Corresponding author: M. A. Kahre, NASA Ames Research Center, MS 245-3, Moffett Field, CA 94035, USA. (firstname.lastname@example.org)
 C. Leovy (personal communication, 2007) speculated that two stable climate states on early Mars could have resulted from interactions between the dust and CO2 cycles. In one state, a highly active dust cycle would prevent atmospheric collapse, and in the second, the collapsed atmosphere would not maintain an active dust cycle. An initial assessment of this idea is presented based on a Mars general circulation model parameter study. A range of global dust loadings, CO2 ice albedos, and obliquities are investigated to explore conditions in which increasing the atmospheric dust content stabilizes an otherwise unstable atmosphere. We find that dust only stabilizes the atmosphere at high obliquity and when the CO2 ice albedo is high. Although results suggest that two stable states could have existed on early Mars under limited conditions, further work is needed to know if the conditions necessary are physically plausible.
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 Many critical questions remain largely unanswered regarding the state of the early Martian atmosphere and climate. Evidence for the existence of flowing and standing liquid water during the late Noachian is abundant through observations of the valley networks and the widespread presence of phyllosilicate minerals on the surface [Carr, 1996; Hynek et al., 2010; Poulet et al., 2005; Ehlmann et al., 2011]. By the early Hesparian, however, valley network and phyllosilicate formation had diminished [Fassett and Head, 2008, 2011]. This marked change in the morphology and mineralogy of the surface strongly suggests that Mars' atmosphere underwent dramatic changes during this time period. The nature of the climate at the Noachian/Hesperian boundary is the focus of this work.
 C. Leovy (personal communication, 2007) speculated that interactions between the dust and CO2 cycles early in Mars' history could have resulted in two stable climate states near the Noachian/Hesperian boundary for moderately massive atmospheres (<100 mbar): an inflated, high-pressure atmosphere with a highly active dust cycle and a collapsed, low-pressure atmosphere with a quiescent dust cycle. In the first case, a thicker, more massive atmosphere would cause high dust lifting rates and an atmosphere dustier than at present. The high levels of atmospheric dust (i.e., high optical depth) would increase the heat transport of the atmosphere and would inhibit CO2 condensation by increasing the downward infrared flux at the surface. In the second case, dust lifting would not be efficient enough to maintain high levels of atmospheric dust, and the atmosphere would collapse, further decreasing the efficiency of dust lifting. This idea raises the possibility that not only could two stable states exist but also that transitions from one stable state to another could occur on relatively short time scales by perturbing the system in some way.
 There are several lines of evidence suggesting that Mars' atmosphere was substantially more massive than it is today. Prevailing formation theories of geologic features such as the valley networks necessitate the presence of flowing liquid water, which implies a warmer climate induced by a much thicker atmosphere. However, the mass of the early Martian atmosphere is not well constrained. Atmospheric mass loss predictions based on estimates of solar wind-induced ion sputtering and photochemical escape processes suggest that between 50% and 90% of Mars' atmosphere has been lost since the late Noachian (~3.8 Gya [Jakosky et al., 1994]). We target the upper end of this range—approximately 80 mbar—for this study.
 It is plausible that the dust cycle would have been more active when the Martian atmosphere was thicker than it is today [Armstrong and Leovy, 2005]. Sagan and Bagnold  first hypothesized that the efficiency of wind erosion could be linked to the variable nature of surface pressure on Mars. A commonly invoked mechanism for dust lifting from the Martian surface is through momentum transfer from the atmosphere to the surface by near-surface winds. The momentum imparted to the surface by winds is governed by the surface stress (τ): τ = ρu*2, where ρ is the near-surface atmospheric density and u* is the surface friction velocity. This relationship dictates that for a given surface friction velocity, the momentum transferred to the surface increases linearly with atmospheric density (or similarly, surface pressure).
 Simple energy balance calculations show that increasing the mass of a CO2 atmosphere decreases atmospheric stability against collapse. As surface pressure increases, the CO2 condensation temperature increases, which makes it easier for CO2 ice caps to form and persist. The obliquity of the planet and the albedo of the surface CO2 ice play important roles in controlling the stability of the atmosphere. As obliquity decreases, the annually averaged solar insolation received at the high latitudes decreases [Ward, 1992], and the atmosphere is more likely to collapse. Similarly, as the surface CO2 ice albedo increases, the atmosphere is more likely to collapse because less energy is retained by the system. Additionally, the presence of a “faint young Sun” that was likely about 25% less luminous than the Sun today [Gough, 1981] makes it more difficult for a more massive atmosphere to have remained stable against collapse. Forget et al.  found that atmospheres between approximately 500 mbar and 2 bars (depending on obliquity) are stable against collapse, while atmospheres that are either more massive than 3 bars or less massive than 500 mbars tend to be unstable against collapse. The processes that could balance the collapsing tendency as the mass of the atmosphere is increased from its current-day value are heat transport and the greenhouse effect of the atmosphere. Airborne dust critically influences the radiative and dynamical states of the current Martian atmosphere, so it is possible that the dust cycle could have played a role in the stability of the early Martian atmosphere.
