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 Click to add notes

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

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

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

John Gipson NVI, Inc./NASA GSFC IERS HF-EOP Model IERS model doesn’t estimate at tidal lines. It uses Ortotides Orthotides 12 orthotides 1996 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 2003 UT1 Libration 11 tidal lines 2010 Lunar torque on tri-axial Earth. That’s it. John Gipson NVI, Inc./NASA GSFC

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)

Orthotide primer

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

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

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

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

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

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

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

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

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

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

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

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

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

≠ 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

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

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

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

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