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Linear Interpretation of Semi-Annual Oscillations of Diurnal Tides in Mesosphere and Lower Thermosphere

This presentation reveals the linear interpretation of semi-annual oscillations of migrating and non-migrating diurnal tides in the mesosphere and lower thermosphere based on different general circulation models.

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Linear Interpretation of Semi-Annual Oscillations of Diurnal Tides in Mesosphere and Lower Thermosphere

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  1. The linear interpretation of semi-annual oscillations of migrating and nonmigrating diurnal tides in the mesosphere and lower thermosphere, revealed from different general circulation models N. Griegera, U. Achatza, H. Schmidtb and C. McLandressc Leibniz-Institute of Atmospheric Physics, Kühlungsborn, Germany Max-Planck Institute of Meteorology, Hamburg, Germany Dept. of Physics, University of Toronto, Canada presented at: EGU General Assembly 2007 Wien, Austria session AS1.12/ST15 19 April 2007 EGS_0407.ppt

  2. Content • Introduction • Tides in GCMs, and their annual variations • Linear interpretation of tides - migrating tide - nonmigrating tides • Tides and their governing equations • Conclusion EGS_0407.ppt

  3. Motivation Are there semi-annual oscillations for nonmigrating tides, too, and is there an important term in the governing tidal equations, which is mainly responsible for the semi-annual period? EGS_0407.ppt

  4. General - tides s ….. zonal wave, s > 0 (< 0) westwards- (eastwards-) traveling component s = 0, standing component n ….. tidal period as part of the solar day, n = 1: diurnal, n = 2: semidiurnal A ….. amplitude F ….. phase C,S ….. cosine-, sine-coefficient EGS_0407.ppt

  5. General – GCMs and linear model CMAM (2 year mean) Beagley, S.R., McLandress, C., Fomichev, V.I., Ward, W.E.,2000: The extended Canadian middle atmosphere model. Geophys.Res.Lett. 27. 2529-2532 WACCM-1 (1 year) Sassi, F., Garcia, R.R., Boville, B.A., Liu, H., 2002: On temperature inversions and the mesospheric surf zone. J.Geophys. Res., 107,D19, 4380, doi:10.1029/2001JD001525. HAMMONIA (20 year mean) Schmidt, H., G. P. Brasseur, M. Charron, E. Manzini, M. A. Giorgetta, V. Formichev, D. Kinnison, D. Marsh and S. Walters, 2006:The HAMMONIA Chemistry Climate Model: Sensitivity of the mesopause region to the 11-year solar cycle and CO2- doubling. Journal of Climate, Spec.Issue LIN-KMCM Grieger, N., Schmitz, G., Achatz, U., 2004: The dependence of the nonmigrating diurnal tide in the mesosphere and lower thermosphere on stationary planetary waves, JASTP, 66 733-754 EGS_0407.ppt

  6. DT annual oscillation: GCMs/observations for s=2,1,0 WACCM HAMM OBSER CMAM s = 2 s = 1 s = 0 Forbes 2003 Huang 2006 Forbes 2003 LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC Forbes 2003: redrawn from: Forbes et al. 2003 J.Geophys.Res. 107 4322 Huang 2006: redrawn from: Huang et al. 2006 J.Geophys.Res.A 111 A10S04 EGS_0407.ppt

  7. DT annual oscillation: GCMs/observations for s=-1,-2,-3 WACCM HAMM OBSER CMAM s = - 3 s = - 1 s = - 2 Forbes 2003 LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC Forbes 2003: redrawn from: Forbes et al. 2003 J.Geophys.Res. 107 4322 EGS_0407.ppt

  8. DT semi-annual oscillation: GCMs/linear for s=1 W H C L s = 1 ALTITUDE [km] 60 ….. 110 LATITUDE [°N] -90 ….. 60 EGS_0407.ppt

  9. DT annual oscillation: HAM for s=2,1,0,-1 s = 1 s = 2 s = 0 s = -1 ALTITUDE [km] 60 ….. 110 LATITUDE [°N] -90 ….. 60 EGS_0407.ppt

  10. Result I The semi-annual oscillations for diurnal tides have been detected for each GCM run and reach maxima of about: 12 [m/s] for s=1, and 6 [m/s] for s=2. EGS_0407.ppt

