Climate Dynamics

, Volume 50, Issue 11–12, pp 4211–4230 | Cite as

Convectively coupled equatorial waves within the MJO during CINDY/DYNAMO: slow Kelvin waves as building blocks

  • Kazuyoshi Kikuchi
  • George N. Kiladis
  • Juliana Dias
  • Tomoe Nasuno


This study examines the relationship between the MJO and convectively coupled equatorial waves (CCEWs) during the CINDY2011/DYNAMO field campaign using satellite-borne infrared radiation data, in order to better understand the interaction between convection and the large-scale circulation. The spatio-temporal wavelet transform (STWT) enables us to document the convective signals within the MJO envelope in terms of CCEWs in great detail, through localization of space–time spectra at any given location and time. Three MJO events that occurred in October, November, and December 2011 are examined. It is, in general, difficult to find universal relationships between the MJO and CCEWs, implying that MJOs are diverse in terms of the types of disturbances that make up its convective envelope. However, it is found in all MJO events that the major convective body of the MJO is made up mainly by slow convectively coupled Kelvin waves. These Kelvin waves have relatively fast phase speeds of 10–13 m s−1 outside of, and slow phase speeds of ~8–9 m s−1 within the MJO. Sometimes even slower eastward propagating signals with 3–5 m s−1 phase speed show up within the MJO, which, as well as the slow Kelvin waves, appear to comprise major building blocks of the MJO. It is also suggested that these eastward propagating waves often occur coincident with n = 1 WIG waves, which is consistent with the schematic model from Nakazawa in 1988. Some practical aspects that facilitate use of the STWT are also elaborated upon and discussed.



This research was supported by NOAA Grant NA13OAR4310165. Additional support was provided by the JAMSTEC through its sponsorship of research activities at the IPRC (JIJI). These results were obtained using the globally-merged full resolution Tb brightness temperature data provided by the climate prediction center/NCEP/NWS (available at The authors acknowledge the use of a package provided by CCSM AMWG to compute Fourier-based zonal wavenumber-frequency power spectrum. We thank three reviewers for their insightful comments. We also benefited from discussion with Paul E. Roundy and Masaki Katsumata. School of Ocean and Earth Science and Technology contribution number 10222 and International Pacific Research Center contribution number 1288.


  1. Addison PS (2002) The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. 1st edn. Taylor & Francis, p 368Google Scholar
  2. Antoine JP, Murenzi R, Vandergheynst P, Ali ST (2004) Two-dimensional wavelets and their relatives. Cambridge University Press, p 458Google Scholar
  3. Benedict JJ, Randall DA (2007) Observed characteristics of the MJO relative to maximum rainfall. J Atmos Sci 64:2332–2354. doi: 10.1175/jas3968.1 CrossRefGoogle Scholar
  4. Chen SS, Houze RA Jr, Mapes BE (1996) Multiscale variability of deep convection in relation to large-scale circulation in TOGA COARE. J Atmos Sci 53:1380–1409CrossRefGoogle Scholar
  5. Dias J, Kiladis GN (2014) Influence of the basic state zonal flow on convectively coupled equatorial waves. Geophys Res Lett 41:6904–6913. doi: 10.1002/2014gl061476 CrossRefGoogle Scholar
