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• W2044702961 abstract "In the shortwave and for a scattering medium, the “exact” radiance can be calculated by solving the radiative transfer equation for each frequency using a line-by-line absorption model. In practice, however, this technique requires exhaustive amounts of computer time. This article describes a fast, accurate method for approximating radiances at the same spectral resolution as satellite observations and for an absorbing and scattering atmosphere that is vertically heterogeneous. In the method, interactions between molecular absorption and scattering are treated using an extension of the Scaling Approximation (SA). The original SA can be applied when the absorption coefficient kv(z) at the frequency v and the altitude z can be factored as kv(z) = h(z)kv(z0). This approximation, however, is only accurate for the Lorentz line wings. For a given atmosphere, the exact radiance is calculated for the profile h(z), which represents the vertical variation of the absorption profile for the line wings and for some absorption coefficients kv(z0) distributed in the interval [0, + ∞[. Due to the slow spectral variation of atmospheric scattering parameters, these calculations can be considered valid for large spectral bands. In the line wings the monochromatic radiances can then be obtained through interpolation. In the more general case, the SA is modified in order to compensate for errors it introduces to the line centres and the intermediate absorbing regimes: kv(z) = h(z)kv∗(z0), thus giving the Modified Scaling Approximation (MSA). The modified absorption coefficient kv∗(z0) is calculated by (1) defining an equivalent reflecting level for the scattering photons and (2) requiring that the absorption of the non-scattering atmosphere, defined by the equivalent reflecting level, be the same for the “exact” vertical absorption profile and the line wings profile h(z). The equivalent reflecting level is obtained from simulations performed for an intermediate absorption regime between the wings and the line centre. The approximate radiances are interpolated according to the modified absorption coefficient. The maximum error introduced to the monochromatic radiance computation, corresponding to the line centre, is less than 10% of the radiance without absorption and typically less than 1% in the wings and the intermediate regimes. Upon integrating the monochromatic radiances over the spectral interval, the maximum error is on the order of 1% for a resolution of 1 cm−1 and on the order of 0.1% above 5 cm−1." @default.
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• W2044702961 date "1996-01-01" @default.
• W2044702961 modified "2023-09-29" @default.
• W2044702961 title "High spectral resolution solar radiative transfer in absorbing and scattering media: Application to the satellite simulation" @default.
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• W2044702961 doi "https://doi.org/10.1016/0022-4073(95)00134-4" @default.
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