1. General presentation of the CEP

2. Programme of the special session CEP (Journees 1998)
3. Contributions to the discussion
4. References
5. Summary of the main issues
6. Questions to the subgroup T5

1. General presentation of the CEP
(N. Capitaine, A. Brzezinski, cf p 155-160, Proceedings of the Journées1998)

Introduction
The coordinate transformation from the Terrestrial Reference System (TRS) to the Celestial Reference System (CRS) makes use of an intermediate pole to which refer precession and nutation. The present pole of reference is the Celestial Ephemeris Pole (CEP) which is supposed to be such that its motion both in space and within the Earth includes only secular and long periodic motions (i.e. longer than one day). This definition presents new difficulties due to the improvement of the accuracy of the theory and observations as well as to the change in the strategy of observations. Recent theories, at a microarsecond accuracy, includes indeed diurnal and sub-diurnal components both in the TRS and the CRS, some of them being of amplitudes larger than the current accuracy of the estimated Earth Orientation Parameters (EOP). Moreover, new strategy of observations provides estimation of these parameters with a sub-diurnal temporal resolution. The pole has therefore to be re-defined in consistency with this new situation (models, accuracy, observations) and the link of this pole to the instantaneous pole of rotation (IPR) has to be clearly specified.

The choice of the CEP
The theory of Earth rotation provides the solution for a ``z axis'' which can be, according to the author, the axis of angular momentum (Fedorov 1963, Kinoshita 1977), the axis of instantaneous rotation (Woolard 1953), the axis of figure or the Tisserand axis for a non-rigid Earth model (Wahr 1981). The transformation between theses axes are given by the Oppolzer terms in the CRS or ``diurnal nutation'' in the TRS.
   The instantaneous pole of rotation (IPR) has been the pole of reference for nutation during nearly one century, from the theory of Oppolzer (1886) to the IAU-1980 theory of nutation (Seidelmann 1982). It was considered at that time to be the most appropriate reference pole; the total forced luni-solar motion of the celestial pole as observed through optical astrometry was then arbitrarily divided into two parts : the celestial precession-nutation of the IPR and the ``diurnal polar motion'' (of the IPR), which was called ``diurnal (or dynamical) variation of latitude'' or ``diurnal nutation''. In the IAU-1964 theory of nutation (Woolard 1953), the reference pole was the IPR, but the geometrical and kinematical relations of the axis of rotation to the other axes considered in the theory of the rigid Earth were largely considered. The ``Oppolzer terms'' from the axis of angular momentum to the other axes were computed providing the forced periodic terms for the axis of figure and axis of rotation and consequently the nutations for the different poles.
    The choice of the axis of rotation has been questioned by Jeffreys (1963) and Atkinson (1973, 1975) and the IPR has been shown, during the discussion preparing the choice of a new theory of nutation from 1970 to 1980, to be not actually observable through the available observations at that time (optical astrometry, satellite observations) (Kinoshita et al. 1979).
Thus, in the IAU-1980 theory of nutation (Seidelmann 1982), a new reference pole has been adopted, the Celestial Ephemeris Pole (CEP) to which the numerical values of the conventional model refers; these numerical values have been computed such as they include the forced diurnal polar motion, which thus has no more to be considered as a separate part of the forced motion of the pole. A tentative conceptual definition of the CEP has been given as the ``pole that has no nearly-diurnal motion with respect to a space-fixed coordinate system or an Earth-fixed coordinate system'', or ``the center of the quasi-circular paths of the stars in the sky''. The geophysical meaning corresponding to such a property was ``the pole of the axis of figure for the mean surface of a model of Earth in which the free motion has zero amplitude''. Such a concept is that used by Wahr (1981) for its B-axis in the theory of rotation of a non-rigid Earth defined as the ``axis of figure for the Tisserand mean outer surface''. This conceptual definition of the CEP was rather confusing and the significance of the change from the instantaneous pole of rotation to the CEP has been largely discussed (Capitaine et al. 1985, Capitaine 1986). However, the use of the CEP does clarify the consideration of the predictable part of the motion of the celestial pole as considering the whole long-period part of this motion in the CRS as being the celestial motion of the CEP. Its realization is really closer to the actually ``observed pole'' than the IPR.

