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Tropical Intraseasonal Variability and the Stochastic Skeleton Method pp 113–120Cite as

Current and Future Research Perspectives

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Part of the book series: Mathematics of Planet Earth ((SBMPE-WCO))

Abstract

Here we briefly discuss several interesting research directions in Tropical Intraseasonal Variability (TISV) which are a natural outgrowth of the material covered in the previous chapters in this monograph. The topics range from data assimilation and real-time prediction for the MJO using the stochastic skeleton model, to the skeleton and “muscle” of the MJO and their interaction, to other MJO theories, and finally to stochastic parameterization to improve operational general circulation models (GCMs).

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References

  • Ajayamohan RS, Khouider B, Majda AJ (2013) Realistic initiation and dynamics of the Madden–Julian oscillation in a coarse resolution aquaplanet GCM. Geophys Res Lett 40(23):6252–6257

    Article  Google Scholar 

  • Ajayamohan RS, Khouider B, Majda AJ (2014) Simulation of monsoon intraseasonal oscillations in a coarse-resolution aquaplanet GCM. Geophys Res Lett 41(15):5662–5669

    Article  Google Scholar 

  • Ajayamohan RS, Khouider B, Majda AJ, Deng Q (2016) Role of stratiform heating on the organization of convection over the monsoon trough. Clim Dyn 47(12):3641–3660

    Article  Google Scholar 

  • Arakawa A (2004) The cumulus parameterization problem: past, present, and future. J Clim 17(13):2493–2525

    Article  Google Scholar 

  • Benedict J, Randall D (2009) Structure of the Madden–Julian oscillation in the superparameterized CAM. J Atmos Sci 66(11):3277–3296

    Article  Google Scholar 

  • Berner J, Achatz U, Batte L, Bengtsson L, Cámara Adl, Christensen HM, Colangeli M, Coleman DRB, Crommelin D, Dolaptchiev SI et al (2017) Stochastic parameterization: toward a new view of weather and climate models. Bull Am Meteorol Soc 98(3):565–588

    Article  Google Scholar 

  • Biello JA, Majda AJ (2005) A new multiscale model for the Madden–Julian oscillation. J Atmos Sci 62:1694–1721

    Article  MathSciNet  Google Scholar 

  • Biello JA, Majda AJ (2006) Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden–Julian oscillation. Dyn Atmos Oceans 42:152–215

    Article  Google Scholar 

  • Buizza R, Miller M, Palmer TN (1999) Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Q J Roy Meteorol Soc 125(560):2887–2908

    Article  Google Scholar 

  • Chao WC (1987) On the origin of the tropical intraseasonal oscillation. J Atmos Sci 44:1940–1949

    Article  Google Scholar 

  • Chen N, Majda AJ (2016) Filtering the stochastic skeleton model for the Madden–Julian oscillation. Mon Weather Rev 144(2):501–527

    Article  Google Scholar 

  • Davini P, von Hardenberg J, Corti S, Christensen HM, Juricke S, Subramanian A, Watson PAG, Weisheimer A, Palmer TN (2017) Climate SPHINX: evaluating the impact of resolution and stochastic physics parameterisations in the EC-Earth global climate model. Geosci Model Dev 10(3):1383

    Article  Google Scholar 

  • De La Chevrotière M, Khouider B, Majda AJ (2014) Calibration of the stochastic multicloud model using bayesian inference. SIAM J Sci Comput 36(3):B538–B560

    Article  MathSciNet  MATH  Google Scholar 

  • De La Chevrotière M, Khouider B, Majda AJ (2016) Stochasticity of convection in Giga-LES data. Clim Dyn 47(5–6):1845–1861

    Article  Google Scholar 

  • Deng Q, Khouider B, Majda AJ (2015) The MJO in a coarse-resolution GCM with a stochastic multicloud parameterization. J Atmos Sci 72:55–74. https://doi.org/10.1175/JAS-D-14-0120.1

    Article  Google Scholar 

  • Deng Q, Khouider B, Majda AJ, Ajayamohan RS (2016) Effect of stratiform heating on the planetary-scale organization of tropical convection. J Atmos Sci 73(1):371–392

    Article  Google Scholar 

  • Dorrestijn J, Crommelin DT, Siebesma AP, Jonker HJJ, Selten F (2016) Stochastic convection parameterization with Markov chains in an intermediate-complexity GCM. J Atmos Sci 73(3):1367–1382

    Article  Google Scholar 

  • Dunkerton TJ, Crum FX (1995) Eastward propagating ∼2- to 15-day equatorial convection and its relation to the tropical intraseasonal oscillation. J Geophys Res 100(D12):25781–25790

    Article  Google Scholar 

  • Emanuel KA (1987) An air–sea interaction model of intraseasonal oscillations in the Tropics. J Atmos Sci 44:2324–2340

