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

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Planetary and Space Science 56 (2008) 181–193 www.elsevier.com/locate/pss

Albedo models for the residual south polar cap on Mars: Implications for the stability of the cap under near-perihelion global dust storm conditions Boncho P. Boneva,b,,1, Gary B. Hansenc, David A. Glenarb,2, Philip B. Jamesd, Jon E. Bjorkmana a

Ritter Astrophysical Research Center, Department of Physics and Astronomy, The University of Toledo, Toledo, OH 43606, USA b Solar System Exploration Division, Code 693, Building 2, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA c Department of Earth and Space Science, University of Washington, Box 351310, Seattle, WA 98195, USA d Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301 Accepted 6 July 2006

Abstract 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. r 2007 Elsevier Ltd. All rights reserved. Keywords: Mars; Polar caps; Residual south polar cap; Surface albedo; Ices; Spectroscopy; Atmospheric dust; Radiative transfer; Dust storms

1. Introduction About 95% of the Martian atmosphere consists of CO2. Between a quarter and a third of this amount is cycled through the polar caps, condensing out in the fall and Corresponding author. Present address. Department of Physics, Catholic University of America, Washington, DC 20064, USA. Tel.: +1 301 286 1804; fax: +1 301 286 0212. E-mail address: [email protected] (B.P. Bonev). 1 Work was finished while at Department of Physics, The Catholic University of America, Washington DC, 20064, USA. 2 NASA Infrared Telescope Facility, USA.

0032-0633/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2007.08.003

winter and sublimating in the spring and summer. This atmosphere–surface interaction defines the planet’s CO2 cycle. The polar caps are the sources and sinks of the exchanged CO2 and therefore play a key role in this cycle. The latent heat released during condensation is a major source for the energy radiated to space by the cap. Solid carbon dioxide sublimes in spring, absorbing latent heat from the insolation as it transitions to a gas phase. Interannual variability in the amount of exchanged CO2 between surface and atmosphere is evidenced by apparent year-to-year variability in the caps’ appearances, which have been studied by ground-based measurements, and

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more recently by space-craft observations (see James et al., 1993, 2005a; Forget, 1998). The polar caps of Mars were among the first features identified by telescopic observers in the eighteenth century. Herschel (1784) documented variations in the polar caps and correctly attributed them to seasonal effects due to the inclination of the Martian axis to its orbital plane. The cyclic waxing and waning of the polar cap boundaries was the primary indicator of the seasonal Martian climate before the space age. Prior to the measurement of atmospheric pressure by Mariner 4, the caps were generally presumed to be composed of water. Following the Mariner 4 measurements, Leighton and Murray (1966) demonstrated that the seasonal caps must be composed of solid CO2. Both north and south seasonal caps consist of carbon dioxide exchanged between the surface and atmosphere. Their annual recession curves in the visible (also referred to as regression or decay curves) are defined from the apparent movement of the mean cap radii toward higher latitudes during spring as the solid-phase CO2 sublimes. There is no strong evidence that either polar cap totally disappears during its respective summer season in the current epoch. The northern residual (‘‘perennial’’) cap (the larger of the two) was shown by Viking to be composed mainly of water ice (Kieffer et al., 1976). However, the much smaller residual south polar cap (RSPC) is composed mainly of CO2 (Kieffer, 1979). Paige and Ingersoll (1985) studied the energy balance of the residual caps and suggested that the RSPC was able to survive total sublimation because of its large visible albedo. Recent Hubble Space Telescope (HST) measurements confirmed that the albedo of the RSPC is sufficient to ensure survival at the current epoch (James et al., 2005b). Is the CO2 residual cap at the south pole a transitory or a permanent fixture of the current Martian climate? The

answer is uncertain. Lowell (1896) reported the RSPC disappeared on October 13, 1894 (Ls ¼ 2971), noting that ‘‘no such occurrence has ever been chronicled before.’’ There seems to have been no independent confirmation of this event; on the contrary, Barnard seems to have measured a ‘‘normal’’ cap in 1894 (Barnard, 1903). In hindsight, there are two other comments in Lowell’s book which call the RSPC disappearance into question. Lowell’s statement that the RSPC region had ‘‘became one yellow stretch’’ suggests obscuration by dust; in fact, a regional dust storm was observed in the south polar cap (SPC) region about that time (Flammarion, 1909). Lowell also states ‘‘that it did return occasionally, as a very small speck;’’ knowing now that the cap consists of CO2, new deposition in summer seems unlikely. Kuiper (1957) reported that the RSPC disappeared in 1956 but reappeared a week later. In this case there is ample documentation that this observation resulted from a temporary obscuration due to dust since the RSPC shows up on photographs from numerous locations during the period. However, clearly observable changes less dramatic than complete disappearance of the RSPC have been documented. Images at similar (200 m) resolution acquired by Mars Global Surveyor (MGS) in 2000, by Viking in 1977, and by Mariner 9 in 1972 at near identical Ls, provide evidence for significant interannual change in the RSPC (Fig. 1). On the other hand, there has been little change in the RSPC at such resolution during the MGS mission. Small scale structure in the RSPC surface was discovered using images acquired by the narrow angle camera of Mars Orbiter Camera (MOC) on MGS (Thomas et al., 2000). The MOC images revealed complicated surface morphology on the perennial cap colloquially referred to as ‘‘Swiss cheese.’’ Subsequently, Malin et al. (2001) compared these features in two Martian years and discovered that the Swiss cheese features were evolving over short time scales,

Fig. 1. Images of the same region from the perennial south polar cap (latitude–86.51, longitude01 for the fork-shaped region) taken during late summer at near identical Ls and spatial resolution of about 200 m: (A) Mars Global Surveyor, 2000; (B) Viking, 1977; and (C) Mariner 9, 1972 (the images are credit to NASA).

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apparently due to net annual sublimation of CO2 that erodes the mesas separating the pits. A careful analysis of the morphology and evolution of these features over three Martian years led Thomas et al. (2005) to conclude that these features actually comprise several different units and that there is evidence for erosion/deposition of some of these units within the last 10–100 Martian years. These authors compared high-resolution Mariner 9 and MOC images of a portion of the RSPC and concluded that at least one of these units has been deposited since the Mariner 9 mission. The processes that result in the great variety of Swiss cheese features and that give rise to the deposition and erosion of CO2 units in the RSPC over short time spans are not clear. A model for gradual erosion of the more symmetric of the features due to variation of insolation across them has been suggested by Byrne and Ingersoll (2003b), but their model does not yet account for the large variety of features seen. In this paper we examine one process that may contribute to this cycle: enhanced sublimation resulting from perihelion season global dust storms. The purpose of this paper is to quantitatively investigate the radiative effects of a global dust storm that starts during late Martian southern spring, on the stability of the perennial SPC. Our approach has been introduced in previous works wherein we investigated the effects of atmospheric dust on the spring-time decay rates of the seasonal SPC (Bonev et al., 2002, 2003). We model the radiative transfer through a dusty planetary atmosphere bounded by a subliming CO2 surface. A critical parameter in our modeling is the frequency-dependent surface albedo spectrum, extending from the near UV to the thermal IR. This paper consists of two principal parts: we present models of surface albedo spectra with parameters constrained from both space-craft and Earth-based observations conducted in multiple wavelengths. A portion of these observations have been reported in previous works (Glenar et al., 2005a; James et al., 2005b; Hansen et al., 2005); here we present new analyses of near-infrared (IR) moderate resolution spectra of the RSPC, acquired at the NASA Infrared Telescope Facility (IRTF), and we synthesize the information from the aforementioned studies in order to create frequency-dependent CO2 albedo spectra indicative of the RSPC. These albedo spectra serve as input parameters for purposes of modeling the effects of a near-perihelion dust storm on the sublimation rates in the RSPC. Our objective is to evaluate the possibility that the advanced recession of the 1972 RSPC relative to later years (see the Mariner 9 image in Fig. 1) might be linked to the 1971 global dust storm. 2. Atmospheric dust and the stability of the residual south polar cap The integrated visible albedos of the RSPC inferred from well-calibrated HST photometric data (James et al., 2005b) were high enough to imply a stability of the perennial cap

