Use of data assimilation via linear low-order models for the initialization of El Nino Southern Oscillation predictions

The utility of a Kalman filter (KF) for initialization of an intermediate nonlinear coupled model for El Nino - Southern Oscillation prediction is studied via an approximation of the nonlinear coupled model by a system of seasonally dependent linear models. The low-dimensional nature of such an approximation allows one to determine a sequence of "perfect" initial states that start a trajectory segment best fitting the observed data. Defining these perfect initial conditions as "true" states of the model, we compute a priori parameters of the KF and test its ability to produce an estimate of the "truth" superior to the less theoretically sound estimates. We find that in this application such a KF does not produce an estimate outperforming a pure observational projection as an initial condition for the coupled model forecast. The violation of standard KF assumptions on temporal whiteness of observational errors and system noise is identified as the reason for this failure.