Jacobians of Light Scattering Properties Based on the Improved Geometric Optics Method (IGOM)

The partial derivatives or Jacobians of single-scattering properties (SSPs) with respect to microphysical properties are essential in variational remote sensing. The SSPs and corresponding Jacobians for small particles with arbitrary shapes are given by the linearized invariant-imbedding T-matrix algorithm, and the ones for large particles with faceted shapes can be obtained by the linearized physical-geometric optics algorithm. However, the efficient linearized geometric optics algorithm applicable to large particles with arbitrary shapes is still absent. The improved geometric optics method (IGOM) is extensively used to compute the SSPs of large particles with arbitrary shapes due to its high accuracy and efficiency. Consequently, the linearized improved geometric optics method (LIGOM) is presented in this study to compute the SSPs and corresponding Jacobians. The LIGOM can be applied to convex, concave, hollow, aggregate and other shapes with different shape parameters, and is verified by the finite difference method (FDM) for more than ten different shapes. Under the same computational environment, LIGOM achieves speedup ratios of 1.38–2.59 relative to FDM for the tested cases. The LIGOM and other linearized algorithms can be incorporated into linearized radiative transfer models and provide an efficient approach for sensitivity analysis and variational retrievals of aerosol and cloud properties.