Influence of gravity waves on the climatology of high-altitude Martian carbon dioxide ice clouds

We next describe the MGCM, outline the implemented whole atmosphere GW parameterization, how it is linked to CO₂ cloud formation in the model, and the setup of numerical experiments.

2.4 Martian General Circulation Model simulations

After a multi-year spinup, the model was run for a full Martian year (669 sols ∼687 Earth days) under the low-dust scenario and for low solar activity conditions. The dust scenario represents a composite of measurements by the Thermal Emission Spectrometer onboard Mars Global Surveyor (MGS-TES) and the Planetary Fourier Spectrometer onboard Mars Express (MEX-PFS) with the global dust storms removed. Two full-Martian-year experiments have been performed: without GWs included (EXP0) and with the GW scheme turned on (EXP1). The results to be presented are based on daily averaged output data.

Figure 1Global annual mean temperature, and cooling by gravity waves and radiative processes in carbon dioxide molecules. (a) Globally averaged annual mean neutral temperature (T, K) with gravity waves (solid line, “EXP1”) and without gravity waves (dashed lines, “EXP0”); (b) globally averaged annual mean gravity wave heating/cooling Q_GW (K sol⁻¹) (orange line) and CO₂ 15 µm cooling (blue line); (c) relative percentage change with respect to EXP0 simulations for the temperature (red) and CO₂ cooling (blue), calculated as $[T^{\left(\mathrm{EXP}\mathrm{1}\right)}-T^{\left(\mathrm{EXP}\mathrm{0}\right)}]/T^{\left(\mathrm{EXP}\mathrm{0}\right)}$ and $[Q_{{\mathrm{CO}}_{\mathrm{2}}}^{\left(\mathrm{EXP}\mathrm{1}\right)}-Q_{{\mathrm{CO}}_{\mathrm{2}}}^{\left(\mathrm{EXP}\mathrm{0}\right)}]/Q_{{\mathrm{CO}}_{\mathrm{2}}}^{\left(\mathrm{EXP}\mathrm{0}\right)}$. In both panels dashed lines represent the simulation without gravity wave effects, while the solid lines are for the simulation with gravity wave propagation from the lower atmosphere upward. The annual mean refers to an averaging over 1 Martian year (669 sols = 687 Earth days) over all longitudes and latitudes.

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Gravity waves can facilitate CO₂ cloud formation in two ways: (a) by cooling down the large-scale atmosphere globally, thus bringing its temperature closer to the condensation threshold, and (b) by locally creating pockets of cold air. In this section, we explore the former effect by comparing the EXP0 (no-GW run) and EXP1 (GW-run) simulations. It is instructive to compare the effects produced by GWs with the other major cooling mechanism in the middle and upper atmosphere of Mars – cooling due to radiative transfer in the IR CO₂ bands. A detailed study of the two mechanisms using two Martian GCMs has been performed for a vernal equinox (Medvedev et al., 2015). Here our emphasis is on the global and seasonal effects.

Figure 2Altitude–latitude distributions of the mean zonal mean fields during vernal equinox and northern summer solstice (aphelion): (a) temperature (T) at equinox, (b) temperature (T) at solstice, (c) zonal wind u (color shaded) and zonal GW drag (acceleration/deceleration) a_x (contour lines), and (d) zonal wind u (color shaded) and zonal GW drag a_x (contour lines). The fields are averaged over L_s=0–20^∘ (42 sols) for vernal equinox and over L_s=90–110^∘ (44 sols) for the Northern Hemisphere summer period. Temperature is in units of K, the zonal wind is in m s⁻¹, and the zonal GW drag is in m s⁻¹ sol⁻¹. Red and blue shadings in the zonal wind plot represent the easterly (westward) and westerly (eastward) wind systems. Dashed and solid lines for the drag are for the easterly and westerly wave drags in intervals of 50 m s⁻¹ sol⁻¹.

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Figure 1 presents the annual global means of the simulated temperature (T), GW-induced thermal heating–cooling rates (Q_GW), and CO₂ radiative cooling rates ($Q_{{\mathrm{CO}}_{\mathrm{2}}}$) for experiments EXP0 (dashed line) and EXP1 (solid line). The left panel demonstrates that inclusion of GW effects cools down the upper atmosphere at all altitudes above 60 km in a global sense; e.g., the temperature in the mesosphere above 100 km is lower by ∼10 K. Note that this change includes both thermal and dynamical influence of GWs. The thermal one is due to GW-induced heating/cooling rates, while the dynamical channel encompasses the temperature field response to acceleration/deceleration of the large-scale wind by small-scale GWs. Here, it is not our goal to explore the two channels in more detail. More important within the context of this paper is to demonstrate the appreciable net cooling effect of GWs.

