The Dust Cycle on Mars at Different Orbital Distances from the Sun: An Investigation of the Impact of Radiatively Active Dust on Land Planet Climate

Changes to the planetary climate due to the direct influence of solar heating are significant but do not generate substantial departures from known climate trends observed on present-day Mars. Figure 1 shows the global, diurnal average values of surface temperature, pressure, and dust mass lifting rates versus aerocentric longitude (L_s), a measure of the time of year based on the planetary orbital position. Mars' low atmospheric density and surface thermal inertia means that S_o has a large impact on the global average surface temperature. At both orbital configurations, the minimum temperatures occur at aphelion (∼L_s = 70°) and maximum temperatures at perihelion (∼L_s = 250°). On average, surface temperatures at Earth orbit exceed those at Mars orbit by approximately 30–50 K. However, even at Earth orbit, global average temperatures do not exceed the water freezing point, a common early indication for habitability, although temperatures can exceed freezing locally. Despite higher average surface temperatures, winter polar temperatures periodically drop below the CO₂ frost point, which initiates CO₂ condensation at southern hemisphere (SH) winter (L_s = 90°) and, to a lesser extent, at northern hemisphere (NH) winter (L_s = 270°). As a result, at both Mars and Earth orbits, the global average surface pressure follows a strong seasonal cycle with a deep pressure minimum at mid southern winter when the south polar cap reaches its maximum size. As is expected for planets with a higher global average surface temperature, the magnitude of the simulated pressure cycle is reduced at Earth orbit compared with Mars orbit, in particular at NH winter solstice (Figure 1(b)). The depth of the pressure minimum at Earth orbit is also reduced due to the shorter year and therefore cumulative time permitting for CO₂ condensation and the growth of the south polar cap.

Zoom In Zoom Out Reset image size

Compared with present-day Mars, the nominal SH summer (L_s = 270°) dusty season at Earth orbit is both dustier and extends longer. Atmospheric dust on Mars is lofted from surface deposits in one of two ways, via convective dust devils or via wind-driven saltation-sandblasting in regions with high local surface wind stress. Figure 1(c) shows the total global average atmospheric dust at both orbits and the contribution of each dust-lifting type. For simulations at Mars orbit, dust devil lifting is the dominant source of atmospheric dust except for a narrow range of L_s near L_s ∼240°, when wind stress lifting peaks (Figure 1(c)). This pattern is expected for simple inert dust simulations with interactive lifting but does not perfectly reproduce the observed seasonality and dust activity on present-day Mars, e.g., the nominal B or C season storms (Kass et al. 2016). More complex parameterizations that include dust and cloud radiative feedbacks generate a closer match to the observed present-day Mars dust cycle. However, for the purpose of this study, which focuses on the broad shifts in dust activity, it is not necessary to capture these finer details.

At Earth orbit, higher surface heating generates stronger winds globally. While wind-driven lifting is almost exclusively restricted to the perihelion summer hemisphere on present-day Mars, surface wind stresses exceed the initiation threshold by a greater amount across a broader fraction of the planetary surface and for a greater proportion of the year when Mars is at Earth's orbital distance. We can see this more clearly by comparing the spatial distribution of surface dust lifting or dust activity at Mars and Earth orbits (Figure 2). At both orbits, the amount of atmospheric dust as well as the magnitude of dust-lifting events is smaller at orbital aphelion compared to orbital perihelion. Regions with high dust activity represent regions with active wind-stress lifting. In inert dust simulations at both Mars and Earth orbits, the background mean surface stress is generally too small to initiate wind-stress lifting. Local augmentation by the thermal tides, slope flows, and transient eddy activity is critical. As on present-day Mars, large diurnal temperature variations, particularly over regions with extreme topographic relief or with spatially varying surface thermal properties, enhance winds and are responsible for the majority of wind-driven dust-lifting events (Richardson & Wilson 2002; Zalucha et al. 2010). For example, NH winter solstitial surface wind stress and dust lifting are highest along the northern rim of Hellas basin, on the eastern rim of Argyre, and at the northern boundary of the receding seasonal polar cap. Importantly, these patterns do not change when the solar forcing is increased. In other words, despite a 2.3-fold increase in the solar heating rate, simulations at Earth orbit remain qualitatively Mars-like when the spatial and temporal patterns of dust lifting are compared. The most significant departure in simulations at Earth orbit is to the overall magnitude of storm systems. Since wind stresses are greater when surface heating is higher, more dust is injected per lifting event and over a larger area of the planet. For example, the maximum mass lifting rate at Earth orbit is 12.24 g m⁻² sol⁻¹, centered along the northwestern edge of Hellas basin, compared with 2.89 g m⁻² sol⁻¹ at approximately the same location in simulations at Mars orbit. In all simulation years, SH summer dust activity produces the highest annual dust loading.

Zoom In Zoom Out Reset image size

Changes to the magnitude of the simulated dust activity in part reflect changes to the large-scale solstitial dynamics (Figure 3). Compared to simulations at Mars orbit, the westerly zonal wind generated at Earth orbit is stronger in the winter hemisphere as latitudinal temperature gradients are tighter. Tropical easterlies also increase. These changes are most pronounced near NH winter solstice (L_s = 270°). The cross-hemispheric Hadley circulation strengthens, but remains structurally similar, having only slightly expanded both vertically and latitudinally near NH winter solstice. Adiabatic warming in the descending branch of the Hadley cell increases polar middle and upper atmospheric temperatures by ∼40 K. Again, while the overall strength of the circulation increases due to higher solar heating rates, the general pattern observed at Mars orbit is preserved. In general, the impact of insolation therefore appears to be a continuous strengthening of observed circulation patterns rather than a wholesale reorganization or departure.

