The Construction of Optimal Perturbations

Abstract

A three-level quasigeostrophic model of the atmosphere is used to refine a method, based on an ensemble of perturbations, for medium-range forecasting. Using as a hypothesis that it is most efficient to use for the perturbations those structures that have maximal growth, given a constraint on the initial perturbation, one arrives at the optimal perturbation method. Optimal perturbations are constructed to have a maximum forecast error in the short range. It is hoped that the perturbations continue to grow up to the medium-range forecast time. Information on vertical covariances, spectral variances, and horizontal variances is accounted for in the constraint. The optimal perturbations are thus by construction consistent with these statistical properties of the initial error. The experiments have been repeated with different durations of the short-range forecast If this duration is sufficiently long, and the ensemble sufficiently large, then the ensemble shows optimal growth for both the short and medium range. With smaller ensembles, the spread in the forecast error is shown to be systematically underestimated as a consequence of neglecting some important components of the error.