Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


Preferences help
enabled [disable] Abstract
Number of results
2015 | 1 | 1 |

Article title

A Suite of Skeleton Models for the MJO with
Refined Vertical Structure


Title variants

Languages of publication



The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere
on intraseasonal timescales and planetary spatial scales. The skeleton model is a minimal dynamical model
that recovers robustly the most fundamental MJO features of (I) a slow eastward speed of roughly 5 ms−1, (II)
a peculiar dispersion relation with dw/dk ≈ 0, and (III) a horizontal quadrupole vortex structure. This model
depicts the MJO as a neutrally-stable atmosphericwave that involves a simple multiscale interaction between
planetary dry dynamics, planetary lower-tropospheric moisture and the planetary envelope of synoptic-scale
activity. Here we propose and analyze a suite of skeleton models that qualitatively reproduce the refined vertical
structure of the MJO in nature. This vertical structure consists of a planetary envelope of convective activity
transitioning from the congestus to the deep to the stratiform type, in addition to a front-to-rear (i.e. tilted)
structure of heating, moisture, winds and temperature. A first example of skeleton model achieving this goal
has been considered recently in work by the authors. The construction of such a model satisfies an energy
conservation principle, such that its solutions at the intraseasonal-planetary scale remain neutrally stable.
Here, additional classes of skeleton models are constructed based on the same principle. In particular, those
new models are more realistic then the former one as they consider fully coupled interactions between the
planetary dry dynamics of the first and second baroclinic mode and the details of the vertical structure of
moisture and convective activity. All models reproduce qualitatively the refined vertical structure of the MJO.
In addition,when considered with a simple stochastic parametrization for the unresolved details of synopticscale
activity, all models show intermittent initiation, propagation and shut down of MJO wave trains, as in
previous studies.








Physical description


27 - 10 - 2015
30 - 11 - 2015
6 - 8 - 2015


  • Department of Mathematics, and Center for Atmosphere Ocean Science,
    Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA
  • Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical
    Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA


