## 2 Materials and Methods
### Correlation, Class Separability, and Feature Selection  
The correlations between the above listed decomposition features were examined using the dB-scaled sigma nought intensity values of the calibrated data, where applicable. Correlations were estimated using a random sample of 50,000 points over land (see Section 2.2.1. Land Cover Reference); thus values and analyses were completed independent of the land cover classes of interest. The squared linear Pearson Correlation Coefficient (\(R^{2}\)) was used in all cases. The coefficient \(R^{2}\) is defined as the squared ratio between the covariance (_Cov_) of two variables (_i:j_) and the product of the individual  
Figure 4: Correlation-Matrix of quad- and dual-polarimetric L-Band ALOS-2 features showing the squared Linear Pearson Correlation Coefficient (\(R^{2}\)) ranging from 0.0 (no correlation) to 1.0 (full linear correlation, determination respectively). \(R^{2}\) was estimated using 50,000 randomly distributed samples on land (roughly 10% of all land pixels). Note that dual-polarimetric data of ALOS-2 were derived as polarimetric subsets and thus are not affected by temporal variations. Feature abbreviations are as follows (see Table 2): ENT (Entropy), ALPT (polarimetric Alpha scattering angle of Coherency Matrix), ALPC (polarimetric Alpha scattering angle of Covariance Matrix), HH/VV/VH (PolSAR Channels), DBL3 (double bounce of the [PERSON] et al. Decomposition [27]), VOL3 (volume scattering of the [PERSON] et al. Decomposition), ODD3 (surface scattering of the Yamaguchi et al. Decomposition), K0–K9 (elements of the Kennaugh Matrix [31]), VOL2 (volume scattering of [30]), GRD2 (ground scattering of [30]), DBL2 (double bounce of [14]), ODD2 (surface scattering of [14]). standard deviations (\(\sigma_{i}\sigma_{j}\)) (10). \(R^{2}\) is frequently used to quantify the degree of determination between two variables, though still can be interpreted as a coefficient that quantifies the correlation. \(R^{2}\) ranges from zero to one; a value of one (zero) indicates perfect (no) linear correlation and a maximum (minimum) determination, 100% (0%) of the explained variance, respectively [45]. \[R^{2}=\left(\frac{Cov(i,j)}{\sigma_{i}\sigma_{j}}\right)^{2} \tag{10}\]  
All PolSAR data were then used in separability analyses to quantify the ability of the polarimetric information to discriminate the land cover classes considered in this research. The _Transformed Divergence_ (TD) (11) [45; 46], _Bhattacharyya Distance_ (BD) (12) [47], and _Jefferys Matusita Distance_ (JD) (13) [45; 46] were processed for each PolSAR feature space and each wavelength for all land cover classes [47]. The features are processed for two classes \(c\) and \(d\) by assessing the classes' mean vectors \(M\) (14) and the classes' covariance matrix \(V\) (15) for a given set of features (as a minimum, two features are required). In the formula \(tr\) denotes the trace of a matrix, formula \(det\) denotes the determinant of a matrix, \({}^{\rm T}\) refers to the matrix/vector transpose, and \(Cov\) denotes the covariance. The separability features TD and JD have been shown to act as meaningful predictors for classification potential, thus a high separability indicates greater potential for class discrimination [48; 49]. \[{\rm TD}=2000\left[1-exp\left(\frac{-0.5\big{(}tr\big{[}(V_{c}-V_{d})\big{(}V _{d}^{-1}-V_{c}^{-1}\big{)}\big{]}+tr\big{[}\big{(}V_{c}^{-1}+V_{d}^{-1}\big{)} (M_{c}-M_{d})(M_{c}-M_{d})^{\rm T}\big{]}\big{)}}{8}\right)\right] \tag{11}\]  
\[{\rm BD}=0.125(M_{c}-M_{d})^{\rm T}0.5(V_{c}+V_{d})(M_{c}-M_{d})+0.5 log\frac{ \det(0.5(V_{c}+V_{d}))}{\sqrt{\det(V_{c})}\sqrt{\det(V_{d})}} \tag{12}\]  
\[{\rm JD}=\sqrt{2(1-{\rm e}^{-BD})} \tag{13}\]  
\[M_{c}=\left( \begin{array}{c}\mu_{c1}\\ \mu_{c2}\\ \vdots\\ \mu_{cn}\end{array} \right) \tag{14}\]  
\[V_{c}=\left( \begin{array}{ccc}Cov_{c}(1,1)&\cdots&Cov_{c}(1,n)\\ \vdots&\ddots&\vdots\\ Cov_{c}(n,1)&\cdots&Cov_{c}(n,n)\end{array}