The large-scale atmosphere prefers a state of near balance, where the motion is predominantly vortical, but insertion of noisy observations in forecast models can excite unrealistic inertia-gravity waves. Historically, spurious fast oscillations have been controlled by initializing the model on a hypothetical slow manifold. In recent years, four-dimensional data assimilation methods have been designed which, given information from observations and the governing dynamics, calculate the most probable time-dependent atmospheric state. However, since fast solutions are admitted by the dynamics, these schemes do not explicitly deliver a balanced state.

We examine the question of how well four-dimensional assimilation can reflect the near-balance found in nature, by applying the Extended Kalman Filter (EKF) to a modification of the Lorenz 1986 low-order model which has chaotic slow dynamics and fast waves. In this model, separation of the fast and slow dynamics holds to good approximation for sufficiently small Rossby number. The EKF forces the model intermittently, using observations of variables that have components on both time scales. The EKF need not respect the separation of the nonlinear fast and slow dynamics. Consequently, the assimilation scheme can constrain the growth of imbalance in a model, but may also generate imbalance from a balanced state, depending on the crudeness of the assimilation errors.