Albedo models for the residual south polar cap on Mars: Implications for the stability of the cap under near-perihelion global dust storm conditions

It is uncertain whether the residual (perennial) south polar cap on Mars is a transitory or a permanent feature in the current Martian climate. While there is no firm evidence for complete disappearance of the cap in the past, clearly observable changes have been documented. Observations suggest that the perennial cap lost more CO₂ material in the spring/summer season prior to the Mariner 9 mission than in those same seasons monitored by Viking and Mars Global Surveyor. In this paper we examine one process that may contribute to these changes—the radiative effects of a planet encircling dust storm that starts during late Martian southern spring on the stability of the perennial south polar cap. To approach this, we model the radiative transfer through a dusty planetary atmosphere bounded by a sublimating CO₂ surface.A critical parameter for this modeling is the surface albedo spectrum from the near-UV to the thermal-IR, which was determined from both space-craft and Earth-based observations covering multiple wavelength regimes. Such a multi-wavelength approach is highly desirable since one spectral band by itself cannot tightly constrain the three-parameter space for polar surface albedo models, namely photon “scattering length” in the CO₂ ice and the amounts of intermixed water and dust.Our results suggest that a planet-encircling dust storm with onset near solstice can affect the perennial cap's stability, leading to advanced sublimation in a “dusty” year. Since the total amount of solid CO₂ removed by a single storm may be less than the total CO₂ thickness, a series of dust storms would be required to remove the entire residual CO₂ ice layer from the south perennial cap.     

A numerical model of the Martian polar cap winds

An investigation of the Martian polar cap winds and their response to a variety of factors is carried out by a series of numerical experiments based on a zonally symmetric primitive equation model. These factors are the seasonal thermal forcing, mass exchange between polar caps and atmosphere, large-scale topography, and polar cap size. The thermal forcing sets up a circulation whose surface winds adjust to achieve angular momentum balance, with low-latitude easterlies and high-latitude westerlies. The maximum westerlies occur roughly where the horizontal temperature gradients are largest. This pattern changes when cap and atmosphere exchange mass. Corriolis forces acting on the net outflow or inflow produce easterlies at the surface during spring (outflow) and westerlies during winter (inflow). Topography appears to have a small effect, but cap size does play a role, the circulation intensity increasing with cap size. Peak surface winds occur when outflow or inflow is a maximum and are 20 m sec^?1 during spring and 30 m sec^?1 during winter for the northern hemisphere. The model results show that surface winds near the edge of a retreating polar cap are substantially enhanced, a result which is consistent with the Viking observations of local dust storm activity near the edge of the south polar cap during spring. The results also indicate that the surficial wind indicators near the south pole are formed during spring and those near the north pole during winter. The implication is that the high-latitude dune fields in the northern hemisphere are formed at a time when the terrain is being covered with frost. It is therefore suggested that the saltating particles are “snowflakes” which have formed by the mechanism proposed by Pollack etal. The model results for the winter simulation, which have formed by the mechanism transport by large-scale eddies, compare favorably with general circulation model (GCM) calculations. This suggests that the eddy transports may be less important than those associated with the net mass flow, and that 2-D climate modeling may be more succesful for Mars than Earth.     

The H Lyman-α emission line from the upper atmosphere of Jupiter: Parametric radiative transfer study and comparison with data

