The n=1 Rossby wave is the fastest Rossby mode on the sphere.
The n=1 Rossby wave, together with the Kelvin wave, provides basic understanding of large-scale circulation in response to tropical heating perturbations, following Gill (1980) and the long-wave approximation.
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Sielmann, Frank; Zagar, Nedjeljka; Lunkeit, Frank (2023). CLICCS-MODES - Modal wave filtering of ERA5 reanalyses with MODES (Version 2.0). World Data Center for Climate (WDCC) at DKRZ. https://doi.org/10.26050/WDCC/CLICCS-A2-M