Sets of backscatter coefficients profiles at 355, 532, and 1064 nm and of extinction coefficients profiles at 355 and 532 nm are the standard output of advanced aerosol Raman lidars based on a single Nd:YAG laser (emitted wavelengths: 355 nm, 532 nm and 1064 nm), e.g., many of the lidar stations in the European Aerosol Research Lidar Network –Advanced Sustainable Observation System (EARLINET-ASOS), see Ref. 5, in principle, can measure this data sets. The Network consists of 20 lidar stations distributed all over Europe. For this reason, there is great interest to obtain detailed characterization of the physical particle properties from that enormous data set.
The mathematical model which relates the optical and the physical particle parameters consists of a Fredholm system of two integral equations of the first kind for the backscatter and extinction coefficients. The treatment of the model is an inversion problem which is ill-posed. This means small input noise from measurements will be amplified during the solution process. Therefore, its solution, the determination of the particle-volume distribution, requires the application of appropriate mathematical regularization techniques. The performances of some regularization algorithms for lidar remote sensing were discussed by Ref. 1-4. Moreover, in solving such problems without the introduction of appropriate mathematical tools such as a suitable discretization and regularization the “solutions” would be highly oscillating even for noiseless data.
Several regularization techniques exist. In spite of this, the first regularization step is performed with discretization, in which the investigated distribution function is approximated by variable B spline functions. In order to reduce the computer time, a collocation projection is used. The projection dimension (number of base function) and the order of the used B splines serve, roughly speaking, as regularization parameters. In the second step, regularization is controlled e.g. by the level of truncated singular-value decomposition or by generalized Tikhonov-Phillips regularization performed during the solution process of the resulting linear equation system.
The highly nonlinear problem of the determination the complex refractive index as a second unknown is handled by introducing a grid of wavelength- and size-independent mean complex refractive indices and by enclosing the area of possible real/imaginary-part combinations through inversion and back-calculation of optical data.
The retrieval algorithms were tested extensively with synthetic data as well as with first real measurement data. Those regularizing inversion techniques are a promising tool to retrieve microphysical particle properties without any additional measurements and costs except computing time.
Acknowledgments: The financial support of this work by the European Commission under grant RICA-025991 is gratefully acknowledged.
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