## 4 SAR Decomposition  
Polarimetric SAR (PolSAR) decomposition is a common method for characterizing the Earth's surface. The Pauli decomposition is widely used as a simple method for mapping the surface according to the three scattering mechanisms, which are single bounce, double bounce, and volume scattering [27, 46, 47]. A three-component scattering decomposition approach proposed by [PERSON] and [PERSON] has been successfully applied to decompose quadruple polarized SAR data under reflection symmetry conditions [29]. [PERSON] _et al._[30, 31] added a fourth helix component to their decomposition to account for non-reflection symmetry conditions. Several other studies have been performed to estimate the volume scattering component considering non-reflection symmetry condition [48, 49, 50] and an extended volume scattering model was proposed to consider randomly orientated diplane scatterers [51]. To resolve anomalous values generated by the previous three- and four-decomposition methods, mathematical operations on the decomposed coherency matrix have also been studied [32, 33, 34]. We used the [PERSON] and Wdowinski ([PERSON]&[PERSON]) [36] scattering component decomposition approach to classify wetland vegetation. This new four-scattering component decomposition method was derived by two of the authors of the current paper to extract a double bounce component from cross-pol, which was developed in accordance with new SAR phase observations (interferograms) in tropical and subtropical wetlands [36]. According to common radar scattering theory, wetland InSAR works because of double-bounce scattering components, which reflect inundated conditions beneath the vegetation. However, an almost identical fringe pattern indicating surface water level changes in both co- and even cross-polarizations has been reported in research in Everglades wetlands [52], signifying that the cross-polarization signal samples the water surface beneath the vegetation. To explain these interesting phase observations from the cross-pol, we adopted a rotated dihedral model, which is the simplest scattering mechanism that accounts for scattering in the cross-pol signal. The decomposition extracts the co-polarization double bounce components which are calculated based on the conventional polarimetric decomposition approach and the cross-polarization double bounce components. The full description and mathematical formulation of the four scattering decomposition model have been described by [PERSON] and [PERSON] [36]. This previous study indicated that the decomposition method showed enhanced distinctions in land cover beyond those revealed with the Yamaguchi decomposition [37]. Thus, we chose the H&W decomposition method to evaluate its performance for classifying wetland vegetation types in the Everglades. [PERSON]'s decomposition has been widely regarded as the most popular method for polarimetric SAR decomposition, and its applicability has been demonstrated. To evaluate the utility of our decomposition particularly for wetland vegetation classification, we compared our classification results with results obtained using [PERSON]'s decomposition method based on rotated coherence matrix [32]. We used a 3 \(\times\) 3 coherency matrix, which was extracted with PolSARpro software [28] to derive the four scattering component model. The coherency matrix was computed using a multi-look process with 1 \(\times\) 2 factors in direction of range and azimuth, respectively. To suppress speckle noise in the SAR image, a relatively large window size of 11 \(\times\) 11 was applied to estimate an ensemble average, accounting for creating reduced spatial resolution. Figure 3 represents the results of the H&W decomposition analysis using the TSX data. The TSX quad-pol decomposition is more sensitive to vegetation variation compared with our previous results using Rad  
Figure 3: Hong & Wdowinski decomposition analysis of TerraSAR-X (TSX) quadruple polarimetric data acquired over the study area.