• Abramowitz, M., and I. A. Stegun, 1964: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 9th ed. Dover, 1046 pp.

    • Search Google Scholar
    • Export Citation
  • Adam, O., 2018: Zonally varying ITCZs in a Matsuno-Gill-type model with an idealized Bjerknes feedback. J. Adv. Model. Earth Syst., 10, 13041318, https://doi.org/10.1029/2017MS001183.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Back, L. E., and C. S. Bretherton, 2009: On the relationship between SST gradients, boundary layer winds, and convergence over the tropical oceans. J. Climate, 22, 41824196, https://doi.org/10.1175/2009JCLI2392.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Battisti, D. S., E. S. Sarachik, and A. C. Hirst, 1999: A consistent model for the large-scale steady surface atmospheric circulation in the tropics. J. Climate, 12, 29562964, https://doi.org/10.1175/1520-0442(1999)012<2956:ACMFTL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bellon, G., and B. Reboredo, 2021: Scale sensitivity of the Gill circulation. Part II: Off-equatorial case. J. Atmos. Sci., https://doi.org/10.1175/JAS-D-21-0068.1, 79, 1930.

    • 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
  • Cauchy, A. L. B., 1821: Cours d’analyse de l’École Royale Polytechnique: Analyse algébrique. Vol. 1. Debure frères, 576 pp.

  • 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
  • Heckley, W. A., and A. E. Gill, 1984: Some simple analytical solutions to the problem of forced equatorial long waves. Quart. J. Roy. Meteor. Soc., 110, 203217, https://doi.org/10.1002/qj.49711046314.

    • 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
  • Iipponen, J., and L. Donner, 2021: Simple analytic solutions for a convectively driven Walker circulation and their relevance to observations. J. Atmos. Sci., 78, 299311, https://doi.org/10.1175/JAS-D-20-0014.1.

    • 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
  • Krueger, A. F., and J. S. Winston, 1974: A comparison of the flow over the tropics during two contrasting circulation regimes. J. Atmos. Sci., 31, 358370, https://doi.org/10.1175/1520-0469(1974)031<0358:ACOTFO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leroux, S., and Coauthors, 2016: Inter-model comparison of subseasonal tropical variability in aquaplanet experiments: Effect of a warm pool. J. Adv. Model. Earth Syst., 8, 15261551, https://doi.org/10.1002/2016MS000683.

    • 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., 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
  • Lintner, B. R., G. Bellon, A. H. Sobel, D. Kim, and J. D. Neelin, 2012: Implementation of the Quasi-Equilibrium Tropical Circulation Model 2 (QTCM2): Global simulations and convection sensitivity to free tropospheric moisture. J. Adv. Model. Earth Syst., 4, M12002, https://doi.org/10.1029/2012MS000174.

    • 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
  • Maloney, E. D., A. H. Sobel, and W. M. Hannah, 2010: Intraseasonal variability in an aquaplanet general circulation model. J. Adv. Model. Earth Syst., 2 (2), https://doi.org/10.3894/JAMES.2010.2.5.

    • Crossref
    • 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
  • Neelin, J. D., 1989: On the interpretation of the Gill model. J. Atmos. Sci., 46, 24662468, https://doi.org/10.1175/1520-0469(1989)046<2466:OTIOTG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neelin, J. D., and N. Zeng, 2000: A quasi-equilibrium tropical circulation model—Formulation. J. Atmos. Sci., 57, 17411766, https://doi.org/10.1175/1520-0469(2000)057<1741:AQETCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pazan, S. E., and G. Meyers, 1982: Interannual fluctuations of the tropical Pacific wind field and the Southern Oscillation. Mon. Wea. Rev., 110, 587600, https://doi.org/10.1175/1520-0493(1982)110<0587:IFOTTP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Philander, S. G. H., 1983: El Niño Southern Oscillation phenomena. Nature, 302, 295301, https://doi.org/10.1038/302295a0.

