• Aiki, H., K. Takaya, and R. J. Greatbatch, 2015: A divergence-form wave-induced pressure inherent in the extension of the Eliassen–Palm theory to a three-dimensional framework for waves at all latitudes. J. Atmos. Sci., 72, 28222849, https://doi.org/10.1175/JAS-D-14-0172.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aiki, H., R. J. Greatbatch, and M. Claus, 2017: Towards a seamlessly diagnosable expression for the energy flux associated with both equatorial and mid-latitude waves. Prog. Earth Planet. Sci., 4, 11, https://doi.org/10.1186/s40645-017-0121-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., and Coauthors, 2001: The quasi-biennial oscillation. Rev. Geophys., 39, 179229, https://doi.org/10.1029/1999RG000073.

  • Brönnimann, S., 2007: Impact of El Niño–Southern Oscillation on European climate. Rev. Geophys., 45, RG3003, https://doi.org/10.1029/2006RG000199.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cai, M., and B. Huang, 2013: A new look at the physics of Rossby waves: A mechanical-Coriolis oscillation. J. Atmos. Sci., 70, 303316, https://doi.org/10.1175/JAS-D-12-094.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cassou, C., 2008: Intraseasonal interaction between the Madden–Julian oscillation and the North Atlantic Oscillation. Nature, 455, 523527, https://doi.org/10.1038/nature07286.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durland, T. S., and J. T. Farrar, 2020: Another note on Rossby wave energy flux. J. Phys. Oceanogr., 50, 531534, https://doi.org/10.1175/JPO-D-19-0237.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and E. Palm, 1960: On the transfer of energy in stationary mountain waves. Geophys. Publ., 22, 123.

  • Frederiksen, J. S., and P. J. Webster, 1988: Alternative theories of atmospheric teleconnections and low-frequency fluctuations. Rev. Geophys., 26, 459–494, https://doi.org/10.1029/RG026i003p00459.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fukutomi, Y., 2019: Tropical synoptic-scale waves propagating across the Maritime Continent and northern Australia. J. Geophys. Res. Atmos., 124, 76657682, https://doi.org/10.1029/2018JD029795.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fukutomi, Y., and T. Yasunari, 2002: Tropical–extratropical interaction associated with the 10–25-day oscillation over the western Pacific during the northern summer. J. Meteor. Soc. Japan, 80, 311331, https://doi.org/10.2151/jmsj.80.311.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gray, L. J., J. A. Anstey, Y. Kawatani, H. Lu, S. Osprey, and V. Schenzinger, 2018: Surface impacts of the quasi biennial oscillation. Atmos. Chem. Phys., 18, 82278247, https://doi.org/10.5194/acp-18-8227-2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harada, Y., and Coauthors, 2016: The JRA-55 Reanalysis: Representation of atmospheric circulation and climate variability. J. Meteor. Soc. Japan, 94, 269302, https://doi.org/10.2151/jmsj.2016-015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harada, Y., K. Sato, T. Kinoshita, R. Yasui, T. Hirooka, and H. Naoe, 2019: Diagnostics of a WN2-type major sudden stratospheric warming event in February 2018 using a new three-dimensional wave activity flux. J. Geophys. Res. Atmos., 124, 61206142, https://doi.org/10.1029/2018JD030162.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendon, H. H., and M. L. Salby, 1996: Planetary-scale circulations forced by intraseasonal variations of observed convection. J. Atmos. Sci., 53, 17511758, https://doi.org/10.1175/1520-0469(1996)053<1751:pscfbi>2.0.co;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 2004: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, 531 pp.

