Decomposition of Atmospheric Disturbances into Standing and Traveling Components, with Application to Northern Hemisphere Planetary Waves and Stratosphere–Troposphere Coupling

This study updates a body of literature that aims to separate atmospheric disturbances into standing and traveling zonal wave components. Classical wavenumber–frequency analysis decomposes longitude- and time-dependent signals into contributions from distinct spatial and temporal scales. Here, an additional decomposition of the spectrum into standing and traveling components is described. Previous methods decompose the power spectrum into standing and traveling parts with no explicit allowance for covariance between the two. This study provides a simple method to calculate the variance of each of these components and the covariance between them. It is shown that this covariance is typically a significant portion of the variance of the total signal. The approach also preserves phase information and allows for the reconstruction of the real-space standing and traveling components. The technique is applied to reanalysis wintertime geopotential height anomalies in the Northern Hemisphere in order to investigate planetary wave interference effects in stratosphere–troposphere coupling. The results show that for planetary waves 1–3, standing waves explain the largest portion of the variance at low frequencies. An exception is for wave 1 in the high-latitude troposphere, where there is a strong westward-traveling wave. Furthermore, the antinodes of the standing waves have preferred longitudes that tend to align with the extremes of the climatological wave, suggesting that standing waves contribute to a linear interference effect that has been shown to be an important part of stratosphere–troposphere interactions.