Lagrangian Data Assimilation and Parameter Estimation of an Idealized Sea Ice Discrete Element Model

Abstract

Abstract 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.

Keywords

• Lagrangian data assimilation
• conditional Gaussian
• sea ice