  • Holton, J. R., and H.-C. Tan, 1980: The influence of the equatorial quasi-biennial oscillation on the global circulation at 50 mb. J. Atmos. Sci., 37, 22002208, https://doi.org/10.1175/1520-0469(1980)037<2200:TIOTEQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horinouchi, T., F. Sassi, and B. A. Boville, 2000: Synoptic-scale Rossby waves and the geographic distribution of lateral transport routes between the tropics and the extratropics in the lower stratosphere. J. Geophys. Res., 105, 26 57926 592, https://doi.org/10.1029/2000JD900281.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38, 11791196, https://doi.org/10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, R., and F. Sun, 1992: Impacts of the tropical western Pacific on the East Asian summer monsoon. J. Meteor. Soc. Japan, 70, 243256, https://doi.org/10.2151/jmsj1965.70.1B_243.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ineson, S., and A. A. Scaife, 2008: The role of the stratosphere in the European climate response to El Niño. Nat. Geosci., 2, 3236, https://doi.org/10.1038/ngeo381.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kawahira, K., 1983: Global structures of stationary planetary waves in the middle atmosphere. J. Meteor. Soc. Japan, 61, 695716, https://doi.org/10.2151/jmsj1965.61.5_695.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kawatani, Y., M. Takahashi, K. Sato, S. P. Alexander, and T. Tsuda, 2009: Global distribution of atmospheric waves in the equatorial upper troposphere and lower stratosphere: AGCM simulation of sources and propagation. J. Geophys. Res., 114, D01102, https://doi.org/10.1029/2008JD010374.

    • 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
  • King, M. P., I. Herceg-Bulić, I. Bladé, J. García-Serrano, N. Keenlyside, F. Kucharski, C. Li, and S. Sobolowski, 2018: Importance of late fall ENSO teleconnection in the Euro-Atlantic sector. Bull. Amer. Meteor. Soc., 99, 13371343, https://doi.org/10.1175/BAMS-D-17-0020.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kobayashi, S., and Coauthors, 2015: The JRA-55 Reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 548, https://doi.org/10.2151/jmsj.2015-001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kosaka, Y., and H. Nakamura, 2006: Structure and dynamics of the summertime Pacific–Japan teleconnection pattern. Quart. J. Roy. Meteor. Soc., 132, 20092030, https://doi.org/10.1256/qj.05.204.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lau, W. K. M., D. E. Waliser, and P. E. Roundy, 2011: Tropical–extratropical interactions. Intraseasonal Variability in the Atmosphere-Ocean Climate System, W. K. M. Lau and D. E. Waliser, Eds., Springer, 497–512.

    • Crossref
    • Export Citation
  • Li, Z., and H. Aiki, 2020: The life cycle of annual waves in the Indian Ocean as identified by seamless diagnosis of the energy flux. Geophys. Res. Lett., 47, e2019GL085670, https://doi.org/10.1029/2019GL085670.

    • Search Google Scholar
    • Export Citation
  • Li, Z., H. Aiki, M. Nagura, and T. Ogata, 2021: The vertical structure of annual wave energy flux in the tropical Indian Ocean. Prog. Earth Planet. Sci., 8, 43, https://doi.org/10.1186/s40645-021-00432-9.

    • 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
  • Longuet-Higgins, M. S., 1964: On group velocity and energy flux in planetary wave motion. Deep-Sea Res., 11, 3542, https://doi.org/10.1016/0011-7471(64)91080-0.

