Idealized quasi-biennial oscillations in an ensemble of dry GCM dynamical cores

Journal of the Atmospheric Sciences

Volumn 72, Issue 6, 2015, Pages 2201-2226

  Yao, Weiye ^a   Jablonowski, Christiane ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Atmospheric circulation; Dynamics; General circulation models; Gravity waves; Model evaluation performance; Quasibiennial oscillation

Indexed keywords

BUDGET CONTROL; DYNAMICS; GRAVITY WAVES; UPPER ATMOSPHERE;

ATMOSPHERIC CIRCULATION; BREWER-DOBSON CIRCULATION; COMMUNITY ATMOSPHERE MODEL; GENERAL CIRCULATION MODEL; MODEL EVALUATION/PERFORMANCE; QUASI-BIENNIAL OSCILLATION; STRATOSPHERIC CIRCULATIONS; TRANSFORMED EULERIAN MEANS;

OSCILLATORS (MECHANICAL);

ATMOSPHERIC DYNAMICS; ATMOSPHERIC GENERAL CIRCULATION MODEL; COMPUTER SIMULATION; ENSEMBLE FORECASTING; GRAVITY WAVE; QUASI-BIENNIAL OSCILLATION; STRATOSPHERE; WAVE FORCE;

EID: 84943392282     PISSN: 00224928     EISSN: 15200469     Source Type: Journal    
DOI: 10.1175/JAS-D-14-0236.1     Document Type: Article

References (95)

