Wave Coupling and Nonlinear Interactions in the Atmospheres of Earth and Mars
Main Article Content
Jeffrey M. Forbes
http://orcid.org/0000-0001-6937-0796
http://orcid.org/0000-0001-6937-0796
Abstract
This paper reviews recent progress on the topic of vertical wave coupling in the atmospheres of Earth and Mars with particular emphasis on (1) nonlinear interactions between planetary waves and solar thermal tides, and on (2) identifying the secondary waves produced by such interactions in satellite-based observations. The secondary waves produce temporal and longitudinal variability that would not otherwise exist in the absence of wave-wave interactions, and thus add to the complexity of atmospheric dynamics at both planets. At Earth, this has implications for re-entry predictions and ionospheric variability, which translates to loss of integrity in communications, navigation and tracking systems. At Mars, atmospheric density predictions in support of aerobraking operations are impacted.
Article Details
How to Cite
FORBES, Jeffrey M..
Wave Coupling and Nonlinear Interactions in the Atmospheres of Earth and Mars.
Quarterly Physics Review, [S.l.], v. 3, n. 3, oct. 2017.
ISSN 2572-701X.
Available at: <https://esmed.org/MRA/qpr/article/view/1439>. Date accessed: 21 dec. 2024.
Section
Review Articles
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References
1. Forbes, J.M., Wave Coupling in Terrestrial Planetary Atmospheres, in Atmospheres in the Solar System: Comparative Aeronomy, Geophys. Monog. 130, 171-190, American Geophysical Union, 2002.
2. Leonard, J.M., J.M. Forbes, and G.H. Born, Impact of tidal density variability on orbital and reentry predictions, Space Weather, 10, S12003, doi:10.1029/2012SW000842, 2012.
3. Moudden, Y., and J.M. Forbes, Density prediction in Mars’ aerobraking region, Space Weather, 13, 86–96, doi:10.1002/2014SW001121, 2015.
4. Forbes, J.M., Zhang, X., and S.L. Bruinsma, New perspectives on thermosphere tides - 2. Penetration to the upper thermosphere, Earth, Planets and Space, 66:122, doi:10.1186/1880-5981-66-122, 2014.
5. Oberheide, J., J.M. Forbes, K. Häusler, Q. Wu, and S.L. Bruinsma, Tropospheric tides from 80 to 400 km: Propagation, interannual variability, and solar cycle effects, J. Geophys. Res., 114, D00I05, doi:10.1029/2009JD012388, 2009.
6. Oberheide, J., J. M. Forbes, X. Zhang, and S. L. Bruinsma, Wave‐driven variability in the ionosphere- thermosphere‐ mesosphere system from TIMED observations: What contributes to the “wave 4”?, J. Geophys. Res., 116, A01306, doi:10.1029/2010JA015911, 2011.
7. Angelats i Coll, M., F. Forget, M. A. Lo´pez-Valverde, P. L. Read, and S. R. Lewis, Upper atmosphere of Mars up to 120 km: Mars Global Surveyor accelerometer data analysis with the LMD general circulation model, J. Geophys. Res., 109, E01011, doi:10.1029/2003JE002163, 2004.
8. Forbes, J.M., Bridger, A.F.C., Bougher, S.W., Hagan, M.E., Hollingsworth, J.L., Keating, G.M., and J. Murphy, Nonmigrating tides in the thermosphere of Mars, J. Geophys. Res., 107(E11), 5113, doi:10.1029/2001JE001582, p. 23-1 to 23-12, 2002.
9. Spizzichino, A., Etude des interactions entre les différentes composantes du vent dans la haute atmosphere, Ann. Geophys., 25, 773-783, 1969.
10. Teitelbaum, H., F. Vial, A. H. Manson, R. Giraldez, and M. Massebeuf, Nonlinear interaction between the diurnal and semidiurnal tides: Terdiurnal and diurnal secondary waves, J. Atmos. Terr. Phys., 51, 627-634, 1989.
