Ocean bathymetry exerts a strong control on ice sheet-ocean interactions
within Antarctic ice-shelf cavities, where it can limit the access of
warm, dense water at depth to the underside of floating ice shelves.
However, ocean bathymetry is challenging to measure within or close to
ice-shelf cavities. It remains unclear how uncertainty in existing
bathymetry datasets affect simulated sub-ice shelf melt rates. Here we
infer linear sensitivities of ice shelf melt rates to bathymetric shape
with grid-scale detail by means of the adjoint of an ocean general
circulation model. Both idealised and realistic-geometry experiments of
sub-ice shelf cavities in West Antarctica reveal that bathymetry has a
strong impact on melt in localised regions such as topographic obstacles
to flow. Moreover, response of melt to bathymetric perturbation is found
to be non-monotonic, with deepening leading to either increased or
decreased melt depending on location. Our computational approach
provides a comprehensive way of identifying regions where refined
knowledge of bathymetry is most impactful, and also where bathymetric
errors have relatively little effect on modelled ice sheet-ocean
interactions.