## 1 Introduction

[2] Space- and ground-based snowfall measurements are necessary when monitoring the impact of winter-type precipitation on the environment in local and global scale. With the presence of radars and passive radiometers onboard satellites, such as NASA's Global Precipitation Measurement, CloudSat, and Aqua missions, and ESA's EarthCARE, there is a demand to know how snowflakes scatter microwave radiation. Due to the large morphological variance of snowflakes, it is also crucial that the computational methods are accurate and efficient in order for them to be operationally useful. There has already been systematic forward modeling at microwave frequencies for single ice crystals by *Liu* [2008] and *Hong et al.* [2009], but not for aggregates of ice crystals due to the many free parameters in such shape models.

[3] The retrieval of snow microphysical parameters from backscattered signals is an ill-conditioned inverse problem. To reduce the number of unknowns, assumptions are needed. Forward scattering modeling can be a valuable aid in choosing the assumptions made. To this end, it is important to have a reliable forward model for the assessment of the impact of different physical properties of snowflakes on scattering. Ideally, such a model should also be conceptually simple and computationally inexpensive.

[4] Accurate computations can be obtained using the discrete-dipole approximation [*Purcell and Pennypacker*, 1973] or other methods that are applicable for arbitrarily shaped scatterers. Although these methods can be expected to give reliable results, they are computationally expensive. The traditional approach has been to simplify the shapes of the snowflakes, modeling them as spheres or spheroids [e.g., *Bohren and Battan*, 1980; *Hogan et al.*, 2000; *Korolev and Isaac*, 2003; *Matrosov*, 2007; *Austin et al.*, 2009] and compute the scattering properties using the exact numerical methods available for such shapes. For spheres, the Mie solution [Mie, 1908] is used; for spheroids, the *T*-matrix method [Waterman, 1965] is commonly applied. However, it has been recognized recently that for snowflakes larger than the wavelength, the backscattering cross-sections given by these shape models can introduce an absolute error as high as orders of magnitude [Ishimoto, 2008; Botta *et al.* 2010; Petty and Huang, 2010; Tyynelä *et al.* 2011].

[5] An alternative approach is to simplify the physics of the scattering theory instead of the target shape. One such theory is the Rayleigh-Gans approximation [Bohren and Huffman, 1983]. The RGA neglects the higher-order interactions of electromagnetic radiation within the particle, considerably simplifying the mathematics of the problem. In RGA, the scattered wave from the whole particle is simply a superposition of the scattered waves originating from different parts of the particle; the interactions between the parts are ignored. This allows the scattering matrix to be determined from a straightforward integration over the particle volume. When the snowflake is represented as a volumetric model composed of small volume elements (such as the dipoles in the DDA), the integral is fast and straightforward to calculate numerically. Another potential benefit is that the simple formula of the Rayleigh-Gans integral allows one to study the scattering properties analytically, providing a tool to connect microphysics and scattering properties.

[6] The Rayleigh-Ganbvs theory has been recognized to be suitable for computing scattering from fractal aggregates [Berry and Percival, 1986] and has been previously applied to snowflakes on theoretical grounds [Matrosov, 1992; Westbrook *et al.* 2006; Hogan *et al.* 2012]. However, no comprehensive validation of the applicability of the RGA on realistically shaped snowflakes has been performed. In this paper, we perform such a validation by comparing the results of the RGA and DDA computations for aggregate snowflakes of different ice crystal types generated with a physically based model. We have chosen nine frequencies from the range that is the most relevant for cloud and precipitation remote sensing: 3, 14, 36, 60, 90, 120, 150, 180, and 220 GHz. For the refractive indices of water ice at different frequencies, we use the formulas by *Jiang and Wu* [2004].