-------------------------------------------------------------------------- IERS Working Group on the ITRF Datum Final Report 15 July 1999 -------------------------------------------------------------------------- Table of Contents ================= 0. Charter 1. Introduction 2. Specifications for the origin of the ITRF and motion of the geocenter Definition of ITRF origin Monitoring geocenter motions Stability of past ITRF origin realizations 3. Specifications for the scale of the ITRF and its time evolution Background General relativistic framework GM Satellite dynamics Troposphere Local eccentricities SLR-specific effects GPS-specific effects VLBI-specific effects DORIS-specific effects Factors in selecting solutions for scale realization Recommendation for ITRF scale realization 4. Specifications for the orientation of the ITRF and its rotational rates Orientation conventions Orientation rates Vertical constraints No-net-rotation constraint Attachment of EOP secular rates 5. Summary of datum specifications Definition of ITRF origin Monitoring geocenter motions Realization of the ITRF scale and its time evolution Conventional orientation of the ITRF and its rotational rates Use of full variance-covariance matrices 6. References -------------------------------------------------------------------------- 0. Charter ========== In May 1995 the Directing Board of the International Earth Rotation Service (IERS) established a Working Group on the International Terrestrial Reference Frame (ITRF) Datum to develop specifications for the precise datum definition to be used for future realizations of the ITRF. It is expected that these specifications will be incorporated into the next edition of the IERS Conventions, either in summary or in full. The members of the Working Group are: Geoff Blewitt Mike Heflin Horst Montag Claude Boucher Tom Herring Jim Ray (chair) Richard Eanes Jan Kouba Pascal Willis Martine Feissel Chopo Ma Valuable contributions to this Working Group have also been made by: Zuheir Altamimi Gerard Petit Hans-Georg Scherneck Marshall Eubanks John Ries Patrick Sillard Daniel Gambis -------------------------------------------------------------------------- 1. Introduction =============== The primary mission of the IERS is to provide timely and accurate data on the Earth's rotation and orientation in inertial space for current, real-time use and for long-term studies. For this purpose it has established and maintains an International Terrestrial Reference Frame (ITRF) and an International Celestial Reference Frame (ICRF). The relative motions of these two frames are monitored regularly by cooperating agencies, using the following space geodetic techniques: Lunar Laser Ranging (LLR) Satellite Laser Ranging (SLR) Very Long Baseline Interferometry (VLBI) Global Positioning System (GPS) Doppler Orbit determination and Radiopositioning Integrated on Satellite (DORIS) The ITRF is a realization of the International Terrestrial Reference System (ITRS); see IERS Conventions 1996 (McCarthy, 1996). The ITRS is specified in accordance with the resolutions of the International Union of Geodesy and Geophysics (IUGG), the International Association of Geodesy (IAG), and the International Astronomical Union (IAU). In particular, IUGG Resolution No. 2 (adopted at the 20th IUGG General Assembly of Vienna, 1991; see Appendix of IERS Standards 1992) applies. Conventionally, the geodetic term "datum" usually refers to a set of mathematical constants used to specify a reference surface against which coordinate values can be expressed. In the present modern context, "datum" is expanded to include the set of detailed specifications used to realize a specific reference frame given a broadly defined reference system. Historically the ITRF has been realized as a set of global Cartesian coordinates and velocities for the various contributing space geodetic observing sites. However, other representations for the ITRF have been suggested and could be considered; for example, using a time series of Cartesian coordinates. The ITRF is assembled from contributed sets of coordinates for the various techniques and analyses. The work is performed by the IERS Terrestrial Frame Section, hosted by the Laboratoire de Recherche en Geodesie (LAREG) of the Institut Geographique National (IGN), Paris. The complementarity of the independent techniques used by the IERS requires that an integrated approach be used to achieve the highest possible accuracy and consistency for the ITRF. All techniques can potentially contribute to the ITRF when given appropriate weights and after allowing for possible systematic differences. The advantage of using as many different techniques and solutions as possible is that the errors of the combined ITRF can be significantly smaller than for any of the individual contributors if the error sources are largely independent. This will also favor greater stability from one ITRF realization to the next and improved reliability. However, it is expected that, in some cases, the dominant errors in individual solutions will be primarily systematic in nature rather than random. This can make the determination of appropriate solution weights problematic. Since the ITRF should be as accurate as possible, and not merely stable from one realization to the next, care must be taken to ensure that the effects of systematic errors are identified and controlled to the extent possible. It is