11. Teitelbaum, H., and F. Vial: On tidal variability induced by nonlinear interaction with planetary waves. J. Geophys. Res. 96, 14,169 - 14,178, 1991.
12.Hagan, M.E., J.M. Forbes, and F. Vial, On modeling migrating solar tides, Geophys. Res. Lett., 22, 893-896, 1995.
13. Hagan, M.E., Comparative Effects of Migrating Solar Sources on Tides in the Mesosphere and Lower Thermosphere, J. Geophys. Res., 101, 21213-21222, 1996.
14. Hagan, M.E., Burrage, M.D., Forbes, J.M., Hackney, J., Randel, W.J., and X.Zhang, GSWM-98: Results for migrating solar tides, J. Geophys. Res.,104(A4), 6813-6827, 1999.
15. Hagan, M. E. and J. M. Forbes, Migrating and nonmigrating diurnal tides in the middle and upper atmosphere excited by tropospheric latent heat release, J. Geophys. Res., 107(D24), 4754, doi: 10.1029/2001JD001236, 2002.
16. Hagan, M.E., and J.M. Forbes, Migrating and nonmigrating semidiurnal tides in the middle and upper atmosphere excited by tropospheric latent heat release, J. Geophys. Res., 108(A2), 1062, doi:10.1029/2002JA009466, 2003.
17. Zhang, X., J.M. Forbes, and M.E. Hagan, Longitudinal variation of tides in the MLT region: 1. Tides driven by tropospheric net radiative heating, J. Geophys. Res., 115, A06316, doi:10.1029/2009JA014897, 2010.
18. Hines, C.O., Internal gravity waves at ionospheric heights, Can. J. Phys., 38, 1441-1481, 1960.
19. Forbes, J.M., Tidal and Planetary Waves (A Tutorial), in the Upper Mesosphere and Lower Thermosphere: A Review of Experiment and Theory, edited by R.M. Johnson and T.L. Killeen, Geophysical Monograph Series, vol. 87, American Geophysical Union, 1995, pp. 356.
20. Beard, A. G., N. J. Mitchell, P. J. S. Williams, and M. Kunitake, Non-linear interactions between tides and planetary waves resulting in periodic tidal variability, J. Atmos.Sol. Terr. Phys., 61, 363–376, 1999.
21. Cevolani, G., and S. Kingsley, Non-linear effects on tidal and planetary waves in the lower thermosphere: Preliminary results, Adv. Space Res., 12(10), 77–80, 1992.
22. Manson, A.H., C.E. Meek, J.B. Gregory, and D.K. Chakrabarty (1982), Fluctuations in tidal (24–12 h) characteristics and oscillations (5-25d) in the mesosphere and lower thermosphere at Saskatoon (52◦N, 107◦W), 1979–1981, Planet. Space Sci., 30, 1283.
23. Harris, T.J. and R.A. Vincent, The quasi-2-day wave observed in the equatorial middle atmosphere, J. Geophys. Res., 98, 10,481–10,490, 1993.
24. Thayaparan, T., W.K. Hocking, and J. MacDougal, Amplitude, phase and period variations of the quasi 2-day wave in the mesosphere and lower thermosphere over London Ontario (43◦N, 81◦W), during 1993 and 1994, J. Geophys. Res., 102, 9461–9478, 1997a.
25. Thayaparan, T., W.K. Hocking, J. MacDougal, A.H. Manson, and C.E. Meek, Simultaneous observations of the 2-day wave at London Ontario (43◦N, 81◦W) and Saskatoon (52◦N, 107◦W) near 91 km altitude during the two years 1993 and 1994, Ann. Geophys., 15, 1324–1339, 1997b.
26. Moudden, Y., and J.M. Forbes, A new interpretation of Mars aerobraking variability: Planetary wave‐tide interactions, J. Geophys. Res., 115, E09005, doi:10.1029/2009JE003542, 2010.
27. Moudden, Y., and J.M. Forbes, Simulated planetary wave‐tide interactions in the atmosphere of Mars, J. Geophys. Res., 116, E01004, doi:10.1029/2010JE003698, 2011a.
