# Two Component Decomposition of Dual Polarimetric HH/VV SAR Data: Case Study for the Tundra Environment of the Mackenzie Delta Region, Canada

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## Abstract

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^{2}values of 0.60 (double bounce) and 0.88 (surface scattering) were observed. The presence of volume scattering led to differences between the features and these were minimized for land cover classes of low vegetation height that showed little volume scattering contribution. In terms of separability, the quad-polarized Radarsat-2 data offered the best separation of the examined tundra land cover types and will be best suited for the classification. This is anticipated as it represents the largest feature space of all tested ones. However; the classes “wetland” and “bare ground” showed clear positions in the feature spaces of the C- and X-Band HH/VV-polarized data and an accurate classification of these land cover types is promising. Among the possible dual-polarization modes of Radarsat-2 the HH/VV was found to be the favorable mode for the characterization of the aforementioned tundra land cover classes due to the coherent acquisition and the preserved co-pol. phase. Contrary, HH/HV-polarized and VV/VH-polarized data were found to be best suited for the characterization of mixed and shrub dominated tundra.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Two Component Decomposition of HH/VV Data

#### 2.2. PolSAR Database

#### 2.3. In Situ Data

#### 2.4. Correlation Analysis

_{s}and P

_{d}were processed for C-Band HH/VV-polarized data and X-Band HH/VV-polarized data. The three component decomposition features P

_{s}, P

_{d}, and P

_{v}were processed using the C-Band quad-polarized data. The alterations between the C-Band two and three component decomposition features P

_{s}(P

_{d}) were then connected to the differences of the models and not to changes caused by temporal variations, since pseudo HH/VV-polarized data were derived from quad-polarized data. Table 3 provides an overview of the investigated features.

^{2}), and the Spearman’s Rank Correlation Coefficient ($\mathsf{\rho}$) were processed for all of the features for each land cover class of each test site using the reference data. The coefficient $\mathrm{R}$ is defined as the ratio between the covariance (Cov) of two variables (i,j) and the product of the individual standard deviations of these two variables (SD) (16) and (17). Similar, $\mathsf{\rho}$ is defined as the ratio between the covariance (Cov) of two ranked variables ($R{G}_{i},R{G}_{j}$) and the product of the individual standard deviations of these two ranked variables (${\sigma}_{R{G}_{i}}{\sigma}_{R{G}_{j}}$) (18).

^{2}). The values of R and R

^{2}range from zero to one, where a value of one (zero) indicates perfect (no) linear correlation and a maximum (minimum) determination, which is 100% (0%) of the explained variance. The values of $\mathsf{\rho}$ range from −1 to +1, where −1/+1 indicate perfect monotonic properties, thus one variable is a function of the other. R and $\mathsf{\rho}$ were investigated to examine the linear and monotonic dependencies among the features. The X-Band data acted as a control variable in this study: A positive correlation between C- and X-Band is expected due to the similar wavelengths of 5 cm and 3 cm, respectively. However; this relationship should be less significant compared to the correlation among the C-Band features due to the temporal decorrelation, the differences in the speckle characteristics, and the differences in absolute radiometric calibration. Therefore it is more statistically reliable to compare C-Band quad-polarized with C-Band synthesized dual-polarized data.

#### 2.5. Regression Analysis

^{2}) does not necessarily infer a high (low) RMSE, e.g., in the case that the classes’ standard deviations are low (high).

#### 2.6. Separability Analysis

^{T}refers to the matrix/vector transpose. C is a 3 × 3 matrix and M a three-element vector for the case that three features are investigated [37].

_{s}/P

_{d}/P

_{v}), C-Band Three Component Decomposition Features without the volume scattering (P

_{s}/P

_{d}), C-Band Two Component Decomposition Features (P

_{s}/P

_{d}), and the X-Band Two Component Decomposition Features (P

_{s}/P

_{d}) (Table 3). The analysis was conducted for the none-water land cover classes (NBG, VLD, VMD, VSD, VWT) to avoid an overestimation of the average separability; the class water is comparably easy to be classified with PolSAR data [31] and a high separability of this class might artificially enhance the results.

## 3. Results and Discussion

#### 3.1. Backscatter Analysis

#### 3.1.1. Results

_{d}are increasing for all features from NBG to VWT (Figure 2a). Contrary, all P

_{s}intensities showed similar value ranges and median values of the vegetation classes (VLD, VMD, VSD) were similar (Figure 2b). The volume scattering P

_{v}of the three component decomposition model showed the most variable value ranges and increasing intensities from NBG to VWT (Figure 2c). P

_{d}and P

_{v}can be considered to be most meaningful for the class characterization and increasing volume scattering, respectively double bounce: The intensities increase with increasing vegetation height and shrub density (from NBG to VLD to VMD to VSD—see Section 2.3 in situ Data).

