Session Papers 241 Electromagnetic Scattering by Spheroidal Particles H. A. Eide, K. Stamnes, and F. M. Schulz University of Alaska, Fairbanks Fairbanks, Alaska J. J. Stamnes University of Bergen Norway Abstract Clouds are of paramount importance for the global energy balance and, thereby, our climate. Changes in cloud cover and phase (liquid water versus ice), for example, through increased greenhouse forcing, may have significant and as of yet unknown impacts on our climate. The global climate models (GCMs) designed to predict future climate, usually model the effects of clouds using the scattering and absorption properties of spherical particles at high latitudes as well as at high enough altitudes anywhere on our planet. This leads to errors of undetermined magnitude because the clouds there consist of ice crystals that are far from spherical in shape. Ice particles usually take on needle-like or flat, disk-like shapes. The GCMs therefore cannot correctly predict the evolution of our climate. We have developed a new method for calculating the single scattering solution for spheroidal particles. The single scattering solution is needed for every particle shape that we want to include in a GCM. The spheroidal particles can easily be made to closely resemble actual ice particles, and we can hence, more accurately model the scattering and absorption of radiation by polar and high altitude clouds. An important part of the single scattering solution for spheroidal particles is the calculation of the expansion coefficients that we need in the angular and radial spheroidal functions. Problems that hampered previous implementations for finding these coefficients have been overcome, and we can now handle realistic sizes and shapes, as well as particle absorption in an effective manner. In this paper, we present our new method for computation of expansion coefficients. Introduction In the separation of variables method (SVM) for scattering by spheroidal particles, a critical point is the calculation of the eigenvectors (or coefficients) for the corresponding eigenfunctions. Traditionally, the method attributed to Bouwkamp (1941) is used for this purpose. Here, we present a new method that yields high precision eigenvalues as well as the eigenvectors (coefficients) needed in the eigenfunction expansions. This is accomplished in an efficient and reliable manner using readily available computer routines. The method is not limited to real or purely imaginary values of the size parameter c, and high precision results have been obtained as well for values of c (c ≤ 40) for which benchmark results are available. When we use this method together with routines for calculating the spheroidal functions, we get excellent agreement with published results (Hanish et al. 1970; Van Buren et al. 1975), but we need to conduct further tests to establish if this new method constitutes an improvement compared to Bouwkamp’s method. In a companion paper (Schulz et al. 1998a), a method for computing the T-matrix with the SVM is presented. In this paper, we show results obtained by using our method to compute the coefficients and this modified SVM approach, and we give an overview of our current and future work on this subject. The Spheroidal Differential Equation As is well known, the Helmholtz scalar wave equation ( 29 0 k 2 2 = Ψ + ∇ is separable in the spheroidal coordinate system. The solution is given by ) ( ) ( R ) ( S φ Φ ξ η = Ψ (1) where S, R, and Φ are the angular, radial, and azimuthal components, respectively. As an example, the radial function of the first kind for the case of a prolate spheroidal particle can be written as