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during years with no significant increase in atmospheric dust over the cap. Although there was a major planetencircling storm in 2001, it had a negligible effect on the RSPC. This observation may be explained by the very large solar incidence angles at the RSPC during the 2001 storm, which reduce the insolation, and by the circumstance that the RSPC was surrounded by more than 1000 km of subliming, CO2 covered surface. It is possible that increased dust in early spring could have the effect of strengthening the polar vortex (see McConnochie et al., 2003), thus strengthening the RSPC isolation from the dust activity around the cap periphery. However, these factors would not apply to a dust storm occurring in the perihelion to solstice time period when the cap is much smaller and incidence angles are maximum. This paper addresses the question of whether a planet encircling dust storm beginning near perihelion, where the amounts of solar insolation reaching the pole are largest, can change the net CO2 sublimation on the RSPC significantly. Many Martian weather phenomena are very repeatable from one year to the next (Cantor et al., 2002). Global dust storms on the other hand remain a highly unpredictable event on Mars. During the four perihelion seasons viewed by MGS there was one major dust storm, in 2001, that started in very early spring in the southern hemisphere. In contrast, during the seven Martian years from 1971 to 1984 there were six major storms observed (two by ground based, one by Mariner 9, three by Viking), of which three occurred in early spring and three occurred near solstice. The first well established planet-encircling storm in 1956 started at perihelion. Although these post-perihelion storms seem, on the basis of limited statistics, as common as the early storms, the synoptic database collected by MGS has yet to include a major post-perihelion storm3. Fig. 1 shows a significant change in the south residual cap’s appearance in 1972 after a planet-encircling dust storm in 1971 which started near solstice and enveloped the cap. When Mariner 9 arrived more than a month after the storm commenced, the cap was visible through heavy obscuration (as a result of its relatively high elevation and the large contrast in visible albedo between the cap and the dusty atmosphere). Notably, telescopic images acquired earlier reveal no sign of the south cap (Hartmann and Raper, 1974). Atmospheric dust affects the sublimation of CO2 from the cap by absorbing visible insolation and emitting thermal IR radiation. Depending on the detailed behavior of the albedo/emissivity of the surface ice, this visible-to-IR redistribution of incident energy can either accelerate or retard the sublimation process (Paige and Ingersoll, 1985; Bonev et al., 2002, 2003). For a high visible albedo surface, such as the RSPC, a dust storm is expected to increase sublimation. For example, Bonev et al. (2002) demonstrated that the early spring 2001 dust storm would have resulted in an early disappearance of the visibly bright 3 Such a storm has been observed in 2007, after the acceptance of this manuscript.

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Mountains of Mitchel feature in accordance with observations (see also Titus and Kieffer, 2002; Benson and James, 2005). 3. Modeling radiative transfer through atmospheric dust 3.1. Radiative transfer model We have examined the effects of atmospheric dust on the sublimation rate of a CO2 surface. Our approach has been described in Bonev et al. (2002). We employed the noniterative Monte Carlo radiative equilibrium code of Bjorkman and Wood (2001), initially developed for astrophysical applications and adapted for the case of a plane-parallel dusty planetary atmosphere. Although this model atmosphere is one dimensional, the radiation transfer code is three dimensional and includes wavelength-dependent dust opacity, anisotropic scattering, and thermal dust emission. The ‘‘altitude’’ variable in this algorithm is the local vertical dust optical depth at 550 nm, measured from the top of the atmosphere. The radiative simulations track individual ‘‘photon packets’’ (as defined by Bjorkman and Wood, 2001) and therefore determine where their energy is absorbed. When a packet is absorbed, it heats a particular cell, raising its temperature. To enforce radiative equilibrium, the dust immediately emits the radiation according to its temperature. Reemitted photons then continue to be scattered, absorbed, and reemitted until they finally either escape from the atmosphere or impact the surface, where the photon’s ‘‘fate’’ depends on the detailed, frequency dependent albedo. In this scheme, the total downward flux incident to the surface is partitioned into reflected and absorbed components, depending on the surface albedo. The surface sublimation flux (in energy units) is then given by the difference between the frequency integrated fluxes absorbed and thermally emitted by the surface. The spectrally integrated surface emission is constant (independent of optical depth) with a temperature equal to a sublimation temperature of 147 K (slight variations of this parameter do not influence our results). Additional details of our non-iterative algorithm for radiative transfer modeling are presented in the original paper (Bjorkman and Wood, 2001) and in Bonev (2005). 3.2. Input parameters and model uncertainties The most important radiative effects in our simulations are (1) the redistribution, from visible to IR wavelengths, of energy reaching the surface due to absorption and reemission by atmospheric dust, and (2) the surface absorption over a wide frequency range. The input parameters needed for modeling these two effects are the absorption and single scattering properties of Martian aerosols, and the surface CO2 albedo spectrum. Both of these parameters have been constrained from observations covering multiple spectral regions.

