Forward and adjoint coupled ocean-ice sheet modelling

The Antarctic Ice Sheet is a giant slab of glacial ice that is the size of Europe and a few kilometres thick. It rests on bedrock that is below sea level, so around the margins where the ice is thinner it floats free of the seabed to form floating ice shelves (Fig. 1).
Over the last few decades it has become clear that the seawater circulating in the cavities beneath ice shelves is melting the Antarctic Ice Sheet at an increasing rate. This impacts on the speed with which glaciers flow towards the ocean and thus is a critical factor in predictions of sea-level rise. West Antarctica represents the largest source of uncertainty in projections of sea level over the 21st Century, with Thwaites Glacier (TG) having greater potential to influence sea level than any other.
The importance of this overall topic and this geographical location in particular led to a recent £20M joint NERC-NSF programme on Thwaites Glacier (https://nerc.ukri.org/press/releases/2018/14-glacier/). A team at Imperial College London, led by Prof. Piggott, is contributing to one of these projects (https://www.bas.ac.uk/project/melting-at-thwaites-grounding-zone-and-its-control-on-sea-level/ led by BAS) through detailed numerical modelling of the critical grounding line region.
Over the past few years there has been progress in the use of flexible mesh methods to simulate the ocean in complex ice shelf cavities (Jordan et al., 2014; Yeager 2018), as well as the use of flexible mesh methods along with the use of adjoint sensitivity techniques in ice sheet modelling (Kyrke-Smith et al., 2017; https://github.com/gahansen/Albany/wiki/PAALS-Tutorial-2016), and fully coupled ocean-ice sheet modelling is now possible (Asay-Davis et al., 2016).
In recent years the ability for automatic code generation to provide easy access to adjoints has been taken up in the development of several ice sheet models (Kyrke-Smith et al., 2017; https://icepack.github.io/index.html). The underlying technology which has facilitated this development (https://www.firedrakeproject.org/) originates from Imperial College London and we have recently used it to generate an adjoint enabled ocean model (https://thetisproject.org/). There is therefore an opportunity here at Imperial to combine these cutting-edge research topics within a single modelling framework: flexible mesh modelling of the coupled ocean and ice sheet, and the use of adjoints for sensitivity analyses and data assimilation.
The ultimate goal is a fully coupled model with an adjoint capability that allows for sensitivities to be propagated between the ocean and ice sheet. This capability can be used for data assimilation, uncertainty quantification, and model calibration and initialisation. In particular, this model will be the first capable of solving the crucial problem of initialisation shock. When ocean and ice models are coupled together, the ice spends centuries adjusting to the ocean model state, and this artificial signal over-rides any real sea-level change. This shock can be avoided by using the coupled adjoint to initialise the ice/ocean model perfectly, thus isolating the real ice sheet change driven by changes in ocean melting.
This work would contribute to the wider activities of the Imperial-BAS team, and in particular would be able to take advantage of the data and modelling activities planned under the above-mentioned NERC-NSF Thwaites glacier project. It is highly likely that the student will get the chance to experience Antarctic fieldwork first-hand, as part of an oceanographic cruse during the project.