# Characteristics of Decomposition Powers of L-Band Multi-Polarimetric SAR in Assessing Tree Growth of Industrial Plantation Forests in the Tropics

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

^{0}) is used as a calculated parameter [5,7–9]. However, there is a great deal of interest in making effective use of other parameters derived from the decomposition of the polarimetric information from the target. The target decomposition theorem has been developed to extract surface features from radar polarimetry data. Both the three-component scattering model developed in [10] and the entropy/alpha decomposition method developed in [11] have been commonly used and are currently being improved for more accurate target classification [12–15]. The Freeman and Durden approach [16] was developed based on the three-component scattering model, which represents the surface, double-bounce and volume (canopy) scatterings. This scheme was further improved by the addition of a helix scattering term as a fourth component and the modification of the volume scattering model [12]. Furthermore, Yamaguchi et al. [13] improved the four-component decomposition scheme using matrix rotation to enhance the results by allowing oriented urban areas previously and mistakenly included in the volume scattering component as double-bounce scattering to be distinguished. In addition to the POLSAR data, there has been an increase in research on the use of Polarimetric Interferometry SAR (POLinSAR) techniques [2,6] particularly for tree height estimations.

^{0}) and the forest stand parameter fits a negative quadratic curve because of the stronger backscattering from approximately two year old trees, and the weaker backscattering from both trees younger than two years and more mature trees; (ii) the optical NDVI values for trees older than two years tend to decrease. These findings suggest that the L-band SAR is strongly affected by the acacia tree foliage.

## 2. Study Area

^{2}with an altitude ranging from 41 to 253 m (average of 111.5 m) above sea level and a slope varying from 0 to 14.9 degree (3.4° on average).

^{2}(equivalent to 47.9%) of the total area of Unit V (the unit area is not used exclusively for industrial plantations). The mean annual rainfall varies between 2,000 and 3,000 mm per year. This area has a tropical climate; a dry season prevails between June and September, and a rainy season prevails between October and May with two rainfall peaks in December–January and March–April. The average daily temperature is 29 °C, the average minimum temperature is 21 °C and the average maximum temperature is 32 °C.

## 3. Data Sets

#### 3.1. Field Measured Forest Biometric Data

#### 3.2. Satellite Data Sets

## 4. Analysis Methodology

#### 4.1. Forest Biometric Parameters

^{3}/ha) as follows:

#### 4.2. Satellite Remote Sensing Data

#### 4.2.1. Covariance and Coherency Matrix

_{VH}= S

_{HV}, the covariance matrix is given as the following:

_{HH}, S

_{VV}and S

_{HV}indicate the scattering matrix components for the HH, VV and HV polarizations, respectively. The coherency matrix can be calculated by the unitary transformation of the covariance matrix using the following equation:

_{p}]) is expressed as

#### 4.2.2 Pre-Processing of the PALSAR Data

^{2}, where Δx is the spatial resolution in the azimuth direction. The applied look number was 3 (1 × 3 window). This window size seems relatively small for reducing the speckle noise [26]. However, we adopted this look number because the spatial scale of some forest stands was exceedingly small, for example, 0.0011 km

^{2}. The filtered covariance and coherency matrices are denoted as 〈[C]〉 and 〈[T]〉, respectively.

#### 4.2.3. Rotation of Coherency Matrix

_{p}(θ)], which are defined as

#### 4.2.4. Decomposition of Covariance and Rotated Covariance Matrices

_{s}, f

_{d}, f

_{c}as well as f

_{h}, and f

_{s(θ)}, f

_{d(θ)}, f

_{c(θ)}and f

_{h(θ)}are the expansion coefficients (f) needing to be evaluated, and 〈[C]〉

_{s}, 〈[C]〉

_{d}, 〈[C]〉

_{c}and 〈[C]〉

_{h}are the scattering models for the surface, double-bounce, canopy and helix scatterings, respectively. Each of the four-component powers, P (P

_{s}, P

_{d}, P

_{c}, P

_{h}) from 〈[C]〉 and P

_{(θ)}(P

_{s(θ)}, P

_{d(θ)}, P

_{c(θ)}, P

_{h(θ)}) from the rotated 〈[C(θ)]〉, can be determined from the traces of f

_{s}〈[C]〉

_{s}, f

_{d}〈[C]〉

_{d}, f

_{c}〈[C]〉

_{c}and f

_{h}〈[C]〉

_{h}and f

_{s(θ)}〈[C]〉

_{s}, f

_{d(θ)}〈[C]〉

_{d}, f

_{c(θ)}〈[C]〉

_{c}and f

_{h(θ)}〈[C]〉

_{h}, respectively.

#### 4.3. Correlation Analysis between Forest Biometric Parameters and Decomposition Powers

_{10}DBH, log

_{10}H and log

_{10}V) and (i) the base 10 logarithms of the decomposition powers, P (log

_{10}P), from the covariance matrix 〈[C]〉, and (ii) those for P

_{(θ)}(log

_{10}P

_{(θ)}) from the rotated covariance matrix 〈[C(θ)]〉.

