Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.gao.spb.ru/english/personal/malkin/publ/zm11a.pdf Äàòà èçìåíåíèÿ: Mon Sep 5 10:05:40 2011 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 03:17:27 2012 Êîäèðîâêà:

J Geod (2011) 85:617­622 DOI 10.1007/s00190-011-0468-9

ORIGIN AL AR TICLE

The impact of celestial pole offset modelling on VLBI UT1 intensive results
Zinovy Malkin

Received: 16 September 2010 / Accepted: 30 March 2011 / Published online: 12 April 2011 © Springer-Verlag 2011

Abstract Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precessionnutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 as. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 as. Obtained results are applicable to the satellite data processing as well. Keywords VLBI · Earth orientation parameters (EOP) · UT1 Intensives · Celestial pole offset (CPO)

1 Introduction Very long baseline interferometry (VLBI) is the principal method for determination of the Universal Time (UT1) nowadays. The most accurate UT1 estimates can be obtained, simultaneously with other Earth rotation parameters (EOP):
Z. Malkin (B) Pulkovo Observatory, Pulkovskoe Ch. 65, St. Petersburg 196140, Russia e-mail: malkin@gao.spb.ru

terrestrial and celestial pole coordinates, from 24-h VLBI sessions carried out on global networks of several, usually 6­8, stations. Their precision and accuracy depends on several factors, such as the number of stations, network geometry, and registration mode (see e.g. Malkin 2009). However, results of these observations are normally available only in 8­15 days after observations. Such a delay of the results causes problems in many real-time applications and influences UT1 prediction accuracy (Luzum and Nothnagel 2010). To get more timely UT1 estimates, special observing programs are conducted in the framework of the International VLBI Service for Geodesy and Astrometry (IVS) activity (SchlÝter and Behrend 2007). These sessions, called Intensives, are carried out on one or two baselines, have 1-h duration, employ electronic data transfer (e-VLBI), and hence provide rapid turnaround time, usually 0.5­2 days. However, the Intensives do not allow us to obtain all the EOP with reasonable accuracy, and only UT1 can be effectively estimated. For this reason, reliable terrestrial and celestial pole coordinates are needed for data processing of the Intensives. In this paper we concentrate on the latter aspect. The PN model errors substantially influence UT1 estimates (Robertson et al. 1985; Titov 2000; Nothnagel and Schnell 2008). In particular, the authors of the latter paper have shown that an error in PN of 1 mas can induce an error in UT1 of up to 30 as, and this error is systematic in its behavior. Since the 24-h VLBI CPO estimates are yet not available during operational processing of the Intensives, the CPO model should also include prediction to provide operational Intensives data processing. The most accurate celestial pole (CP) coordinates can be computed as a sum of the reference precession-nutation (PN) model, currently IAU 2000/2006, and the observed CP offset (CPO). Three CPO models suitable for operational processing of the Intensives are publicly available. They are

123


618

Z. Malkin
0.8 0.6 0.4

computed at the US Naval Observatory (IERS Annual Report 2007), Paris Observatory (Petit and Luzum 2010), and Pulkovo Observatory (Malkin 2007). They are compared in Section 2. All three models are empirical in their nature, and are evaluated by approximation and extrapolation of an observed VLBI CPO series. The authors of these models use different algorithms and reference CPO series, which results in systematic differences between models, and consequently between Intensives UT1 estimates. In this paper, we investigated this differences with emphasis on their systematic part, which is of main concern for the users. For this purpose we performed test processing of the Intensives observations obtained during 2007.0­2010.5. The results are presented and discussed in Section 3.Onthis basis, we discuss the choice of the best CPO model to be recommended for using in the Intensives data processing.