    Article  Google Scholar 

  • Fudeyasu H, Wang Y, Satoh M, Nasuno T, Miura H, Yanase W (2008) Global cloud-system-resolving model NICAM successfully simulated the lifecycles of two real tropical cyclones. Geophys Res Lett 35(22):L22808

    Article  Google Scholar 

  • Fukutomi Y, Kodama C, Yamada Y, Noda AT, Satoh M (2016) Tropical synoptic-scale wave disturbances over the western Pacific simulated by a global cloud-system resolving model. Theor Appl Climatol 124(3–4):737–755

    Article  Google Scholar 

  • Goswami BB, Krishna RPM, Mukhopadhyay P, Khairoutdinov M, Goswami BN (2015) Simulation of the Indian summer monsoon in the superparameterized climate forecast system version 2: preliminary results. J Clim 28(22):8988–9012

    Article  Google Scholar 

  • Goswami BB, Khouider B, Phani R, Mukhopadhyay P, Majda A (2017a) Improving synoptic and intraseasonal variability in CFSv2 via stochastic representation of organized convection. Geophys Res Lett 44(2):1104–1113

    Article  Google Scholar 

  • Goswami BB, Khouider B, Phani R, Mukhopadhyay P, Majda AJ (2017b) Improved tropical modes of variability in the NCEP Climate Forecast System (Version 2) via a stochastic multicloud model. J Atmos Sci 74(10):3339–3366

    Article  Google Scholar 

  • Grabowski WW (2001) Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (CRCP). J Atmos Sci 58:978–997

    Article  Google Scholar 

  • Grabowski WW, Smolarkiewicz PK (1999) CRCP: a cloud resolving convection parameterization for modeling the tropical convecting atmosphere. Phys D Nonlinear Phenomena 133:171–178

    Article  MATH  Google Scholar 

  • Hendon HH, Liebmann B (1994) Organization of convection within the Madden–Julian oscillation. J Geophys Res 99:8073–8084. https://doi.org/10.1029/94JD00045

    Article  Google Scholar 

  • Houze RA Jr, Chen SS, Kingsmill DE, Serra Y, Yuter SE (2000) Convection over the Pacific warm pool in relation to the atmospheric Kelvin–Rossby wave. J Atmos Sci 57:3058–3089

    Article  Google Scholar 

  • Johnson RH, Rickenbach TM, Rutledge SA, Ciesielski PE, Schubert WH (1999) Trimodal characteristics of tropical convection. J Clim 12:2397–2418

    Article  Google Scholar 

  • Khairoutdinov MF, Randall DA (2001) A cloud resolving model as a cloud parameterization in the NCAR Community Climate System Model: preliminary results. Geophys Res Lett 28(18):3617–3620

    Article  Google Scholar 

  • Khouider B, Majda AJ (2006) A simple multicloud parameterization for convectively coupled tropical waves. Part I: linear analysis. J Atmos Sci 63:1308–1323

    MathSciNet  Google Scholar 

  • Khouider B, Majda AJ, Katsoulakis MA (2003) Coarse-grained stochastic models for tropical convection and climate. Proc Natl Acad Sci USA 100(21):11941–11946

    Article  MathSciNet  MATH  Google Scholar 

  • Khouider B, Biello JA, Majda AJ (2010) A stochastic multicloud model for tropical convection. Commun Math Sci 8:187–216

    Article  MathSciNet  MATH  Google Scholar 

  • Khouider B, St-Cyr A, Majda AJ, Tribbia J (2011) The MJO and convectively coupled waves in a coarse-resolution GCM with a simple multicloud parameterization. J Atmos Sci 68:240–264

    Article  Google Scholar 

  • Khouider B, Majda AJ, Stechmann SN (2013) Climate science in the tropics: waves, vortices and PDEs. Nonlinearity 26(1):R1–R68

    Article  MathSciNet  MATH  Google Scholar 

  • Kikuchi K, Takayabu YN (2004) The development of organized convection associated with the MJO during TOGA COARE IOP: trimodal characteristics. Geophys Res Lett 31(10.1029):L10101

    Article  Google Scholar 

  • Kiladis GN, Straub KH, Haertel PT (2005) Zonal and vertical structure of the Madden–Julian oscillation. J Atmos Sci 62:2790–2809

    Article  Google Scholar 

  • Kiladis GN, Wheeler MC, Haertel PT, Straub KH, Roundy PE (2009) Convectively coupled equatorial waves. Rev Geophys 47:RG2003. https://doi.org/10.1029/2008RG000266

    Article  Google Scholar 

  • Kooperman GJ, Pritchard MS, Burt MA, Branson MD, Randall DA (2016) Robust effects of cloud superparameterization on simulated daily rainfall intensity statistics across multiple versions of the Community Earth System Model. J Adv Model Earth Syst 8(1):140–165