assumed that, following the practice begun with the ITRF94 realization, that all future ITRF combinations will use only those solutions which provide full variance-covariance information accompanied by the complete a priori constraint matrices. In this way, the ITRF can be formed and maintained in a rigorous fashion. Alignments in origin and orientation of successive ITRF realizations (see below) rely on the use of the full covariance matrices, which are made available to the ITRF user community. -------------------------------------------------------------------------- 2. Specifications for the origin of the ITRF and motion of the geocenter ======================================================================== Definition of ITRF origin ------------------------- IUGG Resolution No. 2 (1991; see Appendix of IERS Standards 1992) and the IERS Conventions 1996 recommend that the origin of the terrestrial reference system be "the geocenter of the Earth's masses", including oceans and atmosphere. It is realized by observations of the dynamics of satellites moving in the Earth's gravitational field. However, SLR data analyses have shown that the coordinate frame of tracking stations attached to the Earth's crust moves detectably relative to the Earth's center of mass. This translational motion, when viewed from a rigid crust-fixed frame, is known as "geocenter motion" and is caused by the mass movement of planetary fluids, primarily the atmosphere and oceans. The motions likely involve tidal, non-tidal, and secular components. Recognizing this phenomenon it is necessary to elaborate the expression in Chapter 5 of the IERS Conventions 1996 (McCarthy, 1996) for the basic transformation from the ITRF to an Earth-centered inertial frame, ECI, (relatable to the ICRF) as [ECI] = [P][N][R][W] {[ITRF] - [O]} where P, N, R, and W are the usual transformation matrices for precession, nutation, rotation, and wobble; all of these are time-dependent and computed explicitly with respect to the Earth's center of mass. O is a new time-dependent vector which gives the translation from the ITRF origin to the instantaneous geocenter, defined to be the center of mass of the Earth including oceans and atmosphere. The origin of the ECI is then implicitly the geocenter. [Note that the distinction between the geocentric ECI and barycentric ICRF has been somewhat neglected in previous IERS Conventions. The Conventions' transformation is implicitly geocentric whereas the IAU recommendations and IERS procedures for the ICRF are explicitly barycentric. The practical difference is mainly in the value for precession that must be used.] The origin of the ITRF must then be defined in some conventional sense, presumably a convention that miminizes O over an appropriate time interval. The instantaneous vector position of a point on the Earth's surface can be expressed in the ITRF (see Chapter 3 of the IERS Conventions 1996) as X(t) = X_o + V_o * (t - t_o) + Sum{ delta X_i(t) } where X(t) is the vector position of the point relative to the ITRF origin as a function of time t; X_o and V_o are the vector position and velocity of the point at the reference epoch t_o; delta X_i(t) are site-specific corrections due to various time-varying effects including solid Earth tidal displacements (the full tidal correction including the effect of the permanent tide), ocean tidal loading, etc.; The set of positions and velocities at epoch t_o (X_o and V_o) constitutes the ITRF realization. The origin of this system is most conveniently defined as the time-averaged position of the Earth's center of mass (including oceans and atmosphere) over a specified interval. Given the significant effects expected in the diurnal/semi-diurnal band due to tides, the averaging interval should be an integral number of days. To minimize the error in its determination, the averaging interval should be reasonably long. Recognizing that annual and semi-annual variations are probably important also, a multi-year period is indicated. In practice, given the currently limited abilities of the dynamical observing techniques to accurately measure geocenter motions (see IERS Technical Note 25), it is recommended that the origin realized by the ITRF94 frame be adopted as defining the conventional origin of the ITRF. Subsequent ITRF realizations will maintain the initial ITRF94 origin thereafter by successive optimal Helmert alignments. The origin stability of past ITRF realizations is discussed in a following sub-section. Note that no change is recommended in handling the "permanent tide" part of the solid Earth tide site displacements (see Chapter 3 of the IERS Conventions 1996). This convention means that the ITRF coordinates are effectively for a "non-tidal Earth," which is not directly accessible to observation. Whatever theoretical arguments may be offerred in opposition to this practice, they are not sufficient to recommend a change a practice which was made universal within the space geodetic community during the MERIT campaign (Melbourne, et al., 1983). Monitoring geocenter motions ---------------------------- Given the formulation above, which allows for arbitrary (albeit presumably small) translational motions between the Earth's center of mass and the ITRF origin, the IERS must theoretically be prepared to coordinate observations and distribute appropriate results for the geocenter motions that allow the instantaneous origin vector O to be