# Polarimetric Scattering Properties of Landslides in Forested Areas and the Dependence on the Local Incidence Angle

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{s}is dominant among other scattering powers (the double-bounce scattering P

_{d}, the volume scattering P

_{v}and the helix scattering P

_{c}) on the landslide surfaces and on other bare soil surfaces, such as agricultural fields. Watanabe et al. [2] also proposed a decision tree scheme that separates rough surfaces, including landslides from other surfaces in a PolSAR image. In warm and humid regions, such as Japan, the slope adjacent to a landslide or the pre-slide slope is generally covered by vegetation. It is known that the volume scattering power P

_{v}is dominant on vegetated surface. A landslide can be distinguished as the area where P

_{s}surpasses P

_{v}or P

_{s}increased more than P

_{v}[4,5]. Note, however, that the observation geometry has not been taken into consideration in these papers. Additionally, the correlation coefficient between HH (horizontal transmitted and horizontal received) and VV (vertical transmitted and vertical received) polarizations and other polarimetric indices were focused on for landslide detection in Shimada et al. [6]. They revealed that the magnitude of the HH-VV correlation coefficient showed high values at landslides and smooth surfaces. This is because the HH-VV correlation coefficient is a polarimetric index that relates to the surface and the double-bounce scattering processes. As mentioned above, it is known that the surface scattering process is observed on landslide surfaces or on bare soil surfaces. The HH-VV correlation coefficient has been examined for the estimation of surface roughness in [7]. It is reported that the magnitude of the HH-VV correlation coefficient of bare surfaces mainly ranges between 0.6 and 0.9 regardless of the roughness state.

## 2. Methodology and the Data Utilized

#### 2.1. Methodology

#### 2.1.1. Basic Concept of Surface Scattering and the Importance of Orientation Angle Compensation

_{HH}and S

_{VV}) of the scattering matrix [S] are almost in phase [13]. This behavior is characterized by (2). The superscript * denotes complex conjugation.

_{HH}S

_{VV}* term is directly related to the HH-VV correlation coefficient.

#### 2.1.2. Model-Based Scattering Power Decomposition

**Figure 1.**Schematic diagram of the four-component scattering power decomposition with the coherency matrix. Measured scattering matrix [S] is transformed to coherency matrix [T] and is decomposed into the surface scattering power P

_{s}, the double-bounce scattering power P

_{d}, the volume scattering power P

_{v}and the helix scattering power P

_{c}.

_{33}component of the coherency matrix to overcome the reflection symmetry assumption problems. This procedure is equivalent to the orientation angle compensation. Accordingly, Y4R can be done with the following procedures. First, the coherency matrix [T] corresponding to each imaging pixel can be given by definition:

**k**

_{p}is defined as:

_{s}, f

_{d}, f

_{v}and f

_{c}are the expansion coefficients and P

_{s}, P

_{d}, P

_{v}and P

_{c}are the decomposition powers for the surface, the double-bounce, the volume and the helix scattering, respectively.

^{2}[19].

**Figure 2.**Four-component scattering power decomposition image of a portion in the study area. The PolSAR data for this decomposition image was acquired on 26 August 2014 with PALSAR-2 onboard the ALOS-2 satellite. Deep-seated landslides are colored red, which corresponds to surface scattering. The yellow arrow on the top of the image depicts the line of sight of the optical image of a landslide (Figure 3).

**Figure 3.**An optical image of a landslide within the images of Figure 2 and Figure 4. The acquisition date of this optical image is 4 May 2014, which is close to that of the PolSAR data in Figure 2 and Figure 4. It is found that there is no vegetation in the landslide area, while slopes in the vicinity are covered with trees.

