Technical description of solution gsf2019d 2019.12.22 1. Purpose of solution: TRF/CRF and EOP series. 2. Analysis center: GSF (NASA Goddard Space Flight Center). 3. Short narrative description of solution: Solution gsf2019d estimates station position and velocity parameters in order to obtain a terrestrial reference frame (TRF) for computing an EOP time series. Source positions are also estimated. The TRF is defined in such a manner that the positions and velocities of a subset of 41 stable stations have no net translation or rotation with respect to their positions and velocities reported in the ITRF2014 [1] catalog and the resulting series of Earth orientation parameters has only shift and drift with respect to the USNO Finals series over the range [2000.01.01 - 2019.12.05]. The CRF is defined in such a way that the positions of the 303 ICRF3 [2] defining sources do not have any net rotation with respect to their coordinates reported in the ICRF3 catalog. All available dual-band X/S Mark-3/Mark-4/Mark-5/K3/K4/VLBA VLBI sessions from 1979.08.03 through 2019.12.05 with durations of 18 hours and longer (6459 sessions, 15,023,652 group delays) were used in a single solution. The WRMS postfit residual was 24.937 psec and Chi/ndg was 0.967. Parameters are split into three groups: 1) Global parameters estimated over all sessions. 2) Local parameters estimated for each 24-hour session individually. 3) Segmented parameters estimated every 30-60 minutes, or 6 hr time spans. Positions of all stations and velocities of most were estimated as global parameters. The estimation of source positions was done in a manner similar to the generation of the ICRF3. Four gravitational lensed sources (0218+357/0218+35A/0218+35B, 1830-21A/1830-21B/1830-211, 1422+231/1422+23C and 0132-097), several radio stars, supernovas and pulsars were excluded from the dataset. A few sources that fit poorly in global solutions (3C48, 0350+177, 1043-290, 1320-446, 1328+254, 1352-632, 1507-246, 1713+218, 1755+626 and CTA21) were solved for as arc parameters. The positions of the remaining sources were estimated as global parameters. Source positions are in the ICRF3 frame. Two source catalogs are provided: gsf2019d_glo.src - catalog of sources estimated as global parameters. gsf2019d_arc.src - catalog of sources estimated in individual sessions. Mean site gradients were applied. These were computed from the GSFC Data Assimilation Office (DAO) model from met data from 1990-95. 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 references [3] and [4] for more details. 3a. Differences with respect to previous (gsf2016a) solution: 77 additional sessions 458,367 additional observations 3b. Handling of earthquakes: The earthquakes in Chile (Feb. 27, 2010) and of the coast of Japan (March 11, 2011) have complicated the VLBI TRF. Non-linear motions have occurred at nearby stations since these earthquakes. To deal with these, we have used the post-seismic deformation models from ITRF2014 [1]. Two types of functions are used in these models: exponential transient functions of the form A(1 - exp((t-t0)/Tau) and logarithmic functions of the form A log(1 + (t-t0)/Tau), where t0 is the time of the earthquake. The amplitudes A and relaxation times Tau were determined by fitting GPS data for each earthquake. Co-seismic offsets are also provided in the ITRF2014 model. There are models for the following VLBI stations: AIRA, TIGOCONC, GILCREEK, DSS15, KOGENEI, KASHIM34,KASHIM11, VERAMZSW, MISNAO10, SESHAN25, SINTOTU3, TSUKUB32, and