This study uses the adding-doubling radiative transfer method in which we take into account the curvature effect of the planetary atmosphere in order to test the sensitivity of the jovian Ly-α emission line in relation to H column density, eddy diffusion coefficient, frequency redistribution function for photon scattering, temperature vertical profile, and an added hot atomic H layer on the top of the atmosphere. We also focus here on developing new diagnostic tools that will help us to obtain more confidently the underlying thermospheric structure of Jupiter. First, using the brightness distribution for specific wavelength bands as proposed by Ben Jaffel et al. [Ben Jaffel, L., Magnan, C., Vidal-Madjar, A., 1988. Astron. Astrophys. 204, 319-326], we show that the spatial thickness of the atomic H layer above the homopause level can be measured directly as the separation between the vertical positions of respectively the line core and line wing optical limbs. This thickness also constrains the [H] column and the value KH of the eddy diffusion coefficient at the homopause level at the disc location under consideration. We also propose to refine the value of KH and [H], respectively, at a specific planetary latitude, using the Q ratio of the limb peak brightness to the intensity from other regions over the planetary disc. Finally, the relationship between the disc brightness distribution from specific wavelength bands of the emission line and the temperature gradient in the thermosphere is demonstrated, thus providing an accurate tool to access this key information from high resolution observations. Quick, preliminary comparisons with some existing HTS/STIS data show the H layer thickness at auroral latitudes (∼1700 km) is much smaller than at equatorial latitudes (∼3900 km). These results strongly support the existence of a gradient in both H density and KH versus latitude, with higher values of KH at high latitudes and higher values of the H density at the equatorial regions. Such a small H layer thickness at auroral latitudes is consistent with a high mixing in the atmosphere that brings the hydrocarbons upwards, reducing consequently the column of hydrogen that scatters photons. These preliminary results show the strength of the proposed approach and open new horizons to use strong resonant emission lines at high resolution as a diagnostic for the state and structure of planetary upper atmospheres.     

The Martian Hadley circulation: Comparison of “viscous” model predictions to observations

The predictions of an analytical steady thermally forced viscous model for the zonally averaged global circulation of the Martian atmosphere are compared to observations of atmospheric temperatures and eolian feature directions. The temperature of the winter polar atmosphere is a sensitive indicator of the value of the mean eddy diffusivity v of the atmosphere. For global dust storm season, the observed large warming of the atmosphere over the winter (north) pole during the 1977b storm as well as the distribution and azimuths of Type I(b) dust streaks can be well reproduced if v = 10⁷−10⁸cm²sec⁻¹. Observed northeasterly surface winds at high northern latitudes could be produced by plausible fluxes of CO₂ from the northern polar cap. The thermal structure at southern latitudes during this storm is satisfactorily produced, but a major discrepancy exists between observations and predictions of the temperature structure at middle northern latitudes. By comparing these results with those from previous inviscid models of the zonal mean circulation on Mars, we suggest v > 10⁷cm²sec⁻¹ at heights above 30 km and v ⪡ 10⁷cm²sec⁻¹ at lower altitudes may yield a meridional circulation which produces the dynamical warming necessary to account for the observed thermal structure at 0.6 mbar at all latitudes. For late southern summer when the dust content of the atmosphere has decreased to levels characteristic of much of the Martian year, the lack of dynamical warming of the winter pole implies v ≤ 10⁶cm²sec⁻¹. In addition, the predicted surface wind azimuths at this season agree well with the observed azimuths of Type I(d) dust streaks, which are observed to form at this season. The observed latitudinal concentration of the streaks is not explained by the model and may require additional processes which have not been included.     

Precipitation of auroral particles in the central polar cap during a sudden commencement magnetic storm

All-sky camera observations from two stations in the inner (northern) polar cap and an auroral zone station are combined with photometer records from the polar cap station Nord in a study of the brilliant auroral display following the ssc of the storm of 7 November 1970. This display is the large, poleward expanding bulge of a substorm triggered by the ssc. It is composed of brilliant discrete forms embedded in low-intensity diffuse electron and proton aurora. The poleward edge of the diffuse electron aurora is 5° north of the discrete auroras and 3° north of the proton aurora. The intensity of the discrete aurora varies as the strength of the auroral electrojet as shown by magnetograms from auroral zone stations. Succeeding the retreating display a subvisible low-energy electron precipitation, which may be identified as the polar squall (Winningham and Heikkila, 1974) is observed over the polar cap during the main phase of the storm.In the early morning sector already existing diffuse auroras broaden towards the equator from the time of the ssc and at least during the following half hour.Ssc-triggered displays have been found (Feldstein, 1959) to withdraw from the inner polar cap as the initial (positive H) phase of the storm ends. A comparison of the records from seven low-latitude stations shows that during this particular storm the positive phase appears to be composed by two overlapping disturbances, i.e. the proper initial phase, which is generally thought to be due to compression of the inner magnetosphere and a series of positive bays accompanying the negative bays in auroral latitudes. These positive bays are observable over a great range of longitudes with a maximum of amplitude near midnight. As judged from the dayside magnetograms the initial (compression) phase ends at an early stage of the substorm. The observed coincidence between the withdrawal of the display and the cessation of the positive H phase of the storm is a consequence of the fact that the second component—the positive bays—and the auroral display over the polar cap are both signatures of the substorm activity.     