28. Moudden, Y., and J.M. Forbes, First detection of wave interactions in the middle atmosphere of Mars, Geophys. Res . Lett., 38, L04202, doi:10.1029/2010GL045592, 2011b.
29. Forbes, J.M., and Y. Moudden, Quasi-two-day wave-tide interactions as revealed in satellite observations, J. Geophys. Res., 117, D12110, doi:10.1029/2011JD017114, 2012.
30. Pedatella, N.M., and J.M. Forbes, The quasi 2 day wave and spatial-temporal variability of the OH emission and ionosphere, J. Geophys. Res., 117, A01320, doi:10.1029/2011JA017186, 2012.
31. Moudden, Y., and J M. Forbes, Quasi-two-day wave structure, interannual variability, and tidal interactions during the 2002–2011 decade, J. Geophys. Res. Atmos., 119, 2241–2260, doi:10.1002/2013JD020563, 2014.
32. Gasperini, F., J.M. Forbes, E. N. Doornbos, and S. L. Bruinsma, Wave coupling between the lower and middle thermosphere as viewed from TIMED and GOCE, J. Geophys. Res. Space Physics, 120, doi:10.1002/2015JA021300, 2015.
33. Forbes, J.M., and X. Zhang, The Quasi-6-Day Wave and its Interactions with Solar Tides, J. Geophys. Res. Space Physics, 122, doi:10.1002/2017JA023954, 2017.
34. Tolson, R.H., Keating, G.M., Cancro, G.J., Parker, J.S., Noll, S.N., and Wilkerson, B.L., Application of Accelerometer Data to Mars Global Surveyor Aerobraking Operations, J. Spacecr. Rockets, 36(3), 323–329, 1999.
35. Tolson, R.H., Dwyer, A.M., Hanna, J.L., Keating, G.M., George, B.E., Escalera, P.E., and Werner, M.R., Applications of Accelerometer Data to Mars Odyssey Aerobraking and Atmospheric Modeling, J. Spacecr. Rockets, 42(3), 435–443, 2005
36. Tolson, R., E. Bemis, S. Hough, K. Zaleski, G. Keating, J. Shidner, S. Brown, A. Brickler, M. Scher, and P. Thomas , Atmospheric modeling using accelerometer data during Mars Reconnaissance Orbiter aerobraking operations, J. Spacecr. Rockets, 45, 511–518, doi:10.2514/1.34301, 2008.
37. Zurek, R.W., R.A. Tolson, S.W. Bougher, R.A. Lugo, D.T. Baird, J.M. Bell, and B.M. Jakosky, Mars thermosphere as seen in MAVEN accelerometer data, J. Geophys. Res. Space Physics, 122, doi:10.1002/2016JA023641, 2017.
38. England, S. L., et al., Simultaneous observations of atmospheric tides from combined in situ and remote observations at Mars from the MAVEN spacecraft, J. Geophys. Res. Planets, 121, doi:10.1002/2016JE004997, 2016.
39. Liu, G., S. England, R. J. Lillis, P. R. Mahaffy, M. Elrod, M. Benna, and B. Jakosky, Longitudinal structures in Mars’ upper atmosphere as observed by MAVEN/NGIMS, J. Geophys. Res. Space Physics, 122, 1258–1268, doi:10.1002/
2016JA023455, 2017.
40. Moudden Y., J. M. Forbes, Topographic connections with density waves in Mars' aerobraking regime, J. Geophys. Res., 113, E11009, doi:10.1029/2008JE003107, 2008.
41. Palo, S.E., Roble, R.G., and M.E. Hagan, Middle atmosphere effects of the quasi-two-day wave determined from a General Circulation Model, Earth Planets Space, 51, 629-647, 1999.
42. Nguyen, V.A., S.E. Palo, R.S. Liebermann, J.M. Forbes, D.A. Ortland, and D.E. Siskind, Generation of secondary waves arising from nonlinear interaction between the quasi 2 day wave and the migrating diurnal tide, J. Geophys. Res. Atmos., 121, 7762–7780, doi:10.1002/2016JD024794, 2016.
