Antarctic ice shelves are losing mass at drastically different rates, primarily due to differing rates of oceanic heat supply to their bases. However, a generalized theory for the inflow of relatively warm water into ice shelf cavities is lacking. This study proposes such a theory based on a geostrophically constrained inflow, combined with a threshold bathymetric elevation, the Highest Unconnected isoBath (HUB), that obstructs warm water access to ice shelf grounding lines. This theory captures ∼ 90% of the variance in melt rates across a suite of idealized process-oriented ocean/ice shelf simulations with quasi-randomized geometries. Applied to observations of ice shelf geometries and offshore hydrography, the theory captures ∼80% of the variance in measured ice shelf melt rates. These findings provide a generalized theoretical framework for melt resulting from buoyancy-driven warm water access to geometrically complex Antarctic ice shelf cavities.

An assumption of steady-state is a common basis for deep ocean circulation theory and observational strategies. We use GO-SHIP’s Easy Ocean uniformly gridded CTD data from repeat hydrographic sections to test this assumption. In particular, we ask: for what regions of the world ocean is there evidence that the planetary scale deep geostrophic shear and potential vorticity fields, related to potential density gradients, are in quasi steady-state over the past forty years? We find that away from boundary currents, planetary-scale potential density gradients in most parts of the deep ocean are stable from occupation to occupation, to within approximately 15% estimated standard error (lower in many parts of the global ocean interior), with higher variability in a few expected regions and for shorter sections.