Wavelength-dependent dust absorption and single scattering properties (albedo, absorptive opacity) have been adopted from studies by Wolff and Clancy (2003) and Clancy et al. (2003). These properties are the result of combining previous work in the visible and IR with subsequent analysis of TES spectra over a wide range of aerosol loading conditions. The adopted dust albedo and opacity correspond to mean particle radius reff of 1.5 mm— the most commonly observed size consistent with reanalyses of Pathfinder and Viking/Mariner 9 data (see Clancy et al., 2003 and references therein). For dust scattering, we adopted the phase function of Tomasko et al. (1999) at 965 nm for the visible and a Henyey–Greenstein phase function with a frequencydependent value of the asymmetry parameter for the IR. Note that at IR wavelengths absorption starts to dominate over scattering because the dust albedo drops significantly [see Wolff and Clancy (2003) (IR albedos); Clancy et al. (2003) (visible albedos)]. Dust temperature is calculated using the condition of radiative equilibrium. For early southern summer and high dust optical depth we obtain temperatures in the range of 210–240 K. While our algorithm can also be adjusted to accept an input temperature profile as a fixed parameter, measured temperature profiles are not available for global dust storm conditions during the summer and at high southern latitudes. We expect that uncertainties in dust temperature profiles would modify some spectral details of the IR thermal dust emission, but would not significantly change the visible-to-IR frequency redistribution due to absorption and reemission by atmospheric dust. The principal modeling improvement compared to Bonev et al. (2002) is the treatment of surface albedo spectra, described in the following sections. 4. Modeling CO2 surface albedo spectra Our dusty model atmosphere is bounded by a subliming CO2 surface at 147 K. A very important, but somewhat uncertain, model parameter is the strongly wavelengthdependent surface albedo. Constraining this parameter is a fundamental objective of this study, because it determines how the surface would ‘‘respond’’ to the visible-to-IR frequency redistribution (by atmospheric dust) of the flux incident to it. There are several approaches to modeling the surface frost albedo, all of which are similar in terms of the radiative transfer physics but differ in terms of the assumed micro-physics of the ice structure. We have adopted the simple but well-tested approach of Hansen (1999) who approximates the ice medium with a grid of scattering grains and models the radiative transfer of photons penetrating into this medium. The main advantage of Hansen’s approach is that it has successfully reproduced a wide range of Mars polar albedo spectra measured with different instruments and at different wavelengths (see Hansen, 1999; Glenar et al., 2005a; Hansen et al., 2005).

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This approach has also been successfully applied to snow surfaces on Earth (e.g. Wiscombe and Warren, 1980; Warren and Wiscombe, 1980). For the purpose of describing the polar surface energy balance, we are interested in the radiative (versus microphysical) properties of the frost. By incorporating Hansen’s model into our modified version of Bjorkman and Wood’s original code, we aim to reproduce the wide variety of polar ice spectra with a well-understood and well-tested model. This model has one free parameter for pure CO2 ice and three free parameters overall, which are constrained by observations, namely, CO2 ‘‘grain radius,’’ amount of dust intermixed in the frost, and amount of H2O intermixed in the frost. For sizes greater than 1–2 mm, the value of the ‘‘grain radius’’ approximates the photon’s mean free path length between scattering events in the ice, and we refer to this as ‘‘scattering length.’’ 5. Near-infrared and visible observations of the residual south polar cap Three spectral regions are diagnostic for the surface model parameters. Near IR wavelength are particularly diagnostic of scattering length and amount of intermixed water ice. Near 2 mm, the scattering length is constrained from the relative depth of CO2 spectral features and the overall shape of the spectrum between 2.0 and 2.4 mm, while the spectral slope between 3.0 and 3.5 mm is influenced strongly by the amount of intermixed water ice. Visible wavelengths (0.2–0.9 mm) and to a lesser extent the thermal-IR (20–30 mm) are regions diagnostic of all three parameters but especially the amount of intermixed dust. Near IR spectra have been acquired from both spacecraft and ground-based instruments. Hansen et al. (2005) analyzed spectra from the RSPC acquired with the Planetary Fourier Spectrometer (PFS) on board Mars Express (MEX). These spectra are apodized and spectrally smoothed to increase signal-to-noise ratio, resulting in a resolving power lXDl of 450 at 3.2 mm. The spatial resolution for these observations is about 10 km near pericenter. Complementary ground-based observations are described by Glenar et al. (2005a). SPC spectra have been acquired with the SpeX grating spectrometer (Rayner et al., 2003) at the NASA IRTF in both L-band and K-band (the traditional near-IR ‘‘windows’’ for terrestrial atmospheric transmittance). These spectra have much lower spatial resolution (100 km) relative to the space-craft data, but spectral resolution is high enough to fully resolve the CO2 ice spectral features (lXDlE1300 at 2.2 mm, lXDlE1800 at 3.2 mm) with high signal-to-noise ratio. Visible albedos of the residual cap have been measured by James et al. (2005b). Previous measurement at some visible wavelengths were conducted from ground-based (Lumme and James, 1984) and space-craft (James et al., 2001) observations, but suffered from limited spectral

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coverage and calibration uncertainties. The new study was conducted with the High Resolution Camera (HRC) on HST. The major strengths of this data set are improved wavelength coverage,4 good photometric accuracy, and high spatial resolution (10–15 km). The telescopic observations of both Glenar et al. and James et al. were conducted during the very favorable opposition of 2003. 6. Constraining the frost albedo model parameters from multiple spectral regions In order to model the stability of the perennial cap during a global dust storm we have constrained the parameter space for surface models, so that the latter reproduce as closely as possible the albedo spectra in the residual cap. It is desirable to use data from multiple spectral regions, since one region alone cannot tightly constrain the three-parameter space. PFS/MEX spectra between 2.3 and 4.0 mm were used to constrain the scattering length and the content of water intermixed with the CO2 ice. These results are described in Hansen et al. (2005) who show a number of model–data comparisons. Independently L- and K-band measurements from SpeX/IRTF were used to constrain the same two parameters. These results were compared to the retrievals of Hansen et al. and will be described in Section 6.1. Visible albedos of James et al. (2005b) were fit by models with scattering length and water content constrained from near IR measurements, while intermixed dust content was used as a free parameter. This multi-wavelength approach breaks the degeneracy in the parameter space of intermixed dust and water. For a fixed scattering length water ice raises the visible albedo, while dust lowers it, so a range of combinations of the two parameters can produce almost the same visible spectrum. With H2O constrained by Lband measurements, intermixed dust can then be unambiguously measured at visible wavelengths, which is a better diagnostic for this parameter than the near-IR. The visible albedo diagnostics are described in Section 6.2. 6.1. Residual south polar cap parameters from IRTF SpeX measurements Average frost properties of the SPC as it approached (Ls ¼ 2641) its perennial geometry (see Kieffer et al., 2000; Benson and James, 2005) were determined from groundbased spectroscopic imaging in K-band (2.0–2.4 mm) and L-band (3.0–3.5 mm) on September 20, 2003, using the SpeX grating spectrometer at NASA IRTF. Sub-Earth latitude was 19S on the date of the observations which permitted all polar longitudes to be observed near the limb. 4 The HST HRC utilizes eight filters (F250W, F330W, F344N, F435W, F475W, F502N, F658N, and F892N). The three digits in each filter name give the central wavelength in nm, and the W and N stand for ‘‘wide’’ and ‘‘narrow,’’ respectively (see James et al., 2005b for more details on the photometry).

