Sea ice is a complex media composed of discrete interacting elements of various sizes and thicknesses (floes), and at sufficiently small lengthscales it can not be approximated as a continuous media as routinely done at large scales. While the Eulerian data assimilation is a relatively mature field, techniques for assimilation of satellite-derived Lagrangian trajectories of sea ice floes remain poorly explored. Here, an idealized discrete element sea ice model is developed and used as a testbed to quantify the efficacy of the minimum approximation for the Lagrangian data assimilation in an one-way coupled ice-ocean system. First, it is shown that observations of O(100) floes in a 50 km by 50 km domain are needed to achieve a high data assimilation accuracy, with a large observational timestep of 1 day being sufficient to recover the geophysically balanced part of the unobserved ocean flow, while about a 2-h timestep is necessary to recover the unbalanced flows. Second, a simple stochastic parameterization is shown to improve the assimilation accuracy when only a small subset of floes is observed or there is a significant model error resulting for example from simplifying the collision laws between floes. Finally, an efficient expectation-maximization algorithm is developed that succeeds in assimilating the ocean flow and simultaneously estimating individual floe thicknesses and the overall thickness distribution function. Our study implies that the minimum approximation with its closed analytical formulae could potentially provide an efficient data assimilation scheme for satellite observations of sea ice floes.

中文翻译：

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理想化海冰离散元模型的拉格朗日数据同化与参数估计

海冰是一种复杂的介质，由不同大小和厚度的离散相互作用元素（浮冰）组成，在足够小的长度尺度上，它不能像通常在大尺度上所做的那样近似为连续介质。虽然欧拉数据同化是一个相对成熟的领域，但卫星衍生的海冰浮冰拉格朗日轨迹的同化技术仍然缺乏探索。在这里，开发了一种理想化的离散元素海冰模型，并将其用作测试平台，以量化单向耦合冰海系统中拉格朗日数据同化的最小近似效果。首先，它表明需要在 50 km x 50 km 域中对 O(100) 浮流进行观测以实现高数据同化精度，1 天的大观测时间步长足以恢复未观测到的海洋流的地球物理平衡部分，而大约 2 小时的时间步长是恢复不平衡流所必需的。其次，当仅观察到一小部分絮凝物或由于简化絮凝物之间的碰撞规律而导致显着模型误差时，显示简单的随机参数化可提高同化精度。最后，开发了一种有效的期望最大化算法，该算法成功地同化了海洋流量，同时估计了单个浮冰厚度和整体厚度分布函数。