## 1 Introduction

[2] Particle radiation is a comprehensive subject that involves many domains, such as astrophysics, optics, meteorology, and combustion, and that attracts extensive interest and has always been an alluring field in radiation studies [*Cai and Liou*, 1982a, 1982b; *Mishchenko et al*., 2000; *Kokhanovsky*, 2006; *Forster*, 2007; *Shell and Somerville*, 2007; *Liou et al*., 2011]. Currently, much more attention is focused on how to make models closer to the actual situation. Subjects such as nonspherical particle radiation and Gaussian wave incidence [*Wu et al*., 2005; *Han et al*., 2012] have drawn the interests of many scholars. There are various particle morphologies in nature, and previous research has shown that most of these particles are nonspherical and have irregular shapes with no particular habits [*Reid et al*., 2003; *Muñoz et al*., 2006], which makes the modeling of the particle complex difficult. Ping Yang and colleagues [*Yang et al*., 2007] indicated that due to the nonspherical effect, the application of the Lorenz-Mie theory may result in a substantial underestimation or overestimation of radiative forcing. Therefore, many improved numerical methods, such as the Discrete Dipole Approximation [*Mugnai and Wiscombe*, 1986; *Draine and Flatau*, 1994; *Nebeker et al*., 1998; *Yurkin and Hoekstra*, 2007, *Yurkin et al*., 2007], the T-Matrix [*Mishchenko et al*., 1997; *Yang et al*., 2007; *Feng et al*., 2009], the finite difference time domain [*Yang et al*., 2000], and the Geometrical Optics (GOM) [*Cai and Liou*, 1982a, 1982b; *Macke*, 1993] are often applied. In addition, *Yang et al*. [2007] showed that spheroids can be seen as the first-order approximation of the overall shapes of nonspherical particles, and previous research [*Mishchenko et al*., 1997; *Dubovik et al*., 2006] discussed using shape mixtures of randomly oriented spheroids for modeling desert dust aerosols. However, calculations based on simple assumptions are often inaccurate and previous research [*West et al*., 1997; *Zhao et al*., 2003; *Wang et al*., 2003; *Volten et al*., 2005] revealed the inevitable differences caused by low-order approximation of the particle shape [*Yang et al*., 2007]. In this paper, we do not intend to compare the advantages and disadvantages of each method but would like to try to provide a new way of thinking for the modeling of large, complex-shaped particles.

[3] To model particles with various morphologies, two concerns were mainly considered: (1) the model must be capable of recapitulating the external form of the particle with good accuracy. Early research reduced irregular particles to their equivalent sphere so that the Mie theory could be applied. Alternatively, complex particles were converted into spheroid or cylindrical shapes to simplify the calculation, resulting in the loss of much of the shape information. It is logical to infer that more missing information results in a less accurate in the model. (2) The model must have a certain commonality, which means that it is not proposed to fit for just one particular type of particle but is able to calculate particles of different shapes as well as complex constituents. However, the requirements of the accuracy and commonality of the model actually contradict one another; therefore, a balance must be made between the two requirements.

[4] In this paper, a particle superposition model combined with the Monte Carlo ray tracing algorithm is proposed to describe scattering by irregularly shaped particles with overall size and features in the geometric optics regime. The application of a geometrical optics approximation dealing with large particle radiation has been discussed by many scholars [*Cai and Liou*, 1982a, 1982b; *Macke*, 1993; *Yang et al*., 2000; *Gusarov*, 2008, 2010; *Mishchenko et al*., 2011]. Previous research [*Mishchenko et al*., 2011] showed the limits of GOM when dealing with spherical aerosols but also showed that it is quite useful when applied to nonspherical particles. In previous research by *Gusarov* [2008, 2010], rigorous ray-optics calculations were applied (in the case of heterogeneous media) in the limit of geometrical optics and showed no contradiction with the known calculations by ray optics and Monte Carlo simulations and agree with the known experimental data [*Gusarov*, 2008]. The Monte Carlo method (MCM) has a clear physical concept and possesses the advantage of strong adaptability, which is especially suitable for the study of radiation with multidimensional, complex geometrical shape, and complicated boundary conditions. In our opinion, GOM combined with MCM is a simple and intuitively appealing approximation method with credible accuracy, which showed very good fit in our study. *Macke and Mishchenko* [1996] offer a publicly available and well-developed Monte Carlo ray tracing model. The model presented in the current study is based on a similar Monte Carlo ray tracing algorithm but, in addition, provides a simple and flexible way to build an irregularly shaped particle (namely, as a superposition of geometric optics regime spheres of different sizes and levels of overlap).

[5] The basic concept of the model is explained, and a detailed flow chart and a description of the algorithm are provided in section 2. Four different shapes of nonspherical particles were calculated, and the independent radiative characteristics of these particles under monochromatic collimated light were analyzed. Comparisons of data from simple irregular particles were made between the model proposed and the other proven method. The effect of particle orientation under collimated light was also discussed.