J Geod (2017) 91:1503–1512 DOI 10.1007/s00190-017-1039-5 ORIGINAL ARTICLE Influence of subdaily polar motion model on nutation offsets estimated by very long baseline interferometry Natalia Panafidina1 · Urs Hugentobler2 · Manuela Seitz1 · Hana Krásná3 Received: 18 November 2016 / Accepted: 15 May 2017 / Published online: 29 May 2017 © Springer-Verlag Berlin Heidelberg 2017 Abstract This paper studies the connection between the Keywords Terrestrial reference frame · Celestial reference subdaily model for polar motion used in the processing of frame · Earth rotation parameters · Subdaily tidal models · very long baseline interferometry (VLBI) observations and VLBI the estimated nutation offsets. By convention accepted by the International Earth Rotation Service, the subdaily model for polar motion recommended for routine processing of 1 Introduction geodetic observations does not contain any daily retrograde terms due to their one-to-one correlation with the nutation. Very long baseline interferometry (VLBI) is the only space Nevertheless, for a 24-h VLBI solution a part of the signal geodetic technique which provides access to all parame- contained in the polar motion given by the used subdaily ters needed for the transformation between the terrestrial model is numerically mistaken for a retrograde daily side- and the celestial reference systems. In principle, only three real signal. This fictitious retrograde daily signal contributes parameters are needed for such a transformation in a three- to the estimated nutation, leading to systematic differences dimensional space. In space geodesy, five parameters are between the nutation offsets from VLBI solutions computed used traditionally, what implies that these parameters are with different subdaily polar motion models. We demonstrate not fully independent. From these five parameters, two are this effect using solutions for all suitable 24-h VLBI sessions called the polar motion and describe the position of the celes- over a time span of 11 years (2000–2011). By changing the tial intermediate pole (CIP) in the International Terrestrial amplitudes of one tidal term in the underlying subdaily model Reference Frame (ITRF, Petit and Luzum 2010; Altamimi for polar motion and comparing the estimated parameters to et al. 2011). One parameter is needed to locate the Green- the solutions computed with the unchanged subdaily model, wich meridian in the inertial space, it is called the Universal the paper shows and explains theoretically the effects pro- Time (UT1). Two remaining parameters relate the CIP to duced by the individual subdaily terms on the VLBI nutation the pole of the celestial reference frame. They are small estimates. empirical corrections to the nutation offsets given by the precession–nutation model which defines the position of the CIP in the International Celestial Reference Frame (ICRF, Petit and Luzum 2010; Ma et al. 1998). All five transfor- mation parameters are called Earth orientation parameters B Natalia Panafidina (EOP), and a subset of three parameters containing the polar natalia.panafi[email protected] motion and UT1 is usually referred to as Earth rotation 1 Deutsches Geodätisches Forschungsinstitut der TUM, parameters (ERP). Afons-Goppel-Str. 11, 80539 Munich, Germany The VLBI observations are coordinated by the Interna- 2 Technische Universität München, Arcisstr. 21, 80333 tional VLBI Service for Geodesy and Astrometry (IVS, Munich, Germany Schuh and Behrend 2012), which maintains a network of 3 Department of Geodesy and Geoinformation, Technische VLBI stations and organizes regular observation programs Universität Wien, Gußhausstr. 27–29, 1040 Wien, Austria with different objectives. There are daily 1-h intensive ses- 123 1504 N. Panafidina et al. sions scheduled for the Universal Time (UT1) estimation. 2 VLBI data and solutions For all other programs, the observations are normally per- formed in 24-h sessions, and the most regular sessions are The subdaily model for polar motion contains prograde daily devoted specially to the EOP estimation and are held two terms and prograde and retrograde semi-daily terms. The times a week on Monday and Thursday. The 24-h sessions retrograde daily terms correspond to nutation in the iner- with other objectives are usually held several times per year. tial space and thus are conventionally a part of the nutation Together it makes several (at least two) 24-h VLBI sessions model and not a part of the ERP model. This means that per week available for a routine processing by analysis cen- in principle the used subdaily pole model and the estimated ters (ACs) of the IVS. nutation should be fully independent. At the same time, as is The EOP solution for each 24-h session is one of the offi- known from the spectral analysis, over a time span of 24 h cial products of the IVS. The description of the IVS products the prograde and retrograde terms with daily and semi-daily in general and specifically of the EOP time series from VLBI periods cannot be fully separated. For this