Shadow method retrievals of the atmospheric optical depth above Gale crater on Mars using HRSC images

Abstract

The ‘Shadow Method’ is a tool to estimate the Atmospheric Optical Depth (AOD) on Mars from the brightness of shadows. This method is derived from the equations of radiative transfer, but there are several important simplifications that together invoke errors of several tens of percent. Work by us and by others show that these errors are largely systematic and can be minimized by adding an empirical ‘Correction-Factor’ to the equations. To quantify this factor, we compared shadow method retrievals from orbiter images with in-situ measurements by the Curiosity rover. We analysed a set of seven images that was taken by DLR's High Resolution Stereo Camera (HRSC) on-board ESA's orbiter Mars Express. The images were taken in seven channels: NIR, red, green, blue, and in three panchromatic stereo channels S1, Nadir, and S2. All these images show Gale crater and the exploration site of the Curiosity rover therein. Comparing the rover measurement of the AOD with shadow method retrievals from 5 close-by regions yielded the following correction factors: 0.53 ± 0.03 for Nadir, 0.60 ± 0.04 for S1, 0.62 ± 0.03 for S2, 0.66 ± 0.03 for NIR, 0.64 ± 0.03 for Red, 0.55 ± 0.03 for Green, and 0.57 ± 0.03 for Blue.We analysed 71 regions with varying altitudes between −4.6 km to +3.8 km and found that, on an average, the AOD decreases with increasing altitude. The available channels yielded the following averages of atmospheric optical depth before applying the correction factor: Nadir: 0.47; S1: 0.46; S2: 0.52; Red: 0.49; Green: 0.53; Blue: 0.57 and NIR: 0.44 while after applying the correction factor we obtain Nadir: 0.89; S1: 0.77; S2: 0.84; Red: 0.77; Green: 0.96; Blue: 1.0 and NIR: 0.67. The Curiosity rover, at an altitude of −4.87 km, measured a ground-truth AOD of 0.88.The shadowed and sunlit comparison regions that were used for this work range in altitudes from −4.6 km to +3.8 km. The AOD decreases with altitude and the decrease yields the following scale heights: S1: 12.5 + 0.48/−0.35 km; nadir: 11.1 + 0.53/−0.33 km; S2: 14.3 + 0.48/−0.44 km; NIR: 11.1 + 0.56/−0.47 km; red: 14.3 + 0.52/−0.49 km; green: 15.6 + 0.62/−0.59 km; blue: 14.3 + 0.44/−0.42 km. For this area and around that time of day, the Mars Climate Database predicts a pressure scale height of 11.6–12.2 km, which agrees well with the scale heights that we derived for Nadir, S1 and NIR. One region (number 42) contained a cloud with an optical depth of up to 0.6—0.8; i.e., around one third of the total AOD of 1.9 ± 0.01 measured for this area. Region 29 showed the highest AOD of our sample.