The intensity and polarization of sunlight reflected by terrestrial water clouds are computed with the doubling method. The calculations illustrate that this method can be effectively used in problem involving strongly anisotropic phase matrices. The method can therefore be used to derive information about planetary clouds, including those of the earth, from polarimetric observations.
The results of the computations indicate that the polarization is more sensitive than the intensity to cloud microstructure, such as the particle size and shape. Multiple scattering does not wash out features in the polarization as effectively as it does in the intensity, because the polarization arises primarily from photons scattered once or a small number of times. Hence polarization measurements, particularly in the near infrared, are potentially a valuable tool for cloud identification and for studies of the microphysics of clouds.
The computations are made primarily at four wavelengths in the near infrared, from 1.2 to 3.4μ. The results for λ=1.2μ are also applicable to scattering at visual and ultraviolet wavelengths. The other wavelengths are selected to illustrate the basic scattering characteristics in the near infrared for reflection of sunlight from water clouds.
It is shown that the intensity computed with the exact theory including polarization differs by ≲1.0%1.0 from the intensity computed in the common scalar approximation in which the polarization is neglected. Therefore, when only the intensity is required, and not the polarization, it is possible in most cases to neglect polarization entirely.
An approximation obtained by setting the phase matrix elements P34(α) and P43 (α) equal to zero is proposed and tested. It is found that this introduces errors less than one part in 106 for the intensity and errors ≲0.0002 in the degree of polarization. This means that in computing the polarization properties for multiple scattering by spherical particles it is usually adequate to work with 3 by 3 matrices.
An examination is made of the accuracy of the polarization in the approximation in which it is assumed that multiply scattered photons are unpolarized. A modified version of this, which, in addition, takes advantage of the fact that diffracted fight is nearly unpolarized, is also tested. The modified approximation is found to yield an improved accuracy in most cases.
Another approximation,which can be termed a renormalization method, is described and tested. The method consists of modifying the phase matrix for single scattering so that the integrations over zenith angle can he performed with a small number of points. The, order of the approximation (the number of zenith angles in the integrations) can easily be varied and accuracies sufficient for practical applications can be obtained at low orders of approximation. The method is therefore useful for small computers.