  6. Dias J, Pauluis O (2011) Modulations of the phase speed of convectively coupled Kelvin waves by the ITCZ. J Atmos Sci 68:1446–1459. doi: 10.1175/2011jas3630.1 CrossRefGoogle Scholar
  7. Dias J, Tulich SN, Kiladis GN (2012) An object-based approach to assessing the organization of tropical convection. J Atmos Sci 69:2488–2504. doi: 10.1175/jas-d-11-0293.1 CrossRefGoogle Scholar
  8. Dias J, Leroux S, Tulich SN, Kiladis GN (2013) How systematic is organized tropical convection within the MJO? Geophys Res Lett 40:1420–1425. doi: 10.1002/grl.50308 CrossRefGoogle Scholar
  9. Dias J, Sakaeda N, Kiladis GN, Kikuchi K (2017) Influences of the MJO on space-time tropical convection organization. J Geophys Res Atmos. doi: 10.1002/2017JD026526 Google Scholar
  10. Dunkerton TJ, Crum FX (1995) Eastward propagating similar to 2- to 15-day equatorial convection and its relation to the tropical intraseasonal oscillation. J Geophys Res Atmos 100:25781–25790CrossRefGoogle Scholar
  11. Emanuel KA, Neelin JD, Bretherton CS (1994) On large-scale circulations in convecting atmospheres. Q J R Meteorol Soc 120:1111–1143CrossRefGoogle Scholar
  12. Fujita M, Yoneyama K, Mori S, Nasuno T, Satoh M (2011) Diurnal convection peaks over the eastern Indian Ocean off Sumatra during different MJO phases. J Meteorol Soc Jpn 89A:317–330. doi: 10.2151/jmsj.2011-A22 CrossRefGoogle Scholar
  13. Gottschalck J, Roundy PE, Schreck CJ, Vintzileos A, Zhang C (2013) Large-scale atmospheric and oceanic conditions during the 2011–2012 DYNAMO field campaign. Mon Weather Rev 141:4173–4196. doi: 10.1175/mwr-d-13-00022.1 CrossRefGoogle Scholar
  14. Haertel PT, Johnson RH (1998) Two-day disturbances in the equatorial western Pacific. Q J R Metereol Soc 124:615–636CrossRefGoogle Scholar
  15. Haertel PT, Kiladis GN (2004) Dynamics of 2-day equatorial waves. J Atmos Sci 61:2707–2721CrossRefGoogle Scholar
  16. Han Y, Khouider B (2010) Convectively coupled waves in a sheared environment. J Atmos Sci 67:2913–2942CrossRefGoogle Scholar
  17. Hannah WM, Mapes BE, Elsaesser GS (2016) A Lagrangian view of moisture dynamics during DYNAMO. J Atmos Sci 73:1967–1985. doi: 10.1175/jas-d-15-0243.1 CrossRefGoogle Scholar
  18. Hendon HH, Wheeler MC (2008) Some space-time spectral analyses of tropical convection and planetary-scale waves. J Atmos Sci 65:2936–2948CrossRefGoogle Scholar
  19. Hodges KI, Chappell DW, Robinson GJ, Yang G (2000) An improved algorithm for generating global window brightness temperatures from multiple satellite infrared imagery. J Atmos Ocean Technol 17:1296–1312CrossRefGoogle Scholar
  20. Hsu HH, Lee MY (2005) Topographic effects on the eastward propagation and initiation of the Madden–Julian oscillation. J Clim 18:795–809CrossRefGoogle Scholar
  21. Hung MP, Lin JL, Wang WQ, Kim D, Shinoda T, Weaver SJ (2013) MJO and convectively coupled equatorial waves simulated by CMIP5 climate models. J Clim 26:6185–6214. doi: 10.1175/jcli-d-12-00541.1 CrossRefGoogle Scholar
  22. Ichikawa H, Yasunari T (2007) Propagating diurnal disturbances embedded in the Madden–Julian Oscillation. Geophys Res Lett. doi: 10.1029/2007gl030480 Google Scholar
