On the prediction of linear stochastic systems with a low-order model

Three methods for approximating the high-dimensional stochastic system with a low-dimensional model are examined, and the prediction error and predictability of the reduced-order models are evaluated. It is shown that during reduction both the normal modes of deterministic dynamics and the spatial structures of stochastic forcing need to be taken into account. In addition to stability, which determines the asymptotic behavior, non-normality, which controls the error growth at short lead times, should also be preserved. An experiment with tropical Atlantic variability illustrates that the empirical orthogonal function and balanced truncation are superior to modal reduction in capturing the predictable dynamics.