#### 3.1.2. Discussion

_{s}and P

_{d}of the two and three component decomposition were very similar. This fact is underlined by the quantile-quantile plots (Figure 2d,e). The quantiles of the P

_{d}intensities were comparable and linearly arranged, but showed a bias: The intensity values of the double bounce of the two component model were higher compared to the double bounce intensities of the three component model, which was a result of the volume removal and in the order of 5 dB. The quantiles of P

_{s}were highly related and were located close to the one-to-one line for all of the land cover classes. The bias was small and in the order from 1 to 3 dB. This was especially true for the classes with high P

_{s}intensities. This observation is reasonable since P

_{s}is the sum of the co-polarized channels and the removal of the cross-polarized channel does not alter the signal significantly.

#### 3.2. Correlation Analysis

#### 3.2.1. Results

_{s}, P

_{d}, and P

_{v}that were derived using the two and three component decomposition models for both X- and C-Band data. For all of the test sites and features positive linear correlations (R > 0) and medium to high positive monotonies ($\mathsf{\rho}$ > 0.3) were observed. The correlations between the X- and C-Band features were very low and the values of the squared Pearson Correlation Coefficients (R

^{2}) were less than 0.27. This is most likely a result of the different wavelengths and the temporal gap between the acquisitions. Further, no meaningful correlations between the volume scattering and any other feature were observed: All of the R

^{2}values were less than 0.46, which points to the expected statistically independence of the different polarizations. Contrary, the correlation between C-Band surface scattering features P

_{s}of the two and three component models were high (R

^{2}= 0.88) and monotone ($\mathsf{\rho}$ = 0.91).

_{d}of the two and three component models were moderately high (R

^{2}= 0.69) and monotone ($\mathsf{\rho}$ = 0.84). It is of importance to notice that the correlation between P

_{d}and P

_{s}of the two component model is higher than the correlation between P

_{d}and P

_{s}of the three component model. This fact points to a weaker orthogonality of the features of the two component decomposition model, which appears reasonable due to the missing removal of volume scattering, that is potentially present in both components. In the following the correlation of P

_{d}and P

_{s}between both models was studied for each test site, taking the influence of the land cover into account. Figure 3a,b shows the R

^{2}values of the C-Band P

_{d}, and P

_{s}between the two and three component model features for each test site and the average for each land cover class. It was found that the R

^{2}values between two and three component P

_{d}(P

_{s}) decreased from NBG to VWT.

#### 3.2.2. Discussion

_{d}(P

_{s}) is likely due to the increase in volume scattering that was present from NBG to VWT (Figure 2) and a result of the increasing shrub density and vegetation height (Table 2). Thus, the features of the two decompositions were less (more) similar, if the volume scattering contribution was high (low). The drop of the average explained the variance between the classes was up to 0.25 (NBG compared to VWT). Even though this decorrelation was observed, the R

^{2}values were still moderate to high for all land cover classes and in average between 0.65 and 0.85 for P

_{d}and between 0.60 and 0.95 for P

_{s}. For further studies it would be of interest to know up to which vegetation height neglecting the volume component within the decomposition is still acceptable and to use only the co-pol scattering coefficients for retrieval of geo-physical parameters. Figure 3c,d shows the correlation between the two component P

_{d}(P

_{s}) and the three component volume scattering P

_{v}. A similar picture was observed and the correlation between the features decreased from NBG to VWT, respectively with increasing shrub density and vegetation height. Contrary to the aforementioned findings, the overall level of the correlation was much lower and ranged between 0.5 and less than 0.1 in average. Thus there was no meaningful direct linear correlation between the two component decomposition features and the volume scattering.

_{d}and P

_{s}for each model, the land cover classes, and the X- and C-Band data. It was obvious that the three component model facilitated a better orthogonality between P

_{d}and P

_{s}—the correlation between the double bounce and the surface scattering intensities was low and in average less than 0.1; again most likely related to the adjustment of the model to the volume scattering. Contrary, the two component model led to a higher correlation between P

_{d}and P

_{s}intensities which is best pronounced for the HH/VV-polarized X-Band data. However, the R

^{2}values of the correlation between P

_{d}and P

_{s}of the two component models were in average less than 0.4 and therefore the features could still be interpreted as rather independent. The two ground components (surface, dihedral) should be orthogonal, depending on the quality of the volume removal and the degree of perfection in scattering type of the two canonical cases (Bragg surface scattering and Fresnel dihedral scattering) [40]. The components should be statistically independent, if both would optimally fit these canonical mechanisms. However, this ideal case might not be observable for real world data.