  23. Ichikawa H, Yasunari T (2008) Intraseasonal variability in diurnal rainfall over New Guinea and the surrounding oceans during Austral summer. J Clim 21:2852–2868CrossRefGoogle Scholar
  24. Janowiak JE, Joyce RJ, Yarosh Y (2001) A real-time global half-hourly pixel-resolution infrared dataset and its applications. Bull Am Meteorol Soc 82:205–217CrossRefGoogle Scholar
  25. Johnson RH, Ciesielski PE (2013) Structure and properties of Madden–Julian oscillations deduced from DYNAMO sounding arrays. J Atmos Sci 70:3157–3179CrossRefGoogle Scholar
  26. Johnson RH, Ciesielski PE, Ruppert JH Jr, Katsumata M (2015) Sounding-based thermodynamic budgets for DYNAMO. J Atmos Sci 72:598–622. doi: 10.1175/jas-d-14-0202.1 CrossRefGoogle Scholar
  27. Judt F, Chen SS (2014) An explosive convective cloud system and its environmental conditions in MJO initiation observed during DYNAMO. J Geophys Res Atmos 119:2781–2795. doi: 10.1002/2013jd021048 CrossRefGoogle Scholar
  28. Katsumata M, Johnson RH, Ciesielski PE (2009) Observed synoptic-scale variability during the developing phase of an ISO over the Indian Ocean during MISMO. J Atmos Sci 66:3434–3448. doi: 10.1175/2009jas3003.1 CrossRefGoogle Scholar
  29. Kerns BW, Chen SS (2014a) Equatorial dry air intrusion and related synoptic variability in MJO Initiation during DYNAMO. Mon Weather Rev 142:1326–1343. doi: 10.1175/mwr-d-13-00159.1 CrossRefGoogle Scholar
  30. Kerns BW, Chen SS (2014b) ECMWF and GFS model forecast verification during DYNAMO: Multiscale variability in MJO initiation over the equatorial Indian Ocean. J Geophys Res Atmos 119:3736–3755. doi: 10.1002/2013jd020833 CrossRefGoogle Scholar
  31. Kikuchi K (2014) An introduction to combined Fourier-wavelet transform and its application to convectively coupled equatorial waves. Clim Dyn 43:1339–1356. doi: 10.1007/s00382-013-1949-8 CrossRefGoogle Scholar
  32. Kikuchi K, Takayabu YN (2004) The development of organized convection associated with the MJO during TOGA COARE IOP: trimodal characteristics. Geophys Res Lett 31:L10101. doi: 10.1029/2004GL019601 CrossRefGoogle Scholar
  33. Kikuchi K, Wang B (2008) Diurnal precipitation regimes in the global tropics. J Clim 21:2680–2696. doi: 10.1175/2007jcli2051.1 CrossRefGoogle Scholar
  34. Kikuchi K, Wang B (2010) Spatiotemporal wavelet transform and the multiscale behavior of the Madden–Julian oscillation. J Clim 23:3814–3834CrossRefGoogle Scholar
  35. Kikuchi K, Wang B, Kajikawa Y (2012) Bimodal representation of the tropical intraseasonal oscillation. Clim Dyn 38:1989–2000. doi: 10.1007/s00382-011-1159-1 CrossRefGoogle Scholar
  36. Kikuchi K, Kodama C, Nasuno T, Nakano M, Miura H, Satoh M, Noda A, Yamada Y (2017) Tropical intraseasonal oscillation in an AMIP-type experiment by NICAM. Clim Dyn. doi: 10.1007/s00382-016-3219-z Google Scholar
  37. Kiladis GN, Straub KH, Haertel PT (2005) Zonal and vertical structure of the Madden–Julian oscillation. J Atmos Sci 62:2790–2809CrossRefGoogle Scholar
  38. Kiladis GN, Wheeler MC, Haertel PT, Straub KH, Roundy PE (2009) Convectively coupled equatorial waves. Rev Geophys 47:RG2003. doi: 10.1029/2008RG000266 CrossRefGoogle Scholar
  39. Kiladis GN, Dias J, Straub KH, Wheeler MC, Tulich SN, Kikuchi K, Weickmann KM, Ventrice MJ (2014) A comparison of OLR and circulation-based indices for tracking the MJO. Mon Weather Rev 142:1697–1715. doi: 10.1175/mwr-d-13-00301.1 CrossRefGoogle Scholar