  • Pierrehumbert, R. T., and M. Hammond, 2019: Atmospheric circulation of tide-locked exoplanets. Annu. Rev. Fluid Mech., 51, 275303, https://doi.org/10.1146/annurev-fluid-010518-040516.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rostami, M., and V. Zeitlin, 2019: Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane. Phys. Fluids, 31, 21701, https://doi.org/10.1063/1.5080415.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Showman, A. P., and L. M. Polvani, 2010: The Matsuno-Gill model and equatorial superrotation. Geophys. Res. Lett., 37, L18811, https://doi.org/10.1029/2010GL044343.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Showman, A. P., and L. M. Polvani, 2011: Equatorial superrotation on tidally locked exoplanets. Astrophys. J., 738, 71, https://doi.org/10.1088/0004-637X/738/1/71.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., and C. S. Bretherton, 2000: Modeling tropical precipitation in a single column. J. Climate, 13, 43784392, https://doi.org/10.1175/1520-0442(2000)013<4378:MTPIAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., E. D. Maloney, G. Bellon, and D. M. Frierson, 2008: The role of surface heat fluxes in tropical intraseasonal oscillations. Nat. Geosci., 1, 653657, https://doi.org/10.1038/ngeo312.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., E. D. Maloney, G. Bellon, and D. M. Frierson, 2010: Surface fluxes and tropical intraseasonal variability: A reassessment. J. Adv. Model. Earth Syst., 2 (1), https://doi.org/10.3894/JAMES.2010.2.2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stechmann, S. N., and H. R. Ogrosky, 2014: The Walker circulation, diabatic heating, and outgoing longwave radiation. Geophys. Res. Lett., 41, 90979105, https://doi.org/10.1002/2014GL062257.

    • 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
  • Yu, J.-Y., C. Chou, and J. D. Neelin, 1998: Estimating the gross moist stability of the tropical atmosphere. J. Atmos. Sci., 55, 13541372, https://doi.org/10.1175/1520-0469(1998)055<1354:ETGMSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, N., J. D. Neelin, and C. Chou, 2000: A quasi-equilibrium tropical circulation model—Implementation and simulation. J. Atmos. Sci., 57, 17671796, https://doi.org/10.1175/1520-0469(2000)057<1767:AQETCM>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., Á. 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
  • Zhang, Z., and T. N. Krishnamurti, 1996: A generalization of Gill’s heat-induced tropical circulation. J. Atmos. Sci., 53, 10451052, https://doi.org/10.1175/1520-0469(1996)053<1045:AGOGHI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Scale Sensitivity of the Gill Circulation. Part I: Equatorial Case

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  • 1 aDepartment of Physics, University of Auckland, Auckland, New Zealand
  • | 2 bCentre National de Recherches Météorologiques, Université de Toulouse, Météo France, CNRS, Toulouse, France
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Abstract

We investigate the steady dynamical response of the atmosphere on the equatorial β plane to a steady, localized, midtropospheric heating source at the equator. Expanding Gill’s seminal work, we vary the latitudinal and longitudinal scales of the diabatic heating pattern while keeping its total amount fixed. We focus on characteristics of the response that would be particularly important if the circulation interacted with the hydrologic and energy cycles: the overturning circulation and the low-level wind. In the limit of very small scale in either the longitudinal or latitudinal direction, the vertical energy transport balances the diabatic heating and this sets the intensity of the overturning circulation. In this limit, a fast low-level westerly jet is located around the center of diabatic heating. With increasing longitudinal or latitudinal scale of the diabatic heating, the intensity of the overturning circulation decreases and the low-level westerly jet decreases in maximum velocity and spatial extent relative to the spatial extent of this heating. The associated low-level eastward mass transport decreases only with increasing longitudinal scale. These results suggest that moisture-convergence feedbacks will favor small-scale equatorial convective disturbances while surface-heat-flux feedbacks would favor small-scale disturbances in mean westerlies and large-scale disturbances in mean easterlies. Part II investigates the case of off-equatorial heating.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Publisher's Note: This article was revised on 24 March 2022 to fix Fig. 3, which was incomplete when originally published.

Corresponding author: Gilles Bellon, gilles.bellon@auckland.ac.nz

Abstract

We investigate the steady dynamical response of the atmosphere on the equatorial β plane to a steady, localized, midtropospheric heating source at the equator. Expanding Gill’s seminal work, we vary the latitudinal and longitudinal scales of the diabatic heating pattern while keeping its total amount fixed. We focus on characteristics of the response that would be particularly important if the circulation interacted with the hydrologic and energy cycles: the overturning circulation and the low-level wind. In the limit of very small scale in either the longitudinal or latitudinal direction, the vertical energy transport balances the diabatic heating and this sets the intensity of the overturning circulation. In this limit, a fast low-level westerly jet is located around the center of diabatic heating. With increasing longitudinal or latitudinal scale of the diabatic heating, the intensity of the overturning circulation decreases and the low-level westerly jet decreases in maximum velocity and spatial extent relative to the spatial extent of this heating. The associated low-level eastward mass transport decreases only with increasing longitudinal scale. These results suggest that moisture-convergence feedbacks will favor small-scale equatorial convective disturbances while surface-heat-flux feedbacks would favor small-scale disturbances in mean westerlies and large-scale disturbances in mean easterlies. Part II investigates the case of off-equatorial heating.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Publisher's Note: This article was revised on 24 March 2022 to fix Fig. 3, which was incomplete when originally published.

Corresponding author: Gilles Bellon, gilles.bellon@auckland.ac.nz

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