Progressive assimilation of multiscale observations

The description of correlated observation error statistics is a challenge in data assimilation. Currently, the observation errors are assumed uncorrelated (the covariance matrix is diagonal) which is a severe approximation that leads to suboptimal results. It is possible to use multi-scale transformations to retain the diagonal matrix approximation while accounting for some correlation. However this approach can lead to some convergence problems due to scale interactions. In this paper we propose an online scale selection algorithm that improves the convergence properties in such case.