#### 3.3. Regression Analysis

#### 3.3.1. Results

_{s}, P

_{d}, and P

_{v}derived from the two and three component decomposition models for both X- and C-Band data. The interpretation of the axis intercept and the slope of the model is difficult, since no perfect one-to-one relation between the features of the two and three component models can be assumed due to the differences in the total backscattered energy between quad- and dual-polarized data and the C- and X-Band data, respectively. We observe that P

_{d}and P

_{s}of the two component models are biased by approximately 2 to 3 dB compared to P

_{d}and P

_{s}of the three component model. This is also evident from the quantile-quantile-plot in Figure 2. Table 6(c) further indicates the average RMSE error between the P

_{d}and P

_{s}of C-band two and three component model. The RMSEs are comparably low and less than 2 dB, thus underlining that the absolute model error is estimated to be low and a prediction seems therefore reliable.

#### 3.3.2. Discussion

_{d}and P

_{s}between the two and three component model features for each test site and the total average for each land cover class.

_{d}decreases from NBG to VWT and therefore the model error decreases with increasing volume scattering intensities, which is the opposite to our expectations. However, the reason for this observation is the weak linear correlation between the features for the vegetation classes (Figure 3a). Therefore the RMSE becomes a function of the standard deviations of the two variables (SD; see Section 2.4 Regression Analysis), as it is obvious in the graph (compare Table 4 as well). Thus, the behavior of the RMSE can be explained by the SD values, which is also true in Figure 4c–f and partially in Figure 4a for the classes VMD, VSD, and VWT. Figure 5 shows the observations of Figure 3 and Figure 4 in a scatterplot. The RMSE is drawn on the abscissa and the explained variance (R

^{2}) on the ordinate. This plot summarizes the findings made in the aforementioned sections.

^{2}> 0.8) with low RMSE (RMSE < 1 dB) for the surface scattering intensities P

_{s}and for classes with no (NBG), respectively low vegetative coverage and vegetation height (VLD). It is further observed that the correlation between P

_{d}of three and two component model is generally lower and RMSE is higher compared to the findings made for the P

_{s}. Figure 5b graphically summarizes the results of the previous analyses: the correlation between the two component model features and the three component volume scattering is low and the RMSEs were high and in average lager than 1.5 dB, while R

^{2}was in average less than 0.2.

#### 3.4. Separability Analysis

#### 3.4.1. Results

#### 3.4.2. Discussion

#### 3.5. Example—Test Site Tuktoyaktuk (TUK)

#### 3.5.1. Results

_{d}(double bounce), P

_{s}(surface scattering), and P

_{v}(volume scattering) intensities of the three component decomposition derived from C-Band quad-polarized data. The Figure 7b,e shows the double bounce (P

_{d}) and surface scattering (P

_{s}) intensities of the two component decomposition derived from C-Band HH/VV-polarized data. All data are displayed as calibrated sigma nought intensities in decibel. The legend in the lower right corner of the figure lists the minimum and maximum values used for the linear stretch (grayscale). Figure 7f shows the RGB color composite of the three component decomposition features with R = P

_{d}, G = P

_{v}, and B = P

_{s}. It indicates as well the dominating land cover units along the profile line (A → B): low/sparsely vegetated tundra (VLD), wetland (VWT) and shrub dominated tundra (VSD). It is obvious that the class VSD caused a higher volume scattering, which is pronounced in the volume scattering feature (Figure 2c)) via higher intensities and with greenish color in the RGB composite (Figure 7f). The class VWT is characterized by high intensities in the double bounce of the two and three component model (Figure 7a,b). The high intensity further caused a reddish color in the RGB composite (Figure 7f). This is a result of the water to vegetation (double bounce) scattering, the interaction of the wave with the water surface and the vegetation body, respectively. The class VLD indicates medium high intensities in all of the features and it shows up in blueish color in the RGB composite (Figure 7f). Additionally, Figure 7g displays the intensities values of P

_{d}of two and three component model along the profile line (A → B). The intensities are strongly related and show the same peaks and troughs. The influence of the land cover on the double bounce intensities is clearly visible: The wetland vegetation (VWT) causes higher backscatter intensities compared to the other land cover classes, most likely due to dominant dihedral scattering. Both P

_{d}features show similar value ranges and identical intensities for some locations.

_{d}of the profile values. Two clusters are visible, one very close to the one-to-one line and a second cluster that is slightly biased: Nevertheless, a clear positive and linear dependency is visible (overall R

^{2}= 0.75). Figure 7i illustrates the profile values of P

_{s}of two and three component model. Again both lines are related and showed the same peaks and troughs and similar value ranges. Contrary to the observations made for the double bounce, the wetland vegetation (VWT) caused maximum differences between both features.

_{s}of the two component model are most likely related to the missing removal of the volume scattering contribution and differences are in the order of 5 dB. The alterations between P

_{s}of the two and P

_{s}of the three component model are lower for the shrub dominated tundra (VSD) and minimized for low tundra coverage (VLD). For the class named last the profile values are nearly identical aligned and differences between the features of both models are small.

