Changes between Version 1 and Version 2 of ErrorSubspaceTransformkf
 Timestamp:
 Jan 22, 2012, 11:44:44 AM (7 years ago)
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ErrorSubspaceTransformkf
v1 v2 3 3 Recently, we have developed a new filter formulation, the Error Subspace Transform Kalman Filter. Details on this filter will be available in the paper "A unification of ensemble squareroot filters" by L. Nerger, T. Janjic, J. Schroeter, and W. Hiller to appear in the Monthly Weather Review in 2012. 4 4 5 While studying the detailed relationship of the SEIK filter and the Ensemble Transform Kalman Filter (ETKF), we found a possibility to obtain the same minimum transformation of the ensemble (i.e. the distance between the forecast and analysis ensembles is minimal in the Frobenius norm) at a slightly lower computational cost. The new filter results from a modification of the SEIK filter to use consistent projections between the state space and the error subspace represented by the ensemble of model states. (The SEIK filter itself already projects onto the error subspace. However, this projection is not fully consistent and will lead to small differences in the analysis ensemble that depend on the order of the states on the ensemble matrix.) As the new formulation is very similar to the ETKF, but5 While studying the detailed relationship of the SEIK filter and the Ensemble Transform Kalman Filter (ETKF), we found a possibility to obtain the same minimum transformation of the ensemble (i.e. the distance of the ensemble transformation matrix is minimal in the Frobenius norm) at a slightly lower computational cost than that of the ETKF. The new filter results from a modification of the SEIK filter to use consistent projections between the state space and the error subspace represented by the ensemble of model states. (The SEIK filter itself already projects onto the error subspace. However, this projection is not fully consistent and will lead to small differences in the analysis ensemble that depend on the order of the states on the ensemble matrix.) As the new formulation is very similar to the ETKF, but operates directly in the error subspace instead of the ensemblerepresentation of it, the new filter was termed "Errorsubspace Transform Kalman Filter" ESTKF. 6 6 7 7 In the paper, we also tested the use of the symmetric square root in the SEIK filter instead of the Cholesky decomposition that is commonly applied. The symmetric square root is commonly used in the ETKF and will also be the default for the ESTKF. For the SEIK filter, the symmetric squareroot improved state estimates in experiments with the Lorenz96 model, for the case that the ensemble transformation was deterministic.