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In this paper we describe and evaluate the so-called shadow method. This method can be used to estimate the optical depth of the Martian atmosphere from the differences in brightness between shadowed and sunlit regions observed from an orbiter. We present elaborate and simplified versions of the method and analyze the capabilities and the sources of errors. It proves essential to choose shadowed and sunlit comparison regions with similar surface properties. Accurate knowledge of the observing geometry, including the slopes of the observed region, is important as well, since the procedure should be corrected for the non-horizontal surface. Moreover, the elaborate version of the shadow method can be sensitive to (i) the optical model of aerosols and (ii) the assumed bi-directional reflectance function of the surface. To obtain reliable estimates, the analyzed images must have a high spatial resolution, which the HiRISE camera onboard the MRO provides. We tested the shadow method on two HiRISE images of Victoria crater (TRA_0873_1780 and PSP_001414_1780) that were taken while this crater was the exploration site of the Opportunity rover. While the rover measured optical depth τ approximately in the ranges from 0.43 to 0.53 and from 0.53 to 0.59 by imaging the sun, our shadow procedure yielded τ about 0.50 and 0.575, respectively (from the HiRISE's red images). Thus, the agreement is quite good. The obtained estimates of the surface albedo are about 0.20 and 0.17, respectively. [ABSTRACT FROM AUTHOR]

Abstract: The difference in brightness between shadowed and sunlit regions in space images of Mars is a measure of the optical depth of the atmosphere. The translation of this difference into optical depth is what we name the “shadow method”. Our analysis of two HRSC data-sets and a HiRISE data-set indicates that it is possible to estimate the optical depth with the shadow method. In colors between yellow and red the accuracy may be around ±15%, and in some cases ±8–10%. In other colors we found larger errors. We came to these results in two steps. First, we investigated in how far shadow method retrievals are proportional to the true optical depth. To this end we analyzed about 150 locations in Valles Marineris that were imaged by HRSC. Whereas the studied region spans about 8km in altitude we were able to study the relation between altitude and shadow-method retrievals. Retrievals from five HRSC panchromatic (675±90nm) stereo images yielded scale-heights with an average of 12.2±0.7km, which is very close to the expected local pressure scale height. Many studies have shown that the scale-height of optical depth and pressure commonly are similar. This indicates that the shadow method retrievals are on average close to proportional to the optical depth, because otherwise these would probably not yield a correct scale-height. HRSC’s red image yielded very similar results, but the blue, green, and NIR images did not. Next, we compared optical depth measurements by the two MER rovers with shadow method retrievals from orbiter images of the rover exploration sites. Retrievals with the shadow method appear systematically smaller than the rover measurements; dividing the retrievals by a “correction factor” yields an estimate of the real optical depth. Retrievals from three HRSC panchromatic stereo images of a region near the Spirit rover yielded a correction factor of 0.63±0.09 when the sunlit comparison regions were at varying and more or less arbitrary distances from the shadows and 0.71±0.06 when these were close together. Twenty retrievals from a HiRISE red (650±100nm) image of the Opportunity exploration site similarly yielded 0.68±0.09. The results from these two case studies suggest that the shadow method has an accuracy of about ±15% or around ±8–10% in the best cases. [Copyright &y& Elsevier]

Abstract: We measured the optical depth of the Martian atmosphere as a function of altitude above two opposing scree walls of the Valles Marineris, from stereo images that were taken with the High Resolution Stereo Camera (HRSC) of Mars Express on June 3, 2004, during orbit 471. The optical depths were measured from contrast differences between the stereo images with the so called “stereo method”. For 7 regions in the northern wall of the Valles, we estimated the optical depth and found values between 1.0 and 1.6. These regions span more than 6km in altitude and the results show a clear relation with altitude. A fit on these results yielded a scale-height for the optical depth of 14.0km+1.3/−1.1km. The expected local pressure–scale height is smaller: 11.5–12.0km. The difference is most likely explained by small (around 1.5%) offset errors in the intensity calibration of HRSC images. We also selected 9 regions in the opposing southern wall and from these we measured values of optical depth in the range 1.3–1.5. Our result suggests the presence of clouds above this part of the Valles because the optical depth appears almost independent of the surface altitude. Possibly these are banner clouds, forming at the edge of the canyon, that contain dust that is blown over the canyon by winds from the high plains to the South. [Copyright &y& Elsevier]