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An examination of Mars’ north seasonal polar cap using MGS: Composition and infrared radiation balance
Icarus 225 (2013) 869–880
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An examination of Mars’ north seasonal polar cap using MGS: Composition and infrared radiation balance Gary B. Hansen Department of Earth and Space Science, University of Washington 98195-1310, United States
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Article history: Available online 27 February 2013 Keywords: Mars, Polar caps Ices Ices, IR spectroscopy
a b s t r a c t A detailed analysis of data from one revolution of the Mars Global Surveyor (MGS) is presented. Approximately 80% of this revolution observes the mid-winter northern seasonal polar cap, which covers the surface to <60°N, and which is predominantly within polar night. The surface composition and temperature are determined through analysis of 6–50 lm infrared spectra from the Thermal Emission Spectrometer (TES). The infrared radiative balance, which is the entire heat balance in the polar night except for small subsurface and atmospheric advection terms, is calculated for the surface and atmospheric column. The primary constituent, CO2 ice, also dominates the infrared spectral properties by variations in its grain size and by admixtures of dust and water ice, which cause large variations in the 20–50 lm emissivity. This is modified by incomplete areal coverage, and clouds or hazes. This quantitative analysis reveals CO2 grain radii ranging from 100 lm in isolated areas, to 1–5 mm in more widespread regions. The water ice content varies from none to about one part per thousand by mass, with a clear increase towards the periphery of the polar cap. The dust content is typically a few parts per thousand by mass, but is as much as an order of magnitude less abundant in ‘‘cold spot’’ regions, where the low emissivity of pure CO2 ice is revealed. This is the first quantitative analysis of thermal spectra of the seasonal polar cap and the first to estimate water ice content. Our models show that the cold spots represent cleaner, dust-free ice rather than finer grained ice than the background. Our guess is that the dust in cold spots is hidden in the center of the CO2 frost particles rather than not present. The fringes of the cap have more dust and water ice, and become patchy, with warmer water snow filling the gaps on the night side, and warmer bare soil on the day side. A low optical depth (<1 in the visible) water ice atmospheric haze is apparent on the night side, and appears with smaller optical depth on the day side. The infrared radiative balance at the surface is typically 20–25 W m 2 in the central polar cap, with 25% dips in the regions of dust-free CO2. The atmospheric radiative terms are typically 1–3 W m 2. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction The seasonal polar caps of Mars are composed primarily of solid carbon dioxide condensed from the thin 6 mbar atmosphere, which was predicted by simple thermal balance models (Leighton and Murray, 1966), and which was confirmed by early measurements (Neugebauer et al., 1969; Herr and Pimentel, 1969; Larson and Fink, 1972). The conventional seasonal measure for Mars is given by the areocentric longitude of the Sun, LS, with 0° defined as the vernal equinox in the northern hemisphere. The seasonal caps occur from about fall equinox (LS = 180° in the north, LS = 0° in the south) to summer solstice (LS = 90° in the north, LS = 270° in the south). Although the optical properties of CO2 dominate the surface spectrum of, and the outgoing radiation from, the polar caps, water ice/snow and dust also play a role. CO2 has very different properties from dust and water ice in the thermal infrared (Hansen, 1999), so the overall spectral properties depend mainly on the E-mail address: [email protected] 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.02.019
grain size of CO2 and the amount of intimately or spatially mixed water snow or dust. Here I will show results from the analysis of the north seasonal cap in mid-winter, using data from one revolution of the Mars Global Surveyor (MGS). The analysis of infrared spectra from the Thermal Emission Spectrometer (TES) includes the determination of composition, grain size, and thermal radiative balance. The analysis is aided by surface elevation and morphology from the Mars Orbiter Laser Altimeter (MOLA). I will present a brief overview of previous work on composition and radiative balance of the seasonal polar caps. A more comprehensive review is presented in Hansen (1999). The amount of non-CO2 contaminants (dust, H2O ice) in the seasonal caps in the literature is discussed first. Larson and Fink (1972) found abundant CO2 in the southern cap at LS 213°, and determined an upper limit for water ice contamination of about 1%. Near-infrared spectra of the southern seasonal cap at LS 200° were acquired in 1969 by Mariner 7. The solar reflection spectrum below 4 lm was studied by Calvin and Martin (1994), who found variation across the cap in surface coverage near the edge, in water ice contamination,
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Fig. 1. Map of the orbit data analyzed here. The base map is a MOLA mosaic in polar stereographic projection. Each spectrum is a small point, three wide across the track. The cold spots, defined by brightness temperature differences between 25 and 12–18 lm (see Fig. 2), are colored red (>20 K), orange (15–20 K), green (10–15 K), and cyan (5– 10 K), with the rest of the measurements in blue implying <5 K.
and in effective CO2 particle size. The water ice concentration was estimated at 0.1–0.2% and was somewhat larger at the edge and some places in a more central region. Hansen and Martin (1993) modeled two of the Mariner 7 spectra and determined similar
numbers for the grain size and water ice contamination, but the inclusion of a small amount of dust was also found necessary. An example Mariner 9 infrared spectrum (10–50 lm) of the north seasonal cap in mid-winter was modeled in Forget et al. (1995),
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Fig. 2. Recalibrated sample spectrum and average spectra from TES observations on revolution 214, plotted as brightness temperature. The averages are centered around the single spectrum shown. The wavelengths where brightness temperatures are sampled in later figures are marked.
implying a 0.05% (by mass, assuming a dust specific gravity of 2.7) contamination by both dust and water ice. TES spectra of the south polar cap in spring, and the north polar cap in autumn, were analyzed by Hansen (1999). He found that CO2 grain sizes varied from 62 mm to >5 mm in the south and from 2 mm to 10 mm in the north, with dust concentrations of 0.03–0.07%, and no water ice needed. He used the optical constants for martian dust given by Clancy et al. (1995), which may give slightly different results compared to models with the dust optical constants from Hansen (2003) used in this paper. Glenar et al. (2005) and Hansen et al. (2005) studied telescopic and Mars Express near infrared spectra of the south polar seasonal and residual polar caps and found similar values for grain size and composition. Giuranna et al. (2007) modeled the spring north polar cap using Mars Express spectra, finding mm grain sizes and small dust and water contamination. Douté et al. (2007) modeled Mars Express Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA) spectra of the south polar residual cap and found CO2 grain sizes of 50–100 lm and dust and ice concentrations of 0.05–0.10%. Douté et al. (2009) modeled OMEGA spectra of part of the south polar seasonal cap and found CO2 grain sizes of 4–12 cm, or a 4-cm slab over 8mm grains, and a dust concentration of 0.01%. Titus et al. (2001) studied the north polar measurements during the aerobraking phase (including the measurements discussed in this paper), but concentrate on the cold spots and their relation to pure CO2. In this paper, cold spots were considered to be fine-grained CO2 ice and widespread spectra with high emissivity were considered to be slab ice. We show that dusty mm-grained CO2 ice is consistent with the spectra of these widespread regions. Cornwall and Titus (2009) did further work on the long-term behavior of cold spots, and consider dust as modifying the necessary grain size of the CO2 in the cold spots. The heat balance of the martian polar caps was a theoretical exercise with scant observational data until abundant infrared radiometric measurements were returned by the Viking orbiter. The model of Leighton and Murray (1966) was constructed to support the idea that the seasonal polar caps were composed of CO2 and correctly predicted the seasonal variation of atmospheric pressure. Later models were constructed to investigate the range of albedos and emissivities of the polar cap which would satisfy other constraints such as the latitudinal growth and decay of the caps (Cross, 1971; Briggs, 1974; Davies et al., 1977), or additionally (Wood and Paige, 1992; Pollack et al., 1993; Hourdin et al.,
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Fig. 3. Sample model spectra for water snow and water ice clouds. (a) Water snow emissivity models for various grain sizes. Note the slope in the 600–800 cm 1 region. (b) CO2 Water ice cloud model for an isothermal cloud at 155 K and optical depths, s, ranging from 0.1 to 0.8, over a blackbody surface at 142 K.
Fig. 4. The brightness temperature model spectrum of CO2 snow with a grain radius of 2 mm and temperature of 148 K, plus models for CO2 mixed with water ice, dust, and both water ice and dust. The arrow and close-up plot indicate the region where water ice mixtures lower the brightness temperature over water ice free models, causing the spectral drop-off to move to larger wavenumbers.
