1. Introduction
The Martian atmosphere is affected by several asymmetries not present in the terrestrial one. One such asymmetry, referred to as the topographic dichotomy, is that the zonally averaged surface topography is at higher elevation in the Southern Hemisphere than the Northern Hemisphere (Fig. 1). Another asymmetry exists because of Mars’ relatively eccentric orbit (the Martian orbital eccentricity is 0.0934 whereas the terrestrial is 0.0167), which causes the solar insolation to differ by 44% between perihelion and aphelion. Since Southern Hemisphere summer is near perihelion and thus Northern Hemisphere summer is near aphelion, the solar insolation varies greatly between the solstices. Atmospheric dust, important radiatively, also shows a strong seasonal variation, with Southern Hemisphere spring and summer as the favored seasons for large-scale dust storms (Kahn et al. 1992).
Haberle et al. (1993) noted a factor of 2 difference in Hadley cell intensity between the two solstices using the National Aeronautics and Space Administration (NASA) Ames Mars general circulation model (MGCM), which they attributed to the variation in the solar constant between these two seasons. However, Joshi et al. (1995) found that when the solar forcing was held constant between the two seasons, a factor of 1.5 difference in Hadley cell intensity was still present in the Oxford “intermediate” MGCM simulations. Wilson and Hamilton (1996) observed with the Geophysical Fluid Dynamics Laboratory (GFDL) MGCM that the zonal mean component of topography inhibited Hadley cell intensity during Northern Hemisphere summer. Haberle et al. (1993) and Basu et al. (2006) remarked on the sensitivity of the Martian Hadley circulation to off-equatorial heating. Basu et al. (2006) also found that the relative strength of the circulation at the opposite solstices depends on dust loading.
Webster (1977) realized that elevated regions on Mars may act as heat sources for the adjacent atmosphere because the (nondusty) Martian atmosphere is effectively transparent to solar radiation. Two recent studies have focused on the effects of the north–south slope in the zonally averaged topography on the Hadley circulation. Richardson and Wilson (2002) noted in the GFDL MGCM results that the annually averaged zonal mean circulation contained a stronger Northern Hemisphere Hadley cell, which also extended southward across the equator. They performed two further experiments in which the argument of perihelion was shifted by 180° (to test the effect of seasonal differences in the strength of the solar forcing) and in which the zonal mean component of topography was removed (leaving only the mountain or “wave” component). The removal of the zonal mean component of topography created two cells of nearly equal strength and shape, while the shift in the argument of perihelion produced little change from the full MGCM run. These results suggest that the north–south slope in topography is important, but the strength of the solar forcing is secondary.
Similarly, Takahashi et al. (2003) found that in their own MGCM results at equinox the northern cell was stronger than the southern and extended across the equator into the Southern Hemisphere. They conducted three runs at perpetual equinox in which variations in only one of the following were included: topography, surface thermal inertia, and surface albedo. The runs with either surface thermal inertia only or surface albedo only did not match the control run with all three parameters, but the run with topography did. Two subsequent experiments in which either only the zonal mean component of topography or only the zonal wave component were included showed that—as in the study by Richardson and Wilson (2002)—the zonal mean component of topography is the dominant factor in causing an asymmetric Hadley circulation.
Both Richardson and Wilson (2002) and Takahashi et al. (2003) concluded that the cause of the asymmetry was an upslope (i.e., southward) shift in the peak heating. Takahashi et al. (2003) went on to state that the convective heating term was the main influence in this shift. In this paper, we expand the analysis of the effects of convection and the north–south topographic slope to include other seasons, most notably the solstices. We also not only use a simple MGCM, but also apply a modified version of the Hadley cell model of Lindzen and Hou (1988) that includes the effects of topography. To drive both of these models, we use a simple radiation scheme that assumes a gray atmosphere and no dust. While some aspects of the Martian atmosphere may be poorly represented by this assumption, we show that it captures the important aspects of Hadley cell dynamics in section 4d by comparing our scheme with the GFDL MGCM, which contains a nongray radiation scheme. The gray radiation scheme has the advantage of being analytical [such that it can be used in the modified Lindzen and Hou (1988) model] and it allows us to formulate a conceptually simple description of Hadley cell dynamics in the presence of a north–south slope.
In section 2, we develop the simple radiative transfer model that we use to calculate equilibrium temperature. The effects of convection are included in our radiative–convective model but are not included in our “pure” radiative model. The equilibrium temperatures are used in section 3, where we derive a model based on Lindzen and Hou (1988) that predicts the latitude of the dividing streamline and the poleward extent of the Hadley cells in the presence of nonzero topography. We use this model to solve for the boundaries of the Hadley cells with and without the zonal mean component of topography and also explicitly as a function of season [recall that Richardson and Wilson (2002) concentrated their study on the annual average, and Takahashi et al. (2003) focused on the equinox]. In section 4 we present a simple MGCM and compare it to the modified Lindzen and Hou (1988) model in section 5.
2. Calculation of equilibrium temperature
Figures 2 and 3 show zonally averaged Teq,R and Teq,RC given by (1) and (3), respectively, for Ls = 0°, Ls = 90°, and Ls = 270°. The following three topographies are considered: flat topography at zero elevation (“flat”), Mars Orbiter Laser Altimeter (MOLA) topography (“full”; Fig. 4a), and zonal mean MOLA topography (“mean”; Fig. 4b). For the pure radiative case, Teq does not vary between the different topographies—it is as if the surface has been pasted onto the temperature profile. Conversely, the surface modifies the equilibrium temperature aloft in the radiative–convective case. The equilibrium temperature contours appear to be pushed up by the higher surface, changing the meridional temperature gradient so that the equilibrium temperature is higher above an elevated surface.
Our values for Teq,R (and hence Teq,RC) at high altitudes (not shown) are warmer and more isothermal than the corresponding values for Teq,RC plotted in Joshi et al. (1995) and Haberle et al. (1997). While these authors use different radiative transfer models, the discrepancy is likely a result of the choice of τoo and the gray atmosphere assumption, which is not fully accurate for Mars. Hinson et al. (2008) observed in radio occultation data that the depth of the mixed layer varies with elevation, an effect that is not captured in our model. Caballero et al. (2008) derive a radiative–convective model for a semigray atmosphere, which they apply to Mars. Their predicted height of the convective layer in σ coordinates (p/poo) is 0.44 (cf. our value of 0.51 for flat topography).