  40. Kiladis GN, Dias J, Gehne M (2016) The relationship between equatorial mixed Rossby-gravity and eastward inertio-gravity waves. Part I. J Atmos Sci 73:2123–2145. doi: 10.1175/jas-d-15-0230.1 CrossRefGoogle Scholar
  41. Kiranmayi L, Maloney ED (2011) Intraseasonal moist static energy budget in reanalysis data. J Geophys Res Atmos. doi: 10.1029/2011jd016031 Google Scholar
  42. Kubota H, Yoneyama K, Hamada J-I, Wu P, Sudaryanto A, Wahyono IB (2015) Role of Maritime Continent convection during the preconditioning stage of the Madden–Julian oscillation observed in CINDY2011/DYNAMO. J Meteorol Soc Jpn 93A:101–114. doi: 10.2151/jmsj.2015-050 CrossRefGoogle Scholar
  43. Kumar P, FoufoulaGeorgiou E (1997) Wavelet analysis for geophysical applications. Rev Geophys 35:385–412CrossRefGoogle Scholar
  44. Lau WKM, Waliser D (eds) (2012) Intraseasonal variability in the atmosphere–ocean climate system. 2nd edn. Springer, p 614Google Scholar
  45. Madden RA, Julian PR (1971) Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J Atmos Sci 28:702–708CrossRefGoogle Scholar
  46. Madden RA, Julian PR (1972) Description of global-scale circulation cells in tropics with a 40–50 day period. J Atmos Sci 29:1109–1123CrossRefGoogle Scholar
  47. Majda AJ, Stechmann SN (2012) Multiscale theories for the MJO. Intraseasonal variability in the atmosphere–ocean climate system, 2nd edn. Lau KM, Waliser DE (eds) Springer, pp 549–585Google Scholar
  48. Maloney ED, Hartmann DL (1998) Frictional moisture convergence in a composite life cycle of the Madden–Julian oscillation. J Clim 11:2387–2403CrossRefGoogle Scholar
  49. Mapes BE, Houze RA Jr (1993) Cloud clusters and superclusters over the oceanic warm pool. Mon Weather Rev 121:1398–1415CrossRefGoogle Scholar
  50. Masunaga H (2007) Seasonality and regionality of the Madden–Julian oscillation, Kelvin wave, and equatorial Rossby wave. J Atmos Sci 64:4400–4416. doi: 10.1175/2007jas2179.1 CrossRefGoogle Scholar
  51. Masunaga H, L’Ecuyer TS, Kummerow CD (2006) The Madden–Julian oscillation recorded in early observations from the tropical rainfall measuring mission (TRMM). J Atmos Sci 63:2777–2794CrossRefGoogle Scholar
  52. Matsuno T (1966) Quasi-geostrophic motions in the equatorial area. J Meteorol Soc Jpn 44:25–43CrossRefGoogle Scholar
  53. Meyers SD, Kelly BG, Obrien JJ (1993) An introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves. Mon Weather Rev 121:2858–2866CrossRefGoogle Scholar
  54. Miyakawa T, Takayabu YN, Nasuno T, Miura H, Satoh M, Moncrieff MW (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 69:1317–1338. doi: 10.1175/jas-d-11-024.1 CrossRefGoogle Scholar
  55. Mori S, Jun-Ichi H, Tauhid YI, Yamanaka MD (2004) Diurnal land–sea rainfall peak migration over Sumatera Island, Indonesian maritime continent, observed by TRMM satellite and intensive rawinsonde soundings. Mon Weather Rev 132:2021–2039CrossRefGoogle Scholar
  56. Nakazawa T (1988) Tropical super clusters within intraseasonal variations over the western Pacific. J Meteorol Soc Jpn 66:823–839CrossRefGoogle Scholar
