Next-Generation Modelling of Glacial Isostatic Adjustment

Modern-day changes to sea level can be measured using either tide-gauges or with satellite altimetry, and these observations provide vital quantitative information about the effects of anthropogenic climate change. Similarly, satellite-based measurements of the Earth's gravitational field are used to monitor mass-loss from the Greenland and Antarctic ice sheets. Such modern-day measurements cannot, however, be straightforwardly interpreted in terms of modern-day processes due to significant contributions from glacial isostatic adjustment (GIA); this being the on-going deformation of the solid Earth and concomitant sea level change caused by the last deglaciation. It is, therefore, necessary to model and correct for GIA within modern-day observations. Similarly, GIA contributions are also required when determining sea level projections, and hence for assessing and mitigating the risk of specific coastal locations to future sea level rise. At present, errors within GIA corrections constitute a significant, but poorly quantified, source of uncertainty within these various applications. Indeed, the magnitude of GIA corrections can sometimes be as large as the modern-day signals of interest, while the same can be true of the uncertainties on these corrections.

The process by which GIA corrections are obtained involves solution of the so-called GIA inverse problem. An essential step in solving this latter problem is the numerical simulation of GIA using (i) an assumed earth model and (ii) a model of ice sheet evolution back to the last glacial period. To date, most such studies have been based on the assumption that Earth structure (and in particular, mantle viscosity) varies only with depth. Given this assumption, the computational cost of simulating GIA is low, and this allows for simple methods to be applied in solving the inverse problem predicated on the ability to run very many simulations with different input parameters. Substantial 3D variations of viscosity within the Earth's mantle certainly do exist, however, though their specific form remains poorly known. Within the past 20 years or so, a range of studies have shown that such viscosity variations can have a significant effect on GIA. The cost of simulating GIA in 3D earth models is, however, dramatically increased over earlier 1D calculations, and this has rendered useless older methods for solving the inverse problem.

Within the foreseeable future, the only computationally viable approach to the GIA inverse problem that can take account of 3D viscosity variations is to apply gradient-based optimisation (GBO). This approach is widely used in other fields, including weather forecasting, oceanography, and seismic tomography. A key technical aspect of this approach is the application of the so-called adjoint method for calculating the derivatives required to iteratively update the model so as to better fit the data. Recently, the first application of GBO to the GIA inverse problem has been undertaken, and the initial results show great promise. This research has, however, made clear that future large-scale applications of this method are being held back by the computational tools available. The aim of this proposal is, therefore, the development of new and highly efficient numerical methods to facilitate the application of GBO to the GIA inverse problem. Such focused methodological work is necessary to enable future practical studies aimed at increasing the accuracy of GIA corrections, and hence improving our ability to monitor and understand the Earth's changing climate.