Figure 5 shows Teq,R and Teq,RC at a constant pressure level of 3.8 hPa or 5-km log pressure height, which is within the convective layer. It is evident that topography changes the meridional gradient of Teq,RC (cf. the heavy solid and heavy dashed lines). For flat topography, Teq,RC is offset to a higher temperature from Teq,R because in the former convection acts to redistribute heat from the surface into the convective layer. In pure radiative equilibrium, a temperature discontinuity exists between the surface and the atmosphere directly above the surface. The radiative–convective equilibrium temperature profile follows a dry adiabat that is continuous with the surface temperature.
Figure 6 shows a diagram of the two different types of Teq. The gray and black curve is the pure radiative equilibrium solution for Teq as a function of pressure and is the same regardless of surface height. If the surface is located at some elevation po, located at the level of the solid black horizontal line, then the equilibrium surface temperature is given by Tg (black text). If the surface is then located at some higher elevation (lower pressure), represented by the solid gray horizontal line, the equilibrium surface temperature (Tg in gray text) will decrease because of the reduced greenhouse effect. In an optically thin atmosphere such as Mars, however, this effect is extremely small, and the surface temperature can be considered independent of surface height.
The dashed lines in Fig. 6, drawn for both surface elevations, represent adiabats calculated such that the convective layer remains in energy balance with the rest of the atmosphere. Comparing the radiative–convective equilibrium temperatures at some pressure level pa within the convecting layer shows that they are higher above the elevated surface than over the lower surface. The radiative–convective equilibrium temperature profiles are being evaluated at different relative heights above the local surface (the primary heating element for the atmosphere), which dominates over the reduced greenhouse effect at the higher altitude. In this way, the height of the surface modifies the heating profile of the lower atmosphere. Moreover, the change in surface temperature due to the reduced greenhouse effect at higher elevations is again negligible, varying by less than 3 K for a difference in elevation of 5 km.
3. Hadley cell model with topography
Held and Hou (1980) derived a model of the steady, nearly inviscid, Boussinesq, axisymmetric, Hadley circulation in the absence of eddies. Diabatic heating was represented by Newtonian relaxation of temperature at a uniform rate α toward a prescribed distribution of equilibrium temperature θe, which in their case was symmetric about the equator. Through consideration of the constraint of angular momentum conservation, they showed that the Hadley cell is confined to a finite region about the equator; poleward of the edge of the cell, there is no meridional circulation, and temperatures are in radiative equilibrium. Using simple arguments, they were able to solve for the location of the cell edge and other characteristics of the circulation.
Lindzen and Hou (1988) solved the problem in the nonsymmetric case, where the imposed equilibrium temperature maximum is located on the summer side of the equator. They found strong sensitivity—with only a modest shift of the peak of θe off the equator, the rising branch of the circulation shifted much further, and the resulting cross-equatorial cell is much stronger than the opposite cell in the summer hemisphere. Recently, Caballero et al. (2008) revised the Lindzen and Hou (1988) result using a more sophisticated, semigray specification of equilibrium temperature. Their radiation scheme assumed a CO2-like absorber, where absorption is zero everywhere outside of a narrow band at a single wavelength. Given the appropriate radiation parameters (i.e., total broadband optical depth, pressure broadening, and equivalent bandwidth), they derive an analytical solution for the Hadley cell width, depth, energy transport, and mass flux.
The choice of h, taken to be the height of the tropopause on Earth, is not obvious for Mars. If the tropopause is defined as the level where the static stability changes drastically, no clear transition exists analogous to the terrestrial troposphere and stratosphere. The tropopause could also be defined as the level to which convection penetrates in radiative–convective equilibrium, but this definition excludes the pure radiative case. While work with MGCMs has shown that the Martian circulation extends to the mesopause, the mesopause hardly seems like a good definition since most of the mass transport in the Hadley cells is well below this level. Since in our simple MGCM (section 4) 50% of the mass flux is typically located below 15 km, we adopt that value for h.
Since the theory is assumed to be axisymmetric, only two of the topographies described above are relevant here: flat and zonal mean MOLA topography. The value of θe in (21) is evaluated using either the pure radiative equilibrium temperature given by (1) or the radiative–convective equilibrium temperature given by (3), recalling that the temperature must remain above the CO2 frost temperature.
Returning to (16)–(19), Fig. 9 shows the solutions for ϕ+, ϕ1, and ϕ− for each of the two topographies with pure radiative or radiative–convective forcing and physical constants appropriate for Mars. The solutions for flat topography for pure radiative and radiative–convective forcing are nearly equal, such that they lie on same curve in Fig. 9. Hadley cells are most sensitive to the meridional gradient in equilibrium temperature, which is purely a consequence of the meridional gradient in solar heating in the absence of topography. Since the meridional gradient in solar heating is the same for both radiative forcings [cf. (1) and (3)], their solutions are expected to be similar.
For flat topography at equinox, symmetric cells are obtained, which agrees with the limit of Held and Hou (1980). When topography is added in the pure radiative case, ϕ1 is shifted slightly upslope, while the poleward boundary of the winter cell (ϕ+ for 270° < Ls < 360° and ϕ− for 0° < Ls < 90°) shifts downslope. The deviations from the flat topography case may be attributed as the result of integrating over a different vertical range (zb to h instead of 0 to h).
For the case of radiative–convective forcing and zonal mean MOLA topography, ϕ1 is shifted a significant distance upslope, which qualitatively agrees with previous MGCM results. Again the poleward boundary of the winter cell shifts downslope, but the boundary of the summer cell (ϕ− for 270° < Ls < 360° and ϕ+ for 0° < Ls < 90°) shifts upslope. The large shift in the solution compared with the other cases is a result of the thermal effects of the slope on θe. Differential convective heating aloft associated with the slope moves the latitude of maximum equilibrium temperature upslope and away from the subsolar latitude. This change in the location of the maximum equilibrium temperature causes the boundaries of the cells to move relative to the cases with zero topography or without convective forcing.