#### 3.5.2. Discussion

_{s}of the profile values. As observed for the P

_{d}, two clusters were recognizable and a positive dependency was visible, however it was less strong (overall R

^{2}= 0.40). The cluster closer to the one-to-one line corresponds to the samples of the land cover class VLD (high determination, R

^{2}= 0.66), the more scattered samples to VWT and VSD (lower determination, R

^{2}< 0.6). Finally, Figure 7k shows the volume scattering intensity P

_{v}of the three component model. The shrub dominated tundra (VSD) showed the highest volume scattering intensities. The value ranges of the low tundra (VLD) and the wetland (VWT) were comparable and lower than the value range of VSD (−2 to −7 dB). This example made two points clear: First, the double bounce (surface scattering) intensities of both models were closely related for the classes VWT (VLD). For both land cover types VLD and VWT low volume scattering intensities were present (−10 to −17 dB). Second, differences between them were maximized for the land cover class VSD that showed higher volume scattering (−5 to −10 dB).

## 4. Summary and Conclusions

- (1)
- The features of two and three component decomposition scattering components (surface, dihedral) showed similar backscatter characteristics for the examined land cover classes and therefore provided a similar interpretation. The distributions of the features double bounce and surface scattering of the two and three component model were shown to be very similar in the quantile-quantile-plot and the average bias was less than 5 dB for the double bounce and less than 3 dB for the surface scattering.
- (2)
- In average, the correlation between the double bounce features of the two and three component model showed R
^{2}values around 0.69. The R^{2}values observed for the surface scattering features of the two and three component model were around 0.88. Thus, the decomposition features of HH/VV-polarized (derived as polarimetric subset from the quad-polarized data) and quad-polarized data were similar and positively correlated. The RMSE of the linear model was in average less than 2 dB for both features. - (3)
- The presence of volume scattering led to differences between the two and three component decomposition intensities and these differences were maximized when the volume scattering contribution was high. This was indicated by the analysis of the regression and correlation coefficients. The R
^{2}values between double bounce, respectively surface scattering, intensities of the two and three component decomposition model were high for land cover classes that cause the least volume scattering, e.g., bare or sparsely vegetated ground, and were around 0.7 to 0.9 for the double bounce and 0.6 to 0.8 for the surface scattering. The R^{2}values were low for land cover classes that caused high volume scattering, e.g., shrub dominated tundra or wetland vegetation. The observed R^{2}values were then in the order from 0.4 to 0.5. - (4)
- The correlation between double bounce and surface scattering intensities of the two component model was higher (R
^{2}< 0.4) than the correlation between the double bounce and surface scattering intensities of the three component model (R^{2}< 0.2). Thus, the two component model realizes a weaker orthogonality of the features, which is a result of neglecting the cross-polarized information and the removal of an existing volume component—depolarization acts on surface, as well as, on dihedral scattering component in terms of roughness. - (5)
- The volume scattering intensity of the three component decomposition model showed the highest sensitivity to the land cover classes and provided the best separability among the classes, as indicated by the assessment of the separability features, Jeffries Matusita Distance (JM) and Transformed Divergence (TD). Therefore, the quad-polarized data offered in average a better separation than the co-polarized data due to the benefit of having the cross-polarized information. Therefore the quad-polarized data will be better suited for the classification of the examined tundra land cover types. However; the land cover classes of wetland vegetation, bare ground, and low tundra showed clear positions in the feature space of the HH/VV-polarized data and an accurate classification of these land cover types is likely to be done with such dual-polarized SAR data: The JM and TD were highest among the possible dual-polarization modes (HH/VV; HH/HV; VV/VH) and HH/VV was found to be the favorable mode for the characterization of the named land cover classes. The HH/HV-polarized and VV/VH-polarized data were found to be best suited for the characterization of mixed and shrub dominated tundra as indicated by the separability analyses.
- (6)
- None of the HH/VV-polarized features showed a direct linear correlation with the volume scattering, respectively with the cross-polarized information, which is expected in terms of physics causing independence of the two polarimetric scattering types.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

PolSAR | Polarimetric SAR |

R-2 | Radarsat-2 (C-Band SAR Satellite) |

RMSE | Root Mean Square Error |

SAR | Synthetic Aperture Radar |

TDX | TanDEM-X (X-Band SAR Satellite) |

TSX | TerraSAR-X (X-Band SAR Satellite) |

Test Sites | |

ECH | East Channel of the Mackenzie River |

RIS | Richards Island |

TUK | Tuktoyaktuk |

Land Cover Classes | |

NBG | Bare Ground |

VLD | Low Tundra, sparsely vegetated (formations of grasses, mosses and herbs) |

VMD | Mixed Tundra (formations of herbs and dwarf shrubs) |

VSD | Shrub Dominated Tundra (formations of dwarf shrubs and shrubs) |

VWT | Wetlands (reed and sedge formations) |

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**Figure 1.**Test site location: (

**a**) Extent of the investigation areas, locations of the in situ field work and (

**b**) field photographs of frequent land cover classes. The background map in (

**a**) shows the topographic slope derived from intermediate TanDEM-X elevation model data provided by DLR (2012, German Aerospace Center); grey color indicates sloped terrain. Extents of the test sites refer to the common image footprints of the SAR acquisitions of TerraSAR-X/TanDEM-X and Radarsat-2.

