Sea ice profoundly influences the polar environment and the global climate. Traditionally, Sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known as the discrete element method (DEM) models, have been utilized for characterizing the motion of individual sea ice fragments (called floes) at scales of 10 km and smaller, especially in marginal ice zones. This paper develops a multiscale model that couples the particle and the continuum systems to facilitate an effective representation of the dynamical and statistical features of sea ice across different scales. The multiscale model exploits a Boltzmann-type system that links the particle movement with the continuum equations. For the small-scale dynamics, it describes the motion of each sea ice floe. Then, as the large-scale continuum component, it treats the statistical moments of mass density and linear and angular velocities. The evolution of these statistics affects the motion of individual floes, which in turn provides bulk feedback that adjusts the large-scale dynamics. Notably, the particle model characterizing the sea ice floes is localized and fully parallelized, in a framework that is sometimes called superparameterization, which significantly improves computation efficiency. Numerical examples demonstrate the effective performance of the multiscale model. Additionally, the study demonstrates that the multiscale model has a linear-order approximation to the truth model.

翻译：海冰深刻影响极地环境与全球气候。传统上，海冰被建模为欧拉坐标系下的连续介质，通过粘塑性流变学等方法描述其大尺度特征。近年来，拉格朗日粒子模型（亦称离散元方法模型）被用于表征10公里及更小尺度下（尤其是边缘冰区）单个海冰碎块（即碎冰）的运动。本文发展了一种耦合粒子系统与连续介质系统的多尺度模型，以有效表征海冰在不同尺度下的动力学与统计学特征。该多尺度模型利用玻尔兹曼型系统将粒子运动与连续介质方程联系起来。在小尺度动力学层面，它描述了每个海冰碎块的运动；而在大尺度连续介质组分层面，它处理质量密度、线速度与角速度的统计矩。这些统计量的演化影响单个碎冰的运动，而碎冰的运动又通过体反馈调节大尺度动力学。值得注意的是，表征海冰碎块的粒子模型采用局部化与完全并行化架构（有时称为超参数化方法），显著提升了计算效率。数值算例展示了该多尺度模型的有效性能。此外，研究表明该多尺度模型对真实模型具有线性阶近似精度。