• Adames, Á. F., and J. M. Wallace, 2014: Three-dimensional structure and evolution of the MJO and its relation to the mean flow. J. Atmos. Sci., 71, 20072026, https://doi.org/10.1175/JAS-D-13-0254.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Adames, Á. F., and J. M. Wallace, 2015: Three-dimensional structure and evolution of the moisture field in the MJO. J. Atmos. Sci., 72, 37333754, https://doi.org/10.1175/JAS-D-15-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Adames, Á. F., and D. Kim, 2016: The MJO as a dispersive, convectively coupled moisture wave: Theory and observations. J. Atmos. Sci., 73, 913941, https://doi.org/10.1175/JAS-D-15-0170.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Adames, Á. F., D. Kim, A. H. Sobel, A. Del Genio, and J. Wu, 2017: Characterization of moist processes associated with changes in the propagation of the MJO with increasing CO2. J. Adv. Model. Earth Syst., 9, 29462967, https://doi.org/10.1002/2017MS001040.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ahn, M.-S., and Coauthors, 2017: MJO simulation in CMIP5 climate models: MJO skill metrics and process-oriented diagnosis. Climate Dyn., 49, 40234045, https://doi.org/10.1007/s00382-017-3558-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ahn, M.-S., and Coauthors, 2020: MJO propagation across the Maritime Continent: Are CMIP6 models better than CMIP5 models? Geophys. Res. Lett., 47, e2020GL087250, https://doi.org/10.1029/2020GL087250.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andersen, J. A., and Z. Kuang, 2012: Moist static energy budget of MJO-like disturbances in the atmosphere of a zonally symmetric aquaplanet. J. Climate, 25, 27822804, https://doi.org/10.1175/JCLI-D-11-00168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benedict, J. J., and D. A. Randall, 2007: Observed characteristics of the MJO relative to maximum rainfall. J. Atmos. Sci., 64, 23322354, https://doi.org/10.1175/JAS3968.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Biello, J. A., and A. J. Majda, 2005: A new multiscale model for the Madden–Julian oscillation. J. Atmos. Sci., 62, 16941721, https://doi.org/10.1175/JAS3455.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Biello, J. A., A. J. Majda, and M. W. Moncrieff, 2007: Meridional momentum flux and superrotation in the multiscale IPESD MJO model. J. Atmos. Sci., 64, 16361651, https://doi.org/10.1175/JAS3908.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bladé, I., and D. L. Hartmann, 1993: Tropical intraseasonal oscillations in a simple nonlinear model. J. Atmos. Sci., 50, 29222939, https://doi.org/10.1175/1520-0469(1993)050<2922:TIOIAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., and A. H. Sobel, 2003: The Gill model and the weak temperature gradient approximation. J. Atmos. Sci., 60, 451460, https://doi.org/10.1175/1520-0469(2003)060<0451:TGMATW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., M. E. Peters, and L. E. Back, 2004: Relationships between water vapor path and precipitation over the tropical oceans. J. Climate, 17, 15171528, https://doi.org/10.1175/1520-0442(2004)017<1517:RBWVPA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carr, M. T., and C. S. Bretherton, 2001: Convective momentum transport over the tropical Pacific: Budget estimates. J. Atmos. Sci., 58, 16731693, https://doi.org/10.1175/1520-0469(2001)058<1673:CMTOTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, C.-P., 1977: Viscous internal gravity waves and low-frequency oscillations in the tropics. J. Atmos. Sci., 34, 901910, https://doi.org/10.1175/1520-0469(1977)034<0901:VIGWAL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, C.-P., and H. Lim, 1982: On the effects of viscous damping on equatorial Rossby waves. J. Atmos. Sci., 39, 17261733, https://doi.org/10.1175/1520-0469(1982)039<1726:OTEOVD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, N., A. J. Majda, and D. Giannakis, 2014: Predicting the cloud patterns of the Madden-Julian oscillation through a low-order nonlinear stochastic model. Geophys. Res. Lett., 41, 56125619, https://doi.org/10.1002/2014GL060876.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delplace, P., J. B. Marston, and A. Venaille, 2017: Topological origin of equatorial waves. Science, 358, 10751077, https://doi.org/10.1126/science.aan8819.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DeMott, C. A., C. Stan, D. A. Randall, and M. D. Branson, 2014: Intraseasonal variability in coupled GCMs: The roles of ocean feedbacks and model physics. J. Climate, 27, 49704995, https://doi.org/10.1175/JCLI-D-13-00760.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deng, Q., B. Khouider, and A. J. Majda, 2015: The MJO in a coarse-resolution GCM with a stochastic multicloud parameterization. J. Atmos. Sci., 72, 5574, https://doi.org/10.1175/JAS-D-14-0120.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dias, J., and G. N. Kiladis, 2014: Influence of the basic state zonal flow on convectively coupled equatorial waves. Geophys. Res. Lett., 41, 69046913, https://doi.org/10.1002/2014GL061476.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frederiksen, J. S., and H. Lin, 2013: Tropical–extratropical interactions of intraseasonal oscillations. J. Atmos. Sci., 70, 31803197, https://doi.org/10.1175/JAS-D-12-0302.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fuchs, Ž., and D. J. Raymond, 2017: A simple model of intraseasonal oscillations. J. Adv. Model. Earth Syst., 9, 11951211, https://doi.org/10.1002/2017MS000963.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447462, https://doi.org/10.1002/qj.49710644905.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gottschalck, J., P. E. Roundy, C. J. Schreck III, A. Vintzileos, and C. Zhang, 2013: Large-scale atmospheric and oceanic conditions during the 2011–12 DYNAMO field campaign. Mon. Wea. Rev., 141, 41734196, https://doi.org/10.1175/MWR-D-13-00022.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2003: MJO-like coherent structures: Sensitivity simulations using the cloud-resolving convection parameterization (CRCP). J. Atmos. Sci., 60, 847864, https://doi.org/10.1175/1520-0469(2003)060<0847:MLCSSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haertel, P. T., G. N. Kiladis, A. Denno, and T. M. Rickenbach, 2008: Vertical-mode decompositions of 2-day waves and the Madden–Julian oscillation. J. Atmos. Sci., 65, 813833, https://doi.org/10.1175/2007JAS2314.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hashemi, M., 2016: Analytical and numerical studies of thalamo-cortical neural population models during general anesthesia. Thèse doctorat, Université de Lorraine, 199 pp., https://hal.inria.fr/tel-01754610v2/document.