4. Experiments with a simple MGCM
a. Description of the MIT MGCM
We have converted the Massachusetts Institute of Technology (MIT) GCM to physical constants appropriate for the Martian atmosphere, which is assumed to be entirely CO2 and to contain no dust. The dynamical core of the MIT GCM solves the fundamental equations of geophysical fluid dynamics in the hydrostatic approximation using the finite volume method on an Arakawa C grid (Marshall et al. 1997). The default configuration has no viscosity or vertical diffusion but uses an eighth-order Shapiro filter to remove gridscale noise. The horizontal configuration is a cube–sphere grid (Adcroft et al. 2004) with 32 × 32 points per cube face, equivalent to a resolution of 2.8° or 166 km at the equator. Note that the resolution of the MOLA dataset is 1/64° latitude × 1/32° longitude (Smith et al. 2001), which exceeds the horizontal resolution for the simple MGCM.
The vertical grid uses an η coordinate (Adcroft and Campin 2004) with 30 levels, and the grid spacing increases approximately logarithmically with height. Zero elevation corresponds to a pressure of 6 hPa (the observed annual and global average value), which is also used as a reference pressure elsewhere in our calculations. The top level is centered at a pressure of 0.000117 hPa, which corresponds to a log pressure height of 119 km (using the reference pressure above and a scale height of 11 km). This is above the level where nonlocal thermodynamic equilibrium effects may become important (López-Valverde et al. 1998). We do not treat the top levels as realistically modeling the atmosphere in that region, since a sponge layer is also located in the upper levels (described below). Within each vertical level intersecting the surface, the resolution of the topography is increased by inserting subgrids spaced at 10% of the full vertical grid spacing at that level (Adcroft et al. 1997).
b. Experiments
Each experiment was run at constant Ls for the following seasons: Ls = 0°, Ls = 90°, and Ls = 270°. Given the short radiative time scale of the Martian atmosphere (2 sols) and the lack of oceans with high heat capacity, the atmosphere is expected to respond quickly to changes in radiative forcing compared with the length of a season (one quarter of the Martian year or 167 sols). As such, it was unnecessary to integrate the model over several years to achieve a seasonal equilibrium. The model was run for a total of 180 sols or 6 Martian months, where a Martian month is defined to be 30 sols, and was fully spun up from an initial rest state with Teq = 200 K everywhere by the end of the second Martian month. A visual inspection of the zonally and monthly averaged results (i.e., potential temperature, horizontal and vertical velocities, and surface pressure) showed little variation from month to month after the initial spinup.
Figures 10 and 11 show the simple MGCM results for zonally averaged mass streamfunction time averaged for sols 60–180 when forced with the pure radiative equilibrium temperatures (Fig. 2) and radiative–convective equilibrium temperatures (Fig. 3), respectively. With pure radiative forcing, equinox conditions (Ls = 0°), and flat topography (Fig. 10a), the cells are quite symmetric about the equator. When the north–south sloping component of topography is added (i.e., full and mean topographies; Figs. 10d and 10g, respectively), the dividing streamline protrudes slightly into the Southern Hemisphere, but its maximum extent is not past −5°. A slight asymmetry between the strengths of the northern and southern cells develops. For Ls = 90° and pure radiative forcing (Figs. 10b,e,h), no significant difference arises between the three topographies. The same occurs at Ls = 270° (Figs. 10c,f,i).
When convective forcing is allowed, a substantial difference arises at equinox between experiments without the north–south sloping component of topography (i.e., flat; Fig. 11a) and with it (i.e., full and mean; Figs. 11d and 11g, respectively). The flat topography produces symmetric cells, whereas the full and mean produce a stronger northern cell and shift the latitude of the dividing streamline to about −15° in the lower atmosphere (cf. about −20° in Takahashi et al. 2003). At Ls = 90°, the cross-equatorial Hadley cell is stronger when the north–south sloping component is removed (cf. Fig. 11b with Figs. 11e,h). At Ls = 270° the correlation with the presence of the north–south sloping component of topography is less apparent (cf. Figs. 11c,f,i).
c. Comparison of Hadley cell strengths
With pure radiative forcing, the strength of the Hadley cells at a given season varies little among the different topographies and does not appear to be correlated with the presence of the north–south slope. A much different scenario arises for radiative–convective forcing. Figure 12 shows the maximum magnitude of the zonally and time-averaged streamfunction from each of the simple MGCM experiments with radiative–convective forcing. Specifically, the maximum magnitude within each thermally direct cell above the boundary layer is plotted for each topography (black symbols).
For flat topography, the strengths of the northern and southern cells are symmetric at equinox, and the strengths at the opposite solstices are equal. For mean topography, at equinox the northern cell is enhanced, while the southern cell is reduced. It is generally recognized from theory (e.g., Lindzen and Hou 1988) and terrestrial observations (e.g., Peixoto and Oort 1992, their Fig. 7.19) that moving the latitude of maximum equilibrium temperature off the equator (as occurs because of changing seasons) produces a weak cell in the same hemisphere as the maximum and a strong cell that spans both hemispheres. The farther the maximum equilibrium temperature moves off equator, the more pronounced this effect becomes.3 If the north–south slope is acting to shift the maximum equilibrium temperature upslope, as indicated by Figs. 3g and 5a, then at equinox a stronger northern cell and weaker southern cell are expected for the mean topography case.
For flat topography at Ls = 90°, the maximum equilibrium temperature is shifted far northward (Figs. 3b and 5b), producing no summer cell at all and a strong winter cell. For mean topography, the strength of the cell is reduced as compared with flat topography. For flat topography at Ls = 270°, the latitude of maximum equilibrium temperature is shifted far southward, producing a strong “winter” cell in the opposite sense as at Ls = 90°. However, the addition of zonal mean topography at Ls = 270° does not change the strength of the cell as significantly as at Ls = 90°.