specified accurately, much as the EOP service is already done. Before embarking on such an ambitious expansion of IERS responsibilities, however, a better understanding is needed of the magnitude of geocenter motions and of the current ability of the observing techniques to measure the effects. To address these questions, the IERS, during its 1996 Workshop, asked the Working Group to conduct an investigative campaign. A call for participation was issued in January 1997 for the "IERS Analysis Campaign to Investigate Motions of the Geocenter." Researchers from about 30 groups responded with proposals to analyze satellite tracking data for both tidal and non-tidal signals, to analyze data for geophysical excitations (including oceanic, atmospheric, and other fluid motions), and to compare and synthesize the analysis results. The activities of the campaign have been publicized at the Web site http://maia.usno.navy.mil/geoc.html. The campaign culminated in a special session at the Fall 1997 AGU Meeting in San Francisco. The overall impression of the work presented there was that the net motion of the terrestrial reference frame relative to the Earth's center of mass is detectable but small, probably no more than about 1 cm in any component. The diurnal and semi-diurnal tidal variations appear to be well determined and in good agreement with modern ocean tidal models. There seems to be some general agreement of the techniques in detecting seasonal variations, although more work remains to be done in this area. Geophysical computations of the expected motions based on global fluid motions are only roughly consistent with the observations. Reports by the participants in the geocenter campaign have been collected into IERS Technical Note 25. As a result of the geocenter analysis campaign, the following set of recommendations was adopted: 1) A tidal model for the diurnal and semidiurnal geocenter motions should be adopted based on an ocean tide model such as CSR3.0 (M. Watkins & R. Eanes, Geophys. Res. Lett., 24(17), 2231-2234). This model should be included in the next edition of the IERS Conventions. Suggestions to include the geocenter effect into the standard ocean loading coefficients, as a convenience for some users, are not recommended as this could lead to confusion. 2) Because the satellite techniques do not yet seem reliable for measuring variations at other frequencies, a simple seasonal model should be investigated for the principal non-tidal motions. Such an empirical model could be based on a weighted combination of the analysis results, similar to the procedure described by H. Montag (see IERS Technical Note 25). However, results currently available do not yet justify recommending such models for general use. The IERS terrestrial reference frame section at IGN is asked to continue studies of this type to evaluate future improved observational data and analysis methods. 3) General geocenter monitoring can be continued in two ways: the new IERS coordinating center for Monitoring of Global Geodynamical Fluids (MGGF) has a subcenter devoted to computing offsets of the ITRF origin from the geocenter due to large-scale fluid motions; and the ITRF section will soon begin to compute monthly realizations of the terrestrial frame which can be compared with the fluid motion effects. When detection of non-tidal geocenter motions appears feasible the situation can be reassessed. Stability of past ITRF origin realizations ------------------------------------------ The IERS has adopted the origin of the Center for Space Research (CSR, University of Texas) SLR solution as the origin of all ITRF realizations prior to ITRF94. Based on a consensus of the attendees at the ITRF Workshop held in May 1995, the origin definition of ITRF94 was broadened to use the weighted average of the origins of all qualifying SLR and GPS solutions, of which 5 were available. The relationship of the ITRF94 origin to prior realizations is shown in the table below, indicating that the ITRF has attained an origin stability of about 1 cm, with determinations of the Z component being somewhat poorer than X or Y. (Nominally, the ITRF96 and ITRF97 realizations were constrained to maintain the ITRF94 datum in origin, orientation, scale, and their time derivatives.) Translations of origin from ITRF94 to previous ITRF realizations (mm) ---------------------------------- X Y Z -------------------- ITRF88 18 0 -92 ITRF89 23 36 -68 ITRF90 18 12 -30 ITRF91 20 16 -14 ITRF92 8 2 -8 ITRF93 6 -5 -15 ITRF94 reference ITRF96 =0 =0 =0 ITRF97 =0 =0 =0 ---------------------------------- (all at epoch 1988.0) During the past few years, GPS and DORIS have also demonstrated the sensitivities of these satellite techniques to geocenter determinations. Each possesses the advantage of more uniformly global tracking networks compared with the SLR, especially DORIS, and GPS observes continuously a rich constellation of 24 satellites. On the other hand, the relatively high altitude of the GPS satellites and the larger non-gravitational forces which apply reduce the geocenter sensitivity of this technique. It is clear, nonetheless, that improvements in modeling of the non- gravitational forces on the GPS satellites have led to steady improvement of the GPS geocenter estimates. In particular, it has been shown that the GPS frame origin is sensitive to changes in the modeling of small stochastic orbit velocity changes and radiation