Mutual comparison of the combinations of the Earth orientation parameters obtained by different techniques

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1 Mutual comparison of the combinations of the Earth orientation parameters obtained by different techniques C. Ron, J. Vondrák Astronomical Institute, Boční II 141, Praha 4, Czech Republic Abstract. The newly developed combined method of smoothing of observational data of the authors Vondrák and Čepek () is able to combine both the observed time function values and its first derivatives. It was applied on the Earth orientation parameters, especially the universal time and celestial pole offsets measured by VLBI and length-of-day and celestial pole offsets rate measured by GPS. The method and the results are presented in another place of this volume, see Vondrák et al. (1). The classical method of the combination used by IERS leading to the combined series EOPC4 (IERS, ) or the combination of EOP made by Gross (, 1) combine the measured values of different techniques without using the observed first derivatives of EOP. Here, we present the mutual comparison of all the three series mentioned above. The residuals and systematic differences are discussed and there is also mentioned the advantage of the combined smoothing consisting in connection of the long-term stable but less dense VLBI observations with more frequent and short-term stable GPS observations. Keywords. Earth orientation parameters; space techniques, combination 1 Introduction One of the first application of the recently proposed new method of combined smoothing (Vondrák and Čepek, ; Vondrák and Gambis, ) is presented in this volume (Vondrák et al., 1) to combine the components of the celestial pole offsets (CPO) ɛ and ψ observed by VLBI with their rates ε and ψ observed by GPS. Also the time correction UT1-TAI from VLBI was combined with the excess of the length-of-day (l.o.d.) from GPS. Here we compare the resulting series with the ones that can be called traditional combinations provided by IERS Product Center (EOP(IERS) C4) and by JPL (SPACE), to detect the systematic differences with respect to the methods of combination. Since we are at the beginning of the research of the new method, we combined two sets of observed values, each of one provider only. The combination of the other series will be done in the future in frame of the IERS Combination Research Center managed at Astronomical Institute, Prague. Used series.1 Combined smoothing of VLBI and GPS observations We mention here the observations and the used method very briefly. For more details, see Vondrák et al. (1) in this volume. There are presented two combinations one combining UT1 with the l.o.d. and the other combining celestial pole offsets with their rates. In both cases the function values are observed by VLBI and their rates by GPS. The VLBI observations were taken from the solution produced by the Institute of Applied Astronomy (IAA) in St. Petersburg and made available by International VLBI Service for Geodesy and Astrometry (IVS) denoted as [iaao997.eops] (IVS, ). The l.o.d. observations were taken from the solution determined by the International GPS Service (IGS). The rates of CPO, ε and ψ were taken from the solution derived at the Center for Orbit Determination in Europe (CODE). The oscillations in UT and in length of day due to zonal tides for periods under 35 days, as well as the 14-day terms in ψ, ε were not removed and they are present in the series in full size. The a posteriori uncertainties calculated from the residuals are ±4.µs and ±9.5µsd 1 in case UT1 and l.o.d. and ±.148 mas, ±.37 masd 1 for ψ sin ε and ψ sin ε, and ±.1 mas, ±.3 masd 1 for ε and ε in case of CPO (Vondrák et al., 1). We denote this combination of CPO with their rates as IAA/CODE and the combination of UT1 and l.o.d. as IAA/IGS in the following text.

