Diurnally Forced Tropical Gravity Waves under Varying Stability

Ewan Short aSchool of Geography, Earth and Atmospheric Sciences, University of Melbourne, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, University of Melbourne, Melbourne, Victoria, Australia

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Todd P. Lane aSchool of Geography, Earth and Atmospheric Sciences, University of Melbourne, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, University of Melbourne, Melbourne, Victoria, Australia

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Craig H. Bishop aSchool of Geography, Earth and Atmospheric Sciences, University of Melbourne, Melbourne, Victoria, Australia
bARC Centre of Excellence for Climate Extremes, University of Melbourne, Melbourne, Victoria, Australia

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Matthew C. Wheeler cBureau of Meteorology, Melbourne, Victoria, Australia

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Abstract

Diurnal processes play a primary role in tropical weather. A leading hypothesis is that atmospheric gravity waves diurnally forced near coastlines propagate both offshore and inland, encouraging convection as they do so. In this study we extend the linear analytic theory of diurnally forced gravity waves, allowing for discontinuities in stability and for linear changes in stability over a finite-depth “transition layer.” As an illustrative example, we first consider the response to a commonly studied heating function emulating diurnally oscillating coastal temperature gradients, with a low-level stability change between the boundary layer and troposphere. Gravity wave rays resembling the upper branches of “Saint Andrew’s cross” are forced along the coastline at the surface, with the stability changes inducing reflection, refraction, and ducting of the individual waves comprising the rays, with analogous behavior evident in the rays themselves. Refraction occurs smoothly in the transition-layer solution, with substantially less reflection than in the discontinuous solution. Second, we consider a new heating function which emulates an upper-level convective heating diurnal cycle, and consider stability changes associated with the tropical tropopause. Reflection, refraction, and ducting again occur, with the lower branches of Saint Andrew’s cross now evident. We compare these solutions to observations taken during the Years of the Maritime Continent field campaign, noting better qualitative agreement with the transition-layer solution than the discontinuous solution, suggesting the tropopause is an even weaker gravity wave reflector than previously thought.

Significance Statement

This study extends our theoretical understanding of how forced atmospheric gravity waves change with atmospheric structure. Gravity wave behavior depends on atmospheric stability: how much the atmosphere resists vertical displacements of air. Where stability changes, waves reflect and refract, analogously to when light passes from water to air. Our study presents new mathematical tools for understanding this reflection and refraction, demonstrating reflection is substantially weaker when stability increases over “transition layers,” than when stability increases suddenly. Our results suggest the tropical tropopause reflects less gravity wave energy than previously thought, with potential design implications for weather and climate models, to be assessed in future work.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Years of the Maritime Continent Special Collection.

Corresponding author: Ewan Short, shorte1@student.unimelb.edu.au

Abstract

Diurnal processes play a primary role in tropical weather. A leading hypothesis is that atmospheric gravity waves diurnally forced near coastlines propagate both offshore and inland, encouraging convection as they do so. In this study we extend the linear analytic theory of diurnally forced gravity waves, allowing for discontinuities in stability and for linear changes in stability over a finite-depth “transition layer.” As an illustrative example, we first consider the response to a commonly studied heating function emulating diurnally oscillating coastal temperature gradients, with a low-level stability change between the boundary layer and troposphere. Gravity wave rays resembling the upper branches of “Saint Andrew’s cross” are forced along the coastline at the surface, with the stability changes inducing reflection, refraction, and ducting of the individual waves comprising the rays, with analogous behavior evident in the rays themselves. Refraction occurs smoothly in the transition-layer solution, with substantially less reflection than in the discontinuous solution. Second, we consider a new heating function which emulates an upper-level convective heating diurnal cycle, and consider stability changes associated with the tropical tropopause. Reflection, refraction, and ducting again occur, with the lower branches of Saint Andrew’s cross now evident. We compare these solutions to observations taken during the Years of the Maritime Continent field campaign, noting better qualitative agreement with the transition-layer solution than the discontinuous solution, suggesting the tropopause is an even weaker gravity wave reflector than previously thought.

Significance Statement

This study extends our theoretical understanding of how forced atmospheric gravity waves change with atmospheric structure. Gravity wave behavior depends on atmospheric stability: how much the atmosphere resists vertical displacements of air. Where stability changes, waves reflect and refract, analogously to when light passes from water to air. Our study presents new mathematical tools for understanding this reflection and refraction, demonstrating reflection is substantially weaker when stability increases over “transition layers,” than when stability increases suddenly. Our results suggest the tropical tropopause reflects less gravity wave energy than previously thought, with potential design implications for weather and climate models, to be assessed in future work.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Years of the Maritime Continent Special Collection.