#### 2.1.3. Correlation Coefficient in the Linear Polarization Basis

_{1}(x) and s

_{2}(x), also known as complex coherence, can be defined as follows:

_{HH-VV}can be obtained by replacing s

_{1}(x) and s

_{2}(x) in (9) with two polarizations, such as S

_{HH}and S

_{VV}, and is defined as:

_{HH-VV}, S

_{HH}S

_{VV}* term works as a discriminant for the surface scattering mechanism. Accordingly, we employ the positive values for the real part of the complex correlation coefficient, which corresponds to the surface scattering. For retrieving the geophysical parameters properly, the orientation angle compensation is also applied to the calculation of the HH-VV correlation coefficient. Consequently, the polarimetric correlation coefficient used in this study can be expressed as:

_{XX}denotes the S

_{XX}term in the scattering matrix (1) rotated by the angle θ derived by (7). Figure 4 shows the HH-VV correlation coefficient with the orientation angle compensation (Re(γ(θ)

_{HH}

_{-VV})) image in the study area. It is observed from Figure 4 that landslides are dominated by relatively high values (close to 1) of Re(γ(θ)

_{HH}

_{-VV}), while other areas, except for river beds and sparsely-vegetated areas, show low correlation values.

**Figure 4.**The gray-scaled image of the HH-VV correlation coefficient with orientation angle compensation. The image coverage and utilized PolSAR data are the as same as Figure 2. Most of the whitish portions indicate landslides or river bed. The yellow arrow on the top of the image depicts the line of sight of the optical image of a landslide (Figure 3).

**Table 1.**Description of the PolSAR data. The angles of the azimuth (or flight) and range (or illumination) direction are defined as the angles from the north in the clock-wise direction. Pi, Polarimetric and Interferometric.

Scene ID | Acquisition Date | Azimuth Direction (°) | Range Direction (°) | Pixel Spacing Azimuth, Range (m) | |
---|---|---|---|---|---|

PALSAR-2 Descending (Dsc.) | ALOS2013902890 | 26 August 2014 | 195 | 105 | 3, 5 |

PALSAR-2 Ascending (Asc.) | ALOS2014120670 | 27 August 2014 | 354 | 79 | |

Pi-SAR-L2 Nara | L200501 | 18 June 2012 | 270 | 180 | 0.5, 1.7 |

Pi-SAR-L2 Yoshino | L204006 | 8 August 2014 | 225 | 135 |

**Figure 5.**Red crosses indicate deep-seated landslides, which were triggered by torrential rain caused by Typhoon Talas in September 2011 in the study area. Blue and green rectangles show the coverage of PALSAR and Pi-SAR-L2 images, respectively. The flight (azimuth) and the illumination (range) direction for each PolSAR observation are indicated by arrows with labels.

#### 2.2. Description of Polarimetric SAR Data and the Study Area

^{2}/pixel on the ground. For Pi-SAR-L2 data, the window size is 3 (range) by 11 (azimuth) pixels, and that exhibits 30 m

^{2}/pixel on the ground. All of the PolSAR image processing was done by programs written in the MATLAB language.

## 3. Polarimetric Scattering Properties of Landslides

#### 3.1. Results for PALSAR-2 Data Analysis

#### 3.1.1. Scattering Power Decomposition

_{x}defined as follows:

_{s}and the normalized volume scattering power p

_{v}contribution to the total power sampled in white rectangles in Figure 6 are summarized in Table 2 and Table 3, respectively. It is found from Table 2 that the mean values of p

_{s}in landslides ranged from 0.3 to 0.7, although the mean values of p

_{s}in forest were much smaller than those in landslides. It is also found that p

_{v}values in forest were almost stable in spite of the change of observation geometries, although the p

_{v}values in landslides ranged from 0.24 to 0.47. These facts can be summarized as follows; the p

_{s}and the p

_{v}in landslides can change in connection with the change of the observation geometries, while those in forest do not.

**Figure 6.**Scattering power decomposition results for PALSAR-2 data in (

**a**,

**b**) descending and (

**c**,

**d**) ascending orbit observations. Landslide No. 1 (a,c) is on the slope facing toward the radar as contrasted to landslide No. 2 (b,d), which is on the slope facing away from the radar. The values of P

_{s}for landslides (L) and those of neighboring forest (F) were sampled in the white rectangles on the images.

**Table 2.**Statistics of the normalized surface scattering power p

_{s}in landslides and those of neighboring forest.

