Ensemble Forecasting with the Ensemble Transform Kalman Filter

Abstract

The Ensemble Transform Kalman Filter (ETKF) ensemble generation scheme is first introduced and compared with the breeding scheme that is operationally used at NCEP. Instead of directly multiplying each forecast perturbation with a rescaling factor as in the breeding scheme, the ETKF analysis perturbations are generated by transforming forecast perturbations by a transformation matrix. This matrix is chosen by solving the error covariance update equation for an optimal data assimilation scheme within the ensemble perturbation subspace. NCAR CCM3 is used in this comparison. The NCEP/NCAR reanalysis data for the boreal summer in 2000 are used for the initialization of the control forecast and the verifications of the ensemble forecasts. The initial ensemble variance of the ETKF reflects the geographical variations of the observation distribution better than that of the breeding scheme. The ETKF ameliorates the severe rank deficient problem of the breeding scheme. The short-term maximal growth within the ETKF perturbation subspace is found to significantly exceed that of the breeding scheme. The ETKF ensemble mean has lower root mean square errors than the mean of the breeding ensemble. New tests to measure the precision of the ensemble estimated forecast error variance are presented. All of the tests indicate that the ETKF estimates of forecast error variance are considerably more accurate than those of the breeding scheme. For small ensembles (~100), the computational expense of the ETKF ensemble generation is only slightly greater than that of the breeding scheme.

A method to center the initial perturbations on the analysis using spherical simplex points is introduced. This new centering scheme is compared with the commonly used centering method of positive/negative paired perturbations within the ETKF ensemble generation framework. The accuracy of the ensemble means, the accuracy of predictions of forecast error variance and the ability of the ETKF ensembles to resolve inhomogeneities in the observation distribution were all tested. In all of these test categories, the ETKF ensemble with the spherical simplex centering is found to perform better than that with the symmetric positive/negative centering. The computational expense for generating spherical simplex ETKF initial perturbations is about as small as that for the symmetric positive/negative paired ETKF.

Finally, in order to account for residual forecast uncertainties, we apply the dressing method to statistically augment the ETKF ensemble. In the dressing method, statistical perturbations are added to each individual ensemble member at the postprocessing. A dressing kernel from which the dressing perturbations are drawn is built to make the dressed ensemble members indistinguishable from the verification under the second moment measurement on a seasonally averaged basis. In the test categories of rank histogram and skill scores, the ETKF ensemble augmented by this new dressing kernel performs better than the undressed ETKF ensemble. This dressing kernel is also found to provide more reliable dressing perturbations than the best member dressing kernel.