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Bred vectors are a type of finite perturbation used in prediction studies ofatmospheric models that exhibit spatially extended chaos. We study thestructure, spatial correlations, and the growth- rates of logarithmic bredvectors (which are constructed by using a given norm). We find that, after asuitable transformation, logarithmic bred vectors are roughly piecewise copiesof the leading Lyapunov vector. This fact allows us to deduce a scaling law forthe bred vector growth rate as a function of their amplitude. In addition, werelate growth rates with the spectrum of Lyapunov exponents corresponding tothe most expanding directions. We illustrate our results with simulations ofthe Lorenz '96 model.

Logarithmic bred vectors in spatiotemporal chaos: structure and growth