Precise integration method without inverse matrix calculation for structural dynamic equations

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.

Jacobian matrix for near-infrared remote sensing based on vector radiative transfer model

Due to the polarization effects of the Earth’s surface reflection and atmospheric particles’scattering,high-precision retrieval of atmospheric parameters from near-infrared satellite data requires accurate vector atmospheric radiative transfer simulations.This paper presents a near-infrared vector radiative transfer model based on the doubling and adding method.This new model utilizes approximate calculations of the atmospheric transmittance,reflection,and solar scattering radiance for a finitely thin atmospheric layer.To verify its accuracy,the results for four typical scenarios(single molecular layer with Rayleigh scattering,single aerosol layer scattering,multi-layer Rayleigh scattering,and true atmospheric with multi-layer molecular absorption,Rayleigh and aerosol scattering)were compared with benchmarks from a well-known model.The comparison revealed an excellent agreement between the results and the reference data,with accuracy within a few thousandths.Besides,to fulfill the retrieval algorithm,a numerical differentiation-based Jacobian calculation method is developed for the atmospheric and surface parameters.This is coupled with the adding and doubling process for the radiative transfer calculation.The Jacobian matrix produced by the new algorithm is evaluated by comparison with that from the perturbation method.The relative Jacobian matrix deviations between the two methods are within a few thousandths for carbon dioxide and less than 1.0×10-3%for aerosol optical depth.The two methods are consistent for surface albedo,with a deviation below 2.03×10-4%.All validation results suggest that the accuracy of the proposed radiative transfer model is suitable for inversion applications.This model exhibits the potential for simulating near-infrared measurements of greenhouse gas monitoring instruments.