Evidently, a circulation that flows downslope near the surface causes the Hadley cells to lose strength, but that strength is not regained for an upslope flow. This phenomenon further comes into play in comparing full topography and mean topography. In Fig. 12, the strengths for full topography are always less than the strengths for mean topography at the corresponding season. As the circulation flows up and down the mountains and valleys, strength is lost as the air flows downward along the topography but not regained when it flows upward. This diminishing is observed when comparing flat and “wave” (i.e., full topography minus zonal mean; not shown) topographies. For full topography, this mountain effect is superimposed onto the effect (if any) of the mean sloping component. The effect is associated with the radiative–convective forcing, as runs with pure radiative forcing show little difference in Hadley cell intensity for any topography.
d. Comparison with the GFDL MGCM
To demonstrate that our simple radiation scheme captures the effect of topography on the Martian Hadley cell, we compare our simple MGCM results to the GFDL MGCM, which uses a full (nongray) radiation scheme. The GFDL MGCM was originally based on the GFDL SKYHI terrestrial GCM and an early version of the model has been described in Wilson and Hamilton (1996). Subsequent descriptions appear in Richardson and Wilson (2002) and Hinson and Wilson (2004). This model has been used to examine tides and planetary waves (Wilson and Hamilton 1996; Hinson and Wilson 2002; Wilson et al. 2002; Hinson et al. 2003), the water cycle (Richardson and Wilson 2002; Richardson et al. 2002), the dust cycle (Basu et al. 2004, 2006), and cloud radiative effects (Hinson and Wilson 2004; Wilson et al. 2007, 2008). More recently, the physical parameterizations have been adapted to the GFDL Flexible Modeling System (FMS), which includes a choice of dynamical cores [finite difference, finite volume (FV), and spectral] and associated infrastructure. The Mars physics has been tested with all three dynamical cores and we have elected to use the finite volume model.
The model uses the radiation code developed and used by the NASA Ames Mars modeling group (Kahre et al. 2006, 2008). This code is based on a two-stream solution to the radiative transfer equation with CO2 and water vapor opacities calculated using correlated-k values in 12 spectral bands ranging from 0.3 to 250 microns. The two-stream solution is generalized for solar and infrared radiation, with scattering based on the δ-Eddington approximation at visible wavelengths and the hemispheric mean approximation at infrared wavelengths (Toon et al. 1989). The model has been validated with other MGCMs and the available data, and we consider it to be a robust representation of the Martian atmosphere.
Simulations using the GFDL MGCM were carried out with 5° latitude × 6° longitude horizontal resolution and 46 levels. Simulations were run for 50 sols. The CO2 condensation cycle was turned off, such that atmospheric mass remained constant with a global mean surface pressure of 6 hPa. Orbital eccentricity was set to zero to eliminate differences in the solar constant between the two solstice seasons, thus highlighting the asymmetric influence of the topography. Surface albedo and surface thermal inertia were held constant at 0.15 and 350 J m−2 s−1/2 K−1, respectively. Column dust opacity was set to a globally uniform value of 0.3, a low-dust setting. The topographies considered were flat and had idealized zonal mean topography [given by (34)] with β = 20.
Figure 15 shows the results from the GFDL MGCM with (top) flat topography and (bottom) idealized zonal mean topography for Ls = (left) 90° and (right) 270°. The results shown are a 10-sol average centered on the solstices. At Ls = 90°, the addition of zonal mean topography suppresses the maximum strength of the Hadley cell by 55%, whereas at Ls = 270° the addition of zonal mean topography strengthens the cell by only 109%. The qualitative agreement with Figs. 13 and 14 indicates that the simplifications to the simple radiation scheme (section 2) are not centrally important. Additionally, experiments (not shown) with the GFDL MGCM were performed with the same idealized topography used in Figs. 13 and 14. These experiments again showed that the Hadley cell strength at Ls = 90° is sensitive to the steepness of the topographic slope but shows little response to the slope at Ls = 270°.
Quantitative differences in Hadley cell strengths between the simple MGCM and the GFDL MGCM are due to fundamental differences in the radiation schemes. The Hadley cell strengths in the simple MGCM are sensitive to the values used for τoo and kt. The simple radiation code also fails to produce a difference in the Hadley cell strengths at the opposite solstices for flat topography. The eccentricity of the Martian atmosphere creates a large difference in the solar constant; with more energy input into the atmosphere, the Hadley cells ought to be stronger. On the other hand, the boundaries of the cells are in quantitative agreement between the simple and GFDL MGCMs and are less sensitive to the particular aspects of our radiation scheme. This fact, along with qualitative agreement in the behavior of Hadley cell strengths between the two models, lends sufficient credibility to our simple radiation scheme.
e. Comparison with previous simulations
As wind data for the Martian atmosphere above the boundary layer are extremely sparse compared to those for Earth, we are left to compare the simple MGCM streamfunction results with previous models. The results for streamfunction strength from the MGCM of Takahashi et al. (2003) are also plotted in Fig. 12 (gray symbols). Comparison of mean and full topographies at equinox shows that that the northern cell is stronger for the mean topography case, in agreement with our results. Quantitatively, our simple MGCM predicts a weaker cell for full topography at Ls = 270°, a stronger cell for full topography at Ls = 90°, and a weaker northern cell for full and mean topographies at equinox. Quantitative disagreement between the two models arises from differences in the radiation schemes between our model and that of Takahashi et al. (2003).
Finally, Joshi et al. (1995) stated that the Hadley cell at Ls = 270° was a factor of 1.5 stronger than at Ls = 90° in their “intermediate” global circulation model (based on the Oxford MGCM), which most closely corresponds to our radiative–convective forcing and full topography. Our simple MGCM also yielded a factor of ∼1.5 for this setup, whereas Takahashi et al. (2003) obtained a factor of ∼3. Joshi et al. (1995) also noted that the effect was still observed even when solar insolation was kept constant for both seasons. However, they speculated that an enhanced circulation at Ls = 270° occurred because the rising branch is located in an area of lower pressure (i.e., higher elevation) and did not attribute the difference to the thermal affects of the slope.
