# Efficient and Statistically Accurate Lagrangian Data Assimilation of Sea Ice Using Non-Interacting Floes

N. Chen(1), S. Fu(1), and G. Manucharyan(2)

1: University of Wisconsin

2: University of Washington

## Abstract

In this talk, we develop a new efficient and statistically accurate Lagrangian data assimilation strategy of sea ice using non-interacting floes. The new strategy here is applied to a coupled atmosphere-ocean-sea ice model, where the sea ice is modeled by a discrete element method (DEM) while the ocean is described a two-layer quasi geostrophic (QG) model. The new strategy developed here exploits an extremely efficient Fourier domain data assimilation scheme. The forecast uncertainty due to the nonlinearity between different Fourier modes is compensated by the stochastic noise, which allows each Fourier mode to evolve independently in the forecast stage. The reduction of the nonlinearity facilitates the Lagrangian data assimilation. It also allows a significant dimension reduction of the system that accelerates the forecast step. Linear models with multiplicative noise are used to model those highly intermittent modes. The parameters in the linear models are systematically determined by matching the associated statistics with no ad hoc tuning, and the solution of the parameters are given by closed analytic formula even in the presence of complicated multiplicative noise. The coordinate transform between the Lagrangian DEM model and the Eulerian ocean model also becomes much simpler within this new strategy. It is shown that multiplicative noise is essential to capture the non-Gaussian features of nature. Observing 30 floes gives a reasonably skillful data assimilation results (Corr > 0.7 of ocean field) in a 200kmÃ—200km domain in the marginal ice zone. Observing angular displacement helps improve the data assimilation skill. The areas without the observed floes may not necessarily have larger uncertainties. The data assimilation skill of the velocity is the best at the scale of |k| = 4 or 5 while the skill of recovering the vorticity is the best at the largest spatial scale.