Figure 3Altitude–latitude distributions of mean zonal mean cloud probability and gravity wave effects: (a) cloud probability (P) at equinox, (b) cloud probability at solstice, (c) gravity-wave-induced temperature fluctuations ($\left|T^{\prime }\right|=T_{\mathrm{GW}}^{\prime }$) at equinox, and (d) gravity-wave-induced temperature fluctuations at solstice. The fields are averaged over a period of L_s=0–20^∘ (42 sols) for vernal equinox and over L_s=90–110^∘ (44 sols) for Northern Hemisphere summer solstice seasons, i.e., in the same manner as the data presented in Fig. 2. Temperature fluctuations are in units of K and the probability is expressed in terms of percentage.

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Figure 1b shows that CO₂ cooling is present at nearly all altitudes in the middle atmosphere, and peaks at more than −80 K sol⁻¹ around 90 km, steeply decreasing above. By contrast, GW cooling rates increase with altitude, exceeding that of CO₂ in the upper mesosphere and lower thermosphere, and peak at −80 K sol⁻¹ at 140 km. Around the mesopause and lower thermosphere, GWs cool down the atmosphere by ∼5–8 % (Fig. 1c). It is also seen that the GW-induced effects modulate the CO₂ cooling via changes in the background temperature: CO₂ cooling is up to 60 % weaker in the run with GWs. In the rest of the paper, we present the results of simulations that include GW effects (EXP1).

Figure 4Seasonal variations of mean (i.e., daily and zonally averaged) atmospheric fields. (a) Temperature (T) at 80 km, (b) T at 100 km, (c) T at 120 km, (d) zonal wind (u) at 80 km, (e) u at 100 km, and (f) u at 120 km. Temperature is in K and the zonal wind is in m s⁻¹. Red/blue shadings for the wind represent eastward/westward winds. A Martian year has about 669 sols, which is plotted in terms of solar longitude L_s (in degrees) from L_s=0 to 360^∘. $L_{\mathrm{s}}=\mathrm{0}{}^{\circ }$ marks the vernal equinox in the Northern Hemisphere. $L_{\mathrm{s}}=\mathrm{90}{}^{\circ }$ and $L_{\mathrm{s}}=\mathrm{270}{}^{\circ }$ are aphelion and perihelion seasons, respectively.

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Figure 2 illustrates the altitude–latitude distributions of the zonal mean temperature and wind for two characteristic seasons: the vernal equinox (averaged over 42 sols corresponding to L_s=0–20^∘, left panels) and the aphelion solstice (44 sol average, L_s=90–110^∘, right panels). The simulated temperatures below ∼70–80 km are in good agreement with observations, where systematic satellite measurements are available (Smith, 2008). The coldest temperatures on Mars (favoring CO₂ condensation) are near the mesopause. During the equinox, the minimum of 120 K is over the Equator. At the aphelion season, the mesopause is colder and the temperature minimum shifts to the summer hemisphere. This behavior is closely related to the wind distributions. It is seen that, in both seasons, zonal jets reverse their directions near the mesopause. The similar phenomenon is well known in the mesosphere and lower thermosphere of Earth, and is caused by the deposition of zonal momentum (i.e., zonal drag) by GWs of lower atmospheric origin (of up to −250 m s⁻¹ sol⁻¹ in this case), as demonstrated by the black contour lines. During the Northern Hemisphere summer solstice, the asymmetry between the two hemispheres is significant. Easterly and westerly jets dominate in the northern summer and southern winter hemispheres, respectively, with the middle atmospheric jets extending higher up and reversing their directions between 110 and 120 km due to zonal GW drag acting against the mean winds. The zonal mean drag increases from ±50 m s⁻¹ to $\pm \sim \mathrm{1000}$ m s⁻¹ sol⁻¹ from the mesosphere to the lower thermosphere, with relatively asymmetric distribution between hemispheres. The drag of similar magnitudes has been inferred from aerobraking data in the Martian lower atmosphere (Fritts et al., 2006).