5. Comparison of MGCM and modified Lindzen and Hou (1988) models
Figure 16 shows the solution to the modified Lindzen and Hou (1988) model replotted so that ϕ+, ϕ1, and ϕ− for each topography and radiative forcing are displayed together. It is now apparent that as Ls approaches 90° and 270°, ϕ1 approaches the boundary of the summer cell in the summer hemisphere. The physical implication is that the summer cell disappears, which is what is observed in the simple MGCM results (Figs. 10 and 11). Also plotted in Fig. 16 are the values for ϕ+, ϕ1, and ϕ− determined from the MGCM results for the appropriate topographies, seasons, and radiative forcings, including some runs at seasons not discussed in section 4.
The boundaries of the Hadley cells in the simple MGCM results are computed as follows. For each thermally direct cell (one near solstice, two near equinox), the maximum magnitude of the zonally averaged mass streamfunction (above the boundary layer) is found. Then, at the same pressure level as each maximum, the latitude where the streamfunction falls to within 1% of its maximum value is located. The northernmost 1% latitude is ϕ+ and the southernmost is ϕ−. When there is one thermally direct cell, ϕ1 is equal to whichever of ϕ+ or ϕ− is in the summer hemisphere. When there are two thermally direct cells, the average of the two innermost 1% latitudes is taken to be ϕ1. Interpreting the boundaries of the cells from the simple MGCM results can be difficult because in some cases the latitude of the boundary varies with height (e.g., at the boundary in the winter hemisphere at solstice). Also, particularly near equinox on the poleward sides of the cells, multiple 1% latitudes may exist when closed areas of circulation in the opposite direction appear within the thermally direct cell. In this case the innermost 1% latitude is used. Near the solstice, the streamfunction in the summer hemisphere decreases very gradually, which causes the value derived for the boundary to vary slightly depending on the cutoff percentage used (e.g., 1% versus 0.1%).
From Fig. 16, the agreement of ϕ1 between the simple MGCM results and the modified Lindzen and Hou (1988) model is generally good. The solutions for the poleward boundary of the summer cell agree for pure radiative forcing, but the simple MGCM results are offset in the equatorward direction for radiative–convective forcing. The solutions for the poleward boundary of the winter cell do not agree. The simple MGCM results are offset equatorward, and they do not follow the same shape as the modified Lindzen and Hou (1988) model solution. One possible explanation is that in the simple MGCM results the latitudinal boundary of the winter cell varies with height, and in fact extends further poleward at higher altitudes. Another explanation is that the simple MGCM contains eddies, whereas the Lindzen and Hou (1988) model does not, on account of its axisymmetric nature.
Since the modified Lindzen and Hou (1988) model is axisymmetric, it is perhaps more sensible to compare it to an axisymmetric MGCM. We ran our simple MGCM in axisymmetric mode, where the cube–sphere geometry was replaced by grid points evenly spaced at 2.8° of latitude along a single strip of longitude of width 2.8°. When vertical diffusion of momentum was not included, inertial instabilities developed in the tropics that made it impossible to determine ϕ1 near equinox. Adding a constant diffusion of 0.0005 Pa2 s−1 everywhere resolved ϕ1 but induced a Ferrel cell.
Figure 17 shows a plot of the modified Lindzen and Hou (1988) model solutions as in Fig. 16 but with the axisymmetric simple MGCM results instead of the full 3D simple MGCM. The discrepancy in the poleward boundary of the winter cell remains, possibly due to the Ferrel cell created by adding diffusion. In runs without diffusion, the poleward boundary of the winter cell extends nearly to the winter pole, in agreement with the modified Lindzen and Hou (1988) results.
Figure 18 shows the three terms in (36) calculated from the simple MGCM results with radiative–convective forcing and full topography at Ls = 0°, 90°, and 270°. Within the Hadley cells, the planetary term is balanced by the meridional transport by the steady mean circulation during the solstices. At equinox, all three terms are small within the Hadley cells. Outside the Hadley cells, the meridional transport by spatial eddies nearly balances the planetary term. The presence of eddies near the poleward boundary of the Hadley cell, together with the fact that the axisymmetric simple MGCM runs without diffusion (i.e., no spatial eddies), shows better agreement with the Lindzen and Hou (1988) model and suggests that by driving the extratropical Ferrel cell, eddies may be important in determining the poleward boundaries of the Hadley cells at equinox and in the winter hemisphere at the solstices.
Walker and Schneider (2006) showed in idealized GCM simulations that the strength of the Hadley cell is related to the eddy momentum flux divergence. In Fig. 18, the spatial eddy term is greater in the northern (winter) hemisphere at Ls = 270° than in the southern (winter) hemisphere at Ls = 90°. This effect is also seen our simple MGCM simulations with flat topography. Eddies may also be important in addition to the topography in determining the seasonal asymmetry in Hadley cell strength.
6. Discussion and conclusions
We have continued the investigation of the effect of a latitudinally varying slope on the Martian Hadley cells initiated in detail by Richardson and Wilson (2002) and Takahashi et al. (2003). The problem was approached by revising the Hadley cell model of Lindzen and Hou (1988) to include topography, which allowed us to solve for the latitudinal boundaries of the cells. This theory was compared with the results from a simple MGCM. Both models were thermally forced using Newtonian relaxation to one of two equilibrium temperature states: one that included the effects of convection and one that did not. In the case of the latter, almost no dependence on the topography was observed in either model. When convective forcing was allowed, both models predicted that the latitude of the dividing streamline is shifted upslope at equinox. The effect of the slope on the radiative–convective equilibrium temperature aloft was found to dominate over the geometrical effects of the slope.
From the simple MGCM results, an analysis of the strengths of the Hadley cells was carried out. At equinox with radiative–convective forcing, the presence of the slope strengthens the southern cell and weakens the northern cell as the latitude of maximum equilibrium temperature moves upslope. At Ls = 90° with radiative–convective forcing, the cross-equatorial cell is weakened with sloping topography; at Ls = 270°, the strength of the cell is independent of slope. Further experiments with idealized zonal mean topography showed that as the steepness of the slope is increased, the strength of the cell decreases at Ls = 90°.
