Preprints
https://doi.org/10.5194/npg-2021-2
https://doi.org/10.5194/npg-2021-2

  19 Jan 2021

19 Jan 2021

Review status: a revised version of this preprint is currently under review for the journal NPG.

The blessing of dimensionality for the analysis of climate data

Bo Christiansen Bo Christiansen
  • Danish Meteorological Institute, Copenhagen, Denmark

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 length of independent random vectors from the same distribution have almost the same length and that independent vectors are almost orthogonal. In 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.

Bo Christiansen

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2021-2', Anonymous Referee #1, 22 Mar 2021
    • AC1: 'Reply on RC1', Bo Christiansen, 27 Mar 2021
  • RC2: 'Comment on npg-2021-2', Maarten Ambaum, 06 Jul 2021
    • AC2: 'Reply on RC2', Bo Christiansen, 12 Jul 2021

Bo Christiansen

Bo Christiansen

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Short summary
In geophysics large samples of extended fields need to be analysed and we therefore often work with high-dimensional data. Fortunately, high dimensionality can be a blessing and we show how this often allows analytical results to be derived. These results include estimates of correlations between sample members and how the sample mean depends on the sample size. We show that the properties of high dimensionality with success can be applied to climate fields, e.g., those from ensemble modelling.