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The role of the mean flow and gravity wave forcing in the observed seasonal variability of the migrating diurnal tide. David A. Ortland NorthWest Research Associates Charles McLandress University of Toronto

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1.Description of the dynamics of the gravity wave/tide interaction 2.Tidal amplitude modification by GWs? 3.Seasonal variation of tidal amplitude. Main questions: Can variations in gravity wave drag, modulated by mean- flow filtering, account for observed variations in tidal structure? How much does a model of the gravity wave/tide interaction depend on the GW parameterization? Outline:

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Gravity wave parameterizations Source spectrum: pseudo-momentum flux density at source level: F(c,z=0) Saturation criterion: each wave in the spectrum propagates conservatively until saturated. Spectrum modified at each level: either saturated waves are obliterated ( F(c,z)=0) or propagate at the saturated bound ( F(c,z)=F sat (c,z)) (e.g. Lindzen parameterization)

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Saturation criteria Mean flow forcing For all parameterizations where saturated waves are assumed to be obliterated, the forcing may be expressed as: This shows how forcing strength is related to density, slope of the cutoff curve and the shape of the source spectrum.

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Mean flow forcing For all parameterizations where saturated waves are assumed to be obliterated, the forcing may be expressed as: This shows how forcing strength is related to density, slope of the cutoff curve and the shape of the source spectrum.

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Source spectrum Saturation spectra for different altitudes. The cutoff phase speed at each altitude is given by the intersection of this curve with the source spectrum. Cutoff phase speed profile (red). Two curves for westward and eastward propagating waves.

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Saturation for different spectra The shape of the forcing profile will depend on the altitude dependence of the cutoff phase speed, which, in turn, depends on the shape of the source spectrum. Three examples are shown here and the next figure. Saturation spectra for different altitudes (blue)

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Source spectrum determines shape of forcing profile Algebraic source profile (green), as used in the Hines param, produces a force profile that rapidly increases with altitude. Is this realistic?

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Shape of source spectrum important for determining altitude where significant tidal interaction occurs Notice that power law (red) causes forcing to occur more in phase with the tide. This explains why the Hines parameterization amplifies tidal amplitude. Sample tide wind profile (green)

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Comparison of Hines and AD parameterization using the same source spectrum Doppler spreading causes waves to saturate sooner than they would individually. At each level, saturated part of the spectrum has smaller flux than for AD (AD forcing shown with intermittency=.5)

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For gravity wave drag, has real and imaginary part with Im( )<0. A complex implies that the relative phase difference between the GW force and the tide is not 180° Equivalent Rayleigh Friction

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Effect of real part of damping coefficient on tide structure Only factor that has a strong influence on tidal amplitude Small effect on horizontal amplitude structure Introduces latitudinal phase variation

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Efect of imaginary part of damping coefficient (black=classical mode structure, red=damped structure) Im( )>0 (Diffusion): Longer wavelength Im( )<0 (GW drag) Shorter wavelength In this example: Im( ) = -1 Vertical wavelength= 20km

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Phase of forcing relative to the tide depends on source spectrum. The phase shift controls relative magnitude of real and imaginary part of the equivalent Rayleigh friction coefficient

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Phase lag depends on saturation criterion

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Experiments with a time-dependent linearized primitive equation model Model ingredients: Background winds taken from UARS Reference Atmosphere Project (URAP) or Canadian Middle Atmosphere Model (CMAM); (1,1) Hough mode forcing in troposphere derived from CMAM annual mean; Eddy and molecular diffusion in MLT; Alexander-Dunkerton or Hines gravity wave parameterization; Only forcing from momentum deposition due to GW breaking (not parameterized eddy diffusion)

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GW forcing of the mean flow winds: URAP (UARS reference atmosphere) for January radiative equilibrium temperatures from MIDRAD GW force required to maintain climatology GW force computed from AD parameterization

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Background zonal mean zonal winds used in the tidal model

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Meridional wind amplitude URAP background, Alexander-Dunkerton GW parameterization

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Gravity wave effects on tidal structure: narrower horizontal structure shorter vertical wavelength

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Comparison of direct (EP flux divergence) and diffusive gravity wave forcing Time-mean component of GW force Diurnal component of GW force Note similar lat-alt structure of diffusive and direct forcing Relatively weak below 90 km and therefore not likely to have much effect on tidal amplitude

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Adding GW parameterization enhances seasonal variability with URAP winds

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Adding GW parameterization enhances seasonal variability with URAP winds Note: Alexander-Dunkerton GW parameterization reduces amplitude

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Including GW forcing does not enhance seasonal variability with CMAM winds

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Seasonal variation of GW forcing Solstice winds cause a relatively larger in- phase component of forcing, leading to enhanc0ed damping of the tide amplitude. The force is also confined to the winter hemisphere.

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Seasonal variation of GW forcing Seasonal variability depends more on the background winds used and not the GQ parameterization

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Mean wind modulation of GW forcing (Alexander-Dunkerton parameterization) Latitude This GW force enhancement, responsible for the seasonal amplitude variability using URAP background winds is absent using CMAM winds

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Mean flow modulation of GW breaking Why do URAP and CMAM winds cause different behavior in GW forcing? Answer appears to be that CMAM does not produce an equatorward tilt of the winter jet. Low phase speed waves near peak of spectrum break higher, causing larger acceleration, in a stronger winter jet Jet is weak at mid-latitudes

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Mean flow modulation of GW breaking Peak of spectrum shielded by westerly tropospheric jet

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Conclusions Seasonal wind variations modulate the gravity wave forcing and eddy diffusion –Winter hemisphere jet causes waves near the peak of the GW spectrum to break in the mesosphere. Very strong GW drag and eddy diffusion can occur in mid-latitudes at the top of a strong jet. –GW drag has stronger effect on the tide than eddy diffusion –Effect of gravity wave drag likely depends somewhat on GW parameterization, but mostly on the shape of the source spectrum –When the GW effective friction has a large negative imaginary component, GW interaction will reduce the vertical wavelength of the tide and thereby enhance the effects of any ambient diffusion –Seasonal variation of the GW/tide interaction appears to be very sensitive to the structure of the mean flow, and may require a westerly jet tilted equatorward for this to be an effective mechanism of seasonal variability.

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