43. Pedatella, N.M., H.-L. Liu, and M.E. Hagan, Day-to-day migrating and nonmigrating tidal variability due to the six-day planetary wave, J. Geophys. Res., 117, A06301, doi:10.1029/2012JA017581, 2012.
44. Hagan, M.E., A. Maute, and R.G. Roble (2009), Tropospheric tidal effects on the middle and upper atmosphere, J. Geophys. Res., 114, A01302, doi:10.1029/2008JA013637.
45. Yamashita, K., S. Miyahara, Y. Miyoshi, K. Kawano, and J. Ninomiya, Seasonal variation of non-migrating semidiurnal tide in the polar MLT region in a general circulation model, J. Atmos. Sol. Terr. Phys., 64, 1083–1094, 2002.
46. Angelats i Coll, M., and J.M. Forbes, Nonlinear interactions in the upper atmosphere: The s = 1 and s = 3 nonmigrating semidiurnal tides, J. Geophys. Res., 107(A8), 1157, doi:10.1029/2001JA900179, 2002.
47. Liu, H.-L., W. Wang, A. D. Richmond, and R. G. Roble, Ionospheric variability due to planetary waves and tides for solar minimum conditions, J. Geophys. Res., 115, A00G01, doi:10.1029/2009JA015188, 2010.
48. Chang, L.C., S.E. Palo, and H.‐L. Liu, Short‐term variation of the s = 1 nonmigrating semidiurnal tide during the 2002 stratospheric sudden warming, J. Geophys. Res., 114, D03109, doi:10.1029/2008JD010886, 2009.
49. Lieberman, R.S., J. Oberheide, M.E. Hagan, E.E. Remsberg and L.L. Gordley, Variability of diurnal tides and planetary waves during November 1978 - May 1979, J. Atmos. Solar-Terr. Phys., 66, 517-528, 2004.
50. Lieberman, R.S., D.M. Riggin, D.A. Ortland, J. Oberheide, and D.E. Siskind, Global observations and modeling of nonmigrating diurnal tides generated by tide-planetary wave interactions, J. Geophys. Res. Atmos., 120, 11,419–11,437, doi:10.1002/2015JD023739, 2015.
51. Pedatella, N.M., and J.M. Forbes, Evidence for stratosphere sudden warming-ionosphere coupling due to vertically propagating tides, Geophys. Res. Lett., 37, L11104, doi:10.1029/2010GL043560, 2010.
52. Pancheva, D., P. Mukhtarov, and B. Andonov, Nonmigrating tidal activity related to the sudden stratospheric warming in the Arctic winter of 2003/2004, Ann. Geophys., 27, 975–987, 2009.
2. Leonard, J.M., J.M. Forbes, and G.H. Born, Impact of tidal density variability on orbital and reentry predictions, Space Weather, 10, S12003, doi:10.1029/2012SW000842, 2012.
3. Moudden, Y., and J.M. Forbes, Density prediction in Mars’ aerobraking region, Space Weather, 13, 86–96, doi:10.1002/2014SW001121, 2015.
4. Forbes, J.M., Zhang, X., and S.L. Bruinsma, New perspectives on thermosphere tides - 2. Penetration to the upper thermosphere, Earth, Planets and Space, 66:122, doi:10.1186/1880-5981-66-122, 2014.
5. Oberheide, J., J.M. Forbes, K. Häusler, Q. Wu, and S.L. Bruinsma, Tropospheric tides from 80 to 400 km: Propagation, interannual variability, and solar cycle effects, J. Geophys. Res., 114, D00I05, doi:10.1029/2009JD012388, 2009.
6. Oberheide, J., J. M. Forbes, X. Zhang, and S. L. Bruinsma, Wave‐driven variability in the ionosphere- thermosphere‐ mesosphere system from TIMED observations: What contributes to the “wave 4”?, J. Geophys. Res., 116, A01306, doi:10.1029/2010JA015911, 2011.
