Efficient calculation of radiative intensity including the polarization effect in moderately thick atmospheres using a truncation approximation. (January 2022)

• Record Type: Journal Article
• Authors: Momoi, Masahiro; Irie, Hitoshi; Nakajima, Teruyuki; Sekiguchi, Miho
• Is Part Of: Journal of quantitative spectroscopy & radiative transfer. Volume 277(2022)
• Publication Date: 2022-01
• Subjects: Polarization radiative transfer -- Delta-M method -- Truncation correction methods -- Sky radiance measurements; Spectrum analysis -- Periodicals; Radiation -- Periodicals; Analyse spectrale -- Périodiques; Rayonnement -- Périodiques; Radiation; Spectrum analysis; Periodicals; 543.0858
• DOI: 10.1016/j.jqsrt.2021.107976
• Languages: English
• ISSNs: 0022-4073

Abstract

Highlights: Correction methods (P n -IMS) for polarized radiances with the delta-M method were developed under aerosol-laden atmospheres. Methods reconstruct Q and U components within 0.2% with respect to the total radiances in the 340–1020 nm spectral region. P 3 -IMS reconstructs total radiances within 1% with a low stream (~10 in the hemisphere) in the 340–1020 nm spectral region. Abstract: The computational efficiency of solving the radiative transfer equation is an important issue for remote sensing and monitoring of aerosols and radiation. This study developed a novel calculation method for polarized radiance named P n -IMS (Improved Multiple and Single scattering approximation by n -th order multiple scattering correction of the forward Peak P n ), consisting of P 1 -IMS, P 2 -IMS and P 3 -IMS. The P 1 - and P 2 -IMS methods are extended versions of the TMS (Truncated Multiple and Single scattering approximation) and IMS (Improved Multiple and Single scattering approximation) methods of Nakajima and Tanaka (1988), and are, respectively, the first and secondary order scattering corrections of the forward peak of the scattering phase function in the scalar approximation of the radiation field. We extended these methods to include the polarization effect based on the vector radiative transfer theory. We also developed the third order scattering correction named P 3 -IMS method and generalized the formula for any n -th order scattering. A series of numerical tests were performed to indicate that the P 1 -IMS method is accurate enough to reconstruct the Stokes parameters to within 0.2% with a hemispheric Gaussian stream number as low as N = 10 in the hemisphere, except for total radiance. The total radiance in the solar aureole region requires a higher order scattering correction by the P 2 - and P 3 -IMS methods. Numerical tests indicated that the P 2 - and P 3 -IMS methods have an accuracy within 5 and 1%, respectively, with N = 10 in the 340–1020 nm spectral region in a moderately thick atmosphere at an aerosol optical thickness at 500 nm of < 1. Thus, the P 3 -IMS method is an efficient calculation method more than the single scattering correction method required N > 20. Graphical abstract: Image, graphical abstract