Technical description of session EOP solution usn2011a.eopi 2011.04.19 1. Purpose of solution: Determination of UT1 from short, ~1.0 hour, IVS Intensive VLBI sessions. 2. Analysis center: USN (U.S. Naval Observatory). 3. Short narrative description of solution: Solution usn2011a is for the estimation of UT1 from the 1-hour IVS Intensive sessions. Most sessions consist of ~12-30 observations on one baseline. The solution includes most usable Intensive sessions from 2000 July 06. 4. Differences with respect to previous (usn2010a) solution: a. The site and velocity mod files are from the usn2011a solution and are based on VTRF2008 [1]. b. The source position mod file is also from the usn2011a solution and is based on ICRF2 [2]. 5. Estimated parameters: a. UT1 angle. b. Atmosphere path delay offset at each station. c. Coefficients of the second order polynomial of clock functions. 6. Celestial reference frame: a. A priori source positions: usno_2011a_for_int.src. This catalog was created in the usn2011a solution and is based on ICRF2 [2]. b. Source positions adjusted in solution: No 7 - Terrestrial reference frame: a. A priori station positions: usno_2011a_for_int.sit. This catalog was created in the usn2011a solution and is based on VTRF2008 [1]. b. A priori station velocities: usno_2011a_for_int.vel. This catalog was created in the usn2011a solution. c. Reference epoch: 1997.0. d. Station positions/velocities adjusted in solution: No. j. Relativity scale: The terrestrial reference frame is defined using the following metric tensor: G_oo = -(1 - (2W/c^2 + W^2/c^4) + 2L_g ) G_oa = -4W^a/c^3 G_ab = \delta_ab (1 + 2W/c^2 - 2L_g) ) Specifically the old formula 29 in IERS Conventions 1992, page 127-136 was used, although it is known to have a deficiency. THIS METRIC TENSOR DOES NOT CONFORM TO IAU 2000 RESOLUTIONS! k. Permanent tide correction: Yes. "Yes" means that both the permanent and the periodic tides have been modeled, so that the output station position is for after the removal of both the permanent and the periodic tidal effect. The model used includes tide displacements for zero frequency with Love numbers h2(freq=0) = 0.6078, l2(freq=0) = 0.0847 8. Earth orientation: a. A priori Precession-Nutation: IAU2000A Precession-Nutation, IERS Conventions 2003 [3] implementation, modified to use the IAU2006 Precession model. b. A priori short-period tidal variations in X, Y, UT1 were computed in Calc 10.0, IERS Conventions 2003 [3] implementation. c. EOP estimation: UT1 (without any constraints). d. A priori UT1 and polar motion: last_usno_finals.erp Earth orientation parameters series from finals USNO series. Original data were taken from ftp://maia.usno.navy.mil/ser7/finals.all and replaced with ftp://maia.usno.navy.mil/ser7/finals.daily and then linear regerssion was subtracted from those series in order to eliminate shift and drift with respect to series Linear regression was computed on the interval [2000.01.05 , 2011.04.16]. Weights from these files were used /data1/solve/save_files/last.erp. 9. A priori geophysical models: a. Troposphere: NMF dry mapping function; Saastamoinen zenith delay calculated using logged pressure, temperature; a priori mean gradients from VLBI data or DAO weather model. b. Solid Earth tide: IERS Conventions 2003 [3], chapter 7, p. 9, steps 1 and 2, including tides of the 2-nd and 3-rd order. c. Ocean loading: 3D ocean loading displacements computed by SPOTL software. The model of displacements caused by ocean loading contains 18 constituents. The following ocean tide models were used: Harmonic Frequency rad/sec Model k2-a 1.324501D+00 1.458530140651D-04 