Resolving trends in Antarctic Ice Sheet Mass Loss Through Spatio-temporal Kalman Filtering
Schön, Nana; Zammit-Mangion, Andrew; Rougier, Jonathan; Bamber, Jonathan
University of Bristol, UNITED KINGDOM

Increased data availability has led to the possibility of data-driven reconstructions of atmospheric, ice-sheet and solid-earth processes in Antarctica at resolutions which were unachievable previously. However, it is becoming increasingly clear that a conventional approach of using spatially-resolved trends does not allow for source-separation of the key interacting processes which influence both height- and mass-change of the Antarctic Ice Sheet: namely GIA, ice, firn and SMB field fluctuations.
In this study we show how the use of data from ICESat, ENVISAT, GRACE and GPS stations coupled with knowledge of the dynamic and spatial behaviour of the individual processes may be used to distinguish the cause of the observed effects. The statistical framework filters by taking advantage of the spatio-temporal characteristics of the processes, in particular the temporal smoothness of GIA and ice sheet dynamics and the comparative spatial regularity of GIA, SMB and firn densification.
We allow for a comprehensive analysis of uncertainty. For example, we quantitatively show that whilst the state of a single process (e.g. firn densification) might be largely uncertain, the state of a combination of the processes (e.g. firn densification + SMB) might be estimated with higher confidence. In addition an objective assessment of the effect of spatio-temporal averaging becomes possible. Thus, whilst estimates of a single process at a 10km/year resolution might be largely uncertain, on a basin scale over a number of years the uncertainty is reduced to acceptable levels. We show to what extent the uncertainty, attributed largely to the smoothing within the GRACE data, may be remedied through the adoption of forward-models within our statistical framework. The approach allows us to determine rigorous error bounds on mass trends at a given spatial and temporal resolution and it is possible, therefore, to optimize both, or either, resolution to achieve a desired accuracy for the mass trend.