1. Alexander, M. J., and Coauthors, 2010:Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models. Quart. J. Roy. Meteor. Soc., 136, 1103-1124, doi:10.1002/qj.637.
2. Andrews, D. G., 1987:On the interpretation of the Eliassen-Palm flux divergence. Quart. J. Roy. Meteor. Soc., 113, 323-338, doi:10.1002/qj.49711347518.
3. Andrews, D. G., J. D. Mahlman, and R. W. Sinclair, 1983:Eliassen-Palm diagnostics ofwave-mean flow interaction in the GFDL"SKYHI" general circulation model. J. Atmos. Sci., 40, 2768-2784, doi:10.1175/1520-0469(1983)040<2768:ETWATM>2.0.CO;2.
4. Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987:Middle Atmosphere Dynamics. InternationalGeophysics Series, Vol. 40, Academic Press, 489 pp.
5. Arakawa, A., and V. R. Lamb, 1977:Computational design of the basic dynamical process of the UCLA general circulation model. Methods in Computational Physics, J. Chang, Ed., Academic Press, 173-265, doi:10.1016/B978-0-12-460817-7.50009-4.
6. Asselin, R., 1972:Frequency filter for time integrations. Mon. Wea. Rev., 100, 487-490, doi:10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2.
7. Baldwin, M. P., and Coauthors, 2001:The quasi-biennial oscillation. Rev. Geophys., 39, 179-229, doi:10.1029/1999RG000073.
8. Boville, B. A., 1986:Wave-mean flow interactions in a general circulation model of the troposphere and stratosphere. J. Atmos. Sci., 43, 1711-1725, doi:10.1175/1520-0469(1986)043<1711:WFIIAG>2.0.CO;2.
9. Boville, B. A., 1991:Sensitivity of simulated climate to model resolution. J. Climate, 4, 469-485, doi:10.1175/1520-0442(1991)004<0469:SOSCTM>2.0.CO;2.
10. Charney, J. G., and P. G. Drazin, 1961:Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83-109, doi:10.1029/JZ066i001p00083.
11. Charney, J. G., and M. E. Stern, 1962:On the stability of internal baroclinic jets in a rotating atmosphere. J. Atmos. Sci., 19, 159-172, doi:10.1175/1520-0469(1962)019<0159:OTSOIB>2.0.CO;2.
12. Choi, W., H. Lee, W. B. Grant, J. H. Park, J. R. Holton, K.-M. Lee, and B. Naujokat, 2002:On the secondary meridional circulation associated with the quasi-biennial oscillation. Tellus, 54B, 395-406, doi:10.1034/j.1600-0889.2002.201286.x.
13. Dennis, J., and Coauthors, 2012:CAM-SE:A scalable spectral element dynamical core for the Community Atmosphere Model. Int. J. High Perform. Comput. Appl., 26, 74-89, doi:10.1177/1094342011428142.
14. Dunkerton, T. J., 1981:On the inertial stability of the equatorial middle atmosphere. J. Atmos. Sci., 38, 2354-2364, doi:10.1175/1520-0469(1981)038<2354:OTISFT>2.0.CO;2.
15. Dunkerton, T. J., 1991:Nonlinear propagation of zonal winds in an atmosphere with Newtonian cooling and equatorial wavedriving. J. Atmos. Sci., 48, 236-263, doi:10.1175/1520-0469(1991)048<0236:NPOZWI>2.0.CO;2.
16. Dunkerton, T. J., 1997:The role of gravity waves in the quasi-biennial oscillation. J. Geophys. Res., 102, 26 053-26 076, doi:10.1029/96JD02999.
17. Dunkerton, T. J., 2000:Inferences about QBO dynamics from the atmospheric "tape recorder" effect. J. Atmos. Sci., 57, 230-246, doi:10.1175/1520-0469(2000)057<0230:IAQDFT>2.0.CO;2.
18. Ebdon, R. A., 1975:The quasi-biennial oscillation and its association with tropospheric circulation patterns. Meteor. Mag., 104, 282-297.
19. Ern, M., and P. Preusse, 2009:Quantification of the contribution of equatorial Kelvin waves to the QBO wind reversal in the stratosphere. Geophys. Res. Lett., 36, 21 801, doi:10.1029/2009GL040493.
20. Ern, M., and Coauthors, 2014:Interaction of gravity waves with the QBO:A satellite perspective. J. Geophys. Res. Atmos., 119, 2329-2355, doi:10.1002/2013JD020731.
21. Evan, S., M. J. Alexander, and J. Dudhia, 2012:WRF simulations of convectively generated gravity waves in opposite QBO phases. J. Geophys. Res., 117, D12117, doi:10.1029/2011JD017302.
