Dancing on the devil’s staircase: the synchronization of the quasi-biennial oscillation in the tropical stratosphere

Thesis

In this thesis we investigate the variability of the Quasi-Biennial Oscillation (QBO), which is the dominant mode of variability in the tropical stratosphere. In particular, we study the susceptibility of the QBO to the phenomenon of synchronization; that is, the adjustment of the rhythms of the QBO under the influence of a periodic external force. We approach the problem using a combination of theoretical analysis, numerical modelling, and observational study. The dynamics of the QBO are studied in detail using the Holton-Lindzen partial differential equation. We introduce various forcing terms to this equation, to simulate the effects of the Brewer-Dobson circulation, the Semi-Annual Oscillation, the Inter-Tropical Convergence Zone, and tropical wave forcing variations on the QBO. We find that the QBO enters a state of synchronization in its interactions with all of the above forcing terms, with the exception of the Semi-Annual Oscillation. The general structure of QBO synchronization takes the form of either exact frequency locking, discrete multi-cycle periods, or quasiperiodic behaviour. By recasting the Holton-Lindzen equation into the form of a descent rate model, we demonstrate that the dynamics of the QBO period can be described using a simple one-dimensional ordinary differential equation, which is shown to be closely related to the circle map. This simplification greatly reduces the complexity of the model, whilst retaining all the key observed features of synchronization.

We study the dynamics of the QBO in reanalysis and general circulation model datasets, using a combination of Extended Empirical Orthogonal Function analysis and analytic phase techniques. We show that the descent rate of the QBO correlates with the strength of tropical upwelling. Further, by defining a statistical measure for QBO synchronization based on the evolution of QBO periods, we demonstrate that both the observed and modelled QBOs behave in a way that is consistent with synchronization to the annual cycle. The observed QBO is found to be phase synchronized with the Brewer-Dobson circulation, and we find that it jumps irregularly between the 2 : 1, 5 : 2, and 3 : 1 synchronization ratios. We find evidence that the phase slips of the observed QBO tend to occur during periods when the El Niño Southern Oscillation is in a strong positive phase.

Our results make a robust case in favour of the proposition that the QBO is synchronized to the annual cycle via seasonal and inter-annual variations in tropical upwelling strength and tropical wave activity.

Authors: Rajendran, K

• DOI: 10.5287/ora-a4jyzjqpn
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Quasi-Biennial Oscillation; Stratosphere; Synchronization
• Subjects: Atmospheric Physics; Applied mathematics