  • Hayashi, M., and H. Itoh, 2017: A new mechanism of the slow eastward propagation of unstable disturbances with convection in the tropics: Implications for the MJO. J. Atmos. Sci., 74, 37493769, https://doi.org/10.1175/JAS-D-16-0300.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendon, H. H., 2000: Impact of air–sea coupling on the Madden–Julian oscillation in a general circulation model. J. Atmos. Sci., 57, 39393952, https://doi.org/10.1175/1520-0469(2001)058<3939:IOASCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendon, H. H., and M. L. Salby, 1994: The life cycle of the Madden–Julian oscillation. J. Atmos. Sci., 51, 22252237, https://doi.org/10.1175/1520-0469(1994)051<2225:TLCOTM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hsu, H.-H., B. J. Hoskins, and F.-F. Jin, 1990: The 1985/86 intraseasonal oscillation and the role of the extratropics. J. Atmos. Sci., 47, 823839, https://doi.org/10.1175/1520-0469(1990)047<0823:TIOATR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huffman, G. J., and Coauthors, 2007: The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales. J. Hydrometeor., 8, 3855, https://doi.org/10.1175/JHM560.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, X., T. Li, and B. Wang, 2004: Structures and mechanisms of the northward propagating boreal summer intraseasonal oscillation. J. Climate, 17, 10221039, https://doi.org/10.1175/1520-0442(2004)017<1022:SAMOTN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, X., and Coauthors, 2015: Vertical structure and physical processes of the Madden-Julian oscillation: Exploring key model physics in climate simulations. J. Geophys. Res. Atmos., 120, 47184748, https://doi.org/10.1002/2014JD022375.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, X., and Coauthors, 2020: Fifty years of research on the Madden-Julian oscillation: Recent progress, challenges, and perspectives. J. Geophys. Res. Atmos., 125, e2019JD030911, https://doi.org/10.1029/2019JD030911.