    • 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
  • Nitta, T., 1970: A study of generation and conversion of eddy available potential energy in the tropics. J. Meteor. Soc. Japan, 48, 524528, https://doi.org/10.2151/jmsj1965.48.6_524.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nitta, T., 1987: Convective activities in the tropical western Pacific and their impact on the Northern Hemisphere summer circulation. J. Meteor. Soc. Japan, 65, 373390, https://doi.org/10.2151/jmsj1965.65.3_373.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ogata, T., and H. Aiki, 2019: The pathway of intraseasonal wave energy in the tropical Indian Ocean as identified by a seamless diagnostic scheme. SOLA, 15, 262267, https://doi.org/10.2151/sola.2019-047.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orlanski, I., and J. Sheldon, 1993: A case of downstream baroclinic development over western North America. Mon. Wea. Rev., 121, 29292950, https://doi.org/10.1175/1520-0493(1993)121<2929:ACODBD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1986: Three-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of the time-mean flow. J. Atmos. Sci., 43, 16571678, https://doi.org/10.1175/1520-0469(1986)043<1657:TDPOTQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ribstein, B., U. Achatz, and F. Senf, 2015: The interaction between gravity waves and solar tides: Results from 4-D ray tracing coupled to a linear tidal model. J. Geophys. Res. Space Phys., 120, 67956817, https://doi.org/10.1002/2015JA021349.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sato, K., S. Watanabe, Y. Kawatani, Y. Tomikawa, K. Miyazaki, and M. Takahashi, 2009: On the origins of mesospheric gravity waves. Geophys. Res. Lett., 36, L19801, https://doi.org/10.1029/2009GL039908.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scaife, A. A., and Coauthors, 2016: Tropical rainfall, Rossby waves and regional winter climate predictions. Quart. J. Roy. Meteor. Soc., 143, 111, https://doi.org/10.1002/qj.2910.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Serra, Y. L., X. Jiang, B. Tian, J. Amador-Astua, E. D. Maloney, and G. N. Kiladis, 2014: Tropical intraseasonal modes of the atmosphere. Annu. Rev. Environ. Resour., 39, 189215, https://doi.org/10.1146/annurev-environ-020413-134219.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shaman, J., and E. Tziperman, 2005: The effect of ENSO on Tibetan Plateau snow depth: A stationary wave teleconnection mechanism and implications for the South Asian monsoons. J. Climate, 18, 20672079, https://doi.org/10.1175/JCLI3391.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1963: General circulation experiments with the primitive equation. I. The basic experiment. Mon. Wea. Rev., 91, 99165, https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., and C. S. Bretherton, 1999: Development of synoptic-scale disturbances over the summertime tropical northwest Pacific. J. Atmos. Sci., 56, 31063127, https://doi.org/10.1175/1520-0469(1999)056<3106:dossdo>2.0.co;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Song, Q., and H. Aiki, 2020: The climatological horizontal pattern of energy flux in the tropical Atlantic as identified by a unified diagnosis for Rossby and Kelvin waves. J. Geophys. Res. Oceans, 125, e2019JC015407, https://doi.org/10.1029/2019JC015407.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Song, Q., and H. Aiki, 2021: Horizontal energy flux of wind-driven intraseasonal waves in the tropical Atlantic by a unified diagnosis. J. Phys. Oceanogr., 51, 30373050, https://doi.org/10.1175/JPO-D-20-0262.1.

    • Search Google Scholar
    • Export Citation
  • Stan, C., D. M. Straus, J. S. Frederiksen, H. Lin, E. D. Maloney, and C. Schumacher, 2017: Review of tropical-extratropical teleconnections on intraseasonal time scales. Rev. Geophys., 55, 902937, https://doi.org/10.1002/2016RG000538.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Takaya, K., and H. Nakamura, 2001: A formulation of a phase-independent wave-activity flux for stationary and migratory quasigeostrophic eddies on a zonally varying basic flow. J. Atmos. Sci., 58, 608627, https://doi.org/10.1175/1520-0469(2001)058<0608:AFOAPI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Toyoda, T., and Coauthors, 2021: Energy flow diagnosis of ENSO from an ocean reanalysis. J. Climate, 34, 40234042, https://doi.org/10.1175/JCLI-D-20-0704.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Warner, J. L., J. A. Screen, and A. A. Scaife, 2020: Links between Barents-Kara sea ice and the extratropical atmospheric circulation explained by internal variability and tropical forcing. Geophys. Res. Lett., 47, e2019GL085679, https://doi.org/10.1029/2019GL085679.

    • 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
  • Wirth, V., M. Riemer, E. K. M. Chang, and O. Martius, 2018: Rossby wave packets on the midlatitude waveguide—A review. Mon. Wea. Rev., 146, 19652001, https://doi.org/10.1175/MWR-D-16-0483.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yanai, M., and T. Maruyama, 1966: Stratospheric wave disturbances propagating over the equatorial Pacific. J. Meteor. Soc. Japan, 44, 291294, https://doi.org/10.2151/jmsj1965.44.5_291.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yanai, M., T. Maruyama, T. Nitta, and Y. Hayashi, 1968: Power spectra of large-scale disturbances over the tropical Pacific. J. Meteor. Soc. Japan, 46, 308323, https://doi.org/10.2151/jmsj1965.46.4_308.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yasunaga, K., S. Yokoi, K. Inoue, and B. E. Mapes, 2019: Space–time spectral analysis of the moist static energy budget equation. J. Climate, 32, 501529, https://doi.org/10.1175/jcli-d-18-0334.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 460 243 4
Full Text Views 148 100 13
PDF Downloads 167 109 7