2 . EOP(IERS) C 4 The series EOP(IERS) C 4 provided by IERS are described in IERS (). The series are continuous combination, slightly low filtered at daily intervals. It is permanently updated in EOP-Product Center. As the series are given at one-day intervals it can be interpolated linearly to get the value between two midnights. The oscillations in UT and in length of day due to zonal tides for periods under 35 days, as well as the 14-day terms in ψ, ε are present in full size. The contributing series are slightly smoothed by the Vondrák algorithm (Vondrák, 1977) with the period for remaining amplitude of 95% is 6.3 days. The uncertainties of a daily value at interval for UT are equal to ±µs, for l.o.d. ±µsd 1 and for CPO ±.3mas..3 SPACE From the most recent of the annually generated combinations at the JPL (Gross, 1) we selected the combination SPACE, denoted as EOP(JPL) C1 in the IERS database notation (see IERS ()), for the comparison of UT1 and l.o.d. The remaining two combinations provided at the JPL, COMB and POLE are based on the SPACE since eighties and they differ only by adding the observations of optical astrometry before 1981 which gives no influence on the time interval of our interest (the last date being January 6., 1). Only two sets of observations were exploited for the combination UT1 and l.o.d. in SPACE in the interval : NASA/GSFC(GSFa) multi-baseline solution and USNO (NEOS Intensive UT1), see Gross (1). Both are different from the observations used in the IAA solution, i.e. NEOS A VLBI observations and hence the series [iaao997.eops](ivs, ) used for IAA/IGS and SPACE can be viewed as independent. The observations have been combined using a Kalman filter after the application of the preprocessed bias-rate corrections. The Kalman filter used to combine the measurements also interpolates them in order to produce series of one day equally spaced values. The oscillations in UT and in l.o.d. due to zonal tides for periods under 35 days have been added to UT1 and they are present in full size. The SPACE and EOP(IERS) C4 are very consistent with each other after 1987 which is demonstrated by the rms of the differences between these two series ±7µs in case of UT1 and ±18µsd 1 for l.o.d., see Gross (1). 3 Comparisons To compare two series we simply subtract the series EOP(IERS)C4 and SPACE from the series IAA/IGS and IAA/CODE. In case of EOP(IERS)C4 and SPACE we interpolated linearly the values to the moments of IAA/IGS and IAA/CODE series to be able to subtract both series easily. 3.1 Comparison of combinations of celestial pole offsets with their rates The solution of EOP(IERS) C4 is compared with our solution IAA/CODE. The combination SPACE does not contain the CPO. To be able to compare also the time derivatives of the CPO components we must compute the missing values of ε and ψ in EOP(IERS) C4 as the numerical time derivatives of the values ε and ψ. We used the centered differences for the daily equally spaced function values f i = 1 (f i+1 f i 1 ). The spectral analysis of the differences between CPO from IAA/CODE and EOP(IERS) C4 shows beside the expected fortnightly and monthly terms also a significant term with period 58.5 days and amplitude.1 mas, see Fig. 1. This term was detected already in the residuals of the combination IAA/IGS (Vondrák et al., 1) and is caused mostly by systematic deviations in GPS results with period longer than a month. This term in the function values of CPO ε and ψ indicate that the systematic term partly leaked projected from the series of CPO rates into the function values of ε and ψ. The term with the same frequency in the differences of rates is not as significant as in residuals Vondrák et al. (1). Its amplitude is about.masd 1 for both components (see Fig. ) in comparison with the amplitude from residuals that was about.3 masd 1 for both components ε and ψ sin ε. The bias of the IAA/IGS with respect to the EOP(IERS) C4 solution are.4 and.9mas for ψ sin ε and ε with the rms ±.mas 3. Comparison of combinations of UT1 with l.o.d. For UT1 and lod we are able to compare the results of IAA/IGS not only with EOP(IERS) C4 but also with the SPACE where both values of UT1 and l.o.d. are available. Each of the series contains both UT1 and l.o.d. values and it is not necessary to compute the time derivatives. The differences between UT1 of IAA/IGS and both of EOP(IERS) C4 and SPACE are seen

3 3 ε IAA/CODE - EOPC4 ψsinε IAA/CODE - EOPC4 1 1 [mas] -1-1 [mas] d 8.7d 13.7d 58.5d 16.6d 14.1d Fig. 1 Combination IAA/CODE and its comparison with EOP(IERS)C4 solution of celestial pole offsets ε on the left and ψ sin ε on the right. The lower plot amplitude spectrum of the differences. ε. IAA/CODE - EOPC4 ψ. sinε IAA/CODE - EOPC4 [mas/day] [mas/day] d 9.3d d 14.1d...1. Fig. Combination IAA/CODE and its comparison with EOP(IERS)C4 solution of the rates of celestial pole offsets ε on the left and ψ sin ε on the right. The lower plot amplitude spectrum of the differences.

