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A significant fraction of multidecadal fluctuations in the reanalysis-based gridded estimates of the observed climate variability over the past century and a half lie outside of the envelope generated by ensembles of climate-model historical simulations. Several pattern-recognition methods have been previously used to map out a truly global reach of the observed vs. simulated climate-data differences; in our own work we dubbed these global discrepancies the stadium wave to highlight their most striking spatiotemporal characteristic. Here we used a novel combination of such methods in conjunction with a large multi-model ensemble and two popular twentieth-century reanalysis products to: (i) succinctly describe the geographical evolution of the observed stadium wave in the annually sampled near-surface atmospheric temperature and mean sea-level pressure fields in terms of three basic patterns; (ii) show the robustness of this identification with respect to methodological details, including the demonstration of the truly global character of the stadium wave; and (iii) provide essential clues to its dynamical origin. All input time series were first decomposed into the forced signal and the residual internal variability; multi-model forced-signal estimates were also decomposed into their common-evolution part and the individual-model residuals. Analysis of the latter residuals suggests a contribution to the stadium-wave dynamics from a delayed climate response to variable external forcing despite the observed stadium-wave patterns’ exhibiting the magnitudes and the level of global teleconnectivity unmatched by the forced-signal residuals.