Corresponding author: Ewan Short, shorte1@student.unimelb.edu.au

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  • Abramowitz, M., and I. A. Stegun, 1972: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, 1076 pp.

  • Alexander, M. J., P. T. May, and J. H. Beres, 2004: Gravity waves generated by convection in the Darwin area during the Darwin Area Wave Experiment. J. Geophys. Res., 109, D20S04, https://doi.org/10.1029/2004JD004729.

    • Search Google Scholar
    • Export Citation
  • Bergemann, M., C. Jakob, and T. P. Lane, 2015: Global detection and analysis of coastline-associated rainfall using an objective pattern recognition technique. J. Climate, 28, 72257236, https://doi.org/10.1175/JCLI-D-15-0098.1.

    • Search Google Scholar
    • Export Citation
  • Dacie, S., and Coauthors, 2019: A 1D RCE study of factors affecting the tropical tropopause layer and surface climate. J. Climate, 32, 67696782, https://doi.org/10.1175/JCLI-D-18-0778.1.

    • Search Google Scholar
    • Export Citation
  • Dalu, G. A., and R. A. Pielke, 1989: An analytical study of the sea breeze. J. Atmos. Sci., 46, 18151825, https://doi.org/10.1175/1520-0469(1989)046<1815:AASOTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Das Gupta, A. J., A. S. V. Murthy, and R. S. Nanjundiah, 2015: A study of singularities in the inviscid linear theory of sea breezes. Int. J. Adv. Eng. Sci. Appl. Math., 7, 3337, https://doi.org/10.1007/s12572-015-0129-y.

    • Search Google Scholar
    • Export Citation
  • Drobinski, P., R. Rotunno, and T. Dubos, 2011: Linear theory of the sea breeze in a thermal wind. Quart. J. Roy. Meteor. Soc., 137, 16021609, https://doi.org/10.1002/qj.847.

    • Search Google Scholar
    • Export Citation
  • Du, Y., and R. Rotunno, 2015: Thermally driven diurnally periodic wind signals off the east coast of China. J. Atmos. Sci., 72, 28062821, https://doi.org/10.1175/JAS-D-14-0339.1.

    • Search Google Scholar
    • Export Citation
  • Du, Y., and R. Rotunno, 2018: Diurnal cycle of rainfall and winds near the south coast of China. J. Atmos. Sci., 75, 20652082, https://doi.org/10.1175/JAS-D-17-0397.1.

    • Search Google Scholar
    • Export Citation
  • Du, Y., R. Rotunno, and F. Zhang, 2019: Impact of vertical wind shear on gravity wave propagation in the land–sea-breeze circulation at the equator. J. Atmos. Sci., 76, 32473265, https://doi.org/10.1175/JAS-D-19-0069.1.

    • Search Google Scholar
    • Export Citation
  • Feng, S., Y. Fu, and Q. Xiao, 2012: Trends in the global tropopause thickness revealed by radiosondes. Geophys. Res. Lett., 39, L20706, https://doi.org/10.1029/2012GL053460.

    • Search Google Scholar
    • Export Citation
  • Fueglistaler, S., A. E. Dessler, T. J. Dunkerton, I. Folkins, Q. Fu, and P. W. Mote, 2009: Tropical tropopause layer. Rev. Geophys., 47, RG1004, https://doi.org/10.1029/2008RG000267.

    • Search Google Scholar
    • Export Citation
  • Gille, S. T., S. G. L. Smith, and N. M. Statom, 2005: Global observations of the land breeze. Geophys. Res. Lett., 32, L05605, https://doi.org/10.1029/2004GL022139.

    • Search Google Scholar
    • Export Citation
  • Hankinson, M. C. N., M. J. Reeder, and T. P. Lane, 2014: Gravity waves generated by convection during TWP-ICE: I. Inertia-gravity waves. J. Geophys. Res. Atmos., 119, 52695282, https://doi.org/10.1002/2013JD020724.

    • Search Google Scholar
    • Export Citation
  • Hecht, J. H., S. Kovalam, P. T. May, G. Mills, R. A. Vincent, R. L. Walterscheid, and J. Woithe, 2004: Airglow imager observations of atmospheric gravity waves at Alice Springs and Adelaide, Australia during the Darwin Area Wave Experiment (DAWEX). J. Geophys. Res., 109, D20S05, https://doi.org/10.1029/2004JD004697.