Some photometric properties of the Martian south polar cap region during the 1971 apparition

High-quality Earth-based photographs from the Lowell Observatory Planetary Research Center collection have been analyzed to derive some photometric parameters for the Martian south polar cap region during the 1971 apparition. The optical thickness of the atmosphere above the cap varied with wavelength from 0.35 ± 0.05 in red light to 0.58 ± 0.06 inuv light. The effective geometric albedo is calculated from the 30° phase data assuming isotropic scattering; it varies from 0.85 ± 0.04 (in red light) to 0.63 ± 0.05 (in uv light).     

Water ice clouds in the Martian atmosphere: Two Martian years of SPICAM nadir UV measurements

The SPICAM instrument onboard Mars Express has successfully performed two Martian years (MY 27 and MY28) of observations. Water ice cloud optical depths spatial and temporal distribution was retrieved from nadir measurements in the wavelength range 300–320 nm. During the northern spring the cloud hazes complex distribution was monitored. The clouds in the southern hemisphere formed a zonal belt in the latitude range 30–60°S. The edge of the retreating north polar hood merged with the northern tropical clouds in the range 250–350°E. The development of the aphelion cloud belt (ACB) started with the weak hazes formation (cloud optical thickness 0.1–0.3) in the equatorial region. At the end of the northern spring, the ACB cloud optical thickness reached already values of 0.3–1. The ACB decay in the end of the northern summer was accompanied with a presence of clouds in the north mid-latitudes. The expanded north polar hood merged with the north mid-latitude clouds in the eastern hemisphere. The interannual comparison indicates a decrease in cloud activity immediately after a strong dust storm in southern summer of MY28. The strong dust storms of the MY28 may also be a reason of the observed north polar hood edge shifting northward by 5°.     

Measurements of water vapor in Mars' Antarctic

A complete Mars year of measurements of atmospheric water vapor in the south arctic have been obtained from the Viking Orbiters. Analysis of the observations indicates that, except for the south remnant cap, the southern hemisphere of Mars is devoid of any substantial reservoirs of water in contact with the atmosphere, and that, in the summer time, the top layer of soil is desiccated. Small amounts of water ice are incorporated into the annual CO₂ cap; this water is released at the cap margin when it retreats in the spring. The first global dust storm resulted in heating of the south arctic atmosphere and a transport of water in from the equatorial region. The second global dust storm had a negligible effect on atmospheric water vapor; the dust contained little water.     

Solar heating of the Martian dusty atmosphere

This paper examines the solar heating of the Martian atmosphere during the 1971 global dust storm observed by Mariner 9. Radiative scattering as well as absorption is included by utilizing the delta-Eddington approximation to the full radiative transfer equation. The necessary optical parameters are generated by a Mie program which uses a size distribution and a complex refractive index inferred from a number of sources, particularly from recent analyces of Mariner 9 UVS and TV observations. Assuming uniform mixing of the dust, the solar heating per unit mass during a Martian global dust storm is remarkably uniform with height for small solar zenith angles. Heating rates may reach 80°K day^? for overhead sunlight. Overall, 20% of the direct insolation is absorbed by the dust-laden atmosphere. Even optically thin widespread dust hazes may produce heating rates of several degrees Kelvin per day.     

