UBC Theses and Dissertations

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UBC Theses and Dissertations

Noise induced tipping in ocean circulation based on the Stommel model Yin, Ziming


The Atlantic Ocean circulation transports the warmth and salinity northwards and it is a crucial part of the world climate. The flipping of this circulation is hypothesized to be the explanation of several abrupt climate changes over the past 2.6 million years. The pattern of this circulation can be determined from ocean models, and a typical pattern, which is also used in this thesis, is described by the Stommel model. There are two bifurcations in the Stommel model — one is a smooth bifurcation and the other is a non-smooth bifurcation. When the system approaches either bifurcation, the presence of noise makes the system escape from the current state easily. However, the properties of these two bifurcations are widely different. Here for the smooth bifurcation, the probability of tipping is judged by some well-known linear and nonlinear methods, including the linear decay rate, the potential energy and the skewness. Whereas for the non-smooth bifurcation, if there is no discernable trend from the above methods, we find out that one is also able to obtain the early warning signal by a unique feature of the Stommel model: the eigenvalues of the system matrix when approaching the non-smooth bifurcation are complex numbers, which lead to periodic circulations. The change of the periodic circulation can be observed by the variation of its power spectral density, which is important in showing the proximity to tipping. In this thesis, the coherence resonance is used to define this variation. After some extensive studies, we find that the combination of the above methods are able to give us an early warning signal as the system moves closer to the bifurcations.

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