Evaluation of Higher‐Order Quadrature Schemes in Improving Computational Efficiency for Orientation‐Averaged Single‐Scattering Properties of Nonspherical Ice Particles

Abstract

We evaluate several high‐order quadrature schemes for accuracy and efficacy in obtaining orientation‐averaged single‐scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation‐averaged SSPs derived from realistic hydrometeors as input to radiative transfer models (RTM). The DDA has been a popular choice for single‐scattering calculations, due to its versatility with respect to target geometry. However, being iterative‐solver‐based (ISB), the most used DDA codes, for example, DDSCAT and ADDA (formerly, Amsterdam DDA), must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation‐averages can increase drastically and so does the computation cost incurred by the ISB‐DDA methods. MIDAS is a Direct‐Solver‐Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB‐DDA methods. MIDAS, when combined with high‐order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM‐ready SSPs of complex‐shaped hydrometeors than existing ISB‐DDA methods, with the native quadrature schemes they offer.

Fair Evaluation of Orientation‐Averaging Techniques in Light‐Scattering Simulations: Comment on “Evaluation of Higher‐Order Quadrature Schemes in Improving Computational Efficiency for Orientation‐Averaged Single‐Scattering Properties of Nonspherical Ice Particles” by Fenni et al

“…Moreover, one can also add another conclusion to this list, namely inherent smoothing in CBFM can accelerate orientation averaging for a fixed required accuracy (at the cost of more complicated error control). However, the comment shows that many of the quantitative conclusions of Fenni et al (2021), like "can be greater than three orders of magnitude more efficient" are based on very specific test cases, and need significant changes (and further research) to be generalized to other ones.…”

“…Second, the DSB methods with CBFM acceleration may outperform the ISB DDA for backscattering properties of large highly porous and/or very non-compact particles (which volume is much smaller than that of the circumscribing rectangular box), when orientation averaging is required. Note, however, that this specific superiority niche is not accurately described in the abstract of Fenni et al (2021), where too general phrase "complex-shaped" is used. Moreover, one can also add another conclusion to this list, namely inherent smoothing in CBFM can accelerate orientation averaging for a fixed required accuracy (at the cost of more complicated error control).…”

“…Moreover, the errors introduced by some values of these parameters depends on the specific problem, voxel size, and number of orientations. Therefore, further analysis is somewhat speculative due to the limited amount of data in Fenni et al (2021).…”

“…This aggregate has a strong dependence of backscattering intensity on rotation angles with a peak at the default orientation (due to a specular reflection from one plane constituent). Thus, the angular region, where most of the integral value is gathered, happens to be greatly undersampled by the default orientation averaging scheme of DDSCAT, see Figure 11 of Fenni et al (2021). A simple fix for this issue is a random initial (one-time) rotation of the aggregate before further averaging is performed.…”

Response to Comment Paper by Dr. Maxim A. Yurkin for 2021 JGR Paper “Evaluation of Higher‐Order Quadrature Schemes in Improving Computational Efficiency for Orientation‐Averaged Single‐Scattering Properties of Nonspherical Ice Particles”

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In Fenni et al (2021), hereafter F21, subject of the present discussion, we evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use our efficient scattering model MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes.To better frame the discussion, we would like to recall the background of and motivations to the study reported in F21.

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