**Figure 2.**Median sigma nought (σ°) backscatter intensities in decibel (dB) of: (

**a**) double bounce (P

_{d}), (

**b**) surface scattering (P

_{s}) and (

**c**) volume scattering (P

_{v}) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) and for C-Band Radarsat-2 and X-Band TerraSAR-X data. The power decomposition features of “C-Band: HH/VV” and “X-Band: HH/VV” were derived via the purposed two component decomposition. Features of “C-Band: Quad” were calculated using the three component Yamaguchi Decomposition. Schemes (

**d**) and (

**e**) show the quantile-quantile plots of the two and three component decomposition features double bounce (P

_{d}) and surface scattering (P

_{s}) for the quantiles 1%, 25%, 50%, 75%, and 99%. The boxplots show the decomposition features of: (

**f**) C-Band: Quad; (

**g**) C-Band: HH/VV and (

**h**) X-Band: HH/VV. Note that NBG, VLD, VMD, and VSD are in an ordinal scale and vegetation height and density is increasing from NBG to VSD.

**Figure 3.**Squared linear Pearson correlation coefficients (R

^{2}) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) of: (

**a**) double bounce (P

_{d}) of the two and three component decomposition; (

**b**) surface scattering (P

_{s}) of the two and three component decomposition; (

**c**) volume scattering (P

_{v}) of three and P

_{d}of the two component decomposition (C-Band); (

**d**) P

_{v}of three and P

_{s}of the two component decomposition (C-Band); (

**e**) P

_{d}and P

_{s}of the two component decomposition (C-Band); (

**f**) P

_{d}and P

_{s}of the three component decomposition (C-Band) and (

**g**) P

_{d}and P

_{s}of the two component decomposition (X-Band). Abbreviations of the test sites: TUK: Tuktoyaktuk, RIS: Richards Island, ECH: East Channel of the Mackenzie River.

**Figure 4.**Root Mean Square Error (RMSE) of the linear models and the product of standard deviations of the two variables (SD) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) for: (

**a**) double bounce (P

_{d}) of the two and three component decomposition; (

**b**) surface scattering (P

_{s}) of the two and three component decomposition; (

**c**) volume scattering (P

_{v}) of three and P

_{d}of the two component decomposition (C-Band); (

**d**) P

_{v}of three and P

_{s}of the two component decomposition (C-Band); (

**e**) P

_{d}and P

_{s}of the two component decomposition (C-Band); (

**f**) P

_{d}and P

_{s}of the three component decomposition (C-Band) and (

**g**) P

_{d}and P

_{s}of the two component decomposition (X-Band). Note the different value range of the ordinate in sub-figure (

**f**). Abbreviations of the test sites: TUK: Tuktoyaktuk, RIS: Richards Island, ECH: East Channel of the Mackenzie River.

**Figure 5.**Averaged Squared Linear Pearson Correlation Coefficients (R

^{2}) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) versus the Averaged Root Mean Square Errors (RMSE) of the linear models for C-Band features: (

**a**) double bounce (P

_{d}) and surface scattering (P

_{s}) of the two and three component decomposition; (

**b**) volume scattering (P

_{v}). double bounce (P

_{d}), and surface scattering (P

_{s}) of the two component decomposition.

**Figure 6.**Average class separability measured as Jeffries Matusita Distance (JD) and Transformed Divergence (TD) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) and the average of all classes: (

**a**) JDs of the features of two and three component decomposition; (

**b**) TDS of the features of two and three component decomposition; (

**c**) JDs of the intensities of dual- and quad-polarized data and (

**d**) TDs of the intensities of dual- and quad-polarized data. The values of the dimensionless JD range from 0.0 to $\sqrt{2}$. The values of the dimensionless TD range from 0 to 2000. The higher the value of a separability feature the higher is the separation of classes in the feature space and the expected classification accuracy.

**Figure 7.**Profile analysis of C-Band Radarsat-2 data of the test site Tuktoyaktuk (TUK): (

**a**–

**e**) images of the two and three component decomposition features double bounce (P

_{d}), surface scattering (P

_{s}) and volume scattering (P

_{v}); (

**f**) RGB colour composite of three component decomposition; (

**g**) profile values of P

_{d}(two and three component decomposition); (

**h**) scatterplot of P

_{d}of two and three component decomposition; (

**i**) profile values of P

_{s}(two and three component decomposition); (

**j**) scatterplot of P

_{s}of two and three component decomposition and (

**k**) profile values of P

_{v}of the three component decomposition. The abbreviations “VLD”, “VWT”, and “VSD” refer to the dominating land cover units: low/sparse vegetated tundra, wetland and shrub dominated tundra.