A discrepancy arose between our simple MGCM and the modified Lindzen and Hou (1988) model results regarding the latitude of the poleward boundary of the Hadley cell in the winter hemisphere around the solstice seasons. This difference could be caused by eddies, since the simple 3D MGCM allows for their presence but the Lindzen and Hou (1988) model does not. Axisymmetric simple MGCM runs without diffusion and hence without eddies produced better agreement with the modified Lindzen and Hou (1988) model. A breakdown of the momentum budget showed that the spatial eddies are relatively weak within the Hadley cells at the solstices but that eddies are relatively strong outside the Hadley cells. Eddies are stronger during northern winter (Ls = 270) than southern winter (Ls = 90°). Eddies may play a role in determining the strengths and poleward boundaries of the Hadley cell, as also suggested by Walker and Schneider (2006) in idealized GCM runs.
Molnar and Emanuel (1999) considered the radiative–convective equilibrium case when absorbers, namely water vapor, are present within the atmosphere. In the limit in which the atmosphere is opaque to solar radiation, the temperature at any level aloft becomes independent of the height of the surface. The Molnar and Emanuel (1999) study may be applicable to periods when the Martian atmosphere is experiencing very dusty conditions (Viking Lander 1 measured optical depths in excess of 4 during a dust storm; Colburn et al. 1989), since atmospheric dust is a strong absorber. Basu et al. (2006) showed with the GFDL MGCM that as dust optical depth increases, the ratio of the streamfunction maximum at Ls = 270° to Ls = 90° decreases, which implies that dust inhibits the effect of the slope. It would be interesting to use the modified Lindzen and Hou (1988) model to study the effects of increased dust on the Hadley cell boundaries, provided the appropriate changes could be made to our radiation scheme.
Acknowledgments
We thank Jonathan Mitchell, Jude Sabato, and an anonymous reviewer for providing valuable comments. We thank Andrea Molod and Jean-Michel Campin for their assistance with the MIT GCM. A. M. Zalucha was supported in part by NSF Grant ATM-0436288 and NASA Grant NNG05GB65G.
REFERENCES
Adcroft, A., and J-M. Campin, 2004: Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models. Ocean Modell., 7 , 269–284.
Adcroft, A., C. Hill, and J. Marshall, 1997: Representation of topography by shaved cells in a height coordinate ocean model. Mon. Wea. Rev., 125 , 2293–2315.
Adcroft, A., J-M. Campin, C. Hill, and J. Marshall, 2004: Implementation of an atmosphere–ocean general circulation model on the expanded spherical cube. Mon. Wea. Rev., 132 , 2845–2863.
Basu, S., M. I. Richardson, and R. J. Wilson, 2004: Simulation of the Martian dust cycle with the GFDL Mars GCM. J. Geophys. Res., 109 , E11006. doi:10.1029/2004JE002243.
Basu, S., J. Wilson, M. Richardson, and A. Ingersoll, 2006: Simulation of spontaneous and variable global dust storms with the GFDL Mars GCM. J. Geophys. Res., 111 , E09004. doi:10.1029/2005JE002660.
Caballero, R., R. T. Pierrehumbert, and J. L. Mitchell, 2008: Axisymmetric, nearly inviscid circulations in non-condensing radiative–convective atmospheres. Quart. J. Roy. Meteor. Soc., 134 , 1269–1285. doi:10.1002/qj.271.
Colburn, D. S., J. B. Pollack, and R. M. Haberle, 1989: Diurnal variations in optical depth at Mars. Icarus, 79 , 159–189. doi:10.1016/0019-1035(89)90114-0.
Haberle, R. M., J. B. Pollack, J. R. Barnes, R. W. Zurek, C. B. Leovy, J. R. Murphy, H. Lee, and J. Schaeffer, 1993: Mars atmospheric dynamics as simulated by the NASA Ames general circulation model. 1. The zonal-mean circulation. J. Geophys. Res., 98 , (E2). 3093–3123.
Haberle, R. M., H. Houben, J. R. Barnes, and R. E. Young, 1997: A simplified three-dimensional model for Martian climate studies. J. Geophys. Res., 102 , (E4). 9051–9067.
Held, I. M., and A. Y. Hou, 1980: Nonlinear axially symmetric circulations in a nearly inviscid atmosphere. J. Atmos. Sci., 37 , 515–533.
Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75 , 1825–1830.
Hess, S. L., J. A. Ryan, J. E. Tillman, R. M. Henry, and C. B. Leovy, 1980: The annual cycle of pressure on Mars measured by Viking Landers 1 and 2. Geophys. Res. Lett., 7 , 197–200.
Hinson, D. P., and R. J. Wilson, 2002: Transient eddies in the southern hemisphere of Mars. Geophys. Res. Lett., 29 , 1154. doi:10.1029/2001GL014103.
Hinson, D. P., and R. J. Wilson, 2004: Temperature inversions, thermal tides, and water ice clouds in the Martian tropics. J. Geophys. Res., 109 , E01002. doi:10.1029/2003JE002129.
Hinson, D. P., R. J. Wilson, M. D. Smith, and B. J. Conrath, 2003: Stationary planetary waves in the atmosphere of Mars during southern winter. J. Geophys. Res., 108 , 5004. doi:10.1029/2002JE001949.
Hinson, D. P., M. Pätzold, S. Tellmann, B. Häusler, and G. L. Tyler, 2008: The depth of the convective boundary layer on Mars. Icarus, 198 , 57–66. doi:10.1016/j.icarus.2008.07.003.
James, P., H. H. Kiefferand, and D. A. Paige, 1992: The seasonal cycle of carbon dioxide on Mars. Mars, H. H. Kieffer, Ed., University of Arizona Press, 934–968.
Joshi, M. M., S. R. Lewis, P. L. Read, and D. C. Catling, 1995: Western boundary currents in the Martian atmosphere: Numerical simulations and observational evidence. J. Geophys. Res., 100 , (E3). 5485–5500.
Kahn, R. A., T. Z. Martin, R. W. Zurek, and S. W. Lee, 1992: The Martian dust cycle. Mars, H. H. Kieffer, Ed., University of Arizona Press, 1017–1053.
Kahre, M. A., J. R. Murphy, and R. M. Haberle, 2006: Modeling the Martian dust cycle and surface dust reservoirs with the NASA Ames general circulation model. J. Geophys. Res., 111 , E06008. doi:10.1029/2005JE002588.
