Marine ice sheets are highly sensitive to submarine melting in their grounding zones, where they transition between grounded and floating ice. Recently published studies of the complex hydrography of grounding zones suggest that warm ocean water can intrude large distances beneath the ice sheet, with dramatic consequences for ice dynamics. Here we develop a model to capture the feedback between intruded ocean water, the melting it induces and the resulting changes in ice geometry. We reveal a sensitive dependence of the grounding-zone dynamics on this feedback: as the grounding zone widens in response to melting, both temperature and flow velocity in the region increase, further enhancing melting. We find that increases in ocean temperature can lead to a tipping point being passed, beyond which ocean water intrudes in an unbounded manner beneath the ice sheet, via a process of runaway melting. Additionally, this tipping point may not be easily detected with early warning indicators. Although completely unbounded intrusions are not expected in practice, this suggests a mechanism for dramatic changes in grounding-zone behaviour, which are not currently included in ice-sheet models. We consider the susceptibility of present-day Antarctic grounding zones to this process, finding that both warm and cold water cavity ice shelves may be vulnerable. Our results point towards a stronger sensitivity of ice-sheet melting, and thus higher sea-level-rise contribution in a warming climate, than has been previously understood.

海洋冰盖对其接地区的海底融化高度敏感，它们在接地区和浮冰之间过渡。最近发表的关于接地区复杂水文学的研究表明，温暖的海水可以侵入冰盖下方很远的距离，对冰动力学产生巨大的影响。在这里，我们开发了一个模型来捕获侵入的海水、其引起的融化以及由此产生的冰几何形状变化之间的反馈。我们揭示了接地区动力学对这种反馈的敏感依赖性：随着接地区因熔化而变宽，该区域的温度和流速都会增加，从而进一步增强熔化。我们发现，海洋温度的升高会导致超过一个临界点，超过这个临界点，海水就会通过失控的融化过程以无限制的方式侵入冰盖下方。此外，早期预警指标可能无法轻易检测到这一临界点。尽管在实践中预计不会出现完全无限制的入侵，但这表明了接地区行为发生巨大变化的机制，目前冰盖模型中尚未包含这种机制。我们考虑了当今南极接地区对这一过程的敏感性，发现温水腔冰架和冷水腔冰架都可能很脆弱。我们的研究结果表明，与之前的理解相比，冰盖融化的敏感性更强，因此气候变暖对海平面上升的贡献更大。