Implementation of the T-matrix method on a massively parallel machine:: a comparison of hexagonal ice cylinder single-scattering properties using the T-matrix and improved geometric optics methods

This paper describes a series of improvements to an already existing T-matrix implementation for calculating the single-scattering properties of non-axisymmetric particles at large size parameters. The improvements aim to use the computational resources in terms of memory and time as efficiently as possible by taking into account various simplifications of the T-matrix fonnulation. In this paper, the randomly oriented hexagonal ice crystal is considered and the orientational averaging is done analytically. Within the framework of the T-matrix approach, symmetries of the hexagonal cylinders allow the formulation of eight independent subproblems, for each of which the memory demand is reduced by a factor of 144 compared to the general formulation. The memory demand strongly increases as a function of size parameter. For non-axisymmetric particles, memory demand rises approximately as the fourth power of the size parameter. In order to have more memory available, the T-matrix code was parallelized and implemented on a multi-processor CRAY T3E supercomputer. Extended precision is software emulated. With these new developments the single-scattering properties of randomly oriented hexagonal columns can be calculated for size parameters up to about 40. This size parameter reaches into the region of improved geometric optics (IGO), which is applicable down to size parameters of around 20. Comparisons of IGO and T-matrix results for the single-scattering albedo and the extinction efficiency show that at a size parameter of around 30, the single-scattering albedos are generally within about 2%. IGO underpredicts the extinction efficiency by 4% at lambda = 3.775 mum and by 11% at the more absorbing wavelength of lambda = 4.9 mum. This underprediction may be due to the version of IGO used since this does not take into account the inhomogeneity of the refracted wave in an absorbing medium. Crown Copyright (C) 2003 Published by Elsevier Science Ltd. All rights reserved.