    • Search Google Scholar
    • Export Citation
  • Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci., 52, 307319, https://doi.org/10.1175/1520-0469(1995)052<0307:TDRTTH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johnson, R. H., P. E. Ciesielski, J. H. R. Jr, and M. Katsumata, 2015: Sounding-based thermodynamic budgets for DYNAMO. J. Atmos. Sci., 72, 598622, https://doi.org/10.1175/JAS-D-14-0202.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, C., 2009: A homogeneous stochastic model of the Madden–Julian oscillation. J. Climate, 22, 32703288, https://doi.org/10.1175/2008JCLI2609.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kemball-Cook, S., and B. Wang, 2001: Equatorial waves and air–sea interaction in the boreal summer intraseasonal oscillation. J. Climate, 14, 29232942, https://doi.org/10.1175/1520-0442(2001)014<2923:EWAASI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kemball-Cook, S., and B. C. Weare, 2001: The onset of convection in the Madden–Julian oscillation. J. Climate, 14, 780793, https://doi.org/10.1175/1520-0442(2001)014<0780:TOOCIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kerns, B. W., and S. S. Chen, 2014: Equatorial dry air intrusion and related synoptic variability in MJO initiation during DYNAMO. Mon. Wea. Rev., 142, 13261343, https://doi.org/10.1175/MWR-D-13-00159.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., and K. Emanuel, 2018: Intraseasonal variability in a cloud-permitting near-global equatorial aquaplanet model. J. Atmos. Sci., 75, 43374355, https://doi.org/10.1175/JAS-D-18-0152.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khouider, B., Y. Han, A. J. Majda, and S. N. Stechmann, 2012: Multiscale waves in an MJO background and convective momentum transport feedback. J. Atmos. Sci., 69, 915933, https://doi.org/10.1175/JAS-D-11-0152.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kikuchi, K., and Y. N. Takayabu, 2004: The development of organized convection associated with the MJO during TOGA COARE IOP: Trimodal characteristics. Geophys. Res. Lett., 31, L10101, https://doi.org/10.1029/2004GL019601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., K. H. Straub, and P. T. Haertel, 2005: Zonal and vertical structure of the Madden–Julian oscillation. J. Atmos. Sci., 62, 27902809, https://doi.org/10.1175/JAS3520.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., M. C. Wheeler, P. T. Haertel, K. H. Straub, and P. E. Roundy, 2009: Convectively coupled equatorial waves. Rev. Geophys., 47, RG2003, https://doi.org/10.1029/2008RG000266.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., and Coauthors, 2014: A comparison of OLR and circulation-based indices for tracking the MJO. Mon. Wea. Rev., 142, 16971715, https://doi.org/10.1175/MWR-D-13-00301.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, D., A. H. Sobel, and I.-S. Kang, 2011: A mechanism denial study on the Madden-Julian oscillation. J. Adv. Model. Earth Syst., 3, M12007, https://doi.org/10.1029/2011MS000081.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuang, Z., 2008: Modeling the interaction between cumulus convection and linear gravity waves using a limited-domain cloud system–resolving model. J. Atmos. Sci., 65, 576591, https://doi.org/10.1175/2007JAS2399.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuang, Z., 2011: The wavelength dependence of the gross moist stability and the scale selection in the instability of column-integrated moist static energy. J. Atmos. Sci., 68, 6174, https://doi.org/10.1175/2010JAS3591.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lau, K.-M., and L. Peng, 1987: Origin of low-frequency (intraseasonal) oscillations in the tropical atmosphere. Part I: Basic theory. J. Atmos. Sci., 44, 950972, https://doi.org/10.1175/1520-0469(1987)044<0950:OOLFOI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lau, K.-M., P.-J. Sheu, and I.-S. Kang, 1994: Multiscale low-frequency circulation modes in the global atmosphere. J. Atmos. Sci., 51, 11691193, https://doi.org/10.1175/1520-0469(1994)051<1169:MLFCMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, S.-K., C. Wang, and B. E. Mapes, 2009: A simple atmospheric model of the local and teleconnection responses to tropical heating anomalies. J. Climate, 22, 272284, https://doi.org/10.1175/2008JCLI2303.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, J.-L., M. Zhang, and B. Mapes, 2005: Zonal momentum budget of the Madden–Julian oscillation: The source and strength of equivalent linear damping. J. Atmos. Sci., 62, 21722188, https://doi.org/10.1175/JAS3471.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, J.-L., and Coauthors, 2006: Tropical intraseasonal variability in 14 IPCC AR4 climate models. Part I: Convective signals. J. Climate, 19, 26652690, https://doi.org/10.1175/JCLI3735.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, J.-L., B. E. Mapes, and W. Han, 2008: What are the sources of mechanical damping in Matsuno–Gill-type models? J. Climate, 21, 165179, https://doi.org/10.1175/2007JCLI1546.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, X., and R. H. Johnson, 1996: Heating, moistening, and rainfall over the western Pacific warm pool during TOGA COARE. J. Atmos. Sci., 53, 33673383, https://doi.org/10.1175/1520-0469(1996)053<3367:HMAROT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ling, J., C. Zhang, and P. Bechtold, 2013: Large-scale distinctions between MJO and non-MJO convective initiation over the tropical Indian Ocean. J. Atmos. Sci., 70, 26962712, https://doi.org/10.1175/JAS-D-13-029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702708, https://doi.org/10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40–50 day period. J. Atmos. Sci., 29, 11091123, https://doi.org/10.1175/1520-0469(1972)029<1109:DOGSCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Majda, A. J., and S. N. Stechmann, 2009a: A simple dynamical model with features of convective momentum transport. J. Atmos. Sci., 66, 373392, https://doi.org/10.1175/2008JAS2805.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Majda, A. J., and S. N. Stechmann, 2009b: The skeleton of tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA, 106, 84178422, https://doi.org/10.1073/pnas.0903367106.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maloney, E. D., and A. H. Sobel, 2004: Surface fluxes and ocean coupling in the tropical intraseasonal oscillation. J. Climate, 17, 43684386, https://doi.org/10.1175/JCLI-3212.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maloney, E. D., Á. F. Adames, and H. X. Bui, 2019: Madden–Julian oscillation changes under anthropogenic warming. Nat. Climate Change, 9, 2633, https://doi.org/10.1038/s41558-018-0331-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masoliver, J., and J. M. Porrà, 1993: Harmonic oscillators driven by colored noise: Crossovers, resonances, and spectra. Phys. Rev., 48E, 43094319, https://doi.org/10.1103/PhysRevE.48.4309.

