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Abstract The quasi-biennial oscillation (QBO) is the dominant mode of variability in the equatorial stratosphere. It is characterized by alternating descending easterly and westerly jets over a period of approximately 28 months. It has long been known that the QBO interactions with the annual cycle, e.g., through variation in tropical upwelling, lead to variations in the descent rate of the jets and, resultantly, the QBO period. Understanding these interactions, however, has been hindered by the fact that conventional measures of the QBO convolve these interactions. Koopman formalism, derived from dynamical systems, allows one to decompose spatiotemporal datasets (or nonlinear systems) into spatial modes that evolve coherently with distinct frequencies. We use a data-driven approximation of the Koopman operator on zonal-mean zonal wind to find modes that correspond to the annual cycle, the QBO, and the nonlinear interactions between the two. From these modes, we establish a data-driven index for a “pure” QBO that is independent of the annual cycle and investigate how the annual cycle modulates the QBO. We begin with what is already known, quantifying the Holton–Tan effect, a nonlinear interaction between the QBO and the annual cycle of the polar stratospheric vortex. We then use the pure QBO to do something new, quantifying how the annual cycle changes the descent rate of the QBO, revealing annual variations with amplitudes comparable to the 30 m day⁻¹mean descent rate. We compare these results to the annual variation in tropical upwelling and interpret them with a simple model. Significance StatementThe quasi-biennial oscillation (QBO) is a periodic cycle of winds in tropical atmosphere with a period of 28 months. The phase of QBO is known to influence other aspects of the atmosphere, including the polar vortex, but the magnitude of its effects and how it behaves are known to depend on the season. In this study, we use a data-driven method (called a Koopman decomposition) to quantify annual changes in the QBO and investigate their causes. We show that seasonal variations in the stratospheric upwelling play an important but incomplete role. 

Abstract This paper examines probability distributions oflocal wave activity(LWA), a measure of the jet stream's meander, and factors that control them. The observed column‐mean LWA distributions exhibit significant seasonal, interhemispheric, and regional variations but are always positively skewed in the extratropics, and their tail often involves disruptions of the jet stream. A previously derived one‐dimensional (1D) traffic flow model driven by observed spectra of transient eddy forcing qualitatively reproduces the shape of the observed LWA distribution. It is shown that the skewed distribution emerges from nonlinearity in the zonal advection of LWA even though the eddy forcing is symmetrically distributed. A slower jet and stronger transient and stationary eddy forcings, when introduced independently, all broaden the LWA distribution and increase the probability of spontaneous jet disruption. A quasigeostrophic two‐layer model also simulates skewed LWA distributions in the upper layer. However, in the two‐layer model both transient eddy forcing and the jet speed increase with an increasing shear (meridional temperature gradient), and their opposing influence leaves the frequency of jet disruptions insensitive to the vertical shear. When the model's nonlinearity in the zonal flux of potential vorticity is artificially suppressed, it hinders wave‐flow interaction and virtually eliminates reversal of the upper‐layer zonal wind. The study underscores the importance of nonlinearity in the zonal transmission of Rossby waves to the frequency of jet disruptions and associated weather anomalies.