PolSAR Data | Landslide No. 1 | Landslide No. 2 | Forest Adjacent to Landslide No. 1 | Forest Adjacent to Landslide No. 2 | ||||
---|---|---|---|---|---|---|---|---|

Mean (SD) | Mean (SD) | Mean (SD) | Mean (SD) | |||||

PALSAR-2, Descending | 0.70 | (0.16) | 0.32 | (0.18) | 0.18 | (0.17) | 0.12 | (0.13) |

PALSAR-2, Ascending | 0.51 | (0.23) | 0.35 | (0.19) | 0.20 | (0.13) | 0.11 | (0.11) |

**Table 3.**Statistics of the normalized volume scattering power p

_{v}in landslides and those of neighboring forest.

PolSAR Data | Landslide No. 1 | Landslide No. 2 | Forest Adjacent to Landslide No. 1 | Forest Adjacent to Landslide No. 2 | ||||
---|---|---|---|---|---|---|---|---|

Mean (SD) | Mean (SD) | Mean (SD) | Mean (SD) | |||||

PALSAR-2, Descending | 0.24 | (0.14) | 0.47 | (0.18) | 0.66 | (0.19) | 0.70 | (0.17) |

PALSAR-2, Ascending | 0.39 | (0.19) | 0.46 | (0.20) | 0.63 | (0.15) | 0.71 | (0.15) |

#### 3.1.2. Correlation Coefficient of HH and VV Polarizations

_{HH}

_{-VV}) behaved in a similar manner to the p

_{s}, as has been previously described. The values of Re(γ(θ)

_{HH}

_{-VV}) in landslides depend on the observation geometries, while those in forest are stable.

PolSAR Data | Landslide No. 1 | Landslide No. 2 | Forest Adjacent to Landslide No. 1 | Forest Adjacent to Landslide No. 2 |
---|---|---|---|---|

Mean (SD) | Mean (SD) | Mean (SD) | Mean (SD) | |

PALSAR-2, Descending | 0.74 (0.14) | 0.28 (0.21) | 0.24 (0.18) | 0.16 (0.14) |

PALSAR-2, Ascending | 0.55 (0.25) | 0.31 (0.21) | 0.25 (0.14) | 0.15 (0.14) |

**Figure 7.**The HH-VV correlation coefficient Re(γ(θ)

_{HH}

_{-VV}) images for PALSAR-2 data in (

**a**,

**b**) descending and (

**c**,

**d**) ascending orbit observations. The correlation coefficient values for landslides (L) and those of neighboring forest (F) were sampled in the white rectangles on the images.

#### 3.1.3. Dependence on Local Incidence Angle

_{s}, p

_{v}and Re(γ(θ)

_{HH}

_{-VV}) in landslides vary in connection with the directions of observations or sloping surfaces. In a further step, we introduce the local incidence angle displayed in Figure 8. The local incidence angle is the angle between the radar line-of-sight (LOS)

**I**and the normal vector to the slope surface

**N**. The vector

**I**can be obtained by the azimuth and range directions and the off-nadir angle of the radar; and the vector

**N**can be calculated from a digital elevation model (DEM). The DEM utilized in this study is the spatial information infrastructure data distributed by the Geospatial Information Authority of Japan (GSI) [22], and the spatial resolution is approximately 10 meters. The local incidence angle φ can be derived from:

**Figure 8.**Schematic diagram of the radar observation geometry to relate the local incidence angle φ to the ground surface. The angle φ can be derived by the inner product of radar incidence direction

**N**and ground surface normal

**I**vectors.

_{s}and the p

_{v}with respect to the local incidence angle for 22 landslides and forested areas in the vicinity in the study area. The values of the p

_{s}and the p

_{v}were retrieved from the power decomposition results of both descending (Dsc.) and ascending (Asc.) PALSAR data. It is observed that the p

_{s}decreases with the local incidence angle. For example, the p

_{s}values at the incidence angle of around 15° are 0.7, but the values become 0.6 at the angle of around 30°. Furthermore, where the incidence angle is over 60°, the values of the p

_{s}decrease to 0.3. In contrast, the p

_{v}shows the opposite trend to the p

_{s}. For forested areas, both the p

_{s}and the p

_{v}have shown almost a flat behavior. The values of the p

_{s}are lower than 0.2, while the values of the p

_{v}are higher than 0.6 ( ${p}_{s}\le 0.2\text{and}{p}_{v}\ge 0.6$ ), except for a smaller incidence angle.

