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A Stochastic Skeleton Model for the MJO

Sulian ThualDepartment of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, New York

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Andrew J. MajdaDepartment of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, New York

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Samuel N. StechmannDepartment of Mathematics, and Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

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Abstract

The Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal time scales and planetary spatial scales. Despite the primary importance of the MJO and the decades of research progress since its original discovery, a generally accepted theory for its essential mechanisms has remained elusive. In recent work by two of the authors, a minimal dynamical model has been proposed that recovers robustly the most fundamental MJO features of (i) a slow eastward speed of roughly 5 m s−1, (ii) a peculiar dispersion relation with /dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. This model, the skeleton model, depicts the MJO as a neutrally stable atmospheric wave that involves a simple multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture, and the planetary envelope of synoptic-scale activity. In this article, it is shown that the skeleton model can further account for (iv) the intermittent generation of MJO events and (v) the organization of MJO events into wave trains with growth and demise, as seen in nature. The goal is achieved by developing a simple stochastic parameterization for the unresolved details of synoptic-scale activity, which is coupled to otherwise deterministic processes in the skeleton model. In particular, the intermittent initiation, propagation, and shut down of MJO wave trains in the skeleton model occur through these stochastic effects. This includes examples with a background warm pool where some initial MJO-like disturbances propagate through the western region but stall at the peak of background convection/heating corresponding to the Maritime Continent in nature.

Corresponding author address: Sulian Thual, 251 Mercer Street, New York, NY 10012. E-mail: sulian.thual@gmail.com

Abstract

The Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal time scales and planetary spatial scales. Despite the primary importance of the MJO and the decades of research progress since its original discovery, a generally accepted theory for its essential mechanisms has remained elusive. In recent work by two of the authors, a minimal dynamical model has been proposed that recovers robustly the most fundamental MJO features of (i) a slow eastward speed of roughly 5 m s−1, (ii) a peculiar dispersion relation with /dk ≈ 0, and (iii) a horizontal quadrupole vortex structure. This model, the skeleton model, depicts the MJO as a neutrally stable atmospheric wave that involves a simple multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture, and the planetary envelope of synoptic-scale activity. In this article, it is shown that the skeleton model can further account for (iv) the intermittent generation of MJO events and (v) the organization of MJO events into wave trains with growth and demise, as seen in nature. The goal is achieved by developing a simple stochastic parameterization for the unresolved details of synoptic-scale activity, which is coupled to otherwise deterministic processes in the skeleton model. In particular, the intermittent initiation, propagation, and shut down of MJO wave trains in the skeleton model occur through these stochastic effects. This includes examples with a background warm pool where some initial MJO-like disturbances propagate through the western region but stall at the peak of background convection/heating corresponding to the Maritime Continent in nature.

Corresponding author address: Sulian Thual, 251 Mercer Street, New York, NY 10012. E-mail: sulian.thual@gmail.com
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