USUDA64. In the Solve solution, we estimated episodic breaks at most of these sites even though offsets were specified in ITRF2014. The episodic breaks that were estimated are listed in section 6h. 4. Estimated parameters: a. Celestial Frame: Right Ascension, Declination (global and local). b. Terrestrial Frame: X, Y, Z, Xdot, Ydot, Zdot (global). c. Earth Orientation: X-pole, Y-pole, UT1-TAI, Xdot, Ydot, UT1dot, dX-nutation, dY-nutation (local parameters). d. Zenith Troposphere: Linear spline 30-min interval; rate constraint with reciprocal weights generally 50 ps/hr; VMF1/VMF3 wet partial derivative (segmented). e. Troposphere Gradient: 6-hour East and North linear splines at all stations using offset and rate constraints with reciprocal weights of 0.5 mm and 2.0 mm/day (segmented). f. Station Clocks: Quadratic (local) + linear spline with 1-hr interval (segmented); rate constraint with reciprocal weights, generally 5.0E-14. g. Baseline Clocks: As set in initial analysis usually used (local). h. Global antenna axis offsets for 94 stations: AIRA ALGOPARK BR-VLBA CHICHI10 DSS15 DSS45 DSS65 FD-VLBA FORTLEZA GBT-VLBA GGAO7108 GIFU11 GILCREEK GOLDVENU HARTRAO HATCREEK HAYSTACK HN-VLBA HRAS_085 KASHIM11 KASHIM34 KASHIMA KAUAI KOGANEI KOKEE KP-VLBA LA-VLBA MARPOINT MATERA MIAMI20 MIURA MIZNAO10 MK-VLBA MOJAVE12 NL-VLBA NOTO NRAO_140 NRAO20 NRAO85_1 NRAO85_3 OHIGGINS OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 SINTOTU3 SVETLOE TATEYAMA TIGOCONC TIGOWTZL TOMAKO11 TSUKUB32 URUMQI VNDNBERG WESTFORD YEBES YLOW7296 ZELENCHK BADARY CRIMEA DSS65A EFLSBERG HOBART26 MEDICINA NYALES20 ONSALA60 PARKES YEBES40M WETTZELL KWAJAL26 METSAHOV SEST SYOWA TIDBIN64 DSS13 MARCUS TSUKUBA VERAISGK VERAMZSW HOBART12 WARK12M YARRA12M KATH12M KUNMING UCHINOUR HART15M ISHIOKA SEJONG TIANMA65 WETTZ13N RAEGYEB 5. Celestial Reference Frame: a. A priori source positions: /500/oper/solve_save_files/ICRF3.src. Source positions from the ICRF3-SX catalog [2]. b. Source positions adjusted in solution: Yes. Orientation defined by a no-net-rotation tie to the ICRF3 using the 303 ICRF3 defining sources. A galactic aberration model was applied, as in ICRF3, using a galactic aberration constant of 5.8 micro-arc-sec/year in the direction of the galactic center. 6. Terrestrial Reference Frame: a. A priori station positions: /500/oper/solve_save_files/2019d_mod.sit, which is based on ITRF2014. b. A priori station velocities: /500/oper/solve_save_files/2019d_mod.vel, which is based on ITRF2014. c. Reference epoch for site positions: 2014.01.01. d. Station positions/velocities adjusted in solution: Yes. e. Definition of origin, orientation, and their time evolution: No-net-translation and no-net-rotation of positions and velocities with respect to 2019d_apriori.sit and 2019d_apriori.vel for 41 stations: ALGOPARK BR-VLBA DSS45 FD-VLBA FORTLEZA HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART12 HOBART26 ISHIOKA KASHIMA KAUAI KOKEE KATH12M KP-VLBA LA-VLBA MATERA NL-VLBA NOTO NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SEJONG SESHAN25 SVETLOE VNDNBERG WARK12M WESTFORD WETTZ13N WETTZELL YARRA12M YEBES40M Values of right-hand side of no-net-rotation/no-net-translation constraints: RIGHT_PART 0.05477685 0.00225424 0.00538031 * nnt_pos RIGHT_PART 0.03904029 0.16661139 -0.10831820 * nnr_pos RIGHT_PART 0.00308636 0.00267151 0.00198180 * nnt_vel RIGHT_PART -0.00094257 0.01261780 -0.01268406 * nnr_vel Units: meters for