Ultraviolet dust aerosol properties as observed by MARCI

Icarus 208 (2010) 143–155

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Ultraviolet dust aerosol properties as observed by MARCI Michael J. Wolff a,*, R. Todd Clancy a, Jay D. Goguen b, Michael C. Malin c, Bruce A. Cantor c a

Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301, USA Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA c Malin Space Science Systems, P.O. Box 910149, San Diego, CA 92191, USA b

a r t i c l e

i n f o

Article history: Received 20 August 2009 Revised 11 January 2010 Accepted 13 January 2010 Available online 25 January 2010 Keywords: Mars, Atmosphere Ultraviolet observations Radiative transfer

a b s t r a c t Observations by the Mars Color Imager (MARCI) on board the Mars Reconnaissance Orbiter (MRO) in two ultraviolet (UV, Bands 6 and 7; 258 nm, and 320 nm, respectively) and one visible (Band 1, 436 nm) channels of the 2007 planet encircling dust storm are combined with those made by the two Mars Exploration Rovers (MERs) to better characterize the single scattering albedo ðx0 Þ of martian dust aerosols. Exploiting the low contrast of the surface in the UV (and blue) as well as the reduced importance of surface reflectance under very dusty conditions, we utilize the sampling of photometric angles by the MARCI cross-track geometry to synthesize an analog of the classical Emergence Phase Function (EPF). This so-called ‘‘pseudo-EPF”, used in conjunction with the ‘‘ground-truth” measurements provided by the MERs, is able to effectively isolate the effects of the dust x0 . The motivation for this approach is the elimination of a significant portion of the type of uncertainty involved in many previous radiative transfer analyses. Furthermore, we produce a self-consistent set of complex refractive indices ðm ¼ n þ ikÞ through our use of an explicit microphysical representation of the aerosol scattering properties. Because of uncertainty in the exact size of the dust particles during the epoch of the observations, we consider two effective particle radii ðreff Þ to cover the range anticipated from the literature: 1.6 and 1.8 lm. The resulting set of model–data comparisons, x0 , and m are presented along with an assessment of potential sources of error and uncertainty. Analysis of the Band 1 results is limited to x0 as a ‘‘proof-of-concept” for our approach through a comparison to contemporaneous CRISM EPF results at 440 nm. The derived x0 are: assuming r eff ¼ 1:6 lm — 0:619—0:626; 0:648, and 0.765, for Bands 6, 7, and 1, respectively; for reff ¼ 1:8 lm — 0:625—0:635; 0:653; 0:769, for the same band order. For either r eff case, the total estimated error is 0.022, 0.019, and 0.010, again for Bands 6, 7, and 1. We briefly discuss our retrievals, including the asymmetry parameter (g) associated with our model phase functions, within the context of previous efforts, with an emphasis on the improved precision of our results compared to those in the literature. We also suggest several applications of our results, including an extension of the dust climatological record using MARCI Band 7 pseudo-EPFs outside of 2007 global dust event. Initial work on this particular application using a sample of 135 pseudo-EPFs near the MERs suggests that optical depth retrievals with a precision in the range 0.2–0.4 may be possible under moderate loading conditions (i.e., s < 1.5). Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction The ubiquitous nature of dust aerosols in the martian atmosphere can represent a significant challenge to many observational and theoretical studies. In the former case, these particles alter the intrinsic signature of the targeted reflecting surface as well as that of other atmospheric constituents of potential interest. In the latter case, the fundamental role of dust in the absorption of solar radiation makes its radiative properties an important component in robust simulations of martian atmospheric dynamics. As a result, the literature contains a plethora of efforts to characterize both radia* Corresponding author. E-mail address: [email protected] (M.J. Wolff). 0019-1035/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2010.01.010

tive and microphysical properties of dust particles. Recent reviews by Dlugach et al. (2003), Korablev et al. (2005) and Smith (2008) comprise a reasonably comprehensive overview of said characterization efforts. More recent additions to the literature include the analyses of observations of very dusty conditions by Määttänen et al. (2009) and Wolff et al. (2009) for the spectral range 440–4000 nm. Inspection of this body of work reveals that our knowledge of dust properties in the visible/near-infrared and thermal infrared (IR) has advanced appreciably in recent years. The two UV instruments currently orbiting Mars provide a unique opportunity to advance our knowledge of the dust properties in the UV. Dust studies in the UV may be motivated specifically by several considerations, some of which are common to those for other spectral ranges. The absorption of the solar UV flux by dust aerosols can

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alter the incident radiation field in a way that impacts both total solar energy input and the photochemical balance of the martian atmosphere. At a more utilitarian level, improved aerosol properties allow for a more accurate characterization and isolation of surface reflectance properties as well as other atmospheric parameters (e.g., ozone column, water ice optical depths). Finally, the UV offers a unique opportunity to study the constituents of the dust itself via the UV sensitivity to Fe–O charge transfer features even for trace amounts (cf. Cloutis et al., 2008). Focused efforts to study UV dust properties began essentially with the Mariner 9 mission and the Ultraviolet Spectrometer (UVS) experiment (e.g., Barth et al., 1972). The combination of limb viewing observations as well as the global dust event of 1971 stimulated several investigations, including those involving non-spherical particle effects (Ajello and Hord, 1973; Ajello et al., 1973, 1976; Pang et al., 1976; Chy´lek and Grams, 1978). The next 30 years contains scattered efforts using data from a variety of sources such as the Orbiting Astronomical Observatory 2 (Caldwell, 1977), Mars-5 (Krasnopolskii et al., 1980), and the Hubble Space Telescope (e.g., James et al., 1994; Clancy et al., 1996; Goguen et al., 2003). A more comprehensive summary may be found in the review articles mentioned previously. With the arrival of the Mars Express orbiter and the Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) instrument (Bertaux et al., 2006) in late 2003, both the need and opportunity to further characterize UV dust properties such as the single scattering albedo ðx0 Þ and the single scattering phase function ðpðhÞÞ would seem to have presented itself. Although fundamental work on particle sizes and volume mixing ratios above 20 km has emerged from analyses of SPICAM UV data (i.e., Montmessin et al., 2006; Rannou et al., 2006), direct investigation of the x0 and pðhÞ, particularly in the lower two scale-heights, where most of the dust mass is typically contained, appears to be limited currently to the work of Mateshvili et al. (2007). To a large degree, the limited progress in the area of UV dust properties stems from the challenging nature of such retrievals. The basic problem requires the simultaneous treatment of several aerosol parameters (i.e., x0 ; pðhÞ, mixing ratio, column optical depth), as well as the boundary condition(s) associated with surface reflectance. Ideally, one should identify an observational circumstance that allows for the elimination or minimization of the effects contributed by the variables not being ‘‘retrieved”. As discussed (briefly) by Wolff et al. (2009, and references therein), notable previous efforts along this line for the optical/near-IR tend to appeal to a special geometry (e.g., an emission phase function sequence (EPF) or an upward viewing from the surface), a high dust loading, or a combination of the two. Mateshvili et al. (2007) employ the first approach and analyze two local dust storms observed by SPICAM in 2005. Despite the improved insight into the nature of the UV x0 and scattering properties from the Mateshvili et al. (2007) analysis, the limited number of observations and the simplifying modeling assumptions make it difficult to generalize the derived properties to the more ubiquitous ‘‘diffuse dust” component. That is to say, a local dust storm might be expected to contain particles with an effective particle radius that is very different from the 1.4–1.5 lm size typically associated with diffuse dust. In an analogous situation for the visible–NIR, Wolff et al. (2009, hereafter W09) address these issues using EPF observations located near the locations of the two Mars Exploration Rovers (MERs) during the planet encircling dust event of 2007. Such a dataset possesses several desirable characteristics: the use of multiple locations and epochs, an observational geometry and a set of dust loading conditions that reduce the importance of the necessary radiative transfer input variables such as the surface reflectance, and ‘‘ground-truth” optical depth measurements (i.e., Section 2.3) . As a result, W09 are

