We investigate the sensitivity of sub-ice-shelf melt rates under Pine Island Ice Shelf, West Antarctica, to changes in the oceanic state using an adjoint ocean model that is capable of representing the flow in sub-ice-shelf cavities. The adjoint code is based on algorithmic differentiation (AD) of the Massachusetts Institute of Technology’s ocean general circulation model (MITgcm). The adjoint model was extended by adding into the AD process the corresponding sub-ice-shelf cavity code, which implements a three-equation thermodynamic melt-rate parameterization to infer heat and freshwater fluxes at the ice-shelf/ocean boundary. The inferred sensitivities reveal dominant timescales of 30–60 days over which the shelf exit is connected to the deep interior via advective processes. They exhibit rich three-dimensional time-evolving patterns that can be understood in terms of a combination of the buoyancy forcing by inflowing water masses, the cavity geometry and the effect of rotation and topography in steering the flow in the presence of prominent features in the bedrock bathymetry. Dominant sensitivity pathways are found over a sill, as well as ‘shadow regions’ of very low sensitivities. To the extent that these transient patterns are robust they carry important information for decision- making in observation deployment and monitoring.