Zoom In Zoom Out Reset image size

Although the simulated dust cycle is strengthened by increased solar heating, inert dust simulations are still recognizably Mars-like. By contrast, when dust is radiatively active, the climate diverges considerably from this base state. In fact, the impact of radiatively active dust on the overall climate eclipses changes due to increased solar heating alone. Critically, radiative heating by dust warms the planetary atmosphere and surface, generates positive feedbacks that promote further dust lifting, and, through shifts in the large-scale planetary atmospheric dynamics, fundamentally modifies both the spatial distribution of dust lifting and the timing of storms. Simulations that neglect radiative feedbacks by dust may therefore misrepresent land planet climate with broad implications for habitability.

Figure 4 shows the global average surface temperature, surface pressure, dust optical depth, and dust-lifting rates for simulations with radiatively inert and active dust at Earth orbit. The driving difference between these two simulations is therefore the indirect influence of dust radiative heating as opposed to solar insolation as in Section 3.1. Average surface temperatures increase relative to simulations with inert dust by approximately 10–40 K for the duration of the year (Figure 4(a)). Significantly, the magnitude of this increase is comparable to the simulated surface warming due to the increase in S_o (30–50 K). Surface temperatures remain above the water freezing point except for a short period of time around aphelion. Higher wintertime temperatures, which can be partially attributed to the dust greenhouse effect (see Section 3.3), limit solstitial CO₂ condensation. As a result, the annual pressure cycle stabilizes and the CO₂ cycle disappears (Figure 4(b)). The most significant modification, however, is to the simulated dust cycle (Figures 4(c) and (d)). The total atmospheric dust in radiatively active dust simulations increases by almost two orders of magnitude compared with inert dust simulations. The global average visible dust optical depth exceeds ∼15 for the duration of the year and regularly exceeds 30–50, meaning that little sunlight reaches the planetary surface except at the highest elevations (Figure 4(c)). As a result, dust devil lifting halts, and all lifting transitions to wind stress lifting (Figure 4(d)). Notably, the most dramatic increase in dust lifting is at the NH summer solstice (L_s = 90°) where dust devil lifting previously dominated. In simulations with active dust, NH summer solstitial atmospheric dust levels are now within approximately 60% of NH winter solstitial maximum. Rather than a single NH winter solstitial dusty season as on present-day Mars, simulations with radiatively active dust exhibit biannual solstitial dusty seasons. The relative magnitude of the simulated solstitial dust maxima in these simulations results from Mars' eccentric orbit, which causes differences in both the length and total solar heating rate at each solstice, and, importantly, Mars' unique topography. The north to south cross-equatorial slope strongly suppresses the zonal mean circulation at NH summer solstice. This asymmetrical forcing accentuates the difference between the two solstice seasons during low dust conditions (Richardson & Wilson 2002; Zalucha et al. 2010). The inhibiting effect on circulation is reduced as the lower atmosphere is increasingly stabilized with increasing dust loading (Barnes et al. 2017, their Figure 9.11). Seasonal forcing will be modified based on the timescales of dust increase and decay relative to the seasonal cycle, which also depends on the distribution and depth of surface dust reservoirs, the lifted dust size distribution, and dust sink mechanisms (e.g., cloud scavenging).

Zoom In Zoom Out Reset image size

Despite accumulation of large amounts of atmospheric dust that leads to an increase in the planetary albedo (Figure 5(a)) and hence a reduction in absorbed sunlight, surface temperatures in active dust simulations increase globally (Figure 5(b)). This is because the high dust levels in our simulations provide a very strong greenhouse effect. On present-day Mars and on land planets with limited atmospheric dust loading, the majority of sunlight reaches and is absorbed by the planetary surface. Mars' thin atmosphere traps very little outgoing IR thermal radiation, so the emission to space level is at or very near the planetary surface, and the planetary blackbody temperature is approximately equal to the observed or simulated surface temperature. In rare cases, as during global dust events, dust heating can generate moderate surface warming (Elteto & Toon 2010; Streeter et al. 2019). If land planet dust has optical properties similar to those observed on Mars that absorb and emit strongly in the IR, the net emission-to-space level, the level at which the cumulative IR opacity from that point to the top of the atmosphere reaches unity, lifts off the surface and moves upwards as dust accumulates.

Zoom In Zoom Out Reset image size

In radiatively active dust simulations at Earth orbit, the emission to space level rises to approximately 10–30 Pa planetwide, high in the atmosphere where temperatures are much cooler than the surface and average between 210 and 250 K (Figure 5(c)). As the IR opacity increases surface temperatures increase and the radiation to space level must rise to cooler levels in the atmosphere to maintain energy balance. In our simulations, the dust greenhouse raises annual average surface temperatures by ∼10–50 K compared with inert dust simulations (Figure 5(b)). The annual average surface temperature exceeds 273 K at all latitudes equatorward of approximately 40° N and S. Despite significant surface shading, land planets with high atmospheric dust loads and favorable dust optical properties (as determined by the particle size and minerology) therefore can potentially be more habitable than their dust-free counterparts. At the same time, if future observations cannot easily discriminate between the planetary surface and an optically thick high-altitude atmospheric dust layer, it may be easy to erroneously predict prohibitively cold surface temperatures. We discuss the habitability implications of the dust greenhouse in Section 4.2.2 and the greenhouse dependence on particle size and composition in Section 4.3.1.