Figure 5Seasonal variations of cloud formation probability, GW drag, and GW-induced temperature fluctuations: (a) GW-induced temperature fluctuations ($\left|T^{\prime }\right|$) at 80 km, (b) $\left|T^{\prime }\right|$ at 100 km, and (c) $\left|T^{\prime }\right|$ at 120 km, (d) GW zonal drag (a_x) at 80 km, (e) a_x at 100 km, (f) a_x at 120 km, (g) cloud formation probability (P) at 80 km, (h) P at 100 km, and (i) P at 120 km. Probabilities are in percentage; zonal drag is in m s⁻¹ sol⁻¹, and temperature fluctuations are in K. In the drag plots (d–f), red/blue represents eastward/westward GW drag. Presented model data are in terms of daily and zonal averages. Note that the zonal drag is plotted in 200 m s⁻¹ sol⁻¹ intervals. $L_{\mathrm{s}}=\mathrm{0}{}^{\circ }$ marks the vernal equinox in the Northern Hemisphere.

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Figure 3 demonstrates that the probability P of CO₂ cloud formation is strongly determined by the mean temperature. It is seen that the saturation conditions for clouds are more likely to be met during the solstice than the equinox. Specifically, the cloud formation can occur in ∼1 % of the time in the equatorial mesosphere during the equinox. Higher up at around 120 km, the cloud formation probability increases and reaches 4.5 % with larger values found at the northern high latitudes. During the solstice, the probability P is larger in all atmospheric regions. In particular, a very strong cloud formation is seen in the winter polar lower atmosphere (Fig. 3b), which, however, is not the focus of this paper. In the upper atmosphere, the peak values of P exceed 30 % between 100 and 120 km in the Northern Hemisphere at middle and high latitudes. A closer examination of Figs. 2 and 3 reveals that the distributions of P and mean temperature are not identical. GW-induced fluctuations $\left|T^{\prime }\right|$, which are a measure of GW activity, also contribute to CO₂ supersaturation, especially at low to middle latitudes of the middle atmosphere in both seasons and in high-altitude polar regions. Overall, large GW-induced temperature fluctuations prevail above 100 km up to 140 km, primarily located over the Equator and at high latitudes of both hemispheres.

We next investigate the seasonal variations of the simulated temperature and wind in more detail by focusing on three representative altitudes in the mesosphere and lower thermosphere: 80, 100, and 120 km. There are too few observations at these altitudes to date to validate the simulations. The exception is the temperature at ∼80 km (Fig. 4a), which can be directly compared to retrievals from Mars Climate Sounder (MCS) onboard Mars Reconnaissance Orbiter (MRO) (Sefton-Nash et al., 2013). Both observations and simulations demonstrate a relative symmetry with respect to the equatorial distributions during equinoxes ($L_{\mathrm{s}}=\mathrm{0}{}^{\circ },L_{\mathrm{s}}=\mathrm{180}{}^{\circ }$). The lowest and highest temperatures occur in the Southern Hemisphere during winters and summers, respectively. The model generally reproduces the observed temperature well, except that it overestimates it in the Southern Hemisphere winter by up to 20 K. Alternating with seasons, zonal winds at ∼80 km represent an extension of the lower and middle atmosphere jets formed as a consequence of the Coriolis force acting on the summer-to-winter meridional circulation cell.

In the upper mesosphere (100 km, Fig. 4b, e) the simulated temperature and wind show variations similar to that at 80 km, but with noticeably colder temperatures. Around the mesopause (120 km, Fig. 4c, f), the simulated seasonal variations differ significantly from those in the mesosphere. It is seen that the coldest temperatures of down to 90–100 K are found around the summer high latitudes at solstices, and the temperature distributions are hemispherically less symmetric. The summer high-latitude hemispheres are remarkably different. Polar temperatures fall down to 90 K in the summer hemisphere at the aphelion and to 115 K at the perihelion. The zonal winds reverse their directions at 120 km, which is especially well seen during the aphelion season. During other seasons, the simulated winds demonstrate a significant weakening as compared to distributions in the mesosphere. The latter is primarily attributed to the GW drag, which we present next along with GW-induced temperature fluctuations.

Parameterized GW-induced temperature fluctuations ($\left|T^{\prime }\right|$), GW drag (a_x), and probability of cloud formation (P) are studied next in Fig. 5 in the same manner as temperature and zonal winds are presented in Fig. 4. Overall, the seasonal variations of the parameterized GW-induced temperature fluctuations, which are created by GW harmonics that survived propagation from the lower atmosphere, depend on the assumed wave sources and on filtering by the underlying mean winds. In the mesosphere (80 km, Fig. 5a), the fluctuations of up to 16 K enhance at middle to high latitudes and during the solstices with slightly larger magnitudes during winters. The middle column of Fig. 5 shows the seasonal variations of the zonal GW drag, which is largely determined by the background winds below presented in Fig. 4 and characterizes the rate of change in GW momentum fluxes with height. It is seen that it is directed mainly against the mean flow throughout the mesosphere. Finally, the probability P of cloud formation is plotted in the rightmost column of Fig. 5. A continuous presence of P of up to 2–4 % is seen around the Equator at 80 km nearly throughout the entire Martian year. After the northern summer hemisphere solstice (aphelion), regions of cloud formation gradually expand to lower latitudes ($\pm \mathrm{30}{}^{\circ }$), resembling a fork-like structure, in some level of agreement with Sefton-Nash et al. (2013)'s observations. During southern winter solstice, the probability of cold pocket formation is somewhat present around middle latitudes. There is some degree of correlation between the cloud formation probability and GW activity represented as fluctuations and drag.

