Analytical solution to LIDAR return signals from clouds with regard to multiple scattering

An analytical approach to LIDAR return signal calculation with regard to multiple scattering is suggested. Two versions of the method are developed. The first one is completely analytical and undispensible for qualitative studies. The second semianalytical approach provides a sufficient accuracy up to a sounding optical depth about 5. Being somewhat more tedious than the proposed analytical solution, the second approach appears to be time saving in comparison with known methods.