1995), the stronger constraints from the actual atmospheric pressure variation measured by the Viking landers (Hess et al., 1980; Tillman et al., 1993). These models were able to place broad limits on the average polar emissivities and albedos, and could calculate the amount of CO2 condensation. Paige and Ingersoll (1985) built a thermal balance model using solar and thermal fluxes estimated from the actual measurements of surface emission and reflection
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measured by the Viking orbiter. These measurements were compiled for the central polar regions only. Forget and Pollack (1996) performed a similar analysis using the same data, but studied the entire seasonal caps down to 65°. Paige and Ingersoll (1985) measured an infrared upward flux of 19 ± 1 W m 2 for the mid-winter over the central northern polar cap. Forget and Pollack (1996) measured a total infrared flux of 30, 24, and 21 W m 2 for the mid-winter polar cap at 65–70°, 75–80°, and 85–90°N, respectively. Kieffer and Titus (2001) discuss the general thermal properties of the North polar cap including a frost mass budget based on broadband bolometer measurements, which they found to be not well balanced. I will begin by presenting an overview of the location of the measurements, a description of the TES and MOLA data used, a summary of the calibration of the TES spectra, and a review of the optical properties for the CO2, H2O, and dust used in the models. The modeling results fit surface spectra and clouds, with the surface spectra being fractionally CO2 with water frost or blackbody. The fits to eight spectra are shown to illustrate the effects
of CO2 grain size, and dust and water admixtures. The infrared heat fluxes are calculated and displayed for the atmosphere and surface. A study of cold spot evolution follows, including measured spectra and models. This is followed by conclusions and a description of future work.
2. Data overview and calibration 2.1. Location and season The MGS data analyzed here are from revolution 214, in the first science phasing orbit period (SPO-1). It took place in April 1998 (Mars Year 23), with LS 304°, roughly halfway between the winter solstice and the spring equinox. The historical polar cap size is near its maximum extent at this time and extends to 55–60°N. The limit of polar night is at 69°N, and the spacecraft ground track crosses into sunlight at 67°N. The data sequence starts on the night side at 59.5°N for TES and 67.6°N for MOLA in western Utopia
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Fig. 5. Modeling results, including (a) ice amount in wt.%, dust amount in wt.%, CO2 grain radius in microns, 18–25-lm brightness temperature ratio and least squares error of fit with a latitude scale; and (b) fringe properties for both the nighttime and daytime fringes, including fractional CO2 coverage, other material temperature (water frost on the night side and blackbody on the day side) and water ice cloud 12-lm optical depth. The vertical gray lines in (a) indicate the locations of displayed spectra and fits in Fig. 7.
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Fig. 6. CO2 temperature in Kelvins compared to MOLA topography in km with a latitude scale, and the dust to water ice ratio in the CO2. The measured temperature responds inversely to the topography as expected, showing a precision of better than 1 K. The dust to ice ratio responds mainly to the ice amount, which is 0.1–0.2 times the dust in the fringes and very low from the center into the dayside, leading to a very high ratio.
Planitia (257°W). The maximum latitude reached over the elevated residual polar cap is 86.2°N. The data analyzed here ends at 49.2°N on the day side, in Tempe Terra (71°W). The total distance of the ground track is just under 4200 km. Fig. 1 shows a map with the location of the data. 2.2. The TES spectra and their calibration The TES has two parts, a Michelson interferometer measuring from 1650 to 200 cm 1 (6–50 lm) at either 5 or 10 cm 1 spectral resolution, and a two channel bolometric radiometer measuring solar (0.3–2.7 lm) and thermal (5.5–100 lm) spectral regions (Christensen et al., 1992). The solar bolometric data are calibrated as radiance and as effective Lambert albedo. Each section has a boresighted array of 3 2 detectors, each with an 8.3 mrad square field of view, which results in a self-apodization of the spectrometer’s spectral resolution to 6 and 12 cm 1, respectively. The spectra in this revolution are all taken in the 12 cm 1 mode. The theoretical surface resolution varies from 1 to 6 km, with the highest resolution at the end of the sequence, but smear along the orbit path degrades this somewhat. For an isothermal 150 K target, the instrument is effectively noise limited below 10 lm for any reasonable amount of averaging, so surface studies of the central seasonal polar cap are limited to 10–50 lm (1000–200 cm 1). My initial examination of the first available complete TES spectra and ancillary data (revolutions 214–268) revealed serious artifacts in the polar spectra which were difficult to correct. After considerable experimentation, a scheme was developed that produces much improved spectra from the PDS supplied dataset. The calibration of TES spectra includes two steps, instrument sensitivity, and darks. First and most straightforward, the instrument response is linearized to the levels at later time. Early measurements in some revolutions are greatly affected by the automatic calibration using erroneous dark or blackbody measurements. The assumption is that the true sensitivity does not change rapidly in time, and that later times in the sequence are better calibrated. The dark values are a more complicated issue. The darks measured by pointing the mirror up differ from those when pointed to the side or down (Christensen et al., 2001). The offset is a very significant fraction of typical polar spectra (Kieffer et al., 2000). If
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there are limb viewing observations in a revolution, a more realistic dark can be determined by inspecting these. Also, the radiance from a 150 K surface is essentially 0 for wavenumbers larger than 1300 cm 1, providing a source for darks in that region. Unfortunately, all revolutions do not have limb scans—revolutions 214 and 215 must rely on limb data from revolution 216, for example. This is an uncertain process, since the long wavenumber darks are slightly different on each revolution. Therefore, slightly different darks are used for each sequence, matched to the long wavenumber behavior. There is a high-frequency component to the darks as well, which also appears to vary slightly from revolution to revolution. At wavenumbers where there is significant radiance, these patterns are determined by assuming that the surface spectrum averaged over the whole polar cap, outside the atmospheric CO2 band, is smooth. At longer wavenumbers, the dark pattern is determined directly from averages of the coldest spectra. When these new darks are used, both individual spectra and averages of small numbers of spectra are much better behaved, in that the remaining variations have all the characteristics of random noise. I have also found it necessary to shift the assumed wavenumber of the channels near 15 lm by a few cm 1 in some regions to improve the atmospheric model fits. An example TES spectrum and TES spectral averages are shown in Fig. 2 in terms of brightness temperature. The wavenumber regions selected for plotting brightness temperature differences later (two surface temperature proxies on either side of the CO2 15-lm band, and a range in the center of the low-emissivity region between 200 and 500 cm 1) are marked in the graph. 2.3. MOLA data The MOLA is designed to measure the martian radius and topography using a pulsed laser system operating at a wavelength of 1.064 lm (Zuber et al., 1992). Secondary products include the backscattered energy (related to the surface albedo at 1.06 lm), and limited information on the width of the returned pulse, related to surface slope and roughness, and/or to atmospheric scattering. The pulse width is related to the number (1–4) of the matched filter which is used to process the returned pulse. The MOLA can only operate within about 800 km of the surface, and the returned energy measurement saturates when the instrument is operated much below the design altitude near 500 km. The science phasing orbits exceed both these limits on significant portions of the orbit. On revolution 214, the MOLA energy return is saturated for almost three quarters of the distance over the polar cap. For relative topography, the surface along-track resolution is 300–400 m and the vertical resolution is about 30 cm (Smith et al., 1998). Optically thick clouds will generate a return near the cloud-top, but the thin clouds more typical of Mars either produce a weak, broad return detectable in Filters 3 or 4, or scatter the pulse out of the forward direction, preventing a return from either the cloud or the surface underneath (Hansen, 1999; Neumann et al., 2003). Both optically thick and thin polar clouds have been observed by MOLA (Pettengill and Ford, 1998; Ivanov and Muhleman, 2001), but none are visible on revolution 214. In fact, there are only three returns out of almost 9000 over the polar cap that were not detected in the narrowest filter. I use primarily the topographical information and the surface reflectance, in this analysis. 2.4. Optical properties, models, and spectral behavior of CO2, H2O, and dust Dust, water ice, and CO2 have distinct infrared spectra (Hansen, 1999). An problem with fitting dusty CO2 spectra using earlier dust models (Hansen, 1999) is the inaccuracy of the optical constants for Mars dust from Clancy et al. (1995) in the infrared wavelength
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Fig. 7. Eight individual TES spectra and model fits at locations indicated in Fig. 5a. The parameters of the fits are indicated in the upper right of each plot (the fringe spectra have extra lines describing the non-CO2 surface). An attempt was made to illustrate the major regions plus three (anomalous) cold spots.