22. Flury, T., D. L. Wu, and W.G. Read, 2013:Variability in the speed of the Brewer-Dobson circulation as observed by Aura/MLS. Atmos. Chem. Phys., 13, 4563-4575, doi:10.5194/acp-13-4563-2013.
23. Fritts, D. C., 1982:Shear excitation of atmospheric gravity waves. J. Atmos. Sci., 39, 1936-1952, doi:10.1175/1520-0469(1982)039<1936:SEOAGW>2.0.CO;2.
24. Fritts, D. C., 1984:Shear excitation of atmospheric gravity waves. Part II:Nonlinear radiation froma free shear layer. J. Atmos. Sci., 41, 524-537, doi:10.1175/1520-0469(1984)041<0524:SEOAGW>2.0.CO;2.
25. Fritts, D. C., and P. K. Rastogi, 1985:Convective and dynamical instabilities due to gravity wave motions in the lower and middle atmosphere:Theory and observations. Radio Sci., 20, 1247-1277, doi:10.1029/RS020i006p01247.
26. Fritts, D. C., and M. J. Alexander, 2003:Gravitywave dynamics and effects in the middle atmosphere. Rev. Geophys., 41, 1003, doi:10.1029/2001RG000106.
27. Garfinkel, C. I., and D. L. Hartmann, 2011:The influence of the quasi-biennial oscillation on the troposphere in winter in a hierarchy of models. Part I:Simplified dry GCMs. J. Atmos. Sci., 68, 1273-1289, doi:10.1175/2011JAS3665.1.
28. Giorgetta, M. A., E. Manzini, and E. Roeckner, 2002:Forcing of the quasi-biennial oscillation from a broad spectrum of atmospheric waves. Geophys. Res. Lett., 29, 1245, doi:10.1029/2002GL014756.
29. Giorgetta, M. A., E. Manzini, E. Roeckner, M. Esch, and L. Bengtsson, 2006:Climatology and forcing of the quasi-biennial oscillation in the MAECHAM5 model. J. Climate, 19, 3882-3901, doi:10.1175/JCLI3830.1.
30. Hamilton, K., 1984:Mean wind evolution through the quasibiennial cycle in the tropical lower stratosphere. J. Atmos. Sci., 41, 2113-2125, doi:10.1175/1520-0469(1984)041<2113:MWETTQ>2.0.CO;2.
31. Hamilton, K., R. J. Wilson, and R. S. Hemler, 2001:Spontaneous stratospheric QBO-like oscillations simulated by the GFDL SKYHI general circulation model. J. Atmos. Sci., 58, 3271-3292, doi:10.1175/1520-0469(2001)058<3271:SSQLOS>2.0.CO;2.
32. Hayashi, H., M. Shiotani, and J. C. Gille, 2002:Horizontal wind disturbances induced by inertial instability in the equatorial middle atmosphere as seen in rocketsonde observations. J. Geophys. Res., 107, 4228, doi:10.1029/2001JD000922.
33. Haynes, P. H., 1998:The latitudinal structure of the quasi-biennial oscillation. Quart. J. Roy. Meteor. Soc., 124, 2645-2670, doi:10.1002/qj.49712455206.
34. Held, I. M., and M. J. Suarez, 1994:A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 1825-1830, doi:10.1175/1520-0477(1994)075<1825:APFTIO>2.0.CO;2.
35. Hitchman, M. H., C. B. Leovy, J. C. Gille, and P. L. Bailey, 1987:Quasi-stationary zonally asymmetric circulations in the equatorial lower mesosphere. J. Atmos. Sci., 44, 2219-2236, doi:10.1175/1520-0469(1987)044<2219:QSZACI>2.0.CO;2.
36. Holton, J. R., 2004:An Introduction to Dynamic Meteorology. 4th ed. Academic Press, Inc., 535 pp.
37. Holton, J. R., and R. S. Lindzen, 1972:An updated theory for the quasibiennial cycle of the tropical stratosphere. J. Atmos. Sci., 29, 1076-1080, doi:10.1175/1520-0469(1972)029<1076:AUTFTQ>2.0.CO;2.
38. Holton, J. R., and H.-C. Tan, 1980:The influence of the equatorial quasibiennial oscillation on the global circulation at 50mb. J. Atmos. Sci., 37, 2200-2208, doi:10.1175/1520-0469(1980)037<2200:TIOTEQ>2.0.CO;2.
39. Horinouchi, T., and S. Yoden, 1998:Wave-mean flow interaction associated with a QBO-like oscillation simulated in a simplified GCM. J. Atmos. Sci., 55, 502-526, doi:10.1175/1520-0469(1998)055<0502:WMFIAW>2.0.CO;2.
