A data-driven model for constraint of present-day glacial isostatic adjustment in North America

Geodetic measurements of vertical land motion and gravity change are incorporated into an a priori model of present-day glacial isostatic adjustment (GIA) in North America via least-squares adjustment. The result is an updated GIA model wherein the final predicted signal is informed by both observational data, and prior knowledge (or intuition) of GIA inferred from models. The data-driven method allows calculation of the uncertainties of predicted GIA fields, and thus offers a significant advantage over predictions from purely forward GIA models. In order to assess the influence each dataset has on the final GIA prediction, the vertical land motion and GRACE-measured gravity data are incorporated into the model first independently (i.e., one dataset only), then simultaneously. The relative weighting of the datasets and the prior input is iteratively determined by variance component estimation in order to achieve the most statistically appropriate fit to the data. The best-fit model is obtained when both datasets are inverted and gives respective RMS misfits to the GPS and GRACE data of 1.3 mm/yr and 0.8 mm/yr equivalent water layer change. Non-GIA signals (e.g., hydrology) are removed from the datasets prior to inversion. The post-fit residuals between the model predictions and the vertical motion and gravity datasets, however, suggest particular regions where significant non-GIA signals may still be present in the data, including unmodeled hydrological changes in the central Prairies west of Lake Winnipeg. Outside of these regions of misfit, the posterior uncertainty of the predicted model provides a measure of the formal uncertainty associated with the GIA process; results indicate that this quantity is sensitive to the uncertainty and spatial distribution of the input data as well as that of the prior model information. In the study area, the predicted uncertainty of the present-day GIA signal ranges from ∼0.2-1.2 mm/yr for rates of vertical land motion, and from ∼3-4 mm/yr of equivalent water layer change for gravity variations.