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Fig. 7. (continued)
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detectors, which are generated from an interferometer model that is adjusted to fit the measured halfwidths. The model emissivity of water snow with various grain sizes is shown in Fig. 3a. Included are approximately monodisperse distributions for 2, 5, 20, and 200 lm radii, and a wide distribution with an effective radius of 2.4 lm based on the dust models in Toon et al. (1977). The small sizes are consistent with ice particles from the atmosphere, which are found to be of a uniform and fairly narrow distribution with an effective radius between 1 and 4 lm (Pearl et al., 2001). Note that there is a strong slope across the 15-lm (667 cm 1) region, where the atmosphere obscures the surface, for all of the smaller grain sizes. Mixing areal patches of fine-grained snow with the CO2 can produce slopes similar to those produced by warmer water ice clouds over the surface (Pearl et al., 2001). We have modeled both spatially mixed frosts and intimately mixed particles using the Toon et al. (1977) distribution, as well as clouds, when the overlying atmosphere is warmer. Fig. 3b shows our water ice cloud model, which uses a narrow distribution with an effective radius of 2 lm, and allows optical depths at 12 lm of up to 0.8. The visible optical depth is about twice the 12-lm value, so to be consistent with the clear atmosphere from MOLA, the optical depth of any cloud should be less than a few tenths. The cloud model is a simple isothermal layer set to a middle atmospheric temperature, but including scattering and absorption, using the discrete ordinates model of Stamnes et al. (1988). Sample brightness temperature models of pure CO2, CO2 with water ice, CO2 with dust, and CO2 with both water ice and dust are shown in Fig. 4, to illustrate the spectral effects of the various materials. As shown in Hansen (1999), dust mixtures move the centroid of the 20–50 lm low-emissivity feature to smaller wavenumbers (longer wavelength), while water mixtures move it to longer wavenumbers (shorter wavelengths). Water ice imparts smooth spectral shapes to the CO2 spectrum, while dust provides varied, angular shapes. A key property of water ice is its ability to move the spectral slope at >500 cm 1 (<20 lm) to longer wavenumbers (shorter wavelengths). This effect is more subtle than the effects of water ice above 30 lm (below 300 cm 1) but the TES signal/noise is much better at the shorter wavelength, where this effect is often clearly evident when comparing TES spectra with pure or dusty CO2 only.
3. Results 3.1. Modeling of individual spectra and mapping of composition and grain sizes
range >6 lm. For this analysis, I am using the optical constants for martian dust given by Hansen (2003), using an appropriate size distribution (Markiewicz et al., 1999; Tomasko et al., 1999). These improved optical properties fit aerosol spectra better, and also provide for better 20–50 lm fits to observed TES spectra. There exist good optical properties for CO2 ice except in the strong bands, where the data are more uncertain (Hansen, 1997a, 1997b, 2005), but this is of little importance since these regions will always be either very high emissivity or completely obscured by atmospheric CO2 absorption. For water ice, there is more uncertainty, since the spectral structure is not opaque enough in the infrared to be measured accurately using only thin films. I have compiled optical constants which I believe to be accurate for hexagonal ice at 150 K (Hansen, 1996, 1999). The surface models are calculated using the two-stream model described by Wiscombe and Warren (1980), using emission zenith angles of zero. The single-scattering quantities for the materials is computed using Mie code (spheres) (Wiscombe, 1980). The models are all convolved with accurate instrument functions for the TES
The TES spectra are now individually fitted to surface models to map the physical properties and composition across the surface. This is done by first correcting for the atmospheric emission, which is calculated using the models described in the next section. The values at wavelengths where the atmosphere is partially transparent are replaced with an estimate of the surface emission. The regions where the atmosphere is opaque are replaced by a straight-line extrapolation in brightness temperature and are weakly weighted in the ensuing fits. Each atmosphere-removed spectrum is fitted to a spatial mix of another material (water snow, or blackbody) at a different temperature and a ternary mixture of CO2 ice, water ice and dust. If the atmosphere is >1 K warmer than the model surface temperature, a possible cloud is introduced. The minimization used is a fast downhill method, so the initial guess is very important for finding the best fits. Once the sequence is started, each fit is initialized with a median of 11 previous fits, on the assumption that the properties do not change too quickly. The results are shown in Fig. 5.
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Fig. 8. Elements used in the calculation of the infrared radiative balance. (a) The TES infrared radiance spectrum continued to 0 wavenumbers (short dashed line) and filled in the 15-lm CO2 atmospheric band (long dashed line). (b) Atmospheric terms of radiance (black) and transmission (gray). (c) Calculation of surface radiance into all emission angles. (d) Final flux calculations integrated over all angles as described in the legend.
Fig. 9. Radiative balance values as a function of distance. The atmospheric terms are all less than 4 W m 2 except near the fringes. The surface to space and net surface upward are nearly equal because the surface to atmosphere and atmosphere to surface terms nearly cancel out. The surface + atmosphere to space is comparable to, if a little smaller than previous determinations.
3.2. Overview of model results Fig. 5a shows a detailed overview of the models fitting the data from revolution 214. The top three panels display the model fits of a ternary mixture model with CO2 ice dust and water. The fourth panel represents infrared spectral properties, by showing the difference between the 18-lm, and the 25–30-lm brightness temperatures (see Fig. 2). Fine-grained, clean CO2 has a larger temperature difference (‘‘colder’’) than coarse-grained or dusty CO2. The bottom panel shows the least squares error of fit of the model to the spectra. The x-axis is an approximate distance in km of the orbital track over the surface. The corresponding latitudes are marked in the middle of the lower panel.
The CO2 ice grain size varies in ways mostly not related to the occurrence of cold spots. Only in one instance (around 1000 km) is there a reduction of CO2 grain size coincident with a cold spot. In general, the CO2 ice grain size is largest near the center of the polar deposits and at the very edge (1–5 mm), and smaller in other regions (500 lm). The dust amounts are generally large (0.5–1%) except in the regions of cold spots, where the amounts are around 0.01%. The water ice amounts are weakly correlated with the cold spots (less in cold spot locations), but the average values are very low in the central polar cap and approaching 0.1% on the periphery. In Fig. 5b, the polar cap fringe properties are displayed as a function of latitude. The night fringe does not reach the edge of the cap and only sees predominantly CO2 covered areas (80–100%), and whose uncovered areas are colder than the daytime fringe and covered with water frost. The daytime fringe goes to the edge of the cap at 49°N, with a steep decline in CO2 coverage (where it goes from 80% to 20% in 1.5° or about 90 km) at about 52°N. The uncovered patches in this fringe model well as blackbodies at 158–163 K. The water ice cloud 12-lm optical depth is 0.2–0.4 on the night fringe. Its calculation is complicated by the fact that the surface water ice frost and the cloud have a similar spectral properties. The daytime fringe cloud is of lower optical depth (0.05–0.1) but is more precisely determined than the night fringe cloud. Neither cloud appears to continue poleward of 65°N. Beyond this point the atmosphere is colder than the surface, but no 12-lm absorption feature is seen as would be expected. This annular pattern is consistent with the findings of Pearl et al. (2001). Fig. 6 shows how the measured CO2 temperature is consistent with the altitude, being lowest at the 1 km altitude of the top of the polar cap and fringes and highest in the low polar plains at 4 to 5 km. The lower panel shows the ratio of the measured dust/water content. This is not well determined where the water content is very small but otherwise shows a range of 5–10. The vertical, dashed, gray lines in Fig. 5a are eight representative locations whose spectra and fits are plotted in Fig. 7a–h. Included are three
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Fig. 10. Close-up look at the model data near two cold spots. Note how the dust amount signature mimics the brightness temperature difference very closely in both cases, while there is little changes in grain size of the CO2 ice in these locations.
cold spots (7c, 7d, 7g), background regions (7b, 7e, 7f) and fringe regions (7a, 7h). 3.3. Infrared radiative heat balance The infrared radiation balance can be computed if one can estimate the complete emission spectrum over the important wavenumbers for surfaces at 150 K (30–1100 cm 1) and over all emission angles. If in addition, the atmosphere is modeled similarly, the internal terms of atmosphere to surface, etc. can also be calculated. I use a clear atmosphere model, which is a general random band model (Crisp et al., 1986) that has calculated layer transmissions for CO2 for 13 pressures from 0.001 to 10 mbar, 19 temperatures from 110 to 296 K, and 13 angles. The model is calculated using 2.5-cm 1 wide bands over the wavenumber range 450–1500 cm 1 and the latest HITRAN line parameters. It is used for atmospheric temperature inversions and, by making use of the high angle calculations, for the radiative balance model. The steps needed to calculate the terms for an example spectrum are illustrated in Fig. 8, including longwave continuation, atmosphere modeling, angular emissivity estimates, and the calculation of atmospheric radiation terms. The angular behavior of the surface deposits is a function of the nadir emissivity, and low nadir emissivities decrease at high angles using the behavior of surface models as a guide. The flux results in W m 2 are illustrated in Fig. 9. The average level of surface + atmosphere to space is similar to, but a little lower than those of previous workers using Viking data (Paige and Ingersoll, 1985; Forget and Pollack, 1996). The polar short-wave (solar) heat balance can also be calculated, but it is a much more complicated procedure, requiring model bidirectional reflectance models of the surface and clouds. It applies only to the last third of the distance considered here (2700 km to the end) and has not been completed at this time.
