Study On Radiative Transfer Parameterized Solutions For Continuous Variation Of Cloud Micro-physical Properties

In this article, improved two-stream radiative transfer inhomogeneous solutions(including short wave solution and long wave solution) have been proposed to deal with the problem of continuous variation of cloud micro-physics model layers of inhomogeneous optical properties. This algorithm uses the standard perturbation method to include the inhomogeneous effect caused by continuous variation in vertical direction of the asymmetry factor and the single scattering albedo. We found the inhomogeneous solutions are not only suitable for dealing with vertical inhomogeneous clouds, but also for vertical inhomogeneous snow. Therefore, we study the accuracy of the inhomogeneous solutions from the idealized medium, low cloud and pure snow. The results show that the accuracy of the inhomogeneous solution is much higher than the classical two-stream radiative transfer solution(homogenous solution). The concrete results are as follows:(1) Solar wave: for idealized medium, the relative errors in reflection and absorption calculated by the inhomogeneous solution increase with optical depth,and the relative errors can be over 20% in homogeneous solution. However, the relative errors from the inhomogeneous solution are not very sensitive to the optical depth and the relative errors are limited to 4% in most cases. Results in low clouds show: in the spectral band of 0.25-0.69?m, the relative errors in absorption by the inhomogeneous solution are bounded by 1.4%, but the errors by the homogeneous solution can be up to 7.4%. In the spectral band of 0.25-0.69?m, for pure snow the relative errors in absorption by the homogeneous solution are up to 72%, but reduced to less than 40% by using the inhomogeneous solution. At the spectral wavelength of 0.94?m, both for clouds and snow, the results of reflection and absorption by the inhomogeneous solution are also more accurate than those by the homogeneous solution.(2) Long wave: for idealized medium, the relative errors in upward emissivity and downward emissivity calculated by the inhomogeneous solution are obviously less than results calculated by the homogeneous solution. In general, but relative errors for upward emissivity can reach 5% in homogeneous solution, and relative errors from the inhomogeneous solution is not more than 1.4%. For the downward emissivity, the errors of inhomogeneous solution are basically one order less than the homogeneous solutions. The errors of the inhomogeneous solution are less 0.8%,while the relative error of the homogeneous solution can up to 7%. From the results of low clouds, the relative error of the downward emissivity of the inhomogeneous solution is about 1.8%, while the relative error of the homogenous solution is 12%for the 5-8?m band. For the low cloud at the wavelength of 11?m, the relative error of the upward emissivity from inhomogeneous solution is less than 0.5%, and the relative error is about 1.7% in homogenous solution. The relative error of upward emissivity from inhomogeneous solution is about 1.4% The relative error of homogenous solution is more than 9%. The results of pure snow show that the accuracy of the inhomogeneous solution is higher than the homogeneous solution in the 5-8?m band and 11?m wavelength.