Editorial Type:
Article
Article Type:
Research Article

Nonlinear Dynamics and Regional Variations in the MJO Skeleton

Andrew J. Majda Department of Mathematics, and Center for Atmosphere–Ocean Science, Courant Institute, New York University, New York, New York

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Samuel N. Stechmann Department of Mathematics, University of Wisconsin—Madison, Madison, Wisconsin

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Print Publication:
01 Dec 2011
DOI:
https://doi.org/10.1175/JAS-D-11-053.1
Page(s):
3053–3071
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Abstract

A minimal, nonlinear oscillator model is analyzed for the Madden–Julian oscillation (MJO) “skeleton” (i.e., its fundamental features on intraseasonal/planetary scales), which includes the following: (i) a slow eastward phase speed of roughly 5 m s−1, (ii) a peculiar dispersion relation with dω/dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. Originally proposed in recent work by the authors, the fundamental mechanism involves neutrally stable interactions between (i) planetary-scale, lower-tropospheric moisture anomalies and (ii) the envelope of subplanetary-scale, convection/wave activity. Here, the model’s nonlinear dynamics are analyzed in a series of numerical experiments, using either a uniform sea surface temperature (SST) or a warm-pool SST. With a uniform SST, the results show significant variations in the number, strength, and/or locations of MJO events, including, for example, cases of a strong MJO event followed by a weaker MJO event, similar to the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). With a warm-pool SST, MJO events often begin as standing oscillations and then propagate slowly eastward across the warm pool, a behavior imitating MJOs in nature. While displaying the fundamental features of the MJO skeleton, these MJO events had significant variations in their lifetimes and regional extents, and they displayed intense, irregular fluctuations in their amplitudes. The model reproduces all of these features of the MJO skeleton without including mechanisms for the MJO’s “muscle,” such as refined vertical structure and upscale convective momentum transport from subplanetary-scale convection/waves. Besides these numerical experiments, it is also shown that the nonlinear model conserves a total energy that includes a contribution from the convective activity.

Corresponding author address: Samuel N. Stechmann, Department of Mathematics, University of Wisconsin—Madison, 480 Lincoln Dr., Madison, WI 53706. E-mail: stechmann@wisc.edu

Abstract

A minimal, nonlinear oscillator model is analyzed for the Madden–Julian oscillation (MJO) “skeleton” (i.e., its fundamental features on intraseasonal/planetary scales), which includes the following: (i) a slow eastward phase speed of roughly 5 m s−1, (ii) a peculiar dispersion relation with dω/dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. Originally proposed in recent work by the authors, the fundamental mechanism involves neutrally stable interactions between (i) planetary-scale, lower-tropospheric moisture anomalies and (ii) the envelope of subplanetary-scale, convection/wave activity. Here, the model’s nonlinear dynamics are analyzed in a series of numerical experiments, using either a uniform sea surface temperature (SST) or a warm-pool SST. With a uniform SST, the results show significant variations in the number, strength, and/or locations of MJO events, including, for example, cases of a strong MJO event followed by a weaker MJO event, similar to the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). With a warm-pool SST, MJO events often begin as standing oscillations and then propagate slowly eastward across the warm pool, a behavior imitating MJOs in nature. While displaying the fundamental features of the MJO skeleton, these MJO events had significant variations in their lifetimes and regional extents, and they displayed intense, irregular fluctuations in their amplitudes. The model reproduces all of these features of the MJO skeleton without including mechanisms for the MJO’s “muscle,” such as refined vertical structure and upscale convective momentum transport from subplanetary-scale convection/waves. Besides these numerical experiments, it is also shown that the nonlinear model conserves a total energy that includes a contribution from the convective activity.

Corresponding author address: Samuel N. Stechmann, Department of Mathematics, University of Wisconsin—Madison, 480 Lincoln Dr., Madison, WI 53706. E-mail: stechmann@wisc.edu
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