Current realization of the CEP
At the time of the adoption of the IAU-1980 theory of nutation, the CEP was realized by the IAU conventional models for precession (IAU-1976 precession) and nutation (IAU-1980 nutation), whichever was the technique used for the estimation of the EOP. The CEP was supposed to be such that it has no diurnal or quasi-diurnal motions both in space and within the Earth; however, the imperfections due to the conventional models for precession and nutation gave rise to retrograde diurnal terms in the TRS.
   Since 1980, there have been much change in processing observations of EOP and large improvement in the accuracy of the EOP estimates. The IAU conventional models, whereas much improved with respect to the previous ones, appeared to present deficiencies w.r.t. VLBI and LLR observations and to be therefore inadequate for highly accurate observations. Consequently, the VLBI observations provide on a regular basis, since 1980, the celestial pole offsets as observed 24h-estimates of the corrections to the conventional model. Such a procedure gives a position of the celestial pole with a better accuracy (0.1 mas in 1998), but it results in a change in the realization of the CEP and even in its definition. In such a realization, there is indeed no retrograde diurnal polar motion in the TRS and every diurnal prograde motion is absorbed in the residuals.
  More recently, an interim precession-nutation model has been provided (Herring 1995) in the IERS Conventions 1996 (McCarthy 1996) that matches the observations with uncertainties of +/- 1 mas and therefore can be considered as a more accurate realization of the CEP than the IAU conventional model, but not as accurate as that provided by the use of the celestial pole offsets.
   In fact, the definition of the CEP depends on the convention retained for the intermediate reference frame (origin on the equator, intermediate pole) in the transformation between the TRS and the CRS which is used in processing the observations.
 

Using a coordinate transformation expressed through the pole coordinates x_p y_p , the celestial pole coordinates X and Y (Capitaine 1990), and the stellar angle theta,
the CEP can be defined as (Brzezinski & Capitaine 1995) (see Fig. 1):
- the pole (of celestial pole coordinates X_m, Y_m as realized by the conventional model for precession-nutation as it is defined in the IAU-1980 nutation; it corresponds to the IAU 1980 definition of the CEP,
   - the pole (of celestial pole coordinates X', Y') as realized by the IERS 1996 precession-nutation; it corresponds to the pole as provided by the various techniques which estimate the EOP within the IERS Conventions but without using the celestial pole offsets,
   - the pole (of celestial pole coordinates X', Y') as realized through the conventional model for precession-nutation corrected for the celestial pole offsets estimated from observations; X', Y' are such that they include the whole long-period motion in the CRS (i.e. there is no retrograde diurnal motion of the pole in the TRS); it corresponds to the pole as realized through current VLBI one-day EOP estimates.
The total perturbation to be determined from observations which includes geophysical effects as well as deficiencies of the model, is the displacement of the pole axis, T, of the TRS from the pole axis, C', of the CRS' (as realized by an improved precession/nutation). It can be expressed, as converted into complex notation p=x_p-iy_p, P= X+i Y, as (Brzezinski & Capitaine 1993):

         p_t= p - P e^(-i*theta)               (1)

As the coordinate transformation between CRS and TRS is expressed by five parameters, of which only three are independent, there is a full degeneracy between polar motion p and nutation P in (1). For any unambiguous definition of the CEP, it is thus necessary to introduce an additional constraint defining which part of the residual motion is considered as polar motion (p) or nutation (P). In the current estimation of the EOP, the separation between the two parts are different according to the observing technique, processing of data and time resolution of the EOP estimates.
   Moreover, it must be pointed out that any separation becomes unclear for the sub-daily determination of the EOP (daily 1-hour estimate) which may justify to refer in such a case to the IPR as done by Bolotin et al (1997) for the analysis of an intensive VLBI campaign or to use a special procedure in processing the observations.