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Spectrometer ‘‘step scans’’ across the planet are reformatted into three-dimensional (x, y, l) spectral image cubes using pointing information from a boresighted guide camera. A detailed description of the data reduction and spectral analysis steps are described by Glenar et al. (2003, 2005a). Each spatial element in the image cube measures cap properties over a region approximately 150 km in longitude by 300 km in latitude, as limited by ‘‘seeing’’ conditions during the measurements and the large local zenith angle of the cap observations (e.g. Fig. 1(A), Glenar et al. 2005a). Figs. 2 and 3 show self-consistent numerical retrievals of average cap properties from a region of the perennial cap where the ice- features exhibited maximum near-IR spectral contrast with respect to the surrounding darker surface. These retrievals were carried out by fitting measured SpeX spectra to a multi-axis interpolation grid of CO2 ice reflectance models, computed for a range of surface frost properties, using a successive-iteration, linear perturbation method (Craig and Brown, 1986; Conrath et al., 1998). These surface reflectance models were calculated using a discrete-ordinate radiative transfer code (DISORT, Stamnes et al., 1988) assuming a semi-infinite medium of mixed Mie scatterers and independent scattering events, as described in Hansen (1999). Atmospheric CO2 gas opacity near 2 mm was unmixed from the ice spectra (Glenar et al., 2005b) by utilizing a

Fig. 2. Comparison of near-infrared spectral reflectance models with ground-based observations of the south polar cap K-band spectrum using the IRTF/SpeX (Ls ¼ 2641; approximate spot position 86S, 345W). See text for a description of the observations and cap reflectance modeling. For this simulation, the abundances of intermixed water and dust were, respectively, 0.003 and 0.01 wt%. Values of photon scattering length (designated RCO2 in the figure) between 4 and 8 mm yield good overall agreement with the depth of the deep ice reflectance feature at 2.07 mm, as well as the familiar ‘‘grain radius’’ features at 2.29 and 2.35 mm. Additional models above and below show the results of least squares retrievals with RCO2 held fixed at large and small values. The deep band structure between 2.0 and 2.2 mm is mostly due to Mars atmospheric CO2 gas absorption.

Fig. 3. Same cap location as that in Fig. 2, observed in L-band. The spectral slope between 3.1 and 3.5 mm is strongly influenced by the amount of admixed water ice, but is relatively insensitive to scattering length, designated as RCO2 . Water ice fractions of 0.002–0.003 wt% provide satisfactory agreement with the measurements. The contribution to the spectral slope from exposed regolith (typical ‘‘fill factor’’ is 0.5) is accounted for using the spectral shape of an adjacent off-cap location.

separate pre-computed grid of high spectral resolution gas transmittance models which are parameterized in terms of surface pressure and effective gas temperature. Each product spectrum was then convolved to SpeX resolution of 3–4 cm1 (K-band) or 1.5–2.0 cm1 (L-band) and quantitatively compared with the measurements. The set of retrieval parameters also includes the area fill-factor of exposed regolith (typically 40–50%) which is unresolved at ground-based spatial resolution, but which is recovered using the spectral shape of ice-free locations adjacent to the cap. The SpeX observations coincided with a time of spatially variable atmospheric dust loading near the edge of the receding cap, as measured by MGS/TES (Smith, 2004). Spectral effects of atmospheric dust opacity are accounted for via a set of DISORT-generated near-IR dust correction factors for the date and geometry of the observations, together with MGS/TES dust optical depth measurements provided by M. Smith. TES team-provided dust aerosol optical depths are not available until the cold CO2 surface sublimes, because the TES retrieval algorithm is restricted to surface temperatures higher than 220 K (Smith et al., 2001). Therefore we used optical depth measurements near the edge of the cap as a reference, but perturbed this parameter around the measured value to confirm that the exact assumed value does not influence the removal of atmospheric dust effects from our spectra. Fig. 2 compares the measured 2.0–2.4 mm cap spectrum with alternative models for the ice scattering length, with dust and water ice held fixed at 0.01 and 0.003 wt%, respectively. This spectral region, and particularly the weak

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ice bands at 2.29 and 2.35 mm, provide a firm diagnostic of scattering length (see Calvin and Martin, 1994) since it contains CO2 ice features which span several decades in absorption coefficient strength (Hansen, 1997). Cap models with scattering lengths of 4–8 mm show best agreement with the measurements, whereas large and small scattering length models, shown in the upper and lower traces, are not well fit to the measurements. The L-band measurements (Fig. 3), though noisier, are especially sensitive to the concentration of admixed water ice. This occurs because the absorption coefficient of water ice decreases by roughly two orders of magnitude between 3.1 and 3.5 mm (Warren, 1984; Clapp et al., 1995) and thus strongly influences the slope of the CO2 ice reflectance spectrum within this interval. Water ice concentrations of 0.002–0.003 wt% show good agreement with the measurements. One difficulty in this spectral region is the inability of the CO2 reflectance modeling, which contains a single scattering length parameter, to simultaneously fit weak and strong ice features. This inconsistency appears to a lesser extent in K-band spectra, and may indicate a bi-modal, or more complicated, crack-void geometry within the ice. Our retrieved water ice concentration, however, is insensitive to the assumed scattering length, which we illustrate by including models with two different scattering lengths. The assumed dust–CO2 mixing ratio does not strongly influence these retrievals (Figs. 2 and 3); this ratio is much better constrained at visible wavelengths, where small changes in dust content produce large changes in the albedo (see models in Bonev (2005) showing how the albedo is influenced by each frost parameter). The ground-based (SpeX/IRTF) and the space-craft (PFS/MEX) near-IR data sets are complementary in the sense that the SpeX spectra have lower spatial resolution, but higher spectral resolution with better signal-to-noise ratio. The SpeX-derived estimates for scattering length and intermixed water ice content are found to be in agreement with the PFS-based retrievals of Hansen et al. (2005), which imply scattering lengths in the range of 4–10 mm and values for water ice content less than 0.005 wt%. Note that neither the SpeX analysis nor the PFS results are sensitive to admixed water concentrations lower than about 0.0005–0.001 wt%.

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dust, considered in earlier studies a good spectral analog for Mars (Singer, 1982; Morris et al., 1990). For the present calculations the optical constants in the near-IR were reduced and the shape of the resulting visible spectrum was adjusted to match spectra from OMEGA/MEX (e.g. Bibring et al., 2004) taken above dusty (non-ice) regions on the Mars surface. We point out that these modifications do not conflict with the scattering length and intermixed water abundance deduced by Hansen et al. (2005), or the ones described in the previous section, since the K- and L-band near-IR regions are not very diagnostic for the dust amounts. At the second stage of analysis, these new dust optical constants were applied to modeling the visible albedos of CO2 ice with intermixed dust and water. Using a forward modeling approach, we compared a group of plausible visible albedo models with the HRC/HST albedo measurements as shown in Fig. 4. These models correspond to scattering lengths of 5 and 10 mm, intermixed dust and water contents of 0.001–0.005 and 0.001–0.01 wt% respectively, and define a

6.2. Residual south polar cap parameters from HRC/HST measurements The amount of intermixed dust is the surface frost parameter best constrained from the visible wavelength albedo measurements. Modeling visible spectra at the resolution of the HST data set (James et al., 2005b) required two stages of analysis. First, we obtained an updated set of dust optical constants (in the visible and in the near IR). Previously, the dust optical constants for our surface models were adopted from Clancy et al. (1995), who based their results on near IR absorption coefficients retrieved from the reflectance of Mauna Kea palagonite

Fig. 4. Models for the surface albedo spectra with parameters retrieved from multi-wavelength observations of the residual south polar cap. Scattering length RCO2 was retrieved from infrared spectra taken near 2.3 mm (see Fig. 2 and Hansen et al., 2005); intermixed water abundance was retrieved from infrared spectra near 3.22 mm (see Fig. 3 and Hansen et al., 2005). The results of James et al. (2005b) are also presented for comparison with the modeled visible albedos that are diagnostic for the amount of intermixed dust.

