The Aphelion Cloud Belt Phase Function at Gale Crater A.C. Innanen1, B.A. Cooper2, C.L. Campbell1, S.D. Guzewich3, J.L. Kloos4, H.M. Sapers1, J.E. Moores1. 1 Centre for Research in Earth and Space Science, York University, Toronto, Canada (ainnanen@yorku.ca) 2 NOIRlab, Gemini North Observatory, Hilo, USA 3 NASA Goddard Space Flight Center, Greenbelt, USA 4 Department of Astronomy, University of Maryland, College Park, USA Introduction: The Mars Science Laboratory rover (MSL, Curiosity), located in Gale Crater (4.5°S, 137.4°E) has observed Martian clouds since its landing in 2012 (e.g. Moores et al., 2015, Kloos et al. 2018, Cooper et al., 2019). Many of these are water-ice clouds, which are particularly prominent during the Aphelion Cloud Belt (ACB) season (Ls~50°-150°), which is characterized by increased formation of water-ice clouds around the equator (Wolff et al., 1999). The ACB season generally has low inter-annual variability (Wolff et al., 2019), except in the case of years with significant regional or global dust storms (e.g. Benson et al., 2003, Giuranna et al., 2021). ACB clouds exhibit greater diurnal variation, with differences in opacity (Kloos et al., 2018) and altitude (Campbell et al., 2020) between morning and afternoon clouds. Of interest in the study of water-ice clouds is their microphysical properties, such as water-ice crystal size and shape. These can be determined from a cloud’s scattering phase function, which describes the angular distribution of scattered radiation from water-ice crystals within the clouds, as a function of scattering angle. There have been a number of previously derived phase functions of Martian water-ice clouds using various instruments and methodologies. Clancy & Lee (1991) Clancy et al. (2003) analysed emission phase function (EPF) observations taken from Mars orbiters in order to study different water-ice clouds including polar, mid-latitude and ACB clouds. Kloos et al. (2016) also constrained a lower bound scattering phase function of clouds seen by MSL. The Phase Function Sky Survey (PFSS), developed by Cooper et al. (2019), was instituted in MY 34, and has been performed through the ACB seasons of three Mars years. It consists of nine threeframe ‘movies’ at 9 pointings taken with MSL’s navigation cameras (NavCams), forming a dome around the rover. Its purpose is to examine ACB clouds from a large range of scattering angles in order to further constrain the ACB phase function. We compare three Mars years (MY 34, 35 & 36) of ACB average phase functions derived from MSL observations to determine if there are any interannual or diurnal variations in dominant ice-crystal habit and if the global dust storm (GDS) of MY 34 im- pacted ice-crystal habit. Methods: The water-ice clouds of the ACB are often too optically thin to be seen in the raw NavCam frames, so a perturbation movie is made using the three frames at each pointing of the PFSS. The frames undergo mean frame subtraction (MFS), which removes the time-invariant component of each frame, leaving only the time-varying component, in this case the moving clouds. Examples of frames before and after MFS are shown in Figure 1. Figure 1 - The three frames of the sol 2633 pointing 5 movie before (left) and after (right) mean frame subtraction. Cloud features that are not present in the raw frames are clear in the MFS frames. We can then use the resolved clouds to create a radiance map, and determine areas of low and high radiance (empty sky and cloud, respectively) to determine the variation in spectral radiance (Iλ,VAR). We can then compute a value for the phase function (P(Θ)), using the expression derived by Cooper et al. (2019): [1] where Δλ is the bandpass of the NavCams, ΔτMCS is an averaged water ice optical depth from the Mars Climate Sounder (MCS), Fλ is the in-band solar flux, τCOL is the column optical depth below the cloud, taken from the MSL mast cameras (Lemmon et al., 2015), and µ is the cloud viewing angle. While the selected area of low spectral radiance is meant to be empty sky, it is likely it could be a thinner region of the same cloud, meaning our Iλ,VAR should be taken as a lower limit, and thus the calculated phase function is also a lower limit. However, the overall shape of the phase function should be more reliable than its absolute magnitude as the shape encodes differences in radiance at different scattering angles within the same observation at the same opacity. From the calculated phase function values for each PFSS movie, we apply a moving average in order to derive the mean phase function for the entire ACB season. In comparing our phase functions with previously derived phase functions, the shape is of more interest than the absolute magnitude, so our mean curves were normalised by the average value of the Cooper et al. (2019) mean phase function. Results: Figure 2 shows the temporal distribution of the last three years of PFSS observations. The MY 34 results are described in detail in Cooper et al. (2019). Figure 2 – Temporal distributions of PFSS observations for the past 3 Mars years. Observations are distributed between morning and afternoon with a 2.5 hour keepout around local noon. In MY 35, there were a total of 26 PFSS observations, with 13 morning and 13 afternoon observa- tions, spanning Ls=55.0° to Ls=159.4° (sols 2471 to 2691). In MY 36, there were a total of 30 PFSS observations, with 13 morning and 17 afternoon observations, spanning Ls=43.7° to Ls=164.0° (sols 3115 to 3368). Of these, the two penultimate observations (sols 3353 and 3359) were excluded as they were taken during a regional dust storm, and it was not possible to determine if the features seen in the frames were water-ice clouds or dust features. Aside from the above exceptions, every observation contained at least one movie in which clouds could be identified, for a total of 174 movies in MY 35 and 196 movies in MY 36 showing cloud features. The calculated phase function values for MY 35 