4. Cold spot properties and origin Cold spots are transient regions of low 20–50-lm emissivity that occur regularly (Cornwall and Titus, 2009; Titus et al., 2001) in the north seasonal polar cap of Mars, and have some impact on the average radiative balance of the polar caps. They arise from the optical properties of solid CO2 (low emissivity for small grain sizes) and occur almost always (at least in the north) at locations with steep slopes. The accepted explanation is fine-grained CO2 snow deposited as a result of atmospheric dynamics. The emissivity of cold spots has been found to increase with time with a time constant of 5–10 days (Cornwall and Titus, 2009). This change has been attributed to the grain coarsening of fine-grained deposits through ‘‘continued condensation’’ or sintering processes (Eluszkiewicz, 1993). I am proposing an additional, and possibly dominant, process that drives this evolution, namely the migration of dust condensation nuclei from the interior of grains (optically hidden) to the exterior (optically active). As mentioned before, the modeling results show that the CO2 grain radius averages about 1 mm (200 lm–1 cm) and does not change much in the locations of cold spots. The dust mass ratio, however, tracks the cold spots indicated by large 18–25-lm brightness temperatures very well. Two areas are shown in detail in Fig. 10: Area 1 has grain radii across the spot between 600 and 900 lm, while dust varies between 0.01 and 0.1 wt.%. Area 2 has grain radii across the spot of 1.5–2 mm, while the dust concentration varies between 0.008 and 0.05 wt.%. TES spectra from the two areas are shown in Fig. 11; each spectrum (solid lines) is an average of 5–10 individual spectra. In both cases, the ‘‘background’’ spectra are from areas on either side of the cold spot, while the spectrum marked ‘‘center’’ has the lowest 25-lm brightness temperatures. Dusty ice models are fit to the spectra (dashed lines). For comparison, a large-grained model (r = 10 mm with
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Fig. 11. Average TES spectra from these two cold spots from the center, edges and background regions (solid lines). The models that fit these spectra are shown as dashed lines. In both plots a large grained pure CO2 model with the same 25-lm brightness temperature of the background is shown as a dash-dot line, and looks much different from the measured spectra.
0.002 wt.% dust) having a similar 18-lm to 25-lm brightness temperature ratio to the measured background spectra is shown in a dot-dashed line; the TES spectra are clearly more consistent with dustier, finer-grained CO2. These observations suggest a different explanation for the evolution of cold spots. Assuming that the final state of ‘‘decayed’’ cold spots is similar to the immediately surrounding polar cap, the evolution is towards dustier CO2 snow of similar grain size, not towards larger grains. This could be explained by optically ‘‘hiding’’ the dust inside a snow particle initially, with diffusion or other processes eventually causing the migration of these dust grains to CO2 grain boundaries, thus making them optically active. The hidden dust presumably starts as condensation nuclei for snow particles. This is consistent with the increased activity of cold spots when more dust is moved into the north polar regions (Forget and Pollack, 1996; Cornwall and Titus, 2009). How effectively can dust grains be optically hidden in CO2 grains? This was tested by running Mie scattering code for layered spherical objects, using a dust inner layer with an appropriate distribution of sizes (between 0.2 and 9.5 lm), and total radii of between 10 and 100 lm. The results in Fig. 12 are shown as emissivity of a semi-infinite layer; The smallest sizes are modified in the most transparent regions, while sizes larger than 50 lm look much like solid CO2. Microphysical models indicate that atmospheric CO2 particles are 50–100 lm in size when they fall out as surface snow (Forget et al., 1998). As such, they will not show much evidence of their dust core, and may still grow by about a
Fig. 12. Emissivity models of layers of pure CO2 ice and a 1–2 lm dust core surrounded by various amounts of CO2 ice. The top panel shows the smallest grain sizes (10–20 lm) where the dust core raises the emissivity significantly. The bottom two panels show 50 and 100-lm particles where the inclusion of a dust core makes little difference in the spectrum.
factor of 10 (to 1 mm), as their nuclei are liberated. In fact, the grain growth rate must be quite fast, since there are only two or three cold spots that have smaller grain sizes comparable to original snow, while the rest have grown to mm sizes like the background but still show less dust. The decay rates of the cold spots measured by Cornwall and Titus (2009) is primarily the rate of dust removal from the snow grains (5–10 days).
5. Conclusions We have mapped the grain size and contamination by dust and water in the seasonal Mars North polar cap in mid-winter using observations of MGS TES. This is the first time such a quantitative analysis using thermal data comparable to modeling of solar reflected spectra has been done. Most of the reflectance spectral modeling has been of the south polar cap and cannot be done during the polar night. Seasonal CO2 is predominately large-grained (0.5–5.0 mm radius) and dust-rich (0.1–1.0 wt.%) during the polar night. This compares with the results in Giuranna et al. (2007) of 3–5 mm grain size and <0.2 wt.% dust from the north pole in a later season (LS = 40°). In spring, deposits often become cleaner and decrease in grain size, and therefore become brighter in the visible (Hansen, 1999). Low-emissivity regions in this observation are found mostly near large topographic slopes such as scarps, ridges, and craters, and mostly on equator-facing slopes. They likely originate from low-altitude, local, and short-lived (but perhaps sustained) atmospheric condensation (Forget et al., 1998). In the northern seasonal cap, water snow (seemingly diurnal) appears to cover significant areas (up to 30%) in the first several hundred
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kilometers of the southern edge of the cap on the night side. The non-ice areas of the daytime fringe model well as blackbodies. Low optical depth clouds are detected over both fringes up to about 60–65°N. Observations indicate that the effective CO2 grain size varies smoothly over the Mars seasonal polar cap, while effective dust content varies sharply, and is mostly responsible for the observed cold spots. Based on this evidence, we propose that the evolution of low emissivity cold spots over time to higher emissivity is caused by the optical liberation of dust nuclei, rather than by grain coarsening. We hope to study more data in the future, and expect similar results for the mid-winter north pole at least. Many of the individual spectra are quite noisy and the fits may be non-unique (see Fig. 7h), but averages point to spectral models similar to the ones I have used (say in background spectra such as in Fig. 7b–f), rather than for example, slab ice. The south pole seasonal deposits are less dusty on average and may have very different behavior.
6. Future work The dust optical model needs to be improved in the 20–50 lm range, so that mixture models can fit observed spectra better. This discrepancy is obvious when modeling average spectra that have much better signal-to-noise than the individual spectra displayed in Fig. 7 (somewhat visible in the averages in Fig. 11). As mentioned before the short-wave heat balance has only been investigated briefly, and we envision a Monte-Carlo problem to account for cloud scattering and surface scattering. Acknowledgments This work was mostly accomplished with the support of the NASA Mars Data Analysis Program. The MOLA base map for Fig. 1 was kindly provided by Harvey Greenberg at the University of Washington. References Briggs, G.A., 1974. The nature of the residual martian polar caps. Icarus 23, 167–191. Calvin, W.M., Martin, T.Z., 1994. Spatial variability in the seasonal south polar cap of Mars. J. Geophys. Res. 99, 21143–21152. Christensen, P.R. et al., 1992. Thermal emission spectrometer experiment: Mars Observer mission. J. Geophys. Res. 97, 7719–7734. Christensen, P.R. et al., 2001. Mars Global Surveyor Thermal Emission Spectrometer experiment: Investigation description and surface science results. J. Geophys. Res. 106, 23823–23871. Clancy, R.T., Lee, S.W., Gladstone, G.R., McMillan, W.W., Roush, T.L., 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. Cornwall, C., Titus, T.N., 2009. Spatial and temporal distributions of martian north polar cold spots before, during, and after the global dust storm of 2001. J. Geophys. Res. 114, E02003. http://dx.doi.org/10.1029/2008JE003243. Crisp, D., Fels, S.B., Schwarzkopf, M.D., 1986. Approximate methods for finding CO2 15-lm band transmission in planetary atmospheres. J. Geophys. Res. 91, 11851–11866. Cross, C.A., 1971. The heat balance of the martian polar caps. Icarus 15, 110–114. Davies, D.W., Farmer, C.B., LaPorte, D.D., 1977. Behavior of volatiles in Mars’ polar areas: A model incorporating new experimental data. J. Geophys. Res. 82, 3815– 3822. Douté, S. et al., 2007. South pole of Mars: Nature and composition of the icy terrains from Mars Express OMEGA observations. Planet. Space Sci. 55, 113–133. http:// dx.doi.org/10.1016/j.pss.2006.05.035. Douté, S., Schmidt, D., Schmitt, B., Vincendon, M., Langevin, Y., Gondet, B., 2009. Physical State of the ‘‘Bright’’ South Seasonal Polar Cap from OMEGA Observations (abstract). Third International Workshop on Mars Polar Energy Balance and the CO2 Cycle (Seattle, Washington), Abstract #7033. Eluszkiewicz, J., 1993. On the microphysical state of the martian seasonal caps. Icarus 103, 43–48. Forget, F., Pollack, J.B., 1996. Thermal infrared observations of the condensing martian polar caps: CO2 ice temperatures and radiative budget. J. Geophys. Res. 101, 16865–16879.