    Article  Google Scholar 

  • Lau WKM, Waliser DE (eds) (2012) Intraseasonal Variability in the atmosphere–ocean climate system, 2nd edn. Springer, Berlin

    Google Scholar 

  • Lin X, Johnson RH (1996) Kinematic and thermodynamic characteristics of the flow over the western Pacific warm pool during TOGA COARE. J Atmos Sci 53:695–715

    Article  Google Scholar 

  • Lin J, Neelin J (2000) Influence of a stochastic moist convective parameterization on tropical climate variability. Geophys Res Lett 27(22):3691–3694. https://doi.org/10.1029/2000GL011964

    Article  Google Scholar 

  • Lin J, Neelin J (2002) Considerations for stochastic convective parameterization. J Atmos Sci 59(5):959–975

    Article  Google Scholar 

  • Lin J, Neelin J (2003) Toward stochastic deep convective parameterization in general circulation models. Geophys Res Lett 30(4):1162. https://doi.org/10.1029/2002GL016203

    Article  Google Scholar 

  • Liu P, Satoh M, Wang B, Fudeyasu H, Nasuno T, Li T, Miura H, Taniguchi H, Masunaga H, Fu X, et al (2009) An MJO simulated by the NICAM at 14-and 7-km resolutions. Mon Weather Rev 137(10):3254–3268

    Article  Google Scholar 

  • Majda AJ (2016) Introduction to turbulent dynamical systems in complex systems. Springer, Berlin

    Book  MATH  Google Scholar 

  • Majda AJ, Biello JA (2004) A multiscale model for the intraseasonal oscillation. Proc Natl Acad Sci USA 101(14):4736–4741

    Article  MathSciNet  MATH  Google Scholar 

  • Majda AJ, Harlim J (2012) Filtering turbulent complex systems. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Majda A, Khouider B (2002) Stochastic and mesoscopic models for tropical convection. Proc Natl Acad Sci USA 99(3):1123–1128

    Article  MATH  Google Scholar 

  • Majda AJ, Stechmann SN (2009a) A simple dynamical model with features of convective momentum transport. J Atmos Sci 66:373–392

    Article  Google Scholar 

  • Majda AJ, Stechmann SN (2009b) The skeleton of tropical intraseasonal oscillations. Proc Natl Acad Sci USA 106(21):8417–8422

    Article  Google Scholar 

  • Majda AJ, Tong XT (2015) Geometric ergodicity for piecewise contracting processes with applications for tropical stochastic lattice models. Commun Pure Appl Math. https://doi.org/10.1002/cpa.21584

    Article  MathSciNet  MATH  Google Scholar 

  • Majda AJ, Yang Q (2016) A multiscale model for the intraseasonal impact of the diurnal cycle over the maritime continent on the Madden–Julian oscillation. J Atmos Sci 73(2):579–604

    Article  Google Scholar 

  • Mapes BE, Tulich S, Lin JL, Zuidema P (2006) The mesoscale convection life cycle: building block or prototype for large-scale tropical waves? Dyn Atmos Oceans 42:3–29

    Article  Google Scholar 

  • Masunaga H, L’Ecuyer T, Kummerow C (2006) The Madden–Julian oscillation recorded in early observations from the Tropical Rainfall Measuring Mission (TRMM). J Atmos Sci 63(11):2777–2794

    Article  Google Scholar 

  • Moskowitz BM, Bretherton CS (2000) An analysis of frictional feedback on a moist equatorial Kelvin mode. J Atmos Sci 57(13):2188–2206

    Article  Google Scholar 

  • Myers D, Waliser D (2003) Three-dimensional water vapor and cloud variations associated with the Madden–Julian oscillation during Northern Hemisphere winter. J Clim 16(6):929–950

    Article  Google Scholar 

  • Nakazawa T (1988) Tropical super clusters within intraseasonal variations over the western Pacific. J Meterol Soc Jpn 6(6):823–839

    Article  Google Scholar 

  • Neelin JD, Held IM, Cook KH (1987) Evaporation–wind feedback and low-frequency variability in the tropical atmosphere. J Atmos Sci 44:2341–2348

    Article  Google Scholar 

  • Ogrosky HR, Stechmann SN, Majda AJ (2017) Boreal summer intraseasonal oscillations in the MJO skeleton model with observation-based forcing. Dyn Atmos Oceans 78:38–56

    Article  Google Scholar 

  • Palmer TN (2001) A nonlinear dynamical perspective on model error: a proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models. Q J Roy Meteorol Soc 127(572):279–304

    Google Scholar 

  • Peters K, Jakob C, Davies L, Khouider B, Majda AJ (2013) Stochastic behavior of tropical convection in observations and a multicloud model. J Atmos Sci 70(11):3556–3575