 Leovy's idea is based on two theoretical predictions for the behavior of the dust on early Mars. The first is that a thicker Martian atmosphere would be capable of lifting dust more efficiently than Mars' current atmosphere; the second is that the radiative and dynamical effects of large quantities of atmospheric dust would inhibit CO2 condensation and increase the stability of a massive atmosphere. We present a Mars general circulation model (GCM) parameter study designed to investigate the effectiveness of increasing the global dust loading in stabilizing moderately massive (80 mbars) Martian atmospheres. In order to fully understand how dust loading affects atmospheric stability, we explore a range of dust loadings, CO2 ice cap albedos, and obliquities.
2 Numerical Methods
 The NASA Ames Mars general circulation model (MGCM) is used to explore the effects of three parameters—dust loading, CO2 ice cap albedo, and obliquity—on the CO2 cycle and atmospheric collapse. The MGCM is a 3-D finite-difference model of the Martian atmosphere. The version used for this study, v1.7.3, has been utilized for several investigations of the current and past climate of Mars [Kahre et al., 2006, 2008; Kahre and Haberle, 2010; Haberle et al., 2006; Hollingsworth and Kahre, 2010] and was selected for use because it is computationally efficient.
 Dust in Mars' atmosphere significantly affects atmospheric heating through interactions with both solar and infrared radiation [Gierasch and Goody, 1968; Haberle et al., 1982; Madeleine et al., 2011]. Therefore, incorporating the radiative effects of suspended dust in the model is crucial for climate study simulations. The model radiative transfer scheme accounts for suspended dust and gaseous CO2 at both solar and infrared wavelengths [Pollack et al., 1990; Haberle et al., 1999; Kahre and Haberle, 2010]. In the visible, the net solar flux at each vertical layer is calculated using the radiative effects of CO2 and airborne dust. Atmospheric dust is treated in the visible through a series of offline multispectral, multiscattering calculations that are implemented in the model in the form of a look-up table. In the infrared, the spectrum is divided into two intervals within which the dust and CO2 are accounted for: one inside the 15 µm vibrational CO2 band and one outside the 15 µm band. An offline Delta-Eddington two-stream approximation model is used to tabulate dust emissivities for a range of dust optical depths and temperatures for ingestion into the GCM. The radiative properties of the dust that are included in this version of the model are hardwired and derived from Pollack et al. [1979, 1995]. The single scattering albedo employed in the model is 0.86. The asymmetry parameter is 0.79, and the ratio of the visible to infrared opacity (absorption only) is assumed to be 2.
 The single scattering albedo employed here is low compared to more recently derived results [Wolff and Clancy, 2003; Clancy et al., 2003; Wolff et al., 2009; Madeleine et al., 2011], so we explore how a higher dust single scattering albedo would affect the results presented. The most recent NASA Ames radiation code is a two-stream, correlated-k scheme, which allows for the implementation of current dust optical properties. We use a 1-D version of this code (with current dust optical properties) compared to results of the older band-model radiation code (with older dust optical properties) to explore differences in the calculated planetary albedo as a function column dust optical depth. Shown in Figure 1 are the results of this comparison. Although the calculated planetary albedos differ slightly, the models agree well enough for us to have confidence in the general behavior predicted by the older radiation code.
 Twenty-seven simulations were designed and executed for 5 Martian years with a circular orbit (Table 1). We explore a range of global dust loadings from 0.3 to 5.0, surface CO2 ice albedos from 0.3 to 0.7, and obliquities from 30° to 60°. We do not include obliquities less than 30° because we are looking for combinations that lead to stable atmospheres and the atmosphere is extremely unstable at low obliquities. Obliquities higher than 60° are not considered because according to the numerical predictions for the chaotic obliquity of Mars, extremely high obliquities are not expected to have been common occurrences [Laskar, 2004]. The model is initialized with 80 mbars of CO2, and the solar luminosity is set to 75% of the present value. For this study, the GCM has a horizontal resolution of 5° in latitude by 6° in longitude. The quantity of atmospheric dust varies by simulation, but within a simulation, dust is assumed to be constant in time and space (i.e., horizontally and vertically homogenous). Dust is distributed vertically based on the Conrath-ν prescription, which well mixes dust up to a particular pressure level depending on the Conrath-ν parameter (taken to be 0.03 here) [Conrath, 1975]. The model uses a broadband polar cap albedo at visible wavelengths, which is set to a user-defined constant value when CO2 ice is present on the surface.