able to retrieve x0 values present during the 2007 dust event and to construct a self-consistent microphysical model that allows for an extension of the derived dust properties to other conditions such a diffuse dust loading. Unfortunately, the same set of observations do not exist in the UV. Compact Reconnaissance Imaging Spectrometer (CRISM, on board the Mars Reconnaissance Orbiter [MRO]) observations do not contain reliable data short-ward of 440 nm. Furthermore, it does not appear that SPICAM obtained any EPF sequences during the 2007 global event. This latter deficit is likely due to both the complexity of the SPICAM EPF (i.e., the entire spacecraft must slew to sample the desired geometry) and the long lead time present in the operations planning cycle (i.e., several months, which is the scale of the highly elevated dust loading conditions in 2007, Personal Communication, SPICAM Team, 2007). However, one possibility does exist: the use of the cross-track observation geometry present in the MRO/Mars Color Imager (MARCI; e.g., Malin et al., 2008) UV dataset. Exploiting two aspects of the surface in the UV, the low reflectivity of the surface relative to that of the atmosphere under large optical depth conditions and the modest amount of observed surface variability (McCord et al., 1971; Bell and Ansty, 2007; Perrier et al., 2006; Malin et al., 2008), one can construct an EPF-like data product that possesses the same characteristics as that of a CRISM EPF. Specifically, such a MARCI ‘‘pseudo-EPF” seems to manifest the distinctly different phase angle behavior of the reflectivity from a single surface ‘‘unit” and from an atmospheric modulation. Consequently, MARCI observations of the 2007 global dust event offer an opportunity to improve one’s understanding of UV dust aerosol properties. We begin with an overview of the observations to be analyzed, including a general description of the MARCI ‘‘pseudo-EPF”. We limit our description to that necessary for the subsequent analysis, providing citations for the reader interested in greater detail. Because we leverage the basic methodology employed by W09, Section 3 contains an abbreviated description of the algorithms and methods. However, we do provide a discussion of the more important input parameters and adopted constraints. Section 4 presents the retrieved x0 values along with their associated complex refractive indices ðm ¼ n þ ikÞ. Also included is a discussion of the random and systematic errors. Finally, a comparison of our results to those previously derived may be found in Section 5. We also present several potential applications which are enabled by our results, including an extension of the dust climatological record using MARCI observations. 2. Observations Our analyses focus on a set of MARCI images taken during the planet encircling dust event of 2007. To minimize the influence of surface properties while using the column-integrated optical depths obtained by MER/Pancam, we require that the image contain a MER location within 10° of longitude of the nadir for a sol (martian day) with a measured optical depth P3.0. The size of the maximum allowable distance is basically that used by W09, although nature of MARCI dataset provides more the twice the number of samples than that of the CRISM EPF sequences. We list the resulting dataset of 37 observations in Tables 1 and 2; 17 for Spirit (MER-A) and 20 for Opportunity (MER-B). Although our primary focus is the UV regime, we include a visible band (Band 1) to allow for a ‘‘proof-of-concept” of our approach through a direct comparison to near-simultaneous CRISM results. 2.1. MARCI data The MARCI instrument is a wide-angle, 7-color ‘‘push-frame” imager whose overall components, capabilities, and performance

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M.J. Wolff et al. / Icarus 208 (2010) 143–155 Table 1 MARCI observations with nadir point near spirit.

a b c

Observation namea

UTC dateb

LS (°)

MER-A sol

s(880 nm)c

P09_004507_2758_MU_00N198W P09_004520_2764_MU_00N193W P09_004533_2770_MU_00N188W P09_004546_2777_MU_00N183W P09_004586_2796_MU_00N194W P09_004625_2815_MU_00N179W P09_004652_2828_MU_00N196W P09_004665_2834_MU_00N191W P09_004678_2840_MU_00N186W P09_004691_2847_MU_00N181W P09_004731_2866_MU_00N193W P10_004744_2872_MU_00N188W P10_004770_2885_MU_00N178W P10_004823_2910_MU_00N185W P10_004836_2916_MU_00N180W P10_004863_2929_MU_00N197W P10_004876_2935_MU_00N192W

2007/07/13 2007/07/14 2007/07/15 2007/07/16 2007/07/19 2007/07/22 2007/07/24 2007/07/25 2007/07/26 2007/07/27 2007/07/31 2007/08/01 2007/08/03 2007/08/07 2007/08/08 2007/08/10 2007/08/11

275.7 276.4 277.0 277.6 279.6 281.5 282.8 283.4 284.0 284.6 286.6 287.2 288.4 291.0 291.6 292.9 293.5

1253 1254 1255 1256 1259 1262 1264 1265 1266 1267 1270 1271 1273 1277 1278 1280 1281

3.27 3.33 3.29 3.65 3.71 3.40 3.52 4.15 3.94 3.74 3.46 3.32 3.23 3.27 3.35 3.31 3.06

UV band filename. The visible band filename replaces ‘‘MU” with ‘‘MA” for the listed images. Year/month/day of the observation. A conservative estimate of the uncertainty for an optical depth 3 is rðrmsÞ K 0:09. See text (Section 2).

Table 2 MARCI observations with nadir point near opportunity.

a b c

Observation name

UTC datea

LS (°)

MER-B sol

s(880 nm)b

P09_004408_2709_MU_00N015W P09_004421_2716_MU_00N010W P09_004434_2722_MU_00N005W P09_004447_2728_MU_00N000W P09_004474_2742_MU_00N017W P09_004487_2748_MU_00N012W P09_004500_2754_MU_00N007W P09_004513_2761_MU_00N002W P09_004645_2825_MU_00N005W P09_004685_2844_MU_00N017W P09_004698_2850_MU_00N012W P09_004711_2856_MU_00N007W P09_004724_2863_MU_00N002W P09_004725_2863_MU_00N029W P10_004790_2894_MU_00N004W P10_004803_2900_MU_00N359W P10_004830_2913_MU_00N016W P10_004843_2919_MU_00N011W P10_004856_2925_MU_00N006W P10_004869_2932_MU_00N001W

2007/07/05 2007/07/06 2007/07/07 2007/07/08 2007/07/11 2007/07/12 2007/07/13 2007/07/14 2007/07/24 2007/07/27 2007/07/28 2007/07/29 2007/07/30 2007/07/30 2007/08/04 2007/08/05 2007/08/07 2007/08/08 2007/08/09 2007/08/10

270.9 271.5 272.2 272.8 274.1 274.8 275.4 276.0 282.4 284.4 285.0 285.6 286.2 286.3 289.4 290.0 291.3 291.9 292.5 293.1

1225 1226 1227 1228 1230 1231 1232 1233 1243 1246 1247 1248 1249 1249 1254 1255 1257 1258 1259 1260

4.05 3.61 2.96 2.84 2.80 2.77 3.21 3.80 4.02 4.26 4.53 4.60 4.60 4.60 3.68 3.67 3.45 3.39 3.30 3.21

UV band filename. The visible band filename replaces ‘‘MU” with ‘‘MA” for the listed images. Year/month/day of the observation. A conservative estimate of the uncertainty for an optical depth 3 is rðrmsÞ K 0:09. See text (Section 2).

(including calibration methodology) is described in great detail by Malin et al. (2001, 2008) and Bell et al. (2009). As such, we recount briefly only the details of immediate concern to the retrievals presented in this paper. The effective wavelengths of MARCI Bands 1, 6, and 7 are 436 nm, 258 nm, and 320 nm, respectively, with Full-Width HalfMaximum (FWHM) values of 32 nm, 30 nm, and 24 nm (Bell et al., 2009). However, we are more interested in the bandpass centroids that include the effects of the solar irradiance. Although the numbers do not change dramatically, we adopt the solar-weighted centroids as more representative of that sampled by our observations: 436 nm, 263 nm, and 321 nm for Bands 1, 6, and 7. The radiometric precision (i.e., pixel-to-pixel scatter due flat field issues, etc.) of the MARCI observations is of the order 2–3% for the UV bands and 1% for Band 1. The radiometric accuracy is less well-known a priori, at least for band 6, due to currently unresolved issues with the calibration observations provided by the Hubble Space Telescope (HST) in July 2007 (cf. Bell et al.,

