## 2 Materials and Methods
### Database
#### 2.2.2 Polarimetric SAR Data and Decompositions
For HH/HV- and VV/VH-polarized data the Kennaugh Matrix consists of the elements K0, K1, K5 and K6 [31]. Figure 1c shows as a false-color composite of the Kennaugh Matrix elements K1, K2 and K3, which were processed using the quad-polarized R-2 data. For the purpose of comparison Figure 1d shows a Landsat TM true-color RGB composite acquired in summer 2011, concurrent with the R-2 imagery. Eigen-decomposition--The Eigen-decomposition approach is a frequently used to process PolSAR data [25,26]. It decomposes the incoherent signal (usually stored in the Covariance or CoherencyMatrix) using eigenvalues (\(\lambda\)) and eigenvectors (\(u_{x}\)) ((1) and (2)). In the formula \({}^{H}\) denotes the conjugate transpose. Note that the eigenvalues of the Covariance or Coherency Matrix are the same, while the eigenvectors differ. For dual-polarized data two eigenvalues and eigenvectors are obtained (1); while for quad-polarized data three eigenvalues and eigenvectors are obtained (2) when reciprocity is anticipated due to a monostatic acquisition geometry. Consequently, identical scattering from HV and VH is assumed. \[U=\lambda_{1}u_{1}u_{1}^{H}+\lambda_{2}u_{2}u_{2}^{H} \tag{1}\]  
\[U=\lambda_{1}u_{1}u_{1}^{H}+\lambda_{2}u_{2}u_{2}^{H}+\lambda_{3}u_{3}u_{3}^{H} \tag{2}\]  
Entropy/Alpha/Anisotropy--The Eigen-decomposition was used to process additional features that describe scattering processes [25; 26; 42; 43]. The polarimetric Entropy and Alpha Scattering angle describes the scattering properties of incoherent (natural) scatterers. Entropy (3) and (4) can be understood as the degree of randomness of the scattered signal and is described by the logarithmic sum of the pseudo probabilities \(p\) of the eigenvalues, and ranges from zero to one. The polarimetric Alpha scattering angle is calculated as the sum of the inverse cosine of the absolute value of the first eigenvector element and is weighted by the pseudo probabilities \(p\) (5). [PERSON] and [PERSON] also showed a third feature for quad-polarized data that is calculated via the ratio between the normalized difference of the second and third eigenvalue: the Anisotropy (6), which indicates the relevance of secondary scattering processes. Anisotropy, understood in the quad-polarimetric sense, is unavailable for dual-polarized data. In the formulas \(n\) is equal to two for dual-polarized data and three for quad-polarized data. Note that Entropies of the Covariance or Coherency Matrix are the same, but the Alpha scattering angles are different due to the differences between the Eigenvectors. \[p_{i}=\frac{\lambda_{i}}{\sum_{k=1}^{n}\lambda_{k}} \tag{3}\]  
\[H=-\sum_{i=1}^{n}p_{i}\log_{n}(p_{i}) \tag{4}\]  
\[\alpha=\sum_{i=1}^{n}p_{i}\cos^{-1}(|u_{1i}|) \tag{5}\]  
\[A=\frac{\lambda_{2}-\lambda_{3}}{\lambda_{2}+\lambda_{3}} \tag{6}\]  
Model-Based Decompositions--Besides the Kennaugh Matrix elements, the polarimetric intensities and the Eigen-decomposition features, three Model-based decompositions were applied to the data which apply simplified, pre-defined scattering models. For the quad-polarized data of R-2 and ALOS-2, the Three Component Yamaguchi Decomposition [27] was applied. This approach decomposes the total backscattered energy \(P_{\text{Total}}\) into the intensities of surface scattering (\(P_{\text{surface}}\)), double bounce scattering (\(P_{\text{double bounce}}\)) and volume scattering (\(P_{\text{volume}}\)) (7). This frequently used approach is suitable for comprehending and characterizing predominant scattering processes in nature. \[P_{\text{Total}}=P_{\text{surface}}+P_{\text{double bounce}}+P_{\text{ volume}} \tag{7}\]  
As shown by [14] the approach of Yamaguchi can be adopted for HH/VV-polarized data, by decomposing the total backscattered energy \(P_{\text{Total}}\) into the intensities of surface scattering (\(P_{\text{surface}}\)) and double bounce scattering (\(P_{\text{double bounce}}\)) (8).