利用几何范数最大化繁殖向量系综的统计多样性
Maximizing the statistical diversity of an ensemble of bred vectors by using the geometric norm
摘要：
我们发现，选择的规范有很大的影响，建设合奏繁殖载体。几何规范最大化（与其他规范相比，如欧几里德）的统计多样性的合奏，而在同一时间，提高增长率的繁殖矢量和它的投影上的线性最不稳定的方向，即李雅普诺夫矢量。几何范数也是最佳的，在所有的q-范数研究的频谱中提供最小波动的系综维数。我们将我们的结果与玩具模型的大气（Lorenz-96模型）的数值积分，但我们的研究结果预计是通用的空间扩展的混沌系统。
英文摘要：
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 growth rate of the bred vector and its projection 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.
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