Lidar multiple scattering: improvement of Bissonnette's paraxial approximation

It is generally accepted that multiple scattering is important for evaluating backscatter lidar signals in the case of moderate or high optical depths and large receiver fields of view. On one hand, multiple scattering must be considered in inverting signals to obtain backscatter coefficients; on the other hand, it offers the opportunity to derive microphysical parameters of the scattering medium. Bissonnette developed a numerical code for the propagation of a continuous-wave laser beam through an atmosphere including multiple scattering. His model is also applicable to a backscatter lidar approximatively.

In this paper we investigate if the assumptions on which his backscatter lidar application is based are valid for typical atmospheric situations. It is found that for small and moderate optical depths, a prerequisite for the backscatter lidar application is fulfilled: second-order iterations of the solution to the radiative transfer equation can indeed be neglected as proposed by Bissonnette.

Furthermore, we propose an improvement of the simulation for limited fields of view that significantly alters the radial dependences of the backscattered signals. Essentially, on-axis backscattered signals are increased and the profiles tend to be somewhat narrower near the optical axis. The dependence of the radiative distribution on the phase function of the scattering medium, the optical depth, and on the field of view of the receiver is also changed. The modifications only slightly increase the computer time. Examples for typical atmospheric situations are shown, and proposals for intercomparisons with other models and measurements are made.