pressure parameters (see Kouba et al., 1996). Shifts in the Y- and Z-axis directions can be especially significant. Improvements in orbit modeling together with other advances, such as global phase ambiguity resolution, have reduced the scatter of some daily GPS geocenter estimates to the ~1-cm level in X and Y and the few-cm level in Z. Weekly geocenter offset results are available from the IGS as part of their ITRF densification project though the efforts of the three global network associate analysis centers (GNAACs), which form rigorous combinations of GPS station solutions from the seven IGS analysis centers. Recent DORIS results likewise indicate that a similar level of sensitivity may have been attained. Consequently, use of suitable solutions for SLR, GPS, and DORIS, appropriately weighted, should be considered for realization of the ITRF origin and to monitor motions of the geocenter. However, given the much longer observing history available for SLR and the need for long orbit arcs to best define the long-term geocenter location, long-arc SLR analyses should be given greatest weight for definition of the origin. The other dynamical techniques must be shown to give comparable results and their error characteristics (both systematic and random) quantified before being utilized for the ITRF origin and geocenter tracking. -------------------------------------------------------------------------- 3. Specifications for the scale of the ITRF and its time evolution ================================================================== Background ---------- All of the techniques of the IERS are sensitive to the scale of the terrestrial frame at the several ppb (10^-9) level or better, where a 1 ppb scale error corresponds to an global station height error of 6.4 mm. Therefore all techniques could potentially contribute to the definition of the ITRF scale. However, it is expected that the dominant scale errors in individual solutions will be primarily systematic rather than random because determinations of station heights are generally most sensitive to bias effects. Care must therefore be taken to ensure that the effects of systematic errors are controlled to the greatest extent possible. The effects of several known sources of scale error are considered below. Effects of a geophysical nature (such as atmospheric pressure loading), which would apply to any of the techniques, are not discussed here; it is expected that such errors will contribute primarily random type errors to the combined ITRF provided that sufficiently long data spans are available. General relativistic framework ------------------------------ In 1991, the IAU and the IUGG resolved that high-accuracy geodetic systems must recognize the significance of relativistic effects and recommended that results be formulated in a geocentric frame using Geocentric Coordinate Time (TCG). For historic reasons, this is hardly ever (perhaps never) actually done in data analyses. While satellite-observing systems do normally reduce their data in a geocentric frame, the time scale used is generally the previously defined Terrestrial Dynamical Time (TDT = TAI + 32.184 s) or an equivalent. In this case, the resulting terrestrial reference frame will differ in scale from the IAU/IUGG recommended TCG scale by a known amount: X_TCG = [ 1 + Ue] X_TDT where Ue is the Earth's gravitational potential, G*Me/Re, divided by c^2, estimated to have a value of 0.6969... ppb. Likewise, if the IERS Standards 1992 (McCarthy, 1992) are followed for VLBI and the usual TT coordinate timescale is used for the observations, then the scale difference will be the same (G. Petit, private communication, 1996): X_TCG = [ 1 + Ue] X_VLBI(92) On the other hand, if the IERS Standards 1992 are used and the VLBI observations are modelled as geocentric observables by applying the relationship that TCG = TT * (1 + Ue), then the resulting coordinate frame will naturally be geocentric. However, if the IERS Conventions 1996 for the VLBI modeling are used instead together with TT observables, then a different rescaling is needed (G. Petit, private communication, 1996): X_TCG = [ 1 - Ue] X_VLBI(96) In practice, all VLBI analyses apparently use the 1992 Standards and TT timescales. Thus, a rescaling of their coordinate results by (1 + Ue) is necessary. These are truly scale errors in the sense that the estimated terrestrial reference frames can be rescaled after being determined -- with no loss of precision -- in order to be consistent with TCG units. Most other types of scale error mentioned below will be partially absorbed into other parameter estimates which renders a posteriori rescaling ineffective as a method to compensate for neglected effects. In practice, the ITRF first implemented the IAU/IUGG recommendations on TCG in the ITRF94 realization by applying an a posteriori rescaling to all the contributed reference frames of [1 + (0.7 ppb)]. GM -- The appropriate value for GM will depend on the time scale used. For TDT, the rescaling relation given above applies for the value GM = 398600.4415 km^3/sec^2; for a fully geocentric formulation conforming with IAU/IUGG recommendations using TCG, then the value GM = 398600.4418 km^3/sec^2 applies (J. Ries, private communication, 1996). The standard GM value is uncertain by ~2 ppb. This is equivalent to an SLR scale uncertainty of 1.3 ppb, since the SLR frame sensitivity to the value of GM is about 2/3. This