40. Jablonowski, C., 1998:Test der dynamik zweier globaler wettervorhersagemodelle des Deutschen Wetterdienstes:Der Held-Suarez test. M.S. thesis, Dept. of Meteorology, University of Bonn, 140 pp.
41. Jablonowski, C., and D. L. Williamson, 2011:The pros and cons of diffusion, filters, and fixers in atmospheric general circulation models. Numerical Techniques for Global Atmospheric Models, P. H. Lauritzen et al., Eds., Lecture Notes in Science and Engineering, Vol. 80, Springer, 381-493.
42. Kawatani, Y., S. Watanabe, K. Sato, T. J. Dunkerton, S. Miyahara, and M. Takahashi, 2010:The roles of equatorial trapped waves and internal inertia-gravity waves in driving the quasi-biennial oscillation. Part I:Zonal mean wave forcing. J. Atmos. Sci., 67, 963-980, doi:10.1175/2009JAS3222.1.
43. 2 climate. J. Atmos. Sci., 68, 265-283, doi:10.1175/2010JAS3623.1.
44. 2 concentration on the quasibiennial oscillation. J. Atmos. Sci., 69, 1734-1749, doi:10.1175/JAS-D-11-0265.1.
45. 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, doi:10.1029/2008RG000266.
46. Kim, Y., S. Eckermann, and H. Chun, 2003:An overview of the past, present and future of gravity-wave drag parametrization for numerical climate and weather prediction models-Survey article. Atmos.-Ocean, 41, 65-98, doi:10.3137/ao.410105.
47. Kim, Y.-H., A. C. Bushell, D. R. Jackson, and H.-Y. Chun, 2013:Impacts of introducing a convective gravity-wave parameterization upon the QBO in the Met Office Unified Model. Geophys. Res. Lett., 40, 1873-1877, doi:10.1002/grl.50353.
48. Krismer, T. R., 2014:Wave-mean flow interactions driving the quasi-biennial oscillation in ECHAM6. Max-Planck Institut für Meteorologie Tech. Rep. 149, 79 pp. [Available online at http://www.mpimet.mpg.de/fileadmin/publikationen/Reports/WEB_BzE_149.pdf.]
49. Krismer, T. R., and M. A. Giorgetta, 2014:Wave forcing of the quasi-biennial oscillation in the Max Planck Institute Earth System Model. J. Atmos. Sci., 71, 1985-2006, doi:10.1175/JAS-D-13-0310.1.
50. Lin, S.-J., 2004:A"vertically Lagrangian" finite-volume dynamical core for global models. Mon. Wea. Rev., 132, 2293-2307, doi:10.1175/1520-0493(2004)132<2293:AVLFDC>2.0.CO;2.
51. Lin, S.-J., and R. B. Rood, 1996:Multidimensional flux-form semi-Lagrangian transport scheme. Mon. Wea. Rev., 124, 2046-2070, doi:10.1175/1520-0493(1996)124<2046:MFFSLT>2.0.CO;2.
52. Lindzen, R. S., 1981:Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707-9714, doi:10.1029/JC086iC10p09707.
53. Lindzen, R. S., and J. R. Holton, 1968:A theory of the quasi-biennial oscillation. J. Atmos. Sci., 25, 1095-1107, doi:10.1175/1520-0469(1968)025<1095:ATOTQB>2.0.CO;2.
54. Lott, F., and L. Guez, 2013:A stochastic parameterization of the gravity waves due to convection and its impact on the equatorial stratosphere. J. Geophys. Res. Atmos., 118, 8897-8909, doi:10.1002/jgrd.50705.
55. Magaña, V., and M. Yanai, 1995:Mixed Rossby-gravity waves triggered by lateral forcing. J. Atmos. Sci., 52, 1473-1486, doi:10.1175/1520-0469(1995)052<1473:MRWTBL>2.0.CO;2.
56. Marshall, A. G., and A. A. Scaife, 2009:Impact of theQBOon surface winter climate. J. Geophys. Res., 114, D18110, doi:10.1029/2009JD011737.
57. McCalpin, J. D., 1988:A quantitative analysis of the dissipation inherent in semi-Lagrangian advection. Mon. Wea. Rev., 116, 2330-2336, doi:10.1175/1520-0493(1988)116<2330:AQAOTD>2.0.CO;2.
58. Naoe, H., and K. Shibata, 2010:Equatorial quasi-biennial oscillation influence on northern winter extratropical circulation. J. Geophys. Res., 115, D19102, doi:10.1029/2009JD012952.
59. Naujokat, B., 1986:An update of the observed quasi-biennial oscillation of the stratospheric winds over the tropics. J. Atmos. Sci., 43, 1873-1880, doi:10.1175/1520-0469(1986)043<1873:AUOTOQ>2.0.CO;2.