IVS NEOS SL ZM2

dX, mas

0.2 0 -0.2 -0.4 -0.6 2007 0.6 0.4 0.2

2008

2009

2010

Year
IVS NEOS SL ZM2

2 CPO models
dY, mas
0 -0.2 -0.4 -0.6 -0.8 2007

CPO consists of several terms, and can be described by the following formula. CPO = FCN + Ti + Pj , (1)

where Ti are trend components caused e.g. by errors in precession or very low-frequency nutation terms, P j are (quasi) harmonic terms caused e.g. by errors in nutation model or geophysical processes. FCN stands for Free Core Nutation, it is a quasi-harmonic CP motion with an amplitude of about 150­200 as nowadays. The sum of the trend components is in our days of the same order as FCN, and is progressively growing. All three models introduced above are provided as a regularly updated time series of the CPO components dX and dY with prediction for several months. These models are as follows: NEOS series1 computed at the US Naval Observatory by spline smoothing of several selected input VLBI CPO series (IERS Annual Report 2007 2009). It is an official product of the International Earth Rotation and Reference Systems Service (IERS). SL series2 (S. Lambert) computed at the Paris Observatory by least-squares fit of the circular FCN term with period of 430.2 days and a bias over the running 2-year intervals. IERS C04 EOP series is used as input. The bias is not included in the model. The SL model is recommended by the IERS Conventions (2010) as a replacement for CPO (Petit and Luzum 2010).
1 2

2008

2009

2010

Year
Fig. 1 Comparison of three CPO models with the IVS CPO combines series. Unit: mas

ZM2 series3 computed at the Pulkovo Observatory by exponential smoothing of the IVS combined CPO series (Malkin 2007). The IVS combined EOP series is an official IVS product computed by combining datum-free normal equations of up to six IVS analysis centers (BÆckmann et al. 2010). It includes estimates of Pole coordinates with their rates, Universal Time, Length of Day, and CPO for every 24-h VLBI session suitable for accurate EOP determination, two to three sessions a week in average. This series, along with supplement information, is available at the IVS Analysis Coordinator Web site,4 and is supposed to be the most accurate source to our knowledge of the CP motion. Figure 1 shows a comparison of the CPO models with the IVS CPO series, and Fig. 2 presents the differences between the three models. One can see by visual inspection that the ZM2 model represent IVS data better than others, just
3 4

http:// maia.usno.navy.mil/ . http:// syrte.obspm.fr/ ~lambert/ fcn/ .

http:// www.gao.spb.ru/ english/ as/ persac/ index.htm. http:// vlbi.geod.uni- bonn.de/ IVS- AC/ .

123


The impact of celestial pole offset modelling on VLBI UT1 intensive results
0.2
NEOS-ZM2

619
0.4
NEOS-ZM2

dX, mas

0 -0.2 -0.4 2007

dX, mas

0.2 0 -0.2 2007

2008

2009

2010

2008

2009

2010

Year
0.2
SL-ZM2

Year
0.4
SL-ZM2

dX, mas

0 -0.2 -0.4 2007

dX, mas
2008 2009 2010

0.2 0 -0.2 2007

2008

2009

2010

Year dX, mas dX, mas
0.2 0 -0.2 -0.4 2007
SL-NEOS

Year
0.4 0.2 0 -0.2 2007
SL-NEOS

2008

2009

2010

2008

2009

2010

Year
Fig. 2 Differences between CPO models. Unit: mas

Year

Table 1 The rms difference between each of the CPO models and the IVS combined CPO series. Unit: as NEOS dX 159 dY 83 SL dX 129 dY 217 ZM2 dX 70 dY 79

3 Data analysis This study is based on the processing of VLBI data collected from three main Intensives programs from 2007.0 till 2010.5. The observations from the following observing programs were used (see also Fig. 3): Int1: Kokee Park--Wettzell baseline, 803 sessions; Int2: Tsukuba--Wettzell baseline, 462 sessions; Int3: Ny-ålesund--Tsukuba--Wettzell baselines, 96 sessions. All the observations were processed in a uniform way with the only difference in the CPO model used. Source positions were taken from the ICRF2 (the second realization of the International Celestial Reference Frame) catalog (Ma et al. 2009). The computations were made in four variants: with one of the three CPO models listed above and without CPO contribution (in other words, with zero CPO model), and four corresponding UT1 time series were obtained and compared. Results of this computations and comparison of UT1 estimates are depicted in Fig. 4. In Table 2, a comparison of the formal errors and mutual biases are presented. The formal errors are those computed during session data processing, and the bias is computed as the average value over the whole 3.5-year period with respect to the UT1 time series computed without CPO correction. The results show that the CPO modelling has practically no influence on the UT1 uncertainty, and the relative bias.

