Validation of Modelled Uplift Rates with Space Geodetic Data

Models of glacial isostatic adjustment (GIA) simulate the time-delayed viscoelastic response of the solid Earth to surface loading induced mainly by mass redistribution between ice and ocean during the last glacial cycle considering for rotational feedback, floating ice and moving coastlines. These models predict relative sea level change and surface deformation. The GIA component of present-day uplift is responsible for crustal uplift rates of more than 10 mm/year in areas such as Churchill (Canada) and Angermanland (Sweden). As GIA models have several uncertainties, the model output needs to be validated against observational data. Here, we validate displacements predicted by a GIA model code, VILMA-3D, by using space geodetically observed vertical land motion. We have created a GIA model ensemble using geodynamically constrained 3D Earth structures derived from seismic tomography to consider more realistic lateral variations in the GIA response. To validate the modelled uplift rates, we employ a multi-analysis-centre ensemble of GNSS station and geocentre motion coordinate solutions that have been assimilated into the latest international terrestrial reference frame (ITRF2020). Tectonic and weather signatures were reduced in estimating GNSS-derived velocities, and the trend signal is extracted from these GNSS time series with the STL method (seasonal-trend decomposition based on Loess).  Additionally, uplift rates observed within the ITRF2020 of VLBI, DORIS, and SLR are employed in this study. Because the geodetic stations are unevenly distributed, we employ a weighting scheme that involves the network density and the cross-correlation of the stations’ displacement time series. As measures of agreement for global and regional cases, we employ weighted root mean square error (RMSE) and weighted mean absolute error (MAE). With this validation, we determine the GIA model parameters that are most suitable for modelling present-day uplift rates and identify regions with the best and worst agreement.

The results show an agreement between RMSE and MAE for the global case (all stations are considered) and the majority of regional cases, except for the farfield (away from formerly glaciated regions) and for North America. For the global case and for separate regions covered by the major ice sheets during glaciation (North America, Fennoscandia, Antarctica, Greenland), the best fit is performed by the GIA models with 3D Earth structures which show largest lateral variability in viscosity. For the GIA model with the best global fit, the MAE ranges between 0.03 and 0.98 for the respective regions British Isles, Antarctica, farfield, Fennoscandia and North America. In contrast, for the three regions with the lowest amount of observational data, Patagonia, Alaska and Greenland, the MAE is increased to values between 2.07 and 8.63. In general, the MAE ranges between 0.83 and 0.78 for the different GIA models when all stations are considered. Both the RMSE and the MAE show a larger spread between the regions than between the considered GIA models indicating the relevance of also evaluating regional differences in the model performance.