GIA constraints for Greenland from combined GRACE and GNSS observations

Currently, many different glacial isostatic adjustment (GIA) models have been proposed for Greenland, as a consequence of a still largely unknown deglaciation there. GNSS trends are often used to constrain GIA models regionally. However, the GNSS uplift rates contain a large contribution from present-day mass changes (mostly due to ice melting) that must be removed to extract the GIA uplift rates. The elastic uplift rates estimates are potentially affected by uncertainties. They depend on the Earth model chosen (usually PREM-based models) and on high-resolution mass changes estimates, usually obtained from volume changes measured with altimetry. The volume changes need to be converted into mass variations, mostly using models (surface mass balance and firn compaction models) that can introduce biases. Since the elastic uplift rates are proportional to the mass changes, any uncertainty in the mass variations directly affects the elastic uplift rates eventually, as well as the GIA GNSS residuals uplift rates obtained from them. And in turn, these biases reflect directly in the GIA models constrained with those GNSS. Here we propose a novel additional GIA constraint based on both GRACE and GNSS observations. We start from a very simple model, based on three basic and general assumptions: 1) Elastic uplift rates at a given distance from a mass distribution (e.g. a disk changing height) are proportional to the mass variation. 2) The GIA induced uplift rates can be considered proportional to the apparent mass changes produced by GIA gravity changes (e.g. Wahr et al 2000 and Riva et al. 2009). 3) The total uplift rate measured by a GNSS is the sum of the elastic uplift rate caused by any surface mass changes and the GIA induced uplift rate (assuming that uplifts rates due to plate tectonics are negligible in Greenland). We then show that this simple model can be applied to Greenland, and still retain most of its validity. The three points above become three equations in four unknowns, namely the surface mass changes and the related elastic uplift rate, the GIA uplift rate and its related apparent mass change. Using the average uplift rate measured by the whole GNET (Greenland GNSS Network) and the total GMB (Greenland Mass Balance) measured with GRACE, from the three equations we derive a global consistency relation between the average GIA uplift rate and its related apparent mass change for the whole Greenland. In this way, the combined analysis of the GMB from GRACE and GNET provides a very solid constraint for Greenland-wide GIA models. GIA models constrained only regionally might provide estimates that are not consistent in other Greenland regions. The four GIA models that we tested do not respect the consistency relation we found. This relation does not allow to determine the GIA uplift rate uniquely, but we show that together with some basic considerations about the plausible deglaciation scenarios, it allows to identify a reasonable range for the GIA component in the average GNSS uplift rate.