_{HH}

_{-VV}) shows almost the same tendency as seen in the p

_{s}case. This is not surprising, since Re(γ(θ)

_{HH}

_{-VV}) in this study is an index that correlates to the surface scattering process.

**Figure 9.**Normalized powers of the surface and the volume scattering components’ (p

_{s}and p

_{v}) contribution to the total power with respect to the local incidence angle in (

**a**) landslides and (

**b**) forested areas for PALSAR-2 data acquired with ALOS-2 from its descending and ascending orbits.

**Figure 10.**The HH-VV correlation coefficient with respect to the local incidence angle in (

**a**) landslides and (

**b**) forested areas for PALSAR-2 data acquired with ALOS-2 from its descending and ascending orbits.

#### 3.2. Results for Pi-SAR-L2 Data Analysis

_{s}, p

_{v}and Re(γ(θ)

_{HH}

_{-VV})) were also examined with the PolSAR data acquired by the airborne SAR system, Pi-SAR-L2. The spatial resolution of Pi-SAR-L2 is finer than that of PALSAR-2, as shown in Table 2. The results are shown in Figure 11.

_{s}and the Re(γ(θ)

_{HH-VV}) decrease from 0.8, while the p

_{v}values gradually increase with the local incidence angle for landslides. In contrast, all of the indices for forested areas are basically stable regardless of the incidence angle. It is also confirmed from Figure 11c,d that the Re(γ(θ)

_{HH-VV}) and the p

_{s}are around 0.2 ( $Re(\gamma {\left(\theta \right)}_{HH-VV})\cong 0.2\text{and}{p}_{s}\cong 0.2$ ), and the values of the p

_{v}mainly range between 0.4 and 0.7 ( 0.4 ≤ p

_{v}≤ 0.7) for the forested areas. As a result, the polarimetric indices derived from Pi-SAR-L2 data behave quite similar to those from PALSAR-2 data. It is confirmed by this fact that p

_{s}, p

_{v}and Re(γ(θ)

_{HH}

_{-VV}) derived from L-band PolSAR data can change with the incidence angle in landslide areas, whereas those indices do not in forested areas regardless of the spatial resolution.

**Figure 11.**(

**a**) Normalized powers of the surface and the volume scattering components’ (p

_{s}and p

_{v}) contribution to the total power and (

**b**) the correlation coefficient of HH and VV polarizations (Re(γ(θ)

_{HH}

_{-VV})) with respect to the local incidence angle in landslides; (

**c**) the p

_{s}and the p

_{v}contributions; and (

**d**) the HH-VV correlation coefficient in forested areas for the Pi-SAR-L2 datasets named “Nara” and “Yoshino”.

## 4. Discussions

#### 4.1. Polarimetric Scattering Properties of Landslides

_{s}is basically larger than that of the volume scattering P

_{v}for landslides on the slopes with smaller incidence angles (up to 30°). The HH-VV correlation coefficient Re(γ(θ)

_{HH-VV}) for landslides shows a relatively high value (($Re(\gamma {\left(\theta \right)}_{HH-VV})\ge 0.6$). Consequently, landslides can be distinguished from forest by applying these polarimetric properties properly to PolSAR data as far as the landslide occurred on the slope facing toward the radar. While on the other hand, where incidence angle increase from 30° to 45°, this means that the slope is turning away from the radar, and then, the difference between P

_{s}and P

_{v}gradually decreases, while the correlation coefficient also decreases. The effect of observation geometry on polarimetric indices has been suggested by existing research [23,24]; it was quantified based on the analyses of PolSAR data acquired from different observation directions and platforms in this study.