2009). This time period is post-launch for MRO and, as described by Bell et al. (2009) in Section 6.4.1, allowed for simultaneous observations by HST and MARCI. For Band 1, a comparison between pre-launch and HST-based radiometric coefficients shows an agreement to within 2%. Because of problems with the prelaunch radiometric tests for Bands 6 and 7, a similar comparison cannot be made, i.e., the HST observations provide the adopted UV radiometric coefficients. As such, the photometric uncertainty in the UV HST data is the primary contributor of the uncertainty in the MARCI UV accuracy. For Band 7, the estimate of 8% by Bell et al. (2009) remains a reasonably conservative estimate given what is currently known about the final calibration of the F336W Wide Field Planetary Camera 2 (WFPC2) images (Personal Communication, Pey Lian Lim, Space Telescope Science Institute, 2009; see also Bell et al., 2009). A similar degree of confidence is not (presently) available for the Band 6 calibration, even given the large estimated uncertainty of 12–15% (associated with WFPC2 F255W images). However, an independent assessment is possible by

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combining the 2007 HST observations with those obtained during the global dust event in 2001. This latter set of data includes both WFPC2 imaging as well as UV spectroscopy. The resulting analyses, detailed in Appendix A, provides a 15% increase in the Band 6 radiances. The new calibration coefficient for Band 6 is 0.0101 (DN/ms)/(W/m2/lm/sr) under the assumption that the Band 6 integrated solar irradiance at 1 AU (pF(1 AU)) is 132.1 W/m2/lm. The effective accuracy of the resulting radiance factor (i.e., I/F where I is the scene radiance and F is the incident solar radiance) is conservatively estimated to be [10% (see Appendix A). A final point to consider for the MARCI data is the sensitivity of the camera to the polarization state of the incident light. That is to say, the general nature of reflection and transmission at the boundary of a lens will produce a net polarization in the transmitted light. For a wide-angle camera, the changing direction of the surface normal on the lens surface will increase this effect as one moves from nadir (i.e., the optical axis) towards the limb. To address this issue, we re-examine the ground calibration data described by Bell et al. (2009) to derive the necessary Mueller matrix elements for the MARCI UV. The details of this analysis are found in Appendix B. Combining the matrix elements with an examination of the potential distribution of incident polarization states for MARCI Bands 6 and 7 (via a radiative transfer analyses taking into account the full Stokes vector; see Appendix B), we find that one might expect at most a 3% effect on the observed radiance. More typically, this effect will be below 1%. As a result, no polarization correction is necessary and the use of scalar radiative transfer will be adequate. 2.2. Pseudo-EPF The cross-track viewing geometry of MARCI provides a sampling of photometric angles that is very similar to the classical Emission Phase Function (EPF) observation, a schematic of which may be found in either Clancy and Lee (1991, Fig. 1) or Murchie et al. (2007, Fig. 44). One of the primary requirements of the classical EPF concept is that each of the observations view essentially the same surface element. As a result, the degree to which the instrument field-of-view can be controlled to achieve this requirement dictates the level of uncertainty or error that is introduced into an EPF analysis. That is to say, the utility of the data is a function of the degree of surface homogeneity sampled by the observational footprints. Thus, the use of the MARCI data to construct a ‘‘pseudo-EPF” – using the change of photometric angles in the cross-track direction – requires that the surface of Mars be fairly bland in the UV such that each surface element is approximately the same. More specifically, we require that the variation of surface reflectance provides only small perturbations relative to the net radiance contributed by the atmosphere. Ground-based and HST spectroscopic observations in the near-UV suggest that the spatial variations in the MARCI bands are likely to be much more muted than those in the visible (e.g., McCord et al., 1971; Bell et al., 1992; Bell and Ansty, 2007). Examination of the spectra in the cited works indicates spatial variability at or below the 10% level. Of equal importance for the pseudo-EPF is the horizontal homogeneity (or lack thereof) of the atmosphere. In other words, on average, the cross-track geometry pathlengths need to sample similar aerosol loading characteristics. Fig. 1 provides examples of the MARCI pseudo-EPF in Bands 1 and 7 along with contemporaneous CRISM EPF data at 440 nm. The observations are near the Spirit (MER-A) rover on August 3, 2007 and the Pancam 880 nm optical depth is 3.23. Small perturbations suggestive of either surface or atmospheric inhomogeneities are present in both MARCI bands; near emergence angles 40° and 20° for Bands 1 and 7, respectively. Such deviations, which can occur in classical EPFs as well, typically have very little impact on basic retrievals such as single scattering

Fig. 1. MARCI Pseudo-EPFs for Bands 1 and 7 compared with a co-located CRISM EPF. The offset between CRISM and MARCI Band 1 for the larger off-nadir angles reflects the difference in the phase angles associated with these points. In addition, the extent of the pseudo-EPF is several hundred kilometers while that of the CRISM is closer to 1–2 km. Nevertheless, the general shape of the pseudo-EPFs appears quite similar to that of the classical EPF. Small perturbations due to spatial inhomogeneities (dust loading, surface variability) can be seen for both Bands 1 and 7. The displayed observations were obtained on August 3, 2007 near the Spirit rover. The presence of ‘‘negative” emergence angles is a plotting convention. For MARCI, negative angles indicate points on the west side of the image swath. For CRISM, negative angles indicate the ingress portion of the EPF sequence. The error bars for MARCI and CRISM are 4% and 5%, respectively. However, in the case of Band 7, this amplitude is more representative of the precision rather than the absolute accuracy.

albedo or optical depth because the ‘‘best-fit” is applied to the entire (pseudo-)EPF (Wolff et al., 2009). Despite the qualitative evidence that the pseudo-EPFs appear to behave in the needed fashion, it is important to include a more quantitative metric of their validity. This is precisely the motivation for addition of the Band 1 data to our sample of UV observations. By comparing the derived x0 from Band 1 with that of the CRISM 440 nm channel (W09), we will have a direct measure of the equivalence of the pseudo-EPF and the classical EPF, at least under very dusty conditions and in the blue and UV channels. 2.3. Pancam data The Pancam instrument on board the two MER spacecraft is providing an essentially continuous record of column-integrated optical depths at two locations on the martian surface beginning in early 2004. At present, these derived data are available via Planetary Data System (PDS) for observations through the middle of 2008 (http://pds-geosciences.wustl.edu/missions/mer/geo_mer_ datasets.htm). Although some basic discussion of this retrieval methodology may be found on the PDS, the definitive reference remains that of Lemmon et al. (2004). For continuity with the W09 work, as well as concern regarding calibration in the Pancam L8 filter (440 nm), we restrict ourselves to the R8 filter (880 nm) data. As a caveat to the reader, we do also include calibration improvements that have not yet been propagated to the PDS (Mark Lemmon, Private Communication). As described in W09, we compute the uncertainty of the Pancam optical depths listed in Tables 1 and 2 using the mean diurnal root-mean-square (rms) of a sample of individual sols from LS ¼ 270—280 . This produces a mean diurnal rms of 0.09.

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3. Modeling algorithms and methodology The numerical tools and algorithms employed in our analyses are described in the published literature. We are using a slightly modified version of the approach described by W09. We focus on details which differ from those in W09 or are needed for completeness (including some additional references). We introduce the numerical tools before providing the description of the retrieval procedure. 3.1. Radiative transfer As with W09, the core radiative transfer algorithm is provided by the public-domain package DISORT (cf., Stamnes et al., 1988; Thomas and Stamnes, 2002). However, given the importance of Rayleigh scattering processes in the UV (compared with the CRISM regime), we update the Rayleigh cross section component of the driver routine, DISORT_MULTI. We use the recent results of Sneep and Ubachs (2005) and Ityaksov et al. (2008) to calculate explicitly the King factor and refractive index for carbon dioxide. In addition, we determine the atmospheric equation of state by integrating the hydrostatic equation constrained by a temperature profile and surface pressure from a TES-based climatology (Smith, 2004) for the nadir location (and season) of each pseudo-EPF. Although the topographic modulations of the total pressure column in the cross-track direction for the two MER sites are typically modest, we include such effects using a 1°  1° binned Mars Orbiter Laser Altimeter elevation map (http://pds-geosciences.wustl.edu/missions/mgs/megdr.html, see also Smith et al., 2001) and the assumption of an exponential atmosphere with a 10 km scale height. 3.2. Least-squares minimization The minimization engine for the retrievals is the IDL-based MPFIT routines developed by Craig Markwardt (latest version available from http://www.physics.wisc.edu/craigm/idl/fitting. html). The MPFIT code is based upon the well-known and extensively tested MINPACK-1 FORTRAN minimization library (Moré et al., 1984). MPFIT uses the traditional v2 statistic weighted by the estimated errors as the figure of merit for convergence: i.e., v2 ¼ Rððdata  modelÞ=robs Þ2 . The retrieved parameter uncertainties are calculated directly from the diagonal of the covariance matrix. The configuration of the ‘‘driver” implementation of the minimization routine is identical to that of W09, allowing up to four parameters to be retrieved: dust optical depth, water ice optical depth, surface reflectance scaling parameter, and x0 . For this paper, we employ only two combinations: x0 -only (dust, ice, surface fixed) and dust-and-surface (ice, x0 fixed). The first mode is used for x0 derivation, while the second is employed for both surface ‘‘tuning” (using lower dust loading pseudo-EPFs) and as an application to more general dust column retrieval (in Section 5). The underlying assumption in all cases is that no water ice aerosols are present (s [ 0.02–0.03), which we enforce through a visual inspection of Band 7 images. 3.3. Surface reflectance We represent the surface reflectance using the so-called ‘‘Hapke function” (e.g., Hapke, 1993, Chapter 12). In particular, we generalize the 430 nm Pancam results of the Johnson et al. (2006a,b) studies to represent an average surface as viewed by MARCI from orbit. W09 discuss the philosophy of such an approach in terms of a juxtaposition of many surface types. In essence, the initial adopted properties are derived from an average of several soil results from

