Estimation of crustal vertical movements with GPS in a geocentric frame, within the framework of the TIGA project.

Two complementary techniques coexist today to observe sea-level variations. Satellite altimetry observes sea-level on near-global and regular spatial and temporal sampling. However, this technique has not more than a few decades of existence. Due to inter-decadal variations in sea-level, altimetry does not provide access to long-period signals or secular changes. Long-term sea-level variations are accessible today by tide gauge measurements, having some of them continuous records since the 19th century. This technique is therefore the only way to directly observe the sea-level change during the 20th century, which represents a good indicator of climate change. However, the tide gauge estimates are contaminated by long-term vertical movements of the Earth's crust. To obtain the absolute long-term sea-level variation, the vertical movements of tide gauges can now be determined by the GPS technique. This approach is explored in practice since 2001 by the TIGA (Tide Gauge Benchmark Monitoring) pilot project of the International GNSS Service (IGS). Since 2002, the Consortium ULR (University of La Rochelle and the French National Geographic Institute) takes part in this project as a TIGA Analysis Center. Currently, more than 300 GPS stations globally distributed are processed, from which more than 200 are co-located with a tide gauge. My doctoral thesis work deals with the methodological study to improve the estimation of vertical velocities of GPS stations. A first part of my work has involved the study of the best processing strategy of the GPS data. Various models have been tested as, for example, the effects of antennae phase center variation and the tropospheric delay. Due to the large number of stations, the distribution into sub-networks is necessary for processing. An optimal and dynamical distribution of GPS stations has been developed and tested. The results showed that this procedure has greatly improved the quality of the GPS processing. Following the application of this new processing strategy, we obtained and exported products such as the station positions, the satellite orbits, the orientation parameters of the Earth, and the apparent motion geocenter, to be combined within the first GPS data reanalysis campaign of the IGS. The comparison of these products with other high-quality estimates provided a validation of the GPS processing strategy implemented as well as some clues for future improvement. In addition, the participation in this campaign has extended the International Terrestrial Reference Frame (ITRF) to tide gauges. The second part of my work involved the study of the GPS vertical velocity estimation. The coupled effect of periodic signals and discontinuities on the estimated velocities has been highlighted, showing the need to estimate these parameters in a consistent and rigorous way. Particularly, the effect of discontinuities has been reported as the current largest source of error in velocity estimation. The realistic velocity uncertainties were analyzed in depth by taking into account the correlated noise content in time series. By comparing the results of this rigorous analysis with the previous ULR solution, it was found a significant reduction in the correlated noise content. This is mainly due to the improved data processing strategy. The noise analysis has led to the demonstration that the temporal correlation of homogeneously reprocessed time series depends on the data epoch. In this way, it was shown that the noise content of long GPS time series is mainly due to the noise level of the oldest data. However, to get the smallest formal velocity uncertainty, it is necessary to use all the available data. It has been shown that by using the noise model most appropriate for each time series, the formal uncertainty of the velocity field agrees with the velocity differences obtained with respect to the next realization of the International Terrestrial Reference Frame, the ITRF2008.