Table 1. Parameters Used in the MGCM Study
Dust Optical Depth
CO2 Cap Albedo
 An atmosphere is stable when the CO2 that condenses during local fall and winter sublimates entirely during spring and summer. If seasonally condensed CO2 persists in either one or both hemispheres throughout the year, permanent CO2 ice caps form and the atmosphere collapses. Of the 27 simulations executed, 14 resulted in collapsing atmospheres, while 13 remained stable against collapse (Figure 2). All three factors examined—obliquity, CO2 ice cap albedo, and dust loading—affect the stability of the atmosphere (or, in the case of a collapsing atmosphere, how quickly it collapses). As demonstrated in the following sections, changing obliquity and CO2 ice albedo affects atmospheric stability against collapse monotonically, but increasing the dust loading does not. At the lowest obliquity studied (30°), only the simulation with the lowest CO2 ice cap albedo (0.3) and dust loading (optical depth of 0.3) remains stable against collapse. At 45° obliquity, approximately half of the simulations are stable, with low to moderate CO2 ice cap albedo and dust loadings producing stable configurations. At 60° obliquity, all but one simulation is stable; only the simulation with high CO2 ice cap albedo and low dust loading collapses. In the following sections, we show results from simulations that contain the highest and lowest values of albedo and dust loading in order to demonstrate and explain the trends that are evident in the entire suite of experiments. We focus on the 30° obliquity simulations to understand how dust and CO2 ice cap albedo affects CO2 condensation and sublimation before we investigate the effects of increasing obliquity.
3.1 30° Obliquity Results
 Of the simulations conducted at 30° obliquity, the only stable case has the lowest explored dust loading and CO2 ice albedo (optical depth of 0.3 and 0.3, respectively). We therefore investigate how albedo and dust loading affect the atmospheric collapse rates. The albedo of surface CO2 ice regulates the fraction of solar energy absorbed by the polar caps when the Sun is above the horizon. Thus, a higher ice albedo tends to enhance condensation and suppress sublimation along the edges of the growing and receding polar cap, respectively. Not surprisingly, then, for a given atmospheric dust loading, increasing the CO2 ice albedo destabilizes the atmosphere, with the collapse rate increasing with increasing albedo (Figure 3).
 The effect of increasing the atmospheric dust loading is more complicated. In fact, increasing the dust loading can either act to increase or decrease the collapse rate of an 80 mbar atmosphere, depending on the CO2 ice albedo. As shown in Figure 3, increasing the dust loading acts to reduce the atmospheric collapse rate when the CO2 ice albedo is high, and works to increase the atmospheric collapse rate when the CO2 ice albedo is low. To understand why this is true, we must look in detail at how atmospheric dust affects both the growth and recession of the CO2 ice caps.
3.1.1 Effect of Dust on Cap Growth
 As shown in Figures 3 and 4, increasing atmospheric dust results in a decrease in the total amount of CO2 condensed during the growth phase of the CO2 ice cap. Increased dustiness inhibits CO2 condensation both inside and outside of the polar night.
 Increasing the dust loading suppresses CO2 condensation in the polar night, which contributes significantly to an overall reduction in total mass of the CO2 cap. Heat transport at these polar latitudes is weak, so radiative effects in the infrared dominate. Increasing dust enhances the downward infrared radiation at the surface, which acts to suppress surface CO2 condensation (Figure 4). Although atmospheric CO2 condensation increases with increasing dust in the polar night, dust suppresses the total CO2 condensation rate because it reduces the net radiative loss at the top of the atmosphere. This result is consistent with previous work [Pollack et al., 1990; Kahre and Haberle, 2010].
 In the region surrounding the polar night where the Sun is sometimes above the horizon during cap growth, solar wavelength radiative effects and heat transport are important in addition to the infrared radiative effects (Figure 4). As in the polar night, increasing atmospheric dust increases the downward infrared radiation at the surface at these latitudes, which suppresses surface CO2 condensation. Additionally, as dust loading increases, the latitudinal heat transport increases due to the increased strength of the circulation [Pollack et al., 1990; Kahre and Haberle, 2010], which also inhibits CO2 condensation. These two effects dominate over the shielding (cooling) of the surface and the lower atmosphere by atmospheric dust has when the Sun is above the horizon, and ultimately limits the equatorward extent of the CO2 ice cap.
