No abstract

The gravity anomalies at sea level can be used to validate the satellite gravity gradiometry data. Validation of such a data is important prior to downward continuation because of amplification of the data errors through this process. In this paper the second-order radial derivative of the extended Stokes' formula is employed and the emphasis is on least-squares modification of this formula to generate the second-order radial gradient at satellite level. Two methods in this respect are proposed: a) modifying the second-order radial derivative of extended Stokes' formula directly, b) modifying extended Stokes' formula prior to taking the second-order radial derivative. Numerical studies show that the former method works well but the latter is very sensitive to the proper choice of the cap size of integration and degree of modification.

Our GPS velocity field is directly realized in a GIA reference frame. Using this method (named the GIA frame approach) we are able to constrain GIA models with minimal influence of errors in the reference frame or biasing signals from plate tectonics. The drawbacks are more degrees of freedom that might mask real but unmodeled signals. Monte Carlo tests suggest that our approach is robust at the 97% level in terms of correctly separating different models of ice history but, depending on deformation patterns, the identified Earth model may be slightly biased in up to 39% of cases. We compare our results to different one-and three-dimensional GIA models employing different global ice-load histories. The GIA models generally provide good fit to the data but there are still significant discrepancies in some areas. We suggest that these differences are mainly related to inaccuracies in the ice models and/or lateral inhomogeneities in the Earth structure under Fennoscandia. Thus, GIA models still need to be improved, but the GIA frame approach provides a base for further improvements.

[1] We demonstrate a new technique for using geodetic data to update a priori predictions for Glacial Isostatic Adjustment (GIA) in the Fennoscandia region. Global Positioning System (GPS), tide gauge, and Gravity Recovery and Climate Experiment (GRACE) gravity rates are assimilated into our model. The technique allows us to investigate the individual contributions from these data sets to the output GIA model in a self-consistent manner. Another benefit of the technique is that we are able to estimate uncertainties for the output model. These are reduced with each data set assimilated. Any uncertainties in the GPS reference frame are absorbed by reference frame adjustments that are estimated as part of the assimilation. Our updated model shows a spatial pattern and magnitude of peak uplift that is consistent with previous models, but our location of peak uplift is slightly to the east of many of these. We also simultaneously estimate a spatially averaged rate of local sea level rise. This regional rate (∼1.5 mm/yr) is consistent for all solutions, regardless of which data sets are assimilated or the magnitude of a priori GPS reference frame constraints. However, this is only the case if a uniform regional gravity rate, probably representing errors in, or unmodeled contributions to, the low-degree harmonic terms from GRACE, is also estimated for the assimilated GRACE data. Our estimated sea level rate is consistent with estimates obtained using a more traditional approach of direct "correction" using collocated GPS and tide gauge sites.