## 2 Materials and Methods
### Database
#### 2.2.2 Polarimetric SAR Data and Decompositions
These synthetic dual-polarized datasets were thus not affected by temporal variations and showed identical speckle characteristics (compared to the quad-polarized data from which the subsets were taken), as such, this allowed for direct comparison of class separability as a function of polarization diversity, as opposed to differences in moisture, and plant phenology. Second, the Sinclair scattering matrices of all dual- and quad-polarized data of all wavelengths were converted to the corresponding Kennaugh Matrices [31]. Third, the data were multi-looked (minimum of four looks) in order to generate pixels with square ground range resolution. Forth, a simple boxcar filter with a window size of 3 \(\times\) 3 pixels was applied. Fifth, the data were terrain corrected and geocoded using the Range-Doppler Approach [39]. All data were transformed to UTM WGS1984 Zone 8 coordinate system with 12 m spatial resolution using the TanDEM-X intermediate digital elevation model (DEM) and the projected local incidence angle derived from this DEM [40]. The data were processed as sigma nought intensities. All of the preceding steps were completed in SNAP 5.0 (Sentinel Application Platform) released by the European Space Agency (ESA), Paris, France. The terrain corrected Kennaugh Matrices were then used to generate the polarimetric channels, the Yamaguchi Decomposition [27], the Eigen-decomposition with the features Entropy/Alpha/Anisotropy, the Two Component Ground-Volume Decomposition of [30] and the Two Component Surface-Diherdal Decomposition of [14] using IDL 8.5 and ENVI 5.3. All intensity features were scaled to decibels [dB]. The above mentioned decompositions are explained in more detail in the subsequent paragraphs. Kennaugh Matrix--For quad-polarized data the Kennaugh Matrix (Mueller Matrix, respectively [41]) describes the relation between the radiated and received wave as a symmetric 4 \(\times\) 4 matrix using ten real elements (K0-K9). It is the linear transformation of the four-dimensional Stokes vector ([42] p. 43 ff. and p. 83 ff.) in the backscatter-alignment coordinate system. Unlike the Covariance or the Coherency Matrix, the Kennaugh Matrix can describe both coherent and incoherent targets [42,43]. The elements K0, K1 and K2 are intensity-based elements, while K3 and K4 are based on the cross-polarized intensity and the co-polarized phase information. The elements K5, K6, K7, K8 and K9 are phase-only elements that tend to provide unique information from natural targets. All elements of the full Kennaugh Matrix can be grouped as follows [31]: First, the total intensity (K0); second, the absorption elements that describe the loss of polarization during the scattering process (K1, K2, K3); third, diattenuation elements that describe the change of the relation between two amplitude values during reflection (K4, K5, K6); fourth, retardance elements that describe the phase delay during scattering in a particular direction (K7, K8, K9). The definition of the Kennaugh Matrix and its elements for quad-polarized (A1), HH/VV-polarized (A2) and HH/HV- or VV/VH-polarized data (A3) are shown in Appendix A in accordance to [31]. The Kennaugh Matrix elements are linear combinations of the Coherency Matrix and combinations of K0, K1, K2 and K3 describe the diagonal elements of the Coherency Matrix (T\({}_{11}\), T\({}_{22}\), T\({}_{33}\)), while combinations of K4, K5, K6, K7, K8 and K9 describe off-diagonal elements of the Coherency Matrix (T\({}_{12}\), T\({}_{13}\), T\({}_{21}\), T\({}_{23}\), T\({}_{31}\), T\({}_{32}\)) [42]. The conversions of the Kennaugh Matrix to 3 \(\times\) 3 Coherency Matrix (T) of quad-polarized (A4) and 2 \(\times\) 2 T of HH/VV-polarized data (A5) are shown in Appendix A in accordance to [31]. To generate all Kennaugh matrix elements requires quadrature polarized data, thus only a portion of can be generated using dual polarized data. For HH/VV-polarized data the Kennaugh Matrix consists of the elements K0, K3, K4 and K7.