A Posteriori Diagnostics in an Ensemble of Perturbed Analyses

Real-size assimilation systems basically rely on estimation theory in which two sources of information, background and observations, are combined in an optimal way. However, the optimality of such large problems is not guaranteed, since they rely on different approximations. The observed values of the subparts of the cost function measuring the distance between the analysis and the two sources of information can be compared to their theoretical statistical expectations. Such a posteriori diagnostics can be used to optimize the statistics of observation and also background errors. Moreover, the expectations of the subparts of the cost function associated with observations are related to the weights of the different sources of observations in the analysis. It is shown that those theoretical statistical expectations are direct by-products of an ensemble of perturbed assimilations.