----------------------------------------------------------------------------- IERS Conventions Workshop -- Position Paper for Sessions 2 & 5 ----------------------------------------------------------------------------- Principles for Conventional Contributions to Modeled Station Displacements J. Ray, National Geodetic Survey, NOAA (USA) Z. Altamimi, Institut Geographique National (France) T. van Dam, University of Luxembourg (Luxembourg) T. Herring, Massachusetts Institute of Technology (USA) (Final version -- updated 27 September 2007) Introduction ------------ According to Chapter 4 of the IERS Conventions 2003 (McCarthy and Petit, 2004), the modeled instantaneous position of a terrestrial point can be represented as a function of time "t" approximately as X_m(t) = Xo + [Vo * (t - to)] + [SUM_i dX_i(t)] eqn (1) where "Xo" and "Vo" are regularized positions and velocities at the reference epoch "to". In most cases, the velocity term measures primarily long-term tectonic motions although any anomalous local components are also easily captured by empirical measurements provided that the drifts are very nearly linear. Problems arise in the application of this model when the local motions are significantly non-linear, as caused for example by inflation/deflation of volcanic terranes or by episodic tectonic events. In such cases, the affected sites are normally either excluded from consideration in realizing terrestrial reference frames or their motion is treated as a series of discrete linear segments. According to the text of Chapter 4, the summation in eqn (1) above includes various "high-frequency time variations (mainly geophysical ones)" based on a set of conventional "corrections". It should explicitly include effects for "solid Earth tides, ocean loading, pole tide, atmospheric loading, and geocenter motion", even though the actual frequency range for each type of motion is not described. Moreover, Chapter 7 gives incomplete specifications for handling geocenter motions. On the other hand, some of the models provided include significant low-frequency components despite the description in Chapter 4. Some researchers interpret eqn (1) to include non-tidal displacements even though the IERS Conventions give no specific sanction to this view. We take as a self-evident foundational principle that the set of effects to be considered as contributing to local station displacements and the conventional models to be applied for their compensation should be guided by rational and well considered bases, and should not be developed haphazardly or randomly. For historical reasons and general consistency, it might be prudent to retain some past practices even if they are not fully consistent with the adopted principles; but future expansions should be determined by specified rules. This position paper proposes such a set of guidelines and rationales for IERS Conventions updates. Guiding Principles for IERS Conventions Models ---------------------------------------------- Concerning the types of models and effects that should be considered within the scope of the IERS Conventions, we first distinguish three general classes based on their applications: * Class 1 ("reduction") models are those recommended to be used apriori in the reduction of raw space geodetic data in order to determine geodetic parameter estimates, the results of which are then subject to further combination and geophysical analysis. Obviously, the accuracy of these models directly impacts the quality of geodetic determinations; any deficiencies will show up as increased post-fit data residuals or as biased estimates. A good example is the solid Earth tide model for station displacements. Commonly, the Class 1 models are accepted as known apriori and ideally are not adjusted in the data analysis. (This is not strictly true in all cases, such as for the tropospheric delay component of radio observations where no apriori model is sufficient to treat water vapor variations without adjustment.) Therefore, we prefer that Class 1 model accuracy be at least as good as the geodetic data (1 mm or better). Class 1 models are usually derived from geophysical theories. Apart from a few rare exceptions, the models and their numerical constants should be based on developments that are fully independent of the geodetic analyses and results that depend on them. Otherwise a logically circular situation can arise and supposedly geophysical models can be corrupted by obscure technique-related systematic errors. (Again, this ideal cannot always be satisfied fully, such as in modern nutation models where some parameters must be determined from VLBI data.) The geodetic results obtained are intimately and subtly bound to these models and cannot be correctly interpreted otherwise. So it is vital for inter-solution combinations that various analysis groups use the same Class 1 models or very nearly the equivalent. This is the main reason for establishing the original set of modern conventions during the MERIT era (Melbourne et al., 1983). * Class 2 ("conventional") models are those that eliminate an observational singularity and are purely conventional in nature. This includes many of the physical constants. In some cases, a choice can be made to adopt a specific model as a purely conventional representation instead of a physical specification. For instance, one could adopt a specific no- net-rotation (NNR) plate tectonic model as "the" rotational rate datum for the International Terrestrial Reference Frame (ITRF) by convention and no longer follow the physically based recommendation of the International Union of Geodesy and Geophysics (IUGG) that the ITRF rotation rates should integrate to zero over the Earth's actual