  • [1] S. Ajayamohan, B. Khouider, and Andrew J. Majda. Realistic initiation and dynamics of the Madden-Julian Oscillation in acoarse resolution aquaplanet GCM. Geophys. Res. Lett., 40:6252–6257, 2013.[Crossref][WoS]
  • [2] Joseph A. Biello and Andrew J.Majda. A NewMultiscale Model for theMadden-Julian Oscillation. J. Atmos. Sci., 62(6):1694–1721, 2005.[Crossref]
  • [3] Joseph A. Biello and Andrew J. Majda. Modulating synoptic scale convective activity and boundary layer dissipation in theIPESD models of the Madden-Julian oscillation. Dyn. Atm. Oceans, 42, Issue 1-4:152–215, 2006.
  • [4] N. Chen and A. J. Majda. Filtering the Stochastic Skeleton Model for the Madden-Julian Oscillation. 2015. in press.
  • [5] N. Chen, A. J. Majda, and D. Giannakis. Predicting the cloud patterns of the madden-julian oscillation through a low-ordernonlinear stochastic model. GRL, page DOI: 10.1002/2014GL060876, 2014.[Crossref]
  • [6] Q. Deng, B. Khouider, and A. J. Majda. The MJO in a Coarse-Resolution GCM with a Stochastic Multicloud Parameterization.J. Atmos. Sci., 72, 2015. 55-74.[WoS]
  • [7] Yevgeniy Frenkel, Andrew J. Majda, and Boualem Khouider. Using the Stochastic Multicloud Model to Improve TropicalConvective Parameterization: A Paradigm Example. J. Atmos. Sci., 69:1080–1105, 2012.[WoS][Crossref]
  • [8] C. W. Gardiner. Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer, 1994. 442pp.
  • [9] Daniel T. Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem., 81(25):2340–2361, 1977.[Crossref]
  • [10] Harry H. Hendon and Murry L. Salby. The Life Cycle of the Madden-Julian Oscillation. J. Atmos. Sci., 51:2225–2237, 1994.[Crossref]
  • [11] X. Jiang, D. E. Waliser, and coauthors. Vertical structure and physical processes of the Madden-Julian oscillation: Exploringkey model physics in climate simulations. J. Geophys. Res., 2015. doi:10.1002/2014JD022375.[WoS][Crossref]
  • [12] B. Khouider, J. A. Biello, and A. J.Majda. A StochasticMulticloud Model for Tropical Convection. Comm.Math. Sci., 8(1):187–216, 2010.
  • [13] B. Khouider and A. J. Majda. A simple multicloud parametrization for convectively coupled tropical waves. Part I: LinearAnalysis. J. Atmos. Sci., 63:1308–1323, 2006.[Crossref]
  • [14] B. Khouider and A. J. Majda. A simple multicloud parametrization for convectively coupled tropical waves. Part II. Nonlinearsimulations. J Atmos Sci, 64:381–400, 2007.[Crossref][WoS]
  • [15] B. Khouider and A. J.Majda. Equatorial convectively coupled waves in a simple multicloud model. J AtmSci, (65):3376–3397,2008.
  • [16] Boualem Khouider and Andrew J. Majda. Multicloud Models for Organized Tropical Convection: Enhanced Congestus Heating.J. Atmos. Sci., 65(3):895–914, 2008.[WoS][Crossref]
  • [17] Boualem Khouider, Amik St-Cyr, Andrew J. Majda, and Joseph Tribbia. The MJO and convectively coupled waves in a coarseresolutionGCM with a simple multicloud parameterization. J. Atmos. Sci., 68(2):240–264, 2011.[Crossref][WoS]
  • [18] K. Kikuchi and Y. N. Takayabu. The development of organized convection associated with the MJO during TOGA COARE IOP:Trimodal characteristics. Geophys. Res. Lett., 31, 2004. L10101,doi:10.1029/2004GL019601.[Crossref]
  • [19] G. N. Kiladis, K. H. Straub, and Haertel P. T. Zonal and vertical structure of the Madden-Julian oscillation. J Atmos Sci,62:2790–2809, 2005.[Crossref]
  • [20] N.P. Klingaman, X. Jiang, and coauthors. Vertical structure and physical processes of the Madden-Julian oscillation: Synthesisand summary. J. Geophys. Res., 2015. doi:10.1002/2015JD023196.[WoS][Crossref]
  • [21] Gregory F. Lawler. Introduction to Stochastic Processes. Chapman and Hall/CRC, 2006. 192pp.
  • [22] R. E. Madden and P. R. Julian. Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci.,28:702–708, 1971.
  • [23] R. E. Madden and P. R. Julian. Observations of the 40-50 day tropical oscillation-A review. Mon. Wea. Rev., 122:814–837,1994.
