Photometric Modelling for Chang&#8217;e 5 Landing Site and Reiner Gamma Swirl
Authors: Hess Marcel , Wöhler Christian , Qiao Le 
Published: September 2022

&lt;p&gt;&lt;strong&gt;1. Introduction&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Knowing the photometric properties of a surface can give us insight into its physical properties. Images with several different observation conditions can be used to constrain the parameters of a semi-physical model like the Hapke model [1].&lt;/p&gt;
&lt;p&gt;The Wide Angle Camera onboard the Lunar Reconnaissance Orbiter (LROC WAC) [2] provides unprecedented coverage of the lunar surface for a variety of phase angles. The field of view of the Narrow Angle Camera (LROC NAC) [2] is much smaller and therefore, also the possible phase angles are limited but the resolution is around 1 m/pixel.&lt;/p&gt;
&lt;p&gt;Sato et al. [3] have used WAC images to create global maps of the Hapke parameters binned into areas of 1 degree/pixel [3]. In this work, we calculate photometric parameters on the pixel level. Velikodsky et al. [4] investigated the relative contributions of coherent backscatter and shadow hiding opposition effects based on WAC images and, similar to [3], find that the total strength of the opposition effect is inversely correlated with albedo.&lt;/p&gt;
&lt;p&gt;The landing of a spacecraft on the lunar surface can change the physical properties of the regolith [5],&amp;#160;e.g., by compacting the very porous lunar regolith.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;2. Methods&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Our method consists of three main steps. Firstly, the WAC or NAC EDR images are downloaded from the PDS and processed with ISIS3 [6]. This process includes calibration and map projection. The NAC images are mapped to a common resolution of 1.6 m/pixel and the WAC images are mapped to a resolution of 400 m/pixel. The sub-solar and sub-spacecraft points are extracted using the campt command in ISIS3.&lt;/p&gt;
&lt;p&gt;Secondly, suitable images are co-registered in MATLAB to a common reference image and we calculate the incidence, emission, and phase angles based on the trajectory of the LRO, the sub-solar point, and either the GLD100 [7] in the case of WAC images or a Shape from Shading Digital Elevation Model [8] in the case of NAC images. Due to its large field of view, the phase angle changes significantly within one WAC image. For NAC images the emission angle can be assumed as constant for our region of interest.&lt;/p&gt;
&lt;p&gt;Thirdly, we employ the NUTS sampler of pymc3 [9] to infer the posterior density of the parameters of the Hapke model [1] given the data. This Bayesian inference technique [10] also provides us with information about the respective uncertainties. Because several parameters of the Hapke model have a similar influence on the total reflectance, we limit our analysis to three parameters, namely, the single scattering albedo (w), the amplitude of the shadow hiding opposition effect (B&lt;sub&gt;S0&lt;/sub&gt;), and the surface roughness (&amp;#952;&lt;sub&gt;b&lt;/sub&gt;).&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;3. Results&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;For the landing site of Chang&amp;#8217;e 5, we selected and co-registered 19 LROC NAC images, 8 before landing and 11 after landing. The phase angles range from approximately 45 degrees to nearly 90 degrees. For the Reiner Gamma swirl, we selected and coregistered 9 LROC WAC images and selected the wavelength channel at 605 nm. All outcrops of the regions of interest are shown in Figure 1. One can see that the image after the landing is overall brighter compared to that before the landing for a similar phase angle. The western part of the Reiner Gamma swirl is also clearly visible by its increased brightness (see Figure 1c). The resulting maps for albedo, shadow hiding amplitude, and mean of the standard deviation of the likelihood function (&amp;#963;) are shown in Figure 2. The parameter &amp;#963; describes the quality of the fit of the model and the data and can be interpreted similarly to a root mean squared error. Overall, the albedo increases from before the landing to after the landing, and B&lt;sub&gt;S0&lt;/sub&gt; decreases around the rover landing site. Very high values of B&lt;sub&gt;S0&lt;/sub&gt; coincide with shadows of the rover or craters and also&amp;#160;correlate with high&amp;#160;values of &amp;#963;. Values with a &amp;#963; value above 0.07 are labeled as invalid and are, therefore, omitted for future analysis. Pixels with an albedo larger than 0.21 have been labeled as on-swirl or landing-site. The histograms of the B&lt;sub&gt;S0 &lt;/sub&gt;values are shown in Figure 3. They show that the landing site and on-swirl pixels show a significantly weaker shadow hiding effect&amp;#160;than the surrounding surface.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Figure 1: &lt;/em&gt;Images of similar phase angle for the landing site before (a) and after (b) the landing of Chang&amp;#8217;e 5 as well as for the western part of Reiner Gamma (c).&lt;/p&gt;
&lt;p&gt;&lt;em&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Figure 2:&amp;#160;&lt;/em&gt;Maps of Hapke parameters.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Figure 3:&lt;/em&gt; Distribution of B&lt;sub&gt;S0&lt;/sub&gt; for the landing site after the landing and the Reiner Gamma swirl.&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;4. Conclusion&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;The landing of the Chang&amp;#8217;e 5 rover on the Moon has changed the photometric properties of the surface. The albedo has increased and the shadow hiding opposition effect is less strong such that the phase curve has become flatter. This is generally the case for higher albedos but the reduction is nonetheless significantly&amp;#160;even below the value expected&amp;#160;for the brighter highlands [3]. Similarly, swirls show a reduced opposition effect. A physical explanation could be that the porosity of the regolith is reduced&amp;#160;by fast-streaming gas from the landing rocket jet and from a passing comet, respectively (see [5]).&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;[1] B. Hapke (2012).&amp;#160;&lt;em&gt;Theory of reflectance and emittance spectroscopy&lt;/em&gt;,&amp;#160;Cambridge.&lt;/p&gt;
&lt;p&gt;[2] M.S. Robinson et al. (2010). Space science reviews, 150(1):81&amp;#8211;124.&lt;/p&gt;
&lt;p&gt;[3] H. Sato et al. (2014). JGR Planets, 119(8):1775&amp;#8211;1805.&lt;/p&gt;
&lt;p&gt;[4] Y.I. Velikodsky et al. (2016). Icarus, 275:1&amp;#8211;15.&lt;/p&gt;
&lt;p&gt;[5] V.V. Shevchenko (1993). Astronomy Reports, 37:314&amp;#8211;319.&lt;/p&gt;
&lt;p&gt;[6] J. Laura et al. (2022). URL https://doi.org/10.5281/zenodo.6329951.&lt;/p&gt;
&lt;p&gt;[7]&amp;#160;F. Scholten et al. (2012). JGR Planets, 117, E00H17.&lt;/p&gt;
&lt;p&gt;[8] A. Grumpe et al. (2014). Advances in Space Research, 53(12):1735&amp;#8211;1767.&lt;/p&gt;
&lt;p&gt;[9] J. Salvatier et al. (2016). PeerJ Computer Science, 2:e55.&lt;/p&gt;
&lt;p&gt;[10] A. Gelman et al. (1995). &lt;em&gt;Bayesian Data Analysis&lt;/em&gt;, Chapman and Hall/CRC.&lt;/p&gt;