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IERS Conventions Workshop -- Position Paper for Sessions 2 & 5
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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)
(last updated 22 June 2007)
Introduction
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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:
* Class 1 ("essential") 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 are not adjusted in the data analysis. Therefore, we
prefer that their 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. 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 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 a complete and consistent
set of the necessary models of the Class 1 and Class 2 types, including
implementing software. 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 (essential and geophysically based) and
generally obey the following selection criteria:
* include subdaily tidal variations -- Since the beginning of space
geodesy, the basic observational unit 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 by itself is
inadequate for the 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, but any residual model errors will be strongly attenuated in
data processings that use 24-hr integrations (or multiples).
* 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 independent of the geodetic data -- In order to
avoid circular reasoning and the possibility of propagating geodetic
errors into conventional geophysical models, the applied models should
be fully independent of the geodetic analyses which depend on them.
Ideally they 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.
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 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 conventional 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).
Conventional 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, at least for those techniques that observe the
dynamical motions of near-Earth satellites, which 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 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.
* 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 and its special bureaux, together with all necessary supporting
information, implementation documentation, and software. Expansion of
the IERS Conventions, Chapter 7, could include some essential aspects of
this material to inform users, as Class 3 models. Continued research
efforts are strongly encouraged, 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. 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 contaminations and less affected by network
effects, but this is unlikely to be significant for those 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, 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 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 in
aposteriori studies and to better inform users for other research studies
which are strongly encouraged.
* 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
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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