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the Pancam analyses of Johnson et al. (2006a). As with the CRISM analysis (W09), modifications to the surface phase function are adopted, based (in this case) on MARCI Band 7 observations near the MER sites during periods of lower dust loading. Although there is some evidence for differences in the angular distribution function between Spirit and Opportunity, we derive a single set of parameters for both locations. Following the notation of Johnson et al. (2006a), who utilize a two-lobe Henyey–Greenstein phase function (e.g., Henyey and Greenstein, 1941), we adopt the parameters b ¼ 0:30; c ¼ 0:45;  h ¼ 20 ; B0 ¼ 0:8, and h ¼ 0:06. Given the ambiguity in our efforts to find optimized values for Band 6 (i.e., darker surface, increased importance of atmospheric scattering, need for ozone column values), we apply these same Hapke parameters to both UV channels (w does vary between channels, see below). Overall, these values differ from the visible/near-IR (CRISM) analysis of W09 primarily in that the individual components of the surface appear to be more forward-scattering, as might be expected with a decrease in wavelength. In addition, the increased phase angle range provides a greater sensitivity in terms of the forward/backward scattering balance. We determine the wavelength dependence (Band 6 versus Band 7) of the Hapke w using the distribution of radiance factor (I/F) from two days of observations that represent somewhat idealized atmospheric conditions: November 25, 2007 (LS ¼ 353 ; spancam;880 nm ¼ 0:7—0:8, no water ice clouds) and March 30, 2008 (LS ¼ 52 ; spancam;880 nm ¼ 0:25—0:30, some isolated water ice clouds as they are difficult to avoid during this season). To further minimize the effects of the atmospheric pathlength, we include only the pixels with emergence angles less than 5°, incidence angles 45° ± 5°. Using a somewhat simplified radiative transfer analysis (dust-only aerosol optical depth, 6.1 mb atmospheric column, ozone column of 2–3 lm-atm), we find that the mean of observed I/F distributions corresponds to a Lambert surface with an albedo of 0.011 and 0.014 for Bands 6 and 7, respectively. This process relies to some degree on the UV dust properties, such that it is repeated three times during the cycle of iterative solution for the dust scattering properties described in Section 3.6. However, only the first two repetitions produced noticeable changes in the w values. For comparison, Perrier et al. (2006) find a Lambert albedo of 0.008 at 210 nm and 0.015 at 300 nm, while Clancy et al. (1996) adopt values of 0.01 and 0.015 at 200 nm and 330 nm, respectively. We derive w values from our Lambert albedo analysis by requiring that the Hapke functions produce the equivalent reflectance within a few degrees of nadir. This produces a w of 0.0070 for Band 6 and 0.0095 for Band 7. 3.4. Aerosol model We employ the aerosol model of W09 with only minor modifications:  Particle shape. The shape of particle has a strong influence on its single scattering phase function, pðhÞ. Here, rather than attempting to constrain the particle shape directly, we consider instead potential modifications to the pðhÞ produced by the model of W09. They employ T-matrix calculations (i.e., Mishchenko et al., 2002) of pðhÞ without subsequent alteration. However, the shorter wavelengths of the MARCI data and the expanded phase angle coverage of the cross-track geometry emphasize the previously identified mismatch in the backscatter direction. In addition, examination of model–data comparisons indicates the need for a feature in the UV pðhÞ in the side-scatter direction that is not required for the visible wavelengths. Our solution is to apply the backscatter shape from the 444 nm case of Tomasko et al. (1999) for all bands and a simple empirical function to increase side-scattering in accordance with Bands 6 and 7 obser-

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vations. A comparison between the initial T-Matrix and the modified pðhÞ for the three MARCI bands of interest is provided, with additional description, in Fig. 2. The unmodified pðhÞ produces a systematic, considerable overestimation of I/F for (positive) emergence angles above 30°. The side-scatter modification involves additional parameters that are adjusted to optimize model fits to average side-scattering behavior in the pseudoEPF observations. As a result, only a simple function and a few additional iterations of the fitting procedure (cf. next section) are needed to arrive at the final functions.  Particle size. W09 considered a range of average particle sizes (reff ; for definitions, see Hansen and Travis, 1974) in the range 1.2–1.8 lm. However, they present a case for a more probable range of 1.7–1.8 lm during peak dust loading, using both Thermal Infrared Emission Spectrometer particle size retrievals as well as Global Circulation Model dust simulation results (i.e., Clancy et al., 2003; Wolff and Clancy, 2003; Kahre et al., 2008). Consequently, we consider only the cases of r eff ¼ 1:6 and 1.8 lm, where each size distribution is that of a gamma function and characterized additionally by v eff ¼ 0:3. 3.5. Ozone column The presence of ozone in the martian atmosphere will reduce the observed radiance in Band 6, particularly during conditions of substantial ozone abundance. As a result, an accurate treatment of x0 in this channel requires us to consider its effects. For the season and location of our observations, very little ozone is expected (Per-

Fig. 2. Adopted phase functions for MARCI Bands 1, 6, and 7 compared with the first-principle T-Matrix calculations for each band assuming an effective size ðreff Þ of 1.8 lm. The T-Matrix model of Wolff et al. (2009) uses a cylindrical shape (axial ratio D/L = 1) which produces a model–data mismatch in the backscatter direction. The lack of a backscatter peak in aerosol measurements (compared with idealized theoretical calculations) is well-known (e.g. Mishchenko et al., 1997, 1999). With the typical scattering (phase) angles range for the CRISM EPFs compared with those for the MARCI pseudo-EPFs, it is easy to understand why the CRISM data would not be particularly sensitive to this issue. For MARCI, we apply the backscatter shape from the 444 nm case of Tomasko et al. (1999). An additional feature, a minimum near 90° scattering angle, is necessary for only the two UV channels. Although this behavior is consistent with a more elongated particle (cf. Mishchenko et al., 2002, Chapter 10), the combination of our wavelengths and particle sizes prevent the TMatrix code from converging for axial ratios much different than 1. As a result, we employ a simple cosine function to produce a feature centered at 90° that matches smoothly with the base pðhÞ on either side. The depth of the feature is adjusted to provide the best fit to the pseudo-EPFs.

