Data assimilation in a system with two scales—combining two initialization techniques

An ensemble Kalman filter (EnKF) is used to assimilate data onto a non-linear chaotic model, coupling two kinds of variables. The first kind of variables of the system is characterized as large amplitude, slow, large scale, distributed in eight equally spaced locations around a circle. The second kind of variables are small amplitude, fast, and short scale, distributed in 256 equally spaced locations. Synthetic observations are obtained from the model and the observational error is proportional to their respective amplitudes. The performance of the EnKF is affected by differences in the spatial correlation scales of the variables being assimilated. This method allows the simultaneous assimilation of all the variables. The ensemble filter also allows assimilating only the large-scale variables, letting the small-scale variables to freely evolve. Assimilation of the large-scale variables together with a few small-scale variables significantly degrades the filter. These results are explained by the spurious correlations that arise from the sampled ensemble covariances. An alternative approach is to combine two different initialization techniques for the slow and fast variables. Here, the fast variables are initialized by restraining the evolution of the ensemble members, using a Newtonian relaxation toward the observed fast variables. Then, the usual ensemble analysis is used to assimilate the large-scale observations.