultra-Rapid ERP Accuracy IGA observed EOPs updated every 6 hr –latency is 15 hr for each update –each EOP value is integrated over 24 hr –recent polar motion accuracy: <50 µas (1.5 mm) –recent dLOD accuracy: <12 µs (5.6 mm/day) –reported formal errors are generally reliable IGU predicted EOPs updated every 6 hr –for real-time applications –issued 9 hr before EOP epoch –recent polar motion prediction accuracy: ~250 µas (7.7 mm) –recent dLOD prediction accuracy: ~50 µs (23 mm/day) –reported formal errors are too optimistic by a factor of 3 to 4 IGU PM predictions better than use IERS service –IGU dLOD predictions similar to operational services –IGU ERP observations & predictions should be assimilated by operational EOP prediction services 20

21. Rapid Products 21

22. Rapid AC Orbit Comparisons Orbit performance dispersion among ACs is reasonable –but ESA clearly dominates combination 22

23. IGS (Rapid – Final) Polar Motion Differences >98 RF sites  <55 RF sites Clear improvement in PM accuracy when IGb00 reference frame adopted in 2004 –but systematic differences remain & dominate –probably mostly due to Analysis Center rotational deficiencies 23

24. Spectra of (Rapid-Final) PM Differences High-frequency noise consistent with ~30 µas accuracy recently –but longer period errors are most significant –fortnightly feature near 14.2 d signifies subdaily tide model errors (1024 d from Sep. 2006 – Jul. 2009) PM-x PM-y 24

25. Rapid AC LOD Comparisons with Final LOD EMR, JPL, & SIO show strong annual LOD variations –most other ACs show long-period variations –similar features in Final LODs 25

26. Final Products 26

27. Final AC Orbit Comparisons Final AC orbit performance similar to Rapids –Rapid orbits are consistently & significantly better than any single AC Final 27

28. Jumps computed from Berne-model fit to adjacent orbit days –stacked over all SVs & lightly smoothed –“calibrated” for errors due to (fit + extrapolation) method Background errors follow ~flicker noise on seasonal time scales –transition to whiter noise for <14 d A,C,R Spectra of IGS Orbit Day-Jumps odd GPS draconitic harmonics likely fortnightly signals (1024 d from Mar. 2005 – Dec. 2007) 28

29. AC along-track spectra show mostly flicker + white noise Some AC peaks but good agreement only for fortnightly Along-track Spectra of AC Orbit Day-Jumps smoothing effect of CODE 3-d arcs (1024 d from Mar. 2005 – Dec. 2007) 29

30. AC cross-track spectra show 3 rd draconitic & fortnightly bands Some spurious AC peaks & lower white noise floor Cross-track Spectra of AC Orbit Day-Jumps fortnightly band (1024 d from Mar. 2005 – Dec. 2007) 3 rd draconitic harmonic for most ACs 30

31. AC orbit & PM rotational offsets should be self-consistent –but orbit rotations show larger dispersion for all ACs –most ACs show internal rotational inconsistencies –part of problem was caused by IGS combination bug (fixed wk 1702) IGS orbit accuracy probably limited by such rotational effects Orbit/PM Rotational Inconsistencies 31

32. Compute Polar Motion Discontinuities midnight PM discontinuities daily noon PM offset & rate estimates Examine PM day-boundary discontinuities for IGS time series –should be non-zero due to PM excitation & measurement errors 32

33. Power Spectra of IGS PM Discontinuities Common peaks seen in most AC spectra are: –annual + 5 th & 7 th harmonics of GPS year (351 d or 1.040 cpy) –probably aliased errors of subdaily EOP tide model (IERS2003) IGS Repro1 Combination (10 Mar 2005 – 29 Dec 2007) PM-x PM-y 33

34. Spectra of Subdaily EOP Tide Model Differences Compare TPXO7.1 & IERS2003 (used by IGS) EOP models –TPXO7.1 & GOT4.7 test models kindly provided by Richard Ray –assume subdaily EOP model differences expressed fully in IGS PM results PM-x PM-y 34

35. Spectra of PM Discontinuities & Subdaily EOPs Aliasing of subdaily EOP tide model errors probably explains: –annual (K1, P1, T2), 14.2 d (O1), 9.4 d (Q1, N2), & 7.2 d (σ1, 2Q1, 2N2, µ2) Orbit errors presumably responsible for odd 1.04 cpy harmonics effects of orbit model coupling HFEOP (J. Gipson) - IERS2003 35

36. 3 Cornered Hat Decomposition of ERP Errors 3 cornered hat method is sensitive to uncorrelated, random errors –for time series {i, j, k} form time series of differences (i-j), (j-k), (i-k) –then Var(i-j) = Var (i) + Var(j)(assuming R ij = 0 for i ≠ j) –and Var(i) = [Var(i-j) + Var(i-k) – Var(j-k)] / 2 –but true errors also include common-mode effects removed in differencing Apply to IGS Ultra (observed), Rapid, & Final PM & dLOD –consider recent 1461 d from 1 Jan 2008 to 31 Dec 2011 Surprising results: –apparently, Rapids give best polar motion & Ultras give best dLOD –Ultras give similar quality polar motion as Finals –perhaps Finals affected by simultaneously solving for weekly TRFs IGS Product Series σ(PM-x) (μas) σ(PM-y) (μas) σ(dLOD) (μs) Ultra (Obs) 25.827.64.99 Rapid 16.015.45.69 Final 25.331.39.19 36

37. 3 Cornered Hat PM Results with High-Pass Filtering Apply Vondrak high-pass filter before 3 cornered hat for PM –test 4 cutoff frequencies: pass all, >0.5 cpy, >1 cpy, >2 cpy –results below from Paul Rebischung (IGN) IGU & IGR PM errors nearly insensitive to frequency filtering IGS Final PM appears to improve when high-pass filtered –implies low-frequency errors are in IGS Finals or common to IGU & IGR –source of low-frequency error (orbits?, frame?) not yet identified –but internal Analysis Center inconsistencies strongly suspected Freq Cutoff:none0.5 cpy1 cpy2 cpy (μas) σxσx σyσy σxσx σyσy σxσx σyσy σxσx σyσy Ultra (Obs) 25.827.624.225.524.123.7 22.5 Rapid 16.015.416.214.615.616.115.216.8 Final 25.331.320.223.119.419.718.517.3 (filtered results from Paul Rebischung, IGN) 37

38. Conclusions Since 2004.0 IGS Final polar motion accuracy <~30 µas –robust global network is prime factor –Rapid PM is only slightly poorer, <~40 µas GPS PM nearing asymptotic limit for random errors (~20 µas) –smaller systematic errors possible with new GNSSs, better orbit modeling, & better handling of solution constraints –new subdaily EOP tide model required – prospects currently unclear IGS Ultra-rapid observed PM accuracy currently <50 µas –updated 4 times daily with 15 hr latency –could be used to provide some subdaily EOP resolution –should be more heavily used by EOP prediction services ! Leading error sources are systematic –internal rotational inconsistencies by Analysis Centers –errors in IERS subdaily EOP tide model alias into all IGS products 38