Reconsidering the definition of the CEP
    Several reasons require to reconsider the definition of the CEP in order to provide a more accurate realization of the pole of reference :
   - A new International Celestial Reference System, ICRS, realized by the direction of extragalactic radiosources has been adopted starting 1 January 1998 (Ma et al. 1998), in place of the FK5 which was based on positions and proper motions of stars. This provides a quasi-ideal CRS to measure the celestial motion of the CEP, but consequently requires a most accurate definition of this pole.
   - Improvements in the models have been recently achieved for precession-nutation and for diurnal and sub-diurnal polar motion. For precession and nutation, the results have been largely discussed within the IAU/IUGG WG on ``Nutation for a non-rigid Earth Nutation theory'' (Dehant 1999). This can lead to the theoretical realization of the pole of reference in the CRS at a 10 microarsecond level, but the correponding definition of the CEP should then be given at the same order of accuracy. However, the most recent series of nutation includes diurnal and semi-diurnal nutations in space (Bretagnon et al. 1997) with amplitudes of the order of ten microarseconds and recent models for polar motion also include diurnal and semi-diurnal variations with amplitudes of the order of one hundred microarseconds (Herring & Dong 1994) within the Earth due to oceanic tides. Therefore, the definition of the CEP has now to clearly specify how to consider these high frequency parts of amplitudes of the order of 10 microarseconds of the motion in the TRS and the CRS.
   - Recent changes have appeared in the strategy of observations. The sub-daily determinations of the EOP, with a level of accuracy of the order of 1 mas make less clear the distinction between high-frequency polar motion which appears in the terrestrial coordinates of the CEP and nutation which appears in the celestial pole offset. A special procedure has to be used in the processing of the data in order that the definition of the CEP is as accurate as the achievable accuracy of the observed motions of the pole.
    The concept corresponding to the CEP is not clear and does not specify how to consider the high frequency part of the motion in the TRS and in the CRS. Consequently, the definition cannot easily be extended to the most recent models and observations. A new definition of the CEP has therefore to be given in order to be in agreement with modern models and observations. The requirements for such a modern defintion are the following :
   (1) not to introduce any inaccuracy in the results,
   (2) to allow the data to provide the best astronomical and geophysical parameters,
   (3) to be based on clear concepts in consistency with the parameters used in the models and with the parameters actually estimated by observations.

2. Programme of the special session "Concept, definition and observations
of the Celestial Ephemeris Pole"
Journées 1998 "Systèmes de référence spatio-temporels", Paris, 21-23 September 1998
(conveners : N. Capitaine and A. Brzezinski)

Introductory papers, oral communications and posters
N. Capitaine, A. Brzezinski : Introduction to the session. Definition and observation of the pole at a microarcsecond accuracy
S. Mathews: Proposal for a new conceptual definition of the Celestial Ephemeris Pole and procedure for realization of the pole
P. Bretagnon : Diurnal and sub-diurnal nutations for a rigid Earth
A. Brzezinski, S. Petrov : Observational evidence of the free core nutation and  its geophysical excitation
Ch. Bizouard, S. Loyer, O.Titov : Diurnal and subdiurnal terms of geophysical origin in the pole motion
M. Folgeira, J. Souchay : The diurnal and sub-diurnal nutations calculated by different theories of rigid Earth rotation
B. Richter : Relation between precession/nutation and polar motion derived by a synthetic approach
Discussion: Present and future of the CEP

3. Contributions to the discussion  "Present and Future of the CEP"
Journées 1998 "Systèmes de référence spatio-temporels", Paris, 21-23 September 1998

I) COMMENTS ON THE DEFINITION AND DETERMINATION OF THE CEP by Ya. Yatskiv

Definition of the CEP depends on the observational technique used for determination of the Earth's rotation and has to be conventional.
In the 80-ies, this technique provides the determination of polar motion and nutation from observation with sampling interval Dt =1day of which the corresponding Nyquist frequency is s_N=W/2D t = 0.5 W (W being the frequency of Earth rotation).
So, it was useful to specify polar motion (pc) and nutation (nc) by their frequency ranges :

            - 0.5 W  < s <   0.5 W  for p_c
                                                                           in TRS    (A)
            - 1.5 W  < s < - 0.5 W  for n_c

It should be mentioned that from observations, one could determine the total displacement between the poles of TRF and CRF,

        i.e. : e = p_c- n_c

The specification (A) means that nearly diurnal polar motion (retrograde) is nutation. This was justified by relation of amplitudes for this free mode : a _n / a _p  = 430.
In 90-ies, diurnal variations of p_c in TRF and n_c in CRF were found. It means that there is a wide band spectrum of p_c and nc:

How to split e into pc and nc is a conventional problem.