sensitivity value has been demonstrated empirically for SLR, but the corresponding sensitivity for GPS and DORIS remains to be determined. Satellite dynamics ------------------ The satellite-observing techniques should apply appropriate relativistic corrections in modeling the satellite dynamics. Otherwise, there will be scale errors as much as the ~0.7 ppb level, although the effects can be partly absorbed into dynamical parameters. Troposphere ----------- The effect of mismodeling the path delay due to the troposphere can potentially introduce a scale error for any of the techniques. Only the radiometric techniques, however, are sensitive to the "wet" component of the troposphere delay, which is particularly difficult to model apart from including additional parameters in the data analysis. Such troposphere parameters introduce significant correlations between troposphere estimates and the station heights. Errors in the troposphere mapping function used in the data analysis will cause station height errors and hence scale errors. In addition, azimuthal variations in the tropospheric delay, primarily due to the wet component, have been detected in VLBI and GPS analyses. North-south gradients in the "dry" component of the tropospheric delay, due to the equatorial bulge, affect all the techniques. Generally, the tropospheric error is larger for VLBI, GPS, and DORIS than for SLR. It is thought to be ~1 ppb for state-of-the-art tropospheric mapping functions and analysis procedures. Local eccentricities -------------------- A colocation site is one at which two or more geodetic techniques have made measurements, and for which an accurate three-dimensional tie is available to relate the systems. Colocation sites with well determined local ties are of primary importance for the ITRF and are critical to the inter-technique combination. They are currently the sole basis for connecting the individual terrestrial reference frames combined in the ITRF. Errors in the local eccentricities can be large and will be systematic for a given station but their effects can generally be expected to average down to a reasonable level provided that a large enough number of colocation sites is available. The errors can be most pronounced for stations with infrequent occupations over a long time span where a single large eccentricity error will produce a biased velocity estimate. If large enough and at an important colocation site, such errors can bias the frame scale and its time evolution. SLR-specific effects -------------------- Station-dependent ranging biases, which affect the station height determination, can influence the terrestrial frame scale if there are large errors for important colocation sites. Errors of this type are thought to be responsible for the significant difference in the scale rate-of-change seen in the ITRF94 combination, where the CSR SLR frame contracts by about -0.7 ppb/yr compared with four VLBI solutions. In addition, the accuracy of the optical constants used in the Marini- Murray model for SLR data analyses limits the accuracy of the SLR scale to ~0.5 ppb. GPS-specific effects -------------------- Although GPS antennas have an all-sky field of view to permit simultaneous observations of multiple satellites, the phase response of the antennas is unlikely to be perfectly hemispherical. Because the antenna phase patterns are primarily elevation angle-dependent, the effect is largely a shift in the apparent station height and hence frame scale. Until 1996, most GPS analyses were made without applying any corrections for realistic antenna phase patterns. Indeed, when corrections measured under laboratory conditions have been applied for the IGS network of mostly Dorne Margolin (DM) choke-ring antennas, scale increases of 10-15 ppb have been observed relative to ITRF. Consequently, the IGS has decided, for the time being, to apply only measured in situ differential corrections for non-DM antennas with respect to a DM standard and to apply no corrections for the DM antennas themselves (Beutler, 1996). This partially resolves problems with using mixed antenna types but does not address any potential absolute scale effects due to the predominant DM antennas. There are potentially similar effects caused by the GPS satellite transmitting array antennas. These could couple in complex ways with the patterns of the tracking station antennas, perhaps even offsetting one another to some extent. Another type of antenna-related error is caused by multipath effects in the local environment. Some types of signal scattering from the antenna mount itself have been shown to produce systematic shifts in apparent station height (Elosegui et al., 1995). To the extent that such effects may be globally distributed and similarly oriented, especially if they affect colocation sites, the frame scale derived from GPS will be biased. The tropospheric effects have been mentioned above. VLBI-specific effects --------------------- The most important influence on the VLBI scale is likely to be modeling of tropospheric path delay (see above). There are a variety of other antenna-related effects (such as axis offset errors, antenna deformations, etc.) which might also be significant but these are likely to be approximately random on a global scale, given a sufficiently large well-distributed set of VLBI stations. However, the relative sparseness of stations in some parts of the globe, especially