    • Search Google Scholar
    • Export Citation
  • Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan, 44, 2543, https://doi.org/10.2151/jmsj1965.44.1_25.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matthews, A. J., 2008: Primary and successive events in the Madden–Julian oscillation. Quart. J. Roy. Meteor. Soc., 134, 439453, https://doi.org/10.1002/qj.224.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matthews, A. J., B. J. Hoskins, J. M. Slingo, and M. Blackburn, 1996: Development of convection along the SPCZ within a Madden-Julian oscillation. Quart. J. Roy. Meteor. Soc., 122, 669688, https://doi.org/10.1002/qj.49712253106.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meehl, G. A., C. Shields, J. M. Arblaster, H. Annamalai, and R. Neale, 2020: Intraseasonal, seasonal, and interannual characteristics of regional monsoon simulations in CESM2. J. Adv. Model. Earth Sys., 12, e2019MS001962, https://doi.org/10.1029/2019MS001962.

    • Search Google Scholar
    • Export Citation
  • Miyakawa, T., Y. N. Takayabu, T. Nasuno, H. Miura, M. Satoh, and M. W. Moncrieff, 2012: Convective momentum transport by rainbands within a Madden–Julian oscillation in a global nonhydrostatic model with explicit deep convective processes. Part I: Methodology and general results. J. Atmos. Sci., 69, 13171338, https://doi.org/10.1175/JAS-D-11-024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., 1992: Organized convective systems: Archetypal dynamical models, mass and momentum flux theory, and parametrization. Quart. J. Roy. Meteor. Soc., 118, 819850, https://doi.org/10.1002/qj.49711850703.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., 2004: Analytic representation of the large-scale organization of tropical convection. J. Atmos. Sci., 61, 15211538, https://doi.org/10.1175/1520-0469(2004)061<1521:AROTLO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., 2019: Toward a dynamical foundation for organized convection parameterization in GCMs. Geophys. Res. Lett., 46, 14 10314 108, https://doi.org/10.1029/2019GL085316.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moncrieff, M. W., C. Liu, and P. Bogenschutz, 2017: Simulation, modeling, and dynamically based parameterization of organized tropical convection for global climate models. J. Atmos. Sci., 74, 13631380, https://doi.org/10.1175/JAS-D-16-0166.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moore, J. E., 2010: The birth of topological insulators. Nature, 464, 194198, https://doi.org/10.1038/nature08916.

