| 29 Jun 2026
Does the envelope of Rossby wave packets exhibit higher predictability than the underlying wave pattern?
Abstract. This study tests the long-standing hypothesis that Rossby wave packet (RWP) envelopes exhibit enhanced predictability compared to embedded weather systems, here interpreted as the individual troughs and ridges comprising the underlying wave pattern. Using a potential vorticity framework and the saturation fraction of the mean square error as a predictability metric, we derive a tendency equation for envelope errors to diagnose error-growth mechanisms. Contrary to the hypothesis, our analysis does not reveal any evidence of enhanced envelope predictability. The error dynamics of the envelope and the underlying wave pattern are strikingly similar. Crucially, while the envelope discards information about the location of troughs and ridges (phase information), it remains sensitive to the relative phase relationships among constituent wavenumbers. Phase errors in the individual wavenumbers may directly propagate into envelope errors, demonstrating that "the envelope is the wave", i.e, the dynamics of the envelope are intrinsically governed by its underlying wavenumbers, not by larger-scale dynamics. At least up to lead times of 10 days, the longest lead times considered herein, envelope predictability is thus governed by the same dynamical constraints as the synoptic-scale Rossby wave field. The misconception of RWPs as a larger-scale, dynamical phenomenon may arise by noting the continent- or ocean-basin-wide scale of RWP ''objects'' on spatial maps. Confirming previous work, we find enhanced predictability in the presence of RWPs compared to situations without RWPs. This enhanced predictability arises because RWPs organize high-amplitude anomalies coherently over large scales – not from the envelope itself. The spatial coherence of high-amplitude anomalies within RWPs is arguably facilitated by a strong midlatitude waveguide, suggesting waveguide characteristics as a promising target for future predictability research.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Weather and Climate Dynamics.
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