    • Search Google Scholar
    • Export Citation
  • Hu, S., and G. K. Vallis, 2019: Meridional structure and future changes of tropopause height and temperature. Quart. J. Roy. Meteor. Soc., 145, 26982717, https://doi.org/10.1002/qj.3587.

    • Search Google Scholar
    • Export Citation
  • Jiang, Q., 2012a: A linear theory of three-dimensional land–sea breezes. J. Atmos. Sci., 69, 18901909, https://doi.org/10.1175/JAS-D-11-0137.1.

    • Search Google Scholar
    • Export Citation
  • Jiang, Q., 2012b: On offshore propagating diurnal waves. J. Atmos. Sci., 69, 15621581, https://doi.org/10.1175/JAS-D-11-0220.1.

  • Kilpatrick, T., S.-P. Xie, and T. Nasuno, 2017: Diurnal convection-wind coupling in the Bay of Bengal. J. Geophys. Res. Atmos., 122, 97059720, https://doi.org/10.1002/2017JD027271.

    • Search Google Scholar
    • Export Citation
  • Lane, T. P., 2021: Does lower-stratospheric shear influence the mesoscale organization of convection? Geophys. Res. Lett., 48, e2020GL091025, https://doi.org/10.1029/2020GL091025.

    • Search Google Scholar
    • Export Citation
  • Li, Y., and J. Chao, 2016: An analytical solution for three-dimensional sea–land breeze. J. Atmos. Sci., 73, 4154, https://doi.org/10.1175/JAS-D-14-0329.1.

    • Search Google Scholar
    • Export Citation
  • Lin, P., D. Paynter, Y. Ming, and V. Ramaswamy, 2017: Changes of the tropical tropopause layer under global warming. J. Climate, 30, 12451258, https://doi.org/10.1175/JCLI-D-16-0457.1.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., and K.-K. Tung, 1976: Banded convective activity and ducted gravity waves. Mon. Wea. Rev., 104, 16021617, https://doi.org/10.1175/1520-0493(1976)104<1602:BCAADG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mapes, B. E., T. T. Warner, and M. Xu, 2003: Diurnal patterns of rainfall in northwestern South America. Part III: Diurnal gravity waves and nocturnal convection offshore. Mon. Wea. Rev., 131, 830844, https://doi.org/10.1175/1520-0493(2003)131<0830:DPORIN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Minobe, S., and S. Takebayashi, 2015: Diurnal precipitation and high cloud frequency variability over the Gulf Stream and over the Kuroshio. Climate Dyn., 44, 20792095, https://doi.org/10.1007/s00382-014-2245-y.

    • Search Google Scholar
    • Export Citation
  • Mori, S., and Coauthors, 2004: Diurnal land–sea rainfall peak migration over Sumatera Island, Indonesian Maritime Continent, observed by TRMM satellite and intensive rawinsonde soundings. Mon. Wea. Rev., 132, 20212039, https://doi.org/10.1175/1520-0493(2004)132<2021:DLRPMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mowbray, D. E., and B. S. H. Rarity, 1967: A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech., 28, 116, https://doi.org/10.1017/S0022112067001867.

    • Search Google Scholar
    • Export Citation
  • Niino, H., 1987: The linear theory of land and sea breeze circulation. J. Meteor. Soc. Japan, 65, 901921, https://doi.org/10.2151/jmsj1965.65.6_901.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173179, https://doi.org/10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pan, L. L., W. J. Randel, B. L. Gary, M. J. Mahoney, and E. J. Hintsa, 2004: Definitions and sharpness of the extratropical tropopause: A trace gas perspective. J. Geophys. Res., 109, D23103, https://doi.org/10.1029/2004JD004982.

    • Search Google Scholar
    • Export Citation
  • Pandya, R., D. Durran, and C. Bretherton, 1993: Comments on “Thermally forced gravity waves in an atmosphere at rest.” J. Atmos. Sci., 50, 40974101, https://doi.org/10.1175/1520-0469(1993)050<4097:COFGWI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pandya, R., D. Durran, and M. L. Weisman, 2000: The influence of convective thermal forcing on the three-dimensional circulation around squall lines. J. Atmos. Sci., 57, 2945, https://doi.org/10.1175/1520-0469(2000)057<0029:TIOCTF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Protat, A., and I. McRobert, 2020a: RV Investigator IN2019_v06 BASTA radar and radiosonde data. Commonwealth Scientific and Industrial Research Organisation, accessed 23 February 2023, https://doi.org/10.25919/5ef5a70ae2be9.

