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A performance expectation is that Earth system models\udsimulate well the climate mean state and the climate variability. To test\udthis expectation, we decompose two 20th century reanalysis data sets and 12\udCMIP5 model simulations for the years 1901–2005 of the monthly mean\udnear-surface air temperature using randomised multi-channel singular spectrum\udanalysis (RMSSA). Due to the relatively short time span, we concentrate on\udthe representation of multi-annual variability which the RMSSA method\udeffectively captures as separate and mutually orthogonal spatio-temporal\udcomponents. This decomposition is a unique way to separate statistically\udsignificant quasi-periodic oscillations from one another in high-dimensional\uddata sets.  The main results are as follows. First, the total spectra for the two\udreanalysis data sets are remarkably similar in all timescales, except that\udthe spectral power in ERA-20C is systematically slightly higher than in 20CR.\udApart from the slow components related to multi-decadal periodicities, ENSO\udoscillations with approximately 3.5- and 5-year periods are the most prominent\udforms of variability in both reanalyses. In 20CR, these are relatively\udslightly more pronounced than in ERA-20C. Since about the 1970s, the\udamplitudes of the 3.5- and 5-year oscillations have increased, presumably due\udto some combination of forced climate change, intrinsic low-frequency climate\udvariability, or change in global observing network. Second, none of the 12\udcoupled climate models closely reproduce all aspects of the reanalysis\udspectra, although some models represent many aspects well. For instance, the\udGFDL-ESM2M model has two nicely separated ENSO periods although they are\udrelatively too prominent as compared with the reanalyses. There is an\udextensive Supplement and YouTube videos to illustrate the multi-annual\udvariability of the data sets

Multi-annual modes in the 20th century temperature variability in reanalyses and CMIP5 models