One of very simple proposal is to compute the model of nutations for external gravitational forces only for axial-symmetrical Earth (not including terms from gravity terms S₃₁, C₃₁, S₄₁, C₄₁, etc.). It could be called astronomical gravitational nutation for rotational symmetric Earth model.

All other effects (diurnal and subdiurnal in nutations), one could consider as polar motion. Note that diurnal and semi-diurnal variations in nutation is very small, so it could not affect the polar motion determination.

I suggest to preserve the name of ephemeris pole to stress that position of this pole could be calculated and predicted from theory.

II) CONTRIBUTION TO THE DISCUSSION ON THE CEP by J. Vondrak

We have two sources of torques acting on the rotating Earth :

a) external, due to the Moon, Sun and planets (mostly predictable and long-periodic in celestial reference frame),

b) geophysical, due to the transfer of mass within the Earth and its nearest vicinity (mostly unpredictable and long-periodic in terrestrial reference frame).

The observations give the total orientation of the Earth in space (i.e., a sum of polar motion and precession-nutation). The CEP is an additional auxiliary axis that separate these two effects; it can be defined quite arbitrarily. In principle, there are two different approaches (concepts) possible to do it :

    1. Definition of CEP should contain only the predictable part of precession-nutation. In other words, only the terms excited by external torques are to be taken into account, the terms of geophysical origin are interpreted as polar motion.

    2. Precession-nutation on one side and polar motion on the other one should be observationally separable one from the other, independently of the adopted Earth model. This concept requires that different frequency windows (with no overlapping) are reserved for precession-nutation and polar motion.

In 1980, when the concept of CEP was adopted, there seemed to be no contradiction between these two different concepts; the definition as described by Seidelmann et al. was an attempt to reconcile them, on the level of observational accuracy of that epoch.

Now the situation is different: with today's accuracy of observations and progress in theory, there are overlaps of external and geophysical torques in the same frequency regions. Therefore I am convinced that we should select only one of the above mentioned concepts (without advocating any of them). We should not mix them togeteher, so that we have clear definition, well understable by the users and leading to no confusions that we are facing now.

III) CONTRIBUTION TO THE DISCUSSION CONCERNING THE CEP by A. Brzenzinski

Let us consider the following 3 points at the celestial sphere: C', representing direction of the celestial z-axis (i.e. z-axis of the ICRF) after applying the conventional precession/nutation model; T,  representing direction of the terrestrial z-axis (i.e. z-axis of the ITRF) in space; C_e, the Celestial Ephemeris Pole (CEP) representing an intermediate reference direction between C' and T. The motion of C_e relative to C' is called nutation while the motion of C_e relative to T is called polar motion.

Remark 1 : From  the point of view of the transformation ICRF/ITRF as well as of geophysical interpretation of Earth rotation, the only quantity of interest is a total perturbation of the terrestrial
z-axis in space, that is the vector C'T. Hence, any choice of the CEP is only a matter of the current observational practice and the adopted conventions.

Remark 2 : With exception of the cases C_e=C' and C_e=T, there are 4 parameters describing the vector C'T (2 for polar motion and 2 for nutation) while only 2 parameters are necessary. There is a full degeneracy between the polar motion and nutation parameters; see (Brzezinski & Capitaine, 1993; 1995) for details. This redundancy of the Earth orientation parameters (EOP) should be removed by imposing additional constraint which defines how much of the vector C'T is labelled as polar motion and how much as nutation.

Let us describe some possible choices for the CEP :

1. Dynamical approach : C_e =C'.
Nutation means only the astronomical nutation in this case, as expressed by the conventional model, while the whole perturbation C'T, including purely geophysical effects, is treated as polar motion.
This is the so-called polar motion gauge in the terminology of Eubanks (1993). One advantage of this approach is the conceptual clarity. Note, however, that the Free Core Nutation (FCN) appears in this case as a nearly diurnal retrograde polar motion, hence regular sub-diurnal measurements are necessary for monitoring this important signal (see Remark 3 below).