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An examination of Mars’ north seasonal polar cap using MGS: Composition and infrared radiation balance Gary B. Hansen Department of Earth and Space Science, University of Washington 98195-1310, United States
a r t i c l e
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Article history: Available online 27 February 2013 Keywords: Mars, Polar caps Ices Ices, IR spectroscopy
a b s t r a c t A detailed analysis of data from one revolution of the Mars Global Surveyor (MGS) is presented. Approximately 80% of this revolution observes the mid-winter northern seasonal polar cap, which covers the surface to <60°N, and which is predominantly within polar night. The surface composition and temperature are determined through analysis of 6–50 lm infrared spectra from the Thermal Emission Spectrometer (TES). The infrared radiative balance, which is the entire heat balance in the polar night except for small subsurface and atmospheric advection terms, is calculated for the surface and atmospheric column. The primary constituent, CO2 ice, also dominates the infrared spectral properties by variations in its grain size and by admixtures of dust and water ice, which cause large variations in the 20–50 lm emissivity. This is modified by incomplete areal coverage, and clouds or hazes. This quantitative analysis reveals CO2 grain radii ranging from 100 lm in isolated areas, to 1–5 mm in more widespread regions. The water ice content varies from none to about one part per thousand by mass, with a clear increase towards the periphery of the polar cap. The dust content is typically a few parts per thousand by mass, but is as much as an order of magnitude less abundant in ‘‘cold spot’’ regions, where the low emissivity of pure CO2 ice is revealed. This is the first quantitative analysis of thermal spectra of the seasonal polar cap and the first to estimate water ice content. Our models show that the cold spots represent cleaner, dust-free ice rather than finer grained ice than the background. Our guess is that the dust in cold spots is hidden in the center of the CO2 frost particles rather than not present. The fringes of the cap have more dust and water ice, and become patchy, with warmer water snow filling the gaps on the night side, and warmer bare soil on the day side. A low optical depth (<1 in the visible) water ice atmospheric haze is apparent on the night side, and appears with smaller optical depth on the day side. The infrared radiative balance at the surface is typically 20–25 W m 2 in the central polar cap, with 25% dips in the regions of dust-free CO2. The atmospheric radiative terms are typically 1–3 W m 2. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction The seasonal polar caps of Mars are composed primarily of solid carbon dioxide condensed from the thin 6 mbar atmosphere, which was predicted by simple thermal balance models (Leighton and Murray, 1966), and which was confirmed by early measurements (Neugebauer et al., 1969; Herr and Pimentel, 1969; Larson and Fink, 1972). The conventional seasonal measure for Mars is given by the areocentric longitude of the Sun, LS, with 0° defined as the vernal equinox in the northern hemisphere. The seasonal caps occur from about fall equinox (LS = 180° in the north, LS = 0° in the south) to summer solstice (LS = 90° in the north, LS = 270° in the south). Although the optical properties of CO2 dominate the surface spectrum of, and the outgoing radiation from, the polar caps, water ice/snow and dust also play a role. CO2 has very different properties from dust and water ice in the thermal infrared (Hansen, 1999), so the overall spectral properties depend mainly on the E-mail address: [email protected] 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.02.019
grain size of CO2 and the amount of intimately or spatially mixed water snow or dust. Here I will show results from the analysis of the north seasonal cap in mid-winter, using data from one revolution of the Mars Global Surveyor (MGS). The analysis of infrared spectra from the Thermal Emission Spectrometer (TES) includes the determination of composition, grain size, and thermal radiative balance. The analysis is aided by surface elevation and morphology from the Mars Orbiter Laser Altimeter (MOLA). I will present a brief overview of previous work on composition and radiative balance of the seasonal polar caps. A more comprehensive review is presented in Hansen (1999). The amount of non-CO2 contaminants (dust, H2O ice) in the seasonal caps in the literature is discussed first. Larson and Fink (1972) found abundant CO2 in the southern cap at LS 213°, and determined an upper limit for water ice contamination of about 1%. Near-infrared spectra of the southern seasonal cap at LS 200° were acquired in 1969 by Mariner 7. The solar reflection spectrum below 4 lm was studied by Calvin and Martin (1994), who found variation across the cap in surface coverage near the edge, in water ice contamination,
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Fig. 1. Map of the orbit data analyzed here. The base map is a MOLA mosaic in polar stereographic projection. Each spectrum is a small point, three wide across the track. The cold spots, defined by brightness temperature differences between 25 and 12–18 lm (see Fig. 2), are colored red (>20 K), orange (15–20 K), green (10–15 K), and cyan (5– 10 K), with the rest of the measurements in blue implying <5 K.
and in effective CO2 particle size. The water ice concentration was estimated at 0.1–0.2% and was somewhat larger at the edge and some places in a more central region. Hansen and Martin (1993) modeled two of the Mariner 7 spectra and determined similar
numbers for the grain size and water ice contamination, but the inclusion of a small amount of dust was also found necessary. An example Mariner 9 infrared spectrum (10–50 lm) of the north seasonal cap in mid-winter was modeled in Forget et al. (1995),
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(a)
Fig. 2. Recalibrated sample spectrum and average spectra from TES observations on revolution 214, plotted as brightness temperature. The averages are centered around the single spectrum shown. The wavelengths where brightness temperatures are sampled in later figures are marked.
implying a 0.05% (by mass, assuming a dust specific gravity of 2.7) contamination by both dust and water ice. TES spectra of the south polar cap in spring, and the north polar cap in autumn, were analyzed by Hansen (1999). He found that CO2 grain sizes varied from 62 mm to >5 mm in the south and from 2 mm to 10 mm in the north, with dust concentrations of 0.03–0.07%, and no water ice needed. He used the optical constants for martian dust given by Clancy et al. (1995), which may give slightly different results compared to models with the dust optical constants from Hansen (2003) used in this paper. Glenar et al. (2005) and Hansen et al. (2005) studied telescopic and Mars Express near infrared spectra of the south polar seasonal and residual polar caps and found similar values for grain size and composition. Giuranna et al. (2007) modeled the spring north polar cap using Mars Express spectra, finding mm grain sizes and small dust and water contamination. Douté et al. (2007) modeled Mars Express Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA) spectra of the south polar residual cap and found CO2 grain sizes of 50–100 lm and dust and ice concentrations of 0.05–0.10%. Douté et al. (2009) modeled OMEGA spectra of part of the south polar seasonal cap and found CO2 grain sizes of 4–12 cm, or a 4-cm slab over 8mm grains, and a dust concentration of 0.01%. Titus et al. (2001) studied the north polar measurements during the aerobraking phase (including the measurements discussed in this paper), but concentrate on the cold spots and their relation to pure CO2. In this paper, cold spots were considered to be fine-grained CO2 ice and widespread spectra with high emissivity were considered to be slab ice. We show that dusty mm-grained CO2 ice is consistent with the spectra of these widespread regions. Cornwall and Titus (2009) did further work on the long-term behavior of cold spots, and consider dust as modifying the necessary grain size of the CO2 in the cold spots. The heat balance of the martian polar caps was a theoretical exercise with scant observational data until abundant infrared radiometric measurements were returned by the Viking orbiter. The model of Leighton and Murray (1966) was constructed to support the idea that the seasonal polar caps were composed of CO2 and correctly predicted the seasonal variation of atmospheric pressure. Later models were constructed to investigate the range of albedos and emissivities of the polar cap which would satisfy other constraints such as the latitudinal growth and decay of the caps (Cross, 1971; Briggs, 1974; Davies et al., 1977), or additionally (Wood and Paige, 1992; Pollack et al., 1993; Hourdin et al.,
(b)
Fig. 3. Sample model spectra for water snow and water ice clouds. (a) Water snow emissivity models for various grain sizes. Note the slope in the 600–800 cm 1 region. (b) CO2 Water ice cloud model for an isothermal cloud at 155 K and optical depths, s, ranging from 0.1 to 0.8, over a blackbody surface at 142 K.
Fig. 4. The brightness temperature model spectrum of CO2 snow with a grain radius of 2 mm and temperature of 148 K, plus models for CO2 mixed with water ice, dust, and both water ice and dust. The arrow and close-up plot indicate the region where water ice mixtures lower the brightness temperature over water ice free models, causing the spectral drop-off to move to larger wavenumbers.
