## 1. Introduction

[2] ITRF2005, the newest release of the International Terrestrial Reference Frame (ITRF) as a realization of the International Terrestrial Reference Systems (ITRS) [*McCarthy and Petit*, 2004], is a set of positions and velocities of points located on the Earth's surface. For the first time, it is associated with a set of consistent Earth orientation parameters (EOPs) taking an important step to ensure consistency among the International Earth Rotation and Reference System Service (IERS) products [*Altamimi et al.*, 2007]. As with previous versions, the ITRF2005 solution has been computed using data from the four main space geodetic techniques, very long baseline interferometry (VLBI), satellite laser ranging (SLR), Global Positioning System (GPS) and Doppler orbitography and Radio-positioning Integrated by Satellites (DORIS), together with local ties at colocation sites. The use of these four techniques is essential to take advantage of the strengths of each for the benefit of the combined frame. For the first time, ITRF2005 input data are in the form of time series of station positions and EOPs with their full variance-covariance matrices.

[3] The strategy adopted for the ITRF2005 combination has two steps [*Altamimi et al.*, 2007]. The first step is the independent computation of a long-term stacked Terrestrial Reference Frame (TRF) for each measurement technique under the assumption of linear motions. A unique set of positions and velocities is computed for every observing station of each technique in a reference system specific to the technique. The associated EOPs are readjusted simultaneously to make them consistent with their stacked TRFs. Thus for each technique the first computation step produces a consistent set of station positions and velocities, and EOPs together with their full covariance matrix. In the second step these individual secular reference frames are combined making use of local intertechnique ties to yield positions and velocities for every point, with time-varying EOPs, in a consistent and well-defined global frame.

[4] The intertechnique combination requires an assessment of the consistency of the long-term site motions given by the various measurement techniques. Beginning with ITRF2005 it is now possible to assess the nonlinear motions through the residuals of the first computational step. We need to investigate what lessons can be learned from their study to improve the secular reference frame combination process and to probe whether technique-dependent systematic errors are detectable. Only the height component is investigated here because most geophysical signals, as well as most systematic errors, are expected to be largest in this component.

[5] Indeed, due mainly to gravitational attraction by celestial bodies, internal mass flows, and various mass redistributions at the Earth's surface between the ground, the atmosphere and the ocean, the Earth's crust is continuously deforming. This deformation is one of the signals that geophysicists wish to measure and understand. One of the main tasks of geodesy is to try to model as accurately as possible all other effects which may contaminate the measurements. Ever since geodetic coordinate repeatability became sufficiently precise to detect predicted loading motion, geodetic measurements have been used to try to validate geodynamical models. Atmospheric pressure and continental water loading have been detected in various studies, using alternatively GPS [*van Dam et al.*, 1994; *van Dam et al.*, 2001], VLBI [*van Dam and Herring*, 1994; *Petrov and Boy*, 2004], or DORIS observations [*Mangiarotti et al.*, 2001]. Most of the time, these studies provide an acceptable agreement between geodetic positioning and theoretical model predictions but the measurements cannot be fully explained by the models. Power spectra of the GPS coordinate time series have been the most widely studied. *Blewitt and Lavallée* [2002] have analyzed the spectral content of GPS height time series and have clearly detected annual and semiannual signals as well as higher harmonics. *Dong et al.* [2002] tried to explain the significant annual and semiannual (“seasonal”) signals in GPS height time series by investigating all possible individual contributions; less than half of the observed seasonal motion can be explained by known loading effects. More recently, *van Dam et al.* [2007] have compared GPS height residual time series to GRACE gravity field observation over Europe, and show that the agreement is not yet achieved. According to *Titov and Yakovleva* [1999], annual signals have been also detected in VLBI baseline length time series; a semiannual signature has also been identified for some baselines. A more complete study has been led by *Petrov and Ma* [2003]: The motion of every VLBI telescope has been modeled by sums of harmonics whose terms have been estimated simultaneously from the time delay observations. Significant annual signals have been detected and partly attributed to hydrological loading. *Petrov and Ma* [2003] also revealed that VLBI annual vertical motions are positively correlated with the annual motion measured by colocated GPS observations from *Dong et al.* [2002]. *Ding et al.* [2005] have also compared GPS and VLBI computed time series at colocated sites. Their wavelet analysis of the half-monthly sampled GPS and VLBI time series exhibits signals with time-varying amplitudes. The annual signal was in phase for both techniques but exhibited higher amplitude for GPS. Interannual signals have also been proved to be correlated for most of the considered colocated sites. Fewer studies have been conducted concerning nonlinear motions in SLR position time series. More recently, *Ray et al.* [2007] have analyzed the general spectral content of these three techniques by computing stacked periodograms of the ITRF2005 position residuals and loading displacement models. They have emphasized that GPS station positions contain harmonics of the 1.04 cpy frequency, up to the sixth.

[6] These previous studies have emphasized that only a part of the displacement observed could be attributed to the real motion of the ground. Systematic errors may degrade the observed displacements, notably on the height component. Indeed, any nonmodeled or mismodeled contribution affecting the range measurements or the station a priori motions can contribute to the station position time series scattering. Also, as shown by *Stewart et al.* [2005], the impact of unmodeled tidal signals in the geodetic observation processing can cause aliasing into longer-period signals. Thus each space geodetic technique acts as a filter of the measurements, creating its own artifact signals.

[7] Here, we aim at comparing the height measurements provided by GPS, SLR and VLBI which are known to have the best internal precision [*Altamimi et al.*, 2007]. This intertechnique comparison aims at detecting possible individual technique systematic errors with the limitation that any common systematic error will not be detected. This work is an assessment, at the time of the ITRF2005 release, of the agreement in the height estimates among the three techniques. The input time series span more than 10 common years, with continuously weekly samplings for GPS and SLR, and irregular 24-h intervals for VLBI. We have analyzed these three solutions to separate the nonlinear motion of individual points from the global motion and biases that affect the whole set of stations. Unfortunately, this procedure cannot be fully realized since station displacements may alias into the global parameters. We have consequently evaluated the possible error introduced. The comparison of the derived height residuals is then achieved in two main steps. The spectral contents of the height residual time series are first investigated to search for significant common spectral lines in the data sets. The study then focuses on the annual signal which is the most significant common spectral line. Next, we develop a method based on Kalman filtering and maximum likelihood estimation (MLE) to assess height time series similarities and compute correlation coefficients. This method is applied to height time series for sites with sufficient common data spans from multiple techniques.