surface. In that case, users must be aware of the convention adopted and avoid misinterpreting NNR deviations in ITRF velocities as geophysically significant. * Class 3 ("useful") models are those that are beneficial (or even necessary in some sense) but are not required as either Class 1 or 2. This includes, for instance, the zonal tidal variations of UT1/LOD. An accurate zonal tide model is not absolutely required in data analysis though it can be helpful and is very often used internally in a remove/restore approach to regularize the apriori UT1 variations to simplify interpolation and improve parameter estimation. In addition, such a model is very much needed to interpret geodetic LOD results in comparisons with geophysical excitation processes, for instance. However, Class 3 model effects should never be included (that is, removed from the observational estimates) in the external exchange of geodetic results unlike Class 1 effects. Serious misunderstandings can otherwise occur. The IERS Conventions should strive to present as complete and consistent a set of the necessary models of the Class 1 and Class 2 types as possible, including implementing software. In some cases, the individual IERS Technique Services may adopt additional Class 1 models that are unique to a given observational method. These might not in all instances be documented in the IERS Conventions, but it would be very helpful to include references to those external models. Where conventional choices must be made (Class 2), the Conventions provide a unique set of selections to avoid ambiguities among users. The resolutions of the international scientific unions and historical geodetic practice provide guidance when equally valid choices are available, but models of the highest accuracy and precision are always preferred. Examples of Class 3 models are included when their use is likely to be sufficiently common or to minimize potential user confusion. Selection Criteria for Conventional Displacement Contributions -------------------------------------------------------------- The contributions to be considered in the summation term of eqn (1) should be of the Class 1 type (for data reductions and geophysically based) and generally obey the following selection criteria: * include complete subdaily tidal variations -- Since the beginning of space geodesy, the basic observational unit for reference solutions of the highest quality has consisted of data processing integrations for 1 solar day or multiples. This choice provides a natural filter to dampen variations with periods near 24 and 12 hr (and higher harmonics) caused by environmental, geophysical (tidal), and technique-related sources. However, 1-day integration alone is inadequate for the very highest accuracy applications. Unmodeled subdaily site variations can efficiently alias into other geodetic parameters, such as the 12-hr GPS satellite orbits. Moreover, they can alias into longer-term effects, rather than average to zero exactly, under certain conditions (Penna and Stewart, 2003). In order to minimize such difficulties, all tidal displacements with periods near 24/12 hr and having amplitudes of about 1 mm and greater should be included apriori using conventional models. The most accurate models available should be applied; any residual model errors may be further attenuated in data processings that use 24-hr integrations (or multiples). Accurate subdaily models are especially important for positioning when much shorter observational spans are used. * model corrections must be accurate -- It is imperative that when adjustments are applied directly to observational data based on any model, the errors introduced by the model must be much smaller than the effect being removed. This should be true over the full spectral range affected but especially over intervals equal or smaller than the geodetic integration span. If random errors in the subdaily band are increased, for instance, at the expense of reducing systematic variations at seasonal periods in 1-day processing samples, then it is clear that the corrections should not be applied apriori. Instead, suitably filtered corrections may be considered in aposteriori studies without suffering any degradation of the original geodetic analysis. * models must be as independent of geodetic data as possible -- In order to avoid circular reasoning and the possibility of propagating geodetic errors into conventional geophysical models, the applied Class 1 models should ideally be fully independent of the geodetic analyses which depend on them. The models should be founded on geophysical theories and principles that do not directly derive from geodetic results. Only in a few exceptional cases where geophysical theory is inadequate (such as some parameters of the nutation model) is it necessary to rely upon geodetic estimates within an adjusted geophysical framework. * prefer models in closed-form expressions -- For practical reasons of implementation, portability, and independence of processing venue, closed-form analytical models for site displacements are most attractive. This is the norm for most tide models, but it is generally not feasible for non-tidal effects, for instance. * flexibility in interpretation of geodetic results -- To the extent that geodetic results are sensitive to any particular geophysical effect and the models for that effect are not necessarily uniquely well realized or accurate, it is often desirable to measure the relative performance of alternative models. In order to do so easily, geodetic results should be presented to researchers in a form that readily facilitates such comparisons as much as possible. Generally this implies strong preference for aposteriori