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range of plausible boundary conditions for simulating the effects of a near-perihelion dust storm on the RSPC stability (next section). The broad albedo maximum between 20 and 30 mm is a characteristic feature for CO2 ices with fairly small dust-toice mixing ratios, typical of those obtained for the seasonal CO2 frost of the perennial south cap. Using this spectral feature, Hansen (1999) showed that higher dust-to-ice mixing ratios (approaching 1 wt%) may characterize portions of the seasonal cap. The visible HST data are also displayed in Fig. 4. Lower limits for the albedo at three different values of Ls near opposition (2351, 2511, 2651) are shown as diamonds, whereas those corrected for background atmospheric dust during the 2003 observations are shown as stars. Our albedo models are in good agreement with the HST measurements longward of about 430 nm (dashed vertical line on Fig. 4). However, these models cannot reproduce the steep decrease of the albedo for lo400–430 nm. This should not be surprising, since dust optical properties are generally unconstrained at wavelengths shortward of about 380 nm. Very few published measurements include spectrophotometry at these wavelengths (see McCord et al., 1977; Bell III et al., 1990). OMEGA/MEX data and all telescopic spectra from prior to 1990 are void of spectral measurements shortward of lo350 nm. Therefore for modeling the surface energy balance (next section) the following approach was adopted: 1. For lX 430 nm the modeled albedo spectra shown in Fig. 4 were used. 2. For lo430 nm we did not use our albedo models; instead we adopted the values of the observed HST albedos at 330 and 250 nm, and linearly interpolated for wavelengths between 430 and 250 nm in order to take into account the observed steep decrease in albedo at short visible wavelengths.5

exponential decay to pre-dust storm levels at LsE3001, similar to the observed time scale of the event in 1971. For each surface albedo spectrum shown in Fig. 4 we calculated the variation in sublimation flux with Ls for two modeling scenarios: 1. A ‘‘Global dust storm’’ scenario in which the change in sublimation flux is governed by the variable atmospheric opacity and by variable insolation conditions. 2. A ‘‘Background dust’’ scenario, in which the dust optical depth is assumed to be constant (t550 ¼ 0.2) throughout the simulation, so that changes in sublimation flux are solely insolation driven. These two scenarios are presented in Fig. 5, which shows the variation of dust optical depth with time assumed in our Monte Carlo simulations. Our main result is that for all surface models shown in Fig. 4 the sublimation fluxes are notably enhanced in the global dust storm scenario compared to that of constant background dust. Figs. 6–11 show the variation of the CO2 sublimation flux with Ls for several surface albedo spectra under both scenarios. In all plots, the sublimation fluxes are normalized to the flux incident at the top of the atmosphere for LsE3021 (the point where the two curves converge). This was a convenient normalization value for the numerical procedure used, and likewise a convenient way to display the relative change in sublimation flux with dust optical depth. The result for enhanced sublimation flux as a consequence of a near-perihelion dust storm does not depend on the particular surface albedo spectrum used. Instead this conclusion is valid for the whole parameter space presented in Fig. 4.

7. Modeling the sublimation of the residual south polar cap under conditions of a planet-encircling dust storm near perihelion 7.1. Numerical simulations In order to model the effect of a near-perihelion global dust storm, we assumed that the optical depth over the perennial SPC could be represented in time as an abrupt jump from a background opacity level of t550 ¼ 0.2 to t550 ¼ 2.0 at onset (t550 is the dust optical depth at 550 nm). This increase in optical depth at LsE2601 is followed by an 5 Future observations should reveal whether or not the rapid ‘‘rolloff’’ at the shortest visible wavelengths is as steep as our HRC/HST measurements imply. James et al. (2005b) comment that their albedo correction for atmospheric dust suffers from uncertainties in the dust absorptive opacity for lo400 nm. Atmospheric dust which is slightly more absorbing would result in higher surface albedos at blue wavelengths in better agreement with the models presented in Fig. 4.

Fig. 5. Two scenarios for variation of atmospheric dust optical depth at 550 nm with time used to simulate the effect of a near-perihelion planetencircling dust storm on the residual south polar cap stability.

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Fig. 6. Sublimation flux versus Ls for modeled surface albedo spectrum characterized by scattering length RCO2 of 5 mm; intermixed water content—0.001 wt%; and intermixed dust content—0.001 wt%. The sublimation flux is normalized to the flux incident to the top of the atmosphere for the point near Ls3021 where the two curves converge.

Fig. 7. Same as Fig. 6, but for scattering length, intermixed water, and intermixed dust content, respectively, 5 mm, 0.005, and 0.001 wt%.

Figs. 6–11 illustrate quantitatively the effect of atmospheric dust over CO2 surfaces with representative albedo spectra. Each pair of simulations for a particular Ls (‘‘background dust’’ and ‘‘global dust storm’’ scenario respectively) corresponds to the same input parameters except the amount of dust in the atmosphere. The enhanced sublimation in the ‘‘dust storm’’ scenario is a consequence of (1) increased thermal IR flux incident on the surface (while in the ‘‘background dust’’ simulation for LsE2601 presented in Fig. 6, only 7% of the photon packets reaching the surface have wavelengths longer than 3 mm, for the corresponding ‘‘dust storm’’ simulation this value is nearly 40%; see Fig. 12), and (2) the fact that visibly bright surfaces are overall more absorptive at IR wavelengths (Fig. 4).

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Fig. 8. Same as Fig. 6, but for scattering length, intermixed water, and intermixed dust content, respectively, 5 mm, 0.005, and 0.005 wt%.

Fig. 9. Same as Fig. 6, but for scattering length, intermixed water, and intermixed dust content, respectively, 10 mm, 0.002, and 0.001 wt%.

Quantitatively, the increase in sublimation flux is largest for the brightest mean visible albedos which imply the largest differential absorption between visible and IR. Increased sublimation was in fact predicted and observed over the brightest regions of the seasonal SPC affected by the early-spring dust storm in 2001 (Titus and Kieffer, 2002; Bonev et al., 2002; Benson and James, 2005). As mentioned above, in difference to near-perihelion storm, an early-spring dust storm was not expected to affect significantly the perennial cap (see discussion in Section 2). Two different types of atmospheric dust effect are possible: reduced sublimation flux with increased atmospheric dust and no significant change in sublimation flux under dust storm conditions (see Bonev et al., 2003). Both types of effect were in fact observed in different locations

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Fig. 10. Same as Fig. 6, but for scattering length, intermixed water, and intermixed dust content, respectively, 10 mm, 0.002, and 0.002 wt%. The atmospheric CO2 opacity is not included in this calculation. Atmospheric CO2 would influence the details of the spectrum, but should not alter significantly the spectrally integrated (over the whole infrared range of 4–100 microns) flux absorbed by the surface.

