Mid--latitude atmospheric waves are central to large-scale circulation and extreme weather, yet their variability and dynamical characteristics remain incompletely understood.  Here, we introduce a generalized wave power spectral framework that overcomes key limitations of traditional wavenumber–frequency analysis by standardizing to absolute zonal wavelength, removing background noise, and applying wavelength–frequency filtering to isolate specific dynamical modes. After accounting for the β-effect, the generalized spectra reveal a characteristic wavelength of approximately 4,500 km in the Northern Hemisphere and 5,000 km in the Southern Hemisphere, with strong seasonality linked to jet position and intensity. A significant positive trend in global integrated wave activity, driven primarily by changes in the Northern Hemisphere, indicates increasing mid--latitude waviness over the past four decades. Wave characteristics in the wavelength–frequency domain closely follow a linear barotropic Rossby wave dispersion relationship when jet intensity is considered. Further decomposition into eastward and westward, low- and high-frequency modes highlights pronounced differences in their spatial distributions and variability, underscoring the potential importance of westward wave modes in shaping hemispheric teleconnections. The framework also captures leading variability patterns such as the annular modes and event-scale dynamics, exemplified by recurrent Rossby wave packets during the 2019/2020 marine heatwave east of New Zealand. Together, these results demonstrate the utility of the generalized spectral method for advancing dynamical interpretation of mid--latitude wave behavior and improving understanding of circulation variability in a changing climate.

Rossby wave,mid-latitude,waviness