Ensemble Forecasting with the Ensemble Transform Kalman Filter
Final rept. 1 Jan 2000-31 Aug 2004
PENNSYLVANIA STATE UNIV UNIVERSITY PARK DEPT OF METEOROLOGY
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The ensemble transform Kalman filter ETKF initial ensemble perturbation generation scheme is introduced and compared with the simple and masked breeding schemes. Instead of directly multiplying each forecast perturbation with a rescaling factor to generate the initial perturbations as in the breeding schemes, the ETKF generates initial perturbations by postmultiplying the forecast perturbations by a transformation matrix. This matrix is chosen to ensure that the ensemble-based analysis error convariance matrix would be equal to the true analysis error convariance if the convariance matrix of the raw forecast perturbations were equal to the true forecast error convariance matrix and the data assimilation scheme were optimal. For small ensembles 100, the computational expense of the ETKF ensemble generation is only slightly greater than that of the masked breeding scheme.
- Numerical Mathematics