The effects and characteristics of atmospheric dust during martian global dust storm 2001A

We present retrieved trends in dust optical depth, dust effective radius and surface temperature from our analysis of Mars Global Surveyor Thermal Emission Spectrometer daytime data from global dust storm 2001A, and describe their significance for the martian dust cycle. The dust optical depth becomes correlated with surface pressure during southern spring and summer in years both with and without a global dust storm, indicating that global dust mixing processes are important at those seasons. The correlation is low at other times of the year. We found that the observed decay of optical depths at the later stages of the dust storm match, to first-order, theoretical values of clearing from Stokes–Cunningham fallout of the dust. Zonally averaged effective radius is constant within standard deviation of results (between 1.2 and 2.0 μm, with a global mean for all seasons of 1.7 μm), at all latitudes and seasons except at southern latitudes of 35° and higher around equinoxes in both martian years, where it is larger than average (2–3 μm). The emergence and disappearance of these larger particles correlates with observations of polar cap edge storms at those latitudes. Northern latitude observations under similar conditions did not yield a similar trend of larger average effective radii during the equinoxes. We also report on a linear correlation between daytime surface temperature drop and rise in optical depth during the global dust storm. Global dust storm 2001A produced a significant optical depth and surface temperature change.     

Characteristics of the radiation emerging from the top of a Rayleigh atmosphere—II Total upward flux and albedo

The solution of the equation of radiative transfer in a medium exhibiting Rayleigh scattering, as developed by S. Chandrasekhar, has been used for an extensive series of computations(³) of the characteristics of the scattered and diffusely reflected radiation emerging from the top of an atmospheric model which corresponds in many respects to the sunlit portion of the earth's atmosphere. The first part of this two-part discussion dealt with the intensity, degree of polarization, plane of polarization and the neutral points of the emergent light as functions of sun elevation, direction in the downward hemisphere, optical thickness of the model atmosphere and reflectivity of the underlying surface. This second part is concerned with the upward flux obtained by an integration of the intensity over the entire hemisphere, for the incident radiation (a) being independent of wavelength or (b) having the spectral distribution of the extra-terrestrial solar radiation. Integration with respect to wavelength in the latter case, together with an approximation for the sphericity of the atmosphere, yields a value of 7.6 per cent for the earth's planetary albedo due to scattering by the clear atmosphere. An approximation for ozone absorption decreases the computed albedo to 6.9 per cent.     

Theoretical interpretation of photometric properties of the Martian surface and atmosphere

Earth-based UBV photometry, high-quality photographs from the Lowell Observatory collection, and Mariner 9 data have been combined with a new radiative transfer theory to derive physical parameters for the Martian surface and atmosphere, both before and during the 1971 dust storm. We find that the dust particles of the storm had a single-scattering albedo of 0.84 ± 0.02 and an asymmetry factor of 0.35 ± 0.10 in green (V) light. The geometric albedo of Mars was 0.15 and the phase integral 1.83, which yield 0.27 for the Bond albedo. The mean optical thickness of the “clear” atmosphere averaged over the whole planet was 0.15 ± 0.05 and was not detectably dependent on wavelength. Geometric albedos for the surface are 0.25 (light areas) and 0.17 (dark areas) in V, 0.095 in B (both areas), and 0.060 in U (both areas). The soil particles are moderately backward scattering with an asymmetry factor of ?0.20, indicating them to be rather opaque. The mean surface roughness, on a scale larger than that of individual dust particles and therefore large compared with the wavelength, is 0.57. This represents the depth/radius ratio of an average hole and it is only one-half as large as values typical for the Moon and asteroids.     

Yearly comparisons of the martian polar caps: 1999-2003 Mars Orbiter Camera observations

The Mars Global Surveyor Mars Orbiter Camera wide-angle cameras were used to obtain images of the north and south seasonal and residual polar caps between 1999 and 2003. Wide-angle red camera images were used in assembling mosaics of the north and south polar recessions and regression rates were measured and compared. There are small variations in the north polar recession between 2000 and 2002, especially between LS=7° and LS=50°, however there is no evidence for the plateau in the recession curves that has been observed in some prior years. The south polar recession changes very little from year to year, and the 2001 dust storm had little if any effect on the average cap recession that year. Albedo values of the geographic north pole were measured using wide-angle red and blue camera images, and the residual south polar cap configuration was compared between the three years observed by MOC. The albedo of the geographic north pole generally varies between 0.5 and 0.6 as measured from MOC wide-angle red camera images. There were only minor variations near the edges of the residual south polar cap between the three years examined.     