The components of terrestrial planet atmospheric circulation include the zonal mean flow, and spatial and temporal perturbations or eddies of various scales. For a rotating planet, important eddies include baroclinic transient eddies, stationary eddies related to the topography and surface thermal properties, and the thermal tide. It is well established that dust affects these components for present-day Mars. In the following sections, we focus on the impact of radiatively active dust on the mean circulation and the thermal tides, the key components that contribute to the dust distribution and surface lifting patterns. While transient eddy activity associated with baroclinic instabilities along the winter polar vortex contributes to the initiation and growth of storm systems on present-day Mars (Wang et al. 2003, Wu et al. 2022), their subsequent influence on the dust cycle is greatly reduced as atmospheric dust accumulates and the atmospheric stability increases (Mulholland et al. 2016; Lee et al. 2018; Hinson & Wilson 2021). Specifically, in response to the intensification of the zonal mean flow, low level transient wave activity decreases and shifts poleward away from the most active dust lifting regions. We conclude that their effect on simulated dust activity is negligible.

3.4.1. The Zonal Mean Circulation

In comparison to inert dust simulations with the same solar heating rate, the zonal mean circulation, characterized by the winter hemisphere westerly jet and Hadley circulation, is greatly strengthened by dust radiative heating. The meridional extent of the solstitial Hadley circulation is sensitive to the latitude of maximum heating. As on present-day Mars, the rising branch of the Hadley cell in inert dust simulations generally follows the seasonal migration of the subsolar latitude. The highest heating rates occur near the surface. As atmospheric dust accumulates, dust radiative heating can exceed warming due to solar heating of the atmosphere and surface, displacing the latitude and altitude of maximum heating poleward and upwards.

In radiatively active dust simulations at Earth orbit, radiative heating by atmospheric dust in the high summer polar latitudes and cooling in the winter hemisphere (Figure 6, bottom row) drives the vertical and meridional expansion of the seasonal Hadley cell. In the middle atmosphere, circulation extends from nearly pole-to-pole, consistent with behavior for a nearly inviscid, angular-momentum-conserving fluid (Held & Hou 1980; Schneider 1983; Lindzen & Hou 1988) forced by dust radiative heating (Haberle et al. 1982; Schneider 1983; Wilson 1997). Zonal winds in the tropics approach the theoretical limit of −240 m s⁻¹ for angular-momentum-conserving air parcels moving from the pole to the equator. The aphelion and perihelion winter westerly jet is vertically bounded and shifted slightly poleward. Wind speeds reach 157.55 and 173.75 m s⁻¹, respectively (Figure 6, row 1).

Zoom In Zoom Out Reset image size

The zonal mean circulation is responsible for the transport and mixing of atmospheric dust (Figure 6, bottom row). At both solstices, dust is nearly uniformly mixed from 100 Pa to approximately 10–1 Pa. Dust in the lower atmosphere is concentrated in broad plumes associated with the upwelling branch of the Hadley cell. As we will demonstrate in the following sections, heating by dust amplifies the thermal tide and, in particular, the diurnal and semidiurnal harmonics of the tide.

The strengthened solstitial circulation is also responsible for the simulated seasonality in the planetary bond albedo (Figure 5(a)). As on present-day Mars, atmospheric dust raises the average planetary bond albedo since dust scatters light efficiently at visible wavelengths. However, during solstitial dusty seasons larger particles are lofted into the reflective region of the atmosphere (at pressures <10 Pa) and the average particle effective radius increases from approximately 0.9 to >1.3–1.6 μm. Due to the anticorrelation between dust particle size and single scattering albedo (Wolff et al. 2009, Haberle et al. 2019), the total upwards visible light flux is reduced and the bond albedo decreases. Seasonal or cyclic changes to simple observables such as the planetary albedo could provide useful constraints on the planetary climate, for example, indicating that the planet has an atmosphere and active meteorology.

3.4.2. The Thermal Tide

Thermal tides are the atmospheric response to the diurnal cycle in solar heating. To first order, the amplitude of the thermal tide response is dependent on the strength and spatial distribution of the thermal forcing and is therefore modified by the thermal properties of the surface, the mass and composition of the atmosphere, and the optical properties of atmospheric aerosols (Chapman & Lindzen 1970). On land planets with limited surface reservoirs of water and low surface heat capacity, there is significant diurnal variability and strong forcing by the diurnal tide (Zurek 1976; Wilson & Hamilton 1996; Forbes & Miyahara 2006; Barnes et al. 2017). On present-day Mars, the semidiurnal tide response is roughly proportional to the global dust heating rate and is therefore strengthened as the global atmospheric dust load increases (Zurek 1981; Wilson & Richardson 2000; Forbes & Miyahara 2006; Guzewich et al. 2014). Water ice clouds similarly amplify the semidiurnal tide (Kleinböhl et al. 2013, Wilson & Guzewich 2014, Haberle et al. 2019; Hartwick et al. 2019).

