Quantifying the impact of submarine melting on calving is central to understanding the response of marine-terminating glaciers to ocean forcing. Modeling and observational studies suggest the potential for submarine melting to amplify calving (the calving multiplier effect), but there is little consensus as to under what conditions this occurs. Here, by viewing a marine-terminating glacier as an elastic beam, we propose an analytical basis for understanding the presence or absence of the calving multiplier effect. We show that as a terminus becomes undercut it becomes more susceptible to both serac failure (calving only of ice that is undercut, driven by vertical imbalance) and rotational failure (full-thickness calving of ice behind the grounding line, driven by rotational imbalance). By deriving analytical stress thresholds for these two forms of calving, we suggest that the dominant of the two calving styles is determined principally by the shape of melt-undercutting. Uniform undercutting extending from the bed to the waterline promotes serac failure and no multiplier effect, while glaciers experiencing linear undercutting that is greatest at the bed and zero at the waterline are more likely to experience rotational failure and a multiplier effect. Our study offers a quantitative framework for understanding where and when the calving multiplier effect occurs, and, therefore, a route to parameterizing the effect in ice sheet-scale models.

中文翻译：

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熔体底切几何控制的产犊乘数效应

量化海底融化对崩解的影响对于理解海洋终止冰川对海洋强迫的响应至关重要。建模和观察研究表明，海底融化有可能放大产犊（产犊乘数效应），但对于在什么条件下发生这种情况几乎没有共识。在这里，通过将海洋终止冰川视为弹性梁，我们提出了一个分析基础，用于理解产犊乘数效应的存在与否。我们表明，当一个终点被咬边时，它变得更容易受到 serac 故障（仅由垂直不平衡驱动的咬边冰的崩裂）和旋转故障（接地线后面的全层冰崩裂，由旋转不平衡驱动） . 通过推导这两种产犊形式的分析应力阈值，我们认为两种产犊方式的主导地位主要由熔体底切的形状决定。从床到水线的均匀底切促进了serac 破坏和没有乘数效应，而经历线性底切的冰川在床最大和在吃水线为零的冰川更有可能经历旋转破坏和乘数效应。我们的研究提供了一个定量框架，用于了解产犊乘数效应发生的时间和地点，因此，提供了在冰盖尺度模型中参数化该效应的途径。从床到水线的均匀底切促进了serac 破坏和没有乘数效应，而经历线性底切的冰川在床最大和在吃水线为零的冰川更有可能经历旋转破坏和乘数效应。我们的研究提供了一个定量框架，用于了解产犊乘数效应发生的时间和地点，因此，提供了在冰盖尺度模型中参数化该效应的途径。从床到水线的均匀底切促进了serac 破坏和没有乘数效应，而经历线性底切的冰川在床最大和在吃水线为零的冰川更有可能经历旋转破坏和乘数效应。我们的研究提供了一个定量框架，用于了解产犊乘数效应发生的时间和地点，因此，提供了在冰盖尺度模型中参数化该效应的途径。