Issues of nonlinearity and non-gaussianity Contribution to the WWRP/THORPEX workshop on 4D-Var and ensemble Kalman filter inter-comparisons,

From the point of view of mathematical modeling, a data assimilation system consists in a statistical description of a dynamical model (which can be stochastic or not), and of the related observations. The statistics on this system are meant to represent the uncertainty on the true state estimation. The proper statistical modeling depends on how uncertainty evolves under the full data assimilation system. Truncating statistics to the first and second order moments (mean and covariance matrix) leads to a (minimally committed) Gaussian modeling of this statistical system. This truncation is made necessary not only because of the complexity of the fully Bayesian data assimilation algorithms, but also because of the amount of information to be stored (filtering approach especially). However, this is also justified from the point of view of the evolution of the dynamical model. If, in the vicinity of a trajectory, the model can be replaced by its tangent linear, then initial Gaussian statistics will remain so in this vicinity. Non-linearities in the model and insufficient and infrequent observational data are likely to make the statistics diverge from ideal gaussianity. The talks and the subsequent discussion of the session Issues of nonlinearity and non