1995), the stronger constraints from the actual atmospheric pressure variation measured by the Viking landers (Hess et al., 1980; Tillman et al., 1993). These models were able to place broad limits on the average polar emissivities and albedos, and could calculate the amount of CO2 condensation. Paige and Ingersoll (1985) built a thermal balance model using solar and thermal fluxes estimated from the actual measurements of surface emission and reflection
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measured by the Viking orbiter. These measurements were compiled for the central polar regions only. Forget and Pollack (1996) performed a similar analysis using the same data, but studied the entire seasonal caps down to 65°. Paige and Ingersoll (1985) measured an infrared upward flux of 19 ± 1 W m 2 for the mid-winter over the central northern polar cap. Forget and Pollack (1996) measured a total infrared flux of 30, 24, and 21 W m 2 for the mid-winter polar cap at 65–70°, 75–80°, and 85–90°N, respectively. Kieffer and Titus (2001) discuss the general thermal properties of the North polar cap including a frost mass budget based on broadband bolometer measurements, which they found to be not well balanced. I will begin by presenting an overview of the location of the measurements, a description of the TES and MOLA data used, a summary of the calibration of the TES spectra, and a review of the optical properties for the CO2, H2O, and dust used in the models. The modeling results fit surface spectra and clouds, with the surface spectra being fractionally CO2 with water frost or blackbody. The fits to eight spectra are shown to illustrate the effects
of CO2 grain size, and dust and water admixtures. The infrared heat fluxes are calculated and displayed for the atmosphere and surface. A study of cold spot evolution follows, including measured spectra and models. This is followed by conclusions and a description of future work.
2. Data overview and calibration 2.1. Location and season The MGS data analyzed here are from revolution 214, in the first science phasing orbit period (SPO-1). It took place in April 1998 (Mars Year 23), with LS 304°, roughly halfway between the winter solstice and the spring equinox. The historical polar cap size is near its maximum extent at this time and extends to 55–60°N. The limit of polar night is at 69°N, and the spacecraft ground track crosses into sunlight at 67°N. The data sequence starts on the night side at 59.5°N for TES and 67.6°N for MOLA in western Utopia
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Fig. 5. Modeling results, including (a) ice amount in wt.%, dust amount in wt.%, CO2 grain radius in microns, 18–25-lm brightness temperature ratio and least squares error of fit with a latitude scale; and (b) fringe properties for both the nighttime and daytime fringes, including fractional CO2 coverage, other material temperature (water frost on the night side and blackbody on the day side) and water ice cloud 12-lm optical depth. The vertical gray lines in (a) indicate the locations of displayed spectra and fits in Fig. 7.
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Fig. 6. CO2 temperature in Kelvins compared to MOLA topography in km with a latitude scale, and the dust to water ice ratio in the CO2. The measured temperature responds inversely to the topography as expected, showing a precision of better than 1 K. The dust to ice ratio responds mainly to the ice amount, which is 0.1–0.2 times the dust in the fringes and very low from the center into the dayside, leading to a very high ratio.
Planitia (257°W). The maximum latitude reached over the elevated residual polar cap is 86.2°N. The data analyzed here ends at 49.2°N on the day side, in Tempe Terra (71°W). The total distance of the ground track is just under 4200 km. Fig. 1 shows a map with the location of the data. 2.2. The TES spectra and their calibration The TES has two parts, a Michelson interferometer measuring from 1650 to 200 cm 1 (6–50 lm) at either 5 or 10 cm 1 spectral resolution, and a two channel bolometric radiometer measuring solar (0.3–2.7 lm) and thermal (5.5–100 lm) spectral regions (Christensen et al., 1992). The solar bolometric data are calibrated as radiance and as effective Lambert albedo. Each section has a boresighted array of 3 2 detectors, each with an 8.3 mrad square field of view, which results in a self-apodization of the spectrometer’s spectral resolution to 6 and 12 cm 1, respectively. The spectra in this revolution are all taken in the 12 cm 1 mode. The theoretical surface resolution varies from 1 to 6 km, with the highest resolution at the end of the sequence, but smear along the orbit path degrades this somewhat. For an isothermal 150 K target, the instrument is effectively noise limited below 10 lm for any reasonable amount of averaging, so surface studies of the central seasonal polar cap are limited to 10–50 lm (1000–200 cm 1). My initial examination of the first available complete TES spectra and ancillary data (revolutions 214–268) revealed serious artifacts in the polar spectra which were difficult to correct. After considerable experimentation, a scheme was developed that produces much improved spectra from the PDS supplied dataset. The calibration of TES spectra includes two steps, instrument sensitivity, and darks. First and most straightforward, the instrument response is linearized to the levels at later time. Early measurements in some revolutions are greatly affected by the automatic calibration using erroneous dark or blackbody measurements. The assumption is that the true sensitivity does not change rapidly in time, and that later times in the sequence are better calibrated. The dark values are a more complicated issue. The darks measured by pointing the mirror up differ from those when pointed to the side or down (Christensen et al., 2001). The offset is a very significant fraction of typical polar spectra (Kieffer et al., 2000). If
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there are limb viewing observations in a revolution, a more realistic dark can be determined by inspecting these. Also, the radiance from a 150 K surface is essentially 0 for wavenumbers larger than 1300 cm 1, providing a source for darks in that region. Unfortunately, all revolutions do not have limb scans—revolutions 214 and 215 must rely on limb data from revolution 216, for example. This is an uncertain process, since the long wavenumber darks are slightly different on each revolution. Therefore, slightly different darks are used for each sequence, matched to the long wavenumber behavior. There is a high-frequency component to the darks as well, which also appears to vary slightly from revolution to revolution. At wavenumbers where there is significant radiance, these patterns are determined by assuming that the surface spectrum averaged over the whole polar cap, outside the atmospheric CO2 band, is smooth. At longer wavenumbers, the dark pattern is determined directly from averages of the coldest spectra. When these new darks are used, both individual spectra and averages of small numbers of spectra are much better behaved, in that the remaining variations have all the characteristics of random noise. I have also found it necessary to shift the assumed wavenumber of the channels near 15 lm by a few cm 1 in some regions to improve the atmospheric model fits. An example TES spectrum and TES spectral averages are shown in Fig. 2 in terms of brightness temperature. The wavenumber regions selected for plotting brightness temperature differences later (two surface temperature proxies on either side of the CO2 15-lm band, and a range in the center of the low-emissivity region between 200 and 500 cm 1) are marked in the graph. 2.3. MOLA data The MOLA is designed to measure the martian radius and topography using a pulsed laser system operating at a wavelength of 1.064 lm (Zuber et al., 1992). Secondary products include the backscattered energy (related to the surface albedo at 1.06 lm), and limited information on the width of the returned pulse, related to surface slope and roughness, and/or to atmospheric scattering. The pulse width is related to the number (1–4) of the matched filter which is used to process the returned pulse. The MOLA can only operate within about 800 km of the surface, and the returned energy measurement saturates when the instrument is operated much below the design altitude near 500 km. The science phasing orbits exceed both these limits on significant portions of the orbit. On revolution 214, the MOLA energy return is saturated for almost three quarters of the distance over the polar cap. For relative topography, the surface along-track resolution is 300–400 m and the vertical resolution is about 30 cm (Smith et al., 1998). Optically thick clouds will generate a return near the cloud-top, but the thin clouds more typical of Mars either produce a weak, broad return detectable in Filters 3 or 4, or scatter the pulse out of the forward direction, preventing a return from either the cloud or the surface underneath (Hansen, 1999; Neumann et al., 2003). Both optically thick and thin polar clouds have been observed by MOLA (Pettengill and Ford, 1998; Ivanov and Muhleman, 2001), but none are visible on revolution 214. In fact, there are only three returns out of almost 9000 over the polar cap that were not detected in the narrowest filter. I use primarily the topographical information and the surface reflectance, in this analysis. 2.4. Optical properties, models, and spectral behavior of CO2, H2O, and dust Dust, water ice, and CO2 have distinct infrared spectra (Hansen, 1999). An problem with fitting dusty CO2 spectra using earlier dust models (Hansen, 1999) is the inaccuracy of the optical constants for Mars dust from Clancy et al. (1995) in the infrared wavelength
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Fig. 7. Eight individual TES spectra and model fits at locations indicated in Fig. 5a. The parameters of the fits are indicated in the upper right of each plot (the fringe spectra have extra lines describing the non-CO2 surface). An attempt was made to illustrate the major regions plus three (anomalous) cold spots.