2. Frequency domain decomposition.
It is assumed that all perturbations of the vector C'T which are slow in space are treated as nutation while these variations which are slow with respect to the Earth are polar motions. This decomposition, corresponding to the definition of the CEP given by Seidelmann (1982), is routinely realized by the VLBI technique since about 2 decades. Such an approach is also convenient for geophysical interpretation as argued by Brzezinski & Capitaine (1993; 1995), but becomes unclear in the case of sub-diurnal observations because it is not specified how to treat these perturbations which are fast both in space and with respect to the Earth (e.g. diurnal prograde or semidiurnal variations). One possible parameterization for the last case is proposed in this discussion by Matthews.

Remark 3 : The FCN oscillation (Brzezinski & Petrov, this issue which has been observed since 1984 by VLBI, is extremely important from the point of view of geophysical interpretation of the EOP for the following reasons:
- it can be used to estimate the FCN parameters (the period of resonance T, the quality factor Q and the mean power of oscillation P) which are all of great geophysical interest;
- from the time domain comparison of the FCN signal with geophysical estimates of the excitation function, it is possible to constrain some parameters of the global atmospheric/oceanic circulation models.
For such investigations the length of the available FCN signal is a crucial factor, therefore any change in the definition of the CEP or, more generally, in the parameterization of Earth rotation, should be such that the monitoring of the FCN oscillation remains continuing in a homogeneous way.

IV) COMMENTS ON THE RE-DEFINITION OF THE CELESTIAL EPHEMERIS POLE by D.D. McCarthy

1. Current IERS Processing
Currently the IERS requests contributors of Earth orientation data to specify whether they have accounted for diurnal/subdiurnal variations in their analyses. The Central Bureau and the Sub-bureau for Rapid Service and Predictions then combine the data with all diurnal/sub- diurnal variations removed to produce daily estimates of the Earth orientation parameters. IERS Gazette 13 provides directions regarding the proper procedure to be used to interpolate the data and include the diurnal/subdiurnal variations.

2. Background of the CEP
When the currently official definition of the CEP was formulated it was decided that the CEP should in fact refer to a pole which did not move diurnally in space or with respect to the Earth's crust. The word "ephemeris" was chosen to emphasize that the pole was in fact specified by the "ephemeris" provided by the expressions and constants of the IAU 1980 Nutation model.

3. The Need for a Re-definition of the CEP
It is important that the CEP be re-defined to meet the current situation. At the time the current definition was formulated diurnal/subdiurnal variations were considered to be insignificant. The precision with which current observations are available make it necessary to refine the definition to take these variations into account. In fact the current IERS procedure does not agree with the current definition. At this time, when the IAU considering a new precession/nutation model, the definition of the CEP must be clarified so that the appropriate model can be formulated.

4. Considerations for a New Definition
Among the points to be considered in the re- definition of the CEP should be listed the desirability to make sure that the pole does not have large motions with respect to the ITRF. The majority of users of Earth orientation parameters want to be sure that the reference pole does not have extraneous motions due to the definition. It is also important that the definition not be dependent on any technique. The definition should be sufficiently general to include observations from any observational technique.

5. Euler Angles
The use of Euler angles may indeed be the most desirable means of providing the data necessary to transform between the terrestrial and celestial reference systems. The definition of Universal Time in such a formulation may be problematical but this should not be a major consideration since the purpose of the Earth Orientation parameters is chiefly to provide the transformations between the celestial and terrestrial reference systems and not to provide time.

6. Future
The IAU Working Group on Reference Systems needs to consider carefully and expeditiously the definition of the CEP. While the Euler angle representation may be the most desirable, sufficient work to implement the formulation practically has not yet been done. The proposal to base the definition on a division of the frequency spectrum of Earth orientation is attractive and
should be considered.

V) A NEW CONCEPTUAL DEFINITION OF THE CEP by P.M. Mathews

To be complete, the conceptual definition of the CEP should include a characterization of the high frequency parts of its motion in both the CRS and the TRS. It is proposed (see p 161 of the Proceedings of the Journées 1998) that the CEP be defined to be such that the motion of the CEP in the CRS includes all spectral components that are either of low frequency or are retrograde with respect to the CRS, and its motion in the TRS includes all components that are either of low frequency or are prograde with respect to the TRS. Put differently, all spectral components that are of frequencies less than 1/2 cpsd in the CRS (or equivalently, less than -1/2 cpsd in the TRS) are to be included in the celestial motion of the CEP, and all frequencies greater than 1/2 cpsd in the CRS (-1/2 cpsd in the TRS) are to be included in its terrestrial motion.
As a concomitant of such a definition, it would be necessary to specify or suggest necessary modifications of the procedures currently in use for the processing of space-geodetic data, in order to make it possible to extract the high frequency content of the celestial and terrestrial motions of the CEP from the volume of space geodetic data already available and from data being gathered following current practices.