  11. General - LIN-KMCM linearization of a mechanistic circulation model: KMCM 1) background : [u,v,T(j,z)]+ (u,v,T(l,j,z))* thermal forcings: dT/dt derived from GCMs 1)Becker, E., Schmitz, G., 2002: Energy deposition and turbulent dissipation owing to gravity waves in the mesosphere. JAS,59, 54-68 0a EGS_0407.ppt

  12. DT C(v) [m/s] GCM/linear HAMM HAMM s = -3 s = 1 LIN-KMCM LIN-KMCM ALTITUDE [km] 60 ….. 110 LATITUDE [°N] -60 ….. 60 LATITUDE [°N] -60 ….. 60 EGS_0407.ppt

  13. DT v [m/s] s = 1, at 92.5 km GCMs/linear WACCM HAMM CMAM GCM LIN-KMCM LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

  14. General – tides in the linear model semi-annual oscillation for equation (1), only! • X .... tidal component • A .... linearer operator • F .... forcing < > .... time average (year) • d .... time deviation (month) • [ ] .... zonal mean EGS_0407.ppt

  15. DT annual oscillation: HAM for s=2,1,0 forcing/wind/waves s = 2 s = 1 s = 0 WAVES [%] BACKGR. WAVES TOTAL FORCING LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

  16. DT annual oscill.: HAM for s=-1,-2,-3 forcing/wind/waves WAVES [%] BACKGR. WAVES TOTAL s = - 1 s = - 2 s = - 3 FORCING LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

  17. amplitude ratio m(1,2): linear, migrating DT m(2) m(1) EGS_0407.ppt

  18. General – tides in the linear model semi-annual oscillation for equation (1), only! • X .... tidal component • A .... linearer operator • F .... forcing < > .... time average (year) • d .... time deviation (month) • [ ] .... zonal mean EGS_0407.ppt

  19. amplitude ratio m(2): linear, nonmigrating DT m(2) EGS_0407.ppt

  20. Result II The annual variations of diurnal tides can be described by a linear model. These variations are mainly controlled by background field variations for s=1,2,-2,-3 and forcing variations for s=0,-1. EGS_0407.ppt

  21. DT v [m/s], semi-annual osc. at 92.5 km GCMs WACCM HAMM CMAM LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

  22. General – tidal equations Rf vorticity Xf curvature (Andrews et al., 1987, p.126) EGS_0407.ppt

  23. abs. vorticity / curvature term over latitude, 56 km WACCM HAMM CMAM curvature vorticity LATITUDE [°N] -12 ….. 12 TIME [MONTH] JAN … DEC EGS_0407.ppt

  24. abs. vorticity / curvature term over height, 4 N WACCM HAMM CMAM curvature vorticity ALTITUDE [km] 30 ….. 70 TIME [MONTH] JAN … DEC EGS_0407.ppt

  25. DT v [m/s] at 92.5 km LIN-KMCM(HAMM) u(z) u(0-70) u(0-50) u(z)12*cos LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

  26. abs. vorticity / curvature term over latitude, 56 km u(z) u(0-70) u(0-50) u(z)12*cos curvature vorticity LATITUDE [°N] -12 ….. 12 TIME [MONTH] JAN … DEC EGS_0407.ppt

  27. abs. vorticity / curvature term over height, 12 N u(z) u(0-70) u(0-50) u(z)12*cos curvature vorticity ALTITUDE [km] 30 ….. 90 TIME [MONTH] JAN … DEC EGS_0407.ppt

  28. Result III The semi-annual oscillation of the migrating tidal component depends mainly on the curvature term in the governing equation. The wind between 0 and 70 km height is mostly responsible for the tidal propagation. EGS_0407.ppt

  29. Conclusion Annual variations are caused by wind variations for s=2,1,-2,-3, and forcing variations for s=0,-1. The semi-annual oscillation of migrating tides is controlled by the curvature term of the governing equations. The wind between 0 and 70 km height is mostly responsible for tidal propagation. EGS_0407.ppt

  30. end … thank you for your attention! available: www.iap-kborn.de/forschung/index_d.htm EGS_0407.ppt EGS_0407.ppt

  31. General – tides in the linear model, averaging procedure EGS_0407.ppt

  32. DT v [m/s] at 92.5 km linear u(z) u(0-70) u(0-50) WACCM CMAM LATITUDE [°N] -45 ….. 45 TIME [MONTH] JAN … DEC EGS_0407.ppt

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