The tidal response is significantly modified in simulations with active dust compared to simulations with inert dust at the same orbit. In Figure 7 we show the amplitude of the diurnal and semidiurnal components of the temperature and zonal wind versus pressure. The diurnal tide is the strongest component of the thermal tide in both active and inert dust simulations, with maximum values of approximately 20 K and 50 m s⁻¹ and as great as 90 K and 560 m s⁻¹ at SH summer solstice, respectively. However, at the same time, the altitude of peak tidal heating shifts from the top and bottom of the atmosphere in inert dust cases (since the amplitude of the tide is inversely proportional to the atmospheric density and NIR solar radiation has relatively stronger forcing in the upper atmosphere) to the atmospheric level at which the cumulative opacity reaches unity, which is determined by the vertical distribution and in situ thermal forcing of dust. Absorption of solar radiation by dust is positive by day and zero at night; hence the presence of multiple harmonics, including diurnal, semidiurnal, and higher harmonics. Despite maximum solar heating in the summer hemisphere, the amplitudes of the semidiurnal tides in the active dust simulation peak over the winter poles and midlatitudes in the middle atmosphere. The surface influence of the semidiurnal tide is greatest in the midlatitudes (see Section 3.5)

Zoom In Zoom Out Reset image size

The thermal tide also indirectly influences the intensity and structure of the zonal mean circulation. This is most readily illustrated by comparing simulations with and without tides. The latter can be achieved by running the model with diurnally averaged solar insolation. The results are shown in Figures 8 and 9. In the simulation that lacks tides the solstitial atmospheric dust load is reduced, the Hadley cell is weaker, and its meridional and vertical extent is smaller. This indicates that tides strengthen and expand the Hadley circulation. We believe this is accomplished by two separate processes. First, convergence of the tide heat and momentum fluxes broaden the meridional extent of the Hadley circulation (see, for e.g., Zurek & Haberle 1988; Wilson 1997). Second, and perhaps more importantly, tides advect dust directly over the summer pole leading to increased heating in this region (Wilson 1997; Wu et al. 2020). By contrast, the summer polar atmosphere is largely dust free in simulations with no tides. The resulting transport of dust to higher latitudes in the summer hemisphere further strengthens the intensity of the circulation (see Figure 6, bottom row). Thus, a feedback process is initiated between dust lifting and tidal amplitudes that strengthens and broadens the Hadley cell, culminating in a very deep pole-to-pole meridional circulation. Wilson (1997) discusses these mechanisms for solstitial global dust storms on present-day Mars.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Tidal heating also drives equinoctial equatorial superrotation. Tropical westerlies exceed 70 m s⁻¹ in a broad maximum between ∼250 and 10 Pa and extend from the near surface to ∼0.3 Pa. Formation of the equatorial prograde jet results from angular-momentum transfer by the Sun-synchronous diurnal tide (Fels & Lindzen 1974; Lewis & Read 2003) and is absent in simulations with diurnal average heating (Figure 9). Tides are also responsible for vertical closure of midlatitude westerlies and modify the MMC from a dipole to quadrupole structure. These phenomena have been simulated in general circulation models for present-day Mars when equinoctial dust storms temporarily increase atmospheric dust levels and tidal heating (Wilson & Hamilton 1996; Lewis & Read 2003; Inamura et al. 2020). The Earth orbit simulation represents an amplification of this same process with much higher dust forcing and therefore a stronger response. We note that some differences between the diurnal and diurnal average heating simulations result from changes to the atmospheric dust level as seen in Figure 8; however, this difference would not impact the major dynamical structures (e.g., the direction of the tropical jet) in diurnal heating simulations that are forced by the tide.

A surprising result of adding radiatively active dust to simulations of land planets at Earth orbit is the spatial reorganization of the most active dust-lifting regions. At both solstices the maximum zonal mean surface stress for the radiatively active dust case shifts into the winter hemisphere at ∼30° (Figure 10).

Zoom In Zoom Out Reset image size

To illustrate the contribution of individual components of the circulation to this shift we show in Figure 11 the surface wind stress, the zonal mean component of the surface stress, and the diurnal minimum and maximum values. We approximate the zonal mean component of the wind stress using Equation (4) with a constant drag coefficient (C_D ), the zonal and time-averaged atmospheric density (ρ_air), and the zonal and time-averaged wind speed in the lowest atmospheric level (U). The wind speed (U) is calculated using the zonal mean u and v components of the wind speed squared:

$$\begin{eqnarray}&&{\tau }_{* }={\rho }_{\mathrm{air}}{C}_{D}{U}^{2}.\end{eqnarray} \tag{ 4 }$$

Zoom In Zoom Out Reset image size

At both solstices, stronger winds speeds associated with the zonal mean circulation contribute to only a small increase in predicted wind stress in the winter hemisphere. By contrast, there is significant diurnal variability, which suggests that the tide is the controlling dynamic component responsible for the magnitude of surface wind stress. In the winter hemisphere surface wind stress maxima can exceed 100 mN m⁻², well above the threshold wind stress of 22.5 mN m⁻² required for the initiation of wind-driven dust lifting.

