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On the orthogonalization of bred vectors


Kornblueh,  L.
The Ocean in the Earth System, MPI for Meteorology, Max Planck Society;
Director’s Research Group OES, The Ocean in the Earth System, MPI for Meteorology, Max Planck Society;

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Keller, J. D., Hense, A., Kornblueh, L., & Rhodin, A. (2010). On the orthogonalization of bred vectors. Weather and Forecasting, 25, 1219-1234. doi:10.1175/2010WAF2222334.1.

The key to the improvement of the quality of ensemble forecasts assessing the inherent flow uncertainties is the choice of the initial ensemble perturbations. To generate such perturbations, the breeding of growing modes approach has been used for the past two decades. Here, the fastest-growing error modes of the initial model state are estimated. However, the resulting bred vectors (BVs) mainly point in the phase space direction of the leading Lyapunov vector and therefore favor one direction of growing errors. To overcome this characteristic and obtain growing modes pointing to Lyapunov vectors different from the leading one, an orthogonalization implemented as a singular value decomposition based on the similarity between the BVs is applied. This transformation is similar to that used in the ensemble transform technique currently in operational use at NCEP but with certain differences in the metric used and in the implementation. In this study, results of this approach us! ing BVs generated in the Ensemble Forecasting System (EFS) based on the global numerical weather prediction model GME of the German Meteorological Service are presented. The gain in forecast performance achieved with the orthogonalized BV initialization is shown by using different probabilistic forecast scores evaluating ensemble reliability, variance, and resolution. For a 3-month period in summer 2007, the results are compared to forecasts generated with simple BV initializations of the same ensemble prediction system as well as operational ensemble forecasts from ECMWF and NCEP. The orthogonalization vastly improves the GME-EFS scores and makes them competitive with the two other centers.