rier et al., 2006). Modeling and observation results (Lefèvre et al., 2004; Perrier et al., 2006) suggest a range of 0–2 lm-atm in ozone column abundance as conservative end-points for our analysis. As will be seen below, the ultimate effect of this difference in abundance is below the scatter in the x0 of our sample. For simplicity, we define the vertical distribution of the ozone using the ‘‘perihelion” profile of Clancy et al. (1996). 3.6. Retrieval procedure Based upon the above modifications to the W09 methodology for MARCI data analysis, we briefly summarize the iterative procedure used to retrieve the x0 values and derive the refractive indices (m): 1. Set initial values. Our starting assumptions for the angular dependence of the surface properties are discussed briefly above. For the initial w values, we adopt the Spirit 440 nm CRISM analysis value of 0.20. The initial aerosol properties for Bands 6 and 7 are determined by requiring the T-Matrix model to produce x0 ¼ 0:6 (e.g., Clancy et al., 1996). We fix sð880 nmÞ using the Pancam values given in Tables 1 and 2, where the wavelength dependence for the forward-scattering cross sections uses the W09 refractive indices to connect the MARCI and Pancam optical depths for each r eff . 2. Compute dust scattering properties using current m. We use a modified version of the T-Matrix code (TMQ) developed and maintained by M. Mishchenko and collaborators (http:// www.giss.nasa.gov/crmim/). We consider a set of two mean particle radii: reff ¼ 1:6, and 1.8 lm (surface-equivalent radius). 3. Retrieve the x0 for each of the pseudo-EPF observations. Each band is done serially using the ‘‘x0 -only” mode of the leastsquares routine. 4. Derive the imaginary refractive (k) index for the average x0 spectrum using a look-up table of T-Matrix calculations. Derive n from a subtractive Kramers–Kronig (cf. Snook, 1999), using nð500 nmÞ ¼ 1:5 as the fixed point (Tomasko et al., 1999) and including the refractive indices in the range 440–2900 nm from the W09 results. 5. Re-compute the dust properties using the new mð¼ n þ ikÞ. 6. [OPTIONAL] Adjust the surface model w parameter using the new dust properties and the Lambert analysis for the two sols of MARCI observations as discussed above (Section 3.3). This process is executed three times for each iterative sequence, though the third repetition produced essentially no change. 7. Check convergence, based on relative changes in x0 and m. If convergence not satisfied, go to Step 3. Convergence of the above procedure, defined to be a relative change in x0 less than 1%, occurs within five iterations for both UV bands. The goal is to produce a set of m that is consistent with the derived x0 values. From this perspective, we consider a relative change of less than 1% in x0 to represent a state of convergence for m as well. 4. Results The retrieval process produces three distinct products for each channel and reff : model–data fits (for each observation); x0 values (also for each observation); and refractive indices (for the mean x0 ). Accordingly, these items are presented below along with a short discussion of the uncertainties. However, because the Band 1 analysis is only presented as a validation of the pseudo-EPF concept (under dusty conditions), discussions of uncertainties and errors are limited primarily to the UV results.

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4.1. Model–data comparisons To look for potential systematic problems in the input parameters, such as the surface or aerosol phase function, we inspect the results of each fit at the end of an iteration cycle. Here, we provide several examples to give the reader some insight into ‘‘how well” our procedure is performing. Given the negligible difference in the changes of fit quality simply as a function of particle size, we consider examples from a single particle size only ðreff ¼ 1:8 lmÞ. Figs. 3 and 4 illustrate the model–data comparisons for representative dust loading end-members: s880 nm ¼ 3:3 (Spirit) and 4.6 (Opportunity), respectively. The models are from the final iteration of our retrieval procedure. The amplitude of the deviations in the Spirit Bands 6 and 1 are representative of the ‘‘poorer” fits in the sample, even though they are still considered ‘‘good fits” (i.e., v2N1 K 2) . The Opportunity cases shows a more typical set of fits. Although the larger deviations shown in Fig. 3 might raise some concern at first glance, the ‘‘localized” nature of such features minimizes their impact. For example, the retrieved x0 are for Bands 1, 6 and 7 are 0.769 vs. 0.764, 0.617 vs. 0.625, and 0.646 vs. 0.653, respectively. In fact, these differences in x0 (1%) are comparable to the statistical scatter in the sample of the retrieved x0 themselves: 0.003, 0.010, and 0.005 for Bands 1, 6, and 7. Thus, characterizing the types of model–data mismatches illustrated in the examples as representative, we find that such deviations or mismatches do not provide a significant source of bias for our sample.

Fig. 4. Model–data comparisons for all three bands near Opportunity. Same as for Fig. 3, but with s880 nm ¼ 4:6. These comparisons represent the typical fit quality for our sample (for both MER sites), i.e., v2N1  1.

Overall, the retrieval process produces good quality fits ðv2N1  1Þ. Yet, from this, one can only conclude that there is no systematic breakdown in our basic parameter assumptions. Examples of such issues could include the inability of our surface/aerosol phase functions or validity of a single particle size distribution to represent adequately the conditions found in our observations. Although we find no evidence for such behavior in our sample, as indicated by the general quality of our fits and the small scatter in our retrieved x0 , other types of bias may still be present in the primary retrieval parameter, x0 . 4.2. Single-scattering albedo and associated uncertainties

Fig. 3. Model–data comparisons for all three bands near Spirit with s880 nm ¼ 3:3. Examples of deviations or departures associated with a lack of complete (horizontally) spatial homogeneity can be seen in all bands. This particular comparison provides examples of the larger amplitude mismatches from our sample (Band 1 at larger positive emergence angles, Band 6 on both sides of the angle range). However, even these fits are still of good quality from the point of view of the fitting figure of merit: (i.e., ðv2N1 K 2Þ).

As discussed previously, our numerical approach involves the assumption of horizontal homogeneity in both the surface and atmosphere. Inspection of model–data comparisons reveals spatially correlated mismatches that would be consistent with local variability in either surface properties (i.e., w parameter) or atmospheric loading (i.e., plumes, variable dust mixing ratios). However, when such localized deviations occur, they do not typically provide a significant bias in the retrieved x0 . Nevertheless, the use of the average and standard deviation remains our choice to characterize the results of the retrieval process, using the observed dispersion employed as an estimate of the random error component. Table 3 lists the mean and standard deviations for each of the MARCI bands considered. In all cases, the dispersion exceeds that of the formal uncertainty determined from the covariance matrix, where the latter is [0.003 for all bands. For our ‘‘proof-of-concept” (Band 1) dataset, one would hope to find a reasonable agreement of the MARCI x0 with those of the

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analogous CRISM analysis. In fact, the correspondence of the x0 in the CRISM 440 nm channel with Band 1 for both the r eff ¼ 1:6 and 1.8 lm cases is excellent: 0.771 ± 0.002 and 0.772 ± 0.002, respectively (W09). Although this provides a degree of validation for our use of the pseudo-EPF, at least under very dusty conditions, it is important that one do not over-interpret the very small differences observed between the MARCI and CRISM x0 values as being indicative of the level of systematic error inherent in our methodology. The common surface and aerosol models between Band 1 and the CRISM 440 nm can potentially mask some of the systematic biases likely to be present in the UV bands. Examples of such factors include uncertainty in the adopted dust optical depths ðs880 nm Þ and the w surface parameter. In addition, there is the issue of the radiometric accuracy. Fortunately, these can be addressed through direct computation. The importance of the precise nature of the surface model is diminished by the large optical depths of our sample. Unfortunately, optical depths of even 3–4 are not large enough to completely decouple the effects of the surface. Nevertheless, even 20% perturbations to the adopted w values change the resulting mean x0 by less than 0.003 for both UV bands. This observation is equivalent to that found by W09: a change of 0.001–0.002 for a 10% perturbation in w. Another source of systematic error originates in the uncertainty associated with the adopted Pancam optical depths. If one allows for a 25% uncertainty in s880 nm (150% greater than that estimated s = 3.0, see Section 2.3), one finds differences in the retrieved x0 to be, at most, 0.008–0.009. This type of perturbation is asymmetric, producing the larger change for the lower bound on the optical depth. However, for a more realistic uncertainty of Ds  0:1, the associated uncertainty in x0 is typically less than 0.002 for each UV channel. A final source of systematic bias to consider is the accuracy of the radiometric calibration itself. Unfortunately, given its direct effect on the ‘‘observed” radiance, it is also potentially the largest. A 10% error in the radiance factor translates into a Dx0 of 0.02 for each of the two UV bands (independent of which particle size distribution). Clearly, the contribution of radiometric calibration is likely to be the dominant source of systematic error, at least given the adopted uncertainties of 10% and 8% for Bands 6 and 7, respectively. Overall, if we allow the random error to be set by the standard deviation of the sample of retrieval values and the systematic error set by the limitation of the radiometric calibration, a total error for the retrieved x0 can be derived simply under the assumption of uncorrelated error terms. This results in estimate of 0.022 and 0.019 for Bands 6 and 7, respectively (and for both r eff cases). A

