Multiple-scattering effects on single-wavelength lidar sounding of multi-layered clouds

Abstract. We performed Monte Carlo simulations of single-wavelength lidar signals from multi-layered clouds with special attention focused on multiple-scattering (MS) effect in regions of the cloud-free molecular atmosphere, i.e. between layers or outside a cloud system. Despite the fact that the strength of lidar signals from molecular atmosphere is much lower compared to the in-cloud intervals, studies of MS effects in such regions are of interest from scientific and practical points of view. The MS effect on lidar signals is always decreasing with the increasing distance from the cloud far edge. The decreasing is the direct consequence of the fact that the forward peak of particles phase functions is much larger than the receiver field of view (RFOV). Therefore, the photons scattered within the forward peak escape the sampling volume formed by the RFOV, i.e. the escape effect. We demonstrated that the escape effect is an inherent part of MS properties within the free atmosphere beyond the cloud far edge. In the cases of the ground-based lidar, the MS contribution is lower than 5 % within the regions of the cloud-free molecular atmosphere having the distance from the cloud far edge about 1 km or higher. In the cases of the space-borne lidar, the decreasing rate of the MS contribution is so slow that the threshold of 5 % can hardly be reached. In addition, the effect of non-uniform beam filling is extremely strong. Therefore, practitioners should employ with proper precautions lidar data from regions below the cloud base when treating data of a space-borne lidar. In the case of two-layered cloud, the distance of 1 km is sufficiently large that the scattered photons emerging from the first layer do not affect signals from the second layer when we are dealing with the ground-based lidar. In contrast, signals from the near edge of the second cloud layer are severely affected by the photons emerging from the first layer in the case of a space-borne lidar. We evaluated the Eloranta model (EM) in extreme conditions and showed its good performance in the cases of ground-based and space-borne lidars. At the same time, we revealed the shortcoming that can affect practical applications of the EM. Namely, values of the key parameters, i.e. the ratios of phase functions in the backscatter direction for the nth-order-scattered photon and a singly scattered photon depend not only on the particles phase function, but also on the distance from a lidar to the cloud and the receiver field of view. Those ratios vary within a quite large range and the MS contribution to lidar signals can be largely overestimated or underestimated if erroneous values of the ratios are assigned to the EM.