in the southern hemisphere, could lead to significant scale-like distortions of the frame. DORIS-specific effects ---------------------- As for the other techniques, any systematic error affecting the measurements could influence the scale. The troposhere is of course a major source, considering that presently no analysis group considers a gradient approach in modeling the wet delay. Concerning the ionosphere, the correction should be excellent as the two DORIS frequencies are far apart (2 GHz and 400 MHz). Nevertheless, it must be noted that all analysis groups use the same correction computed by CNES and given in the measurements files. Even if they are mostly unlikely, the possibility of a small systematic error still exists here. Concerning antenna effects, DORIS is very specific because only two types of antenna are used by all the stations (starec and alcatel). Multipath effects (which would appear at the satellite as it is an up-link system) have never been detected. Another specific aspect of DORIS is that a significant number of beacons are located on islands where some short-term vertical motions have been detected for some stations. Factors in selecting solutions for scale realization ---------------------------------------------------- The IERS adopted the scale of the CSR SLR solutions as the scale of all ITRF realizations prior to ITRF94. Based on a consensus of the attendees at the ITRF Workshop held in May 1995, the scale definition of ITRF94 was broadened to use the weighted average of all qualifying VLBI, SLR,and GPS solutions, of which 7 were used. Unlike previous realizations ITRF94 was rescaled a posteriori (by 1 + 0.7 ppb) in an attempt to comply with the effect of IAU/IUGG resolutions recommending a geocentric frame and TCG units. The relationship of the ITRF94 scale to prior realizations is shown in the table below, indicating that the ITRF has attained a scale stability of ~1 ppb or < 1 cm in station height. (Nominally, the ITRF96 and ITRF97 realizations were constrained to maintain the ITRF94 datum in origin, orientation, scale, and their time derivatives.) Scale differences from ITRF94 to previous ITRF realizations ---------------------------------- D D* dH ppb ppb mm -------------------- ITRF88 7.4 8.1 52 ITRF89 4.3 5.0 32 ITRF90 0.9 1.6 10 ITRF91 0.6 1.3 8 ITRF92 -0.8 -0.1 -1 ITRF93 0.4 1.1 7 ITRF94 reference ITRF96 =0 =0 ITRF97 =0 =0 ---------------------------------- D = reported scale differences at epoch 1988.0 D* = D + 0.7 ppb, to "correct" for shift in ITRF94 GR frame dH = equivalent station height shift of D* scale difference As noted above, all IERS techniques, properly weighted, should be considered for defining the ITRF scale. However, given the current uncertainties concerning the absolute calibration of the GPS scale due to antenna effects, a more prudent course might be to exclude the use of GPS solutions until the matter is resolved. The IGS weekly combinations of global GPS results have found scales from the 7 Analysis Centers which differ from ITRF by several ppb. Some consideration should be given to selective editting of solution results before combination when suspiciously large vertical velocity values are determined and where evidence exists to cast doubt on the legitimacy of the result. Particular attention should be given to incorrect system bias or local eccentricity values, especially for colocation sites. Analysis Centers should consider prior editting of such data based on their expertise or should indicate those results they believe to be suspect. It appears likely that errors of this type are responsible for the scale rate-of-change difference of about -0.7 ppb/yr observed between the CSR SLR frame and four VLBI solutions used in ITRF94. This discrepancy corresponds to station height changes of 4.5 mm/yr, an effect large compared to important geophysical processes such as sea level change and post-glacial rebound. Recommendation for ITRF scale realization ----------------------------------------- The ITRF scale should not be considered subject to conventional definition (which would be equivalent to redefining the timescale). Each ITRF realization should inherit the optimally weighted scale (and time evolution) of the input frames that are combined, after applying any rescaling that may be needed to account for differences from TCG time. Until it is demonstrated that the absolute scale of GPS-based frames is reliable at about the 1 ppb level, these should not be used in the realization of the ITRF scale. -------------------------------------------------------------------------- 4. Specifications for the orientation of the ITRF and its rotational rates ========================================================================== Orientation conventions ----------------------- Basically, it is recommended that the procedures previously used (Boucher et al., 1996) to rotationally orient ITRF94 and to establish its rotational time evolution be retained for future realizations with minor modifications. The orientation is intended to maintain the Conventional International Origin (CIO) definition for the reference pole and the International Reference Meridian (IRM) approximately aligned with the Greenwich meridian. The CIO was established as the mean location of the Earth's pole of rotation between the years 1900 and 1905 as measured by the five observatories of the International Latitude Service (ILS). The CIO and