VI) AN USEFUL GRAPHICAL REPRESENTATION OF THE PERIODIC EARTH'S ROTATION MOTIONS by S. Loyer

The recent sub-diurnal (up to 1 hour resolution) determinations of the Earth Orientation Parameters (EOP) raise some new problems concerning the definition of the intermediate axis used by the astronomical community to split the observed Earth's orientation variations into celestial and terrestrial parts. The lack of a clear definition appears particularly critical in the diurnal and sub-diurnal bands of the spectrum of the variations.

    Figure 3 put all together in the same quadrant the three hyperbolic parts of the curve defined by the relation T_e = T_W T_S / (T_W-T_S), (where T_W = 1 sidereal day),  taking into account all the possible values of T_S (corresponding to the spatial-frequency s_S) and T_e (corresponding to the Earth-frequency s_e). The retrograde (resp. prograde) motions, that correspond to a negative (resp. positive) value  of  the period, are marked on the graph with the - sign (resp. + sign). This provides a synthetic representation of the different Earth's motions of rotation as viewed from Earth or space which can help to choose a future definition.
    For example, the choice to include the new diurnal and sub-diurnal motions into the terrestrial parameters can be represented as a vertical line at T_S=2 days, such that all the sub-diurnal motions as the prograde diurnal motions are  expressed in the terrestrial frame. This conventional choice gives a preference to the terrestrial point of view for diurnal and sub-diurnal motions.
 
 

VII) COMMENTS ON THE EOP PARAMETERS by M. Rothacher

Subdaily estimations of EOP will be available on a regular basis very soon and the estimation of five unknown every 2 hours is not possible; a constraint to apply is that there is no retrograde diurnal polar motion. A proposal can be to estimate only three parameters which could be the Euler's angles including both polar motion and nutation.

VIII) REMARKS ABOUT THE OBSERVATIONS AND THE EOP PARAMETERS by H. Schuh

 1. The quality of the nutation series observed by VLBI is very poor before January 1984 because of the geometry of the VLBI network in these early days. That's why we (at DGFI) usually don't use these data for our nutation analyses.

2. The statement by Markus Rothacher to use three Earth orientation angles instead of five parameters had been proposed by several other colleagues in the past, too.
This idea seems to be good but its realization will show that many additional problems will occur and that's why it finally would complicate the situation and decrease the quality of the results.
The use of three parameters will cause very large diurnal variations because what could be expressed so far very elegantly by two nutation coefficients per 24 hours (in the celestial reference system) will need a very high resolution of the diurnal motion (in the  terrestrial reference system). Moreover, it will not give any benefit to those who analyse and interpret the data because later on the two effects (nutation, polar motion) which have different causes have to be split up anyway.  