We also show in Figure 12 the amplitude of the diurnal and semidiurnal harmonics of the surface zonal wind component of the thermal tide for the active and inert dust simulations for the solstitial seasons. Since a large fraction of the incoming solar radiation reaches the planetary surface in inert dust simulations with low atmospheric dust levels, the diurnal tide has the most significant surface influence. By contrast, in active dust simulations the semidiurnal tide clearly dominates the near-surface response. Maximum amplitudes at both solstices exceed 20 m s⁻¹ at ∼30° in the winter hemisphere, which are the same latitudes as the largest zonal average wind stresses and lifting rates (see Figures 10 and 11). The longitudinal structure results from constructive and destructive interference between the migrating and nonmigrating tides. The latter are excited by longitudinal variations in dust and surface properties (e.g., topography, albedo, thermal inertia; Wilson & Hamilton 1996).

Zoom In Zoom Out Reset image size

The dominance of the semidiurnal and higher harmonic tidal components over the diurnal tide in active dust simulations is a result of deeply mixed dust that shifts the peak thermal forcing to higher in the atmosphere (see Figure 6). Thus the semidiurnal tide, which has very long vertical wavelengths, efficiently responds while the diurnal tide, which has shorter vertical wavelengths, and has a more muted response at the surface.

Even small increases in the surface wind stress can contribute to significant increases in the atmospheric dust mass since the mass lifting rate is proportional to the wind stress cubed (see Equation (1)). As the tidal amplitude grows, more dust is lifted. Lifted dust is transported meridionally and vertically by the zonal mean circulation where, in the upper atmosphere, it further augments the tide. This feedback between the level of atmospheric dust, the planetary mean circulation and tides, and the distribution of surface dust activity demonstrates the unique complexity of dust-dominated, land planet climates. Dust activity is controlled by surface winds that are directly modified by the distribution and properties of dust itself. If dust availability is nearly unlimited, this feedback strengthens as the planetary orbit decreases and the solar heating and corresponding dust heating rates increase.

Future study of land planet climate will necessarily require extrapolation based on limited observational evidence. Where possible, identifying simple diagnostic relationships between concrete, more easily observed planetary features (e.g., the orbital radius, planetary size, and stellar type) and more complex climatological patterns will be the gold standard. In the following section, our goal is to probe the relationship between solar insolation rates or planetary orbital radius and simple land planet climate types. Based on our analysis of Mars-like exoplanets at Mars and Earth orbits we identify three dust-lifting regimes. Dust-lifting regimes are characterized by the dominant mechanisms for injection of surface dust into the atmosphere (e.g., either dust devil or wind stress lifting) and the spatial distribution of the most active dust-lifting regions (for example, in the summer or winter hemisphere). Because dust activity is directly related to the surface energy budget and magnitude and distribution of surface wind speeds that are modified by large-scale circulation patterns, dust activity is a particularly useful metric for overall climate. For example, as we have shown in the analysis of a Mars-like exoplanet at Earth orbit with radiatively active dust, the shift in lifting from the summer to winter hemisphere is driven primarily by the surface influence of the semidiurnal and higher harmonic thermal tides. These modifications to the global dynamics result from dust mixing by the zonal mean circulation and dust radiative heating in the middle atmosphere. This pattern of lifting is uniquely accessible in land planet climates with significant atmospheric dust and positive dust radiational heating. We summarize the three dust-lifting regimes or land planet climate types below.

Regime I. The dominant mechanism for dust lifting in regime I climates is dust devil lifting. Dust devil frequency increases when the atmospheric static stability drops. As a result, most lifting will occur in the summer hemisphere following the subsolar latitude. In general, atmospheric dust levels remain low. Low surface wind speeds limit or entirely suppress wind stress lifting.

Regime II. In regime II, surface wind speeds more regularly exceed the surface wind stress threshold required to initiate saltation. Lifting is concentrated in regions where surface winds can be accelerated above the background mean by the thermal tide, transient and stationary eddies or their interactions. Most lifting is concentrated in the summer hemisphere, however flushing storms that travel from the winter to summer hemisphere may trigger dust activity that grows storm systems from local to regional or even global scales. The radiative impact of dust is small but nonnegligible.

Regime III. Unlike regimes I and II, which represent two physically distinct lifting mechanisms, both regimes II and III loft dust predominantly via wind stress lifting. However, lifting shifts from the summer hemisphere to the winter hemisphere due to the surface influence of the semidiurnal tide. Whereas planetary-scale dust activity must be initiated in regimes I and II, regime III season dust activity is embedded in a perpetual or seasonal global dust storm. A hallmark of regime III is therefore the reduced role of transient waves, which are important for storm expansion and growth, and the concurrent amplification of the semidiurnal and higher harmonic tides, which enhance winter hemisphere midlatitudes surface wind speeds and, via dust advection to the summer polar hemisphere, strengthen the seasonal Hadley circulation. Dust radiative feedbacks are critical and drive the shift between regimes II and III.

Due to Mars' eccentric orbit and the large variation in solar heating rates with season (for example, at present-day Mars orbit, S_o = 589 W m⁻², the maximum heating rate exceeds 717 W m⁻² at NH winter solstice while the minimum falls to 493 W m⁻² at NH summer solstice), Mars-like planets can potentially experience multiple regimes at the same orbital radius. Dust activity in simulations at Mars orbit follows regime I at NH summer solstice but shifts to regime II at NH winter solstice. By contrast, Earth orbit simulations show regime III dust activity throughout the entire year, suggesting that the S_o limit for regime III is less than the NH summer solstice forcing (1148 W m⁻²).

