Geodesy  
VLBI geodetic precision with different models
Erhu WEI, Jingnan LIU, Peijing PAN


Very Long Baseline Interferometry (VLBI) is the unique space geodetic technique which can provide the Celestial Reference Frame (CRF), the Terrestrial Reference Frame (TRF) and the relationship between the two frames — Earth Orientation Parameters (EOP) at the same time. VLBI has a widely usage in space geodetic, ground geodetic, geophysical fields and so on. Presently, it can determine the position of the radio source outside the galaxy with 1mas precision, and determine several kilometers length of baseline on the earth’s surface with 1cm precision. Due to its high stability and high precision character, the Celestial Reference Frame outside the galaxy based on VLBI has been the best realization of the quasiinertial referenceframe since 1980s. VLBI stations are the most important benchmarks in the International Terrestrial Reference Frame (ITRF), and VLBI is one main supporting technique which determines EOP. Till now, space and ground VLBI have accumulated more than 20 years’ data. They provide continuous and longterm data guarantee for space geodetic, ground geodetic and geographical research. Though there are several kinds of common ocean tide and nutation models, there have no article giving us the best model combination through special comparison and analysis. This paper firstly introduces several common ocean tide models and nutation models, and then computes the global VLBI data during 20012007 using the OCCAM 5.0 software platform. It compares and analyzes the precision of geodetic parameter’s result using these models, and gives us the best ocean tide and nutation model combination. Model introductionOCCAM is a common software in processing space VLBI and ground VLBI data. It is used in describing the physical model of time delay and time delay rate, computing and adjusting all parameters’ partial derivative. Generally speaking, there are three physical models in this software[1]: 1) Computing model and setting up Standard Data File (SDF) model: the preparation of the data (DTAU0), precession and nutation and (PN), the correction of station’s displacement and partial derivative (STATION), geometry model (GEOMET), all five parts. OCCAM 5.0 software is made up of several executing programs. Only operating in definite sequence, we can get the accurate VLBI computing results. In this paper, we will compute with multibaseline Kalman filter method, the detailed processing please refers to [2]. EANES model (CSR4.0 ocean loading model)The EANES model[3] used in this paper is the CSR 4.0 ocean tide model, which is computed on the basis of the Orthotide model of Eanes et al., Center of Space Research, University of Austin, Texas, kindly made available to the world in April 1999. It is a further development of CSR 3.0 and contains 239 circles (about 6.4 years) of TOPEX/POSEIDON altimetry. Like the CSR3.0 ocean tide model, CSR4.0’s grid resolution is 0.5º×0.5º. It has the same orthotide frequency model; and it comprises the diurnal and semidiurnal bands. For the computation of the loading effects, a landocean mask was constructed from ETOPO5. The same mask was used in CSR3.0. The reason for this is that many coastal model nodes of CSR3.0 inundate ETOPO5 land. Since the altimetry solution does not impose local water mass continuity conditions, the masking does not degrade global mass conservation (which is a more important error source in loading effects than in the tide elevation itself), but improves the realism of the load distribution. This model still uses concentrated load circling method and computes the close load through gradual reduction discrete points in the integral. RAY model (GOT99.2b ocean loading model)RAY Ocean tide model[4] is a long wavelength adjustment of FES94.1 using TOPEX/POSEIDON data and is given on a 0.5 by 0.5 degree grid. 