3.1.2 Effect of Dust on Cap Recession
 Cap sublimation occurs when the Sun is above the horizon, so latitudinal heat transport and the balance between the solar and infrared dust radiative effects are keys to understanding how dust affects cap recession. The efficiency of the CO2 cap recession phase is critical for determining whether an atmosphere will collapse or remain stable.
 Along the edge of the retreating CO2 ice cap where sublimation rates are at a maximum, increasing the dust loading decreases the downward solar flux at the surface and increases the downward infrared at the surface (Figure 5). The solar flux absorbed by the surface decreases further as the CO2 ice albedo increases. The total energy absorbed by the surface (absorbed solar plus infrared) either increases or decreases with increasing atmospheric dust, depending on the CO2 ice albedo. When the CO2 ice albedo is low, increasing atmospheric dust decreases the total energy absorbed by the surface and thus decreases the CO2 sublimation rates. When the CO2 ice albedo is high, the opposite is true. This result can be further understood by examining the effect of increasing the dust loading over low- and high-albedo surfaces on the planetary albedo. As shown in Figure 5, the planetary albedo is raised when dust is added over a low-albedo surface but is reduced when dust is added over a high-albedo surface. Thus, the increase or decrease of the planetary albedo is reflected in the reduced or enhanced CO2 sublimation rates during cap retreat.
3.1.3 Net Effect of Dust on Atmospheric Collapse
 The net effect of dust on atmospheric stability depends on the combined effects of dust on CO2 cap growth and recession. Results show that increasing atmospheric dust loading does not monotonically affect the tendency for an 80 mbar atmosphere to collapse. Dust decreases the rate at which the atmosphere collapses when the cap albedo is high because it suppresses CO2 condensation more than it impedes CO2 sublimation. Conversely, dust increases the tendency for the atmosphere to collapse when the cap albedo is low because it impedes CO2 sublimation more than it suppresses CO2 condensation. Although dust decreases the rate at which the atmosphere collapses in certain cases, it is important to note that dust never stabilizes an otherwise unstable atmosphere at 30° obliquity.
3.2 Higher Obliquity Results
 The obliquity of Mars determines the latitudinal distribution of insolation and therefore strongly regulates the growth and recession of the CO2 polar ice caps. As obliquity increases, the annual mean insolation increases at high latitudes (> ~ 40°) and decreases at low latitudes (<40°). At obliquities lower than 54°, the equator receives more solar insolation than the poles, but at obliquities higher than 54°, the poles receive more solar insolation than the equator [Ward, 1992]. As shown in Haberle et al.  and Newman et al. , increasing obliquity significantly affects both the mass and latitudinal extent of the seasonal CO2 ice caps.
 As shown in Figures 6 and 7, increasing obliquity increases the tendency for 80 mbar atmospheres to be stable. The seasonal CO2 ice caps grow more massive and extend farther equatorward during local autumn and winter as obliquity increases because the winter hemisphere receives progressively less solar insolation. However, these more massive, more extensive ice caps recede quickly during spring and summer, due to the much greater solar insolation received at high latitudes in the summer hemisphere. The net effect of increasing obliquity is that, while more atmospheric mass cycles in and out of the CO2 ice caps annually, the increased CO2 sublimation during cap retreat more easily dominates over CO2 condensation, leading to increased atmospheric stability.
 Similar to the 30° obliquity simulations, the most stable simulations at 45° and 60° obliquity occur when both the CO2 ice cap albedo and the atmospheric dust loading are low or moderately low (see Figure 2). At 45° obliquity, there are no stable cases with the highest dust loading (a dust optical depth of 5.0) or with the highest CO2 ice albedo (0.7; Figures 2 and 6). Thus, like at 30° obliquity, dust does not stabilize an otherwise unstable configuration at 45° obliquity. However, there are stable configurations at 60° obliquity with high dust loading (optical depth > 1.0) and high CO2 ice albedo (0.7; Figures 2 and 7). When the CO2 ice cap albedo is high, the increased dust loading is responsible for stabilizing an otherwise unstable atmosphere. As discussed below, the only hint that two stable states regulated by the dust cycle could occur is at very high obliquity.