Kahre, M. A., J. L. Hollingsworth, R. M. Haberle, and J. R. Murphy, 2008: Investigations of the variability of dust particle sizes in the Martian atmosphere using the NASA Ames general circulation model. Icarus, 195 , 576–597. doi:10.1016/j.icarus.2008.01.023.
Lewis, S. R., P. L. Read, and M. Collins, 1996: Martian atmospheric data assimilation with a simplified general circulation model: Orbiter and lander networks. Planet. Space Sci., 44 , 1395–1409.
Lindzen, R. S., and A. Y. Hou, 1988: Hadley circulations for zonally averaged heating centered off the equator. J. Atmos. Sci., 45 , 2416–2427.
López-Valverde, M. A., D. P. Edwards, M. López-Puertas, and C. Roldán, 1998: Non-local thermodynamic equilibrium in general circulation models of the Martian atmosphere 1. Effects of the local thermodynamic equilibrium approximation on thermal cooling and solar heating. J. Geophys. Res., 103 , (E7). 16799–16811.
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102 , (C3). 5753–5766.
Molnar, P., and K. A. Emanuel, 1999: Temperature profiles in radiative–convective equilibrium above surfaces at different heights. J. Geophys. Res., 104 , (D20). 24265–24271.
Nayvelt, L., P. J. Gierash, and K. H. Cook, 1997: Modeling and observations of Martian stationary waves. J. Atmos. Sci., 54 , 986–1013.
Peixoto, J. P., and A. H. Oort, 1992: Physics of Climate. Springer, 520 pp.
Richardson, M. I., and R. J. Wilson, 2002: A topographically forced asymmetry in the Martian circulation and climate. Nature, 416 , 298–301.
Richardson, M. I., R. J. Wilson, and A. V. Rodin, 2002: Water ice clouds in the Martian atmosphere: General circulation model experiments with a simple cloud scheme. J. Geophys. Res., 107 , 5064. doi:10.1029/2001JE001804.
Showman, A., C. S. Cooper, J. J. Fortney, and M. S. Marley, 2008: Atmospheric circulation of hot Jupiters: Three-dimensional circulation models of HD 209458b and HD 189733b with simplified forcing. Astrophys. J., 682 , 559–576. doi:10.1086/589325.
Smith, D. E., and Coauthors, 1999: The global topography of Mars and implications for surface evolution. Science, 284 , 1495–1503.
Smith, D. E., and Coauthors, 2001: Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. J. Geophys. Res., 106 , (E10). 23689–23722.
Takahashi, Y. O., H. Fujiwara, H. Fukunishi, M. Odaka, Y-Y. Hayashi, and S. Watanabe, 2003: Topographically induced north–south asymmetry of the meridional circulation in the Martian atmosphere. J. Geophys. Res., 108 , 5018. doi:10.1029/2001JE001638.
Toon, O. B., C. P. McKay, T. P. Ackerman, and K. Santhanam, 1989: Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres. J. Geophys. Res., 94 , (D13). 16287–16301.
Walker, C. C., and T. Schneider, 2006: Eddy influences on Hadley circulations: Simulations with an idealized GCM. J. Atmos. Sci., 63 , 3333–3350.
Webster, P. J., 1977: The low-latitude circulation of Mars. Icarus, 30 , 626–649.
Wilson, R. J., and K. Hamilton, 1996: Comprehensive model simulations of thermal tides in the Martian atmosphere. J. Atmos. Sci., 53 , 1290–1326.
Wilson, R. J., D. Banfield, B. J. Conrath, and M. D. Smith, 2002: Traveling waves in the northern hemisphere of Mars. Geophys. Res. Lett., 29 , 1684. doi:10.1029/2002GL014866.
Wilson, R. J., G. A. Neumann, and M. D. Smith, 2007: Diurnal variation and radiative influence of Martian water ice clouds. Geophys. Res. Lett., 34 , L02710. doi:10.1029/2006GL027976.
Wilson, R. J., S. R. Lewis, L. Montabone, and M. D. Smith, 2008: Influence of water ice clouds on Martian tropical atmospheric temperatures. Geophys. Res. Lett., 35 , L07202. doi:10.1029/2007GL032405.
Zonally averaged Martian topography measured by the Mars Orbiter Laser Altimeter instrument (Smith et al. 1999). Martian topography slopes downward from the Southern Hemisphere to the Northern Hemisphere.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Zonally averaged pure radiative equilibrium temperature (K). Latitude is plotted on the x axis, pressure is plotted on the left y axis, and log pressure height is plotted on the right y axis, assuming a scale height of 11 km and a reference pressure of 6 hPa. Only temperatures below ∼0.2 hPa (40-km log pressure height) are shown. From left to right, the columns are Ls = 0°, 90°, and 270°, respectively. From top to bottom, the rows are flat, full, and mean topography. Contour interval is 15 K.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
As in Fig. 2, but for zonally averaged radiative–convective equilibrium temperature (K).
