Some Statistical Properties of the ELITE Data Set

We present some remarkable results of our analysis of the lidar data set of the ELITE measurements at 1.06 um. The data are obtained from Dr. W. Renger (Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V., DLR Institut für Fysik der Atmosphäre) and from Dr. J. Pelon (Service d'Aeronomie du CNRS, Paris). From the ELFTE data set, that contains about 200 Mbytes of data, a selection has been made to study statistical properties of cirrus clouds. The work is carried out in a current project funded by ESA (ESTEC contract No. 11766/96/NL/CN). We have estimated statistics concerning moments, (cross-) correlations, spectral power density distributions and two-point variance (structure function) distributions. In this paper we include some results in addition to those presented during the oral presentation at the workshop. The main conclusion is that spectra that represent the whole data set, obtained after averaging many local spectra, clearly show the characteristics of Brownial fractals, namely, they can be fitted well by A.f 'P distributions (A and p are constants, f denotes the spatial frequency). For the vertical direction we find p = 2.2, for the horizontal direction p = 1.4. A quick-look comparison with spectra that we calculated for part of the ELAC campaign data (LEANDRE flights in France) supports the findings

Fractal properties and denoising of lidar signals from cirrus clouds

Airborne lidar signals of cirrus clouds are analyzed to determine the cloud structure. Climate modeling and numerical weather prediction benefit from accurate modeling of cirrus clouds. Airborne lidar measurements of the European Lidar in Space Technology Experiment (ELITE) campaign were analyzed by combining shots to obtain the backscatter at constant altitude. The signal at high altitude was analyzed for horizontal structure of cirrus clouds. The power spectrum and the structure function show straight lines on a double logarithmic plot. This behavior is characteristic for a Brownian fractal. Wavelet analysis using the Haar wavelet confirms the fractal aspects. It is shown that the horizontal structure of cirrus can be described by a fractal with a dimension of 1.8 over length scales that vary 4 orders of magnitude. We use the fractal properties in a new denoising method. Denoising is required for future lidar measurements from space that have a low signal to noise ratio. Our wavelet denoising is based on the Haar wavelet and uses the statistical fractal properties of cirrus clouds in a method based on the maximum a posteriori (MAP) probability. This denoising based on wavelets is tested on airborne lidar signals from ELITE using added Gaussian noise. Superior results with respect to averaging are obtained. Copyright 2000 by the American Geophysical Union