Figure 13 shows the solstitial zonal average dust activity for four new intermediary orbits. At summer hemisphere summer solstice (L_s = 270°), we observe an almost immediate shift from regime II (wind stress, summer hemisphere) to regime III (wind stress, winter hemisphere) between Mars orbit and intermediate orbit 1 (NH winter solstice heating 717 and 973 W m⁻², respectively). As the orbit decreases and seasonal heating rates continue to rise, lifting in the winter hemisphere (NH midlatitudes) becomes progressively more dominant. Positive feedbacks between atmospheric dust heating and additional dust lifting leads to a simultaneous increase in the atmospheric dust optical depth from below 1 at Mars orbit to greater than 40–50 at Earth orbit. At NH summer solstice (L_s = 90°), we first identify a transition from regime I lifting (dust devil, summer hemisphere) to regime II (wind stress, summer hemisphere) between Mars orbit and intermediate orbit 1 (aphelion heating 493 and 669 W m⁻², respectively). By intermediate orbit 3 (aphelion heating 1004 W m⁻²) regime III dust activity is initiated all year round. We identify transition states between regimes I and II (similar levels of wind stress and dust devil lifting) at L_s = 90° intermediate orbit 1 (669 W m⁻²) and between regimes II and III (simultaneous lifting in both the summer and winter hemispheres) at L_s = 270°, intermediate orbit 1 (973 W m⁻²) and L_s = 90°, intermediate orbit 2 (836 W m⁻²).

Zoom In Zoom Out Reset image size

Our findings are summarized in Table 2. We identify the dust-lifting regime at both solstices and the associated seasonal solar heating rate in the summer hemisphere. Based on this analysis we identify the following S_o limits for each regime:

• Regime I: S_o < 669 W m⁻².
• Regime II : 669 W m⁻² < S_o < 1004 W m⁻².
• Regime III : S_o > 1004 W m⁻².

While these limits provide a useful first constraint for the expected land planet climate as a function of solar heating rate, we caution the reader that the exact solar flux boundaries for each regime is highly dependent on several factors, including the planetary topography, the mineralogy and radiative properties of lifted dust, the solar spectrum and stellar type, the planetary atmospheric density and composition, and the planetary size, obliquity and eccentricity. For example, simulations with no topography and uniform surface thermal properties generally have much lower wind stress dust injection rates overall since surface winds speeds are not accelerated across topographic and thermal gradients. The nonlinear dependence of dust injection on wind stress (Equation (1)) means that localized enhancement of stress due to topographic slope effects greatly amplify dust injection (see Figure 14). The shift to regime II requires higher solar heating rates at both L_s = 90° and L_s = 270° (occurring at intermediate orbit 2 and intermediate orbit 1, respectively). The shift to regime III at L_s = 270° is similarly delayed from approximately 973 W m⁻² with topography to S_o = 1217 W m⁻² without topography. At L_s = 90°, summer hemisphere wind stress lifting is maintained at smaller orbits (e.g intermediate orbit 3). As we noted previously, topography also controls the nonmigrating component of the diurnal and higher harmonic thermal tides. As a result, simulations with topography show more meridional asymmetry in the distribution of active lifting regions in the winter midlatitudes compared with billiard ball simulations. Further, dust composition and grain size can dramatically alter the radiative forcing, e.g., from warming to cooling. This factor should be carefully considered.

Zoom In Zoom Out Reset image size

Rather than relying on rigid S_o benchmarks, we therefore instead encourage thinking in broad climate trends that vary with orbit. In general, land planets will be dustier at closer orbits. Lifting will transition from dust devil to wind stress dominated, and the most active dust-lifting regions will shift from the summer to winter hemisphere. If the land planet in question is orbiting close to its central star and has a flat or nonvarying spectrum with season, we are therefore more likely to predict a dusty regime III-like climate compared with a very distantly orbiting planet also with a nonvarying spectrum (in this case, we are likely observing the surface rather than a high-altitude dust layer, a regime I climate). Future papers will continue to probe the complexities of these regimes, including in relation to the planetary size, atmospheric density and composition, stellar type, and coupling with the hydrological cycle.

A critical component of exoplanet climatological studies is understanding the potential spectral signatures of different planetary and climate types. Observational data will be extremely limited, and spectra may not provide conclusive evidence of a particular planetary climate. In fact, it is possible that vastly different climates could produce very similar spectral shapes, particularly in the case of flat or nearly featureless spectra. Our primary goal must therefore be to both evaluate planetary climate and potential habitability but also gain a thorough understanding of how these planets and climate types may be easily distinguished between near neighbors and spectral doppelgangers. As a first step, we utilize the PICASO software package (Batalha et al. 2019) to generate theoretical exoplanet reflectance spectra for both the Mars and Earth orbit land planet simulations (Figure 15). We replicate the LUVOIR-A wavelength range since this is the most likely candidate to directly observe terrestrial planets at more distant orbits. PICASO requires inputs for the wavelength-dependent surface albedo, the vertical temperature, pressure, and atmospheric constituents (here, CO₂, and water vapor) as well as the vertical distribution and wavelength-dependent layer optical depths for any atmospheric aerosols. We prescribe a constant surface albedo based on the CRISM wavelength-dependent surface albedo generated by Madden & Kaltenegger (2018). We note that at closer orbits simulated here, the surface albedo may be altered. In particular, the distribution and total amount of surface dust may vary as a result of elevated lifting simulated at Earth orbit and, as surface temperature increase, surface water ice may sublimate while surface liquid water could accumulate or modify the moisture of regolith. We do not consider this source of potential variability at this time. However, since the spectral impact of the surface is reduced at greater dust optical depths, we believe the conclusions presented here are robust.