60. Neale, R. B., and Coauthors, 2010:Description of the NCAR Community Atmosphere Model (CAM 5.0). NCAR Tech. Note NCAR/TN-4861STR, National Center for Atmospheric Research, Boulder, Colorado, 282 pp. [Available online at http://www.cesm.ucar.edu/models/cesm1.0/cam/docs/description/cam5_ desc.pdf.]
61. Nissen, K. M., P. Braesicke, and U. Langematz, 2000:QBO, SAO, and tropical waves in the Berlin TSM GCM:Sensitivity to radiation, vertical resolution, and convection. J. Geophys. Res., 105, 24 771-24 790, doi:10.1029/2000JD900270.
62. Orr, A., P. Bechthold, J. Scinocca, M. Ern, and M. Janiskova, 2010:Improved middle atmosphere climate and forecasts in the ECMWF model through a non-orographic gravity wave drag parameterization. J. Climate, 23, 5905-5926, doi:10.1175/2010JCLI3490.1.
63. Osprey, S. M., L. J. Gray, S. C. Hardiman, N. Butchart, and T. J. Hinton, 2013:Stratospheric variability in twentieth-century CMIP5 simulations of the Met Office Climate Model:High top versus low top. J. Climate, 26, 1595-1606, doi:10.1175/JCLI-D-12-00147.1.
64. O'Sullivan, D. J., and M. H. Hitchman, 1992:Inertial instability and Rossby wave breaking in a numerical model. J. Atmos. Sci., 49, 991-1002, doi:10.1175/1520-0469(1992)049<0991:IIARWB>2.0.CO;2.
65. Pascoe, C. L., L. J. Gray, S. A. Crooks, M. N. Juckes, and M. P. Baldwin, 2005:The quasi-biennial oscillation:Analysis using ERA-40 data. J. Geophys. Res., 110, D08105, doi:10.1029/2004JD004941.
66. Pawson, S., and M. Fiorino, 1998:A comparison of reanalyses in the tropical stratosphere. Part 2:The quasi-biennial oscillation. Climate Dyn., 14, 645-658, doi:10.1007/s003820050247.
67. Plougonven, R., H. Teitelbaum, and V. Zeitlin, 2003:Inertia gravity wave generation by the tropospheric midlatitude jet as given by the Fronts and Atlantic Storm-Track Experiment radio soundings. J. Geophys. Res., 108, 4686, doi:10.1029/2003JD003535.
68. Plumb, R. A., 1977:The interaction of two internal waves with the mean flow:Implications for the theory of the quasi-biennial oscillation. J. Atmos. Sci., 34, 1847-1858, doi:10.1175/1520-0469(1977)034<1847:TIOTIW>2.0.CO;2.
69. Plumb, R. A., and R. C. Bell, 1982:Amodel of the quasi-biennial oscillation on an equatorial beta-plane. Quart. J. Roy. Meteor. Soc., 108, 335-352, doi:10.1002/qj.49710845604.
70. Richter, J. H., A. Solomon, and J. Bacmeister, 2014:On the simulation of the quasi-biennial oscillation in the Community Atmosphere Model, version 5. J. Geophys. Res. Atmos., 119, 3045-3062, doi:10.1002/2013JD021122.
71. Rosenlof, K. H., 1995:Seasonal cycle of the residual mean meridional circulation in the stratosphere. J. Geophys. Res., 100, 5173-5191, doi:10.1029/94JD03122.
72. Scaife, A. A., N. Butchart, C. D. Warner, D. Stainforth, W. A. Norton, and J. Austin, 2000:Realistic quasi-biennial oscillations in a simulation of the global climate. Geophys. Res. Lett., 27, 3481-3484, doi:10.1029/2000GL011625.
73. Scaife, A. A., N. Butchart, C. D. Warner, and R. Swinbank, 2002:Impact of a spectral gravity wave parameterization on the stratosphere in the Met Office Unified Model. J. Atmos. Sci., 59, 1473-1489, doi:10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2.
74. Schirber, S., E. Manzini, and M. J. Alexander, 2014:A convection-based gravity wave parameterization in a general circulation model:Implementation and improvements on the QBO. J. Adv. Model. Earth Syst., 6, 264-279, doi:10.1002/2013MS000286.
75. Schoeberl, M. R., A. R. Douglass, R. S. Stolarski, S. Pawson, S. E. Strahan, and W. Read, 2008:Comparison of lower stratospheric tropical mean vertical velocities. J. Geophys. Res., 113, D24109, doi:10.1029/2008JD010221.
