The ensemble transform Kalman filter (ET KF) scheme uses estimation theory to more accurately express the breeding method's fundamental hypothesis that analysis errors are filtered forecast errors. The ET KF scheme transforms forecast perturbations into analysis perturbations by ensuring that the ensemble based analysis error covariance matrix would be equal to the true analysis error covariance if the covariance matrix of the raw forecast perturbations were equal to the true forecast error covariance matrix and the data assimilation scheme were optimal. As such, perturbation amplitude is reduced near observation sites more than it is away from observation sites. Furthermore, consistent with the filtering theory of an optimal data assimilation scheme, ensemble variance is reduced in directions corresponding to large forecast error variance more than it is in directions corresponding to small forecast error variance. Thus the ET KF ensemble retains a wide range of growing directions. Besides, its computational expense is only slightly greater than that of the breeding method.
To test our expectations about the quantitative difference between the two techniques, we ran 8-member T42 CCM3 ensembles starting from the NCEP/NCAR reanalysis data for both schemes for the boreal summer in 2000. The maximal likelihood parameter estimation theory was used to ensure that the 12-hour forecast ensemble variance is consistent with control forecast error variance at rawinsonde observation sites.
It was found that 1) the spatial variation of initial ET KF ensemble perturbations better represents inhomogeneities in analysis errors due to inhomogeneities in the observational network than that of the initial breeding ensemble perturbations; 2) the spectrum of eigenvalues of the 12-hour forecast error covariance matrices produced by the ET KF ensemble is much flatter than that produced by the breeding ensemble, that is, the ET KF ensemble produces ensemble spread in much more directions than the breeding ensemble; and 3) forecast errors of the ET KF ensemble correlate with each other much less than that of the breeding ensemble.