A first approach to unsupervised Entropy-Alpha-classification of full-polarimetric weather-radar data

Typically only the copolar channels of weather radar data is used for extracting various parameters or observables. ZDR, kDP and PhiDP for example are prominent extracts from Zxx and Zyy and have quite a lot of applications in the field of precipitation measurements. Nevertheless, the use of the full polarimetric coherent scattering matrix to extract physical properties according to the scattering process has only poorly been addressed, particularly due to high costs in establishing such complicated systems being able to coherently measure co- and crosspolar scattering amplitudes and phases. However, DLRs "POLDIRAD" is such a fully polarimetric weather radar operating in C-band, able to acquire time series (raw) data, containing all the information needed to apply polarimetric decomposition techniques in order to extract physical information about the illuminated scatterers from the observed scattering process.

This paper presents a study about the possibilities of applying coherent polarimetric techniques to time series (raw) data, and the aim is to evaluate an understanding of the potential of such techniques with regard to weather radar data. It will concentrate on the Entropy-Alpha decomposition, based on Pauli-matrices, because the physical interpretation is pretty much straight forward and easy to understand and therefore a good point to start from. This decomposition has originally been developed for application to Synthetic Aperture Radar (SAR) data, and hence all the advances in this technique concentrate on targets on the earth's surface rather than meteorological targets as raindrops, snow or hail.

The first step is to prepare the data, i.e. changes in phase due to propagation through the medium have to be corrected as well as phase shifts due to Doppler effects. The second step involves calculating the Covariance (or Coherence) matrix from the scattering matrix time series per range bin. Therefrom this matrix contains the statistical fluctuations of targets over time. By diagonalysing the hermitian Covariance matrix in the third step it is possible to extract the dominant physical scattering mechanisms. The observables Entropy and Alpha-angle are quite simple measures, which help to interpret the results. The forth step consists of choosing areas in the Entropy-Alpha plane in order to classify the data. Refinement of this classification using the first Eigenvalue (intensity) might be necessary and thus investigated as well.

The results will show that it is clearly possible to distinguish between different types of scattering, and moreover that there is sufficient variation in scattering types to be able to apply a reasonable classification. It is not only possible to differentiate meteorological targets, but also to detect ground clutter or areas with high noise levels, which simplifies the process of pre-classifying weather radar data. Furthermore the results will be compared to "traditional" classification methods in order to analyse, if this new method provides additional, complementary or maybe even completely new information or relations.