## 1. Introduction

[2] Saharan sand grains are irregularly shaped particles with a rounded shape and a surface covered with structures in many scales. They are also internally inhomogeneous. The importance of these details for light scattering depends on the particle size relative to the wavelength of light considered. The larger the particle, the more important the particle geometry is for scattering. For example, comparison of simulations using spherical and spheroidal shapes clearly shows that simplifications in shape can result in large errors in remote sensing of atmospheric mineral aerosols [e.g., *Mishchenko et al.*, 1995, 1997; *Pilinis and Li*, 1998]. How well the detailed shape and inhomogeneity can be taken into consideration in light-scattering modeling depends on the model used; the choice of usable methods depends mostly on the particle size relative to the wavelength of light considered.

[3] For atmospheric mineral particles with a radius over a micron, for which we can expect the shape and structure to be most important at visible wavelengths, there are very few applicable light-scattering methods in which detailed particle geometry can be taken into account [see, e.g., *Mishchenko et al.*, 2000c]. Most analytical methods are restricted to quite simple particle geometries. Numerical volume-integral methods, otherwise quite flexible, are presently limited to rather small particles due to the computational burden. The surface-integral methods can handle only rather simple and large-scale nonsphericities, and they generally cannot handle internal inhomogeneity. When the scale of inhomogeneity is significantly larger than the wavelength of light considered, inhomogeneity cannot be even indirectly incorporated by applying so-called effective-medium approximations [e.g., *Chýlek et al.*, 2000]. It is indeed difficult to accurately model single scattering by large, irregular, inhomogeneous particles.

[4] If the particles are sufficiently large, however, the so-called ray optics approximation (ROA) can be used. In the ROA it is assumed that the curvature of the particle surface is much larger than the wavelength of the incident radiation everywhere on the particle and the surface can thus be considered locally a plane. In addition, it is assumed that the phase differences between internal and external fields across the surface irregularities are sufficiently large to suppress the interference effects associated with the irregularities [*Muinonen et al.*, 1997]. In practice, ROA appears to be valid for smaller nonspherical than spherical particles, even though a sphere is a shape maximizing the surface curvature. This is because, for spherical or other highly symmetric particles, effects due to interference are strong and they are not included in the ROA. If particles are absorbing, then the usability of the ROA for small particles improves further [see, e.g., *Mishchenko et al.*, 2000c, and references therein]. There is not yet a method available to study the lower limit of particle sizes that the ROA method can handle accurately if the shapes are truly irregular. The ROA can handle realistic mineral-particle shapes; it can also, in principle, handle the inhomogeneity. While atmospheric mineral particles are mostly too small for the ROA to be valid under normal conditions at visible wavelengths, there are occasions when most scattering comes from particles that are in the ray optics domain: for example, a sand storm [*d'Almeida*, 1987; *Ichoku et al.*, 1999].

[5] In the geometric optics part of the ROA, the planar surface is thought to reflect incident light specularly. If a particle surface is smooth, such as with liquid droplets, this approach works well. If, on the other hand, there is small-scale roughness on the surface, each plane element can be thought to scatter light rather diffusely. In such conditions, the ROA is in principle not valid. It can be argued, however, that such conditions can be dealt with by modifying the reflection law.

[6] In the present work, we study the possibility of incorporating the small-scale surface roughness and internal inhomogeneity into ROA and estimate its importance in the case of large Saharan dust particles. Such a study is highly relevant for the atmospheres of Earth and Mars, for example, as mineral dust is the most predominant aerosol class observed from space for both atmospheres, and can significantly affect the radiative properties of these atmospheres [e.g., *World Climate Programme*, 1983; *Kieffer et al.*, 1992; *Husar et al.*, 1997]. We expect our results to be applicable also for other particles with similar refractive index, shape, and size, as well as for modeling of surface albedos in sand-like regolith. In addition to the radiative energy budget, aerosol particles are important in many remote sensing applications, as their presence affects the measurements of other atmospheric constituents or meteorological quantities.

[7] Our aim is realistic particle shape modeling, so we apply a statistical shape model, a so-called Gaussian random sphere geometry [e.g., *Muinonen*, 2000b], with statistical parameters derived from a shape analysis. The details of the shape model and the shape analysis are given in section 2.1. We use a traditional ray optics approximation and modify it for diffusely reflecting surface elements and internal structures. We note that it is not a new idea to include inhomogeneity into a ROA model; for example, *Macke et al.* [1996a] used spherical inclusions to mimic the effect of soot particles and air bubbles inside ice crystals in a similar fashion, and *C.-Labonnote et al.* [2001] applied this method to interpret ADEOS-POLDER intensity and polarization measurements over ice clouds. The method has also been applied to planetary regolith particles [see *Macke*, 2000, and references therein]. The surface roughness has also been incorporated previously in the ROA models and used for ice crystals [see, e.g., *Macke et al.*, 1996b; *Yang and Liou*, 1998]. However, the handling of roughness in these papers is different from ours: we also try to account for effects arising from roughness in a scale too small to be taken explicitly into account by ray tracing. Our model bears also some resemblance to the scalar, semi-empirical scattering theory by *Pollack and Cuzzi* [1980]. Our ROA model and the key characteristics of single scattering are considered in section 2.2. In section 2.3, we describe a radiative transfer model used to study the radiative properties of our model particles. We compare the ray optics results with those obtained using the Lorenz-Mie theory, and with laboratory measurements of Saharan particles. The measurements by *Volten et al.* [2001], reviewed in section 3, are especially valuable for us as they include all the independent nonzero scattering matrix elements. Unfortunately, other information about measured scattering matrices of natural mineral aerosol particles is sparse. The results of the single scattering simulations and the radiative transfer simulations are given in section 4. Further discussion of results and their physical interpretation is given in section 5. Finally, the conclusions are drawn in section 6.