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
The topography of Mars: (a) the full topography measured by MOLA (“full”) and (b) the zonal mean MOLA topography (“mean”). Elevations are in km; contour interval is 0.5 km.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Equilibrium temperature at a constant pressure of 3.8 hPa (5-km log pressure height), for Ls = (a) 0°, (b) 90°, and (c) 270°. The thin solid line is Teq,R (independent of topography), the heavy solid line is Teq,RC with flat topography, and the dashed solid line is Teq,RC with mean topography.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Schematic of equilibrium temperatures for two different surface elevations (black and gray horizontal lines). The pure radiative equilibrium temperature (black and gray curve) is the same at a given level aloft (pa) for any surface height. The surface equilibrium temperature (Tg) in pure radiative equilibrium is lower for the elevated surface because of the reduced greenhouse effect, but this effect is negligible in the optically thin Martian atmosphere. The dashed lines are adiabats drawn in radiative–convective equilibrium. For this case, the equilibrium temperature at some level pa is warmer above the elevated surface.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Parameters in the model of Lindzen and Hou (1988) with a bottom topography zb(ϕ) added. The x axis is latitude; the y axis is height. Arrows indicate the direction of flow.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
(a) Forcing function given by (21) for Ls = 0°, 90°, and 270°. The black curve is flat topography and the gray curve is zonal mean topography. Each curve has been normalized such that its value at the equator is subtracted from each point in the curve. Regions where the temperature is equal to the CO2 condensation temperature are not plotted. (b) Latitudinal derivative of the forcing function given in (a). The noise in the curves with topography is a result of the fact that the derivative of the measured topography is noisy. The net affect of topography is to reduce the latitudinal derivative of the forcing function.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Solutions to (16)–(19), for (a) ϕ+, (b) ϕ1, and (c) ϕ−. The heavy solid line is the solution for flat topography for both pure radiative and radiative–convective forcing, which differ by less than 2%. The thin dashed line (barely visible as it is almost indistinguishable from the heavy solid line) is the solution for zonal mean MOLA topography with pure radiative forcing, and the heavy dashed line is the same but for radiative–convective forcing.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Simple MGCM results for zonally and time averaged mass streamfunction with pure radiative forcing, Units are 108 kg s−1. Positive flow is counterclockwise; negative contours are shaded. Latitude is plotted on the x axis, pressure is plotted on the left y axis, and log pressure height is plotted on the right y axis, assuming a scale height of 11 km and a reference pressure of 6 hPa. Only results below ∼0.2 hPa (40-km log pressure height) are shown. From left to right, the columns are Ls = 0°, 90°, and 270°. From top to bottom, the rows are flat, full, and mean topography. Note the different contour intervals (1 × 108 kg s−1 for Ls = 0° and 10 × 108 kg s−1 for Ls = 90° and Ls = 270°).
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
As in Fig. 10, but with radiative–convective forcing. Note the different contour intervals (4 × 108 kg s−1 for Ls = 0° and 15 × 108 kg s−1 for Ls = 90° and Ls = 270°).
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Maximum magnitude (above the boundary layer) of the zonally and time averaged mass streamfunction from the simple MGCM results with radiative–convective forcing (black symbols). The gray symbols are from Takahashi et al. (2003). The results are grouped by the various topographies. The squares are for Ls = 90°, the triangles are for Ls = 270°, the circles are for the northern cell at Ls = 0°, and the diamonds are for the southern cell at Ls = 0°.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Zonally averaged mass streamfunction simple MGCM results for Ls = 90°, radiative–convective forcing, and idealized zonal mean topography. Units are 108 kg s−1. Positive flow is counterclockwise; negative contours are shaded. Contour interval is 15 × 108 kg s−1. Latitude is plotted on the x axis, pressure is plotted on the left y axis, and log pressure height is plotted on the right y axis, assuming a scale height of 11 km and a reference pressure of 6 hPa. Only results below ∼0.2 hPa (40-km log pressure height) are shown. Results are shown for (a) flat topography (as in Fig. 11b), and (b)–(d) idealized zonal mean topography of increasing steepness (β equal to 40, 20, and 10, respectively). The maximum magnitudes for (a)–(d) are 161, 106, 80, and 77 × 108 kg s−1, respectively; thus, streamfunction strength decreases as the topographic slope’s steepness increases.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
As in Fig. 13, but for Ls = 270°, radiative–convective forcing, and idealized zonal mean topography. The maximum magnitudes for panels (a)–(d) are 163, 144, 140, and 140 × 108 kg s−1, respectively; thus, streamfunction strength is independent of the topographic slope’s steepness, contrary to at Ls = 90° (cf. Fig. 13).
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Zonally averaged mass streamfunction results from the GFDL MGCM, which uses a full radiation scheme. Units are 108 kg s−1. Only temperatures below ∼0.2 hPa (40 km) are shown. The top row is for flat topography; the bottom is for idealized zonal mean topography (β = 20). The left column is Ls = 90° and the right is Ls = 270°. Positive flow is counterclockwise; negative contours are shaded. Latitude is plotted on the x axis, pressure is plotted on the left y axis, and height is plotted on the right y axis. Contour interval is 15 × 108 kg s−1. The maximum magnitudes for panels (a)–(d) are 117, 121, 65, and 131 × 108 kg s−1, respectively.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Solutions to (16)–(19): (a) the solution for pure radiative forcing with flat topography; (b) as in (a), but with zonal mean MOLA topography; (c) radiative–convective forcing with flat topography; and (d) as in (c), but with zonal mean MOLA topography. In each panel, the dashed line is ϕ+, the solid is ϕ1, and the dotted is ϕ−. Also plotted are the boundaries of cells obtained from the simple MGCM results. The triangles are ϕ+, the squares are ϕ1, and the circles are ϕ−. As Ls approaches 90° and 270°, ϕ1 and the poleward boundary of the summer cell becomes indistinguishable, and the value of ϕ1 is not plotted.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
As in Fig. 16, but the results for the axisymmetric simple MGCM are shown instead of the 3D simple MGCM.
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Simple MGCM results with radiative–convective forcing for the momentum budget derived in (36). Units are m2 s−2. Latitude is plotted on the x axis, pressure is plotted on the left y axis, and log pressure height is plotted on the right y axis, assuming a scale height of 11 km and a reference pressure of 6 hPa. Only results below ∼0.2 hPa (40 km log pressure height) are shown. From left to right, the columns are Ls = 0°, 90°, and 270°. From top to bottom, the rows are the meridional transport by spatial eddies [first term on the lhs of (36)], combined meridional and vertical transport by the steady mean circulation [second and third terms on the lhs of (36)], and the planetary term [rhs of (36)]. Negative contours are shaded. Note the different contour intervals (100 m2 s−2 for the top row and 200 m2 s−2 otherwise).
Citation: Journal of the Atmospheric Sciences 67, 3; 10.1175/2009JAS3130.1
Seasons on Mars are described by the ecliptic longitude of the sun, denoted by Ls. By definition, Ls = 0° corresponds to the vernal equinox, Ls = 90° to the Northern Hemisphere summer solstice, Ls = 180° to the autumnal equinox, and Ls = 270° to the Northern Hemisphere winter solstice.
A sol is a Martian solar day.
Compared with Earth, the difference between the equinoctial and solstitial circulations is much more dramatic, since the heat capacity of Martian soil is less than that of Earth’s oceans (Haberle et al. 1993). Without the mediating influence of the ocean, the latitude of maximum equilibrium temperature can move well off the equator.
