On the interaction of gravity waves and thermal tides in the middle atmosphere Fabian Senf, Erich Becker Leibniz Institute for Atmospheric Physics, Kühlungsborn Ulrich Achatz Goethe University, Frankfurt (Main)

Introduction - Gravity waves and thermal tides in the middle atmosphere - On gravity – tidal wave interaction studies Model - Ray tracing method - Experiments of different complexity Results - modulation of gravity-wave frequencies and phase velocities - refraction of horizontal wave vector - amplitude of gravity-wave force - equivalent friction coefficients Overview: Fabian

zonally averaged HAMMONIA zonal wind and temperature for north winter dynamics of middle atmosphere Introduction: latitude altitude [km] latitude

zonally averaged HAMMONIA zonal wind and temperature for north winter dynamics of middle atmosphere Introduction: latitude altitude [km] latitudeBreite tropospheric sources gravity wave force meridional circulation adiabatic cooling adiabatic warming Fabian drives

Meso-scale gravity waves are essential for large-scale dynamics, but hardly resolved in complex circulation models! parameterizations with crude assumptions high-resolution, mechanistic modelling Fabian dynamics of middle atmosphere Introduction:

thermal tides planetary-scale buoyancy oscillations induced by solar heating sun heating tides north pole earth Introduction: Fabian

zonal wind amplitude meridional wind amplitude HAMMONIA diurnal tides as background (from Hauke Schmidt) Introduction: latitude altitude [km] total altitude [km] migratingnon-migrating

Introduction: Thermal tides induce extreme changes in the conditions for gravity wave propagation in the middle atmosphere. Fabian thermal tides interaction between gravity waves and thermal tides is not deeply understood and also not sufficiently investigated because most studies focus on the interaction between thermal tides and gravity-wave parameterizations!

Fabian Past Studies of the interaction between thermal tides and gravity-wave parameterizations: highly idealized models: Fritts & Vincent (1987), Lu & Fritts (1993) linear modeling: Forbes et. al. (1991); Miyahara & Forbes (1991,1994), McLandress (1997), Meyer (1997), Ortland & Alexander (2006) non-linear GCM results: Mayr et. al. (1998,2001), Akmaev (2001), McLandress (2002) Main outcome: shrinking of vertical phase structure but different effects on tidal amplitude (different source and turbulence parameterization seem to be responsible) But, with crude assumptions: gravity wave parameterizations in vertical columns assumed: stationarity of background flow and instantaneous adjustment Introduction:

Fabian Our strategy: relaxing of the assumptions made for gravity wave propagation successively including temporal and horizontal dependence of the background flow BUT, keeping other aspects as simple as possible!  highly simplified lower boundary conditions (or GW sources)  saturation at convective instability threshold to estimate turbulent diffusion coefficients Introduction: ray tracing of gravity waves

Ray tracing in thermal tidesModel: Fabian wave parcel group velocity c g ray tracing and wave parcel concept t = 1 h t = 6 ht = 10 h zonal wind profile altitude longitude c wave parcel: small volume of GW field ray tracing: following the path of wave parcel

Ray tracing in thermal tidesModel: Fabian ray tracing and wave parcel concept zonal wind profile c wave parcel: small volume of GW field ray tracing: following the path of wave parcel

Ray tracing equations and symmetries of WKB theory: transience  frequency modulation horizontal gradients  refraction vertical gradients Model: Fabian

Conventional GW Parametrization: transience  frequency modulation horizontal gradients  refraction vertical gradients Model: Fabian

RAPAGI – RAy PArametrization of Gravity wave Impacts: global ray tracing model for time-dependent flows conservation of wave action and diffusion according to simple saturation theory (Lindzen, 1981) Model: Fabian

gravity wave spectrum in use: 14 gravity wave fields in different directions: - horizontal wave length with about 400 km to 600 km - periods in the range of hours - momentum fluxes between 0.3 to 0.5 mPa c = 33 m/s c = 10 m/s Model: extremely simple, but reproduces average gravity wave forces

Ray tracing experiments: Model: Fabian full complex ray tracing simulation noREF simple ray tracing – simulation TS conventional vertical column transience included no transience, instantaneously adjusting horizontal refraction and propagation included no horizontal refraction and propagation increasing complexity

Vertical column thinking 15°S latitude (TS) expected height of strongest gravity wave forcing moves downward with tidal phase transient critical layers? Fabian Results: phase velocity altitude [km] velocity [m/s]

Fabian Results: Vertical column thinking is NOT appropriate for tides due to frequency modulation! less critical layer filtering! 15°S latitude (TS) phase velocity altitude [km] velocity [m/s] 15°S latitude (TS) altitude [km] velocity [m/s]

Understanding frequency modulation: simplified equations: Results: Fabian local positive tendency of wind leads to increase of phase speed local negative tendency of wind leads to decrease of phase speed t = 1 h t = 4 h

Fabian horizontal phase velocity follows the shape of the background (BG) wind (Contours: BG Wind) longitudinal variations of phase velocity longitude altitude [km] [m/s] Results:

Fabian meridional gradients of the zonal wind induce refraction of gravity waves into the jet maximum in which their travel time is minimized longitude latitude refraction of horizontal wave vectors Results:

latitude altitude [km] latitude average gravity wave flow arrows:average group velocity, colors:initial meridional position, contours:wind in wave direction Fabian Results: O W N S O W N S

latitude altitude [km] latitude Fabian O W N S O W N S average gravity wave flow arrows:average group velocity, colors:initial meridional position, contours:wind in wave direction Results:

meridional displacement displacements of 50° in latitude occur often! displacements larger than 100° in latitude are possible! Fabian Results:

Fabian amplitude of zonal diurnal gravity wave force latitude altitude [km] [m/s per day] conventional GW parameterizations extremely overestimate zonal GW drag amplitude simulations without horizontal refraction slightly overestimate zonal GW drag amplitude

Fabian tidal wind force e.g.180° phase shift projection on tidal wind force on tidal amplitude Results: phase relation between force and tides tidal wind e.g. 90° phase shift projection on tidal acceleration advancing of tide force on phase structure force

projections of the diurnal gravity wave force on - tidal wind  real part of equivalent friction coefficient if positive: local decrease of tidal amplitude - tidal acceleration  imaginary part of equivalent friction coefficent if negative: local vertical shrinking tidal phase structure Results: Fabian

Fabian conventional parameterizations extremely over-estimate the decrease of tidal amplitude latitude altitude [km] real parts of equivalent friction coefficients [per 10 6 s] Results:

conventional parameterizations mainly over-estimate the decrease of tidal vertical wave length Results: Fabian latitude altitude [km] imaginary parts of equivalent friction coefficients [per 10 6 s]

Summary: WKB theory and ray tracing has been used describing propagation and dissipation of a spectrum of GWs monthly averaged data + diurnal tides from HAMMONIA as background for GW propagation comparison with conventional GW parameterizations show:  overestimation of GW drag frequency modulation reduces diurnal gravity wave forces horizontal refraction leads to formation of wave guides and large meridional displacements GW drag induces decrease of tidal vertical wave length and amplitude Fabian Thank you for your attention!

Fabian THE END!

Breite Höhe [km] Fabian Ergebnisse: Refraktion des horizontalen Wellenvektors Westwind-Jet Ostwind-Jet NP / Winter SP / Sommer EQ u0u0 Schnitt in Stratopause

Fabian Ergebnisse: Refraktion des horizontalen Wellenvektors Westwind-Jet Ostwind-Jet NP / Winter SP / Sommer EQ u0u0