7. Angelats i Coll, M., F. Forget, M. A. Lo´pez-Valverde, P. L. Read, and S. R. Lewis, Upper atmosphere of Mars up to 120 km: Mars Global Surveyor accelerometer data analysis with the LMD general circulation model, J. Geophys. Res., 109, E01011, doi:10.1029/2003JE002163, 2004.
8. Forbes, J.M., Bridger, A.F.C., Bougher, S.W., Hagan, M.E., Hollingsworth, J.L., Keating, G.M., and J. Murphy, Nonmigrating tides in the thermosphere of Mars, J. Geophys. Res., 107(E11), 5113, doi:10.1029/2001JE001582, p. 23-1 to 23-12, 2002.
9. Spizzichino, A., Etude des interactions entre les différentes composantes du vent dans la haute atmosphere, Ann. Geophys., 25, 773-783, 1969.
10. Teitelbaum, H., F. Vial, A. H. Manson, R. Giraldez, and M. Massebeuf, Nonlinear interaction between the diurnal and semidiurnal tides: Terdiurnal and diurnal secondary waves, J. Atmos. Terr. Phys., 51, 627-634, 1989.
11. Teitelbaum, H., and F. Vial: On tidal variability induced by nonlinear interaction with planetary waves. J. Geophys. Res. 96, 14,169 - 14,178, 1991.
12.Hagan, M.E., J.M. Forbes, and F. Vial, On modeling migrating solar tides, Geophys. Res. Lett., 22, 893-896, 1995.
13. Hagan, M.E., Comparative Effects of Migrating Solar Sources on Tides in the Mesosphere and Lower Thermosphere, J. Geophys. Res., 101, 21213-21222, 1996.
14. Hagan, M.E., Burrage, M.D., Forbes, J.M., Hackney, J., Randel, W.J., and X.Zhang, GSWM-98: Results for migrating solar tides, J. Geophys. Res.,104(A4), 6813-6827, 1999.
15. Hagan, M. E. and J. M. Forbes, Migrating and nonmigrating diurnal tides in the middle and upper atmosphere excited by tropospheric latent heat release, J. Geophys. Res., 107(D24), 4754, doi: 10.1029/2001JD001236, 2002.
16. Hagan, M.E., and J.M. Forbes, Migrating and nonmigrating semidiurnal tides in the middle and upper atmosphere excited by tropospheric latent heat release, J. Geophys. Res., 108(A2), 1062, doi:10.1029/2002JA009466, 2003.
17. Zhang, X., J.M. Forbes, and M.E. Hagan, Longitudinal variation of tides in the MLT region: 1. Tides driven by tropospheric net radiative heating, J. Geophys. Res., 115, A06316, doi:10.1029/2009JA014897, 2010.
18. Hines, C.O., Internal gravity waves at ionospheric heights, Can. J. Phys., 38, 1441-1481, 1960.
19. Forbes, J.M., Tidal and Planetary Waves (A Tutorial), in the Upper Mesosphere and Lower Thermosphere: A Review of Experiment and Theory, edited by R.M. Johnson and T.L. Killeen, Geophysical Monograph Series, vol. 87, American Geophysical Union, 1995, pp. 356.
20. Beard, A. G., N. J. Mitchell, P. J. S. Williams, and M. Kunitake, Non-linear interactions between tides and planetary waves resulting in periodic tidal variability, J. Atmos.Sol. Terr. Phys., 61, 363–376, 1999.
21. Cevolani, G., and S. Kingsley, Non-linear effects on tidal and planetary waves in the lower thermosphere: Preliminary results, Adv. Space Res., 12(10), 77–80, 1992.
22. Manson, A.H., C.E. Meek, J.B. Gregory, and D.K. Chakrabarty (1982), Fluctuations in tidal (24–12 h) characteristics and oscillations (5-25d) in the mesosphere and lower thermosphere at Saskatoon (52◦N, 107◦W), 1979–1981, Planet. Space Sci., 30, 1283.