because of how it is evaluated. The NEOS model is close to ZM2, but seems to have extra high-frequency terms, which most probably comes from the incoming data noise. A bias between ZM2 and NEOS models seen in some periods evidently comes from the difference between the IVS and NEOS combined CPO series. The SL model is centered around the time axis and has a significant bias with respect to the IVS series, which can be expected from the method used for its computation, as described above. This bias corresponds to two last terms of (1) and is variable with time. Table 1 shows the rms difference between each of the CPO models and the IVS combined CPO series at the interval 2007­2010.5, (that is, the rms difference of the series shown in Fig. 1). Detailed analysis of the differences between CPO models and their origins is beyond the scope of this paper, although it is an interesting task which is worth a separate study. However, our comparison clearly shows that significant differences up to several hundred as between the CPO models do exist, which can induce differences between the UT1 estimates computed using various models.

123


620

Z. Malkin

Table 3. The weights were computed from the formal errors of UT1 estimates. The phase is given at the epoch of minimum variance, the same for each observing program. These results show that the impact of CPO modelling on Int2 results is more than twice larger than that for Int1. Addition of a third station to Int2, i.e. using the Int3 network, somewhat reduces the amplitude of the annual term, but does not principally change the result. A comparison of results presented in Table 3 confirms that the systematic differences between UT1 time series computed with two full CPO models, NEOS and ZM2, are relatively small, whereas differences with UT1 time series computed with the FCN/SL model are about twice larger. It is also interesting to notice that the differences between UT1 series NEOS­ZM2 and SL­NEOS are more noisy than that for SL­ZM2. This may indicate that an extra noise component in the NEOS series propagates to UT1 estimates too.

4 Conclusions
Fig. 3 Stations and baselines participating in the analyzed observing programs

However, one can see that neglecting CPO modelling causes time-dependent systematic errors with amplitudes of up to 20 as. As previously noticed by Nothnagel and Schnell (2008), the effect is larger for Int2 sessions as compared with Int1. It should be mentioned that differences between UT1 estimates obtained above may also depend on other factors like observation scheduling as it has been shown in previous investigations of the Intensives results (Hefty and Gontier 1997; Titov 2000). This is also confirmed by the results presented in Fig. 4 and Table 3 below which show different influence of CPO modelling on UT1 time series obtained in the framework of different observing programs. For this reason, one should be careful about too strict comparison of those differences with the differences in CPO models. On the other hand, the differences between the UT1 time series obtained with different CPO models depend only on this factor, and allow us to make a conclusion on its impact on the Intensives results, which is the primary goal of this paper. Further comparison of the UT1 time series revealed more complicated impact of the CPO modelling on the systematic behavior of UT1 estimates, as can be seen in Fig. 4, 4th raw, where the systematic differences between UT1 estimates obtained with different CPO models with amplitude of up to 10 as are clearly present. Since these differences look like (quasi-)periodic signal, we performed spectral analysis (the lower raw) which showed only one statistically significant harmonic term with period of about 1 year. The amplitude and phase of the annual term computed by weighted least-squares adjustment of UT1 differences are presented in

In this paper, we investigated and compared the impact of three CPO models on UT1 estimates obtained from VLBI Intensives. The NEOS and ZM2 models computed at the US Naval Observatory and Pulkovo Observatory respectively, are full CPO models, and can be considered providing the most complete correction to the a priori IAU precessionnutation model. Different from that the SL model computed at the Paris Observatory is an FCN model. The latter is recommended by the IERS Conventions (2010) for applications requiring highly accurate coordinate transformation. Based on the test processing of the Intensives data collected in the framework of three IVS observing programs, Int1, Int2, and Int3, using different CPO models we can draw several conclusions. First, we numerically confirmed that proper CPO modelling is necessary to obtain highly accurate UT1 estimates from the Intensives. Neglecting CPO leads to large systematic errors with amplitudes of up to 20 as. It was also demonstrated that an FCN model (e.g. SL) provides only partial compensation of this error as can be seen from Fig. 4 and Table 3. A simple way to mitigate the difference between the IERS recommended SL model and CPO determined by VLBI (see Fig. 2) would be inclusion of the bias in the SL model, which has been intentionally excluded so far. Although the SL model yet seems to be excessively smoothed, which may be important for other applications. Our comparison of UT1 time series computed with NEOS, SL, and ZM2 models has shown practically no influence of CPO modelling on the UT1 uncertainty, and the relative bias. However, significant differences was found between these series including an annual term and (pseudo)-noise component. It is important that even though no significant biases average over the whole time interval was found, the annual