  • [24] A. J. Majda and J. A. Biello. A multiscale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA, 101:4736–4741, 2004.[Crossref]
  • [25] A. J.Majda, S. N. Stechmann, and B. Khouider. Madden-Julian oscillation analog and intraseasonal variability in amulticloudmodel above the equator. Proc. Natl. Acad. Sci. USA, 104:9919–9924, 2007.[Crossref]
  • [26] Andrew J. Majda and Samuel N. Stechmann. A Simple Dynamical Model with Features of Convective Momentum Transport.J. Atmos. Sci., 66:373–392, 2009.[WoS][Crossref]
  • [27] Andrew J. Majda and Samuel N. Stechmann. The skeleton of tropical intraseasonal oscillations. Proc. Natl. Acad. Sci.,106:8417–8422, 2009.[Crossref]
  • [28] Andrew J. Majda and Samuel N. Stechmann. Nonlinear Dynamics and Regional Variations in the MJO Skeleton. J. Atmos.Sci., 68:3053–3071, 2011.[Crossref][WoS]
  • [29] A. J. Matthews. Primary and successive events in the Madden-Julian Oscillation. Quart. J. Roy. Meteor. Soc., 134:439–453,2008.[Crossref][WoS]
  • [30] T. Miyakawa, Y.N. Takayabu, T. Nasuno, H. Miura, M. Satoh, and M.W. Moncrieff. Convective momentum transport by rainbandswithin a Madden-Julian oscillation in a global nonhydrostatic model with explicit deep convective processes. Part I:Methodology and general results. J. Atmos. Sci., 69:1317–1338, 2012.[Crossref][WoS]
  • [31] M. W. Moncrieff, M. Shapiro, J. Slingo, and F. Molteni. Collaborative research at the intersection of weather and climate.WMO Bull., 56:204–211, 2007.
  • [32] MW Moncrieff. Analytic representation of the large-scale organization of tropical convection. Quart. J. Roy. Meteor. Soc.,130:1521–1538, 2004.
  • [33] J. D. Neelin and N. Zeng. A quasi-equilibrium tropical circulation model:formulation. J. Atmos. Sci., 57:1741–1766, 2000.[Crossref]
  • [34] H. R. Ogrosky and S. N. Stechmann. The mjo skeleton model with observation-based background state and forcing. Q. J.Roy. Met. Soc., 2015. DOI: 10.1002/qj.2552.[Crossref]
  • [35] A. H. Sobel, J. Nilsson, and L. M. Polvani. The Weak Temperature Gradient Approximation and Balanced Tropical MoistureWaves. J. Atmos. Sci., 58:3650–3665, 2001.[Crossref]
  • [36] J. P. Stachnik, D. E.Waliser, and A.J.Majda. Precursor environmental conditions associated with the termination ofmaddenjulianoscillation events. J. Atmos. Sci., 2015. doi: http://dx.doi.org/10.1175/JAS-D-14-0254.1.[Crossref]
  • [37] S. Stechmann, A. J. Majda, and D. Skjorshammer. Convectively coupled wave-environment interactions. Theor. Comp. FluidDyn., 27:513–532, 2013.[Crossref]
  • [38] S. N. Stechmann and A. J.Majda. Identifying the skeleton of themadden-julian oscillation in observational data. Mon. Wea.Rev., 143:395–416, 2015.[WoS]
  • [39] S. Thual and A. J. Majda. A skeleton model for the MJO with refined vertial structure. Clim. Dyn., 2015. accepted.
  • [40] S. Thual, A.-J. Majda, and S. N. Stechmann. Asymmetric intraseasonal events in the skeleton MJO model with seasonalcycle. Clim. Dyn., 2015. doi:10.1007/s00382-014-2256-8.[Crossref][WoS]
  • [41] S. Thual, Andrew J. Majda, and S. N. Stechmann. A stochastic skeleton model for the MJO. J. Atmos. Sci., 71:697–715, 2014.[Crossref]
  • [42] B. Tian, D. Waliser, E. Fetzer, B. Lambrigsten, Y. Yung, and B. Wang. Vertical moist thermodynamic structure and spatialtemporalevolution of the MJO in AIRS observations. J. Atmos. Sci., 63:2462–2485, 2006.[Crossref]
  • [43] Matthew Wheeler and George N. Kiladis. Convectively Coupled Equatorial Waves: Analysis of Clouds and Temperature inthe Wavenumber-Frequency Domain. J. Atmos. Sci., 56:374–399, 1999.[Crossref][WoS]
  • [44] P. K. Xavier, J. C. Petch, and coauthors. Vertical structure and physical processes of the Madden-Julian Oscillation: Biasesand uncertainties at short range. J. Geophys. Res., 2015. doi:10.1002/2014JD022718.[Crossref][WoS]
  • [45] Chidong Zhang. Madden-Julian Oscillation. Rev. Geophys., 43, 2005. RG2003, doi:10.1029/2004RG000158.[Crossref]

Document Type

Publication order reference


YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.