Randomised multichannel singular spectrum analysis of the 20th century climate data

Abstract

In this article, we introduce a new algorithm called randomised multichannel singular spectrum analysis (RMSSA), which is a generalisation of the traditional multichannel singular spectrum analysis (MSSA) into problems of arbitrarily large dimension. RMSSA consists of (1) a dimension reduction of the original data via random projections, (2) the standard MSSA step and (3) a recovery of the MSSA eigenmodes from the reduced space back to the original space. The RMSSA algorithm is presented in detail and additionally we show how to integrate it with a significance test based on a red noise null-hypothesis by Monte-Carlo simulation. Finally, RMSSA is applied to decompose the 20th century global monthly mean near-surface temperature variability into its low-frequency components. The decomposition of a reanalysis data set and two climate model simulations reveals, for instance, that the 2-6 yr variability centred in the Pacific Ocean is captured by all the data sets with some differences in statistical significance and spatial patterns.