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：海冰深刻影响着极地环境与全球气候。传统上，海冰在欧拉坐标系下被建模为连续体，例如采用粘塑性流变学来描述其大尺度特征。近年来，拉格朗日粒子模型（又称离散元方法模型）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（称为浮冰）的运动。本文发展了一种耦合粒子与连续体系统的多尺度模型，以有效表征海冰在不同尺度上的动力学与统计特征。该多尺度模型利用玻尔兹曼型系统将粒子运动与连续体方程相链接。在小尺度动力学方面，模型描述每个海冰浮冰的运动；而在大尺度连续体分量方面，则处理质量密度、线速度及角速度的统计矩。这些统计量的演化影响单个浮冰运动，而后者又通过提供体反馈来调整大尺度动力学。值得注意的是，表征海冰浮冰的粒子模型具有局部性与全并行化特性，采用被称为超参数化的框架，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逼近精度。