Presentation Information
[U02-P16]Phase reduction analysis of the synchronization of the quasi-biennial oscillation to the annual cycle
*Ayumi Ozawa1, Yoji Kawamura1 (1.Japan Agency for Marine-Earth Science and Technology)
Keywords:
QBO,synchronization,phase reduction
The quasi-biennial oscillation (QBO) is characterized by alternating eastward and westward zonal-mean zonal winds in the equatorial stratosphere [1]. While the QBO has an average period of about 28 months, it has been pointed out that the period of the oscillation varies and is to some extent synchronized to the annual cycle [1]. While numerical studies, e.g. [2], have reproduced this synchronization phenomenon and offered predictions, simple theoretical frameworks that explain these results remain limited.
Meanwhile, the phase reduction theory [3, 4] has been successfully utilized to understand various synchronization phenomena. By using this theory, an oscillatory dynamical system is reduced to a phase equation, in which the response of the rhythm to perturbations is quantified by the phase sensitivity function. However, the application of the phase-reduction theory to the synchronization of the QBO has been limited.
Here, we formulate a phase reduction method for a simple model of the QBO [5] and obtain the phase sensitivity function. The theory provides conditions under which the QBO is synchronized to a given annual forcing. It also suggests the waveform of the annual cycle that entrains the QBO most efficiently to the annual cycle. Thus, our theory provides insights into dynamical properties of the QBO and its synchronization to the annual cycle.
[1] Baldwin, M. P., L. J. Gray, T. J. Dunkerton, et al. “The Quasi-Biennial Oscillation.” Reviews of Geophysics 39, no. 2 (2001): 179–229.
[2] Rajendran, Kylash, Irene M. Moroz, Peter L. Read, and Scott M. Osprey. “Synchronisation of the Equatorial QBO by the Annual Cycle in Tropical Upwelling in a Warming Climate.” Quarterly Journal of the Royal Meteorological Society 142, no. 695 (2016): 1111–20.
[3] Brown, Eric, Jeff Moehlis, and Philip Holmes. “On the Phase Reduction and Response Dynamics of Neural Oscillator Populations.” Neural Computation 16, no. 4 (2004): 673–715.
[4] Kuramoto, Yoshiki. Chemical Oscillations, Waves, and Turbulence. Edited by Hermann Haken. Vol. 19. Springer Series in Synergetics. Springer, 1984.
[5] Plumb, R. A. The Interaction of Two Internal Waves with the Mean Flow: Implications for the Theory of the Quasi-Biennial Oscillation. Journal of the Atmospheric Sciences. December 1, 1977.
Meanwhile, the phase reduction theory [3, 4] has been successfully utilized to understand various synchronization phenomena. By using this theory, an oscillatory dynamical system is reduced to a phase equation, in which the response of the rhythm to perturbations is quantified by the phase sensitivity function. However, the application of the phase-reduction theory to the synchronization of the QBO has been limited.
Here, we formulate a phase reduction method for a simple model of the QBO [5] and obtain the phase sensitivity function. The theory provides conditions under which the QBO is synchronized to a given annual forcing. It also suggests the waveform of the annual cycle that entrains the QBO most efficiently to the annual cycle. Thus, our theory provides insights into dynamical properties of the QBO and its synchronization to the annual cycle.
[1] Baldwin, M. P., L. J. Gray, T. J. Dunkerton, et al. “The Quasi-Biennial Oscillation.” Reviews of Geophysics 39, no. 2 (2001): 179–229.
[2] Rajendran, Kylash, Irene M. Moroz, Peter L. Read, and Scott M. Osprey. “Synchronisation of the Equatorial QBO by the Annual Cycle in Tropical Upwelling in a Warming Climate.” Quarterly Journal of the Royal Meteorological Society 142, no. 695 (2016): 1111–20.
[3] Brown, Eric, Jeff Moehlis, and Philip Holmes. “On the Phase Reduction and Response Dynamics of Neural Oscillator Populations.” Neural Computation 16, no. 4 (2004): 673–715.
[4] Kuramoto, Yoshiki. Chemical Oscillations, Waves, and Turbulence. Edited by Hermann Haken. Vol. 19. Springer Series in Synergetics. Springer, 1984.
[5] Plumb, R. A. The Interaction of Two Internal Waves with the Mean Flow: Implications for the Theory of the Quasi-Biennial Oscillation. Journal of the Atmospheric Sciences. December 1, 1977.