Assimilation of sea-ice concentration in a global climate model — physical and statistical aspects

We investigate the initialization of Northern-hemisphere sea ice in the global climate model ECHAM5/MPI-OM by assimilating sea-ice concentration data. The analysis updates for concentration are given by Newtonian relaxation, and we discuss different ways of specifying the analysis updates for mean thickness. Because the conservation of mean ice thickness or actual ice thickness in the analysis updates leads to poor assimilation performance, we introduce a proportional dependence between concentration and mean thickness analysis updates. Assimilation with these proportional mean-thickness analysis updates significantly reduces assimilation error both in identical-twin experiments and when assimilating sea-ice observations, reducing the concentration error by a factor of four to six, and the thickness error by a factor of two. To understand the physical aspects of assimilation errors, we construct a simple prognostic model of the sea-ice thermodynamics, and analyse its response to the assimilation. We find that the strong dependence of thermodynamic ice growth on ice concentration necessitates an adjustment of mean ice thickness in the analysis update. To understand the statistical aspects of assimilation errors, we study the model background error covariance between ice concentration and ice thickness. We find that the spatial structure of covariances is best represented by the proportional mean-thickness analysis updates. Both physical and statistical evidence supports the experimental finding that proportional mean-thickness updates are superior to the other two methods considered and enable us to assimilate sea ice in a global climate model using simple Newtonian relaxation.