Solar Semidiurnal Tide in the Dusty Atmosphere of Mars

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JULY 2006 FORBES AND MIYAHARA 1803high-dust conditions ( 5.0). The diurnal heating profilefor 2.3 is also provided, and we assume thesemidiurnal profile to have the same shape and thesame maximum value relative to the diurnal componentas 5.0. Zurek (1986) also provides the noontimeequatorial dusty 0.67J(III) profile from the Leovy andZurek (1979) study. [In this notation a vertical profileof heating per unit mass (J) is denoted s J(I, II, III),where s is the fraction of solar radiation absorbed bydust in the atmosphere, I denotes a low-dust verticalprofile shape that mainly simulates surface heating, andII and III are two different vertical profile shapes thatsimulate the effects of atmospheric heating by airbornedust]. This provides an unambiguous means to calibratethe low-dust profile, designated 0.10J(I) in Leovy andZurek (1979). Comparing Fig. 1 of Zurek (1986) withFig. 10 of Leovy and Zurek (1979), a peak heating rateof 3.2 W kg 1 for 0.67J(III) implies a peak diurnalequatorial noontime heating rate (at the ground) of1.34 W kg 1 for 0.1J(I). The relative amplitude of thesemidiurnal heating for this low-dust case is given inLeovy and Zurek (1979), and we note that the correctsign in the exponential expression for J(I) as noted byZurek (1986) is used here.c. Zonal mean heating rates and backgroundatmosphereAlthough our emphasis in this paper is on the solarsemidiurnal tide, it is necessary to introduce dissipativeprocesses and a zonal mean wind distribution in orderto provide some realism to the propagation conditionsencountered by the tide. Given the virtual absence ofdirect wind observations in Mars’s atmosphere, weadopt a simplistic approach guided by existing Marsgeneral circulation models (GCMs) that have had somesuccess in capturing the salient features of other observablesin Mars’s atmosphere, and on gradient winds below60 km determined from temperatures measured bythe Thermal Emission Spectrometer (TES) instrumenton Mars Global Surveyor (Smith et al. 2001). Towardthis end, we introduce zonal mean thermal forcing inthe model that is antisymmetric about the equator witha cos dependence ( colatitude), consistent withSouthern Hemisphere summer conditions. The verticaldistributions of heating are Gaussian-shaped functionswhose peak altitudes and amplitudes are chosen so thatthe zonal mean wind and temperature distributionssimulated by recent GCMs for the middle atmosphere(Forget et al. 1999) and thermosphere (Bougher et al.2000) are approximated (see below). For the radiativecooling we utilize the same Newtonian cooling parameterizationdetailed in Forbes et al. (2002). Aboveabout 80 km, in the non-LTE region,(where LTE stands for local thermodynamic equilibrium)this is based on exact 15-m cooling calculationsover a range of reference temperatures and pressures,which are then used to choose an average profile that isrepresentative of the range of temperature deviationsfrom the mean reflected in the calculations. At loweraltitudes, the rates closely approximate those illustratedin Barnes (1984, 1990) that are based on the detailedradiative calculations of Barnes (1983). The two coolingprofiles are merged together in the 70–80-km heightregion.The zonal-mean zonal, meridional, and vertical windsand perturbation temperatures due to the heating ratesspecified above are illustrated in Fig. 3, for low-dustconditions. The main features of the zonal winds depictedin dynamical models of Mars’s atmosphere(Théodore et al. 1993; Collins et al. 1997; Forget et al.1999; Joshi et al. 1995; Bougher et al. 2000) are exhibitedhere. Zonal mean eastward (winter) and westward(summer) jets of order 60–80 m s 1 in the thermosphere,and 100–120 m s 1 for the corresponding jetsin the middle atmosphere, with some degree of closureof the middle-atmosphere jets above 70 km. The latterfeature is caused by resolved-scale wave drag and tosome extent parameterizations introduced into thesemodels to account for subgrid-scale wave stresses.Given our inability