spanned scattering angles 32.9° to 154.2° and had normalised phase function values between 2.84×10-3 and 0.718. The values for MY 36 spanned scattering angles 39.6° to 139.9° and had normalised phase function values between 6.66×10-3 and 0.556. It was difficult to see cloud features at smaller scattering angles due to the solar keepout and due to image artifacts as the frames moved closer to the sun, obscuring clouds which may have been present. A moving average with a window size of 25 was used to produce the mean curves for both Mars years. For both phase functions, shown in Figure 3 plotted alongside the MY 34 mean curve, there is a greater magnitude at scattering angles <60°, which decreases as scattering angle increases, until the curve flattens after about 100°. As mentioned, we are primarily interested in the shape of the curve rather than the absolute magnitude. The three phase functions all have a similar shape, with small differences in normalised magnitude falling within their 95% confidence intervals. We do not see any increase in normalised magnitude towards lower scattering angles, and in fact the three curves seem to decrease at scattering angles <40°. In attempting to determine the dominant waterice crystal geometry, we also compared the MY 35 and 36 mean curves with the phase function curves of seven modelled ice crystal geometries: hollow and solid hexagonal columns, bullet rosettes, plates, aggregates, spheres and droxtals (Yang & Liou, 1996; Yang et al., 2010). This comparison is shown in Figure 4. We found that there was no good agreement with any one of these modelled water-ice crystal habits, and that spheres in particular, which have been assumed by climate modellers, do not fit our mean phase functions well. Figure 3 – Comparison of the three last years of ACB cloud phase functions. Figure 4 – Comparison of MY 35 and 36 mean phase function curves to seven water-ice crystal habits modeled by Yang & Liou (1996) and Yang et al. (2010). We were also interested in any difference between the morning and afternoon water-ice crystal habit. As described earlier, pervious works have found differences in optical thickness and altitude in morning and afternoon clouds, which could indicate different formation mechanisms (Kloos et al., 2018; Campbell et al., 2019). We separated the morning and afternoon observations for both Mars years. In MY 35, 78 of the 172 data points were morning observations, and the remaining 94 were afternoon. In MY 35, 80 of 196 were morning observations, with the remaining 116 being afternoon. The comparisons for both Mars years are shown in Figure 5. In both cases, the same normalisation around the Cooper et al (2019) mean curve is used. In both Mars years, the morning and afternoon phase functions are nearly identical in shape and magnitude. major impact on the dominant ice crystal geometry within the clouds. The similarities in the mean curves for both morning and afternoon phase functions also indicate that there is no difference in ice crystal habit in these clouds, even if they are formed by different mechanisms. It is difficult to say just what the dominant ice crystal geometry is for these clouds, although the lack of a strong agreement with any single one of the modeled ice crystal phase functions could indicate that the clouds contain more than one shape of ice crystal. Acknowledgements: This work was funded in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) Technologies for Exo-planetary Science (TEPS) Collaborative Research and Training Experience (CREATE) program and the Canadian Space Agency’s MSL Participating Scientist Program. The authors also wish to thank the Mars Science Laboratory science team. Figure 5 – Morning and afternoon mean phase functions plotted together for (a) MY 35 and (b) MY 36. Discussion & Conclusions: The main discrepancy in our derived phase functions is the lack of an increase in magnitude towards the forward scattering direction. This increase can be seen in the seven modelled ice crystal habits, and in other derived Martian phase functions of both water-ice clouds (e.g. Clancy & Lee, 1991; Clancy et al., 2003) and dust (e.g. Tomasko et al, 1999). While there is a lack of data at scattering angles close to 0°, we would still expect to see this increase in magnitude at scattering angles <40°. It is likely that this lack of a forward scattering increase is not an actual indication of the scattering properties of the ACB clouds. Other studies do see this increase, and the physics of scattering would predict this feature for any reasonable cloud particles. Instead, we hypothesise that the apparent flattening of the mean curve at angles below 40° is an artifact. It may be the case that the proximity of the sun at lower scattering angles, which rendered some frames completely unusable, interfered with the phase function calculation. As a result, the curve becomes untrustworthy at scattering angles >~40°. If we consider only the mean phase function curves above 40°, we see an agreement between the MYs 34, 35 and 36 ACB phase functions. This indicates that the MY 34 GDS likely did not have any References: [1] Moores, J.E. et al (2015) Adv. Sp. Res., 55, 2217–2238. [2] Kloos, J.L. et al (2018) JGR: Planets, 123, 233-245. [3] Cooper, B.A. et al (2019) P&SS, 168, 62-72. [4] Wolff, M.J. et al (1999) JGR, 104, 90279042. [5] Wolff, M.J. et al (2019) Icarus, 332, 24-49. [6] Benson, J.L. et al. (2003) Icarus, 165, 34-52. [7] Giuranna, M. et al. (2021) Icarus, 353, 113406. [8] Campbell, C.L. et al. (2020) P&SS, 182, 104785. [9] Clancy, R.T. & Lee, S.W. (1991) Icarus, 93 (1), 135-158. [10] Clancy, R.T. et al. (2003) JGR, 108 (E9), 5098. [11] Kloos, J.L. et al. (2016) Adv. Sp. Res., 57 (5), 1223-1240. [12] Lemmon, M.T. et al. (2015) Icarus, 251, 96111. [13] Yang, P. & Liou, K.N. (1996) Appl. Opt., 35 (33), 6568. [14] Yang, P. et al. (2003) JQSRT, 79-80, 11591169. [15] Tomasko, M.G. et al. (1999) JGR: Planets, 104 (E4), 8987-9007.