Sensor | Acquisition Date | Acquisition Mode | Polarization | Incidence Angle (°) | Test Site Coverage ^{1} |
---|---|---|---|---|---|

TDX | 4 September 2012 | Stripmap | HH/VV | 31.7 | RIS |

TSX | 15 September 2012 | Stripmap | HH/VV | 32.8 | RIS |

TSX | 3 August 2011 | Stripmap | HH/VV | 38.8 | TUK |

TDX | 4 September 2012 | Stripmap | HH/VV | 31.7 | ECH |

TSX | 15 September 2012 | Stripmap | HH/VV | 32.8 | ECH |

R-2 | 5 August 2010 | Fine | HH/HV/VH/VV | 46.1 | RIS |

R-2 | 25 August 2010 | Fine | HH/HV/VH/VV | 40.7 | RIS |

R-2 | 19 August 2011 | Fine | HH/HV/VH/VV | 40.5 | TUK |

R-2 | 5 August 2010 | Fine | HH/HV/VH/VV | 39.3 | ECH |

R-2 | 25 August 2010 | Fine | HH/HV/VH/VV | 39.0 | ECH |

^{1}RIS = Richards Island, TUK = Tuktoyaktuk, ECH = East Channel of the Mackenzie River.

Class Name | VWT | NBG | VLD | VMD | VSD |
---|---|---|---|---|---|

Wetland | Bare Substrate/Non-Vegetated Ground | Low/Grass and Herb Dominated Tundra | Medium/Mixed Tundra | High/Shrub Dominated Tundra | |

Scheme | |||||

Description | vegetation in standing water dominated by reed and sedge formations | exposed soil substrate and bedrock of varying grain sizes and material | open to closed vegetative cover dominated by formations of grasses, mosses and herbs | closed vegetative cover dominated by formations of herbs and dwarf shrubs | closed vegetative cover dominated by formations of dwarf shrubs and shrubs |

Vegetation Height | ~10–50 cm | n/a | ~5–30 cm | ~20–50 cm | ~30–100 cm |

Shrub Density | n/a | n/a | low | moderate | high |

Feature | Name | Wavelength | Polarization | Decomposition Model |
---|---|---|---|---|

${\mathrm{P}}_{\mathrm{d}}$ | Double Bounce | X-Band | HH/VV | Two Component |

${\mathrm{P}}_{\mathrm{s}}$ | Surface Scattering | X-Band | HH/VV | Two Component |

${\mathrm{P}}_{\mathrm{d}}$ | Double Bounce | C-Band | HH/VV | Two Component |

${\mathrm{P}}_{\mathrm{s}}$ | Surface Scattering | C-Band | HH/VV | Two Component |

${\mathrm{P}}_{\mathrm{d}}$ | Double Bounce | C-Band | Quad | Three Component |

${\mathrm{P}}_{\mathrm{s}}$ | Surface Scattering | C-Band | Quad | Three Component |

${\mathrm{P}}_{\mathrm{v}}$ | Volume Scattering | C-Band | Quad | Three Component |

**Table 4.**Descriptive statistics—maximum (max), 99% quantile (q99), 1% quantile (q1), minimum (min), mean and standard deviation (sd)—of the investigated features double bounce (P

_{d}), surface scattering (P

_{s}) and volume scattering (P

_{v}) for none-water land cover classes (NBG, VLD, VMD, VSD, VWT) and for C-Band R-2 and X-Band TSX/TDX data. The data show the average of the three test sites Richards Island (RIS), Tuktoyaktuk (TUK) and East Channel (ECH) in the unit decibel (dB).

(a) C-Band (Pseudo HH/VV): P_{d} | (b) C-Band (Pseudo HH/VV): P_{s} | ||||||||||

NBG | VLD | VMD | VSD | VWT | NBG | VLD | VMD | VSD | VWT | ||

max | −5.9 | −10.1 | −6.3 | −5.9 | −2.8 | max | −0.4 | −7.9 | −5.0 | −3.1 | −4.2 |

q99 | −8.7 | −11.4 | −8.5 | −8.3 | −5.5 | q99 | −3.0 | −9.3 | −7.5 | −6.2 | −5.7 |

q1 | −24.3 | −17.6 | −15.9 | −14.4 | −12.6 | q1 | −19.7 | −14.8 | −12.9 | −12.1 | −12.4 |

min | −24.6 | −48.3 | −17.6 | −48.3 | −18.6 | min | −21.0 | −46.7 | −14.9 | −46.8 | −19.6 |