    Article  Google Scholar 

  • Peters K, Crueger T, Jakob C, Möbis B (2017) Improved MJO simulation in ECHAM6.3 by coupling a stochastic multicloud model to the convection scheme. J Adv Model Earth Syst 9(1):193–219

    Article  Google Scholar 

  • Plant R, Craig G (2008) A stochastic parameterization for deep convection based on equilibrium statistics. J Atmos Sci 65(1):87–105

    Article  Google Scholar 

  • Randall D, Khairoutdinov M, Arakawa A, Grabowski W (2003) Breaking the cloud parameterization deadlock. Bull Am Meteorol Soc 84:1547–1564

    Article  Google Scholar 

  • Raymond DJ (2001) A new model of the Madden–Julian oscillation. J Atmos Sci 58:2807–2819

    Article  Google Scholar 

  • Salby ML, Garcia RR, Hendon HH (1994) Planetary-scale circulations in the presence of climatological and wave-induced heating. J Atmos Sci 51:2344–2367

    Article  Google Scholar 

  • Satoh M, Matsuno T, Tomita H, Miura H, Nasuno T, Iga SI (2008) Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations. J Comput Phys 227(7):3486–3514

    Article  MathSciNet  MATH  Google Scholar 

  • Sobel A, Maloney E (2012) An idealized semi-empirical framework for modeling the Madden–Julian oscillation. J Atmos Sci 69(5):1691–1705

    Article  Google Scholar 

  • Teixeira J, Reynolds CA (2008) Stochastic nature of physical parameterizations in ensemble prediction: a stochastic convection approach. Mon Weather Rev 136(2):483–496

    Article  Google Scholar 

  • Thual S, Majda AJ, Stechmann SN (2015) Asymmetric intraseasonal events in the stochastic skeleton MJO model with seasonal cycle. Clim Dyn 45:603–618

    Article  Google Scholar 

  • Tian B, Waliser D, Fetzer E, Lambrigtsen B, Yung Y, Wang B (2006) Vertical moist thermodynamic structure and spatial–temporal evolution of the MJO in AIRS observations. J Atmos Sci 63(10):2462–2485

    Article  Google Scholar 

  • Tong XT, Majda AJ (2016) Moment bounds and geometric ergodicity of diffusions with random switching and unbounded transition rates. Res Math Sci 3(1):41

    Article  MathSciNet  MATH  Google Scholar 

  • Wang B, Rui H (1990) Dynamics of the coupled moist Kelvin–Rossby wave on an equatorial beta-plane. J Atmos Sci 47:397–413

    Article  Google Scholar 

  • Wang Y, Zhang GJ, Craig GC (2016) Stochastic convective parameterization improving the simulation of tropical precipitation variability in the NCAR CAM5. Geophys Res Lett 43(12):6612–6619

    Article  Google Scholar 

  • Yanai M, Chen B, Tung WW (2000) The Madden–Julian oscillation observed during the TOGA COARE IOP: global view. J Atmos Sci 57:2374–2396

    Article  Google Scholar 

  • Yang Q, Majda AJ (2017) Upscale impact of mesoscale disturbances of tropical convection on synoptic-scale equatorial waves in two-dimensional flows. J Atmos Sci 74(9):3099–3120

    Article  Google Scholar 

  • Yashiro H, Kajikawa Y, Miyamoto Y, Yamaura T, Yoshida R, Tomita H (2016) Resolution dependence of the diurnal cycle of precipitation simulated by a global cloud-system resolving model. SOLA 12:272–276

    Article  Google Scholar 

  • Zhang C (2005) Madden–Julian Oscillation. Rev Geophys 43:RG2003. https://doi.org/10.1029/2004RG000158

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Andrew J. Majda

  2. Center for Prototype Climate Modeling, NYU Abu Dhabi, Abu Dhabi, United Arab Emirates

    Andrew J. Majda

  3. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA

    Samuel N. Stechmann

  4. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, China

    Shengqian Chen

  5. Nanjing University of Information Science and Technology, Nanjing, China

    H. Reed Ogrosky

  6. Department of Atmospheric and Oceanic Sciences, Fudan University, Shanghai, China

    Sulian Thual

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  1. Andrew J. Majda
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  2. Samuel N. Stechmann
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  3. Shengqian Chen
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  4. H. Reed Ogrosky
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  5. Sulian Thual
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Majda, A.J., Stechmann, S.N., Chen, S., Ogrosky, H.R., Thual, S. (2019). Current and Future Research Perspectives. In: Tropical Intraseasonal Variability and the Stochastic Skeleton Method. Mathematics of Planet Earth(). Springer, Cham. https://doi.org/10.1007/978-3-030-22247-5_7

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