  57. Nasuno T, Li T, Kikuchi K (2015) Moistening processes before the convective initiation of Madden–Julian oscillation events during the CINDY2011/DYNAMO period. Mon Weather Rev 143:622–643. doi: 10.1175/mwr-d-14-00132.1 CrossRefGoogle Scholar
  58. Oh J-H, Kim K-Y, Lim G-H (2012) Impact of MJO on the diurnal cycle of rainfall over the western Maritime Continent in the Austral summer. Clim Dyn 38:1167–1180. doi: 10.1007/s00382-011-1237-4 CrossRefGoogle Scholar
  59. Peatman SC, Matthews AJ, Stevens DP (2014) Propagation of the Madden–Julian oscillation through the Maritime Continent and scale interaction with the diurnal cycle of precipitation. Q J R Meteorol Soc 140:814–825. doi: 10.1002/qj.2161 CrossRefGoogle Scholar
  60. Powell SW, Houze RA Jr (2015a) Effect of dry large-scale vertical motions on initial MJO convective onset. J Geophys Res Atmos 120:4783–4805. doi: 10.1002/2014jd022961 CrossRefGoogle Scholar
  61. Powell SW, Houze RA Jr (2015b) Evolution of precipitation and convective echo top heights observed by TRMM radar over the Indian Ocean during DYNAMO. J Geophys Res Atmos 120:3906–3919. doi: 10.1002/2014jd022934 CrossRefGoogle Scholar
  62. Powell SW, Houze RA, Jr. (2013) The cloud population and onset of the Madden–Julian Oscillation over the Indian Ocean during DYNAMO-AMIE. J Geophys Res Atmos 118:11979–11995, doi: 10.1002/2013jd020421
  63. Rauniyar SP, Walsh KJE (2011) Scale interaction of the diurnal cycle of rainfall over the Maritime Continent and Australia: influence of the MJO. J Clim 24:325–348. doi: 10.1175/2010jcli3673.1 CrossRefGoogle Scholar
  64. Ridout JA, Flatau MK (2011) Kelvin wave time scale propagation features of the Madden–Julian Oscillation (MJO) as measured by the Chen-MJO index. J Geophys Res Atmos. doi: 10.1029/2011jd015925 Google Scholar
  65. Roundy PE (2008) Analysis of convectively coupled Kelvin waves in the Indian ocean MJO. J Atmos Sci 65:1342–1359CrossRefGoogle Scholar
  66. Roundy PE (2012) Observed structure of convectively coupled waves as a function of equivalent depth: Kelvin waves and the Madden–Julian Oscillation. J Atmos Sci 69:2097–2106. doi: 10.1175/jas-d-12-03.1 CrossRefGoogle Scholar
  67. Roundy PE (2014) Regression analysis of zonally narrow components of the MJO. J Atmos Sci 71:4253–4275. doi: 10.1175/jas-d-13-0288.1 CrossRefGoogle Scholar
  68. Roundy PE, Frank WM (2004) A climatology of waves in the equatorial region. J Atmos Sci 61:2105–2132CrossRefGoogle Scholar
  69. Serra YL, Kiladis GN, Cronin MF (2008) Horizontal and vertical structure of easterly waves in the Pacific ITCZ. J Atmos Sci 65:1266–1284CrossRefGoogle Scholar
  70. Sobel A, Wang S, Kim D (2014) Moist static energy budget of the MJO during DYNAMO. J Atmos Sci 71:4276–4291. doi: 10.1175/jas-d-14-0052.1 CrossRefGoogle Scholar
  71. Takayabu YN (1994a) Large-scale cloud disturbances associated with equatorial waves. Part I: Spectral features of the cloud disturbances. J Meteorol Soc Jpn 72:433–449CrossRefGoogle Scholar
  72. Takayabu YN (1994b) Large-scale cloud disturbances associated with equatorial waves. Part II: Westward-propagating inertio-gravity waves. J Meteorol Soc Japan 72:451–465CrossRefGoogle Scholar
  73. Takayabu YN, Nitta T (1993) 3–5 day-period disturbances coupled with convection over the tropical Pacific Ocean. J Meteorol Soc Jpn 71:221–246CrossRefGoogle Scholar