treatment of model displacements that are outside the subdaily band rather than requiring multiple processings of the same data with various different apriori models. Note that this recommended practice is consistent with the traditional approach that has been used to interpret excitation of Earth orientation variations, for example. In consequence, use of Class 3 models apriori in data analyses should be avoided, at least for operational IERS solutions. Recommended Revision of Conventions Introduction ------------------------------------------------ It is recommended that the Introduction of the IERS Conventions be amended to include, in substance, the guiding principles and the selection criteria for conventional displacements presented above. Recommended Revision of Conventions Chapter 4 --------------------------------------------- Based on the above considerations, it is recommended that the text of the IERS Conventions, Chapter 4, section 4.1.3, be replaced starting from the 4th paragraph to the end of the section with the following new text (see also Ray et al., 2004): "The general model connecting the instantaneous apriori position of a point anchored on the Earth's crust at epoch t, X(t), and a regularized position X_R(t) is X(t) = X_R(t) + [SUM_i dX_i(t)] (11) The purpose of the introduction of a regularized position is to remove mostly high-frequency time variations (mainly geophysically excited) using regularization corrections dX_i(t) in order to obtain a position with regular time evolution. Among other reasons, such a regularization permits improved estimation of the actual instantaneous station positions based on observational data. In this case, X_R(t) can be expressed by using simple models and numerical values. The current station motion model is linear (position at a reference epoch t_o and velocity): X_R(t) = X_o + X-dot * (t - t_o). (12) The numerical values are (X_o, X-dot), which collectively constitute a specific TRF realization for a set of stations determined consistently. For some stations it is necessary to consider several discrete linear segments in order to account for abrupt discontinuities in position (for example, due to earthquakes or to changes in observing equipment). Recommended models are presented in Chapter 7 for the presently recognized dX_i(t) corrections, namely those due to solid Earth (body) tides, ocean tidal loading, polar motion-induce deformation of the solid Earth (pole tide), ocean pole tide loading, and loading from the atmospheric S1/S2 pressure tides. All of these models, except the atmospheric S1/S2 pressure tides, include long-period variations outside the subdaily band. While not necessary, this approach is recommended in order to maintain consistency with longstanding practice and to minimize user confusion. Station displacements due to non-tidal loadings are not recommended to be included in operational solutions but studies for research purposes are encouraged. The compensating counter motions of the solid Earth due to all the fluid loading effects ("geocenter motion" of the observing networks relative to the ITRF origin) should generally be included in the modeled station displacements described by the regularization corrections, at least for those techniques that observe the dynamical motions of near-Earth satellites and respond to the center of mass of the total Earth system. Additional station-dependent corrections may be recommended by the various Technique Services due to effects that are not geophysically based but nonetheless can cause position-like displacements. These generally affect each observing methods in distinct ways so the appropriate models are technique-dependent and not specified by the IERS Conventions." Handling Non-Tidal Displacements in Data Reductions --------------------------------------------------- It is our specific recommendation that displacements due to non-tidal geophysical loadings not be included in the apriori modeled station positions, that is, the summed dX_i(t) contributions in eqn (1). These effects fail all of our contribution selection criteria given above. Even if the somewhat arbitrary preference for models in closed-form expression (which is inconsistent with non-tidal models) is relaxed, the other more important criteria cannot be ignored. The most serious obstacles are: * reliability in the subdaily band -- At best, non-tidal environmental models attempt to compensate mostly for seasonal variations, which are well outside the normal integration intervals for space geodetic data. None of the available global circulation models properly accounts for dynamic barometric pressure compensation by the oceans at periods less than about two weeks. Instead, both "inverted barometer" (IB) and non-IB implementations are produced as crude approximations of the actual Earth system behavior even though these are both recognized as unreliable in the high-frequency regime. While effective at longer periods (especially seasonal), the undesirable and unknown degradation that would affect subdaily integrations (not only for geodetic parameters, but also for any other parameters estimated from the observations) is not an acceptable side-effect. This is particularly compelling when one considers that non-tidal loading effects can be readily considered in aposteriori studies with no loss whatsoever. * inaccuracies of the models -- The basic types of studies and analyses that are normally considered a precondition to adoption of a conventional model are mostly lacking for non-tidal models. Documentation of error analyses is a basic requirement that must be fulfilled. In their statistical comparison of several publicly available atmospheric pressure loading services, van