Noise induced tipping in ocean circulation based on the Stommel model
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Yin, Ziming
issued: 2018-08-20T15:41:21Z
issued: 2018
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: 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.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/66830
note: Noise Induced Tipping in Ocean Circulation Based on theStommel ModelbyZiming YinB.Sc., Beijing Jiaotong University, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Mathematics)The University of British Columbia(Vancouver)August 2018c© Ziming Yin, 2018The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled:Noise Induced Tipping in Ocean Circulation Based on the Stommel Modelsubmitted by Ziming Yin in partial fulfillment of the requirements of the degree ofMaster of Science in Applied Mathematics.Examining Committee:Rachel Kuske, Professor of MathematicsSupervisorWayne NagataSupervisory Committee MemberiiAbstractThe Atlantic Ocean circulation transports the warmth and salinity northwards andit is a crucial part of the world climate. The flipping of this circulation is hypothe-sized to be the explanation of several abrupt climate changes over the past 2.6 mil-lion 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 Stommelmodel. There are two bifurcations in the Stommel model — one is a smooth bi-furcation and the other is a non-smooth bifurcation. When the system approacheseither bifurcation, the presence of noise makes the system escape from the currentstate easily. However, the properties of these two bifurcations are widely differ-ent. Here for the smooth bifurcation, the probability of tipping is judged by somewell-known linear and nonlinear methods, including the linear decay rate, the po-tential energy and the skewness. Whereas for the non-smooth bifurcation, if thereis no discernable trend from the above methods, we find out that one is also ableto obtain the early warning signal by a unique feature of the Stommel model: theeigenvalues of the system matrix when app…
has type: Thesis/Dissertation
date issued: 2018-09
is shown at: 10.14288/1.0371132
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/66830