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Fig. 7. (continued)
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detectors, which are generated from an interferometer model that is adjusted to fit the measured halfwidths. The model emissivity of water snow with various grain sizes is shown in Fig. 3a. Included are approximately monodisperse distributions for 2, 5, 20, and 200 lm radii, and a wide distribution with an effective radius of 2.4 lm based on the dust models in Toon et al. (1977). The small sizes are consistent with ice particles from the atmosphere, which are found to be of a uniform and fairly narrow distribution with an effective radius between 1 and 4 lm (Pearl et al., 2001). Note that there is a strong slope across the 15-lm (667 cm 1) region, where the atmosphere obscures the surface, for all of the smaller grain sizes. Mixing areal patches of fine-grained snow with the CO2 can produce slopes similar to those produced by warmer water ice clouds over the surface (Pearl et al., 2001). We have modeled both spatially mixed frosts and intimately mixed particles using the Toon et al. (1977) distribution, as well as clouds, when the overlying atmosphere is warmer. Fig. 3b shows our water ice cloud model, which uses a narrow distribution with an effective radius of 2 lm, and allows optical depths at 12 lm of up to 0.8. The visible optical depth is about twice the 12-lm value, so to be consistent with the clear atmosphere from MOLA, the optical depth of any cloud should be less than a few tenths. The cloud model is a simple isothermal layer set to a middle atmospheric temperature, but including scattering and absorption, using the discrete ordinates model of Stamnes et al. (1988). Sample brightness temperature models of pure CO2, CO2 with water ice, CO2 with dust, and CO2 with both water ice and dust are shown in Fig. 4, to illustrate the spectral effects of the various materials. As shown in Hansen (1999), dust mixtures move the centroid of the 20–50 lm low-emissivity feature to smaller wavenumbers (longer wavelength), while water mixtures move it to longer wavenumbers (shorter wavelengths). Water ice imparts smooth spectral shapes to the CO2 spectrum, while dust provides varied, angular shapes. A key property of water ice is its ability to move the spectral slope at >500 cm 1 (<20 lm) to longer wavenumbers (shorter wavelengths). This effect is more subtle than the effects of water ice above 30 lm (below 300 cm 1) but the TES signal/noise is much better at the shorter wavelength, where this effect is often clearly evident when comparing TES spectra with pure or dusty CO2 only.
3. Results 3.1. Modeling of individual spectra and mapping of composition and grain sizes
range >6 lm. For this analysis, I am using the optical constants for martian dust given by Hansen (2003), using an appropriate size distribution (Markiewicz et al., 1999; Tomasko et al., 1999). These improved optical properties fit aerosol spectra better, and also provide for better 20–50 lm fits to observed TES spectra. There exist good optical properties for CO2 ice except in the strong bands, where the data are more uncertain (Hansen, 1997a, 1997b, 2005), but this is of little importance since these regions will always be either very high emissivity or completely obscured by atmospheric CO2 absorption. For water ice, there is more uncertainty, since the spectral structure is not opaque enough in the infrared to be measured accurately using only thin films. I have compiled optical constants which I believe to be accurate for hexagonal ice at 150 K (Hansen, 1996, 1999). The surface models are calculated using the two-stream model described by Wiscombe and Warren (1980), using emission zenith angles of zero. The single-scattering quantities for the materials is computed using Mie code (spheres) (Wiscombe, 1980). The models are all convolved with accurate instrument functions for the TES
The TES spectra are now individually fitted to surface models to map the physical properties and composition across the surface. This is done by first correcting for the atmospheric emission, which is calculated using the models described in the next section. The values at wavelengths where the atmosphere is partially transparent are replaced with an estimate of the surface emission. The regions where the atmosphere is opaque are replaced by a straight-line extrapolation in brightness temperature and are weakly weighted in the ensuing fits. Each atmosphere-removed spectrum is fitted to a spatial mix of another material (water snow, or blackbody) at a different temperature and a ternary mixture of CO2 ice, water ice and dust. If the atmosphere is >1 K warmer than the model surface temperature, a possible cloud is introduced. The minimization used is a fast downhill method, so the initial guess is very important for finding the best fits. Once the sequence is started, each fit is initialized with a median of 11 previous fits, on the assumption that the properties do not change too quickly. The results are shown in Fig. 5.
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Fig. 8. Elements used in the calculation of the infrared radiative balance. (a) The TES infrared radiance spectrum continued to 0 wavenumbers (short dashed line) and filled in the 15-lm CO2 atmospheric band (long dashed line). (b) Atmospheric terms of radiance (black) and transmission (gray). (c) Calculation of surface radiance into all emission angles. (d) Final flux calculations integrated over all angles as described in the legend.
Fig. 9. Radiative balance values as a function of distance. The atmospheric terms are all less than 4 W m 2 except near the fringes. The surface to space and net surface upward are nearly equal because the surface to atmosphere and atmosphere to surface terms nearly cancel out. The surface + atmosphere to space is comparable to, if a little smaller than previous determinations.
3.2. Overview of model results Fig. 5a shows a detailed overview of the models fitting the data from revolution 214. The top three panels display the model fits of a ternary mixture model with CO2 ice dust and water. The fourth panel represents infrared spectral properties, by showing the difference between the 18-lm, and the 25–30-lm brightness temperatures (see Fig. 2). Fine-grained, clean CO2 has a larger temperature difference (‘‘colder’’) than coarse-grained or dusty CO2. The bottom panel shows the least squares error of fit of the model to the spectra. The x-axis is an approximate distance in km of the orbital track over the surface. The corresponding latitudes are marked in the middle of the lower panel.
The CO2 ice grain size varies in ways mostly not related to the occurrence of cold spots. Only in one instance (around 1000 km) is there a reduction of CO2 grain size coincident with a cold spot. In general, the CO2 ice grain size is largest near the center of the polar deposits and at the very edge (1–5 mm), and smaller in other regions (500 lm). The dust amounts are generally large (0.5–1%) except in the regions of cold spots, where the amounts are around 0.01%. The water ice amounts are weakly correlated with the cold spots (less in cold spot locations), but the average values are very low in the central polar cap and approaching 0.1% on the periphery. In Fig. 5b, the polar cap fringe properties are displayed as a function of latitude. The night fringe does not reach the edge of the cap and only sees predominantly CO2 covered areas (80–100%), and whose uncovered areas are colder than the daytime fringe and covered with water frost. The daytime fringe goes to the edge of the cap at 49°N, with a steep decline in CO2 coverage (where it goes from 80% to 20% in 1.5° or about 90 km) at about 52°N. The uncovered patches in this fringe model well as blackbodies at 158–163 K. The water ice cloud 12-lm optical depth is 0.2–0.4 on the night fringe. Its calculation is complicated by the fact that the surface water ice frost and the cloud have a similar spectral properties. The daytime fringe cloud is of lower optical depth (0.05–0.1) but is more precisely determined than the night fringe cloud. Neither cloud appears to continue poleward of 65°N. Beyond this point the atmosphere is colder than the surface, but no 12-lm absorption feature is seen as would be expected. This annular pattern is consistent with the findings of Pearl et al. (2001). Fig. 6 shows how the measured CO2 temperature is consistent with the altitude, being lowest at the 1 km altitude of the top of the polar cap and fringes and highest in the low polar plains at 4 to 5 km. The lower panel shows the ratio of the measured dust/water content. This is not well determined where the water content is very small but otherwise shows a range of 5–10. The vertical, dashed, gray lines in Fig. 5a are eight representative locations whose spectra and fits are plotted in Fig. 7a–h. Included are three
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Area 1
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Fig. 10. Close-up look at the model data near two cold spots. Note how the dust amount signature mimics the brightness temperature difference very closely in both cases, while there is little changes in grain size of the CO2 ice in these locations.
cold spots (7c, 7d, 7g), background regions (7b, 7e, 7f) and fringe regions (7a, 7h). 3.3. Infrared radiative heat balance The infrared radiation balance can be computed if one can estimate the complete emission spectrum over the important wavenumbers for surfaces at 150 K (30–1100 cm 1) and over all emission angles. If in addition, the atmosphere is modeled similarly, the internal terms of atmosphere to surface, etc. can also be calculated. I use a clear atmosphere model, which is a general random band model (Crisp et al., 1986) that has calculated layer transmissions for CO2 for 13 pressures from 0.001 to 10 mbar, 19 temperatures from 110 to 296 K, and 13 angles. The model is calculated using 2.5-cm 1 wide bands over the wavenumber range 450–1500 cm 1 and the latest HITRAN line parameters. It is used for atmospheric temperature inversions and, by making use of the high angle calculations, for the radiative balance model. The steps needed to calculate the terms for an example spectrum are illustrated in Fig. 8, including longwave continuation, atmosphere modeling, angular emissivity estimates, and the calculation of atmospheric radiation terms. The angular behavior of the surface deposits is a function of the nadir emissivity, and low nadir emissivities decrease at high angles using the behavior of surface models as a guide. The flux results in W m 2 are illustrated in Fig. 9. The average level of surface + atmosphere to space is similar to, but a little lower than those of previous workers using Viking data (Paige and Ingersoll, 1985; Forget and Pollack, 1996). The polar short-wave (solar) heat balance can also be calculated, but it is a much more complicated procedure, requiring model bidirectional reflectance models of the surface and clouds. It applies only to the last third of the distance considered here (2700 km to the end) and has not been completed at this time.