Dam and Mendes Cerveira (2007) have identified differences up to several mm (RMS) due to effects of varying model parameters and input data choices. This study does not account for possible common-mode error sources. Before general users can be expected to routinely utilize non-tidal loading services sensibly, it is vital that the major sources of systematic differences identified in such studies be resolved. Studies of other loading effects are also mandatory. The approach considered by Koot et al. (2006) in their study of various models for atmospheric angular momentum (AAM) is a good example of how a combined series might be formed to reduce series-specific noise. This type of development should be considered in the provision of all non-tidal loading results, partly as a convenience to users as well as a potentially improved product. * must be free of tidal effects -- Any non-tidal displacement corrections applied should be strictly free of residual tidal contaminations, otherwise the geodetic results will be adversely affected by aliasing and possible duplication of the directly modeled tidal signals. This is not always assured in operational loading services currently available. * long-term biases in the reference frame -- Because available environmental models do not yet conserve overall mass or properly account for exchange of fluids between states, use of non-tidal models in solutions for the terrestrial reference frame will generally suffer from long-term drifts and biases that are entirely artificial. This is a completey unacceptable circumstance. Before routine adoption of such models, methods must be found to overcome these types of problems. * new datum requirements for the reference frame -- Introducing pressure-dependent non-tidal site displacement contributions into standard geodetic solutions would necessitate the adoption of a global reference atmospheric pressure field. The ITRF reference coordinates (mainly height) for any given site would depend directly on the associated reference pressure for that site. In order to minimize deviations from the established frame, one would probably prefer that the reference pressures closely match long-term average pressure values at every possible geodetic site. But the lack of long-term in situ met data from many locations could make such a goal unreachable. Furthermore, many ITRF users would probably not welcome nor understand the expansion of the ITRF datum to include such non-geodetic quantities as reference pressures. In certain other non-tidal loading cases, it might also be necessary to consider additional non-geodetic quantities as reference datum contributors (such as local mean temperatures). If non-tidal displacements are not allowed, then there is no ITRF requirement to adopt a conventional reference pressure field, though this might still be considered and might be useful for other reasons. Note that it is important to continue development of improved, unbiased methods to derive local apriori pressure values globally in order to properly model tropospheric delay effects optimally, which in turn is necessary for accurate station height estimates. * need to easily test alternative models -- As noted above, it is vital to be able to compare different non-tidal models easily and efficiently, something that is not facilitated by direct inclusion of the models apriori into geodetic analyses. It is far simpler to make such comparisons and studies aposteriori as has been done for many years in research into the excitation of Earth orientation variations. However, in solutions where non-tidal displacements have nonetheless been applied, it is imperative that the full field of corrections used must be reported in new SINEX blocks that will need to be documented. The availability of such information will permit only an approximate removal of the non-tidal corrections, though, if the applied sampling is finer than the geodetic integration interval. We recommend that models of non-tidal station displacements be made available to the user community through the IERS Global Geophysical Fluid Center (GGFC) and its special bureaux, together with all necessary supporting information, implementation documentation, and software. The GGFC should provide the most reliable and consistent set of "validated" Class 3 loading models at the top level of its service websites. Models for each fluid load should be as consistent as possible with those of all the other loads, though this goal is inherently limited by the available fluid circulation models. The GGFC should also undertake to provide the necessary accurate assessments, considering errors in the raw fluid fields as well as modeling errors and choices. Additional non-tidal loading models may also be distributed for other specialized or research purposes, but these should be clearly distinguished from the set described above. Expansion of the IERS Conventions, Chapter 7, is recommended to include some essential aspects of this material to inform users, as Class 3 models. Continued research efforts are strongly encouraged into all aspects of using non-tidal loading models, particularly to address the outstanding issues listed above. However, in the meantime non-tidal displacements must not be included in operational data reductions that are contributed to the IERS to support its products and services. Consideration of Non-Tidal Displacements in ITRF ------------------------------------------------ Not withstanding the preceding remarks, we believe that further research is warranted into the possible utility of including non-tidal loading displacements in the formation of ITRF, aposteriori to the reduction of the space geodetic data. It is currently assumed