  • Myers, D. S., and D. E. Waliser, 2003: Three-dimensional water vapor and cloud variations associated with the Madden–Julian oscillation during Northern Hemisphere winter. J. Climate, 16, 929950, https://doi.org/10.1175/1520-0442(2003)016<0929:TDWVAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • National Academies of Sciences, Engineering, and Medicine, 2016: Next Generation Earth System Prediction: Strategies for Subseasonal to Seasonal Forecasts. National Academies Press, 350 pp.

  • Neelin, J. D., 1988: A simple model for surface stress and low-level flow in the tropical atmosphere driven by prescribed heating. Quart. J. Roy. Meteor. Soc., 114, 747770, https://doi.org/10.1002/qj.49711448110.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., I. M. Held, and K. H. Cook, 1987: Evaporation-wind feedback and low-frequency variability in the tropical atmosphere. J. Atmos. Sci., 44, 23412348, https://doi.org/10.1175/1520-0469(1987)044<2341:EWFALF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oh, J.-H., X. Jiang, D. E. Waliser, M. W. Moncrieff, and R. H. Johnson, 2015: Convective momentum transport associated with the Madden–Julian oscillation based on a reanalysis dataset. J. Climate, 28, 57635782, https://doi.org/10.1175/JCLI-D-14-00570.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Popper, K., 1959: The Logic of Scientific Discovery. Routledge, 479 pp.

  • Powell, S. W., 2017: Successive MJO propagation in MERRA-2 reanalysis. Geophys. Res. Lett., 44, 51785186, https://doi.org/10.1002/2017GL073399.

  • Powell, S. W., and R. A. Houze Jr., 2015: Effect of dry large-scale vertical motions on initial MJO convective onset. J. Geophys. Res. Atmos., 120, 47834805, https://doi.org/10.1002/2014JD022961.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pritchard, M. S., and D. Yang, 2016: Response of the superparameterized Madden–Julian oscillation to extreme climate and basic-state variation challenges a moisture mode view. J. Climate, 29, 49955008, https://doi.org/10.1175/JCLI-D-15-0790.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Qi, Y., R. Zhang, X. Rong, J. Li, and L. Li, 2019: Boreal summer intraseasonal oscillation in the Asian–Pacific monsoon region simulated in CAMS-CSM. J. Meteor. Res., 33, 6679, https://doi.org/10.1007/s13351-019-8080-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ray, P., C. Zhang, J. Dudhia, and S. S. Chen, 2009: A numerical case study on the initiation of the Madden–Julian oscillation. J. Atmos. Sci., 66, 310331, https://doi.org/10.1175/2008JAS2701.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., 2001: A new model of the Madden–Julian oscillation. J. Atmos. Sci., 58, 28072819, https://doi.org/10.1175/1520-0469(2001)058<2807:ANMOTM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and X. Zeng, 2000: Instability and large-scale circulations in a two-column model of the tropical troposphere. Quart. J. Roy. Meteor. Soc., 126, 31173135, https://doi.org/10.1002/qj.49712657007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and Ž. Fuchs, 2009: Moisture modes and the Madden–Julian oscillation. J. Climate, 22, 30313046, https://doi.org/10.1175/2008JCLI2739.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2012: Weak pressure gradient approximation and its analytical solutions. J. Atmos. Sci., 69, 28352845, https://doi.org/10.1175/JAS-D-11-0336.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2014: Rayleigh damping in the free troposphere. J. Atmos. Sci., 71, 553565, https://doi.org/10.1175/JAS-D-13-062.1.

