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We present a new algorithm for the retrieval of the volume distribution - and thus, other relevant microphysical properties such as the effective radius - of stratospheric and tropospheric aerosols from multiwavelength lidar data. We consider the basic equation as a linear ill-posed problem and solve the linear system derived from spline collocation. Starting from here, algorithmical improvements for the inversion process are proposed. While a standard approach consisting of spline collocation and a regularization method such as truncated singular value decomposition or Tikhonov-Philips regularization proves sufficient in some cases, that kind of algorithm is not suitable for a more general case; the base points of the spline collocation take a key role here. Indeed, there is a direct connection between the number and position of the base points on the solution, as the problem of the correct regularization parameter - which is represented here by both location and number of base points - and its implications on over- or underregularization of the solution have to be investigated. Here, we present an algorithm that makes use of the fact that smoother areas of the solution require less base points in the vicinity for a proper reconstruction, combined with a Padé-type iterative regularization method. The algorithm starts with equidistant base points, then moves these base points during the calculation away from the smoother areas of the solution. This algorithm proved to work very well in many different simulation cases. Different weight functions for the base point shift are investigated, leading to slightly different results. Also, an improvement on this algoritm is proposed which, in addition to the position of the base points, also actively controls the actual number of base points, as solutions that more smooth in a global sense require less base points. Finally, we also take a look at how this new algorithm can also help us in simultaneously retrieving the particle distribution and the complex refractive index of the particles.
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