the IRM were maintained by the Bureau International d'Heure (BIH) independently following their adjustment in 1967. Subsequently the IERS has maintained its own reference pole (IRP) and IRM consistent the BIH orientations for epoch 1984.0 within an uncertainty of 5 mas. The overall uncertainty in the tie of the IRP with the CIO is about 30 mas. The current procedure to align the axes of each new combination of results from the various techniques is to remove any net rotational offsets relative to the previous realization at reference epoch 1988.0. For ITRF94 relative to ITRF92 (ITRF93 was not used because rotational offsets had been introduced in that realization) the alignments were determined at the 0.1 mas level. One aspect of this procedure could be considered for revision. The reference epoch 1988.0 may no longer be appropriate considering that GPS and DORIS data were not available until the past few years. Consideration should be given to shifting the reference epoch to a more current date. Orientation rates ----------------- If the possibility of relative motions between points on the surface of the Earth is allowed (e.g., tectonic plate movements, among others) then three singularities arise when estimating simultaneously station velocities and EOPs. That is, a global rotational rate for the terrestrial frame is indistinguishable from an opposing drift rate in the EOP rates. Various approaches can be considered to resolve this rank deficiency. Following the IUGG Resolution No. 2 (1991; see Appendix of IERS Standards 1992) recommendation that the ITRS "have no global residual rotation with respect to horizontal motions of the Earth's surface", the ITRF is constrained such that there are no net rotational rates relative to the NNR-NUVEL-1A global plate motion model. For ITRF94 relative to ITRF92, the rotation rates were determined at the 0.01 mas/yr level. These constraints are applied using only one point per site in order to avoid over-weighting sites with numerous colocated stations. Stations located with tectonically unstable regions are excluded from the constraint. Vertical constraints -------------------- In the ITRF94 realization the time evolution condition was actually applied to 7 degrees of freedom rather than to the 3 listed above. That is, the NNR-NUVEL-1A rotational condition was augmented with the additional requirement that there be no net vertical motion, to also remove any net translational motion of the origin and any net change of scale. While these additional adjustments are certainly reasonable given the significant number of suspiciously large vertical motions included in some of the contributing solutions, this approach might not provide the most stable long-term framework. In particular, the global vertical velocity field probably does possess low degree deviations from zero (certainly post-glacial rebound effects are expected) which, combined with the highly non-uniform distribution of ITRF sites, could introduce slight velocity biases. Since the techniques themselves should be sensitive to the motion of the origin (except for VLBI) and to scale changes, it might be preferable to rely more heavily upon the data to determine these quantities. However, to do so reliably may require more careful screening of submitted results in order to remove or suppress erroneous or suspicious velocity values (see above). No-net-rotation constraint -------------------------- The actual list of sites included in the no-net-rotation constraint should be made explicit. Sites located in regions of known tectonic deformation, such as near plate boundaries, and which are not used for the no-net-rotation constraint should be identified for ITRF users. Attachment of EOP secular rates ------------------------------- Closely related to rotational rates of the sites is the effect on the secular drifts of the EOPs. With the current IERS treatment of EOPs and TRFs independently, significant differences in EOP rates between solutions are common. This creates difficulties in forming EOP combinations. Theoretically this problem might be resolved by combining TRF and EOP (and CRF) results simultaneously, using the full variance- covariance matrices. In this way, EOP rates and TRF velocities should be consistent. Based upon recommendations that emerged during the IERS 1996 Workshop, the IERS Directing Board is committed to pursuing larger scale combination efforts but it will probably be some time before any operational capability exists. The Analysis Centers and the technique services are encouraged to develop methods and procedures to facilitate this effort. -------------------------------------------------------------------------- 5. Summary of datum specifications ================================== Definition of ITRF origin ------------------------- To account for geocenter motions, it is necessary to elaborate the expression in Chapter 5 of the IERS Conventions 1996 (McCarthy, 1996) for the basic transformation from the ITRF to an Earth-centered inertial frame, ECI, (relatable to the ICRF) as [ECI] = [P][N][R][W] {[ITRF] - [O]} where P, N, R, and W are the usual transformation matrices for precession, nutation, rotation, and wobble; all of these are time-dependent and computed explicitly with respect to the Earth's center of mass. O is a new time-dependent vector which gives the translation from the ITRF origin to the instantaneous geocenter, defined to be the