  • Rostami, M., and V. Zeitlin, 2019: Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane. Phys. Fluids, 31, 021701, https://doi.org/10.1063/1.5080415.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roundy, P. E., 2012: The spectrum of convectively coupled Kelvin waves and the Madden–Julian oscillation in regions of low-level easterly and westerly background flow. J. Atmos. Sci., 69, 21072111, https://doi.org/10.1175/JAS-D-12-060.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roundy, P. E., 2014: Some aspects of western hemisphere circulation and the Madden–Julian oscillation. J. Atmos. Sci., 71, 20272039, https://doi.org/10.1175/JAS-D-13-0210.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roundy, P. E., 2019: Interpretation of the spectrum of eastward-moving tropical convective anomalies. Quart. J. Roy. Meteor. Soc., 146, 795806, https://doi.org/10.1002/qj.3709.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sakaeda, N., and P. E. Roundy, 2016: The development of upper-tropospheric geopotential height anomaly in the Western Hemisphere during MJO convective initiations. Quart. J. Roy. Meteor. Soc., 142, 942956, https://doi.org/10.1002/qj.2696.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salby, M. L., and R. R. Garcia, 1987: Transient response to localized episodic heating in the tropics. Part I: Excitation and short-time near-field behavior. J. Atmos. Sci., 44, 458498, https://doi.org/10.1175/1520-0469(1987)044<0458:TRTLEH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seager, R., 1991: A simple model of the climatology and variability of the low-level wind field in the tropics. J. Climate, 4, 164179, https://doi.org/10.1175/1520-0442(1991)004<0164:ASMOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shi, X., D. Kim, Á. F. Adames, and J. Sukhatme, 2018: WISHE-moisture mode in an aquaplanet simulation. J. Adv. Model. Earth Syst., 10, 23932407, https://doi.org/10.1029/2018MS001441.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sikka, D. R., and S. Gadgil, 1980: On the maximum cloud zone and the ITCZ over Indian longitudes during the southwest monsoon. Mon. Wea. Rev., 108, 18401853, https://doi.org/10.1175/1520-0493(1980)108<1840:OTMCZA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A., and E. Maloney, 2012: An idealized semi-empirical framework for modeling the Madden–Julian oscillation. J. Atmos. Sci., 69, 16911705, https://doi.org/10.1175/JAS-D-11-0118.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Son, S.-W., Y. Lim, C. Yoo, H. H. Hendon, and J. Kim, 2017: Stratospheric control of the Madden–Julian oscillation. J. Climate, 30, 19091922, https://doi.org/10.1175/JCLI-D-16-0620.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sperber, K. R., S. Gualdi, S. Legutke, and V. Gayler, 2005: The Madden–Julian oscillation in ECHAM4 coupled and uncoupled general circulation models. Climate Dyn., 25, 117140, https://doi.org/10.1007/s00382-005-0026-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stechmann, S. N., and S. Hottovy, 2017: Unified spectrum of tropical rainfall and waves in a simple stochastic model. Geophys. Res. Lett., 44, 10 71310 724, https://doi.org/10.1002/2017GL075754.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugiyama, M., 2009: The moisture mode in the quasi-equilibrium tropical circulation model. Part II: Nonlinear behavior on an equatorial β plane. J. Atmos. Sci., 66, 15251542, https://doi.org/10.1175/2008JAS2691.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thual, S., A. J. Majda, and S. N. Stechmann, 2014: A stochastic skeleton model for the MJO. J. Atmos. Sci., 71, 697715, https://doi.org/10.1175/JAS-D-13-0186.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tung, W.-W., and M. Yanai, 2002: Convective momentum transport observed during the TOGA COARE IOP. Part II: Case studies. J. Atmos. Sci., 59, 25352549, https://doi.org/10.1175/1520-0469(2002)059<2535:CMTODT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Virts, K. S., and J. M. Wallace, 2014: Observations of temperature, wind, cirrus, and trace gases in the tropical tropopause transition layer during the MJO. J. Atmos. Sci., 71, 11431157, https://doi.org/10.1175/JAS-D-13-0178.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waliser, D. E., K. M. Lau, W. Stern, and C. Jones, 2003: Potential predictability of the Madden–Julian oscillation. Bull. Amer. Meteor. Soc., 84, 3350, https://doi.org/10.1175/BAMS-84-1-33.