Data assimilation: A fully nonlinear approach to ensemble formation using indistinguishable states

The Kalman filter (KF) provides the optimal closed-form solution to a general linear stochastic (perfect model) case, while the target of the problem has not even been defined in the case of imperfect models. Data assimilation in a nonlinear, perfect-model scenario is considered.

It is shown that a new fully nonlinear approach based upon the indistinguishable states (IS) systematically outperforms the ensemble Kalman filter (EnKF). The IS provides an ensemble of initial conditions, consistent with (i) the model dynamics, (ii) the observational noise model, and (iii) the particular observations over a window. It is argued that this is the relevant limit to consider in data assimilation, when the desire is to place high probability density in the vicinity of the target state.