reason in a 24-h can be found on the IVS web site (http://ivscc.gsfc.nasa.gov). solution, a part of the signal contained in the subdaily polar The quality of the EOP solutions from the individual analy- motion given by a model is numerically mistaken for a ret- sis centers as well as the quality of the combined solutions rograde daily sidereal signal. This fictitious retrograde daily is checked by internal comparisons between the VLBI solu- signal contributes to nutation and will be corrected for by tions and by external comparisons with the combined C04 the estimated nutation offsets. In this way, the nutation cor- EOP time series provided by the International Earth Rotation rections estimated from VLBI observations always contain Service (IERS). a small part induced by the errors of the used subdaily pole Since VLBI is the only space geodetic technique which model. allows the determination of the orientation of the Earth in This effect can be seen if we compare two VLBI solutions inertial space, the interpretation of the VLBI results for nuta- computed with different subdaily polar motion models. If tion is of special interest. Recognizing the effects influencing within the considered solutions the ERP are estimated with a the estimation of nutation offsets can contribute to a better subdaily resolution (e.g., 1 h), the change in the subdaily understanding of the VLBI solutions. In this paper, we focus model would be absorbed by the estimated polar motion on one of such effects demonstrating how the used subdaily parameters, leaving the nutation estimates unaffected. In such model for polar motion affects the estimated nutation offsets. a case, the time series of the nutation offsets from the two The a priori polar motion used in the processing has to include solutions would show no systematic differences. It needs the subdaily variations, since the Earth rotation is noticeably to be shortly mentioned that estimating the subdaily polar influenced on the subdaily timescales by the daily and semi- motion together with nutation is possible only with an addi- daily ocean tides and other tidal phenomena. Neglecting the tional constraint on polar motion to block the retrograde daily subdaily variations leads to systematic errors in the estimated signal. In case of a standard VLBI solution (e.g., the routine parameters (Ray and McCarthy 1996). Acknowledging this, EOP solutions made by the IVS ACs) where the ERP and the IERS recommends to use in the routine processing of their rates are estimated once per 24 h, the subdaily model geodetic observations a model for subdaily variations in the cannot be corrected by the ERP themselves. In this case, the ERP. The standard IERS subdaily model can be found in the estimated nutation offsets absorb a part of the signal from IERS Conventions (2010) (Petit and Luzum 2010). It was the subdaily polar motion model corresponding to the fic- derived from an ocean tide model based on satellite altimetry titious retrograde daily signal. Theoretically, this fictitious and provides the amplitudes of variations in the polar motion retrograde signal could be absorbed also by the radiosource and UT1 for a set of tidal frequencies. The latest IERS sub- positions if the nutation was kept fixed and the coordinates of daily model for the Earth rotation parameters contains 71 the sources estimated freely. However, in practice it is never tidal terms. done this way: If the radiosource positions are estimated, the In this paper, we study a connection between the nuta- nutation is estimated as well and a no-net-rotation condition tion offsets from VLBI solutions and the subdaily model for is applied on the source coordinates preventing them from the polar motion. In Sect. 2 the nature of this connection is absorbing the retrograde daily signal. discussed, and the VLBI data and the solutions computed The celestial pole offsets (CPO) which we will further to demonstrate the effect are described. In Sect. 3 the influ- refer to as the nutation corrections are measured in two ence of changes in the individual tidal terms from a subdaily directions (dX and dY), and the contribution of the ficti- polar motion model on the estimated nutation is shown and tious retrograde daily term is also measured in two directions compared to the theoretically computed effect induced by the as the amplitude of the sine term and the amplitude of the respective tidal terms. Finally, in Sect. 4 we shortly consider cosine term. Different subdaily polar motion models con- the influence of the subdaily models on the estimated daily tain fictitious retrograde daily signals with different sine and polar motion. cosine amplitudes, and the nutation corrections are shifted 123 Influence of subdaily polar motion model on nutation offsets estimated by very long baseline... 1505 respectively differently. As a result, time series of the nutation time. The amplitudes of both sine and cosine for a selected differences between the standard VLBI solutions computed tidal term were changed by 100 μas.