Critical Transition Analysis of the Deterministic Wind-Driven Ocean Circulation - A Flux-Based Network Approach

A new method for constructing complex networks from fluid flow fields is proposed. The approach focuses on spatial properties of the flow field, namely, on the topology of the streamline field. The network approach is applied to a model of the wind-driven ocean circulation, which exhibits the prototype of a critical transition, that is, a back-to-back saddle-node bifurcation related to two separate dynamical regimes. The network analysis enables a structural characterization of, on the one hand, the viscous regime as a weakly-connected and highly-assortative regime, and, on the other hand, of the inertial regime as a highly-connected and weakly-assortative regime. Moreover, the network analysis enables a robust early-warning signal of the critical transition emerging from the viscous regime: The upcoming global regime change induced by the critical transition may be anticipated by a drastic decrease in the overall closeness of the network, which reflects a preceding local regime change in the flow field. Hence, the results support the application of network-based topology measures complementary to time-series based statistical properties as leading indicators of critical transitions.

[1]  Peter Cox,et al.  Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Robert Marsh,et al.  Using GENIE to study a tipping point in the climate system , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  S. Pierini A Kuroshio Extension System Model Study: Decadal Chaotic Self-Sustained Oscillations , 2006 .

[4]  J. Overpeck,et al.  Abrupt Climate Change , 2003, Science.

[5]  Wolfgang Lucht,et al.  Tipping elements in the Earth's climate system , 2008, Proceedings of the National Academy of Sciences.

[6]  M. Scheffer,et al.  Slowing down as an early warning signal for abrupt climate change , 2008, Proceedings of the National Academy of Sciences.

[7]  Marten Scheffer,et al.  Spatial correlation as leading indicator of catastrophic shifts , 2010, Theoretical Ecology.

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  M. Scheffer,et al.  Slowing Down in Spatially Patterned Ecosystems at the Brink of Collapse , 2011, The American Naturalist.

[10]  M. Rietkerk,et al.  Self-Organized Patchiness and Catastrophic Shifts in Ecosystems , 2004, Science.

[11]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[12]  C. Kuehn A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics , 2011, 1101.2899.

[13]  Paul J. Roebber,et al.  The architecture of the climate network , 2004 .

[14]  Tilo Winkler,et al.  Self-organized patchiness in asthma as a prelude to catastrophic shifts , 2005, Nature.

[15]  Norbert Marwan,et al.  The backbone of the climate network , 2009, 1002.2100.

[16]  Peter U. Clark,et al.  The role of the thermohaline circulation in abrupt climate change , 2002, Nature.

[17]  S. Carpenter,et al.  Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data , 2012, PloS one.

[18]  Hermann Held,et al.  The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation , 2003 .

[19]  Patrick E. McSharry,et al.  Prediction of epileptic seizures: are nonlinear methods relevant? , 2003, Nature Medicine.

[20]  S. Carpenter,et al.  Turning back from the brink: Detecting an impending regime shift in time to avert it , 2009, Proceedings of the National Academy of Sciences.

[21]  Anastasios A. Tsonis,et al.  Climate Mode Covariability and Climate shifts , 2011, Int. J. Bifurc. Chaos.

[22]  G. Haug,et al.  Rapid oceanic and atmospheric changes during the Younger Dryas cold period , 2009 .

[23]  Potsdam,et al.  Complex networks in climate dynamics. Comparing linear and nonlinear network construction methods , 2009, 0907.4359.

[24]  Glenn R. Ierley,et al.  Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip , 1995 .

[25]  S. Carpenter,et al.  Anticipating Critical Transitions , 2012, Science.

[26]  Characterization of the multiple equilibria regime in a global ocean model , 2007 .

[27]  C. Wissel A universal law of the characteristic return time near thresholds , 1984, Oecologia.

[28]  S. Drijfhout,et al.  An Indicator of the Multiple Equilibria Regime of the Atlantic Meridional Overturning Circulation , 2010 .

[29]  Ed Hawkins,et al.  Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport , 2011 .

[30]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[31]  Eliezer Kit,et al.  Spatial versus temporal instabilities in a parametrically forced stratified mixing layer , 2006, Journal of Fluid Mechanics.

[32]  G. Vallis Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation , 2017 .

[33]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[34]  J. Kurths,et al.  Analytical framework for recurrence network analysis of time series. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[36]  S. Carpenter,et al.  Catastrophic shifts in ecosystems , 2001, Nature.

[37]  S. Meacham,et al.  On the stability of the wind-driven circulation , 1998 .

[38]  Sergey Kravtsov,et al.  A new dynamical mechanism for major climate shifts , 2007 .

[39]  Hugo Fort,et al.  Early Warnings for Catastrophic Shifts in Ecosystems: Comparison between Spatial and Temporal Indicators , 2010, Int. J. Bifurc. Chaos.

[40]  V. A. Sheremet,et al.  Eigenanalysis of the two-dimensional wind-driven ocean circulation problem , 1997 .

[41]  Bo Qiu,et al.  Variability of the Kuroshio Extension Jet, Recirculation Gyre, and Mesoscale Eddies on Decadal Time Scales , 2005 .

[42]  Michael Small,et al.  Recurrence-based time series analysis by means of complex network methods , 2010, Int. J. Bifurc. Chaos.

[43]  J. Jouzel,et al.  Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica , 1999, Nature.

[44]  George Sugihara,et al.  Complex systems: Ecology for bankers , 2008, Nature.

[45]  Henk A. Dijkstra Nonlinear Physical Oceanography , 2010 .

[46]  Jürgen Kurths,et al.  Recurrence networks—a novel paradigm for nonlinear time series analysis , 2009, 0908.3447.

[47]  Marten Scheffer,et al.  Slow Recovery from Perturbations as a Generic Indicator of a Nearby Catastrophic Shift , 2007, The American Naturalist.

[48]  R. Temam,et al.  Structural Bifurcation of 2-D Incompressible Flows , 2001 .

[49]  S. Meacham,et al.  Barotropic, wind-driven circulation in a small basin , 1997 .

[50]  J. Kurths,et al.  Interaction network based early warning indicators for the Atlantic MOC collapse , 2013 .

[51]  J. Michael T. Thompson,et al.  Predicting Climate tipping as a Noisy bifurcation: a Review , 2011, Int. J. Bifurc. Chaos.

[52]  S. Rahmstorf Bifurcations of the Atlantic thermohaline circulation in response to changes in the hydrological cycle , 1995, Nature.

[53]  T. Lenton Early warning of climate tipping points , 2011 .

[54]  Paul J. Roebber,et al.  What Do Networks Have to Do with Climate , 2006 .

[55]  S. Carpenter,et al.  Rising variance: a leading indicator of ecological transition. , 2006, Ecology letters.