Solar Semidiurnal Tide in the Dusty Atmosphere of Mars

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JULY 2006 FORBES AND MIYAHARA 1799lower altitudes (0–50 km) occurs because of enhancedsolar radiation absorption by globally elevated dust.This problem is of interest for several reasons. First,because of its relatively long wavelength, the semidiurnaltide has the potential to propagate into the thermosphereand produce significant density variations ataerobraking altitudes (ca. 100–170 km). Estimates ofsuch effects are of interest, as existing measurementshave inadequate local time coverage to delineate semidiurnalvariations in Mars’s thermosphere. In addition,molecular dissipation of the tide above 100 km will inducemomentum and heat flux divergences that accelerateand heat the thermosphere, but the magnitude ofthese effects remain unknown. Breaking (convective instability)of the semidiurnal tide may, however, be acritical factor in determining how efficiently the tidecouples the lower and upper atmospheres of Mars. Earlierwork (Hamilton 1982; Zurek 1986; Zurek and Haberle1988) suggests that the semidiurnal tide achievesconvective instability by about 40 km and significantlymodifies the zonal mean state of Mars’s atmosphere.However, the implications of convective instability onthe continued upward propagation of the semidiurnaltide, and on the zonal mean circulation and thermalstructure of the atmosphere at higher altitudes, remainsunexplored. Eddy mixing of the atmosphere that accompaniestidal breaking is relevant to minor constituenttransport, establishment of the homopause (Leovy1982), and therefore the planetary escape rate of lightgases (Hunten 1973, 1974). It is the purpose of thepresent work to address the above issues pertaining tothe semidiurnal tide in Mars’s dusty atmosphere. In theremainder of this section, we introduce the tidal nomenclatureused throughout the paper, and then set theproblem into the broader context of solar thermal tidesin planetary atmospheres, and of previous work relatingto Mars.Solar thermal tides are oscillations in temperature,density, pressure, and winds induced by the daily cyclicabsorption of solar energy in an atmosphere or planetarysurface. Assuming continuity in space and timearound a latitude circle, solar thermal tidal fields arerepresented in the formA n,s cosnt s n,s ,where t time (sols for Mars, where 1 sol 24.6 h),rotation rate of the planetary atmosphere ( 2sol 1 for Mars), longitude, n ( 1, 2, . . .) denotesa subharmonic of a sol, s ( .... 3, 2, . . . 0, 1,2, ....) is the zonal wavenumber, and the amplitudeA n,s and phase n,s are functions of height and latitude.In this context, n 1 and 2 represent oscillations withperiods corresponding to 1.0 and 0.5 sols, and hence are1referred to as diurnal and semidiurnal tides, respectively.Eastward (westward) propagation correspondsto s 0(s 0). At any height and latitude the totaltidal response is obtained as a sum over n and s.Rewriting (1) in terms of local time t LT t /,wehaveA n,s cosnt LT s n n,s .Tidal components with s n yield local time variationsthat are independent of longitude, and thus correspondto solar radiation absorption by a zonally symmetricatmosphere or surface. From (1) such components correspondto a zonal phase speed C ph d/dt n/s , in other words westward-propagating at the samespeed as the apparent motion or migration of the sun toa ground-based observer. These sun-synchronous tidalcomponents are referred to as migrating tides. In responseto the zonally asymmetric (longitude dependent)absorption of solar energy by a planetary atmosphereor surface, the local time structure of the atmosphere(at a given height and latitude) is dependent onlongitude. In this case, Fourier representation must involvea range of zonal wavenumbers of both signs, correspondingto waves propagating to the east (s 0) orwest (s 0) (Chapman and Lindzen 1970); these tidalcomponents are commonly referred to as nonmigratingtides. From (2) it is evident that from sun-synchronousorbit (t LT constant) a tide characterized by a given sand n appears as a variation in longitude with wavenumber|s n|. Conversely, a longitude variation observedfrom sun-synchronous orbit with wavenumber|s n| can be produced by multiple combinations of sand n.Diurnal and semidiurnal solar thermal tides play animportant role in determining the mean circulation andthermal structure of terrestrial planetary atmospheres(Venus, Earth, and Mars), in addition to their moreobvious contributions to variability about the zonalmean state (see review by Forbes 2002). In Earth’s atmosphere,solar tides begin to dominate flow patternsabove about 80 km. At 95 km, migrating tides are thelargest components, but nonmigrating tides are nearlyas important and introduce significant longitude variabilityinto the tidal structures (Forbes et al. 2003). Inthe region between about 100 and 150 km, moleculardissipation of solar tides induces zonal mean accelerationsthat strongly influence the mean circulation ofthat height region (i.e., Miyahara and Wu 1989; Angelatsi Coll and Forbes 2002). On Venus, tides play a keyrole in maintaining superrotation of the atmospherenear the cloud tops around 65 km (i.e., Newman andLeovy 1992). However, although the solar semidiurnaltide is observed to propagate to the lower thermo-2
