Abstract: Error breeding is a popular and simple method to generate flow-adapted perturbations for use in ensemble forecasting. It has traditionally been believed that the norm type used in periodic normalizations of bred vectors (BVs) does not have an important effect on the performance of BVs within ensemble forecasting systems. However, we have recently reported that the geometric norm has nice properties (e.g. enhancement of the ensemble diversity) that in principle render it more adequate to construct ensembles than other norm types like the Euclidean one. These advantages are clearly demonstrated here in a simple experiment of ensemble forecasting for the Lorenz-96 model with ensembles of BVs. Our simple numerical assimilation experiment shows how the increased statistical diversity of geometric BVs leads to improved scores regarding forecasting capabilities as compared with BVs constructed with the standard Euclidean norm. Moreover, we provide a theoretical basis for all these results by resorting to generic properties of spatially extended chaotic systems.

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