Dynamical systems modeling of low-frequency variability in low-order atmospheric models

Previous Article
Gevrey and analytic local models for families of vector fields
DCDS-B Home
This Issue
Next Article
The flow of the equal-mass spatial 3-body problem in the neighborhood of the equilateral relative equilibrium

September 2008, 10(2&3, September): 401-419. doi: 10.3934/dcdsb.2008.10.401

Dynamical systems modeling of low-frequency variability in low-order atmospheric models

1.	Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, Netherlands
2.	College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, EX4 4QF, Exeter, United Kingdom

Received October 2006 Revised May 2007 Published June 2008

Abstract
Related Papers

The understanding of atmospheric and oceanic low-frequency variability is an old problem having both theoretical interest and practical importance, e.g., for the assessment of climate change. In this paper possible relations with dynamical systems theory are given, in particular through bifurcation theory. Firstly, a specific type of oceanic low frequency variability is described, the so-called Atlantic Multidecadal Oscillation (AMO). Then recent work is reviewed, that investigates bifurcations as these occur in a few low-order models of the atmospheric circulation. It is shown that the Shil′nikov bifurcation in the Hopf-saddle-node bifurcation scenario takes place in each of the above atmospheric models. Related strange attractors and intermittency behavior are also found, both in agreement with the theoretical expectations and with qualitative aspects of the climate variability, like the AMO. It is discussed how the latter connection may be consolidated in higher dimensional and in PDE models.

Keywords: intermittency, atmospheric dynamics, low-dimensional models., Shil$'$nikov bifurcation.

Mathematics Subject Classification: Primary: 37G35, 70K44; Secondary: 37D45, 85A2.

Citation: H. W. Broer, Renato Vitolo. Dynamical systems modeling of low-frequency variability in low-order atmospheric models. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 401-419. doi: 10.3934/dcdsb.2008.10.401

[1]	F.J. Herranz, J. de Lucas, C. Sardón. Jacobi--Lie systems: Fundamentals and low-dimensional classification. Conference Publications, 2015, 2015 (special) : 605-614. doi: 10.3934/proc.2015.0605
[2]	Mickaël D. Chekroun, Michael Ghil, Honghu Liu, Shouhong Wang. Low-dimensional Galerkin approximations of nonlinear delay differential equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4133-4177. doi: 10.3934/dcds.2016.36.4133
[3]	Chui-Jie Wu. Large optimal truncated low-dimensional dynamical systems. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 559-583. doi: 10.3934/dcds.1996.2.559
[4]	Dmitrii Rachinskii. Realization of arbitrary hysteresis by a low-dimensional gradient flow. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 227-243. doi: 10.3934/dcdsb.2016.21.227
[5]	Andrey Sarychev. Controllability of the cubic Schroedinger equation via a low-dimensional source term. Mathematical Control & Related Fields, 2012, 2 (3) : 247-270. doi: 10.3934/mcrf.2012.2.247
[6]	Chui-Jie Wu, Hongliang Zhao. Generalized HWD-POD method and coupling low-dimensional dynamical system of turbulence. Conference Publications, 2001, 2001 (Special) : 371-379. doi: 10.3934/proc.2001.2001.371
[7]	Andrey Sarychev. Errata: Controllability of the cubic Schroedinger equation via a low-dimensional source term. Mathematical Control & Related Fields, 2014, 4 (2) : 261-261. doi: 10.3934/mcrf.2014.4.261
[8]	Jing Zhou, Zhibin Deng. A low-dimensional SDP relaxation based spatial branch and bound method for nonconvex quadratic programs. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2019044
[9]	Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417
[10]	David Julitz. Numerical approximation of atmospheric-ocean models with subdivision algorithm. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 429-447. doi: 10.3934/dcds.2007.18.429
[11]	Brittan Farmer, Cassandra Hall, Selim Esedoḡlu. Source identification from line integral measurements and simple atmospheric models. Inverse Problems & Imaging, 2013, 7 (2) : 471-490. doi: 10.3934/ipi.2013.7.471
[12]	Julián López-Gómez, Marcela Molina-Meyer, Andrea Tellini. Intricate bifurcation diagrams for a class of one-dimensional superlinear indefinite problems of interest in population dynamics. Conference Publications, 2013, 2013 (special) : 515-524. doi: 10.3934/proc.2013.2013.515
[13]	Zhouchen Lin. A review on low-rank models in data analysis. Big Data & Information Analytics, 2016, 1 (2&3) : 139-161. doi: 10.3934/bdia.2016001
[14]	Qixuan Wang, Hans G. Othmer. The performance of discrete models of low reynolds number swimmers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1303-1320. doi: 10.3934/mbe.2015.12.1303
[15]	Wenxiang Cong, Ge Wang, Qingsong Yang, Jia Li, Jiang Hsieh, Rongjie Lai. CT image reconstruction on a low dimensional manifold. Inverse Problems & Imaging, 2019, 13 (3) : 449-460. doi: 10.3934/ipi.2019022
[16]	Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445-458. doi: 10.3934/mbe.2006.3.445
[17]	Anatoly N. Kochubei, Yuri Kondratiev. Fractional kinetic hierarchies and intermittency. Kinetic & Related Models, 2017, 10 (3) : 725-740. doi: 10.3934/krm.2017029
[18]	James Walsh, Esther Widiasih. A dynamics approach to a low-order climate model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 257-279. doi: 10.3934/dcdsb.2014.19.257
[19]	Daniele Castorina, Pierpaolo Esposito, Berardino Sciunzi. Low dimensional instability for semilinear and quasilinear problems in $\mathbb{R}^N$. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1779-1793. doi: 10.3934/cpaa.2009.8.1779
[20]	Jianyu Chen, Hong-Kun Zhang. Statistical properties of one-dimensional expanding maps with singularities of low regularity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 4955-4977. doi: 10.3934/dcds.2019203

2017 Impact Factor: 0.972

American Institute of Mathematical Sciences