1800 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63sphere of Venus (Schofield and Taylor 1983), its effectson the zonal mean structure of the Venusian atmosphereabove the cloud tops is not known. Modelingstudies for Mars (Lewis and Read 2003; Wilson andHamilton 1996) suggest that thermal tides drive a superrotating(eastward) jet below about 30 km in theequatorial region, in much the same fashion that progradewinds are driven within the cloud region of Venus(Fels and Lindzen 1974). The jet is strongest nearequinox and under conditions of high dust loading ofthe atmosphere. Retrograde (westward) winds occur atupper levels over the equator, presumably due to dissipationof the thermal tides as they propagate upward.The thermosphere of Mars (ca. 100–250 km) is therecipient of a spectrum of diurnal and semidiurnal tidespropagating upward from the lower atmosphere (Angelatsi Coll et al. 2004) that appear to account for muchof the longitude variability in total mass density in theaerobraking regime (100–170 km) inferred from MarsGlobal Surveyor (MGS) accelerometer measurements(Keating et al. 1998; Forbes and Hagan 2000; Wilson2000, 2002; Forbes et al. 2003; Withers et al. 2003).Some of the most important tidal components includethe eastward-propagating diurnal tides with s 1,2, and 3, each producing on the order of 15% densityvariation near 115 km (Angelats i Coll et al. 2004).Note from Eq. (2) and related discussion that thesewaves appear as wave-2, wave-3, and wave-4 longitudinalstructures from sun-synchronous orbit. As on Earth,eastward-propagating tides have significantly longervertical wavelengths than their westward-propagatingcounterparts, and hence penetrate to thermosphere altitudesmuch more efficiently (Ekanayake et al. 1997).The eastward-propagating semidiurnal tide with s 1may also contribute significantly to the wave-3 variationin thermosphere density, particularly at high latitudes(Wilson 2002; Withers et al. 2003). As shown inthe general circulation model (GCM) simulations ofAngelats i Coll et al. (2004), response of Mars’s upperatmosphere to the vertically propagating component ofthe migrating diurnal tide is rather weak during solsticeconditions, producing barely a 2% relative density perturbationat 115 km. In addition, as dust loading of theatmosphere increases, the semidiurnal atmospheric responseat the surface and aloft increases in importancecompared to the diurnal response (Wilson and Hamilton1996; Wilson and Richardson 2000). There are severalreasons for these differences in diurnal and semidiurnaltidal response. First, as noted above, the relativelyshort vertical wavelength (30–35 km) of thediurnal propagating tide makes it more susceptible todissipation, thus hindering its propagation into the thermosphere.Second, under solstice conditions the latitudedistribution of diurnal heating does not projecteffectively onto the first propagating diurnal tidalmode, which is symmetric about the equator. Third,under globally dusty conditions the vertical distributionof heating (0 to 40–50 km) projects well onto thevertical structure of the long-wavelength semidiurnaltide, but its projection onto the diurnal propagating tidetends to undergo changes of sign within the heatingregion, resulting in phase interference effects that diminishthe atmospheric response aloft. However, quitelarge (20–45 K) diurnal temperature perturbationsare possible within the heating region during planetencirclingdust storms (Smith et al. 2002), due to excitationof evanescent modes of the diurnal tide, whichhave very long vertical scales.Since our main focus is on vertical coupling betweenthe lower atmosphere and upper atmosphere duringglobally dusty conditions, we primarily restrict our attentionto the migrating solar semidiurnal tide duringthe Southern Hemisphere summer season. Several previousinvestigations were devoted to the semidiurnalmigrating in Mars’s atmosphere and its interaction withthe zonal mean flow (Hamilton 1982; Zurek 1986;Zurek and Haberle 1988) under similar conditions, butwith emphasis on the atmosphere below about 40–60km. These works used classical atmospheric tidaltheory (Chapman and Lindzen 1970) to estimate tidalamplitudes that resulted from realistic thermal forcing,that is, heating rates that yielded tidal variations in surfacepressure consistent with those measured by theViking 1 and Viking 2 landers over a range of dustconditions (i.e., Zurek and Leovy 1981). In all casestidal amplitudes easily reached unstable amplitudes byabout 40 km. Dissipation of the waves gave rise to zonalmean momentum and heat flux divergences of majorimportance to Mars’s momentum and heat budgets. Itwas furthermore established that the semidiurnal tide(as opposed to the diurnal tide) was of primary importancewith regard to these coupling effects, for the reasonsnoted previously.The above works did not consider propagation of thesemidiurnal tide above the middle atmosphere. Theonly attempt to address this problem was in the work ofBougher et al. (1993) wherein they crudely estimated asemidiurnal tide lower boundary condition for the Marsthermosphere general circulation model (TGCM) at100 km, and examined the thermosphere amplitudesthat resulted. They did this for a range of boundaryconditions that were thought to be representative ofdusty and nondusty conditions in the lower atmosphere.They found dramatic changes in horizontal andvertical wind patterns, and temperature and atomicoxygen distributions, when the semidiurnal forcing was
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Solar Semidiurnal Tide in the Dusty Atmosphere of Mars

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