Abstract Ice shelves fringing the Antarctic continent experience low or high basal melt rates depending on local shelf conditions, ocean circulation and intensity of ice‐sea‐air exchanges. Recent studies have uncovered potential cold‐to‐warm transitions in specific ice‐shelf cavities, which could lead to a dramatic increase in sea‐level rise. Here we demonstrate that brine rejection in coastal polynyas promotes bistable dynamics in ice‐shelf cavities, which would be otherwise monostable, for a broad diversity of Circumpolar Deep Water temperatures. We develop a generic low‐dimensional box model featuring warm and cold circulation modes and apply it to nine ice‐shelf cavities. We find that most ice‐shelf cavities are in a bistable regime and are therefore susceptible to irreversible abrupt transitions for a realistic range of sea‐ice formation rates. Bistability is robust to changes in cavity parameterization. However, the vertical mixing scheme at the ice‐shelf front can be tuned to make the transitions reversible.

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