Table 3 Average derived dust single scattering albedo (x0 ). r eff (lm) 1.6 1.8

x0 a Band 6,b case 1c

Band 6,b case 2c

Band 7b

Band 1b,d

0.619 ± 0.010 0.625 ± 0.011

0.626 ± 0.011 0.635 ± 0.011

0.648 ± 0.005 0.653 ± 0.005

0.765 ± 0.002 0.769 ± 0.003

a The tabulated values are the mean and standard deviation for distribution of x0 retrieved from the observations listed in Tables 1 and 2. The formal uncertainty for the retrieval (from the covariance matrix) provided by MPFIT is [0.003 (for all bands). b The centroids of Bands 1, 6, and 7 are 436 nm, 258 nm, and 320 nm, respectively. c Two end-member cases for ozone abundance: case 1: 0 lm-atm; case 2: 2 lmatm. The vertical distribution of the ozone is that of the ‘‘perihelion” profile of Clancy et al. (1996). d Band 1 is included as a proof-of-concept. These values are in excellent agreement with the CRISM 440 nm results of Wolff et al. (2009); see text.

similar exercise for our ‘‘proof-of-concept” sample, Band 1, yields a total error estimate of 0.010. 4.3. Refractive indices The derived refractive indices are listed in Table 4 for both of the particle size distributions considered here. The uncertainty for k follows directly from the estimate of the total error in x0 for each channel. That is to say, we simply compute k as described in Section 3.6 for x0 , and x0  rx0 . We calculate the associated uncertainty in the real refractive indices (n) by performing the subtractive Kramers–Kronig analysis for each perturbed value of k. 5. Discussion Although we have used a unique and robust dataset to retrieve dust aerosol properties for two wavelengths in the UV, it is of interest to compare our results to previous work, as well as to place such comparisons in the appropriate context. Finally, it would be worthwhile to briefly discuss potential applications of our results. 5.1. Comparison with previous work 5.1.1. x0 (and asymmetry parameter) The average x0 values for Bands 6 and 7 for both reff cases are quite consistent with much of the previous work, though this is due in part to the large uncertainties ascribed (by the authors or by us) to some of the retrievals. Results from the HST/WFPC2 and HST/Faint Object Spectrograph for wavelengths in the range 240–330 nm provide values in the range 0.57–0.60 (Wolff et al., 1997; Clancy et al., 1999), while the more recent analysis of HST/ Space Telescope Imaging Spectrograph (STIS) observations of the 2001 global dust event finds x0 (260 nm) = 0.64 (Goguen et al., 2003). Though no uncertainty is given in these works, the simple treatment of aerosol scattering (i.e., Henyey–Greenstein phase function) and the inherent limitations of the HST observational geometry limitations would lead to at least ±0.05–0.06 (though the spectral resolution of the STIS data may allow for something closer to ±0.04). More recently, Mateshvili et al. (2007) derived x0 (213 nm) = 0.60 ± 0.05 and x0 (300 nm) = 0.64 ± 0.04. The early Mariner 9 UVS work also appears consistent with the values reported here, though the use of the retrieval quantity x0  pðhÞ makes it more difficult to compare specifically. A potential discrepancy appears with the comparison to the Ockert-Bell et al. (1997) results of x0 (210 nm) = 0.72 and x0 (300 nm) = 0.61. No Rayleigh scattering is taking into account in their approach, even for the 210 nm result. Rather, they determine an effective surface reflectance in the UV by simply scaling the data to match a visible spectrum. As a result, it is likely that systematic effects and uncertainties are present at levels appreciably higher than those for the HST observations. Some of the earlier investigations assume an analytical form for the dust phase function, providing an additional ‘‘retrievable” parameter. The most common is that of the asymmetry parameter, g, which is the average cosine of the scattering angle as weighted by pðhÞ (e.g., Bohren and Huffman, 1983, p. 72). Essentially, it is a measure of the direction that light is preferentially scattered. Our aerosol model treatment provides this quantity, though we do not use it as a model constraint. Nonetheless, it still remains useful to compare an integral moment of our pðhÞ with those of previous efforts. Our g values for the phase functions employed in our analysis may be found in Table 5. Unfortunately, only a few studies report g for UV wavelengths. Ockert-Bell et al. (1997) find 0.81 and 0.88 for 210 and 300 nm, respectively. Goguen et al. (2003) derives a value of 0.84 at 260 nm. Finally, Mateshvili et al. (2007) retrieve a

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Band 6, case 1a n

k

1.6

1.486b

0.0155

1.8

b

1.488

Band 6, case 2a

0.0133

+0.0032 0.0022 +0.0027 0.0022

Band 7

n

k

1.486b

0.0147

b

1.488

0.0125

n +0.0033 0.0021 +0.0022 0.0022

k

1.493b

0.0146

b

0.0127

1.494

+0.0024 0.0020 +0.0019 0.0015

a Two end-member cases for ozone abundance: case 1: 0 lm-atm; case 2: 2 lm-atm. The vertical distribution of the ozone is that of the ‘‘perihelion” profile of Clancy et al. (1996). b Range of n values associated with uncertainty in k is [0.001 for all cases.

g(213 nm) of 0.88 ± 0.04 and a g(300 nm) of 0.86 ± 0.03. As with x0 , our values are in reasonable agreement with those of earlier analyses. 5.1.2. Refractive indices The refractive index represents one of the fundamental quantities in a ‘‘first principles” light scattering calculation. With it, one can calculate the scattering properties of particles with arbitrary sizes and shapes (subject to the limitations of one’s numerical electrodynamical technique, of course). A common source of such information is the laboratory measurement of terrestrial materials. However, in the absence of the required compositional knowledge, an observationally-derived set of values is likely to be more appropriate. Because such retrievals will be dependent on the assumed microphysical properties such as particle size, it is important to have some understanding of the range of such parameters. Based upon the analysis of W09 which makes the case for reff ¼ 1:7—1:8 lm as being representative of the conditions for the epoch of our observations, we have explicitly considered the cases of r eff ¼ 1:6 and 1.8 lm; see Table 4. However, this same dependence on the grain microphysics makes direct comparison with other results problematic. On the other hand, the paucity of similar retrievals relevant to Bands 6 and 7 simplifies the situation. The most relevant comparison is with the results of Pang et al. (1976). They find an imaginary index (k) of 0.02 at 268 nm and 0.01 at 305 nm. However, they also report a real part (n) of 1.8, much higher than ours. Other works find n much closer to those found by us, but the associated k values are much smaller (i.e., Dlugach et al., 2003 and references therein). Again, as with x0 and g values, the presence of large uncertainties, whether reported or deduced by us in the absence of such numbers, allows one to state that our analysis is consistent with some of the earlier analyses. 5.2. Potential applications The basic consistency of the MARCI-based x0 ; k, and g values with those reported in the literature, while reassuring, does not indicate an insensitivity of the radiation field to the precise value employed. For example, under the observational conditions studied here, a 10% perturbation in the radiance factor is equivalent to a change of ±0.02 in x0 (or equivalently, a perturbation of 0.002 in k). For uncertainties associated with previous efforts, say

Table 5 Aerosol Model Asymmetry Parameter g r eff (lm)

1.6 1.8 a b

Band 6

Band 7

Originala

Modifiedb

Originala

Modifiedb

0.88 0.88

0.90 0.90

0.85 0.86

0.87 0.88

Phase function calculated directly with T-Matrix method. Phase function modified from ‘‘Original” as described in Section 3.4.

