Ensemble forecasting with the ensemble transform Kalman filter

A new initial perturbation generation method, the ensemble transform Kalman filter (ETKF), is introduced and compared with the breeding scheme. The ETKF generates initial perturbations by postmultiplying forecast perturbations by a transformation matrix. This matrix is chosen to solve the error covariance update equation for an optimal data assimilation scheme within the ensemble perturbation subspace. Version 3 of the community climate model (CCM3) developed at National Center for Atmospheric Research is used to test and compare the ETKF and breeding schemes. It is found that with only a little more computational expense, the ETKF samples initial condition uncertainties significantly better than the breeding. The ETKF ensemble mean and ensemble covariance are considerably more accurate than those of the breeding.; A new method to center initial ensemble perturbations on the initial analysis is introduced and compared with the commonly used centering method of positive-negative paired perturbations. In the new method, called spherical simplex centering, 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 the new initial perturbations are equally likely. 16-member CCM3 ETKF ensemble initially centered by the new method is found to be more skillful than that centered by the positive-negative paired method.; A new ensemble postprocessing method that reduces seasonally averaged second moment errors of the ensemble forecasts is introduced. The method involves adding ("dressing") independent sets of statistical perturbations to each member of a dynamical ensemble forecast. The new dressing method mathematically constrains the stochastic process used to generate the statistical perturbations so that it entirely removes seasonally averaged errors in the second moment measures. ETKF ensembles dressed with this new method are found to be more skillful than the undressed ETKF ensembles. It is shown that the previously proposed "best member" dressing method fails to reliably predict the second moment of the distribution of forecast errors whereas the new dressing method reliably predicts this second moment.