On initialization, error and flux conservation in the doubling method

Details On initialization, error and flux conservation in the doubling method On initialization, error and flux conservation in the doubling method

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976jqsrt..16..637w&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 16, Aug. 1976, p. 637-658.

Physics

Optics

25

Atmospheric Optics, Radiative Transfer, Reflectance, Transmissivity, Truncation Errors, Albedo, Atmospheric Scattering, Atmospheric Stratification, Error Analysis, Optical Thickness

Scientific paper

The doubling method is used to perform radiative transfer calculations for plane-parallel, horizontally homogeneous, absorbing-scattering atmospheres. This paper examines truncation and flux conservation errors in the doubling method. The error analysis is performed for five different initial-layer approximations (initializations) as a function of initial layer size, layer optical depth, single-scattering albedo, and phase function asymmetry parameter. The following new results are obtained: (1) derivation of the single-scattering approximation directly from doubling; (2) analytic error estimates useful when the layer optical depth does not exceed 10; and (3) methods for avoiding round-off error when doubling results of high accuracy are desired.

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