Dynamic tipping in the non-smooth Stommel-box model, with fast oscillatory forcing

Chris Budd; Cody Griffith; Rachel Kuske

doi:10.1016/j.physd.2021.132948

Dynamic tipping in the non-smooth Stommel-box model, with fast oscillatory forcing

Chris Budd, Cody Griffith, Rachel Kuske

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Abstract

We study the behavior at tipping points close to non-smooth fold bifurcations in non-autonomous systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous dynamical systems, modeling thermohaline circulation. We obtain explicit asymptotic expressions for the behavior at tipping points in the settings of both slowly varying freshwater forcing and rapidly oscillatory fluctuations. The results, based on combined multiple scale and local analyses, provide conditions for the sudden transitions between temperature-dominated and salinity-dominated states. In the context of high frequency oscillations, a multiple scale averaging approach can be used instead of the usual geometric approach normally required for piecewise-smooth continuous systems. The explicit parametric dependencies of advances and lags in the tipping show a competition between dynamic features of the model. We make a contrast between the behavior of tipping points close to both smooth Saddle–Node Bifurcations and the non-smooth systems studied on this paper. In particular we show that the non-smooth case has earlier and more abrupt transitions. This result has clear implications for the design of early warning signals for tipping in the case of the non-smooth dynamical systems which often arise in climate models.

Original language	English
Article number	132948
Journal	Physica D: Nonlinear Phenomena
Volume	432
Early online date	12 May 2021
DOIs	https://doi.org/10.1016/j.physd.2021.132948
Publication status	Published - 30 Apr 2022

Bibliographical note

Funding Information:
This research was supported in part by a NSERC, Canada Discovery Accelerator Grant, a Simons Foundation, USA Fellowship, and the Isaac Newton Institute for Mathematical Sciences, UK . The authors are grateful for helpful discussions during the 2016 Climate Modeling Workshop at the Centre de Recerca Matemàtica (CRM), part the Intensive Research Program Advances in Nonsmooth Dynamics.

COVID-19 Revised guidance regarding Other Exceptions:
41. Where it has not been possible for an output that is in scope (as defined at paragraph 223 of the ‘Guidance on submissions’) of the open access requirements to meet these requirements due to COVID-19, the institution may apply the ‘other exception’. This exception is described at paragraph 255.a. of the ‘Guidance on submissions’. This includes effects due to individual circumstances (such as ill health, caring responsibilities); other personal circumstances related to COVID-19 (such as furloughed staff, health-related or clinical staff diverted to frontline services, staff resource diverted to other priority areas within the HEI in response to COVID-19); and/or external factors related to COVID-19.

Keywords

Border collision
Conceptual climate models
Dynamic bifurcation
Non-autonomous systems
Non-smooth dynamics
Tipping

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.physd.2021.132948

Stommel.PDFAccepted author manuscript, 894 KBLicence: CC BY-NC-ND

Cite this

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title = "Dynamic tipping in the non-smooth Stommel-box model, with fast oscillatory forcing",

abstract = "We study the behavior at tipping points close to non-smooth fold bifurcations in non-autonomous systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous dynamical systems, modeling thermohaline circulation. We obtain explicit asymptotic expressions for the behavior at tipping points in the settings of both slowly varying freshwater forcing and rapidly oscillatory fluctuations. The results, based on combined multiple scale and local analyses, provide conditions for the sudden transitions between temperature-dominated and salinity-dominated states. In the context of high frequency oscillations, a multiple scale averaging approach can be used instead of the usual geometric approach normally required for piecewise-smooth continuous systems. The explicit parametric dependencies of advances and lags in the tipping show a competition between dynamic features of the model. We make a contrast between the behavior of tipping points close to both smooth Saddle–Node Bifurcations and the non-smooth systems studied on this paper. In particular we show that the non-smooth case has earlier and more abrupt transitions. This result has clear implications for the design of early warning signals for tipping in the case of the non-smooth dynamical systems which often arise in climate models.",

keywords = "Border collision, Conceptual climate models, Dynamic bifurcation, Non-autonomous systems, Non-smooth dynamics, Tipping",

author = "Chris Budd and Cody Griffith and Rachel Kuske",

note = "Funding Information: This research was supported in part by a NSERC, Canada Discovery Accelerator Grant, a Simons Foundation, USA Fellowship, and the Isaac Newton Institute for Mathematical Sciences, UK . The authors are grateful for helpful discussions during the 2016 Climate Modeling Workshop at the Centre de Recerca Matem{\`a}tica (CRM), part the Intensive Research Program Advances in Nonsmooth Dynamics. COVID-19 Revised guidance regarding Other Exceptions: 41. Where it has not been possible for an output that is in scope (as defined at paragraph 223 of the {\textquoteleft}Guidance on submissions{\textquoteright}) of the open access requirements to meet these requirements due to COVID-19, the institution may apply the {\textquoteleft}other exception{\textquoteright}. This exception is described at paragraph 255.a. of the {\textquoteleft}Guidance on submissions{\textquoteright}. This includes effects due to individual circumstances (such as ill health, caring responsibilities); other personal circumstances related to COVID-19 (such as furloughed staff, health-related or clinical staff diverted to frontline services, staff resource diverted to other priority areas within the HEI in response to COVID-19); and/or external factors related to COVID-19. ",

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N2 - We study the behavior at tipping points close to non-smooth fold bifurcations in non-autonomous systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous dynamical systems, modeling thermohaline circulation. We obtain explicit asymptotic expressions for the behavior at tipping points in the settings of both slowly varying freshwater forcing and rapidly oscillatory fluctuations. The results, based on combined multiple scale and local analyses, provide conditions for the sudden transitions between temperature-dominated and salinity-dominated states. In the context of high frequency oscillations, a multiple scale averaging approach can be used instead of the usual geometric approach normally required for piecewise-smooth continuous systems. The explicit parametric dependencies of advances and lags in the tipping show a competition between dynamic features of the model. We make a contrast between the behavior of tipping points close to both smooth Saddle–Node Bifurcations and the non-smooth systems studied on this paper. In particular we show that the non-smooth case has earlier and more abrupt transitions. This result has clear implications for the design of early warning signals for tipping in the case of the non-smooth dynamical systems which often arise in climate models.

AB - We study the behavior at tipping points close to non-smooth fold bifurcations in non-autonomous systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous dynamical systems, modeling thermohaline circulation. We obtain explicit asymptotic expressions for the behavior at tipping points in the settings of both slowly varying freshwater forcing and rapidly oscillatory fluctuations. The results, based on combined multiple scale and local analyses, provide conditions for the sudden transitions between temperature-dominated and salinity-dominated states. In the context of high frequency oscillations, a multiple scale averaging approach can be used instead of the usual geometric approach normally required for piecewise-smooth continuous systems. The explicit parametric dependencies of advances and lags in the tipping show a competition between dynamic features of the model. We make a contrast between the behavior of tipping points close to both smooth Saddle–Node Bifurcations and the non-smooth systems studied on this paper. In particular we show that the non-smooth case has earlier and more abrupt transitions. This result has clear implications for the design of early warning signals for tipping in the case of the non-smooth dynamical systems which often arise in climate models.

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JO - Physica D: Nonlinear Phenomena

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M1 - 132948

ER -

Dynamic tipping in the non-smooth Stommel-box model, with fast oscillatory forcing

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

UN SDGs

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