Descent Rate Models of the Synchronization of the Quasi-Biennial Oscillation by the Annual Cycle in Tropical Upwelling

The response of the quasi-biennial oscillation (QBO) to an imposed mean upwelling with a periodic modulation is studied, by modeling the dynamics of the zero wind line at the equator using a class of equations known as descent rate models. These are simple mathematical models that capture the essence of QBO synchronization by focusing on the dynamics of the height of the zero wind line. A heuristic descent rate model for the zero wind line is described and is shown to capture many of the synchronization features seen in previous studies of the QBO. It is then demonstrated using a simple transformation that the standard Holton–Lindzen model of the QBO can itself be put into the form of a descent rate model if a quadratic velocity profile is assumed below the zero wind line. The resulting nonautonomous ordinary differential equation captures much of the synchronization behavior observed in the full Holton–Lindzen partial differential equation. The new class of models provides a novel framework within which to understand synchronization of the QBO, and we demonstrate a close relationship between these models and the circle map well known in the mathematics literature. Finally, we analyze reanalysis datasets to validate some of the predictions of our descent rate models and find statistically significant evidence for synchronization of the QBO that is consistent with model behavior.