  4. References

Atkinson, R.d'E., 1973, ``On the dynamical variation of latitude'', AJ 78, 147.
Atkinson, R.d'E., 1975, ``On the Earth's axes of rotation and figure'', MNRAS, 171, 381.
Bolotin, S., Bizouard, C., Capitaine N., 1997, ``High frequency variations of the Earth's instantaneous angular velocity vector :determination from VLBI analysis'', A&A 317, 601-609.
Bretagnon P., Rocher P., and Simon J.-L., 1997, ``Theory of the rotation of the rigid Earth.", A&A 319, 305-317.
Brzezinski A. and Capitaine N., 1993, ``The use of the precise observations of the Celestial Ephemeris Pole in the analysis of geophysical excitation of earth rotation", JGR 98, No. B4, 6667-6675.
Brzezinski A. and Capitaine N., 1995, ``Celestial Ephemeris Pole (definition, observability and determinations)'', in Proc. Journées Systèmes de Référence Spatio-Temporels 1995, N. Capitaine, B. Kolaczek and S. Débarbat, eds, pp 53-60.
Capitaine, N., 1986, ``The Earth rotation parameters : conceptual and conventional definitions'', A&A 162, 323-329.
Capitaine, N., 1990, ``The celestial pole coordinates'', Celest. Mech. Dyn. Astr.48, 127-143. Capitaine, N., Williams, J.G., Seidelmann, P. K. 1985, "Clarifications concerning the definition and determination of the Celestial Ephemeris Pole'', A&A 146, 381-383.
Dehant, V., 1999, Report of the WG ``Non-rigid Earth nutation theory'', in Proc. Journées Systèmes de Référence Spatio-Temporels 1998, N. Capitaine ed, Observatoire de Paris, p 73-78.
Eubanks T. M. (1993). Variations in the orientation of the Earth, in: Contributions of Space Geodesy to Geodynamics: Earth Dynamics, Geodynamics Series, 24, edited by D.E. Smith and D.L. Turcotte, 1-54, American Geophysical Union, Washington,
Fedorov, E.P., 1963, ``Nutation and forced motion of the Earth's pole", Pergamon Press, Ltd, Oxford.
Herring T.A., 1995, ``A priori model for the reduction of the nutation observations.", Highlights of Astronomy, Vol. 10, pp 222-227.
Herring, T.A. and D. Dong, 1994, ``Measurement of diurnal and semi- diurnal rotational variations and tidal parameters of Earth", JGR 99, 18051-18071.
Jeffreys, H., 1963, Forward (p xi) to ``Nutation and forced motion of the Earth's pole", by E.P. Fedorov, Pergamon Press, Ltd.
Kinoshita H., 1977, ``Theory of the rotation of the rigid Earth.", Celest. Mech. 15, 277-326.
Kinoshita H., Nakajima K., Kubo Y., Nakagawa I., Sasao T. and Yokohama K., 1979, ``Note on nutation in ephemerides'', Publ. Int. Lat. Obs. Mizusawa, 12, 71-108.
Ma, C.,Arias, E.F., Eubaks, M. Fey, A.L., Gontier, A.-M., Jacobs, C.S., Archninal, B.A., Charlot, P., 1998, ``The International Celestial Reference Frame as realized by Very Long Baseline Interferometry'', AJ 116, 516-546.
McCarthy D.D., 1996, ``IERS Conventions'', IERS Technical Note 21, Observatoire de Paris.
Oppolzer, T., 1886, ``Traité de détermination des orbites'', Gauthiers-Villars, Paris.
Seidelmann, P. K., 1982, 1980 IAU Theory of Nutation: the final report of the IAU working group on nutation, Celest. Mech. , 27, 79-106.
Wahr J.M., 1981, ``The forced nutations of an elliptical, rotating, elastic and oceanless Earth.", GJRAS, 64, 705-727.
Woolard, E. W., 1953, ``Theory of the rotation of the Earth around its center of mass'', Astr. Pap. Amer. Ephem. Naut. Almanach XV, I, 1-165.

5. Summary of the main issues of the discussion on the new definition of the CEP

The discussion has confirmed that a new definition of the CEP is necessary.
Several proposals have been presented in order to take into account the high frequency parts of the motion of the pole both in the CRS and the TRS. However, further discussions are necessary, especially with people involved in the processing of VLBI data, to choose the best way of considering the motions in the softwares.

This discussion will be continued within the subgroup T5 of the "ICRS" IAU Working Group and especially by the consideration of the questions in section 6.

It must be recalled that this discussion is based upon the 5 EOP representation (motions of the pole in the CRS and in the TRS + UT1). The comparison between other parameters representation (for example 3 angles) will be an other issue which will be considered inthe next Newsletter.

A summary of the main issues of the discussion is given below.

5.1 Current realization of the pole

The current realization of the pole uses the CEP as an intermediary pole separating the motion into:
- celestial motion of the CEP = long period terms in the CRS
- terrestrial motion of the CEP = long period terms in the TRS.

At the time of the adoption of the CEP, due to the required accuracy, the convention was such that:
- long periodic terms in the CRS = nutation,
- long periodic terms in the TRS = polar motion,

long periodic terms meaning periods > 2days , i.e -1/2 < s < +1/2 (with the frequency, s, in c.p.d.), except for the FCN which can be considered in the TRS.
 