 We can make an initial assessment of the viability of Leovy's idea that there could have been two stable climate states on early Mars that were modulated by the dust cycle. Our modeling study suggests that his idea may be possible, but only under limited conditions. Situations must be found in which adding dust stabilizes an otherwise unstable atmosphere. Of the simulations conducted with 80 mbar atmospheres, this only occurs at high obliquity (60°), and only when the CO2 ice cap albedo is high (0.7). In order to better understand exactly how high the obliquity, CO2 ice cap albedo, and dust loading must be for two stable states to be possible, we executed additional simulations ranging between 45° and 60°. It is important to note that the precise transition point of obliquity, CO2 ice albedo, and dust loading are sensitive to model parameters such as the optical properties of airborne dust and the assumed vertical and horizontal dust distribution. It could also depend greatly on the initial mass of the atmosphere, which has been fixed for the current study. Nonetheless, simulations with an 80 mbar atmosphere indicate that the obliquity must be at least ~55°, the CO2 ice albedo must be high (>0.6), and the global atmospheric dust optical depth must be ~ unity or higher for dust to stabilize an otherwise unstable situation. The minimum obliquity required is very close to the obliquity at which more solar insolation is delivered annually to the poles than the equator (54°), which may not be coincidental. The minimum CO2 ice albedo required depends on what value the planetary albedo asymptotes to over the poles as the dust loading is increased to near unity (~0.6 for the dust single scattering albedo used here). This is because the stabilizing or destabilizing effect of dust is related to whether adding dust to the atmosphere increases or decreases the planetary albedo. It is not yet known if the combination of high obliquity, high CO2 ice albedo, and a highly dusty atmosphere could occur in a self-consistent system.
 Although it seems plausible that a massive atmosphere could be dusty at high obliquity [Haberle et al., 2003; Newman et al., 2005], we do not know how dusty the atmosphere would be or how dust would vary spatially or seasonally. The spatial and seasonal distribution of dust could be critically important. For instance, the global dust loading could be high but there could be very little dust in the polar night to suppress CO2 condensation. Fully interactive dust cycle modeling at high obliquity that includes the lifting, transport, and removal of dust would help us understand the behavior of the dust cycle in massive atmospheres.
 The most challenging requirement in the scenario that leads to dust stabilizing the atmosphere is the high cap albedo. In order for dust to stabilize the atmosphere at high obliquity, the CO2 ice caps need to remain clean of dust. This is difficult to reconcile with the likelihood that increasing the dust loading of the atmosphere would lead to increased dust fallout at high latitudes in the region of the growing CO2 cap, thus lowering the albedo of the CO2 ice surface. Again, fully interactive dust cycle modeling could be used to address this issue. Additional physics must be included to allow for the prediction of CO2 ice cap albedos based on the relative fraction of ice and dust on the surface.
 If the conditions necessary for two stable climate states are possible, an interesting question becomes whether or not transitions could occur between the dusty, inflated atmosphere state and the clear, collapsed atmosphere state without the aid of longer-term variations in the planet's orbit parameters (i.e., obliquity). Transitions away from the inflated state could theoretically occur due to small perturbations in the dust cycle. For example, if the dust cycle was slightly less active during 1 year relative to previous years, the atmosphere could destabilize and collapse would begin. The decrease in the atmospheric mass as collapse occurs would likely further reduce the vigor of the dust cycle in subsequent years, which in turn would accelerate the collapse process. Transitions away from the collapsed state could be possible as the result of perturbations to the CO2 cycle. If slightly more CO2 entered the atmosphere 1 year relative to previous years, the increase in atmospheric mass could potentially generate a more vigorous dust cycle. Increasing the atmospheric dust loading would then reinforce the increased CO2 sublimation rates, resulting in an inflation of the atmosphere. Both of these transition scenarios are highly speculative and would require that the albedo of the CO2 ice caps would remain high and relatively insensitive to the rigor of the dust cycle. Additionally, it is difficult to identify specific processes that would allow for drastic enough perturbations in the dust and CO2 cycles for these transitions to occur.
 We have conducted an initial GCM study to assess whether the dust cycle could have led to two stable climate states on early Mars. For dust to stabilize a moderately thick (80 mbar) atmosphere, increasing the atmospheric dustiness must act to prevent CO2 caps from persisting year-round. A range of dust loadings, CO2 ice cap albedos, and obliquities was explored to study how increasing atmospheric dust affects atmospheric stability for moderately thick (80 mbar) atmospheres. Of the simulations conducted, increasing the dustiness of the atmosphere only stabilizes an otherwise unstable atmosphere when the CO2 ice cap albedo and the obliquity are both high (>0.6° and >50°, respectively). Although our preliminary conclusion is that two stable states are possible for a limited set of conditions, further work must be done to know if the conditions necessary are physically plausible.
 This project would not have come about if it were not for Conway Leovy. His participation in this ongoing work will be greatly missed. This work was funded by the Mars Fundamental Research Program. The authors thank Claire Newman and an anonymous reviewer for their insightful comments and suggestions.