Dx0 of 0.04 or even 0.06, the impact will be much larger. Although the same level changes in x0 or k for lower dust loading conditions will have a smaller impact, the effects of observational geometry and the importance of the form of the pðhÞ will become enhanced. That is to say, the integral nature of g can hide very different pðhÞ behavior. Consequently, the weight that one places on a given set of values should be determined by the perceived robustness of the observational sample and the associated retrieval techniques. In this light, we would suggest that our sample, combined with a self-consistent (non-spherical) aerosol model, provides a useful set of constraints on the properties of martian dust aerosol particles. Potential applications for our work include: 1. An extended dust climatology. While ongoing CRISM EPF observations offer the opportunity for moderately accurate orbital dust optical depth retrievals (i.e., ±0.1–0.2 at low-to-moderate loading conditions, W09), the very discrete spatial sampling (on the scale of kilometers) inherent in the measurements limits their utility in building a (spatially) global climatology. On the other hand, if the MARCI pseudo-EPF in Band 7 could retain some of its utility under less dusty conditions, a more spatially complete record could be constructed. Initial experiments for pseudo-EPFs obtained near the MER sites before the 2007 event (i.e., January–June 2007) indicate that regular dust optical depths are potentially retrievable from the Band 7 observations. From this sample of 135 pseudo-EPFs, we find that difference between the MARCI and MER/Pancam retrievals, adjusted for wavelength differences, is typically in the 0.2–0.4 range for s < 1:5. These are done under using scattering properties computed for reff ¼ 1:4 lm. However, this ‘‘test” is somewhat idealized in that the Hapke surface parameters were ‘‘tuned” using these two general locations. Further testing using the CRISM EPF-based s values will be carried out in the near future. These will include the impact of isolated water ice clouds as well as more uniform, thin clouds. 2. Retrievals of other atmospheric quantities from MARCI (or other UV datasets) such as water ice cloud optical depths or columnintegrated ozone abundances. The inverse problem for both of these quantities is quite sensitive to the details of the aerosol model including the phase function and single scattering albedo. As discussed above, the larger uncertainties associated with previous determinations of UV scattering properties introduces an increased range in the possible contributions of dust to the observed radiance, even outside of large-scale dust events. In addition, application of the n and k reported here allows for a translation to different particle size regimes, even if one restricts themselves to a simple aerosol model involving Miebased x0 and a Henyey–Greenstein phase function. 3. Surface studies. Although the wavelength sampling of MARCI may not be ideal for unambiguous surface mapping studies, it is true that this aspect of the UV has been greatly hampered by uncertainties associated with ‘‘atmospheric removal”. Given the ubiquity of dust in the martian atmosphere, improvements

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in one’s ability to treat its scattering properties may allow for new efforts to commence. For example, the combination of CRISM EPFs and MARCI UV pseudo-EPFs near the MER locations offers the potential for both an extension of existing in situ and orbital results.

6. Summary The MARCI observations during the planet encircling dust event of 2007 provide an excellent opportunity to investigate the UV scattering properties of martian dust aerosol particles. Although MARCI does not possess the capability to obtain a ‘‘classical” EPF sequence, the combination of the variation of the photometric angles in the cross-track direction along with the low surface contrast in the UV (and blue) are used to construct a nearly-equivalent ‘‘pseudo-EPF” sequence. Using a series of observations in close proximity to both MER locations during this epoch, we are able to leverage the ‘‘ground-truth” aspect of the Pancam column-integrated optical depth and blue (430 nm) surface photometry measurements. Using both datasets, we isolate the single scattering albedo ðx0 Þ through the elimination of a significant portion of the uncertainty associated with the standard radiative transfer input parameters. Our choice of a ‘‘first principles” microphysical approach to represent the dust particle properties translates directly into a capability to produce a set of self-consistent refractive indices ðm ¼ n þ ikÞ. Although previous work places some constraints on the size distribution associated with the epoch of our observations, we perform the analyses for multiple values of the cross section weighted mean particle radii: reff ¼ 1:6 and 1.8 lm. Ultimately, the retrieval process produces a set of model–data comparisons (for process control and potential‘‘tuning” of surface parameters), x0 , and m. Our analysis includes an estimate of the random and systematic errors associated with the numerical approach. In terms of specific values, we find:  For the r eff ¼ 1:6 lm case, x0 (Band 6) = 0.619–0.626, depending upon the abundance of ozone in the atmosphere; x0 (Band 7) = 0.648; and x0 (Band 1) = 0.765. The total estimated error for each band is 0.022, 0.019, and 0.010, respectively. The derived refractive indices are 1:486 þ i0:0155 (Band 6, no ozone), 1:486 þ i0:0147 (Band 6, 2 lm-atm of ozone), and 1:493 þ i0:0146 (Band 7). The uncertainty in the imaginary part (k) is typically 0.002–0.003.  For the r eff ¼ 1:8 lm case, x0 (Band 6) = 0.625–0.635, depending upon the abundance of ozone in the atmosphere; x0 (Band 7) = 0.653; and x0 (Band 1) = 0.769. The total estimated error are the same as for the other reff case. The derived refractive indices are 1:488 þ i0:0133 (Band 6, no ozone), 1:486 þ i0:0125 (Band 6, 2 lm-atm of ozone), and 1:493 þ i0:0127 (Band 7), with a similar range in the uncertainty of k. Our discussion focuses on two issues: 1. The context of our results ðx0 ; m; gÞ within the frame work of previous efforts, with an emphasis on the most applicable or relevant work. We include the x0 -only values for Band 1 as a ‘‘proof-of-concept” through a comparison to contemporaneous CRISM EPF results at 440 nm for which the agreement is excellent. For the UV results, find a general consistency (within the errors) with several earlier studies. However, the improved precision of our results with respect to earlier work offers a distinct advantage. For example, the uncertainty associated with the radiation field using our retrievals is at least a factor of two smaller than that obtained using most precise existing work (i.e., Mateshvili et al., 2007). In addition, the derivation of

refractive indices allows one to extend the dust properties to other size distributions such as those associated with diffuse loading. 2. Several potential applications enabled by our results: extension of the dust climatological record, retrieval of water ice optical depth and ozone column abundance, and UV surface studies. Initial work on the first of these applications reveals that from a sample of 135 pseudo-EPFs near the MER sites, one finds the potential for dust optical retrievals under moderate loading conditions ðs < 1:5Þ from Band 7 observations with a typical error in the 0.2–0.4 range. However, this sample may benefit from the use of ‘‘tuned” surface parameters. Further work is ongoing. Acknowledgments The authors wish to express a deep appreciation to the engineering team at Malin Space Science Systems (in particular, Mike Caplinger, Tony Ghaemi, and Mike Ravine) for their extensive efforts in producing the MARCI camera, which is nothing short of amazing: limb-to-limb images with a radiometric fidelity capable of precision photometric work in both the UV and visible. We also gratefully acknowledge indispensable software and tactical support from the Joe Fahle, Kim Supulver, and the MSSS Operations team. We had helpful conversations with Pey Lian Lim (of STScI) and the members of the MARCI science team. This work was supported by NASA through JPL Contract 1275776 and Space Telescope Science Institute DD Grant 11314. Appendix A. MARCI Band 6 radiometric update As discussed by Bell et al. (2009), the radiometric calibration of the MARCI UV channels was accomplished through near-simultaneous observations with MARCI and the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2). These data were obtained in July 2007 during the planet encircling dust event. Similar WFPC2 observations, as well as UV and near-UV spectroscopy from the Space Telescope Imaging Spectrometer (STIS; Goguen et al. (2003), Bell and Ansty (2007)), were obtained in during the 2001 planet-wide dust event. We can improve the MARCI UV calibration by taking advantage of the STIS spectral resolution thereby avoiding the inherent uncertainty associated with the F255W calibration as well as with the potentially problematic nature of the photometric transformation previously employed to convert the 2007 WFPC2 F255W observations to that of the MARCI Band 6. The observational characteristics of the August 2001 and July 2007 are quite similar: approximately 2 weeks past the peak optical depth at low-latitudes with similar column-integrated optical depths (cf. Clancy et al., 2003; Wolff and Clancy, 2003; Wolff et al., 2009) and very comparable phase angles of 40.8° and 43.3° for August 18, 2001 and July 27, 2007, respectively. The WFPC2 observations are in good agreement between the two epochs (Fig. 5; additional details may be found in the figure caption). For similar atmospheric conditions and photometric angles, the I/F values for separate observations would be expected to possess similar distribution functions. As such, histograms are a useful tool to compare data from different observations and as well as from multiple instruments. In other words, the similarity of the 2001 and 2007 WFPC2 histograms in Fig. 5 provides a high degree of observational support for the use of the 2001 STIS spectra in assessing the MARCI UV calibration. STIS observations on August 9, 2001 (G430LB grating, 290– 540 nm) and August 18, 2001 (G230LB grating, below 200 nm through 310 nm) offer similar observational geometries to those of the WFPC2 images as well as very complementary wavelength

