Abstract
Abstract. 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.
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