Determination of confidence bounds for the graphical estimation of particle size distribution parameters from optical backscatter and extinction measurements

The use of multi-wavelength lidar measurements can in principle be used to estimate aerosol extinction and backscatter profiles. From the resultant multi-wavelength profiles, an estimate of particle size distribution parameters can be inferred. At present the standard approach is to assess error by adding noise with given covariance properties and inverting the ensemble of signals. Unfortunately, the inversion is often affected by algorithm convergance issues and poor a-priori guesses. On the other hand, graphical estimation of confidence bounds does not require inversion of the optical data and therefore is more robust and with pre-constructed databases isvery efficient. However, determination of appropriate confidence bounds can be quite difficult since correlated optical data ratios are used and simple Gaussian statistics no longer applies. In this paper, several confidence bound estimates are explored and compared to the results from direct inversion of the signal ensemble. Using the appropriate confidendence bounds, we then apply the graphical technique to multiwavelength elastic and raman lidar. In particular, the improvement of the retrieval from additional extinction data obtained from a Raman Lidar system in comparison with a prototypical three wavelength backscatter lidar is examined