mean | −15.7 | −14.3 | −12.7 | −11.6 | −9.0 | mean | −10.0 | −11.4 | −10.3 | −9.6 | −8.9 |

sd | 3.6 | 2.9 | 1.5 | 1.5 | 1.5 | sd | 3.8 | 2.8 | 1.1 | 1.5 | 1.6 |

(c) X-Band (HH/VV): P_{d} | (d) X-Band (HH/VV): P_{s} | ||||||||||

NBG | VLD | VMD | VSD | VWT | NBG | VLD | VMD | VSD | VWT | ||

max | −3.8 | −8.4 | −7.4 | −7.4 | 0.2 | max | 2.0 | −5.5 | −4.5 | −4.1 | 0.5 |

q99 | −8.5 | −9.2 | −7.9 | −8.0 | −3.4 | q99 | −2.3 | −8.0 | −8.2 | −6.5 | −3.7 |

q1 | −17.9 | −13.9 | −13.6 | −13.1 | −10.9 | q1 | −13.4 | −11.2 | −11.2 | −10.7 | −10.5 |

min | −18.5 | −14.1 | −14.3 | −14.6 | −16.3 | min | −17.8 | −11.5 | −11.8 | −14.6 | −18.3 |

mean | −12.9 | −11.9 | −11.4 | −10.3 | −7.2 | mean | −7.5 | −9.9 | −9.6 | −9.0 | −7.5 |

sd | 1.8 | 1.3 | 1.4 | 1.4 | 1.6 | sd | 2.4 | 0.7 | 0.6 | 0.8 | 1.5 |

(e) C-Band (Quad): P_{d} | (f) C-Band (Quad): P_{s} | ||||||||||

NBG | VLD | VMD | VSD | VWT | NBG | VLD | VMD | VSD | VWT | ||

max | −5.2 | −15.7 | −11.6 | −10.5 | −3.1 | max | −0.8 | −9.3 | −6.1 | −4.0 | −5.3 |

q99 | −13.9 | −17.0 | −14.0 | −13.7 | −6.1 | q99 | −3.4 | −10.5 | −9.4 | −7.7 | −7.1 |

q1 | −28.6 | −23.3 | −21.8 | −20.3 | −17.6 | q1 | −20.3 | −15.3 | −14.0 | −13.6 | −15.2 |

min | −28.9 | −24.6 | −23.1 | −21.5 | −22.0 | min | −21.6 | −17.3 | −16.1 | −27.2 | −22.2 |

mean | −20.3 | −19.8 | −18.4 | −17.4 | −13.0 | mean | −10.5 | −12.4 | −11.7 | −11.2 | −11.2 |

sd | 3.3 | 1.6 | 1.6 | 1.3 | 2.5 | sd | 3.8 | 1.0 | 1.0 | 1.2 | 1.8 |

(g) C-Band (Quad): P_{v} | |||||||||||

NBG | VLD | VMD | VSD | VWT | |||||||

max | −7.3 | −10.2 | −6.5 | −3.9 | −6.8 | ||||||

q99 | −8.4 | −10.7 | −8.3 | −7.6 | −7.5 | ||||||

q1 | −24.8 | −17.0 | −15.3 | −13.5 | −16.3 | ||||||

min | −25.0 | −18.8 | −17.0 | −27.0 | −21.9 | ||||||

mean | −16.6 | −13.6 | −12.1 | −10.9 | −10.4 | ||||||

sd | 3.9 | 1.5 | 1.5 | 1.2 | 1.8 |

**Table 5.**Average Pearson (

**a**), squared Pearson

**(b**) and Spearman (

**c**) correlation coefficients of C-Band Radarsat-2 and X-Band TerraSAR-X data for two and three component decomposition features double bounce (P

_{d}), surface scattering (P

_{s}), and volume scattering (P

_{v}).

(a) Pearson (R)—Linear Dependence | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

1.00 | 0.52 | 0.42 | 0.20 | 0.45 | 0.36 | 0.47 | X-HH/VV | P_{d} |

1.00 | 0.83 | 0.14 | 0.14 | 0.10 | 0.68 | C-HH/VV | ||

1.00 | 0.10 | 0.47 | 0.57 | 0.35 | C-Quad | |||

1.00 | 0.14 | 0.10 | 0.10 | X-HH/VV | P_{s} | |||

1.00 | 0.94 | 0.64 | C-HH/VV | |||||

1.00 | 0.46 | C-Quad | ||||||

1.00 | C-Quad | P_{v} | ||||||

(b) Squared Pearson (R^{2})—Explained Variance | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

