Data Assimilation in a Multi-Scale Model

AbstractData assimilation for multi-scale models is an important contemporary research topic. Especially the role of unresolved scales and model error in data assimilation needs to be systematically addressed. Here we examine these issues using the Ensemble Kalman filter (EnKF) with the two-level Lorenz-96 model as a conceptual prototype model of the multi-scale climate system. We use stochastic parameterization schemes to mitigate the model errors from the unresolved scales. Our results indicate that a third-order autoregressive process performs better than a first-order autoregressive process in the stochastic parameterization schemes, especially for the system with a large time-scale separation.Model errors can also arise from imprecise model parameters. We find that the accuracy of the analysis (an optimal estimate of a model state) is linearly correlated to the forcing error in the Lorenz-96 model. Furthermore, we propose novel observation strategies to deal with the fact that the dimension of the observations is much smaller than the model states. We also propose a new analog method to increase the size of the ensemble when its size is too small.