1. Diurnal and Semi-Diurnal Earth Rotation from 37 Years of VLBI Data
John Gipson
Linnea Hesslow
NVI,Inc/NASA GSFC
July 10-12
2017 UAW
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2. Brief History of HF-EOP
Year
What
1990
Observation of HF-UT1 variation in VLBI data. Herring & Dong.
1991
Prediction of Libration Effect on EOP. Chao et al.
1993
First models of HF-EOP of larger terms estimated from VLBI data. Includes effect of Libration. Sovers et al; Gipson et al; Herring and Dong
1994
Models derived from SLR. Watkins and Eanes; E. Pavlis
1996
IERS standards include HF-EOP variation (w/o Libration) based on tidal models. R. Eanes ortho_eop.f
Estimation of HF-EOP variation of smaller terms from VLBI. Gipson
2003
IERS standards include Libration for PM.
2006
Estimates of HF-EOP variation from GPS, Steigenberger et al
2009
Estimate of HF-EOP from VLBI. Boehm (nee Englich)
2010
IERS standards include Libration for UT1
2011
HF-EOP Estimated from a combination of VLBI and GPS data. Artz et al
2016
HF-EOP based on Topex. Estimated at tidal lines. Desai & Sibois
John Gipson NVI, Inc./NASA GSFC

3. Semi-Diurnal Tidal Potential
We expect variation at the frequencies of the tidal lines.
There should be no long term coherent variation at other frequencies.
John Gipson NVI, Inc./NASA GSFC

4. Characteristics of Models
Tidal Models
Space Geodesy Models
How Derived
Satellite Altimetry
Estimated from Space Geodesy data
Intermediate Step
Tidal Model
None (Gipson, Artz)
Hourly EOP Estimates (Steigenberger, Boehm (formerly Englich))
Math
Global Integration of ocean heights, currents
Standard Least Squares
Functional Form
Orthotides
Tidal Lines
Number of Parameters
12x3
2x3xNum_Lines
Assumption
HF EOP determined by large tides and implicit admittance function.
Tidal lines (except sidelobes) are independent
John Gipson NVI, Inc./NASA GSFC

5. John Gipson NVI, Inc./NASA GSFC
IERS HF-EOP Model
IERS model doesn’t estimate at tidal lines. It uses Ortotides
Orthotides 12 orthotides
An equivalent formulation is in terms of 71 tidal lines, but these are not independent. They are derived from the orthotides.
PM Libration 10 tidal lines
UT1 Libration 11 tidal lines
Lunar torque on tri-axial Earth.
That’s it.
John Gipson NVI, Inc./NASA GSFC

6. Orthotide primer Functions derived from the tidal potential
Orthogonal over 18.6 years
Automatically take into account sidelobes of tidal potential which differ by 1 cycle in 18.6 years.
Can expand ANY tidally induced physical behavior in terms of orthotides
Supposed to ‘catch’ most of the signal in the first few terms
Lower order orthotides are almost orthogonal over shorter terms (eg, 1yr)

7. Orthotide primer

8. Correlation of Orthotides
Correlation coefficients evaluated over 1 year.
John Gipson NVI, Inc./NASA GSFC
IVS Working Group IV

9. John Gipson NVI, Inc./NASA GSFC
Empirical VLBI Model
John Gipson NVI, Inc./NASA GSFC

10. New Empirical VLBI Model
John Gipson NVI, Inc./NASA GSFC

11. New Empirical VLBI Model
John Gipson NVI, Inc./NASA GSFC

12. How Large are the Errors?
Diurnal tide error bars ~ 0.07 microseconds.
Semidiurnal error bars ~ 0.04 microseconds.
Safe bet to triple these.
John Gipson NVI, Inc./NASA GSFC

13. How Large are the Errors?
Diurnal Tides ~ 1.2 micro-arcseconds
Semi-diurnal Tides ~ 0.8 micro-arcseconds
Realistic errors ~ 3 micro-arcseconds.
John Gipson NVI, Inc./NASA GSFC

14. John Gipson NVI, Inc./NASA GSFC
Effect of Model VLBI
Above zero means empirical model is better.
VLBI derived model has less baseline scatter than IERS model.
John Gipson NVI, Inc./NASA GSFC

15. John Gipson NVI, Inc./NASA GSFC
Still Residual Signal
John Gipson NVI, Inc./NASA GSFC

16. Spectrum Residual Signal
John Gipson NVI, Inc./NASA GSFC

17. Orthotide Coefficients from VLBI
John Gipson NVI, Inc./NASA GSFC

18. More Orthotide Coefficients
John Gipson NVI, Inc./NASA GSFC

19. John Gipson NVI, Inc./NASA GSFC
Effect of # of Terms
John Gipson NVI, Inc./NASA GSFC

20. Agreement of HF-EOP Models
RMS Difference in UT1 time series.
Units are microseconds.
IERS
TPX71
GOT47
GIPSONORTHO
GIPSON LINE
Artz
Steig.
Boehm
1.87
1.73
2.55
2.66
2.52
3.5
1.31
2.79
2.4
2.63
3.39
2.56
2.65
2.62
2.47
3.36
GIP_ORTHO
2.1
2.24
2.31
2.87
GIP_LINE
1.76
2.04
2.67
1.54
2.78
Steig
2.84
Tidal Models are generally consistent with each other.
Space Geodesy Models are generally consistent with each other.
Greater disagreement between families of models than within the families.
John Gipson NVI, Inc./NASA GSFC

21. ≠ The Issue Semi-Empirical Models of HF-EOP derived
from models of the Ocean Tides
from Satellite altimetry data ≠
Empirical Models of HF-EOP
estimated
from Space Geodesy (VLBI, GPS, SLR)
John Gipson NVI, Inc./NASA GSFC

22. John Gipson NVI, Inc./NASA GSFC
Conclusions
IERS HF-EOP model differs from Space Geodesy derived models.
Using different models can have significant impact on estimated quantities—station position, EOP, etc.
Increasing number of terms in orthotide expansion for IERS model will not help (much).
Is it time to change our paradigm?
Data is strong enough to estimate HF-EOP at tidal lines.
John Gipson NVI, Inc./NASA GSFC

23. John Gipson NVI, Inc./NASA GSFC
Questions & Comments ?
John Gipson NVI, Inc./NASA GSFC

24. Comparison of UT1 Predictions
John Gipson NVI, Inc./NASA GSFC

25. John Gipson NVI, Inc./NASA GSFC
Admittance
Red line is IERS admittance
John Gipson NVI, Inc./NASA GSFC