23. Harris, T.J. and R.A. Vincent, The quasi-2-day wave observed in the equatorial middle atmosphere, J. Geophys. Res., 98, 10,481–10,490, 1993.
24. Thayaparan, T., W.K. Hocking, and J. MacDougal, Amplitude, phase and period variations of the quasi 2-day wave in the mesosphere and lower thermosphere over London Ontario (43◦N, 81◦W), during 1993 and 1994, J. Geophys. Res., 102, 9461–9478, 1997a.
25. Thayaparan, T., W.K. Hocking, J. MacDougal, A.H. Manson, and C.E. Meek, Simultaneous observations of the 2-day wave at London Ontario (43◦N, 81◦W) and Saskatoon (52◦N, 107◦W) near 91 km altitude during the two years 1993 and 1994, Ann. Geophys., 15, 1324–1339, 1997b.
26. Moudden, Y., and J.M. Forbes, A new interpretation of Mars aerobraking variability: Planetary wave‐tide interactions, J. Geophys. Res., 115, E09005, doi:10.1029/2009JE003542, 2010.
27. Moudden, Y., and J.M. Forbes, Simulated planetary wave‐tide interactions in the atmosphere of Mars, J. Geophys. Res., 116, E01004, doi:10.1029/2010JE003698, 2011a.
28. Moudden, Y., and J.M. Forbes, First detection of wave interactions in the middle atmosphere of Mars, Geophys. Res . Lett., 38, L04202, doi:10.1029/2010GL045592, 2011b.
29. Forbes, J.M., and Y. Moudden, Quasi-two-day wave-tide interactions as revealed in satellite observations, J. Geophys. Res., 117, D12110, doi:10.1029/2011JD017114, 2012.
30. Pedatella, N.M., and J.M. Forbes, The quasi 2 day wave and spatial-temporal variability of the OH emission and ionosphere, J. Geophys. Res., 117, A01320, doi:10.1029/2011JA017186, 2012.
31. Moudden, Y., and J M. Forbes, Quasi-two-day wave structure, interannual variability, and tidal interactions during the 2002–2011 decade, J. Geophys. Res. Atmos., 119, 2241–2260, doi:10.1002/2013JD020563, 2014.
32. Gasperini, F., J.M. Forbes, E. N. Doornbos, and S. L. Bruinsma, Wave coupling between the lower and middle thermosphere as viewed from TIMED and GOCE, J. Geophys. Res. Space Physics, 120, doi:10.1002/2015JA021300, 2015.
33. Forbes, J.M., and X. Zhang, The Quasi-6-Day Wave and its Interactions with Solar Tides, J. Geophys. Res. Space Physics, 122, doi:10.1002/2017JA023954, 2017.
34. Tolson, R.H., Keating, G.M., Cancro, G.J., Parker, J.S., Noll, S.N., and Wilkerson, B.L., Application of Accelerometer Data to Mars Global Surveyor Aerobraking Operations, J. Spacecr. Rockets, 36(3), 323–329, 1999.
35. Tolson, R.H., Dwyer, A.M., Hanna, J.L., Keating, G.M., George, B.E., Escalera, P.E., and Werner, M.R., Applications of Accelerometer Data to Mars Odyssey Aerobraking and Atmospheric Modeling, J. Spacecr. Rockets, 42(3), 435–443, 2005
36. Tolson, R., E. Bemis, S. Hough, K. Zaleski, G. Keating, J. Shidner, S. Brown, A. Brickler, M. Scher, and P. Thomas , Atmospheric modeling using accelerometer data during Mars Reconnaissance Orbiter aerobraking operations, J. Spacecr. Rockets, 45, 511–518, doi:10.2514/1.34301, 2008.
37. Zurek, R.W., R.A. Tolson, S.W. Bougher, R.A. Lugo, D.T. Baird, J.M. Bell, and B.M. Jakosky, Mars thermosphere as seen in MAVEN accelerometer data, J. Geophys. Res. Space Physics, 122, doi:10.1002/2016JA023641, 2017.
