  The discrete element method (DEM) is providing a new modeling approach for
describing sea ice dynamics. It exploits particle-based methods to characterize
the physical quantities of each sea ice floe along its trajectory under
Lagrangian coordinates. One major challenge in applying the DEM models is the
heavy computational cost when the number of floes becomes large. In this paper,
an efficient Lagrangian parameterization algorithm is developed, which aims at
reducing the computational cost of simulating the DEM models while preserving
the key features of the sea ice. The new parameterization takes advantage of a
small number of artificial ice floes, named the superfloes, to effectively
approximate a considerable number of the floes, where the parameterization
scheme satisfies several important physics constraints. The physics constraints
guarantee the superfloe parameterized system will have similar short-term
dynamical behavior as the full system. These constraints also allow the
superfloe parameterized system to accurately quantify the long-range
uncertainty, especially the non-Gaussian statistical features, of the full
system. In addition, the superfloe parameterization facilitates a systematic
noise inflation strategy that significantly advances an ensemble-based data
assimilation algorithm for recovering the unobserved ocean field underneath the
sea ice. Such a new noise inflation method avoids ad hoc tunings as in many
traditional algorithms and is computationally extremely efficient. Numerical
experiments based on an idealized DEM model with multiscale features illustrate
the success of the superfloe parameterization in quantifying the uncertainty
and assimilating both the sea ice and the associated ocean field.