  • Protat, A., and I. McRobert, 2020b: Three-dimensional wind profiles using a stabilized shipborne cloud radar in wind profiler mode. Atmos. Meas. Tech., 13, 36093620, https://doi.org/10.5194/amt-13-3609-2020.

    • Search Google Scholar
    • Export Citation
  • Protat, A., V. Louf, J. Soderholm, J. Brook, and W. Ponsonby, 2022: Three-way calibration checks using ground-based, ship-based, and spaceborne radars. Atmos. Meas. Tech., 15, 915926, https://doi.org/10.5194/amt-15-915-2022.

    • Search Google Scholar
    • Export Citation
  • Qian, T., C. C. Epifanio, and F. Zhang, 2009: Linear theory calculations for the sea breeze in a background wind: The equatorial case. J. Atmos. Sci., 66, 17491763, https://doi.org/10.1175/2008JAS2851.1.

    • Search Google Scholar
    • Export Citation
  • Qian, T., C. C. Epifanio, and F. Zhang, 2012: Topographic effects on the tropical land and sea breeze. J. Atmos. Sci., 69, 130149, https://doi.org/10.1175/JAS-D-11-011.1.

    • Search Google Scholar
    • Export Citation
  • Robinson, F. J., S. C. Sherwood, and Y. Li, 2008: Resonant response of deep convection to surface hot spots. J. Atmos. Sci., 65, 276286, https://doi.org/10.1175/2007JAS2398.1.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 1983: On the linear theory of the land and sea breeze. J. Atmos. Sci., 40, 19992009, https://doi.org/10.1175/1520-0469(1983)040<1999:OTLTOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schmidt, T., G. Beyerle, S. Heise, J. Wickert, and M. Rothacher, 2006: A climatology of multiple tropopauses derived from GPS radio occultations with CHAMP and SAC-C. Geophys. Res. Lett., 33, L04808, https://doi.org/10.1029/2005GL024600.

    • Search Google Scholar
    • Export Citation
  • Short, E., 2023: rotunno83. GitHub, accessed 17 March 2023, https://github.com/eshort0401/rotunno83.

  • Sutherland, B. R., 2010: Internal Gravity Waves. Cambridge University Press, 377 pp., https://doi.org/10.1017/CBO9780511780318.

  • Vincent, C. L., and T. P. Lane, 2016: Evolution of the diurnal precipitation cycle with the passage of a Madden–Julian oscillation event through the Maritime Continent. Mon. Wea. Rev., 144, 19832005, https://doi.org/10.1175/MWR-D-15-0326.1.

    • Search Google Scholar
    • Export Citation
  • Vincent, C. L., and T. P. Lane, 2018: Mesoscale variation in diabatic heating around Sumatra, and its modulation with the Madden–Julian oscillation. Mon. Wea. Rev., 146, 25992614, https://doi.org/10.1175/MWR-D-17-0392.1.

    • Search Google Scholar
    • Export Citation
  • Vincent, R. A., A. MacKinnon, I. M. Reid, and M. J. Alexander, 2004: VHF profiler observations of winds and waves in the troposphere during the Darwin Area Wave Experiment (DAWEX). J. Geophys. Res., 109, D20S02, https://doi.org/10.1029/2004JD004714.

    • Search Google Scholar
    • Export Citation
  • Whittaker, E. T., and G. N. Watson, 1996: A Course of Modern Analysis. 4th ed. Cambridge Mathematical Library, Cambridge University Press, 608 pp., https://doi.org/10.1017/CBO9780511608759.

  • Wünsche, A., 2003: Generalized Hermite polynomials associated with functions of parabolic cylinder. Appl. Math. Comput., 141, 197213, https://doi.org/10.1016/S0096-3003(02)00333-8.

    • Search Google Scholar
    • Export Citation
  • Yan, H., and R. A. Anthes, 1987: The effect of latitude on the sea breeze. Mon. Wea. Rev., 115, 936956, https://doi.org/10.1175/1520-0493(1987)115<0936:TEOLOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., and J. Slingo, 2001: The diurnal cycle in the tropics. Mon. Wea. Rev., 129, 784801, https://doi.org/10.1175/1520-0493(2001)129<0784:TDCITT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yoneyama, K., and C. Zhang, 2020: Years of the Maritime Continent. Geophys. Res. Lett., 47, e2020GL087182, https://doi.org/10.1029/2020GL087182.

    • Search Google Scholar
    • Export Citation
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