Reports of increasing temperatures suggest that Earth’s climate is changing (average temperature increased by 0.6^{◦} C in the past 100 years, Houghton, 2000, IPCC, 2007). The processes behind these changes are not as clear. Two of the biggest uncertainties in understanding and predicting climate change are the effects of clouds and aerosols. Aerosol effect (direct and indirect effects) roughly describes the alternation of energy in the tropopause, and thus may be used for researching the global climate change.

The extinction- and the backscatter coefficient are two of the so called optical parameters, which quantify the loss of light intensity and the attenuation caused by scattering at angles from 90° to 180° respectively. LIDAR (Light Detection And Ranging) method is used to retrieve aerosol optical parameters and vertical profiling of aerosols, via the lidar equation. This method is based on detecting and analyzing the returning light from a laser striking the system of interest. Additional information is needed in conjunction with lidar equation in order to determine these optical parameters unambiguously (forward problem). Towards this direction, we follow the technique of the group of A. Ansmann and U. Wandinger, which suggests using measurements of the (inelastic) Raman backscatter of the nitrogen molecules of the atmosphere, binding these parameters with a second relation.

Although lidar method is highly promising, there is always a height range in the lower atmosphere that is not covered by the lidar telescope collecting the backscattered light. This is known as the overlap effect, and is partly corrected by determination of lidar overlap profile. On the other hand, sun photometers refer to the whole range of the atmosphere from the ground to the stratosphere. These systems detect the direct sun radiance and the diffuse sky radiance at several wavelengths. However, such measurements can only be carried out during clear-sky conditions and at daytime and also there is no information available, which specific height range the retrieved parameters refer to. By use of height-resolved profiles of the aerosol particle concentration, which show where the aerosol is located, the assignment of the properties to a certain layer and a better classification would be possible. Finally, a combination of high resolved lidar aerosol profiles and sun photometer measurements seems to be very prospective and will be part of our project.

Research topic: Solving the inverse problem.

We focus on multi-wavelength lidar technology and depolarization signals (used to distinguish between liquid and solid phases of water in the atmosphere) to extract the microphysical properties of aerosol particles. Given, the optical parameters Γ(λ) measured by multiple wavelength (λ) lidar setup, the Kernel functions K_{ext/bsca}, which summarize the size, shape and composition of particles, sensible particle size bounds r_{min}, r_{max} corresponding to an imaginary sphere, we wish to solve for the volume distribution v(r) of the particles modeled by a Fredholm integral

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and further gain some insight on how the refractive index, the particle effective radius and other microphysical parameters are distributed with respect to different sizes.

This is a highly non-linear mathematical problem, the complexity of which is considerably risen, if the refractive index m is assumed to be unknown. Predefining a grid of viable

options for the refractive index, we come across the main pathology for such integral equations: Instability. This results in a highly variational behavior of the unknown function in the presence of arbitrarily small fluctuations in our data (noise), which is always the case.

Solving for v(r) leads to an inverse ill posed problem. The kernel functions come first on the black list for this situation, as primary studies shows, that they have a smoothing effect on v(r); they force v(r) to appear smoother than it really is, as observed by our input data Γ(λ), causing magnification of –possible- higher frequency components of the data. Numerical treatment of such problems consists of two parts: Discretization and Regularization. Discretization involves the transformation of the continuous problem (integral equation) into a discrete analog (system of equations) so that our problem can be handled by the finite precision of computers. Regularization consists of variations of the following two methods: using filter functions to restrict the inherent data noise or applying some constraints to our functional space so that our unknown function (v(r)) is described by a finite set of functions (projection methods). Next step is the automatization of finding the required parameters for regularization, which is the subject of parameter choice rules methods.

A lot of work has already been done for the derivation of microphysical properties of spherical particles using a variety of methods. At a first stage, we will test/extend this work using real-life data from different Earlinet stations, combine methods and learn how to marry observations from different sources (lidar, sun photometer) improving data quality. Our ultimate goal is to make a step forward considering more realistic non-spherical particles. As research for non-spherical particles is currently developing, our primary aim is to experiment on simulation data and extend our notion through a mathematical approach.