The Energy Flux of Three-Dimensional Waves in the Atmosphere: Exact Expression for a Basic Model Diagnosis with No Equatorial Gap

Hidenori AikiaInstitute for Space-Earth Environmental Research, Nagoya University, Aichi, Japan

Search for other papers by Hidenori Aiki in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-0604-9900
,
Yoshiki FukutomiaInstitute for Space-Earth Environmental Research, Nagoya University, Aichi, Japan

Search for other papers by Yoshiki Fukutomi in
Current site
Google Scholar
PubMed
Close
,
Yuki KannobCentral Research Institute of Electric Power Industry, Chiba, Japan

Search for other papers by Yuki Kanno in
Current site
Google Scholar
PubMed
Close
,
Tomomichi OgatacJapan Agency for Marine-Earth Science and Technology, Kanagawa, Japan

Search for other papers by Tomomichi Ogata in
Current site
Google Scholar
PubMed
Close
,
Takahiro ToyodadMeteorological Research Institute, Ibaraki, Japan

Search for other papers by Takahiro Toyoda in
Current site
Google Scholar
PubMed
Close
, and
Hideyuki NakanodMeteorological Research Institute, Ibaraki, Japan

Search for other papers by Hideyuki Nakano in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A model diagnosis for the energy flux of off-equatorial Rossby waves in the atmosphere has previously been done using quasigeostrophic equations and is singular at the equator. The energy flux of equatorial waves has been separately investigated in previous studies using a space–time spectral analysis or a ray theory. A recent analytical study has derived an exact universal expression for the energy flux, which can indicate the direction of the group velocity for linear shallow water waves at all latitudes. This analytical result is extended in the present study to a height-dependent framework for three-dimensional waves in the atmosphere. This is achieved by investigating the classical analytical solution of both equatorial and off-equatorial waves in a Boussinesq fluid. For the horizontal component of the energy flux, the same expression has been obtained between equatorial waves and off-equatorial waves in the height-dependent framework, which is linked to a scalar quantity inverted from the isentropic perturbation of Ertel’s potential vorticity. The expression of the vertical component of the energy flux requires computation of another scalar quantity that may be obtained from the meridional integral of geopotential anomaly in a wavenumber–frequency space. The exact version of the universal expression is explored and illustrated for three-dimensional waves induced by an idealized Madden–Julian oscillation forcing in a basic model experiment. The zonal and vertical fluxes manifest the energy transfer of both equatorial Kelvin waves and off-equatorial Rossby waves with a smooth transition at around 10°S and around 10°N. The meridional flux of wave energy represents connection between off-equatorial divergence regions and equatorial convergence regions.

© 2021 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: Hidenori Aiki, aiki@nagoya-u.jp

Abstract

A model diagnosis for the energy flux of off-equatorial Rossby waves in the atmosphere has previously been done using quasigeostrophic equations and is singular at the equator. The energy flux of equatorial waves has been separately investigated in previous studies using a space–time spectral analysis or a ray theory. A recent analytical study has derived an exact universal expression for the energy flux, which can indicate the direction of the group velocity for linear shallow water waves at all latitudes. This analytical result is extended in the present study to a height-dependent framework for three-dimensional waves in the atmosphere. This is achieved by investigating the classical analytical solution of both equatorial and off-equatorial waves in a Boussinesq fluid. For the horizontal component of the energy flux, the same expression has been obtained between equatorial waves and off-equatorial waves in the height-dependent framework, which is linked to a scalar quantity inverted from the isentropic perturbation of Ertel’s potential vorticity. The expression of the vertical component of the energy flux requires computation of another scalar quantity that may be obtained from the meridional integral of geopotential anomaly in a wavenumber–frequency space. The exact version of the universal expression is explored and illustrated for three-dimensional waves induced by an idealized Madden–Julian oscillation forcing in a basic model experiment. The zonal and vertical fluxes manifest the energy transfer of both equatorial Kelvin waves and off-equatorial Rossby waves with a smooth transition at around 10°S and around 10°N. The meridional flux of wave energy represents connection between off-equatorial divergence regions and equatorial convergence regions.

© 2021 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: Hidenori Aiki, aiki@nagoya-u.jp

Supplementary Materials

    • Supplemental Materials (PDF 237.98 KB)
Save