 RADIATIVE TRANSFER IN CLUSTERS OF REGOLITH PARTICLES: FUNDAMENTAL SCATTERING UNIT?  K. M. Pitman1, M. J. Wolff2, and E. A. Cloutis3. 1Planetary Science Institute, 1700 E. Fort Lowell Road, Suite 106, Tucson, AZ 85719 USA <pitman@psi.edu>, 2Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301 USA, 3Dept. of Geography, University of Winnipeg, Winnipeg, Manitoba, Canada, R3B 2E9. Introduction: Some assumptions that are held for granted in the theory behind planetary remote sensing interpretation have not yet been fully vetted against first principles physics.  For example, a major assumption that is routinely made in radiative transfer analyses of surface and atmospheric composition is that the individual regolith particle is the fundamental scattering unit. In other words, individual dust and soil particles are considered to be sufficiently well separated (by at least 3 particle radii [1]) such that their interactions with the propagating electromagnetic fields take place in the "far-field." While it is generally recognized that coherent and near-field particle interactions can be important to single scattering phase function and albedo (e.g., increased light scattering at midphase angles, loss of the diffraction peak, and coherent backscatter opposition effect; [2]), adopting the farfield assumption significantly simplifies equations and reduces numerical burden (cf., [3-4]).  Thus, the farfield simplification is used in many applications of classical radiative transfer (RT), both to atmospheres and also to particulate surfaces, including the formulation extensively developed by B. Hapke and collaborators [5 and references therein]. However, for planetary surfaces, this assumption has been challenged in the literature, based in part on experimental measurements of scattering parameters [5-7].  Groups of particles may actually be the fundamental scatterers.  If true, then this would pose a serious problem for interpreting surface properties of Mars, since its constituents (e.g., clays and hydrated sulfates) are especially prone to forming clusters.  Numerical codes and computational firepower now exist to tackle these issues, but what few numerical tests have been attempted in the past were run using a limited number of refractive index datasets, not all of which were relevant to Mars.   In this work, we will conduct a series of numerical experiments that examine these "near-field" effects in a collection of particles within a finite volume using a publicly-available Extended Boundary Condition Method (EBCM) code to understand porosity clustering effects in the Martian surface.  Methodology:  Past numerical studies [8] have explored the range of volume packing fractions for a limited range from less than 1% (i.e., where RT theory is clearly valid; [3]) to about 25%, and those results clearly manifested coherent backscatter (i.e., opposition effect) at the larger volume fractions.  In this work, we will explore a wider range of porosities via a publicly available Extended Boundary Condition Method (EBCM) model: the multisphere T-matrix (MSTM) code [9].  For a group of particles with a specific porosity or packing configuration, each model run generates the scattering, absorption, and extinction efficiencies and cross sections that make up the single scattering albedo; asymmetry parameters; Stokes scattering matrix elements, including the phase function; and maps of electric field distributions.  This particular model has been applied to compute light scattering by layers of particles that are densely packed on planetary surfaces [10-13].  Our numerical experiments will explore the effects of particle packing and clustering on Mars and answer some basic, but important, questions: What happens to scattering properties (single scattering albedo, phase function, etc.) when near-field effects, at least on some scales, are included? Can the individual particle be replaced by a cluster of particles as the fundamental scattering unit (and if so, over what scale; i.e., what cluster size is large enough to include the important effects but remain a numerically tractable problem)?  We will first investigate the effect of modifying the size distribution of particles in a cluster to achieve more realistic filling factors for regolith (52% [7], 43% [2]).  Initially, we will restrict ourselves to a smaller numbers of sphere sizes (e.g., 2-5) that are based on real Mars laboratory analog data. Significance:  We will perform these experiments using representative minerals from the different classes of Mars materials, starting with sulfates. The ultimate goal of this task is to clearly identify and characterize the compositional and size regimes where near-field or clustering effects will fundamentally change the way that Mars spectral and photometric observations are changed.  We will quantify how much clustering lowers the single scattering albedo and modifies the phase function in Mars dust minerals.  When spacecraft data are analyzed, it is generally assumed, for simplicity, that minerals do not form clusters. As a community, we know that this assumption is wrong, especially for Mars aqueous minerals; what is not known is quantitatively how wrong making this assumption is and if it misleads mineral identifications. These numerical experiments will address this directly. Acknowledgments: This work was supported by the Mars Fundamental Research Program (NNX12AH94G; PI Pitman). References:  [1] van de Hulst H. C. (1957) Light scattering by small particles (New York: Dover).  [2] Hapke B. W. et al. (2009) Icarus, 199, 210-218.  [3] Mishchenko M. I. (2006) JQSRT, 101, 540-555.  [4] Mishchenko M. I. (2008) Rev. Geophys., 46, RG2003.  [5] Hapke, B.W. (1993). Theory of reflectance and emittance spectroscopy. Cambridge Univ. Press, New York.  [6] Piatek J. L. et al. (2004) Icarus, 171, 531545.  [7] Hapke B.W. (2008) Icarus, 195, 918-926.  [8] Mishchenko M. I. et al. (2007) Optics Express, 15, 2822-2836. [9] Mackowski D. Multisphere T-matrix (MSTM)http://eng.auburn.edu/users/dmckwski/scatcod es/.  [10] Mishchenko M. I. et al. (2009) ApJ. Lett., 705, L118-L122.  [11] Mishchenko M. I. and Dlugach J. M. (2009) JQSRT, 110, 1706-1712.  [12] Mishchenko M. I. et al. (2010)  Polarimetric remote sensing of solar system objects,. Kyiv, Akademperiodika, 291 [13] Dlugach J. M. et al. (2011) JQSRT, 112, 18641870.  [14] NASA/JPL-Caltech/University of Arizona/Max Planck Institute Surface Stereo Imager Credit:NASA/JPL-Caltech/Univ.AZ/TexasA&M, http://www.nasa.gov/mission_pages/phoenix/news/pho enix-20080626.html    Fig 1: MSTM calculations for clusters of spheres within a circumscribing volume of size parameters X = 2πR/λ =50.  Each individual sphere has size parameter = 5 and complex refractive index of 1.5+0.1i (similar to that of kieserite).  [Top panel] As the number of particles in the cluster increases, the single scattering albedo drops by as much as 15-20%.  [Bottom panel] The evolution of F11 (normalized scattering phase function) as the packing fraction goes from 1% (a single sphere) to 30% clearly demonstrates the importance of properly treating clustering or "near-field" effects.  In a diffuse medium, there would be no change in properties with the addition of more spheres.       Fig 2: [Top panel] Clumps of "Rosy Red" Martian soil particles returned from NASA's Phoenix Mars Lander.  Resolution = 30 µm.  Date: June 20, 2008. Image Credit: [14].  [Middle panel] What look like single "grains" of kieserite in Mars  analog laboratory experiments (left) are actually clusters of smaller particles (average size = 125 microns at 100x zoom).  We will model the clustering behavior of Mars laboratory analogs (right)  using size distributions based on sieve fraction histograms. [Bottom panel] MSTM modeled phase functions of hexahydrite at λ = 0.5 µm for different filling factors (1 - porosity).  41.1% corresponds to a volume of X=46 filled with 25 smaller spheres of size parameter X=10 and 120 spheres of X=5.  18.5% is a 60 sphere system.   