#### 4.2. Multiple Threshold Settings for Better Landslide Detection

_{s}in landslides and the thresholds for landslide detection with the polarimetric scattering power decomposition method have been discussed in the literature [2,3,4,5]. The range of the p

_{s}and the threshold values are summarized in Table 5 ([2,3,4,5]) with our results for the sake of comparison. In Cases 1, 2a and 4 and in this paper, the four-component scattering power decomposition was applied, and the three-component power decomposition was employed in other cases, so that the values of each case are incomparable in the strict sense. However, for most of the cases, the value of the p

_{s}widely range from 20% to 50%, and this fact indicates the difficulty in defining a single threshold of the p

_{s}to be applied to the whole PolSAR image. Hence, we propose to apply multiple thresholds based on the local incidence angle for a more accurate landslide detection result.

**Table 5.**The ranges of the p

_{s}value in landslides and the proposed thresholds for landslide detection.

Study Case | Range | Threshold |
---|---|---|

Case 1 [4] | N/A | p_{s} > 0.6 |

Case 2a [2] | 0.349 to 0.463 | p_{s} > 0.1, with p_{v} < 0.65 and p_{d} < 0.1 |

Case 2b [2] | 0.381 to 0.485 | N/A |

Case 3 [3] | 0.165 to 0.246 | N/A |

Case 4 [5] | N/A (0.4 to 0.7) | N/A |

Present case | 0.09 to 0.88 | (1) at LIA < 30° p_{s} > 0.6 and p_{s} > p_{v} (2) at 30° < LIA < 60° p _{s} > 0.4 and p_{s} > p_{v} (3) at 60° < LIA Not detectable (p _{s} < p_{v}) |

_{v}exceeds P

_{s}, and the correlation coefficient becomes around 0.2. Since the correlation coefficient of forest is also around 0.2 and that is independent of the incidence angle, it is difficult to distinguish landslides from forest by the relationship between P

_{s}and P

_{v}or the value of Re(γ(θ)

_{HH}

_{-VV}). Therefore, in order to detect a landslide that occurred on the slope facing away from the radar, it should be effective to observe from different directions with polarimetric SAR or to combine other remote sensing techniques (aerial photographs, optical satellite imagery, LiDAR, etc.) with SAR observations. The proposed methodology is applicable to detect landslides in a densely-vegetated environment.

## 5. Conclusions

_{s}and the volume scattering P

_{v}are effectual indices for landslide recognition from PolSAR data. The availability of the real part of the HH-VV polarization correlation coefficient with orientation angle compensation Re(γ(θ)

_{HH}

_{-VV}) was also examined.

_{s}and p

_{v}and the HH-VV correlation coefficient Re(γ(θ)

_{HH}

_{-VV}) has been also analyzed. We found that in landslide areas, polarimetric indices p

_{s}, p

_{v}and Re(γ(θ)

_{HH}

_{-VV}) change drastically with the local incidence angle, whereas in forested areas, those indices are stable regardless of the local incidence angle change. Hence, it is important to set up multiple thresholds based on the local incidence angle to improve the accuracy of landslide detection in forested mountainous areas.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Shibayama, T.; Yamaguchi, Y.; Yamada, H.
Polarimetric Scattering Properties of Landslides in Forested Areas and the Dependence on the Local Incidence Angle. *Remote Sens.* **2015**, *7*, 15424-15442.
https://doi.org/10.3390/rs71115424

**AMA Style**

Shibayama T, Yamaguchi Y, Yamada H.
Polarimetric Scattering Properties of Landslides in Forested Areas and the Dependence on the Local Incidence Angle. *Remote Sensing*. 2015; 7(11):15424-15442.
https://doi.org/10.3390/rs71115424

**Chicago/Turabian Style**

Shibayama, Takashi, Yoshio Yamaguchi, and Hiroyoshi Yamada.
2015. "Polarimetric Scattering Properties of Landslides in Forested Areas and the Dependence on the Local Incidence Angle" *Remote Sensing* 7, no. 11: 15424-15442.
https://doi.org/10.3390/rs71115424