1.00 | 0.27 | 0.18 | 0.04 | 0.20 | 0.13 | 0.22 | X-HH/VV | P_{d} |

1.00 | 0.69 | 0.02 | 0.02 | 0.01 | 0.46 | C-HH/VV | ||

1.00 | 0.01 | 0.22 | 0.32 | 0.12 | C-Quad | |||

1.00 | 0.02 | 0.01 | 0.01 | X-HH/VV | P_{s} | |||

1.00 | 0.88 | 0.41 | C-HH/VV | |||||

1.00 | 0.21 | C-Quad | ||||||

1.00 | C-Quad | P_{v} | ||||||

(c) Spearman ($\mathsf{\rho}$)—Monotonic Dependence | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

1.00 | 0.62 | 0.53 | 0.64 | 0.60 | 0.49 | 0.61 | X-HH/VV | P_{d} |

1.00 | 0.84 | 0.38 | 0.67 | 0.54 | 0.78 | C-HH/VV | ||

1.00 | 0.33 | 0.55 | 0.48 | 0.53 | C-Quad | |||

1.00 | 0.44 | 0.38 | 0.39 | X-HH/VV | P_{s} | |||

1.00 | 0.91 | 0.68 | C-HH/VV | |||||

1.00 | 0.51 | C-Quad | ||||||

1.00 | C-Quad | P_{v} |

**Table 6.**Average linear model parameters: axis intercept (

**a**), slope (

**b**) and Root Mean Square Error (

**c**) of C-Band Radarsat-2 and X-Band TerraSAR-X data for two and three component decomposition features double bounce (P

_{d}), surface scattering (P

_{s}) and volume scattering (P

_{v}).

(a) Linear Model—Axis Intercept—(dB) | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

0.00 | −7.84 | −9.15 | −7.15 | −8.74 | −9.94 | −8.48 | X-HH/VV | P_{d} |

0.00 | −3.42 | −6.51 | −7.19 | −9.30 | −5.32 | C-HH/VV | ||

0.00 | −7.30 | −5.98 | −15.42 | −19.69 | C-Quad | |||

0.00 | −6.95 | −7.82 | −6.92 | X-HH/VV | P_{s} | |||

0.00 | −2.46 | −3.87 | C-HH/VV | |||||

0.00 | −11.05 | C-Quad | ||||||

0.00 | C-Quad | P_{v} | ||||||

(b) Linear Model—Slope | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

1.00 | 0.23 | 0.09 | 0.44 | 0.20 | 0.08 | 0.18 | X-HH/VV | P_{d} |

1.00 | 0.49 | 0.17 | 0.58 | 0.32 | 0.59 | C-HH/VV | ||

1.00 | 0.08 | 0.20 | 0.32 | −0.10 | C-Quad | |||

1.00 | 0.18 | 0.08 | 0.14 | X-HH/VV | P_{s} | |||

1.00 | 0.64 | 0.47 | C-HH/VV | |||||

1.00 | 0.16 | C-Quad | ||||||

1.00 | C-Quad | P_{v} | ||||||

(c) Linear Model—Root Mean Square Error (RMSE)—(dB) | ||||||||

P_{d} | P_{s} | P_{v} | ||||||

X-HH/VV | C-HH/VV | C-Quad | X-HH/VV | C-HH/VV | C-Quad | C-Quad | ||

0.00 | 1.38 | 1.44 | 1.24 | 1.41 | 1.45 | 1.38 | X-HH/VV | P_{d} |

0.00 | 1.78 | 1.45 | 1.85 | 2.22 | 1.85 | C-HH/VV | ||

0.00 | 1.48 | 2.10 | 3.87 | 3.87 | C-Quad | |||

0.00 | 1.45 | 1.47 | 1.44 | X-HH/VV | P_{s} | |||

0.00 | 1.05 | 1.64 | C-HH/VV | |||||

0.00 | 2.19 | C-Quad | ||||||

0.00 | C-Quad | P_{v} |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ullmann, T.; Schmitt, A.; Jagdhuber, T. Two Component Decomposition of Dual Polarimetric HH/VV SAR Data: Case Study for the Tundra Environment of the Mackenzie Delta Region, Canada. *Remote Sens.* **2016**, *8*, 1027.
https://doi.org/10.3390/rs8121027

**AMA Style**

Ullmann T, Schmitt A, Jagdhuber T. Two Component Decomposition of Dual Polarimetric HH/VV SAR Data: Case Study for the Tundra Environment of the Mackenzie Delta Region, Canada. *Remote Sensing*. 2016; 8(12):1027.
https://doi.org/10.3390/rs8121027

**Chicago/Turabian Style**

Ullmann, Tobias, Andreas Schmitt, and Thomas Jagdhuber. 2016. "Two Component Decomposition of Dual Polarimetric HH/VV SAR Data: Case Study for the Tundra Environment of the Mackenzie Delta Region, Canada" *Remote Sensing* 8, no. 12: 1027.
https://doi.org/10.3390/rs8121027