center of mass of the Earth including oceans and atmosphere. The instantaneous vector position of a point on the Earth's surface can be expressed in the ITRF (see Chapter 3 of the IERS Conventions 1996) as X(t) = X_o + V_o * (t - t_o) + Sum{ delta X_i(t) } where X(t) is the vector position of the point relative to the ITRF origin as a function of time t; X_o and V_o are the vector position and velocity of the point at the reference epoch t_o; the set {X_o, V_o} is usually regarded as constituting the ITRF realization; delta X_i(t) are site-specific corrections due to various time-varying effects including solid Earth tidal displacements (the full tidal correction including the effect of the permanent tide), ocean tidal loading, etc.; The origin realized by the ITRF94 frame is adopted as defining the conventional origin of the ITRF. Subsequent ITRF realizations will maintain the ITRF94 origin thereafter by successive optimal Helmert alignments. Monitoring geocenter motions ---------------------------- A tidal model for the diurnal and semidiurnal geocenter motions should be adopted based on an ocean tide model such as CSR3.0 (M. Watkins & R. Eanes, Geophys. Res. Lett., 24(17), 2231-2234). Because the satellite techniques do not yet seem reliable for measuring variations at other frequencies, a simple seasonal model should be investigated for the principal non-tidal motions. However, results currently available do not yet justify recommending such models for general use. Realization of the ITRF scale and its time evolution ---------------------------------------------------- The ITRF scale should not be considered subject to conventional definition (which would be equivalent to redefining the timescale). Each ITRF realization should inherit the optimally weighted scale (and time evolution) of the input frames that are combined. In practice, it is usually necessary to apply a rescaling of [1 + Ue], equivalent to [1 + (0.7 ppb)], to all the contributed reference frames in order to comply with the IAU/IUGG recommendations on the use of the TCG timescale. Until it is demonstrated that the absolute scale of GPS-based frames is reliable at about the 1 ppb level, these should not be used in the realization of the ITRF scale. Conventional orientation of the ITRF and its rotational rates ------------------------------------------------------------- No change is recommended in the current procedure of aligning the axes of each new ITRF realization to remove any net rotational offsets relative to the previous realization. In this way, the IERS successively maintains its International Reference Pole (IRP) -- aligned within the measurement error with the previous Conventional International Origin (CIO) -- and International Reference Meridian (IRM), approximately aligned with the Greenwich meridian. The IUGG recommends that the ITRF have no global residual rotation with respect to horizontal motions of the Earth's surface. This is achieved by constraining the ITRF so that there are no net rotational rates relative to a global plate motion model; currently the NNR-NUVEL-1A model, with possible recent refinements, is regarded as best for this purpose. The list of actual sites included in the no-net-rotation constraint should be published. Sites located in regions of known tectonic deformation, such as near plate boundaries, and which are not used for the no-net-rotation constraint should be identified for ITRF users. Use of full variance-covariance matrices ---------------------------------------- Future ITRF combinations should use only those solutions which are submitted with full variance-covariance information accompanied by the complete a priori constraint matrices. Alignments in origin and orientation of successive ITRF realizations rely on the use of the full covariance matrices. The Analysis Centers and the technique services are encouraged to develop methods and procedures to include Earth orientation parameters together with their terrestrial frames. This would allow joint simultaneous combinations of TRF and EOP results and should permit greater consistency to be achieved between EOP and TRF results. -------------------------------------------------------------------------- 6. References ============= Beutler, G., Executive summary, in Proceedings of the 1996 IGS Analysis Center Workshop (Silver Spring, MD), edited by P. VanScoy and R.E. Neilan, Pasadena, CA, Jet Propulsion Laboratory, JPL Publication 96-23, xi-xvi, 1996. Boucher, C., Z. Altamimi, M. Feissel, and P. Sillard, Results and analysis of the ITRF94, IERS Tech. Note 20, Obs. de Paris, 1996. Elosegui, P., et al., Geodesy using the Global Positioning System: The effects of signal scattering on estimates of site position, J. Geophys. Res., 100(B7), 9921-9934, 1995. Kouba, J., G. Beutler, and Y. Mireault, GPS orbit/clock combinations and modeling, in Proceedings of the 1996 IGS Analysis Center Workshop (Silver Spring, MD), edited by P. VanScoy and R.E. Neilan, Pasadena, CA, Jet Propulsion Laboratory, JPL Publication 96-23, 3-8, 1996. McCarthy, D.D. (Ed.), IERS Standards 1992, IERS Tech. Note 13, Obs. de Paris, 1992 (Appendix contains IAU, IAG, and IUGG Resolutions). McCarthy, D.D. (Ed.), IERS Conventions 1996, IERS Tech. Note 21, Obs. de Paris, 1996. Melbourne, W., R. Anderle, M. Feissel, R. King, D. McCarthy, D. Smith, B. Tapley, and R. Vicente, Project MERIT Standards, U.S. Naval Observatory Circular No. 167, 1983.