We have derived an analytic form of the thickness redistribution function, Ψ, and compressive strength of sea ice using variational principles. By using the technique of coarse‐graining vertical sea ice deformation, or ridging, in the momentum equation of the pack, we isolate frictional energy loss from potential energy gain in the collision of floes. The method accounts for macroporosity of ridge rubble, ϕ_R, and by including this in the state space of the pack, we expand the sea ice thickness distribution, g(h), to a bivariate distribution, g(h,ϕ_R). The effect of macroporosity is for the first time included in the large‐scale mass conservation and momentum equations of frozen oceans. We make assumptions that have simplified the problem, such as treating sea ice as a granular material in ridges, and assuming that bending moments associated with ridging are perturbations around an isostatic state. Regardless of these simplifications, the coarse‐grained ridge model is highly predictive of macroporosity and ridge shape. By ensuring that vertical sea ice deformation observes a variational principle both at the scale of individual ridges and over the pack as a whole, we can predict distributions of ridge shapes using equations that can be solved in Earth system models. Our method also offers the possibility of more accurate derivations of sea ice thickness from ice freeboard measured by space‐borne altimeters over polar oceans.

中文翻译：

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地球系统模型中海冰残留的变分方法

我们使用变分原理推导了厚度重新分布函数and和海冰抗压强度的解析形式。通过在包装的动量方程中使用粗粒度的垂直海冰变形或起皱技术，可以将絮凝物碰撞中的摩擦能量损失与势能增加隔离开来。该方法占山脊瓦砾，大孔隙的φ _{- [R} ，并且通过包括此在包的状态空间，我们扩展海冰的厚度分布，克（ħ），到一个二维分布，克（ħ，φ _ř）。大孔隙度的影响首次被包括在冰冻海洋的大规模质量守恒和动量方程中。我们进行了简化该问题的假设，例如将海冰视为山脊中的颗粒材料，并假设与起皱相关的弯矩是围绕等静态的扰动。不管这些简化如何，粗糙的山脊模型都可以很好地预测大孔隙和山脊的形状。通过确保垂直海冰变形在单个山脊的尺度上以及整个山体整体上都遵循变化原理，我们可以使用可以在地球系统模型中求解的方程来预测山脊形状的分布。