Fig. 12. Spectral energy distributions of the radiation incident to the polar surface for background dust (t550 ¼ 0.2) and dust storm (t550 ¼ 2.0) scenarios (see Fig. 5). These results correspond to the simulation shown in Fig. 6 for LsE2601 and demonstrate the modeled visible to infrared frequency redistribution of incident flux.

occurs at Ls ¼ 260–2701 where the combination of small solar zenith angle (minimum at Ls ¼ 2701; solstice) and small heliocentric distance (minimum at Ls ¼ 2501; perihelion) promotes the largest sublimation flux. The rapid decline in sublimation flux after Ls2801 is caused by decreased insolation, which will reduce the effect of dust storms whose onset is later in the summer season. Increased atmospheric dust near perihelion is expected to have the largest effect on the perennial cap stability. 7.2. Estimated net loss of solid CO2

Fig. 11. Same as Fig. 6, but for scattering length, intermixed water, and intermixed dust content, respectively, 10 mm, 0.005, and 0.001 wt%.

within the seasonal SPC after the early-spring 2001 dust storm. TES/MGS observations showed that the visibly darkest regions decayed more slowly than during a year without a global dust storm (Titus and Kieffer, 2002), while the visible mean cap regression curves measured by MOC/ MGS in 1999, 2001, and 2003 (two relatively dust-free years versus one year with a major dust storm) were very similar (Benson and James, 2005). However, in order to predict either of these alternative scenarios in our simulations for the perennial cap, one needs to lower its mean visible albedo to values that disagree with observations. In the background dust scenario, the changes in sublimation flux are insolation driven. Maximum surface absorption (which produces most intense sublimation)

Our results for the dust storm scenario imply an advanced recession of the residual cap observed after the 1971 near-perihelion dust storm compared to later ‘‘nondusty’’ years. This is consistent with the observations shown in Fig. 1, which motivated us to address the issue of total net loss of material during a dust storm scenario, compared to the background dust scenario. We first integrated our modeled normalized sublimation fluxes over time and converted these results to mass of sublimated material per unit area (kg m2) by multiplying the normalization factor (the flux incident to the top of the atmosphere for Ls ¼ 302.41; 243 W m2), and by dividing out the latent heat for CO2 sublimation (5.902  105 J kg1). These results are displayed in Table 1 for the full set of surface albedo spectra used. The last column of this table shows the depth of an equivalent CO2 layer lost as a result of the positive net sublimated material in the dust storm case. Note that this estimate suffers from the factor of two uncertainty in the ice density which we assume equal to 700 kg m3. Dust storm caused an increase in sublimated CO2 of between 40 and 110 kg m2 during the simulated storm for LsE260–3021. For a CO2 density of 700 kg m3 this would

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Table 1 Net loss of material in the ‘‘dust storm’’ simulation compared to the ‘‘background dust’’ case Dust (wt.%)

Water (wt.%)

‘‘Scattering length’’ ¼ 5 mm 0.001 0.001 0.001 0.002 0.001 0.005 0.001 0.010 0.002 0.001 0.002 0.002 0.002 0.005 0.002 0.010 0.005 0.005 0.005 0.010 ‘‘Scattering length’’ ¼ 10 mm 0.001 0.001 0.001 0.002 0.001 0.005 0.001 0.010 0.002 0.002 0.002 0.005 0.002 0.010 0.005 0.010 a

SCO2 (kg m2)a Dust storm scenario

SCO2 (kg m2)a Background dust scenario

DSCO2 (kg m2)

Equivalent layer lostb (cm)

548 531 495 462 625 602 554 510 658 598

482 455 400 352 585 551 479 417 623 537

66 76 95 110 40 51 75 93 35 61

9 11 14 16 6 7 11 13 5 9

620 582 522 475 660 584 525 617

567 513 427 363 621 513 431 557

53 69 95 112 39 71 94 60

8 10 14 16 6 10 13 9

Mass of sublimated material per unit area. Equals DSCO2 =r, where the assumed density r ¼ 700 kg m3.

b

result in a loss of 6–16 cm of equivalent CO2 layer. This excess sublimation is smaller than the inferred 1 m thickness of residual CO2, although this is an upper limit so that the thickness of CO2 could be substantially smaller in some areas. Therefore multiple storms would be necessary to remove the entire CO2 layer. On the other hand, a single late-spring global dust storm could partially influence the perennial cap’s stability, leading to advanced sublimation in the ‘‘dusty’’ year, followed by subsequent reaccumulation of surface ice deposits.

7.3. Possible feedback mechanisms. Effects of increased surface dust and exposure of water ice Three positive feedback mechanisms from a dust storm scenario can be considered plausible. First, even if the CO2 layer is not entirely removed, early exposure of the residual CO2 deposits beneath the seasonal ice could enhance sublimation, especially if the residual frost has lower visible albedo than the seasonal frost. Second, dust deposited on the surface as a result of planet-encircling storm could increase the surface absorption and hence the sublimation flux. Because the visible albedo is very sensitive to the dust-to-ice mixing ratio, a small change in this parameter, within the relatively narrow parameter space shown in Fig. 4 results in considerable change in surface absorption. The effect of increased surface dust is illustrated in Table 1 and in the direct comparison between Figs. 7 and 8, and between Figs. 9 and 10. Each pair of figures corresponds to surface albedo

spectra having the same scattering length and water content, but with different amounts of intermixed dust. The third possible feedback mechanism in the dust-storm scenario is related to exposure of water ice. Sublimation of seasonal CO2 will leave a lag deposit of water ice that will accumulate into a near surface layer of H2O if the residual CO2 also sublimes. Sublimation of exposed H2O will enhance the H2O vapor above the RSPC. Such measurements from ground-based observatories have been reported, placing into question the existence of the perennial cap in 1969 (see Jakosky and Barker, 1984). More recently Byrne and Ingersoll (2003a) modeled the evolution of south polar ice surface features observed with the narrow angle camera of MOC/MGS. Their modeling suggested that a layer of H2O ice might be ‘‘capped’’ by the residual CO2 ice. Space-craft observations from three Mars missions (MGS, Odyssey, and MEX) have increased the body of observational evidence (indirect and direct) for water icerich deposits in the RSPC (Boynton et al., 2002; Titus et al., 2003; Bibring et al., 2004). Exposed H2O ice could also contribute to interannual variability by increasing the thermal inertia of the surface, thereby delaying seasonal CO2 redeposition until the water layer completely sublimes. 8. Conclusions The most important radiative effects in our Monte Carlo simulations depend on the frequency-dependent absorptive properties of atmospheric dust (examined by Clancy et al. (2003) and Wolff and Clancy (2003)] and of the CO2 surface (examined in this paper). If the visible albedo of the

