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Jeffrey M. Forbes
and
Henry B. Garrett

Abstract

The solar diurnal tide in the thermosphere excited by in situ absorption of EUV and UV solar radiation for equinox conditions is determined by numerically integrating the linearized tidal equations for a spherical, rotating, viscous atmosphere. The model takes into account eddy viscosity, Newtonian cooling, molecular viscosity and conductivity, Coriolis acceleration and anisotropic ion drag. Owing to the inseparability of the mathematical system in height and the latitude, vertical structures of all tidal fields are found to vary with latitude; or equivalently, the horizontal structures vary with height, contrary to classical inviscid tidal theory. Tidal structures also vary with the level of solar activity, since the altitudes where diffusion and hydromagnetic ion drag dominate the momentum balance depend upon the background temperature and ionospheric structures. Increased ion drag (i.e., associated with more active solar conditions) inhibits acceleration of the neutral winds via transfer of momentum to the (denser) ionospheric plasma; however, the concomitant suppression of subsidence heating, which is nearly in antiphase with the EUV heat source, gives rise to increased temperature amplitudes. A factor of 2 increase in the integrated solar heat input from minimum to maximum sunspot conditions thus leads to a factor of 3 increase in the diurnal thermospheric temperature oscillation, but relatively little difference in the velocity fields. Solar heat inputs of 0.4 erg cm−2 s−1 at sunspot minimum and 0.8 erg cm−2 s−1 at sunspot maximum are found to yield thermospheric tides which are consistent with incoherent scatter measurements and satellite density data. Consistency is also maintained with Hinteregger's (1970) solar flux values for medium solar activity combined with a heating efficiency of 30%. In addition we demonstrate the ability of an equivalent gravity wave f-plane formalism to locally approximate our three-dimensional tidal solutions.

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Jeffrey M. Forbes
and
Saburo Miyahara

Abstract

Vertical coupling due to the solar semidiurnal tide in Mars's atmosphere, and effects on zonal mean temperature and wind structures, are investigated using a numerical model. The model provides self-consistent solutions to the coupled zonal mean and tidal equations from the surface to 250 km. Breaking (convective instability) of the semidiurnal tide is parameterized using a linear saturation scheme with associated eddy diffusivities. Thermal forcing in the model gives rise to surface pressure perturbations and middle-atmosphere zonal mean winds and temperatures that are consistent with available measurements and general circulation models. Results presented here primarily focus on globally elevated dust levels during Southern Hemisphere summer, conditions similar to those experienced by the Viking 1 and Viking 2 landers during the 1977 global dust storms. Semidiurnal temperature and wind amplitudes maximize in the winter hemisphere and exceed 50 K and 100 m s−1 above 150 km and are typically 10–20 K and 10–20 m s−1 at 50 km. Perturbation densities are of order 50%–70% between 90 and 150 km, and thus contribute significantly to variability of the aerobraking regime in Mars's atmosphere.

Eddy diffusivities associated with the breaking parameterization reach values of order 103–104 m2 s−1 between 100 and 150 km, and can be of order 1–10 m2 s−1 between 0 and 50 km. Dissipation of the semidiurnal tide induces zonal mean westward winds of order 10–30 m s−1 below 100 km, and in excess of 200 m s−1 above 150 km. The corresponding temperature perturbations range between −20 and −70 K over most of the thermosphere, with 10–20-K increases in temperature at high winter latitudes between 50 and 100 km. All of the wave and zonal mean perturbations noted above represent very significant modifications to the thermal and dynamical structure of Mars's atmosphere.

Estimates are also provided for the eastward-propagating diurnal tides with zonal wavenumbers s = −1 and s = −2. These waves also have long vertical wavelengths and hence are capable of effectively coupling the lower and upper atmospheres of Mars. However, the perturbation and zonal mean effects of these waves are a factor of 2 or more smaller than those cited above for the semidiurnal tide under dusty conditions.

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Jeffrey M. Forbes
and
Dong Wu

Abstract

Temperatures between 25 and 86 km measured by the Microwave Limb Sounder (MLS) experiment on the Upper Atmosphere Research Satellite (UARS) are analyzed to delineate diurnal, semidiurnal, and terdiurnal tidal structures and stationary planetary waves. These Fourier components are determined from temperatures averaged in bins covering 5° latitude, 30° longitude and 1 h in local time. This study confirms the presence of diurnal nonmigrating tides with zonal wavenumbers s = 0, 2, −3 [s > 0 (s < 0) implying westward (eastward) propagation] and semidiurnal tides with s = 1 and 3, and some components of lesser importance that were previously determined from UARS wind measurements near 95 km. The seasonal–latitudinal and height structures of these components are now revealed, and utilized to aid in interpreting their behaviors and ascertaining their origins. New discoveries include the terdiurnal s = 2 and s = 4 components, and trapped nonmigrating diurnal tides with s = 0 and s = 2. The former are likely to arise from nonlinear interaction between the migrating (s = 3) terdiurnal tide and the stationary planetary wave with s = 1. The latter may reflect the presence of a longitude-dependent in situ heat source, or in situ nonlinear interaction between the migrating diurnal tide and a stationary planetary wave with s = 1. The present results provide a rich mixture of observational results to challenge both mechanistic and general circulation models of the middle atmosphere. In addition, internal consistency is established between the MLS tidal temperatures at 86 km and previously derived tidal winds at 95 km within the context of tidal theory. This result represents one step in the validation of measurements required for successful application of data-model assimilation techniques to the mesosphere and lower thermosphere.

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Jeffrey M. Forbes
and
Henry B. Garrett

Abstract

The seasonal-latitudinal structure of the diurnal thermospheric tide is investigated for minimum and maximum levels of solar activity by numerically solving the linearized inseparable tidal equations for a spherical, rotating, viscous atmosphere with anisotropic ion drag. Variations in F-region ionospheric structure and the solar zenith angle dependence of the EUV heat source are major factors controlling the seasonal-latitudinal structure of the diurnal thermospheric tide. The combined interaction of the solar-cycle dependent background temperature profile (which controls the altitude of diffusion dominance) and variations in the seasonal structure of the ionospheric plasma with sunspot activity leads to a solar-cycle variation of the seasonal-latitudinal morphology of the diurnal tide. For instance, summer-winter differences in tidal winds at a given height are more pronounced during SSMAX as opposed to SSMIN. At a given level of solar activity, westerly winds, vertical winds and temperatures are generally larger in the summer hemisphere, whereas the amplitude of the northerly wind is greatest during winter. There also exist summer-winter phase differences in the tidal fields ranging from 1 to 6 h, depending upon height, latitude and sunspot activity. Computations of diurnal oscillations in O and N2 are presented which similarly demonstrate a complex dependence of tidal effects on height, latitude, season and solar activity. In particular, the temperature-atomic oxygen phase difference (the so-called “phase anomaly”) at 300 km varies from about 7 to −2 h at SSMAX and 2 to −2 h at SSMIN, between 80°S and 80°N, respectively, at December solstice. The above results suggest that related seasonal-latitudinal and solar-cycle variations exist in midlatitude ionospheric structure, the F-region equatorial anomaly, the tidal distributions of O2, Ar, He and H, and magnetic and electric fields generated by the E-region dynamo mechanism. Finally, it is concluded that static diffusion models based on families of empirical temperature profiles cannot simultaneously yield realistic diurnal variations in O, N2 and temperature below 200 km for SSMIN and 300 km for SSMAX.

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