We give a simple description of the blessing of dimensionality with the main focus on the concentration phenomena. These phenomena imply that in high dimensions the lengths of independent random vectors from the same distribution have almost the same length and that independent vectors are almost orthogonal. In the climate and atmospheric sciences we rely increasingly on ensemble modelling and face the challenge of analysing large samples of long time series and spatially extended fields. We show how the properties of high dimensions allow us to obtain analytical results for e.g. correlations between sample members and the behaviour of the sample mean when the size of the sample grows. We find that the properties of high dimensionality with reasonable success can be applied to climate data. This is the case although most climate data show strong anisotropy and both spatial and temporal dependence, resulting in effective dimensions around 25–100.

中文翻译：

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维度对气候数据分析的加持

我们对维度加持进行了简单的描述，主要关注集中现象。这些现象意味着在高维中，来自同一分布的独立随机向量的长度几乎相同，并且独立向量几乎是正交的。在气候和大气科学中，我们越来越依赖于集合建模，并面临着分析长时间序列和空间扩展领域的大样本的挑战。我们展示了高维度的属性如何使我们能够获得分析结果，例如样本成员之间的相关性和样本大小增加时样本均值的行为。我们发现具有合理成功的高维属性可以应用于气候数据。