Parameters of Dust Particles in the Martian Atmosphere

A critical analysis of the methods and results of estimating the optical thickness of the dust component in the Martian atmosphere ₀, the particle size r ₀, and the imaginary part of the refractive index n _ihas shown the following. (1) Observational data on the brightness distribution over the Martian disk as well as the phase dependences of diffusely reflected light and the azimuthal dependences of diffusely transmitted light are most appropriate to use only for verifying the reliability of the aerosol parameters determined by other methods. (2) If the morning and evening fogs in the atmosphere are disregarded, the Bouguer–Lambert–Beer method used to analyze the solar-brightness attenuation measured on the planetary surface yields overestimated extraatmospheric solar intensity I ₀and atmospheric optical depth ₀. At the Viking 1landing site, I ₀and ₀could be overestimated by a factor of 1.7 and by 0.35, respectively. (3) The aerosol size determined by analyzing measurements of the azimuthal dependences for the Martian sky brightness at low elevations of the Sun most likely corresponds to the fog particles. (4) If overestimated values of I ₀were used to standardize the observations of the solar radiation transmitted by the Martian atmosphere, then n _iwere also overestimated; using overestimated ₀also affected the reliability of the latter. (5) The problem of reliability of the available ₀and r ₀estimates for periods of high atmospheric transparency is yet to be solved. For the highest activity of the dust storm in 1971, it was found that 4.5 r ₀ 7.5 m for the lognormal particle size distribution with ²= 0.2 and the optical thickness of a dust cloud ₀ 15. (6) The spectral values of the apparent albedo of Mars measured in October 1971 at a phase angle of 42° in the spectral range 0.250 0.717 allowed the imaginary part of the refractive index to be estimated in terms of a model of a dust cloud composed of spherical particles with the lognormal size distribution with r ₀= 4.5 m and ²= 0.2.     

Constraints on the composition of the martian south polar cap from gravity and topography

The polar caps of Mars have long been acknowledged to be composed of unknown proportions of water ice, solid CO₂ (dry ice), and dust. Gravity and topography data are here analyzed over the southern cap to place constraints on its density, and hence composition. Using a localized spectral analysis combined with a lithospheric flexure model of ice cap loading, the best fit density of the volatile-rich south polar layered deposits is found to be 1271 kg m⁻³ with 1-σ limits of 1166 and 1391 kg m⁻³. The best fit elastic thickness of this geologically young deposit is 140 km, though any value greater than 102 km can fit the observations. The best fit density implies that about 55% dry ice by volume could be sequestered in these deposits if they were completely dust free. Alternatively, if these deposits were completely free of solid CO₂, the dust content would be constrained to lie between about 14 and 28% by volume. The bulk thermal conductivity of the polar cap is not significantly affected by these maximum allowable concentrations of dust. However, even if a moderate quantity of solid CO₂ were present as horizontal layers, the bulk thermal conductivity of the polar cap would be significantly reduced. Reasonable estimates of the present day heat flow of Mars predict that dry ice beneath the thicker portions of the south polar cap would have melted. Depending on the quantity of solid CO₂ in these deposits today, it is even possible that water ice could melt where the cap is thickest. If independent estimates for either the dust or CO₂ content of the south polar cap could be obtained, and if radar sounding data could determine whether this polar cap is presently experiencing basal melting or not, it would be possible to use these observations to place tight constraints on the present day heat flow of Mars.     

Saturn's Rings: Azimuthal variations,phase curves,and radial profiles in four colors

Four-color photographic photometry of Saturn for the 1977–1979 apparitions has been analyzed to determine the dependence of ring brightness on wavelength, solar phase angle, ring particle orbital phase angle (azimuthal effect), declination of the Earth relative to the ring plane (tilt angle), and radial distance from Saturn. Azimuthal brightness variations up to ±20% relative to the ansae are clearly apparent for the maximum of ring A, but are not detectable for ring B or the outer portion of ring A. The shape of the intensity (I) versus orbital phase angle (θ) curve varies with ring tilt (B) and probably with wavelength, and shows 180° symmetry. As characterized by its slope near the ansae, this curve suggests that the azimuthal effect increases as B decreases from 26 to ≈11°. The phase curves l(α) for the ansae show very little dependence on ring tilt (26° > B > 6°), on wavelength, or on radial distance from Saturn; possibly the curves are somewhat steeper at the smallest tilt angles and for ring A relative to ring B. The radial profile of both rings becomes flatter with decreasing tilt angle and with decreasing wavelength. The latter effect is a natural result of the classical, many-particle-thick ring model.     

