References

Foundational method

  • Plass, G. N., Kattawar, G. W., & Catchings, F. E. (1973). Matrix operator theory of radiative transfer. 1: Rayleigh scattering. Applied Optics, 12(2), 314–329.

  • Hansen, J. E. (1971). Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds. Journal of the Atmospheric Sciences, 28(8), 1400–1426.

Doubling extensions

  • Wiscombe, W. J. (1975). On initialization, error and flux conservation in the doubling method. Journal of Quantitative Spectroscopy and Radiative Transfer, 16, 637–658.

  • Wiscombe, W. J. (1976). Extension of the doubling method to inhomogeneous sources. Journal of Quantitative Spectroscopy and Radiative Transfer, 16, 477–489.

  • Wiscombe, W. J. (1977). The delta-M method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. Journal of the Atmospheric Sciences, 34(9), 1408–1422.

Linearisation and remote sensing

The analytic temperature-Jacobian propagation follows the linearisation of the interaction principle; the accompanying literature (in the repository’s literature/ directory) develops the linearised / doubling–adding machinery used here:

  • Spurr, R., & Christi, M. Linearization of the interaction principle: analytic Jacobians. (literature/Spurr_Christi.pdf.)

  • Hasekamp, O. P., & Landgraf, J. (2001). Ozone profile retrieval from backscattered ultraviolet radiances: The inverse problem solved by regularization. (literature/Hasekamp_Landgraf_2001.pdf.)

  • Hasekamp, O. P., & Landgraf, J. (2005). Linearization of vector radiative transfer with respect to aerosol properties and its use in satellite remote sensing. (literature/Hasekamp_2005.pdf.)

  • Liu, Q., & Weng, F. (2006). Advanced doubling–adding method for radiative transfer in planetary atmospheres. Journal of the Atmospheric Sciences, 63(12), 3459–3465. (literature/Liu_Weng_2006.pdf.)

Project documents

The tex/ directory of the repository contains the internal project notes this documentation is based on:

  • adding_doubling_description.tex — the mathematical description of the forward solver (Theory).

  • temperature_jacobian_plan.tex — the analytic temperature-Jacobian implementation plan (Analytic temperature Jacobians).

  • heating_jacobian_depth_limit.tex — analysis of the depth limit and conditioning of the heating-rate Jacobian (Depth limit of the heating Jacobian).