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Maximizing the statistical diversity of an ensemble of bred vectors by using the geometric norm

Journal: Journal of Atmospheric Sciences
Year: 2010  
Status: Published
In this status since: 2 Mar 2011
PDF file: 2011_Pazo_jas.pdf
DOI: doi: 10.1175/2011JAS3729.1
Pazó, D., , López, J.M.

We show that the choice of the norm has a great impact on the construction of ensembles of bred vectors. The geometric norm maximizes (in comparison with other norms like the Euclidean one) the statistical diversity of the ensemble while, at the same time, enhances the projection of the bred vector on the linearly most unstable direction, i.e. the Lyapunov vector. The geometric norm is also
optimal in providing the least fluctuating ensemble dimension among all the spectrum of q-norms studied. We exemplify our results with numerical integrations of a toy model of the atmosphere (the Lorenz-96 model), but our findings are expected to be generic for spatially extended chaotic systems due to the generic multiplicative character of error growth.