Light Scattering by Aggregate Particles Comparable in Size to Wavelength: Application to Cometary Dust

Many naturally occurring particles (including, most likely, cometary dust) have an aggregate structure. We study the scattering properties of polydisperse independent aggregate particles (clusters) comparable in size to visible wavelengths. The sizes of the monomers constituting a cluster play a significant role in forming the angular dependences of intensity and linear polarization of the scattered light. Irregularly structured aggregates composed of a moderate number of spheres (<50) with size parameters 1.3–1.65 exhibit properties typical of cometary dust particles: a slight increase in backscattering intensity, a negative polarization at small phase angles, an inversion phase angle close to the observed one, an increase in brightness, and a linear polarization with increasing wavelength. In this case, the imaginary part of the refractive index for particles can increase with decreasing wavelength in the visible spectral range, which is typical of silicates with an admixture of iron or organic material. The spectral dependence of extinction efficiency for aggregates is less steep than that for equivalent spherical particles, and its maximum is shifted to larger size parameters. Therefore, when analyzing extinction measurements, the scatterer shape must be taken into account to avoid underestimation of the scattering-particle sizes.     

MOC observations of the 2001 Mars planet-encircling dust storm

From 15 September 1997 through 21 January 2006, only a single planet-encircling martian dust storm was observed by MGS-MOC. The onset of the storm occurred on 26 June 2001 (Ls=184.7°), earliest recorded to date. It was initiated in the southern mid-to-low latitudes by a series of local dust storm pulses that developed along the seasonal cap edge in Malea and in Hellas basin (Ls=176.2°-184.4°). The initial expansion of the storm, though asymmetric, was very rapid in all directions (3-32 m s⁻¹). The main direction of propagation, however, was to the east, with the storm becoming planet encircling in the southern hemisphere on Ls=192.3°. Several distinct centers of active dust lifting were associated with the storm, with the longest persisting for 86 sols (Syria-Claritas). These regional storms helped generate and sustain a dust cloud (“haze”), which reached an altitude of about 60 km and a peak opacity of τdust∼5.0. By Ls=197.0°, the cloud had encircled the entire planet between 59.0° S and 60.0° N, obscuring all but the largest volcanoes. The decay phase began around Ls∼200.4° with atmospheric dust concentrations returning to nominal seasonal low-levels at Ls∼304.0°. Exponential decay time constants ranged from 30-117 sols. The storm caused substantial regional albedo changes (darkening and brightening) as a result of the redistribution (removal and deposition) of a thin veneer of surface dust at least 0.1-11.1 μm thick. It also caused changes in meteorological phenomena (i.e., dust storms, dust devils, clouds, recession of the polar caps, and possibly surface temperatures) that persisted for just a few weeks to more than a single Mars year. The redistribution of dust by large annual regional storms might help explain the long period (∼30 years) between the largest planet-encircling dust storms events.     

The influence of the Martian polar caps on the diurnal tide

The large horizontal heating gradients that exist near the edge of the Martian polar caps during spring are shown to be capable of exciting large oscillations in the diurnal tide. To a lesser extent, the daily mass cycling between cap and atmosphere can also contribute. The calculations which demonstrate this are based on classical tidal theory as applied to the cylindrical coordinate system. This is done to facilitate the representation of the heating function. Results are presented for the horizontal surface winds only. They indicate a circulation at the cap edge somewhat analogous to the smaller scale terrestrial sea breeze. The amplitude of the zonal component is largest and is increased from 1 to 10 m sec^?1 by the modeled influence of the polar cap. When coupled with the basic flow these cap-edge tides can produce strong surface winds during spring. Such a mechanism may contribute to the ability of the south polar cap winds to generate the local dust storms observed near the cap edge at this season.