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present-day residual cap is representative of the current Martian climate, it will evidently ensure its stability under conditions of background amounts of atmospheric dust (Paige and Ingersoll, 1985; James et al., 2005b). On the other hand, it is very likely that a planet-encircling dust storm with onset near solstice can disrupt the residual cap’s stability, and spawn a sequence of: (1) advanced CO2 sublimation in the ‘‘dusty’’ year, (2) subsequent accumulation of surface ice deposits, and (3) formation of new surface features. In this scenario, a series of dust storms would be required to remove the entire CO2 ice layer from the south residual cap. Acknowledgments We thank Jim Murphy for his very helpful referee comments. We also thank M.J. Wolff for providing a set of single scattering properties of Martian dust, D. Blaney and G. Bjoraker for their assistance with the SpeX observations, and W. Maguire for useful discussions on part of these results. We gratefully acknowledge support from the Mars Data Analysis Program (to P.B.J., and G.B.H), NASA Planetary Astronomy Program (to D.A.G), and the National Science Foundation (to J.E.B.). The SpeX grating spectrometer operates at the NASA Infrared Telescope Facility atop Mauna Kea, Hawaii. The NASA IRTF is operated by the University of Hawaii under Cooperative Agreement number NCC 5-538 with the NASA OSS Planetary Astronomy Program. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. References Barnard, E.E., 1903. The south polar cap of Mars. Astrophys. J. 17, 249–257. Bell III, J.F., McCord, T.B., Owensby, P.D., 1990. Observational evidence of crystalline iron oxides on Mars. J. Geophys. Res. 95, 14447–14461. Benson, J.L., James, P.B., 2005. Yearly comparisons of the Martian polar caps: 1999–2003 Mars Orbiter Camera observations. Icarus 174, 513–523. Bibring, J.-P., Langevin, Y., Poulet, F., Gendrin, A., Gondet, B., Berthe, M., Soufflot, A., Drossart, P., Combes, M., Bellucci, G., Maroz, V., Mangold, N., Schmitt, B., The OMEGA team, 2004. Perennial water ice identified in the south polar cap of Mars. Nature 428, 627–630. Bjorkman, J.E., Wood, K., 2001. Radiative equilibrium and temperature correction in Monte Carlo radiation transfer. Astrophys. J. 554, 615–623. Bonev, B.P., 2005. Towards a chemical taxonomy of comets: infrared spectroscopic methods for quantitative measurements of cometary water (with an independent chapter on Mars polar science). Ph.D. Thesis, The University of Toledo, Toledo, Ohio, USA, /astrobiology.gsfc.nasa.govS. Bonev, B.P., James, P.B., Bjorkman, J.E., Wolff, M.J., 2002. Regression of the Mountains of Mitchel polar ice after the onset of a global dust storm on Mars. Geophys. Res. Lett. 29 (21), 2017. Bonev, B.P., James, P.B., Wolff, M.J., Bjorkman, J.E., Hansen, G.B., Benson, J.L., 2003. Modeling the seasonal south polar cap sublimation

rates at dust storm conditions. In: Proceedings of the Sixth International Conference on Mars, Pasadena, CA. Boynton, W.V., Feldman, W.C., Squyres, S.W., Prettyman, T.H., Bru¨ckner, J., Evans, L.G., Reedy, R.C., Starr, R., Arnold, J.R., Drake, D.M., Englert, P.A.J., Metzger, A.E., Mitrofanov, I., Trombka, J.I., d’Uston, C., Wa¨nke, H., Gasnault, O., Hamara, D.K., Janes, D.M., Marcialis, R.L., Maurice, S., Mikheeva, I., Taylor, G.J., Tokar, R., Shinohara, C., 2002. Distribution of hydrogen in the near surface of Mars: evidence for subsurface ice deposits. Science 297, 81–85. Byrne, S., Ingersoll, A.P., 2003a. A sublimation model for Martian south polar ice features. Science 299, 1051–1053. Byrne, S., Ingersoll, A.P., 2003b. Martian climatic events on timescales of centuries: evidence from feature morphology in the residual south polar ice cap. Geophys. Res. Lett. 30 (13), 1696. Calvin, W.M., Martin, T.Z., 1994. Spatial variability in the seasonal south polar cap of Mars. J. Geophys. Res. 99, 21143–21152. Cantor, B.A., Malin, M.C., Edgett, K.S., 2002. Multiyear Mars Orbiter Camera (MOC) observations of repeated Martian weather phenomena during the northern summer season. J. Geophys. Res. 107 (E3), 5014. Clancy, R.T., Lee, S.W., Gladstone, G.R., McMillan, W.W., Rousch, T., 1995. A new model for Mars atmospheric dust based upon analysis of ultraviolet through infrared observations from Mariner 9, Viking, and PHOBOS. J. Geophys. Res. 100, 5251–5263. Clancy, R.T., Wolff, M.J., Christensen, P.R., 2003. Mars aerosol studies with the MGS TES emission phase function observations: optical depths, particle sizes, and ice cloud types versus latitude and solar longitude. J. Geophys. Res. 108 (E9), 5098. Clapp, M.L., Miller, R.E., Worsnop, D.R., 1995. Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra. J. Phys. Chem. 99, 6317–6326. Conrath, B.J., Gierasch, P.J., Ustinov, E.A., 1998. Thermal structure and para hydrogen fraction on the outer planets from Voyager IRIS measurements. Icarus 135, 501–517. Craig, I.J.D., Brown, J.C., 1986. Inverse Problems in Astronomy: A Guide to Inversions Strategies for Remotely Sensed Data. Adam Hilger, Boston, MA, ISBN 0-85274-369-6. Flammarion, C., 1909. La Planete Mars et ses Conditions d’Habitabilite, vol. 2, Gauthier-Villars et Fils, Paris. Forget, F., 1998. Mars CO2 ice polar caps Solar System Ices. In: Schmitt, B. et al. (Eds.), Solar System Ices. Kluwer Academic Publishers, Netherlands. Glenar, D.A., Hansen, G., Bjoraker, G., Smith, M., Pearl, J., Blaney, D., 2005a. Bright-region radiative properties within the Mars south polar cap (Ls ¼ 231) from near-infrared spectroscopic imaging. Icarus 174, 600–603. Glenar, D.A., Maguire, W.C., Bjoraker, G., Smith, M., Blaney, D., 2005b. The Mars 2 micron atmospheric CO2 band: a lower atmosphere thermometer. Bull. Am. Astron. Soc. 37, 665. Glenar, D.A., Samuelson, R.E., Pearl, J.C., Bjoraker, G.L., Blaney, D., 2003. Spectral imaging of Martian water ice clouds and their diurnal behavior during the 1999 aphelion season (Ls ¼ 1301). Icarus 161, 297–318. Hansen, G.B., 1999. Control of the radiative properties of the Martian polar caps by surface CO2 ice: evidence from Mars Global Surveyor measurements. J. Geophys. Res. 104, 16471–16486. Hansen, G.B., 1997. The infrared absorption spectrum of carbon dioxide ice from 1.8 to 333 mm. J. Geophys. Res. 102, 21569–21587. Hansen, G., Giuranna, M., Formisano, V., Fontic, S., Grassi, D., Hirsh, H., Ignatiev, N., Maturilli, A., Orleanski, P., Piccionig, G., Rataj, M., Saggin, B., Zasova, L., 2005. PFS-MEX observation of ices in the residual south polar cap of Mars. Planet. Space Sci. 53, 1089–1095. Hartmann, W.K., Raper, O., 1974. The New Mars. Scientific and Technical Information Office, NASA, Washington, DC. Herschel, W., 1784. On the remarkable appearances of the polar caps of the planet Mars, the inclination of its axis, the position of its poles, and its spheroidical figure; with a few hints relating to its real diameter and atmosphere. Phil. Trans. 74, 233–273.