These periodic terms can be represented as follows (with frequency s, such taht : s_TRS = s_CRS- 1) :

The VLBI estimates of the "celestial pole offsets" on a daily basis provide a strict realization of this separation. But, other techniques, not estimating the celestial pole offsets, do not provide the same pole and nothing is specified for the high frequency motion both in the CRS and TRS.

5.2 Extension of the conceptual definition of the CEP

In order to take account of :
- the diurnal and subdiurnal motions of the pole in the TRS at the microarsecond level,
- the prograde diurnal and semi-diurnal nutations in the CRS at the microarsecond level,
and to be not dependent on the techniques and strategy of observations,

two approaches are possible for giving a new conceptual definition of the CEP:

A) Dynamical approach : separation according to the physical cause

A.1. - the whole predictable part of the motion in the CRS, including diurnal and subdiurnal terms, is considered as the celestial motion of the CEP,
- other part of the motion of the pole is considered as polar motion of the CEP,

A.2. - the whole predictable part of the motion in the CRS, including diurnal and subdiurnal terms, is considered as the celestial motion of the CEP,
- the whole predictable part of the motion in the TRS, including diurnal and subdiurnal terms, is considered as the terrestrial motion of the CEP. This corresponds to the present IERS procedure (see 3. IV).

A.3. - the long periodic part of the predictable motion in the CRS is considered as the celestial motion of the CEP,
- the other part of the motion of the pole is considered as polar motion of the CEP.
This corresponds to the proposal 3. I).

B) Frequency approach separating the motion according to the frequency domain

B.1 Extension of the current definition of the CEP such that :
- all the motions of frequency s< 1/2 in the CRS are considered as celestial motion of the CEP,
- all the motions of frequency s> 3/2 in the CRS are considered as terrestrial motion of the CEP.

Such a definition keeps the symmetry in the frequency band between polar motion and celestial motion of the CEP, which is very logical. It corresponds to proposal 3. V).

B.2 Extension of the current definition of the CEP such that :
- all the motions of frequency existing in the CRS for the precession/nutation model (long periodic motions as well as prograde nearly-diurnal and semi-diurnal terms) are considered as celestial motion of the CEP,
- all the motions of frequency existing in the TRS for the diurnal and sub-diurnal motion of the pole are considered as terrestrial motion of the CEP.
This takes into account the motion according to its frequencies of the predictable motion both in the CRS and TRS.

5.3 Extension of the realization of the CEP

The conceptual definition of the CEP can be extended according to one of the options proposed in the previous section. However, it must be stressed that, whichever is the chosen conceptual definition, the separation into frequency domain becomes unclear for subdiurnal observations.

This is therefore not sufficient for realizing the CEP in an unambiguous manner and the realized CEP actually depends on the procedure which is used in processing the data. It is necessary to choose a procedure in order to make possible to extract the high frequency signal both in the CRS and the TRS.

Several procedures are possible:

C.1: to use the proposal 3. V) which allows to extract the high frequency signal in the processing of the observations, following the conceptual definition B.1.

C.2: to use the proposal 3. I), which put all the diurnal and sub-diurnal motions both in the CRS and the TRS, into estimated polar motion of the CEP which can be analyzed in a second step for providing the high frequency signal.

C.3: to process the observations in order to extract, in one step, all the diurnal and sub-diurnal motions in the CRS or the TRS in the estimated coordinates of the pole in the TRS .

C.4: to refer the motion of the pole, except the long-periodic precession and nutation, to the instantaneous axis of rotation whose kinematical properties are such that its motions in the TRS and CRS are linked by well-known kinematical relations. Such a procedure is based on the estimation of derivative of infinitesimal angles (Bolotin et al . 1997) in the coordinate transformation between CRS and TRS used in the processing of the observations.

6. Questions to the sub-group T5
 

1. Do you agree that a new definition of the CEP is necessary ?

2. Which option do you support for a new conceptual definition : dynamic approach (A1, A2 or A3) ?
or frequency approach (B1 or B2) ?

3. Which option do you support for a new realization of the CEP (C1, C2, C3 or C4) ?

4. Do you think that the use of one of these options can resolve the overlapping between terrestrial and celestial motions in the case of few hours estimates of the EOP ?

5. Do you think that such option can be implemented easily in the software for processing the data ?

6. Have you another suggestion which can be discussed among the subgroup T5 ?
 
 

Answers to be sent to : capitain@danof.obspm.fr