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B., 1988a: Comments on “An air–sea interaction model of intraseasonal oscillation in the tropics.” J. Atmos. Sci., 45, 35213525, https://doi.org/10.1175/1520-0469(1988)045<3521:COAIMO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B., 1988b: Dynamics of tropical low-frequency waves: An analysis of the moist Kelvin wave. J. Atmos. Sci., 45, 20512065, https://doi.org/10.1175/1520-0469(1988)045<2051:DOTLFW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B., and H. Rui, 1990: Dynamics of the coupled moist Kelvin–Rossby wave on an equatorial β-plane. J. Atmos. Sci., 47, 397413, https://doi.org/10.1175/1520-0469(1990)047<0397:DOTCMK>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B., F. Liu, and G. Chen, 2016: A trio-interaction theory for Madden–Julian oscillation. Geosci. Lett., 3, 34, https://doi.org/10.1186/s40562-016-0066-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weare, B. C., 2003: Composite singular value decomposition analysis of moisture variations associated with the Madden–Julian oscillation. J. Climate, 16, 37793792, https://doi.org/10.1175/1520-0442(2003)016<3779:CSVDAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, P. J., 1972: Response of the tropical atmosphere to local, steady forcing. Mon. Wea. Rev., 100, 518541, https://doi.org/10.1175/1520-0493(1972)100<0518:ROTTAT>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wheeler, M., and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci., 56, 374399, https://doi.org/10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, Z., D. S. Battisti, and E. S. Sarachik, 2000: Rayleigh friction, Newtonian cooling, and the linear response to steady tropical heating. J. Atmos. Sci., 57, 19371957, https://doi.org/10.1175/1520-0469(2000)057<1937:RFNCAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, Z., E. S. Sarachik, and D. S. Battisti, 2001: Thermally driven tropical circulations under Rayleigh friction and Newtonian cooling: Analytic solutions. J. Atmos. Sci., 58, 724741, https://doi.org/10.1175/1520-0469(2001)058<0724:TDTCUR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, D., and A. P. Ingersoll, 2013: Triggered convection, gravity waves, and the MJO: A shallow-water model. J. Atmos. Sci., 70, 24762486, https://doi.org/10.1175/JAS-D-12-0255.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, D., and A. P. Ingersoll, 2014: A theory of the MJO horizontal scale. Geophys. Res. Lett., 41, 10591064, https://doi.org/10.1002/2013GL058542.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Q., A. J. Majda, and M. W. Moncrieff, 2019: Upscale impact of mesoscale convective systems and its parameterization in an idealized GCM for an MJO analog above the equator. J. Atmos. Sci., 76, 865892, https://doi.org/10.1175/JAS-D-18-0260.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yano, J.-I., and J. J. Tribbia, 2017: Tropical atmospheric Madden–Julian oscillation: A strongly nonlinear free solitary Rossby wave? J. Atmos. Sci., 74, 34733489, https://doi.org/10.1175/JAS-D-16-0319.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yasunari, T., 1979: Cloudiness fluctuations associated with the Northern Hemisphere summer monsoon. J. Meteor. Soc. Japan, 57, 227242, https://doi.org/10.2151/jmsj1965.57.3_227.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yasunari, T., 1980: A quasi-stationary appearance of 30- to 40-day period in the cloudiness fluctuations during the summer monsoon over India. J. Meteor. Soc. Japan, 58, 225229, https://doi.org/10.2151/jmsj1965.58.3_225.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yu, J.-Y., and J. D. Neelin, 1994: Modes of tropical variability under convective adjustment and the Madden–Julian oscillation. Part II: Numerical results. J. Atmos. Sci., 51, 18951914, https://doi.org/10.1175/1520-0469(1994)051<1895:MOTVUC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yu, J.-Y., and J. D. Neelin, 1997: Analytic approximations for moist convectively adjusted regions. J. Atmos. Sci., 54, 10541063, https://doi.org/10.1175/1520-0469(1997)054<1054:AAFMCA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., 2005: Madden-Julian oscillation. Rev. Geophys., 43, RG2003, https://doi.org/10.1029/2004RG000158.