ARTICLE IN PRESS B.P. Bonev et al. / Planetary and Space Science 56 (2008) 181–193 James, P.B., Hansen, G.B., Titus, T.N., 2005a. The carbon dioxide cycle. Adv. Space Res. 35, 14–20. James, P.B., Bonev, P.B., Wolff, M.J., 2005b. Visible albedo of Mars’ south polar cap: 2003 HST observations. Icarus 174, 596–599. James, P.B., Cantor, B.A., Davis, S., 2001. Mars Orbiter Camera observations of the Martian south polar cap in 1999–2000. J. Geophys. Res. 106, 23635–23652. James, P.B., Kieffer, H.H., Paige, D.A., 1993. The seasonal cycle of carbon dioxide on Mars. In: Kieffer, H.H., et al. (Eds.), Mars. University of Arizona Press, Tucson, AZ, pp. 934–969. Jakosky, B.M., Barker, E.S., 1984. Comparison of ground-based and Viking Orbiter measurements of Martian water vapor—variability of the seasonal cycle. Icarus 57, 322–334. Kieffer, H.H., 1979. Mars south polar spring and summer temperatures: a residual CO2 frost. J. Geophys. Res. 84, 8263–8288. Kieffer, H.H., Titus, T.N., Mullins, K.F., Christensen, P.R., 2000. Mars South polar spring and summer behavior observed by TES: seasonal cap evolution controlled by frost grain size. J. Geophys. Res. 105, 9653–9699. Kieffer, H.H., Martin, T.Z., Chase Jr., S.C., Miner, E.D., Palluconi, F.D., 1976. Martian north pole summer temperatures—dirty water ice. Science 194, 1341–1344. Kuiper, G.P., 1957. Visual observations of Mars, 1956. Astrophys. J. 125, 307–317. Leighton, R.B., Murray, B.C., 1966. Behavior of carbon dioxide and other volatiles on Mars. Science 153, 136–144. Lowell, P., 1896. Mars. Houghton Mifflin, Boston, USA. Lumme, K., James, P.B., 1984. Some photometric properties of the Martian south polar cap region during the 1971 apparition. Icarus 58, 363–376. McConnochie, T.H., Conrath, B.J., Gierasch, P.J., Banfield, D., Smith, M.D., 2003. Observations of the Mars Polar Vortex. In: Proceedings of the Sixth International Conference on Mars, Pasadena, CA. Malin, M.C., Caplinger, M.A., Davis, S.D., 2001. Observational evidence for an active surface reservoir of solid carbon dioxide on Mars. Science 294, 2146–2148. McCord, T.B., Huguenin, R.L., Mink, D., Pieters, C., 1977. Icarus 31, 25–39. Morris, R.V., Gooding, J.L., Lauer Jr., H.V., Singer, R.B., 1990. Origins of Marslike spectral and magnetic properties of a Hawaiian palagonitic soil. J. Geophys. Res. 95, 14427–14434.

193

Paige, D.A., Ingersoll, A.P., 1985. Annual heat balance of Martian polar caps: Viking observations. Science 228, 1160–1168. Rayner, J.T., Toomey, D.W., Onaka, P.M., Denault, A.J., Stahlberger, W.E., Vacca, W.D., Cushing, M.C., Wang, S., 2003. SpeX: a mediumresolution 0.8–5.5 micron spectrograph and imager for the NASA Infrared Telescope Facility. Pub. Astron. Soc. Pac. 155, 362–382. Singer, R., 1982. Spectral evidence for the mineralogy of high albedo soils and dust on Mars. J. Geophys. Res. 87, 10159–10168. Smith, M.D., 2004. Interannual variability in TES atmospheric observations of Mars during 1999–2003. Icarus 167, 148–165. Smith, M.D., Pearl, J.C., Conrath, B.J., Christensen, P.R., 2001. Thermal Emission Spectrometer results: Mars atmospheric thermal structure and aerosol distribution. J. Geophys. Res. 106, 23,929–23,945. Stamnes, K., Tsay, S.C., Jayaweera, K., Wiscombe, W., 1988. Numerically stable algorithm for discrete ordinate method radiative transfer in multiple scattering and emitting layered media. Appl. Opt. 27, 2502–2509. Thomas, P.C., Malin, M.C., James, P.B., Cantor, B.A., Williams, R.M.E., Gierasch, P., 2005. South polar residual cap of Mars: features, stratigraphy, and changes. Icarus 174, 535–559. Thomas, P.C., Malin, M.C., Edgett, K.S., Carr, M.H., Hartmann, W.K., Ingersoll, A.P., James, P.B., Soderblom, L.A., Veverka, J., Sullivan, R., 2000. North–south geological differences between the residual polar caps on Mars. Nature 404, 161–164. Titus, T., Kieffer, H.H., Christensen, P.R., 2003. Exposed water ice discovered near the South Pole of Mars. Science 299, 1048–1051. Titus, T.N., Kieffer, H.H., 2002. A comparison of the Mars south polar recession rates between 1999 and 2001. In: Lunar and Planetary Science, vol. XXXIII, Houston, TX. Tomasko, M.G., Doose, L.R., Lemmon, M., Smith, P.H., Wegryn, E., 1999. Properties of dust in the Martian atmosphere from the Imager on Mars Pathfinder. J. Geophys. Res. 104, 8987–9007. Warren, S.G., 1984. Optical constants of ice from the ultraviolet to the microwave. Appl. Opt. 23, 1206–1225. Warren, S.G., Wiscombe, W.J., 1980. A model for the spectral albedo of snow II: snow containing atmospheric aerosols. J. Atmos. Sci. 37, 2734–2745. Wiscombe, W.J., Warren, S.G., 1980. A model for the spectral albedo of snow. I: pure snow. J. Atmos. Sci. 37, 2712–2733. Wolff, M.J., Clancy, R.T., 2003. Constraints on the size of Martian aerosols from Thermal Emission Spectrometer observations. J. Geophys. Res. 108 (E9).