4 4 IAA/IGS - EOPC4 IAA/IGS - SPACE UT1 [µs] [µs] , y 7.6d 13.66d Fig. 3 Combination IAA/IGS and its comparison with EOP(IERS)C4 (the left column) and with SPACE (the right column) solution of UT1. The lower plot amplitude spectrum of the differences. IAA/IGS - EOPC4 IAA/IGS - SPACE l.o.d. [µsd -1 ] [µsd -1 ] Fig. 4 Combination IAA/IGS and its comparison with EOP(IERS)C4 (on the left) and with SPACE (on the right) solution of the excess length of day. The lower plot amplitude spectrum of the differences.

5 5 in Fig. 3. The dispersion is visibly smaller for the SPACE. The rms of the difference σ is ±3.6µs and ±3.1µs for SPACE and IERS(EOP) C4, respectively. Compare it with the value of ±7µs at the end of Sect..3. It can be caused by smaller number of series used in combination of SPACE for this time interval ( ) than for EOP(IERS) C4. The spectrum for SPACE shows several significant terms: the annual term has the amplitude of 7µs, monthly term of 5µs and the fortnightly term has the amplitude of 8.5µs. The differences in the l.o.d. between IAA/IGS and both of EOP(IERS)C 4 and SPACE are shown in Fig. 4. The rms with respect to SPACE is equal to ±16.1µsd 1 what is again smaller than the rms with respect to EOP(IERS) C4 being equal ±1.4µsd 1. The difference appears for the same reason as in case of UT1. The biases are in both cases very small,.µsd 1 and.µsd 1 for EOP(IERS) C4 and SPACE, respectively. 4 Conclusions The combination of the celestial pole offsets ε and ψ observed by VLBI with the rates of the components ε and ψ observed by GPS (IAA/CODE) and similarly the combination of UT1 from VLBI with the series of the excess of the length of day from GPS (IAA/IGS) were compared with two independent series of Earth orientation parameters produced at IERS Product Center and JPL, respectively. The comparison detected no rough systematic deviations that could degrade the new method of combined smoothing of the authors Vondrák and Čepek (). The systematic deviation with the period 58.5 days, which is seen in the comparison of the CPO components ε and ψ, has already been detected in the series of the rates of CPO ε and ψ from the GPS produced by CODE (see Vondrák et al. (1)). The further study deserves such leaking into the CPO components by using the method of combined smoothing. References Gross, R. S. (). Combinations of Earth orientation measurements: SPACE97, COMB97 and POLE97. J. Geodesy, vol. 73, pp Gross, R. S. (1). Combinations of Earth Orientation Measurements: SPACE, COMB and POLE. Tech. Rep. 1-, JPL, Pasadena, CA. IERS () IERS Annual Report. Obs. de Paris, France. IVS (). IVS: International VLBI Service products available electronically at Vondrák, J. (1977). Problem of Smoothing Observational Data II. Bull. Astron. Inst. Czechosl., vol. 8, pp Vondrák, J. and D. Gambis (). Accuracy of Earth orientation parameters series obtained by different techniques in different frequency windows. In: Journés 1999 Systèmes de réfŕence spatio-temporels & IX. Lohrmann-Kolloquiium, (eds.) M. Soffel and N. Capitaine. Lohrmann-Observatorium, TU Dresden. Vondrák, J. and A. Čepek (). Combined smoothing method and its use in combining Earth orientation parameters measure by space techniques. Astron. Astrophys. Suppl. Ser., vol. 147, pp Vondrák, J., R. Weber and C. Ron (1). Earth Orientation Parameters Combination of the Results Obtained by Different Techniques. In: this volume. Acknowledgments The support of the Ministry of Education, Youth and Sport of the Czech Republic to this study by means of grant No. LN5 is appreciated.