4. Cold spot properties and origin Cold spots are transient regions of low 20–50-lm emissivity that occur regularly (Cornwall and Titus, 2009; Titus et al., 2001) in the north seasonal polar cap of Mars, and have some impact on the average radiative balance of the polar caps. They arise from the optical properties of solid CO2 (low emissivity for small grain sizes) and occur almost always (at least in the north) at locations with steep slopes. The accepted explanation is fine-grained CO2 snow deposited as a result of atmospheric dynamics. The emissivity of cold spots has been found to increase with time with a time constant of 5–10 days (Cornwall and Titus, 2009). This change has been attributed to the grain coarsening of fine-grained deposits through ‘‘continued condensation’’ or sintering processes (Eluszkiewicz, 1993). I am proposing an additional, and possibly dominant, process that drives this evolution, namely the migration of dust condensation nuclei from the interior of grains (optically hidden) to the exterior (optically active). As mentioned before, the modeling results show that the CO2 grain radius averages about 1 mm (200 lm–1 cm) and does not change much in the locations of cold spots. The dust mass ratio, however, tracks the cold spots indicated by large 18–25-lm brightness temperatures very well. Two areas are shown in detail in Fig. 10: Area 1 has grain radii across the spot between 600 and 900 lm, while dust varies between 0.01 and 0.1 wt.%. Area 2 has grain radii across the spot of 1.5–2 mm, while the dust concentration varies between 0.008 and 0.05 wt.%. TES spectra from the two areas are shown in Fig. 11; each spectrum (solid lines) is an average of 5–10 individual spectra. In both cases, the ‘‘background’’ spectra are from areas on either side of the cold spot, while the spectrum marked ‘‘center’’ has the lowest 25-lm brightness temperatures. Dusty ice models are fit to the spectra (dashed lines). For comparison, a large-grained model (r = 10 mm with
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Fig. 11. Average TES spectra from these two cold spots from the center, edges and background regions (solid lines). The models that fit these spectra are shown as dashed lines. In both plots a large grained pure CO2 model with the same 25-lm brightness temperature of the background is shown as a dash-dot line, and looks much different from the measured spectra.
0.002 wt.% dust) having a similar 18-lm to 25-lm brightness temperature ratio to the measured background spectra is shown in a dot-dashed line; the TES spectra are clearly more consistent with dustier, finer-grained CO2. These observations suggest a different explanation for the evolution of cold spots. Assuming that the final state of ‘‘decayed’’ cold spots is similar to the immediately surrounding polar cap, the evolution is towards dustier CO2 snow of similar grain size, not towards larger grains. This could be explained by optically ‘‘hiding’’ the dust inside a snow particle initially, with diffusion or other processes eventually causing the migration of these dust grains to CO2 grain boundaries, thus making them optically active. The hidden dust presumably starts as condensation nuclei for snow particles. This is consistent with the increased activity of cold spots when more dust is moved into the north polar regions (Forget and Pollack, 1996; Cornwall and Titus, 2009). How effectively can dust grains be optically hidden in CO2 grains? This was tested by running Mie scattering code for layered spherical objects, using a dust inner layer with an appropriate distribution of sizes (between 0.2 and 9.5 lm), and total radii of between 10 and 100 lm. The results in Fig. 12 are shown as emissivity of a semi-infinite layer; The smallest sizes are modified in the most transparent regions, while sizes larger than 50 lm look much like solid CO2. Microphysical models indicate that atmospheric CO2 particles are 50–100 lm in size when they fall out as surface snow (Forget et al., 1998). As such, they will not show much evidence of their dust core, and may still grow by about a
Fig. 12. Emissivity models of layers of pure CO2 ice and a 1–2 lm dust core surrounded by various amounts of CO2 ice. The top panel shows the smallest grain sizes (10–20 lm) where the dust core raises the emissivity significantly. The bottom two panels show 50 and 100-lm particles where the inclusion of a dust core makes little difference in the spectrum.
factor of 10 (to 1 mm), as their nuclei are liberated. In fact, the grain growth rate must be quite fast, since there are only two or three cold spots that have smaller grain sizes comparable to original snow, while the rest have grown to mm sizes like the background but still show less dust. The decay rates of the cold spots measured by Cornwall and Titus (2009) is primarily the rate of dust removal from the snow grains (5–10 days).
5. Conclusions We have mapped the grain size and contamination by dust and water in the seasonal Mars North polar cap in mid-winter using observations of MGS TES. This is the first time such a quantitative analysis using thermal data comparable to modeling of solar reflected spectra has been done. Most of the reflectance spectral modeling has been of the south polar cap and cannot be done during the polar night. Seasonal CO2 is predominately large-grained (0.5–5.0 mm radius) and dust-rich (0.1–1.0 wt.%) during the polar night. This compares with the results in Giuranna et al. (2007) of 3–5 mm grain size and <0.2 wt.% dust from the north pole in a later season (LS = 40°). In spring, deposits often become cleaner and decrease in grain size, and therefore become brighter in the visible (Hansen, 1999). Low-emissivity regions in this observation are found mostly near large topographic slopes such as scarps, ridges, and craters, and mostly on equator-facing slopes. They likely originate from low-altitude, local, and short-lived (but perhaps sustained) atmospheric condensation (Forget et al., 1998). In the northern seasonal cap, water snow (seemingly diurnal) appears to cover significant areas (up to 30%) in the first several hundred
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kilometers of the southern edge of the cap on the night side. The non-ice areas of the daytime fringe model well as blackbodies. Low optical depth clouds are detected over both fringes up to about 60–65°N. Observations indicate that the effective CO2 grain size varies smoothly over the Mars seasonal polar cap, while effective dust content varies sharply, and is mostly responsible for the observed cold spots. Based on this evidence, we propose that the evolution of low emissivity cold spots over time to higher emissivity is caused by the optical liberation of dust nuclei, rather than by grain coarsening. We hope to study more data in the future, and expect similar results for the mid-winter north pole at least. Many of the individual spectra are quite noisy and the fits may be non-unique (see Fig. 7h), but averages point to spectral models similar to the ones I have used (say in background spectra such as in Fig. 7b–f), rather than for example, slab ice. The south pole seasonal deposits are less dusty on average and may have very different behavior.
6. Future work The dust optical model needs to be improved in the 20–50 lm range, so that mixture models can fit observed spectra better. This discrepancy is obvious when modeling average spectra that have much better signal-to-noise than the individual spectra displayed in Fig. 7 (somewhat visible in the averages in Fig. 11). As mentioned before the short-wave heat balance has only been investigated briefly, and we envision a Monte-Carlo problem to account for cloud scattering and surface scattering. Acknowledgments This work was mostly accomplished with the support of the NASA Mars Data Analysis Program. The MOLA base map for Fig. 1 was kindly provided by Harvey Greenberg at the University of Washington. References Briggs, G.A., 1974. The nature of the residual martian polar caps. Icarus 23, 167–191. Calvin, W.M., Martin, T.Z., 1994. Spatial variability in the seasonal south polar cap of Mars. J. Geophys. Res. 99, 21143–21152. Christensen, P.R. et al., 1992. Thermal emission spectrometer experiment: Mars Observer mission. J. Geophys. Res. 97, 7719–7734. Christensen, P.R. et al., 2001. Mars Global Surveyor Thermal Emission Spectrometer experiment: Investigation description and surface science results. J. Geophys. Res. 106, 23823–23871. Clancy, R.T., Lee, S.W., Gladstone, G.R., McMillan, W.W., Roush, T.L., 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. Cornwall, C., Titus, T.N., 2009. Spatial and temporal distributions of martian north polar cold spots before, during, and after the global dust storm of 2001. J. Geophys. Res. 114, E02003. http://dx.doi.org/10.1029/2008JE003243. Crisp, D., Fels, S.B., Schwarzkopf, M.D., 1986. Approximate methods for finding CO2 15-lm band transmission in planetary atmospheres. J. Geophys. Res. 91, 11851–11866. Cross, C.A., 1971. The heat balance of the martian polar caps. Icarus 15, 110–114. Davies, D.W., Farmer, C.B., LaPorte, D.D., 1977. Behavior of volatiles in Mars’ polar areas: A model incorporating new experimental data. J. Geophys. Res. 82, 3815– 3822. Douté, S. et al., 2007. South pole of Mars: Nature and composition of the icy terrains from Mars Express OMEGA observations. Planet. Space Sci. 55, 113–133. http:// dx.doi.org/10.1016/j.pss.2006.05.035. Douté, S., Schmidt, D., Schmitt, B., Vincendon, M., Langevin, Y., Gondet, B., 2009. Physical State of the ‘‘Bright’’ South Seasonal Polar Cap from OMEGA Observations (abstract). Third International Workshop on Mars Polar Energy Balance and the CO2 Cycle (Seattle, Washington), Abstract #7033. Eluszkiewicz, J., 1993. On the microphysical state of the martian seasonal caps. Icarus 103, 43–48. Forget, F., Pollack, J.B., 1996. Thermal infrared observations of the condensing martian polar caps: CO2 ice temperatures and radiative budget. J. Geophys. Res. 101, 16865–16879.
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