EAGER: Develop Robust Light-Scattering Computational Capability Based on the Method of Separation of Variables in Spheroidal Coordinates for Small-to-Large Spheroids

Texas A&M University, College Station TX

Investigators

Abstract

Dust aerosols affect global climate by partially absorbing and reflecting incoming sunlight and heat energy emitted by the atmosphere and the surface. The optical properties of dust particles are critical to reducing uncertainties in the current knowledge of the role of dust aerosols in the climate system, and thus are important for predicting future climate. The dust particle optical properties are also fundamental for inferring dust aerosol characteristics from space-borne and ground-based remote sensing observations. Dust particles are almost exclusively nonspherical. It has been extensively demonstrated that the spheroidal particle shape model represents a quantum leap forward, compared to the spherical model, for computing the optical properties of nonspherical particles. At present, the optical properties of small-to-large particles can be computed only for spheres. There is a pressing need to have an exact and robust computational capability to compute the optical properties of spheroidal particles. Leveraging advances in computational mathematics, advances in electromagnetic scattering theories, and modern computer technologies and computer coding techniques, this project aims to develop a novel program to compute the optical properties of spheroidal particle in the small-to-large particle size range. Because many bacteria, microweeds, oceanic particles, and interstellar dust particles have approximately spheroidal shapes, the outcome of this project will also find extensive applications in climate science (particularly the radiative energy budget in the climate system), remote sensing, industry, bio-optics, oceanic optics, astrophysics, planetary sciences, and other fields beyond atmospheric sciences. Because this project focuses on a major unsolved interdisciplinary problem and because of significant challenges, particularly from the perspective of computational electromagnetics and mathematics, this project is exploratory but potentially transformative, i.e., “high risk – high payoff”. In addition to its scientific merit, this project contains an educational component to train an early-career researcher in the interdisciplinary area mentioned above. This project aims to solve light scattering by a spheroid in spheroidal coordinates. Although solving the electromagnetic wave equation via the method of separation of variables in spheroid coordinates has been explored, the previously developed models are applicable only to particles that are small with respect to the incident wavelength and have little practical use. The major challenge encountered by the previous effort is numerical instability of spheroidal harmonic functions. This project will seek to achieve numerical stability of spheroidal harmonic functions by using advanced algorithms, such as expressing spheroidal functions in terms of the Wigner-d function. The key to computing spheroidal functions is to find eigenvalues of corresponding spheroidal equations. The radial and angular spheroidal equations are of the Sturm-Liouville type. The eigenvalues will be calculated by the invariant-imbedding method, which is expected to be numerically stable and accurate. Thus, the spheroidal functions are expected to be accurate even with extreme parameters. The overarching goal of this project is to develop a numerically stable capability for accurately computing the optical properties of a spheroid beyond the currently applicable particle size and aspect ratio ranges of other existing computational capabilities, such as the discrete dipole approximation method (DDA), the finite-difference time domain (FDTD) method, the extended boundary condition method (EBCM), and the invariant imbedding T-matrix method (IITM). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.