Computing the angular dependence of the radiation of a planetary atmosphere

Details Computing the angular dependence of the radiation of a planetary atmosphere Computing the angular dependence of the radiation of a planetary atmosphere

May 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981jqsrt..25..403k&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 25, May 1981, p. 403-412.

Computer Science

Numerical Analysis

16

Atmospheric Radiation, Numerical Analysis, Planetary Atmospheres, Radiative Transfer, Accuracy, Interpolation, Spline Functions

Scientific paper

The numerical methods used for solving the transfer equation for a planetary atmosphere often give the specific intensity at a predetermined set of zenith angles, often the Gauss quadrature points. Since these ordinates are not always the ones at which the intensities are needed, some form of interpolation is needed. First, we show that the intensities computed from the moments derived from the spherical harmonics method are identical to those computed from the discrete ordinates method at the Gauss quadrature points. After a discussion of the various contributions to the errors, we compare three interpolation schemes. By far the most accurate way to interpolate the intensity curve is to use the integration of the source function method. We show how this method can be used with a minimum of computational effort. Although less accurate, interpolations are much faster. Not surprisingly, we find that Lagrange interpolation can produce very inaccurate values of the intensities and should not be used. Spline interpolation, on the other hand, always produces reasonable intensities. The accuracy of the spline interpolation can be improved greatly by supplementing the intensities at the Gauss points with values computed by the integration of the source function method at a few key ordinates.

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