to simulate the resolvable wavestresses accounted for in the GCMs, and the ad hocnature of the gravity wave parameterizations, the sameeffect is accomplished here through introduction of aRayleigh friction distribution peaking at 5.0 sol 1 near80 km, the estimated breaking height for topographicgravity waves in Mars’s atmosphere (Joshi et al. 1995).The middle-atmosphere westward jet is very similar inmagnitude and latitudinal extent compared to the gradientwinds estimated from MGS/TES temperatures(Smith et al. 2001), but the eastward middleatmospherejet maximum (120 m s 1 )is40ms 1 lessthan that of Smith et al. (2001). Intrusion of the westwardjet into the Northern Hemisphere, and the highlatitudelocation and intensification of the eastward jetin the Northern Hemisphere are also features exhibitedin Mars middle-atmosphere models and gradient winds.The zonal mean temperature perturbations correspondingto these calculations are similarly consistentin broad features with those of the cited GCM resultsand with observations. For instance, the 20-K warmingat 60–80 km in the high-latitude winter hemisphereis due to subsidence heating by the descending branchof a global Hadley cell (refer to Fig. 3) whose polewardmotion is accelerated by Coriolis and centrifugal forcesdue to the westward mean winds intruding into theNorthern Hemisphere. The latter feature results from
1804 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63FIG. 3. Modeled zonal mean parameters vs height and latitude for low dust conditions in Mars’s atmosphere, withzonal mean forcing only: (a) eastward wind, (b) southward wind, (c) temperature perturbation from global mean,and (d) vertical wind.conservation of angular momentum for a meridionalflow driven by strong pole to pole heating gradient; anatmospheric particle can leave the high latitudes of theSouthern Hemisphere, cross the equator at high altitude,and reach the high northern latitudes while conservingits angular momentum (Wilson 1997; Forget etal. 1999). The warming of the high-latitude middle atmosphererelative to radiative equilibrium values hasalso been noted from observational studies (Deming etal. 1986; Théodore et al. 1993; Martin and Kieffer 1979;Jakosky and Martin 1987; Santee and Crisp 1993; Smithet al. 2001). We have not made any attempt to reproduceanything but the salient features of the GCM andgradient wind patterns due to the uncertainties andlimitations involved. We have also not attempted toreproduce GCM winds in the lower 10 km of the atmosphere,since these are inconsequential to the verticalpropagation of the tidal disturbances into the middleand upper atmosphere of Mars, the primary focus ofthis paper.Coefficients for molecular diffusion of heat and momentumare consistent with the formulation in Miyaharaand Wu (1989), with the numerical constants adjustedfor Mars’s chemical composition. The choice ofeddy diffusion coefficient is subject to considerable uncertainty,as values used by 1D photochemical modelsmost likely include the lumped effects of mixing bylarge-scale dynamics (Bougher and Roble 1991;Bougher et al. 1999, 2000). For instance, in his 3D dynamicalmodel, Bougher obtained realistic results forlower thermosphere chemistry with eddy diffusion valuesof order 750 m 2 s 1 , whereas photochemical modelsutilize values in the range of 1–5 10 3 m 2 s 1 . Closer tothe surface (i.e., 25 km) little information is available;estimates range between about 50–100 m 2 s 1 (Krasitskii1978; Krasnopolsky 1993; Leovy and Zurek1979). Here, we assume a profile with values of 50m 2 s 1 from the surface to 25 km, increasing linearlywith height to a value of 350 m 2 s 1 at 75 km, andconstant with height above 75 to 105 km where moleculardiffusion begins to dominate, above which the eddydiffusion value decreases with height. Eddy diffusivitiesof these magnitudes are unimportant for the verticalpropagation of the semidiurnal tide (see below), and so
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Solar Semidiurnal Tide in the Dusty Atmosphere of Mars

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