nnt_pos, meters/Earth_radius for nnr_pos, mm/yr for nnt_vel, mm/(yr*Earth_radius) for nnr_vel f. Station parameter estimation: X, Y, Z, Xdot, Ydot, Zdot - globally for all stations, some with constraints. g. Stations with constraints: A priori velocities for U, E, and N components of 38 stations were constrained to their apriori velocities with reciprocal weights 0.1, 3.0, and 3.0 mm/yr respectively, because these stations have very short histories of observations. Many are mobile sites occupied only once. AUSTINTX AZORES BERMUDA BLOOMIND BREST CARNUSTY CARROLGA CHLBOLTN CTVASBAY CTVASTJ DAITO GRASSE HOFN HOHENFRG HOHNBERG KAINAN KANOZAN KARLBURG KIRSBERG LEONRDOK MCD_7850 METSHOVI MILESMON NOBEY_6M OCOTILLO SAGARA SEST SUWON TIDBIN64 TITIJIMA TOMAKO11 TOULOUSE USSURISK VERAIRIK VERAOGSW USUDA64 VICTORIA UCHINOUR The velocities of 25 groups of stations were constrained to be the same. DSS15 DSS13 GOLDVENU GOLDMARS DSS45 TIDBIN64 DSS36 DSS34 DSS65 DSS65A ROBLED32 MADRID64 FORTORDS FORT_ORD GIFU11 GIFU3 GGAO7108 GORF7102 HARTRAO HART15M HRAS_085 FTD_7900 MCD_7850 HOBART26 HOBART12 KASHIM34 KASHIM11 KASHIMA KAUAI HALEAKAL KOGANEI KOGANEI3 METSAHOV METSHOVI MIZNAO10 MIZUSGSI VERAMZSW MIZNAO10 MIZUSGSI MOJAVE12 MOJ_7288 NRAO20 GBT-VLBA NRAO_140 NRAO85_1 NRAO85_3 ONSALA60 MV2ONSLA ONSALA85 OVRO_130 OVR_7853 RICHMOND MIAMI20 SINTOTU SINTOTU3 TSUKUB32 TSUKU3 TSUKUBA WETTZELL WETTZ13N TIGOWTZL YEBES40M YEBES RAEGYEB YLOW7296 YELLOWKN h. Stations with discontinuous positions and date of discontinuity: YAKATAGA 871201 * Earthquake SOURDOGH 871201 * Earthquake WHTHORSE 871201 * Earthquake FORTORDS 891001 * Seismic event PRESIDIO 891001 * Seismic event MOJAVE12 920627 * Earthquake DSS15 920627 * Earthquake MEDICINA 960601 * Rail reparing EFLSBERG 961001 * Rail reparing DSS65 970415 * Rail reparing MIURA 000901 * Dike intrusion, June-Aug. 2000 TATEYAMA 000901 * Dike intrusion, June-Aug. 2000 GGAO7108 030101 * Station relocation SINTOTU3 030915 * h/z MK-VLBA 061015 * Earthquake ZELENCHK 070701 * Rail repair ?????? AIRA 080614 * M7.2 Iwate Miyagi Nairiku earthquake CHICHI10 080614 * M7.2 Iwate Miyagi Nairiku earthquake KASHIM34 080614 * M7.2 Iwate Miyagi Nairiku earthquake TSUKUB32 080614 * M7.2 Iwate Miyagi Nairiku earthquake VERAMZSW 080614 * M7.2 Iwate Miyagi Nairiku earthquake TIGOCONC 100227 * Big Earthquake TSUKUB32 110311 * Big Earthquake in Japan KASHIM11 110311 * Big Earthquake in Japan KASHIM34 110311 * Big Earthquake in Japan VERAMZSW 110311 * Big Earthquake in Japan VERAISGK 110311 * Big Earthquake in Japan SINTOTU3 110311 * Big Earthquake in Japan KOGANEI 110311 * Big Earthquake in Japan USUDA64 110311 * Big Earthquake in Japan URUMQI 140601 * Repairs MK-VLBA 180503 * Kilauea eruption Also, the eccentricity vector for station TSUKUB32 was assigned as (0.0, 0.0, -0.0437) meters in North, East, Up in local topocentric reference frame before 1999.05.01 and (0.0, 0.0, 0.0) after 1999.05.01, according to the results of geodetic surveys [5]. Changes in the eccentricity vector were caused by repairs to the concrete foundation slab. i. Stations with nonlinear velocities: Spline functions were used to model the motion at the following stations, due to non-linear behavior for all or part of their observing histories. HRAS_085, GILCREEK, PIETOWN Gilcreek experienced non-linear behavior after a nearby earthquake. Pietown's non-linear motion is believed to be due to the effects of a varying tilt of its azimuth axis and perhaps local deformation. HRAS_085's non-linear motion was also believed to be due to some unexplained local deformation. j. Permanent tide contribution: Yes. "Yes" means that both the permanent and the periodic tides have been modeled. The model used includes tide displacements for zero frequency with Love numbers h2(freq=0) = 0.6078, l2(freq=0) = 0.0847. The Earth tide computation complies with the IERS 2010 Conventions. 