The QBO, the annual cycle, and their interactions: Isolating periodic modes with Koopman analysis

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, leading to variations in the descent rate of the jets and, resultingly, 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 spatio-temporal 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 $30 \, \mathrm{m} \, \mathrm{day}^{-1}$ mean descent rate. We compare these results to the annual variation in tropical upwelling and interpret then with a simple model.