In the upper mesosphere (100 km, middle row), GW-induced temperature fluctuations increase, along with the GW drag imposed on the mean circulation, and the cloud formation probability demonstrates a more definitive correlation with the GW activity during all seasons. Cold pockets occur more frequently at middle and high latitudes (P∼16 %–20 %), exceeding the equatorial cloud probability rate. Around the mesopause, GW-induced fluctuations increase further, maximizing at middle and high latitudes with values of up to 26 K during both aphelion and perihelion. The probability P increases to more than ∼30 % correspondingly.

As mentioned in the description of the model, the CO₂ condensation/sublimation scheme employed in the MPI-MGCM is able to resolve CO₂ ice formation and annihilation when temperature in a grid point crosses the condensation threshold. In our simulations, there were very few occurrences of such clouds in the mesosphere above 60 km to offer reliable statistics. Inclusion of GW effects leads, generally, to colder simulated temperatures, which provide favorable conditions for cloud formation. This cooling in the mesosphere is mainly produced via the dynamical channel due to GW-induced changes in the winds that affect temperature through the thermal wind relation, rather than via the thermal channel due to direct heating/cooling by dissipating GW harmonics. The latter clearly transpires in experiments with thermal effects of the parameterized waves turned on and off (not shown). The direct thermal effects of GWs increasingly grow with height and become important near the mesopause and above.

The vast majority of studies report on cloud observations in the Martian mesosphere below ∼80 km. Sefton-Nash et al. (2013) analyzed data from Mars Climate Sounder (MCS) onboard the Mars Reconnaissance Orbiter (Graf et al., 2005; Zurek and Smrekar, 2007) (MRO) during dayside and nightside local times over 2 Martian years and provided a global picture of high-altitude clouds. They found out that the distribution of clouds over latitude and season does not appear to vary between each Martian year and that clouds occurred more often in low latitudes during the aphelion season and concentrated around two mid-latitude bands during perihelion. Using two different observational modes, Sefton-Nash et al. (2013) showed that the latitudinal distributions of clouds varied little between the different local times in the second half of the year. It must be noted that Sefton-Nash et al. (2013) could not discriminate between CO₂ and water clouds. The majority of positively identified CO₂ cloud observations took place in the first half of the year, with only a few detections in the second half. On the other hand, water ice clouds usually do not extend higher than ∼40 km except during perihelion, when they rise to 60–65 km. Therefore, all clouds observed above 70 km are likely not water ice clouds. The question regarding the nature of these detected clouds is still open. Our simulations illustrate that favorable conditions for CO₂ condensation in the mesosphere exist in low latitudes throughout the year (Fig. 5g). This is because the mean temperature is lowest around the Equator at all seasons (Fig. 4a), while GW-induced temperature fluctuations are contrastingly small (Fig. 5a). The model also predicts a higher probability of cloud formation in middle latitudes of the summer hemisphere during both solstices.

It is observationally challenging to determine the precise altitude of CO₂ ice clouds and there are intrinsic limitations of the retrieval algorithms associated with CO₂ cross sections (Määttänen et al., 2013). Nevertheless, our modeling results can qualitatively be compared with Sefton-Nash et al. (2013)'s analysis of the seasonal variation of Martian high-altitude clouds. The observations show that during Northern Hemisphere summer, clouds formed in the mesosphere more rarely than during perihelion and were located mainly around the Equator. Previous analysis of the data from the Thermal Emission Spectrometer (TES) onboard the Mars Global Surveyor (MGS) (Clancy et al., 2007) also indicated that cloud occurrences were confined to a narrow latitude sector of $\pm \mathrm{15}{}^{\circ }$ during the aphelion season (L_s=30–150^∘). In agreement with observations, our simulations show higher probabilities of cloud formation in low latitudes throughout all seasons (Fig. 5g). The latter is simply a consequence of the temperature minimum near the equatorial mesopause. The model reproduces more favorable conditions for CO₂ condensation in the mid-latitude regions during wintertime. It agrees with observations in that mesospheric clouds occur more frequently during perihelion (Fig. 5g). Cold pockets with supersaturated temperatures occur in the model only in less than 10 % of the time at ∼80 km, but their probabilities grow with height. At 100 km, maxima of P of up to ∼18 % are seen in middle latitudes of the summer hemispheres (Fig. 5h), while higher up at ∼120 km these maxima exceed ∼30 % and shift poleward (Fig. 5i). Such behavior is due to growth with height amplitudes of GWs and the associated temperature fluctuations (Fig. 5a–c). The shift of maxima of cloud probabilities first to middle and then to high latitudes is caused by the cold anomaly of the mean temperature, which is induced by GWs in the mesosphere. The similar GW-induced cold summer mesopause anomaly is well known in the atmosphere of Earth (Garcia and Solomon, 1985).

