| Assimilation of observations, which plays an increasing role in meteorology and oceanography, is closely linked to predictability in that it requires to determine, in one form or another, the temporal evolution of the uncertainty on the state of the flow. The large numerical dimension of the problem to be solved (in real time ...) and the chaotic character of the flow make assimilation a particularly difficult and challenging task. The present tendency is to develop ensemble methods, in which the uncertainty on the state of the system is described by an ensemble of points in state space, meant to sample the underlying conditional probability distribution. The two main classes of algorithms that are used for assimilation of meteorological and oceanographical observations (namely, variational assimilation and Ensemble Kalman Filter, which are pragmatic extensions to mildly nonlinear and nongaussian cases of methods that are fundamentally linear and gaussian) are presented. They are discussed as to their capability of describing the temporal evolution of the uncertainty on the state of the system. Particle filters are fully nonlinear and nongaussian algorithms that can in principle evolve the uncertainty on the state of the system under the most general conditions. Their numerical cost is however high, and a basic practical question is whether that cost can be reduced so as to make them usable for meteorological and oceanographical applications. Recently, Trevisan and colleagues have proposed to explicitly restrict the estimation to the modes that have been unstable in the recent past, and in which the uncertainty must be concentrated. That approach, called Assimilation in the Unstable Subspace (AUS), opens new algorithmic possibilities. |
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