123


The impact of celestial pole offset modelling on VLBI UT1 intensive results

621

UT1(IAU+NEOS) - UT1(IAU), µas 30 30

UT1(IAU+NEOS) - UT1(IAU), µas 30

UT1(IAU+NEOS) - UT1(IAU), µas

0

0

0

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

UT1(IAU+SL) - UT1(IAU), µas 30 30

UT1(IAU+SL) - UT1(IAU), µas 30

UT1(IAU+SL) - UT1(IAU), µas

0

0

0

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

UT1(IAU+ZM2) - UT1(IAU), µas 30 30

UT1(IAU+ZM2) - UT1(IAU), µas 30

UT1(IAU+ZM2) - UT1(IAU), µas

0

0

0

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

-30 2007

2007.5

2008

2008.5

2009

2009.5

2010

2010.5

Differences between CPO models, µas 10 0 -10 2007 2007.5
NEOS-ZM2

Differences between CPO models, µas 10 0 -10 10 0 -10 2007.5
NEOS-ZM2

Differences between CPO models, µas

2008

2008.5

2009

2009.5

2010

2010.5

2007

2008

2008.5

2009

2009.5

2010

2010.5

2007

2007.5
NEOS-ZM2

2008

2008.5

2009

2009.5

2010

2010.5

SL-ZM2

SL-NEOS

SL-ZM2

SL-NEOS

SL-ZM2

SL-NEOS

Power spectrum of the differences between CPO models, arbitrary units

Power spectrum of the differences between CPO models, arbitrary units

Power spectrum of the differences between CPO models, arbitrary units

1

NEOS-ZM2 SL-ZM2 SL-NEOS

1

NEOS-ZM2 SL-ZM2 SL-NEOS

1

NEOS-ZM2 SL-ZM2 SL-NEOS

0 0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 0.25

0

0.5

0.75

1

1.25

1.5

1.75

2

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Period,yr

Period,yr

Period, yr

Fig. 4 The impact of CPO model on UT1 Intensives result. Three columns correspond to three Intensives observing programs. Three upper plots display the differences between UT1 estimates obtained with one of the given CPO models (from top to bottom: NEOS, SL, ZM2) and the

UT1 estimates uncertainty. In obtained with plots show the

obtained without CPO correction, vertical bars show 1 the 4th raw, the differences between the UT1 estimates the three CPO models are plotted, unit: as. The lower spectra of these differences in arbitrary units

Table 2 Median formal error of the UT1 estimates and relative bias of the UT1 time series computed with different CPO models. Unit: as Model Formal error Int1 Zero CPO NEOS SL ZM2 10.3 10.3 10.4 10.3 Int2 9.1 9.0 9.0 9.0 Int3 8.0 8.0 8.0 8.0 Bias Int1 0 -0 . 7 -0 . 1 -0 . 7 Int2 0 +0 . 1 +0 . 1 -0 . 2 Int3 0 +0 . 2 +0 . 3 -0 . 1

term can cause local (in time) biases affecting operational combination. For non-operational processing of the many-year Intensives time series, important for densification of the UT1 series obtained from the 24-h VLBI sessions, both NEOS and ZM2 models can be used with relatively small systematic differences between them, except some intervals where the difference between the two models is substantial (see Figs. 2, 4), e.g. in the end of 2008. The systematic part of this difference can be presumably explained by the difference between the IVS and NEOS combined CPO series (Fig. 1) which would be worth a special study. However, the NEOS model seems to

123


622 Table 3 The amplitude and phase of the annual term in differences between UT1 estimates computed with different CPO models Amplitude, as Int1 NEOS ­ ZM2 SL ­ ZM2 SL ­ NEOS 1.3 ± 0.1 3.5 ± 0.1 2 .7 ± 0 .1 Int2 3.8 ± 0.1 7.5 ± 0.1 6.3 ± 0.2 Int3 2 .8 ± 0 .2 6.1 ± 0.3 5.8 ± 0.3