Erhu WEI, Jingnan LIU, Peijing PAN


IAU 1980 nutation modelIn 1979, J.Wahr and H.Kinoshita introduced recomprehensive calculation for a practical nutation of the earth, they considered the force generated from earth’s solid tide to earth itself — deformation, nutation and rotation rate changes, and at the same time, they HERING nutation modelThe HERRING nutation model[1] in this software will compute the complete KSV_1996_3 nutation series with the associated corrections for planetary nutation, the freely excited Free CoreNutation (FCN), the precession constant change and a rate of change of obliquity. This model is designed from several aspects as following: 1) The Souchay and Kinoshita Rigid Earth KSRE95 nutation series; MHB_2000 nutation modelVLBI and LLR observations[6] showed that there are obvious defect existing in the IAU 1976 precession model and IAU 1980 nutation theory which have been the criterion for a long time. For example, these theoretical model doesn’t include the changing rate of obliquity in nutation that can’t be observed; the precession rate exists the difference about 3.0mas/yr between observation value and adoption value (the adoption value is too high); for nutation, the difference between observation model and adoption model exists about 20mas between each top. In short, the difference between the observations and models used in the past has exceeded the achieved observation precision far more. We need to get the nutation theory with including ocean tide’s and atmosphere’s nonrigid body and all in the order of magnitude of 0.1mas level known effect, and get the nutation series reaching the level of 5mas new rigid body earth. Based on many years of research, IAU 2000 convention[7] decided that the newly IAU 2000A precessionnutation model, that is MHB_2000 model (up to the level of the accuracy of 0.2mas) and IAU 2000B precessionnutation model (up to the level of the accuracy of 1mas) will replace the IAU 1976 precession model and IAU 1980 nutation theory. Improved precession rate, obliquity nutation changing rate, as well as the Celestial pole offsets consistent with newly precessionnutation model on J2000.0 epoch will be given in IERS 2003 convention. MHB_2000 model[8] was proposed by Mathews, and it was developedon the basis of setting the problem of linear dynamic equation for wobbly nutation. It uses the estimated value of 7 parameters in the theory, obtains one newly precessionnutation VLBI data sequence in the theory of least squares. This nutation sequence depends on rigid earth nutation sequence found by Souchay (1999). It explains the change of geodynamical ellipticity implied by the observing correction of equator lunarsolar precession by the multiplier of 1.000012249. The new model contains the deviation between reference frames, geodetic precession and geodetic nutation. The Free Core Nutation (FCN) can’t be strictly forecast, so this model doesn’t include it. New precessionnutation model avoids the artificial separation in precession and nutation, but the precession model and nutation model is used separately in the system based on the spring equinox. Tidal fluctuations in water height and currents will induce retrograde diurnal variation of equatorial oceanic angular momentum (OAM), hence small perturbation on nutation at the level of 1mas and most important contributions come from water height variations[9]. Considering the influence of anelasticity covering effect, the ocean tidal effect, electromagnetism coupling effect, which produced from the liquid outer core and solid core and the nonlinearity item. The MHB_2000 nutation model improves the accuracy of IAU 1980 nutation theory. 

Erhu WEI, Jingnan LIU, Peijing PAN


The method of experimentThe data resource The method of model combination The analyze of the experiment resultBased on the combination of the above models, we compute the data following the chronological order: In the data processing on April 24 2001, we can see that if we choose ALGOPARK and FORTLEZA as the reference station for adjustment, in addition to the fourth group, the effects of the others are not ideal. After removing the results of these two stations, we average the other four stations, and then we get the first group of average. 

Erhu WEI, Jingnan LIU, Peijing PAN


Tidal fluctuations in water height and currents will induce retrograde diurnal variation of equatorial oceanic angular momentum (OAM), hence small perturbation on nutation at the level of 1mas and most important contributions come from water height variations[9]. Considering the influence of anelasticity covering effect, the ocean tidal effect, electromagnetism coupling effect, which produced from the liquid outer core and solid core and the nonlinearity item. The MHB_2000 nutation model improves the accuracy of IAU 1980 nutation theory. The method of experimentThe data resource The analyze of the experiment resultBased on the combination of the above models, we compute the data following the chronological order: The compare result by adopting the data of 2001 In the data processing on April 24 2001, we can see that if we choose ALGOPARK and FORTLEZA as the reference station for adjustment, in addition to the fourth group, the effects of the others are not ideal. After removing the results of these two stations, we average the other four stations, and then we get the first group of average. Table 1 the processing result of 010424XE.NGS Table 2 the processing result of 020711XE.NGS Table 3 the processing result of 031021XE.NGS Table 4 the processing result of 040601XA.NGS 

Erhu WEI, Jingnan LIU, Peijing PAN


Table 5 the processing result of 2005.08.25, 2006.09.21 and 2007.10.21 Table 6 the general result of all kinds of combination The compare result by adopting the data of 2002 In the data processing on July 11 2002, we can see that if we choose FORTLEZA and ALGOPARK as the reference station for adjustment, in addition to the first group, the effects of the others are not ideal. When choosing MATERA as the reference station to calculate, all six groups’ precision are not ideal. After removing the results of these three stations, we average the other three stations, and then we get the second group of average. The compare result by adopting the data of 2003 In the data processing on June 1 2004, we can see that if we choose TIGOCONC and WESTFORD as the reference station for adjustment, in addition to the Figure 1 the general result of all kinds of combination second and sixth group, the effects of the others are not ideal. After removing the results of these two stations, we average the other three stations, and then we get the third group of average. The result by adopting the data of 20052007 Compared results From figure 1 and table 6, we can see that in these six kinds of categories, the fourth model of the results of the final classification sought by the CHISQ value is 0.9728, the closest to 1.00. Though the precision of the other combinations is near 1.00 too, their gap is very small. We believe that in the same circumstance, choosing the combination of RAY ocean tide model and IAU_1980 nutation model is the best choice. Conclusion AcknowledgementThis research is funded by the national ‘973 Project’ of China (No 2006CB701301), the national ‘863 Project’ of China (No. 2008AA12Z308) the National Natural Science Foundation of China(No. 40774007), and the project of university education and research of Hubei province (No. 20053039). Reference1] O.Titov, V.Tesmer, J.Bohem. OCCAM 5.0 USER’S GUIDE 