There are certain disagreements between the modeled cloud formation probabilities and existing observations at high altitudes (80 km and above). In particular, the dayside observations of Sefton-Nash et al. (2013) demonstrate a greater symmetry with respect to the equatorial distribution of CO₂ clouds during the first part of the year. They do not show a “pause” near the equinox around $L_{\mathrm{s}}=\mathrm{180}{}^{\circ }$, which is clearly seen in Fig. 5h, f. It is worth noting that the superposition of the simulated patterns at 80 and 100 km is close to the superposition of the observed night and day patterns (Sefton-Nash et al., 2013) attributed to the 80 km altitude. Finally, there is no statistically significant observational support for the predicted cloud formation probability above 80 km. We, therefore, discuss possible reasons and shortcomings of the modeling methodology.

One source of uncertainty in our simulations is the assumed degree of supersaturation, which is currently 35 % based on previous experimental constraints (Glandorf et al., 2002). However, a variable with a height supersaturation threshold is possible, which could modulate P in our numerical experiments. This variable threshold may reflect the microphysics of cloud formation, which implies an existence of nuclei and strong dependence on their sizes. It is likely that the existence of cold pockets (the necessary condition for cloud formation) is far from sufficient for clouds to form, especially in the upper atmosphere. Thus, the lack of nuclei in the upper atmosphere may prevent cloud formation. If formed, ice particles must be small (being of submicron size) and clouds are too thin to be previously detected.

In all our simulations, only probabilities of GW-induced clouds were calculated and, thus, no radiative effects of such clouds were taken into account. Such radiative feedback has been considered, for example, in the work by Siskind and Stevens (2006) in the Earth context. However, one can expect that, given that IR CO₂ and GW thermal effects together dominate the energy budget of the mesosphere (Medvedev et al., 2015), secondary radiative processes are likely to play a relatively minor role in the cloud formation by producing local modulations of temperature. A more comprehensive examination of the radiative feedback processes in the Martian environment would require a two-way coupling between microphysics and small- and large-scale dynamics. Interestingly, using a one-dimensional radiative–convective model, Mischna et al. (2000) demonstrated that the lower atmospheric CO₂ clouds have a potential to produce an additional cooling of the Martian surface by reflecting the incoming solar radiation. A further source of uncertainty is the use of a one-dimensional atomic oxygen profile, which may affect neutral temperatures.

An obvious candidate for explaining mismatches between the modeling and observations is the specification of sources in the GW parameterization. In the simulations, we assumed a globally uniform and constant-with-time distribution of GW momentum fluxes. The magnitudes of the fluxes were chosen from observations to capture the “background” effect of small-scale waves, as described in detail in our earlier works (Medvedev et al., 2011a, b). Recently, using a high-resolution Martian GCM, Kuroda et al. (2015, 2016) have shown a strong seasonal and latitudinal variation of GW momentum fluxes in the lower atmosphere and, as a result, significant variations of GW-induced activity in the middle atmosphere. Constraining wave sources is a logical next step in model development, which can potentially improve simulations of clouds.

Finally, other limitations in the model can result in imperfections with the simulated mean fields and, as a consequence, erroneous estimates of cloud formation probability P. The reviewer suggested that accounting for radiative effects of water clouds and for a more realistic dust scenario (mainly associated with its vertical distribution) may affect the simulated P. These and other undertaken paths of MGCM sophistication, like self-consistent modeling of water and aerosol cycles, can potentially bring observations and simulations of CO₂ clouds closer.

Upon request, the data used for the publication of this research are available from Erdal Yiğit (eyigit@gmu.edu).

EY performed the simulations and wrote a substantial portion of the paper. ASM significantly contributed to writing and analysis of research results. PH contributed to the discussion of results.

The authors declare that they have no conflict of interest.