Z. Malkin

Models

Phase, deg Int1 175 ± 2 220 ± 1 239 ± 2 Int2 235 ± 2 292 ± 1 322 ± 1 Int3 341 ± 5 50 ± 3 77 ± 3

need stronger smoothing to remove the high-frequency signal coming most probably from incoming VLBI EOP series. For real-time data processing, when one has to use predicted CPO, the ZM2 model may have an advantage due to better prediction accuracy (Malkin 2010). Finally, it was shown that using different CPO models leads to significant, mostly systematic, differences in the UT1 estimates obtained from the Intensives observing programs. So, the best way to account for this effect, and corresponding recommendations to space geodesy analysis centers should be thoroughly discussed, and a corresponding update of the IERS Conventions should be considered. In particular, it seems to be advisable to use a CPO model which is the best compared to the IVS combined EOP series. Also, a careful comparison of the IVS and IERS combined CPO series is needed in the framework of this discussion. It should be noted that the obtained results and conclusions are applicable to the SLR and GNSS data processing as well, in particular for precise orbit determination.
Acknowledgments This paper is based on processing of VLBI observations collected on the international IVS network.5 The author wishes to express his gratitude to all the people working hard to make this data available. Critical comments and valuable suggestions of three anonymous referees are highly appreciated.

References
BÆckmann S, Artz T, Nothnagel A, Tesmer V (2010). J Geophys Res 115:B04404. doi:10.1029/ 2009JB006465 Hefty J, Gontier A-M (1997) Sensitivity of UT1 determined by single-baseline VLBI to atmospheric delay model, terrestrial and celestial reference frames. J Geod 71:253­261 IERS Annual Report 2007 (2009) Verlag des Bundesamts fÝr Kartographie und GeodÄsie, Frankfurt am Main

Luzum B, Nothnagel A (2010) Improved UT1 predictions through lowlatency VLBI observations. J Geod 84:399­402. doi:10.1007/ s00190- 010- 0372- 8 Ma C, Arias EF, Bianco G, Boboltz DA, Bolotin SL, Charlot P, Engelhardt G, Fey AL, Gaume RA, Gontier A-M, Heinkelmann R, Jacobs CS, Kurdubov S, Lambert SB, Malkin ZM, Nothnagel AN, Petrov L, Skurikhina E, Sokolova JR, Souchay J, Sovers OJ, Tesmer V, Titov OA, Wang G, Zharov VE, Barache C, BÆckmann S, Collioud A, Gipson JM, Gordon D, Lytvyn SO, MacMillan DS, Ojha R (2009) The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry In: Fey AL, Gordon D, Jacobs CS (eds) IERS Technical Note No. 35. Verlag des Bundesamts fÝr Kartographie und GeodÄsie, Frankfurt am Main Malkin ZM (2007) Empiric models of the Earth's free core nutation. Solar System Res 41:492­497. doi:10.1134/ S0038094607060044 Malkin Z (2009) On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs. J Geod 83:547­556. doi:10.1007/ s00190- 008- 0265- 2 Malkin Z (2010) Analysis of the accuracy of prediction of the celestial pole motion. Astron Rep 54:1053­1061. doi:10.1134/ S1063772910110119 Nothnagel A, Schnell D (2008) The impact of errors in polar motion and nutation on UT1 determinations from VLBI Intensive observations. J Geod 82:863­869. doi:10.1007/ s00190- 008- 0212- 2 Petit G, Luzum B (eds) (2010) IERS Conventions (2010), IERS Technical Note No. 36, Verlag des Bundesamts fÝr Kartographie und GeodÄsie, Frankfurt am Main Robertson DS, Carter WE, Campbell J, Schuh H (1985) Daily Earth rotation determinations from IRIS very long baseline interferometry. Nature 316(6027):424­427 SchlÝter W, Behrend D (2007) The international VLBI service for geodesy and astrometry (IVS): current capabilities and future prospects. J Geod 81:379­387. doi:10.1007/ s00190- 006- 0131- z Titov OA (2000) Influence of adopted nutation model on VLBI NEOS-intensives data analysis. In: Johnston KJ, McCarthy DD, Luzum BJ, Kaplan GH (eds) Proceedings of the IAU colloquium 180 "Towards models and constants for sub-microarcsecond astrometry", March 2000, pp 259­262

5

ftp:// cddis.gsfc.nasa.gov/ vlbi/ ivsdata/ .

123