Monte Carlo calculations of multiple-scattered contributions to the total energy received in a lidar beam have been made for a representative cirrus ice-cloud scattering phase function. The phase function is varied arbitrarily near the back direction to give three different scattering patterns. The Monte Carlo method of Plass and Kattawar (1971) has been modified and extended to give a greatly increased efficiency for a small decrease in accuracy. This modification has reduced the computation time by ∼80% allowing routine calculations to be made on many different cloud models. When applied to two water cloud models the method gives results which agree well with those obtained by previous workers, The purpose of. the calculations is to investigate the apparent reduction in the cloud optical depth due to multiple scattering when measured by a lidar. This reduction is described here by a multiple scattering factor η It is found that for cirrus clouds the factor η varies considerably with the depth of cloud penetration, with the cloud optical depth and with the cloud extinction coefficient.
The calculations show for the first time the pattern of contribution from each order of scattering separately. It is shown that for cloud optical depths ≳0.1 a model which considers double scattering only is inadequate.