7. Earth orientation: a. A priori precession/nutation model: IAU2006/2000A Precession/Nutation, IERS Conventions 2010 [6] as implementation in Calc 11. b. A priori short-period tidal variations in X, Y, UT1 due to short period tidal and nutation effects were applied. These were computed by Calc 11, as recommended in the IERS 2010 Conventions [6], chapter 5, p. 50-51. d. EOP estimation: Two tables are given: gsf2019d.eoxy: X, Y, UT1, Xdot, Ydot, UT1dot, dX-nutation, dY-nutation, each session. Using a priori error of 45 mas for pole and 3 ms for UT1, 45 mas/day and 3 ms/day for pole rate and UT1 rate to allow estimation for one-baseline sessions; dX-nutation and dY-nutation are relative to the IAU2000A/2006 Nutation/Precession models. The time tags of the EOP series are the middle epochs of the observing sessions. gsf2019d.eops: X, Y, UT1, Xdot, Ydot, UT1dot, Deps, Dpsi, for each session. Deps and Dpsi are relative to the IAU 1976 precession and IAU 1980 nutation models. {Internally, Calc/Solve estimates offsets to the X and Y precession/nutation quantities, relative to the IAU2000A/2006 nutation/precession models, using the IERS 2010 Conventions [6] implementation. These were converted to classical Dpsi and Deps nutation offsets relative to the IAU 2000A nutation model. These were then converted to the IAU 1976/1980 precession/nutation (Wahr) model by adding the following terms: Deps: -25.24*Cent - 6.8192 (m-arc-sec), and Dpsi: -299.65*Cent - 41.775 (m-arc-sec), where Cent is the epoch in fractional centuries since 2000.0 (Julian date 2451545.0). This conversion is not quite correct though. There are some long term drifts that are not accounted for.} High frequency variations in polar motion and UT1, as computed by Calc 11, were added to the a priori EOP during the Solve/Globl solution. The reported values of polar motion and UT1 are the sum of the adjustments and the apriori EOP without the contribution due to high frequency variations. Thus, the final series of polar motion and UT1 do not contain contributions due to high frequency variations. The networks of each individual session fall into 4 categories: 1) Very small network: baselines shorter than 150 km; 2) Small network: baselines in the range 150-1500 km; 3) Singular network: single baseline network with baseline length longer than 1500 km; 4) Global network: three or more stations with baselines longer than 1500 km. The EOPs were not estimated for very small networks. The EOPs were estimated for small networks but with strong constraints applied. The records related to these experiments were eliminated from the output EOP file. The EOP's from the remaining sessions were put into files gsf2019d.eoxy and gsf2019d.eops. The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output files and their values and formal uncertainties were replaced with "-0 ". The singular networks provided reasonable estimates of nutation angles. 