implicitly in the ITRF procedures that varying site deformations, such as those due to loading, average out in the long-term stacking of time series of coordinate frames from each technique. If the loading models have a SNR greater than 1, at least at seasonal periods, then the averaging should be more effective if the load corrections are applied during the stacking. Furthermore, any effects of sparse networks and non-continuous observing ("network effects") should also be reduced. This is likely to be more important for the weaker SLR and VLBI networks than for GPS and DORIS. Such an approach could be implemented in the first step of the ITRF process, where the individual technique coordinate frame time series are stacked, by HELMERT{ XYZ_k(x,t) - LOAD(x,t) } --> TRF_k(x,v) where HELMERT{} represents the long-term Helmert alignment of the time series of frames XYZ_k from technique k with the total non-tidal displacement effects, LOAD, being applied. Each of the load contributions would need to be integrated over the same time intervals as the frame increments. The result would be a long-term frame TRF_k for each technique consisting of the usual reference positions x and velocities v. Time series of station residuals could be generated in two ways Res_k.withload(x,t) = XYZ_k(x,t) - TRF_k(x,v) and/or Res_k.noload(x,t) = (XYZ_k(x,t) - LOAD(x,t)) - TRF_k(x,v) and the characteristics of each compared and assessed. The time series of the Helmert parameters would be nominally free of loading effects and at least some part of the network effects. This is likely to be most significant for those parameters dominated by the SLR or VLBI contributions, such as the overall ITRF scale variations and geocenter motions (the Helmert translations from SLR). The EOP time series would also be free of loading components affecting station positions and less affected by network effects, but this is unlikely to be significant for those EOP components dominated by GPS observations. In the second step of ITRF formation, to combine the technique long-term frames, no further loading corrections are needed. Before such a procedure as this could be considered for operational use, careful studies would be required. Among other things, the issues raised in the previous section must be carefully evaluated, particularly the possibility of long-term biases in the loading models that could adversely affect the stability of ITRF. If this is a problem, the loading fields could be detrended for secular variations before being used in the ITRF stackings, for instance. Consideration would also be needed of the consequences for user applications and interpretation, particularly for the EOPs. Use of non-tidal loading models in this aposteriori way would affect only globally integrated estimates (Helmert parameters, EOPs, and ITRF itself). The potentially degrading effects discussed before of applying the models apriori at the observation level would be avoided. The inter-station vectors of individual technique coordinate frames, for example, would not be affected by high-frequency noise from the load models and simultaneously estimated non-geodetic parameters would be similarly unaffected. Summary of Recommendations -------------------------- * revise IERS Conventions Introduction -- It is recommended that the Introduction of the IERS Conventions be amended to include, in substance, the guiding principles and the selection criteria for conventional displacements presented here. * revise Conventions Chapter 4 -- It is recommended that the text of the IERS Conventions, Chapter 4, section 4.1.3, be modified as given above to clarify which contributions should be treated as conventional. * handling non-tidal displacements -- It is recommended that non-tidal station displacements not be included as conventional contributions. However, it is further recommended that IERS Conventions, Chapter 7, be expanded to include the essential aspects of using non-tidal models as Class 3 models in aposteriori studies and to better inform users for other research studies which are strongly encouraged. The GGFC is encouraged to provide accuracy assessments for all recommended non-tidal loading models and to establish "validation" standards for a consistent set of loading models. * study of non-tidal displacements in ITRF -- It is recommended that methods and the possible benefits of applying aposteriori corrections for non-tidal station displacements be carefully investigated in the stacking of ITRF solutions. However, no changes to actual ITRF operations are advocated at the present time. References ---------- Koot L, de Viron O, Dehant V (2006) Atmospheric angular momentum time-series: Characterization of their internal noise and creation of a combined series. J Geod 79:663-674. DOI 10.1007/s00190-005-0019-3 McCarthy DD, Petit G (2004) IERS Conventions 2003. IERS Technical Note 32, Frankfurt am Main: Verlag des Bundesamts fuer Kartographie und Geodaesie Melbourne W, Anderle R, Feissel M, King R, McCarthy D, Smith D, Tapley B, Vicente R (1983) Project MERIT Standards. U.S Naval Observatory Circular No. 167 Penna NT, Stewart MP (2003) Aliased tidal signatures in continuous GPS height time series. Geophys Res Lett 30(23):2184. DOI 10.1029/2003GL018828 Ray J, Dong D, Altamimi Z (2004) IGS reference frames: Status and future improvements. GPS Solutions 8:251-266. DOI 10.1007/s10291-004-0110-x van Dam TM, Mendes Cerveira PJ (2007) Statistical comparison of publicly available atmospheric loading corrections. Proc. IERS Workshop on Combination, GeoForschungsZentrum, Potsdam, Germany, 10-11 October 2005 (in press); see also presentation at http://www.iers.org/documents/workshop2005/presentations/ Session-4_van_Dam.pdf