GOT00 admittance k2 3.506941D+00 1.458423171028D-04 GOT00 s2 6.283185D+00 1.454441043329D-04 GOT00 s2-a 4.312500D-02 1.452450074576D-04 GOT00 admittance m2 2.169437D+00 1.405189027044D-04 GOT00 m2-a 1.210284D+00 1.405082057420D-04 GOT00 admittance n2 6.097067D+00 1.378796996516D-04 GOT00 k1-a 1.141827D+00 7.293185551375D-05 GOT00 admittance k1 3.324267D+00 7.292115855138D-05 GOT00 k1-b 2.365113D+00 7.291046158901D-05 GOT00 admittance p1 2.958919D+00 7.252294578148D-05 GOT00 p1-a 3.002044D+00 7.232384890619D-05 GOT00 admittance o1 5.128356D+00 6.759774415297D-05 GOT00 o1-a 1.027610D+00 6.758704719061D-05 GOT00 admittance q1 2.772800D+00 6.495854110023D-05 GOT00 q1-a 4.955240D+00 6.494784413786D-05 GOT00 admittance mtm-a 4.652212D+00 7.973314413516D-06 NAO99.l admittance mtm 5.514660D-01 7.962617451151D-06 NAO99.l mf-a 2.296657D+00 5.334111360775D-06 NAO99.l admittance mf 4.479096D+00 5.323414398410D-06 NAO99.l msf 9.721550D-01 4.925201628510D-06 NAO99.l mm 5.497148D+00 2.639203052741D-06 NAO99.l msm 4.899785D+00 2.285998575769D-06 NAO99.l ssa 3.653480D-01 3.982127698995D-07 NAO99.l paw 5.012885D+00 1.991063797295D-07 equilibrium sa 3.098467D+00 1.990968752920D-07 NAO99.l pcw 2.003605D+00 1.671771314171D-07 equilibrium 18.6 4.100746D+00 1.069696236521D-08 equilibrium d. Pole tide: Mean pole coordinates used for computation of pole tide deformation were set to the IERS 2003 Conventions [3] recommended values (Chapter 7, p. 15). e. Mean site gradients were computed from the GSFC Data Assimilation Office (DAO) model for met data for ICRF2 [2] (icrf2-gd2.mgr). The atmospheric gradient delay is modeled as: tau = m_grad(el) * [GN*cos(az)+GE*sin(az)], where el and az are the elevation and azimuth of the observation and the gradient mapping function is m_grad. The gradient vector has East and North components GE and GN. Refer to [4], [5]. f. Antenna thermal deformation: Antenna heights were adjusted, based on the average daily temperatures, using the IVS antenna thermal deformation model of Nothnagel 2008 [6]. 10. Data type: Group delays. 11. Data editing: Manual, elevation cutoff 5 degrees. 12. Data weighting. Weights are defined as follows: 1/sqrt ( f**2 + a**2 ) where "f" is formal uncertainty of the ionosphere free linear combination of group delays at X- and S-band obtained by fringe fitting on the base of achieved signal to noise ratio. Session-dependent parameter "a" was computed for each session by an iterative procedure such that the ratio of the sum of squares of weighted residuals to the estimate of their mathematical expectation is about unity. 13. Standard errors reported: All errors derived from least-squares estimation propagated from the data weights and the constraints applied to the troposphere, clock and EOP parameters. 14. Software: CALC 10.0, SOLVE revision date 2010.05.21. References: 1. VTRF2008a 2. IERS Technical Note 35, 'The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry'; A.L. Fey, D. Gordon, C.S. Jacobs, editors; 2009. http://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn35.html 3. McCarthy, D.D., Petit, G., IERS Technical Note 32, IERS Conventions (2003), 2003. 4. MacMillan, D.S. and C. Ma, "Atmospheric Gradients from Very Long Baseline Interferometry Observations", Geophys. Res. Lett., 22, 1041-1044, 1995. 5. MacMillan, D.S. and C. Ma, "Atmospheric Gradients and the VLBI Terrestrial and Celestial Reference Frames", Geophys. Res. Lett., 24, 453-456, 1997. 6. Nothnagel, A., "Short Note: Conventions on Thermal Expansion Modelling of Radio Telescopes for Geodetic and Astrometric VLBI," Journal of Geodesy, DOI: 10.1007/s00190-008-0284-z, 2008.