Feature-based Data Assimilation in Geophysics
Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by denying likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. Using large amounts of steady state data is unnecessary because these data are redundant. It is impossible to assimilate data of complex systems into low-dimensional models, or to assimilate data, collected over long time scales, into chaotic models. One can address these issues by denying likelihoods based on suitable low-dimensional \features" of the data, rather than by the mismatch of model output and \raw" data. Our goal is to contribute to a more fundamental understanding of such a feature-based approach to data assimilation. We present noise models based on perturbed observations to de ne feature-based likelihood functions that lead to computationally efficient solutions. We also explain how a feature-based approach enables us to effectively assimilate selected aspects of data into models, and how this can be interpreted by a reduction in effective dimension. Numerical implementation of these ideas are illustrated in four examples.