76. Scinocca, J. F., N. A. McFarlane, M. Lazare, J. Li, and D. Plummer, 2008:Technical note:The CCCma third generation AGCM and its extension into the middle atmosphere. Atmos. Chem. Phys., 8, 7055-7074, doi:10.5194/acp-8-7055-2008.
77. Seviour, W. J. M., N. Butchart, and S. C. Hardiman, 2012:The Brewer-Dobson circulation inferred from ERA-Interim. Quart. J. Roy. Meteor. Soc., 138, 878-888, doi:10.1002/qj.966.
78. Shuckburgh, E., W. Norton, A. Iwi, and P. Haynes, 2001:Influence of the quasi-biennial oscillation on isentropic transport and mixing in the tropics and subtropics. J. Geophys. Res., 106, 14 327, doi:10.1029/2000JD900664.
79. Simmons, A. J., and D. M. Burridge, 1981:An energy and angularmomentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758-766, doi:10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2.
80. Straub, K. H., and G. N. Kiladis, 2003:Extratropical forcing of convectively coupled Kelvin waves during austral winter. J. Atmos. Sci., 60, 526-543, doi:10.1175/1520-0469(2003)060<0526:EFOCCK>2.0.CO;2.
81. Takahashi, M., 1996:Simulation of the stratospheric quasi-biennial oscillation using a general circulation model. Geophys. Res. Lett., 23, 661-664, doi:10.1029/95GL03413.
82. Takahashi, M., 1999:Simulation of the quasi-biennial oscillation in a general circulation model. Geophys. Res. Lett., 26, 1307-1310, doi:10.1029/1999GL900188.
83. Taylor, M. A., and A. Fournier, 2010:A compatible and conservative spectral element method on unstructured grids. J. Comput. Phys., 229, 5879-5895, doi:10.1016/j.jcp.2010.04.008.
84. Tindall, J. C., J. Thuburn, and E. J. Highwood, 2006:Equatorial waves in the lower stratosphere. I:A novel detection method. Quart. J. Roy. Meteor. Soc., 132, 177-194, doi:10.1256/qj.04.152.
85. Wan, H., M. A. Giorgetta, and L. Bonaventura, 2008:Ensemble Held-Suarez test with a spectral transform model:Variability, sensitivity, and convergence. Mon. Wea. Rev., 136, 1075-1092, doi:10.1175/2007MWR2044.1.
86. 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, 374-399, doi:10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2.
87. Whitehead, J. P., C. Jablonowski, R. B. Rood, and P. H. Lauritzen, 2011:Astability analysis of divergence damping on a latitude-longitude grid. Mon. Wea. Rev., 139, 2976-2993, doi:10.1175/2011MWR3607.1.
88. Williamson, D. L., 2007:The evolution of dynamical cores for global atmospheric models. J. Meteor. Soc. Japan, 85B, 241-269, doi:10.2151/jmsj.85B.241.
89. Xue, X., H. Liu, and X. Dou, 2012:Parameterization of the inertial gravity waves and generation of the quasi-biennial oscillation. J. Geophys. Res., 117, D06103, doi:10.1029/2011JD016778.
90. Yang, G.-Y., B. Hoskins, and J. Slingo, 2007:Convectively coupled equatorial waves. Part III:Synthesis structures and their forcing and evolution. J. Atmos. Sci., 64, 3438-3451, doi:10.1175/JAS4019.1.
91. Yang, G.-Y., B. Hoskins, and J. Slingo, 2011:Equatorial waves in opposite QBO phases. J. Atmos. Sci., 68, 839-862, doi:10.1175/2010JAS3514.1.
92. Yang, G.-Y., B. Hoskins, and L. Gray, 2012:The Influence of the QBO on the propagation of equatorial waves into the stratosphere. J. Atmos. Sci., 69, 2959-2982, doi:10.1175/JAS-D-11-0342.1.
93. Yao, W., 2014:An assessment of the quasi-biennial oscillation (QBO) and sudden stratospheric warmings (SSWs) with idealized general circulation models. Ph. D. dissertation, University of Michigan, 178 pp.
94. Yao, W., and C. Jablonowski, 2013:Spontaneous QBO-like oscillations in an atmospheric model dynamical core. Geophys. Res. Lett., 40, 3772-3776, doi:10.1002/grl.50723.
95. Yoden, S., and J. R. Holton, 1988:A new look at equatorial quasi-biennial oscillation models. J. Atmos. Sci., 45, 2703-2717, doi:10.1175/1520-0469(1988)045<2703:ANLAEQ>2.0.CO;2.