Which is better, an ensemble of positive-negative pairs or a centered spherical simplex ensemble?

Abstract

New methods to center the initial ensemble perturbations on the analysis are introduced and compared with the commonly used centering method of positive-negative paired perturbations. In the new method, one linearly dependent perturbation is added to a set of linearly independent initial perturbations to ensure that the sum of the new initial perturbations equals zero; the covariance calculated from the new initial perturbations is equal to the analysis error covariance estimated by the independent initial perturbations, and all of the new initial perturbations are equally likely. The new method is illustrated by applying it to the ensemble transform Kalman filter (ETKF) ensemble forecast sc..