  • Zhang, C., 2013: Madden–Julian oscillation: Bridging weather and climate. Bull. Amer. Meteor. Soc., 94, 18491870, https://doi.org/10.1175/BAMS-D-12-00026.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., and J. Ling, 2012: Potential vorticity of the Madden–Julian oscillation. J. Atmos. Sci., 69, 6578, https://doi.org/10.1175/JAS-D-11-081.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., and J. Ling, 2017: Barrier effect of the Indo-Pacific maritime continent on the MJO: Perspectives from tracking MJO precipitation. J. Climate, 30, 34393459, https://doi.org/10.1175/JCLI-D-16-0614.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., Á. F. Adames, B. Khouider, B. Wang, and D. Yang, 2020: Four theories of the Madden-Julian oscillation. Rev. Geophys., 58, e2019RG000685, https://doi.org/10.1029/2019RG000685.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhen, B., and Coauthors, 2015: Spawning rings of exceptional points out of Dirac cones. Nature, 525, 354358, https://doi.org/10.1038/nature14889.

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Core Dynamics of the MJO

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  • 1 Center for Climate Physics, Institute for Basic Science, Busan, South Korea
  • | 2 Pusan National University, Busan, South Korea
  • | 3 NOAA/Pacific Marine Environmental Laboratory, Seattle, Washington
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Abstract

The Madden–Julian oscillation (MJO) is a large-scale eastward-moving system that dominates tropical subseasonal perturbations with far-reaching impacts on global weather–climate. For nearly a half century since its discovery, there has not been a consensus on the most fundamental dynamics of the MJO, despite intensive studies with a number of theories proposed. In this study, using a simple analytical approach, we found a solution to the linear equatorial shallow-water equations with momentum damping that resembles a harmonic oscillator. This solution exhibits the key characteristics of the observed MJO: its intraseasonal periodicity at the planetary scale and eastward propagation. In contrast to theories that interpret the MJO as a new mode of variability emerging from the evolution in moisture, our solution emphasizes that the core of the MJO resides in the dynamics without explicit fluctuations in moisture. Moisture still plays a role in supplying energy to the core dynamics of the MJO, and determining the value of the equivalent depth required by the theory. The energy source may come from stochastic forcing in the tropics or from the extratropics. The scale selection for the MJO comes from scale-dependent responses to scale-independent Rayleigh damping. We also demonstrate that the MJO solution introduced here reproduces the observed swallowtail structure and the phase relation between zonal wind and geopotential of the MJO, and the continuum nature of the transition between the MJO and Kelvin waves. Roles of feedback mechanisms in the MJO are also discussed using the same simple mathematical framework.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ji-Eun Kim, jieunkim@pusan.ac.kr

Abstract

The Madden–Julian oscillation (MJO) is a large-scale eastward-moving system that dominates tropical subseasonal perturbations with far-reaching impacts on global weather–climate. For nearly a half century since its discovery, there has not been a consensus on the most fundamental dynamics of the MJO, despite intensive studies with a number of theories proposed. In this study, using a simple analytical approach, we found a solution to the linear equatorial shallow-water equations with momentum damping that resembles a harmonic oscillator. This solution exhibits the key characteristics of the observed MJO: its intraseasonal periodicity at the planetary scale and eastward propagation. In contrast to theories that interpret the MJO as a new mode of variability emerging from the evolution in moisture, our solution emphasizes that the core of the MJO resides in the dynamics without explicit fluctuations in moisture. Moisture still plays a role in supplying energy to the core dynamics of the MJO, and determining the value of the equivalent depth required by the theory. The energy source may come from stochastic forcing in the tropics or from the extratropics. The scale selection for the MJO comes from scale-dependent responses to scale-independent Rayleigh damping. We also demonstrate that the MJO solution introduced here reproduces the observed swallowtail structure and the phase relation between zonal wind and geopotential of the MJO, and the continuum nature of the transition between the MJO and Kelvin waves. Roles of feedback mechanisms in the MJO are also discussed using the same simple mathematical framework.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ji-Eun Kim, jieunkim@pusan.ac.kr
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