8. A priori geophysical models: a. Troposphere: VMF1 or VMF3 total (dry+wet) mapping function; Saastamoinen zenith delay calculated using logged pressure and temperature; a priori mean gradients from DAO weather model. b. Solid Earth tide: IERS Conventions 2010 [6], chapter 7, steps 1 and 2, including tides of the 2-nd and 3-rd order. c. Ocean loading: 3D ocean loading displacements computed using the Hardisp model. Ocean loading coefficients computed using the TPXO7.2 model. These were obtained from the ocean loading web site at http://holt.oso.chalmers.se/loading/, which is provided by H.-G. Scherneck, Onsala Space Observatory. d. Pole tide: Secular pole coordinates were used for computation of the pole tide deformation as given in the 2018/02/01 update of the IERS Conventions (2010) [6], chapter 7, pages 15-17. [9] (http://iers-conventions.obspm.fr/content/chapter7/icc7.pdf), This is expected to be the recommended procedure in the next IERS Conventions (expected in 2022). (This is also the procedure required for VLBI contributions for ITRF2020.) Coordinate of the secular pole were computed as: x = 55.0 + 1.677 * (t - 2000.0) mas; (where t = the date in years) y = 320.5 + 3.460 * (t - 2000.0) mas e. Ocean pole tide loading: An ocean pole tide loading correction was applied, using the model of Desai 2002 [7]. These were computed by Calc 11, and are described in the IERS Conventions (2010), chapter 7, pages 116-118. This small correction should have an ~14 month period. f. Antenna thermal deformation: Antenna heights were adjusted, based on the average daily temperatures, using the IVS antenna thermal deformation model of Nothnagel 2008 [8]. 9. Data type: Group delays only. 10. Data editing: 5 deg elevation cutoff. 11. Data weighting: Weights are defined as follows: 1/sqrt ( f**2 + a**2 ). Quantity "f" is the formal uncertainty of the ionosphere free linear combination of group delays at X- and S-band obtained by fringe fitting. The station-dependent parameter "a" was computed for each session by an iterative procedure such that the ratio of the sum of the squares of the weighted residuals to the estimate of their mathematical expectation is about 1.0. 12. Standard errors reported: All errors derived from least-squares estimation propagated from the data weights and the constraints applied to the estimated parameters. 13. Software: Calc 11, SOLVE revision date 2019.04.19. References: 1. Altamimi, Z., P. Rebischung, L. Métivier, and X. Collilieux, "ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions, J. Geophys. Res. Solid Earth, vol. 121, Issue #8, pp. 6109-6131, 2016. doi:10.1002/2016JB013098. 2. Charlot, P., et al, 'The Third Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry'; Astronomy and Astrophysics, 2019, in preparation. Also see: https://iers.obspm.fr/icrs-pc/newwww/icrf/ 3. MacMillan, D.S. and C. Ma, "Atmospheric gradients from very long baseline interferometry observations", Geophys. Res. Lett., 22, 1041-1044, 1995. 4. MacMillan, D.S. and C. Ma, "Atmospheric gradients and the VLBI terrestrial and celestial reference frames", Geophys. Res. Lett., 24, 453-456, 1997. 5. Takashima, K., et al., "Status and Results of GSI Domestic VLBI Network", Bulletin of the Geographical Survey Institute, Vol. 46, March 2000, p. 1-9. 6. Petit, Gerard and Luzum, Brian, 'IERS Conventions (2010), IERS Technical Note 36, 2010. 7. Desai, S.D., "Observing the pole tide with satellite altimetry," J. Geophysical Research, vol. 107 (C11), p.3186. doi:10.1029/2002JC001224. 8. 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. 9. http://iers-conventions.obspm.fr/conventions_material.php - Update to the IERS Conventions (2010).