Zoom In Zoom Out Reset image size

For simplicity, and given the long observational time required to image Mars-like land planets, we utilize the global annual average from simulations. To calculate the wavelength-dependent optical depth due to atmospheric dust, we calculate extinction and scattering coefficients for a constant log-normal distribution of particles with R_eff = 1.5 μm, v_eff = 0.5. Layer optical depth is calculated using Equations (5)–(7):

$$\begin{eqnarray}&&\sigma =\sqrt{\mathrm{log}}\left(1+{V}_{\mathrm{eff}}\right),\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{R}_{g}={R}_{\mathrm{eff}}\cdot \exp \left(-1.5{\sigma }^{2}\right),\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&\tau ={Q}_{\mathrm{ext}}\left(\lambda \right)\cdot \pi {R}_{s}^{2}\cdot {N}_{o}\cdot \displaystyle \frac{{dP}}{g}.\end{eqnarray} \tag{ 7 }$$

Here, R_g is the distribution radius necessary to find the total geometric cross section of the particle distribution. R_eff and v_eff are the effective radius and variance of a constant, level-independent log-normal distribution of dust particles, here 1.5 μm and 0.5, respectively. Q_ext is the distribution weighted extinction coefficient versus wavelength. N_o is the dust number density in #kg⁻¹. dP g⁻¹ represents the atmospheric layer mass per unit area. Simplifying assumptions regarding the size distribution of particles introduce some inaccuracies into the final optical depth calculation. However, given the expected observational integration time, we expect variations with location and time to introduce minimal errors.

At Mars orbit, the structure and major features of the simulated reflectance spectrum mirror the surface albedo map (Figure 15). This is expected due to the thin Martian atmosphere and the limited atmospheric dust. Dashed lines show the simulated spectrum without aerosols. At Mars orbit, the impact of aerosols is minimal. Major absorption features correspond to surface dust and ice deposits and atmospheric CO₂. In the extreme-UV at wavelengths shorter than approximately 0.75 μm, there is a deep absorption band due to charge transfer absorption of Fe³⁺. Another significant absorption feature appears at approximately 2 μm due to CO₂. We also identify absorption features due to surface water ice (between 1.4 and 1.7 μm), olivine and pyroxene (Fe²⁺, 1 μm), and hydrated minerals at 2.2 μm (Hu et al. 2012). The simulated Mars orbit spectrum matches reasonably well with Earth-based and in situ observational spectra of present-day Mars (Hu et al. 2012). At Earth orbit, high levels of atmospheric dust mute surface spectral features and shift the overall shape of the simulated spectra to look more similar to the spectrum of Martian dust. As at Mars orbit, significant absorption is apparent due to Fe³⁺ and Fe²⁺. However, the CO₂ absorption band as well as absorption bands due to surface water ice are damped. Significantly, terrestrial land planets with significant levels of atmospheric dust can potentially have relatively flat spectra that could make the unique identification of high-altitude cloud decks versus dust decks more difficult. Similarly, short-wavelength absorption may not be easily discriminable from scattering due to photochemical hazes. We acknowledge that the Earth orbit spectrum is highly dependent on the chosen dust optical properties as well as the dust emission parameterization. For example, our current simulations do not prescribe finite surface dust reservoirs (see Section 4.3.2). If surface dust is depleted on seasonal or shorter timescales, spectral cycling between a dusty flat spectrum and a spectrum with clear surface features could help differentiate between high dust layers and a cold featureless planet. Even in our simple simulations, there is some variation with season that, if resolvable, would hint at an optically thick aerosol layer as opposed to a dust-free planet with a spectrally flat surface. Future work to identify identifying spectral features and dust-driven seasonal variability for these planets will be important.

Doppler shifts of absorption bands in high-resolution transmission spectra have aided in the identification of superrotation on hot Jupiters and brown dwarves where winds can exceed 1 km s _⁻¹ (Snellen et al. 2010). Future observations with greater signal-to-noise ratios could potentially look for equinoctial superrotation as a signature of regime III, dusty land planet climates.

As dust accumulates in the land planet atmosphere, the prevailing climate shifts from one that is similar to present-day Mars to one that more closely resembles present-day Venus. This surprising transformation results from the absorption of solar and IR light by atmospheric dust. As on Venus, the peak heating shifts off the surface into the middle atmosphere (Figure 6). Greenhouse warming raises the surface temperature above the theoretical blackbody temperature (Figure 5). A superrotating zonal flow dominates the tropics, extending from approximately 30N to 30S compared to ∼50N to 50S. Wind speeds peak at ∼70 m s⁻¹ compared to 100 m s⁻¹ for our simulated Mars-like land planet and Venus, respectively (Sánchez-Lavega et al. 2017). Winds peak at a similar altitude. While the Venusian forcing is less clear-cut, with contributions from the thermal tide as well as the mean meridional circulation (Yamamoto et al. 2019; Horinouchi et al. 2020; Inamura et al. 2020), the mechanism generating these features on simulated Mars-like land planets is unambiguously the amplification of the thermal tides by atmospheric dust.