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Fig. 5. Histogram of the radiance factors (I/F) for WFPC2 F255W and F336W observations from the 2001 (August 18) and 2007 (July 23 and 27) planet encircling dust events. The vertical lines indicate the mean of each histogram. The histograms are created using a bin of 0.002 and are restricted to using data for which the latitude is equator-ward of 50° and the incidence and emergence angles are smaller than 60°. The 2001 histrograms are scaled by 0.25 due to larger angle subtended by the martian disk at this epoch. A description of the processing and image navigation involved can be found in Wolff et al. (1999), although an addition correction is made for recent changes in the UV throughput in the WFPC2 F255W as discussed by Bell et al. (2009).

ranges. Unfortunately, neither completely covers both MARCI bandpasses. As a result, our approach is to compute the synthetic bandpass ratio using the G230LB data with the Band 7 region completed through a linear extrapolation of the smoothed I/F (the photometric integral is still performed in radiance space). The justification for this extrapolation is taken from an examination of the G430LB I/F data in the 310–370 nm range, which exhibits modest spectral dependence. The validity of this assumption is supported by direct comparison of the synthetic Band 7 numbers from both gratings in Fig. 6. Here, the Band 7 distributions are very similar (particularly those of the synthetic photometry) and the moments agree with each other to within 5%. The smaller dispersion in the MARCI histograms is directly related to the restricted incidence angle geometry viewed by the MRO spacecraft. From these comparisons, one is able to obtain an additional degree of confidence in the Bell et al. (2009) radiometric coefficient for Band 7. Yet, the Band 6 histograms clearly show a significant bias of the MARCI (WFPC2-based calibration) radiances relative to those from the STIS radiance over the same bandpass. In other words, a correction is needed to reconcile the MARCI Band 6 absolute calibration with the STIS results. The ‘‘ratio” value in Fig. 6 is defined to be (Band 6 I/F)/(Band 7 I/ F). For the STIS synthetic photometry ratio, we use the STIS230LB data with its extrapolated synthetic Band 7 radiance factor. The 5% difference between the two STIS Band 7 numbers is consistent with both the STIS absolute calibration limitations (e.g., Dressel et al., 2007). To change the smallest number of parameters (i.e., apply Occam’s Razor), we adopt the synthetic 230LB-based radiance for the ratio calculation and adjust the Band 6 radiometric calibration to match, a change of 15%. This gives a new radiometric coefficient of 0.0101 (DN/ms)/(W/m2/lm/sr) under the assumption that the Band 6 integrated solar irradiance at 1 AU (pF(1 AU)) is

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Fig. 6. Histogram of the radiance factors (I/F) and the ratios for MARCI Bands 6 and 7, including the synthetic photometry obtained from the STIS G230LB and G430LB observations. The vertical lines indicate the mean of each I/F distribution. The MARCI and G430LB histograms are scaled as indicated in the figure legends. To provide the best correspondence in terms of viewing geometry, the histograms from all data sources are restricted to values for which the incidence angle is between 25° and 60° (i.e., the restricted solar illumination geometry of the MARCI ground-track), the emergence angle is less than 60°, the phase angles for the MARCI data must be within 2° of that of the STIS data (which is essentially fixed across the disk, i.e., 41°), and the latitude is equator-ward of 50°. The general processing and navigation details are presented by Goguen et al. (2003), Bell and Ansty (2007), and Dressel et al. (2007). As suggested by Jessup et al. (2007), we correct for scattered light in the G230LB data using the depths of solar Fraunhofer lines. Because of our lower resolution and signal-to-noise, we use an average of the corrections derived from the Mg II and Mg I lines (near 280 and 285 nm, respectively). The wavelength dependence of the scattered light is taken from Fig. 6 of Gregg et al. (2006). Our calculations remove approximately 9% of the radiance-on-sensor as scattered light.

132.1 W/m2/lm. Accordingly, an estimate of the absolute radiometric accuracy for Band 6 will depend on the uncertainty of the Band 7 absolute calibration. Allowing for an additional 5% of undetermined (but systematic) uncertainty, we estimate the accuracy to be [10%. Appendix B. MARCI sensitivity to polarized light Bell et al. (2009) discuss a series of measurements taken during the laboratory calibration campaign to examine the sensitivity of the MARCI UV bands to the polarization state of the incident light. The optical behavior of most wide-angle camera systems will manifest a sensitivity to the polarization state of the incident light (i.e., even the MARCI visible bands) due to the preferential reflection of the transverse mode of light at larger incidence angles with respect to the surface normal. However, it is only in the UV where one typically need consider the possibility of significant incident polarization for martian remote sensing observations due to the

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Fig. 7. Sensitivity of the MARCI UV camera to incident polarized light. b=a and c=a represent relative contribution to the observed radiance (I) by the Q and U components of the incident radiation. For reference, a camera angle of 60° is equivalent to a surface emergence angle of 70° at a spacecraft altitude of 300 km.

potentially significant polarization contribution from Rayleigh scattering near 90° phase angle. The calibration observations provide three sets of observations, one set for each angle of the linear polarizer. Because the light exiting an integrating sphere is essentially unpolarized light (e.g., McClain et al., 1995), the Stokes vector of the light after passing through the linear polarizer is assumed to be 100% polarized. Using standard Mueller matrix notation and the Stokes vector for transmission through a linear polarizer (cf. Bohren and Huffman, 1983), we are left with a set of three equations and three unknowns: Ij =I0 ¼ a þ bcos 2hj þ csin 2hj , where j = 1, 2, 3 indicates the observations ðIj Þ for the linear polarization position angles ðhj Þ of 0°, 60°, and 120°, and I0 is the measured radiance without the linear polarizer in the beam. The angles are defined with respect to the cross-track direction of the camera (i.e., the long axis of the ‘‘taco shell”; see Fig. 1 in Bell et al. (2009)). The coefficients a; b, and c represent the transmission efficiency for the Stokes I; Q , and U components, respectively. As such, our primary interest is in the Q and U sensitivity normalized to the unpolarized component, b=a and c=a. For each angle with respect to the optical axis of the camera system, the system of equations is easily solved analytically. Fig. 7 illustrates the derived b=a and c=a values as a function of the camera angle. Both MARCI UV bands have approximately the same degree of sensitivity to the incident polarization. However, it is important to keep in mind that the effect on the measured radiance is a function of the polarization state of the incident light: I ¼ aI0 þ bQ 0 þ cU 0 . For a camera angle of 60° (70° emergence angle for a spacecraft altitude of 300 km), a scene with a Q 0 =I0 of 10% represents less than a 2% effect on the measured radiance compared to the case of unpolarized light. The same amount of U polarization produces changes of less than 0.5%. These numbers are significantly smaller than the radiometric uncertainty. Furthermore, as will be discussed briefly below, the level of 10% for the Q and U components represents an upper limit. Consequently, the use of the scalar radiative transfer equation will not introduce an appreciable error or uncertainty in our data analysis. To examine the range of polarization states for typical MARCI scenes, we employ the rt3 program described by Evans and

Fig. 8. Histogram of the normalized Stokes Q and U parameters for representative sample of atmospheric conditions and viewing geometries. The histograms are created using bins of 0.02. The dust aerosols are represented by oblate cylinders (D/ L = 1) with r eff ¼ 1:8 lmðv eff ¼ 0:3Þ and a complex refractive index of 1:49 þ 0:014i. sRay ¼ 0:022 and 0.057 are the Rayleigh optical depths in a 6.1 mb hydrostatic atmosphere for Bands 6 and 7, respectively.

Stephens (1991) and kindly supported by Frank Evans (http:// nit.colorado.edu/polrad.html). We construct a very simple threelayer martian atmosphere with Rayleigh scattering, uniformly mixed dust aerosols, and a Lambertian surface (AL = 0.02; see figure caption for additional aerosol details). In order to simulate MARCIlike viewing, we fix the incidence angle at 45° and vary the emergence and azimuth angles in the ranges of 0–70° and 0–180°, respectively. The histograms of the resulting normalized Stokes parameters from four ‘‘representative” cases may be seen in Fig. 8. Although the work in this paper is best represented by the higher optical depth conditions, we include low and moderate cases for completeness. The few models which have Q or U fractions above 10% cluster typically possess phase angles near 90°. Thus, even considering these extreme cases, the effect of the scene polarization state on the detected radiance will be at most 3% (for a camera angle of 60°, Q =I  20%). More typically, the errors introduced by ignoring polarization are [1%.

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