  74. Takayabu YN, Lau KM, Sui CH (1996) Observation of a quasi-2-day wave during TOGA COARE. Mon Weather Rev 124:1892–1913CrossRefGoogle Scholar
  75. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78CrossRefGoogle Scholar
  76. Waliser D (2012) Predictability and forecasting. Intraseasonal variability in the atmosphere–ocean climate system, 2nd edn. Lau WKM, Waliser DE (eds) Praxis Publishing, pp 433–476Google Scholar
  77. Wang B (2012) Theories. Intraseasonal variability in the atmosphere–ocean climate system, 2nd edn. Lau KM, Waliser DE (eds) Springer, pp 335–398Google Scholar
  78. Wheeler MC, Hendon HH (2004) An all-season real-time multivariate MJO index: development of an index for monitoring and prediction. Mon Weather Rev 132:1917–1932CrossRefGoogle Scholar
  79. Wheeler M, Kiladis GN (1999) Convectively coupled equatorial waves: analysis of clouds and temperature in the wavenumber-frequency domain. J Atmos Sci 56:374–399CrossRefGoogle Scholar
  80. Wilks DS (2006) Statistical methods in the atmospheric sciences. 2nd edn. Academic Press, p 648Google Scholar
  81. Wu C-H, Hsu H-H (2009) Topographic influence on the MJO in the maritime continent. J Clim 22:5433–5448. doi: 10.1175/2009jcli2825.1 CrossRefGoogle Scholar
  82. Yamada H, Yoneyama K, Katsumata M, Shirooka R (2010) Observations of a super cloud cluster accompanied by synoptic-scale eastward-propagating precipitating systems over the Indian Ocean. J Atmos Sci 67:1456–1473CrossRefGoogle Scholar
  83. Yang GY, Slingo J (2001) The diurnal cycle in the tropics. Mon Weather Rev 129:784–801CrossRefGoogle Scholar
  84. Yang G-Y, Slingo J, Hoskins B (2009) Convectively coupled equatorial waves in high-resolution Hadley Centre climate models. J Clim 22:1897–1919. doi: 10.1175/2008jcli2630.1 CrossRefGoogle Scholar
  85. Yasunaga K, Mapes B (2012) Differences between more divergent and more rotational types of convectively coupled equatorial waves. Part II: Composite analysis based on space-time filtering. J Atmos Sci 69:17–34CrossRefGoogle Scholar
  86. Yokoi S, Sobel A (2015) Intraseasonal variability and seasonal march of the moist static energy budget over the eastern Maritime Continent during CINDY2011/DYNAMO. J Meteorol Soc Jpn 93A:81–100. doi: 10.2151/jmsj.2015-041 CrossRefGoogle Scholar
  87. Yoneyama K, Zhang C, Long CN (2013) Tracking pulses of the Madden–Julian oscillation. Bull Am Meteorol Soc 94:1871–1891. doi: 10.1175/bams-d-12-00157.1 CrossRefGoogle Scholar
  88. Zhang CD (2005) Madden–Julian oscillation. Rev Geophys 43:RG2003. doi: 10.1029/2004RG000158 Google Scholar
  89. Zhang CD (2013) Madden–Julian oscillation: bridging weather and climate. Bull Am Meteorol Soc 94:1849–1870. doi: 10.1175/bams-d-12-00026.1 CrossRefGoogle Scholar
  90. Zhao C, Li T, Zhou T (2013) Precursor signals and processes associated with MJO initiation over the tropical Indian Ocean. J Clim 26:291–307. doi: 10.1175/jcli-d-12-00113.1 CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.International Pacific Research Center, School of Ocean and Earth Science and TechnologyUniversity of Hawaii at ManoaHonoluluUSA
  2. 2.Physical Sciences Division, NOAA Earth System Research LaboratoryBoulderUSA
  3. 3.Japan Agency for Marine-Earth Science and TechnologyYokohamaJapan

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