Dusty atmospheres complicate our ability to easily assess land planet habitability. Shading by atmospheric dust may be the key to reducing surface temperatures and generating habitable environments, as is the case for tidally locked land planets orbiting M stars in Boutle et al. (2020). By contrast, as in this work, high levels of atmospheric dust act as a greenhouse warming agent, raising temperatures above the freezing point of water. Dust may also play a critical role for the long-range transport of nutrients (Ridgwell 2002) or, in the case of ferrous dust, in shading the surface from damaging levels of UV irradiation (Pierson et al. 1992). On the other hand, high levels of atmospheric dust limit the surface flux of visible light and therefore limits the most abundant energy source for life (Section 4.3.1). Further, for small planets such as Mars, dust mixed to the high atmosphere may act as a conveyor belt for atmospheric water loss, drawing into question the long-term planetary habitability (Section 4.3.2). Additional complications arise since these effects will be modified by the unique optical properties, minerology, and size distribution of dust on planets with different evolutionary histories.

4.2.1. Limitations Due to Reduced Surface Solar Flux

Classic prescriptions for habitability only require sufficiently high surface temperatures to sustain liquid water over long periods. At Earth orbit, simulated land planet surface temperatures in the extratropics and along the equator remain above freezing for the entire year. Given a large enough planetary budget of water to support life, a Mars-like land planet with radiatively active dust at higher instellations could be conceivably habitable over some fraction of the planetary surface. However, positive feedbacks between atmospheric dust levels and further dust lifting complicate this simple picture of planetary habitability.

As atmospheric dust accumulates the fraction of sunlight reaching the planetary surface, and therefore the surface energy budget for potential photosynthetic life-forms, is decreased. Previous studies have identified very low minimum light limits for photosynthetic light (Littler et al. 1986; Raven et al. 2000; McKay 2014). On average, even our dustiest simulations would therefore permit limited growth (see Figure 16). However, the surface flux of sunlight near NH winter solstice (Figure 16(e)) falls below minimum photon flux rates (0.01 μmol m⁻² s⁻¹) for photosynthetic life over a large fraction of the NH. Photosynthetic life-forms would therefore be restricted to the SH or require a seasonal hibernation cycle that coincides with biannual dust storms. Further, in our Earth orbit simulations with radiatively active dust, the greatest surface solar fluxes exist at the highest altitudes where atmospheric pressures are lowest and surface liquid water is most unstable. In land planet studies we must therefore additionally consider dust-driven limitations on photosynthetic habitability. These limits are strongly based on the radiative properties of dust and could be different for planets orbiting different stellar types.

Zoom In Zoom Out Reset image size

4.2.2. Planetary Water Budget

4.3.1. Dust Radiative Properties, Coagulation, and Loss of Thermal Contact

4.3.2. Dust Availability

The major negative control on regime III is the planetary availability of dust; or, stated differently, given a specific solar insolation, is there sufficient dust to modify the Hadley cell and transition lifting to regime III? The simulations described in this paper prescribe an infinite source of dust distributed evenly across the surface. As the spatial distribution of surface winds change, regions of dust activity shift across the planet. Based on local topography and surface thermal properties, winds may be magnified and lead to more dust lifting, or decreased, lowering the total mass of dust lifted.

A more realistic distribution of finite depth dust reservoirs will respond to changed surface winds in complex nonlinear ways. Notably, if the highest surface wind speeds are not spatially correlated with the largest dust deposits or if surface dust reservoirs can be rapidly depleted over short timescales, then modifications to climate due to dust radiative feedbacks may be transient or short-lived. Depletion of surface dust reservoirs is a known process for present-day Mars, which has perennially active dust-lifting centers but also regions that are periodically activated or appear to be cleared of dust on short timescales (Kahre et al. 2005; Newman & Richardson 2015). Reservoir exhaustion likely contributes to the timing and growth of large-scale and global dust storms. By the same manner, the spatial distribution of surface dust reservoirs with unique clearing and replenishment timescales could generate significant variability in the timing and total mass of dust-lifting events and therefore the specific dust-lifting regime and overall land planet climate.

On average, for simulations at Earth orbit with radiatively active dust, lifting rates in the midlatitudes equate to cumulative erosion rates between 1 and 10 mm per year (Figure 17(b)). Dust is nearly exclusively lofted from midlatitude reservoirs (Figure 17(a), filled contours) and redistributed across a broader fraction of the planetary surface (Figure 17(a), contour lines). Given reasonable assumptions for reservoir depths of tens to thousands of meters and assuming no reservoir replenishment, the dust cycle in our simulations would "turn off" in as little as thousands of years. If winds rapidly deplete reservoirs which cannot be easily replenished a land planet may counterintuitively have progressively clearer skies as it moves closer to its host star. Similarly, depending on the distribution of dust lifting versus dust sedimentation, the planet could cycle between eras of regime I and II lifting and regime III lifting as dust activity shifts to new reservoirs which are then periodically depleted.

Zoom In Zoom Out Reset image size

4.3.3. The Hydrological Cycle