38. England, S. L., et al., Simultaneous observations of atmospheric tides from combined in situ and remote observations at Mars from the MAVEN spacecraft, J. Geophys. Res. Planets, 121, doi:10.1002/2016JE004997, 2016.
39. Liu, G., S. England, R. J. Lillis, P. R. Mahaffy, M. Elrod, M. Benna, and B. Jakosky, Longitudinal structures in Mars’ upper atmosphere as observed by MAVEN/NGIMS, J. Geophys. Res. Space Physics, 122, 1258–1268, doi:10.1002/
2016JA023455, 2017.
40. Moudden Y., J. M. Forbes, Topographic connections with density waves in Mars' aerobraking regime, J. Geophys. Res., 113, E11009, doi:10.1029/2008JE003107, 2008.
41. Palo, S.E., Roble, R.G., and M.E. Hagan, Middle atmosphere effects of the quasi-two-day wave determined from a General Circulation Model, Earth Planets Space, 51, 629-647, 1999.
42. Nguyen, V.A., S.E. Palo, R.S. Liebermann, J.M. Forbes, D.A. Ortland, and D.E. Siskind, Generation of secondary waves arising from nonlinear interaction between the quasi 2 day wave and the migrating diurnal tide, J. Geophys. Res. Atmos., 121, 7762–7780, doi:10.1002/2016JD024794, 2016.
43. Pedatella, N.M., H.-L. Liu, and M.E. Hagan, Day-to-day migrating and nonmigrating tidal variability due to the six-day planetary wave, J. Geophys. Res., 117, A06301, doi:10.1029/2012JA017581, 2012.
44. Hagan, M.E., A. Maute, and R.G. Roble (2009), Tropospheric tidal effects on the middle and upper atmosphere, J. Geophys. Res., 114, A01302, doi:10.1029/2008JA013637.
45. Yamashita, K., S. Miyahara, Y. Miyoshi, K. Kawano, and J. Ninomiya, Seasonal variation of non-migrating semidiurnal tide in the polar MLT region in a general circulation model, J. Atmos. Sol. Terr. Phys., 64, 1083–1094, 2002.
46. Angelats i Coll, M., and J.M. Forbes, Nonlinear interactions in the upper atmosphere: The s = 1 and s = 3 nonmigrating semidiurnal tides, J. Geophys. Res., 107(A8), 1157, doi:10.1029/2001JA900179, 2002.
47. Liu, H.-L., W. Wang, A. D. Richmond, and R. G. Roble, Ionospheric variability due to planetary waves and tides for solar minimum conditions, J. Geophys. Res., 115, A00G01, doi:10.1029/2009JA015188, 2010.
48. Chang, L.C., S.E. Palo, and H.‐L. Liu, Short‐term variation of the s = 1 nonmigrating semidiurnal tide during the 2002 stratospheric sudden warming, J. Geophys. Res., 114, D03109, doi:10.1029/2008JD010886, 2009.
49. Lieberman, R.S., J. Oberheide, M.E. Hagan, E.E. Remsberg and L.L. Gordley, Variability of diurnal tides and planetary waves during November 1978 - May 1979, J. Atmos. Solar-Terr. Phys., 66, 517-528, 2004.
50. Lieberman, R.S., D.M. Riggin, D.A. Ortland, J. Oberheide, and D.E. Siskind, Global observations and modeling of nonmigrating diurnal tides generated by tide-planetary wave interactions, J. Geophys. Res. Atmos., 120, 11,419–11,437, doi:10.1002/2015JD023739, 2015.
51. Pedatella, N.M., and J.M. Forbes, Evidence for stratosphere sudden warming-ionosphere coupling due to vertically propagating tides, Geophys. Res. Lett., 37, L11104, doi:10.1029/2010GL043560, 2010.
52. Pancheva, D., P. Mukhtarov, and B. Andonov, Nonmigrating tidal activity related to the sudden stratospheric warming in the Arctic winter of 2003/2004, Ann. Geophys., 27, 975–987, 2009.