Accounting for Gaussian quadrature in four-stream radiative transfer algorithms

- Various Gaussian quadrature (GQ) have been systematically discussed.
- All types of GQ have aaplied to four-stream solar and infrared radiative transfer algorithms.
- The satellite observation data are used to evaluate the GQ schemes.
- For solar radiation, GQ with moment power m=1 produces more accurate results than other GQ schemes.
- For infrared radiation, the GQ with moment powers m=0 and m=2 show superior accuracy in heating rate and flux.

The Gaussian-Legendre, Gaussian-Lobatto, Gaussian-Chebyshev and Gaussian quadrature (GQ) with different moment powers have been investigated by applying them into the four-stream solar and infrared radiative transfer algorithms. For solar radiative transfer, the Gaussian-Chebyshev and GQ with moment power m=0 show relatively accurate results compared to other types of 2GQ in a single-layer scattering medium. In a real atmospheric profile including gaseous transmission, Gaussian-Chebyshev and GQ with moment power m=0 are comparable in accuracy for cloud heating rate. GQ with moment power m=0 produces more accurate results in the upward flux at the top of the atmosphere, while Gaussian-Chebyshev produces more accurate results in the downward flux at the surface. These results have been confirmed in evaluations by using satellite observation data. For infrared radiative transfer, the GQ with moment powers m=0,2,4 show relatively accurate results in effective emissivity for a single-layer scattering medium. In a real atmospheric profile, the GQ with moment powers m=0 and m=2 show superior accuracy in heating rate and flux. In addition, the evaluations using satellite observation data also show that the accuracy of GQ with moment powers m=0 and m=2 is comparable. Both the schemes are the best candidates for the four-stream radiation algorithms.