Hydrometeor Mixtures in Polarimetric Radar Measurements: Bin-based and Neighborhood-based De-mixing

The issue of hydrometeor mixtures affects radar sampling volumes without a clear dominant hydrometeor type. Containing a number of different hydrometeor types which significantly contribute to the polarimetric variables, these volumes are likely to occur in the vicinity of the melting layer and mainly, at large distance from a given radar. Motivated by potential benefits for both quantitative and qualitative applications of dual-pol radar, we study the possibilities for the identification of hydrometeor mixtures and their subsequent de-mixing. This study is intrinsically related to our recently proposed semi-supervised approach for hydrometeor classification.

The mentioned classification approach performs labeling of radar sampling volumes by using as a criterion the Euclidean distance with respect to five-dimensional centroids, depicting nine hydrometeor classes. The positions of the centroids in the space formed by four radar moments and a (possibly external) phase indicator, are derived through a technique of k-medoids clustering, applied on a selected representative set of radar observations, and coupled with statistical testing which introduces the assumed microphysical properties of the different hydrometeor types.

Aside from a hydrometeor type label, each radar sampling volume is characterized by an entropy estimate, indicating the uncertainty of the classification. This concept of entropy is revisited in order to emphasize its presumed potential for the identification of hydrometeor mixtures. The calculation of entropy is based on the estimate of the probability (p_i) that the observation corresponds to the hydrometeor type i(i=1,... 9). The probability is derived from the Euclidean distance (d_i) of the observation to the centroid characterizing the hydrometeor type i. The parametrization of the d→p transform is conducted in a controlled environment, using synthetic polarimetric radar datasets. It ensures balanced entropy values: low for pure volumes, and high for different possible combinations of mixed hydrometeors.

The linear bin-based approach is founded on the hypothesis of Rayleigh single backscattering of different hydrometeor types populating a single radar sampling volume. In this case, inspired by the linear de-mixing employed in hyperspectral remote sensing community, we reduce the de-mixing operation to the bin-based routine which basically converts the Euclidean distance d_i to the proportion of hydrometeor type i. In the neighborhood-based approach we simultaneously consider, influenced by the incoherent target decompositions used in SAR polarimetry, a set of presumably similar mixtures in order to get an insight into the individual radar sampling volumes.

As main outcome, the proposed linear bin-based de-mixing approach, applied to real polarimetric C and X band radar datasets, allows to provide plausible proportions of the different hydrometeors contained in a given radar sampling volume. The performance analysis part involves as well collocated Multi-Angle-Snowflake-Camera (MASC) measurements. As for the neighborhood-based de-mixing, we comparatively apply diverse techniques (PCA, ICA, Kernel PCA) and discuss the limitations of the conventional target decomposition methods in the framework of weather radar remote sensing.