Recovering non-linear vertical land movement from multi-mission altimetry, tide gauge and GPS records

Driven by postglacial rebound, surface mass redistribution, inter- and intra-plate tectonic stress and anthropogenic effects, vertical land motion (VLM) of the Earth's crust occurs over a range of spatial and temporal scales. VLM provides a link between absolute sea-level (ASL) observed by a satellite altimeter (ALT) and relative sea-level (RSL) observed at the coast by a tide gauge (TG). Accurate estimates of VLM are critical for improving our understanding of the impact of sea-level changes at the coast. VLM at TG locations are often obtained from the Global Positioning System (GPS) or, in many cases, predicted from models of glacial isostatic adjustment (GIA) - both of which have limitations across space and time. Several studies have, alternatively, attempted to estimate VLM at TGs using the difference between ALT ASL and TG RSL records, although this approach has several potential restrictions: 1) residual altimeter systematic errors over regional domains may be non-negligible but remain to be investigated; 2) VLM is represented by a linear model which neglects any temporal variability; and 3) the method assumes that there is no trend or substantial non-linear variability in ASL between the ALT and TG measurement locations, often up to 150 km. This thesis focuses primarily on addressing the first two of these issues. The third issue is partially investigated by assessing the VLM differences obtained when using altimetry located on and off the continental shelf, as well as assessing improvements gained when using non-reference mission data with typically improved spatial sampling closer to TG locations. The aim of this thesis is to advance the ALT-TG approach through the development of a Kalman filter and smoother to simultaneously estimate the first two of these temporal evolution of altimeter-specific systematic errors and site-specific VLM in a regional context, commencing from the early 1990s. A multi-stage solution approach is offered to enable gradual decorrelation of otherwise highly-correlated parameters in a geocentric reference frame, using observations from multi-mission ALT-TG combinations, ASL differences at tandem and dual crossovers, and GPS bedrock heights at locations within the TG region. Key components of the approach include time-correlated noise modelling and the determination of space-time covariances of each observational set through semi-variance analysis. The tuning of the measurement noise and state process noise is dependent on a priori assumptions and configurations built into the measurement equation and dynamic model, adopted from the intrinsic characteristics of the chosen study regions. missions in the Baltic Sea where GIA is the dominant driver of VLM, assuming both VLM and altimeter systematic errors behave linearly. The approach suggests the localised variability in VLM at specific TGs, up to ‚Äöv†¬¿4.5 mm/yr, which improves the spatial coherence of the resultant ASL trends at TGs with a ‚Äöv†¬¿20% decrease in the RMSE of latitudinal variability in comparison with those inferred from spatially interpolated GPS or GIA velocities. The estimated regional altimeter systematic errors are typically within ‚Äöv†¬¿¬¨¬±0.5‚ÄövÑv¨2.5 mm/yr (within mission specifications that are assessed globally), contributing to a reduction of ‚Äöv†¬¿0.3 mm/yr in the average ASL rate and narrowing the gap between the ASL estimates from TG and ALT records across the region. A suite of experiments is then undertaken to explore the sensitivity and overall performance of the technique. Second, the method is further developed to include along-track datasets of the complete multi-mission altimeter constellation and to enable the estimation of time-variability in altimeter systematic errors and VLM around continental Australia. The approach successfully resolves a coastal-wide subsidence that cannot be explained by GIA effects alone. Further, localised VLM trends of up to ~1.5 mm/yr are detected at some TG locations, again highlighting short spatial-scale variability in VLM (also present across GPS networks) which improves the spatial coherency of the derived ASL trends. The average magnitudes of mission-specific systematic errors are within ~¬¨¬±0.5-1.0 mm/yr, combining to have very little influence (‚Äöv†¬¿0.1 mm/yr) on the derived ASL trends over the full record. Investigation of time-variable altimeter errors did however show an anomaly reaching ~2.8 mm/yr during 3.5 years (~2008.5-2012) of the Jason-2 mission along with an unusually large La Ni‚àö¬±a event, which is in part supported by independent findings from the Bass Strait altimeter validation facility. Stacked estimates of time-variable VLM at TGs show some coherence to similar stacks computed from GPS sites within 100 km of the coast. Further investigations reveal the impacts of residual oceanographic signals in increasing the observational residual, and preventing the robust extraction of small post-seismic signals at TGs located on the northwest coast of Australia following the far-field Sumatran earthquakes that have been previously observed by GPS. The highest noise magnitudes were often associated with CPs located off the continental shelf where significant residual signals of oceanic original likely exist between the TG and offshore ALT locations. The ATG observations formed using CPs located off the shelf were also shown to bias the VLM estimates by~¬¨¬±0.1-0.5 mm/yr, highlighting an important limitation of the technique. Several sensitivity tests were also undertaken to investigate the solution dependence to a priori assumptions and solution configuration. The multi-mission approach notably shows significant improvements over the reference-mission-only implementation, through improved spatial sampling closer to the TGs, a ~13% further reduction in the RMSE of latitudinal ASL variability, ~35% lowering of the formal TG VLM uncertainties, and a ~54% increase in the correlation coefficient between the non-linear VLM stacks at TGs and nearby GPS sites. Finally, the approach is extended to allow its application to highly dynamic regions where abrupt changes in VLM and significant non-linear deformation occurs because of earthquakes and time-variable surface-mass loading. Specifically, the 2010 Mw8.8 Maule, 2014 Mw8.2 Iquique, and 2015 Mw8.3 Illapel earthquakes along the Chilean coast are investigated, as well the response to recent ice mass loss on the Antarctic Peninsula after the breakup of the Larsen-B ice shelf. Co-seismic jumps in addition to post-seismic changes in VLM are readily detected with magnitudes in reasonable agreement with published modelled deformation fields and GPS-derived results (noting large spatial variability given the specific earthquake fault geometry). In the Antarctic Peninsula, VLM estimates for the Palmer and Vernadsky TG sites show rapid uplift following the breakup of Larsen-B Ice Shelf in ~2002, supporting results in the literature from the Palmer GPS site. Across this overall study region, the method detects some evidence of time-variability in the Jason-1 systematic error which requires further investigations. Together, these results highlight the ability of the technique to densify otherwise sparse estimates of VLM thereby enabling the improved geophysical interpretation of the signal of interest, or improved inversion of solid-Earth properties in forward modelling activities. This thesis has set out to advance the ALT-TG technique by developing a flexible framework for retrieving TG VLM and its time-variability, exploring the regional budget of altimeter systematic errors, and modelling time-correlated noise of all input observations. The work has not rigorously tested the assumption that any residual oceanographic signal between the TG and ALT measurement locations occurs over a specific frequency band and does not contain a trend ‚ÄövÑv¨ this is a reasonable assumption for gauges with direct connection to the open ocean and differenced against reasonably close ALT observations. The research does however explore this and other limitations such as inferring TG VLMs either from the spatially interpolated GPS or from GIA models. In doing so, this work contributes to the improved monitoring of solid-Earth deformation and sea-level change along the coast. With the limitations in mind, the technique shows broad applicability to further regional- and global-scale studies. This underscores the need to continuously observe our changing planet using numerous space- and land-based geodetic techniques and further improve methods of data analysis to address limitations, motivating ongoing research into the future.