_{(θ)}, normalized by the total power (TP), namely, P

_{(θ)}/TP (P

_{s(θ)}/TP, P

_{d(θ)}/TP, P

_{c(θ)}/TP and P

_{h(θ)}/TP). This calculation indicates the variation in the ratio of the decomposition powers to the total power between pixels. The TP is calculated as follows:

^{2}in area (equal to 120 m × 120 m) were excluded from further analysis. Consequently, 26 forest stands remained as those with PSPs, and only the edge-eroded forest stands with enough dimensions were utilized in the following analyses.

## 5. Data Analysis Results

#### 5.1. Visual Interpretation of Decomposition SAR Image

_{10}P, log

_{10}P

_{(θ)}and P

_{(θ)}/TP, respectively, for the forest stands in Unit V. There was not much difference between the first two images (Figure 3(a–b)), whereas the P

_{(θ)}/TP image (Figure 3(c)) showed a significant color change relative to those for the log

_{10}P and log

_{10}P

_{(θ)}.

#### 5.2. Forest Biometric Parameters and Decomposition Powers

_{10}DBH (Figure 5(a)), log

_{10}H (Figure 5(b)) and log

_{10}V (Figure 5(c)) on the x-axis and the base 10 logarithms of each of the decomposition powers (log

_{10}P) on the y-axis.

_{s}, the surface scattering (the blue colored squares), (2) P

_{d}, the double-bounce scattering (red colored triangles), (3) P

_{c}, the canopy scattering (green colored circles) and (4) P

_{h}, the helix scattering (cross marks). The same symbols and colors are also used in Figures 6–7. The fourth helix scattering is known to primarily occur in urban areas but not natural land-cover environments and is only shown for reference.

_{(θ)}. A Pearson’s correlation coefficient (R) was calculated to evaluate the linear dependence of log

_{10}P and log

_{10}P

_{(θ)}on the forest parameters (Table 1(a–b)).

_{10}P and log

_{10}P

_{(θ)}on the one side and the base 10 logarithm of DBH, H and V on the other side are almost identical for each scattered power. However, the P

_{(θ)}correlation (Figure 6) is slightly better than that of P (Figure 5) for the surface and canopy scatterings. The surface scattering has a significantly negative correlation (R ≈ −0.70) and the canopy scattering has a medium positive correlation (R ≈ 0.50) with the forest parameters as the forest grows older, whereas the double-bounce scattering does not show any correlation (R ≈ ±0.10).

_{(θ)}/TP. The correlations became clearer and stronger than those of P (Figure 5(a–c)) and P

_{(θ)}(Figure 6(a–c)) for all the decomposition powers. The correlation coefficients were substantially improved especially for the double-bounce and canopy scatterings, which have correlation coefficients above 0.50 and 0.65, respectively. The P-values were less than 0.001 for the surface and volume scatterings and less than 0.002 for the double-bounce scattering (except for H), which indicate the statistical significance of the correlations (Table 2).

#### 5.3. Forest Stand Volume Estimation using Decomposition Powers

_{s}(θ)/TP, P

_{d}(θ)/TP and P

_{c}(θ)/TP:

_{10}V) on the y-axis. The determinant coefficient (R

^{2}) is 0.557 for a P-value below 0.001. The statistical test results of the nonlinear regression analysis and the analysis of variance are shown in Table 3.

## 6. Discussion

#### 6.1. Differences among Decomposition Powers

_{(θ)}scattered powers are characterized by the same correlation to the forest parameters: a high negative correlation for the surface scattering, a medium positive correlation for the canopy scattering and no correlation for the double-bounce scattering. Two of the composite images (Figure 3(a,b)) did not show any clear distinctions between these parameters. However, P

_{(θ)}, which is derived from the rotated matrix, showed a slightly higher correlation than P for both the surface and canopy scatterings.

^{0}level for both young and more mature trees. Hence, ratio calculations would be an effective approach to determine the forest structural parameters, especially in the present study area.

_{(θ)}/TP image in Figure 4(a) and the tree age in Figure 4(b) clearly demarcates the bare ground and less vegetated land, either because of harvesting or other causes. This explicitly demonstrates that the decomposition images derived from the multi-polarimetric SAR data have potential for forest management studies.

#### 6.2. Physical Understanding of Scattering Characteristics

#### 6.3. Possibility of Estimating the Forest Stand Volume

_{(θ)}/TP (Equation (13)) is presented (Figure 8), aided by Equation (14) and achieved a relatively high correlation (R

^{2}= 0.557, P-value < 0.001). Only 26 sample data plots were available for our analysis, which is statistically very small, especially for young trees. However, this sample size compares favorably to previous works [1,2,4,6], where the number of plots ranged from 13 to 27, which strongly emphasizes the need for more field observations. For our future work, we will strive to collect and accumulate basic data for the purpose of such an application. Although single-year data are used in the current study, we expect to be able to model and realize stem volume and forest biomass estimations based on data compiled over several years with more sample plots.

#### 6.4. Uncertainties in the Relationship between the Decomposition Powers and Forest Structural Parameters

_{(θ)}/TP (Equation (13)). However, the double-bounce scattering had the weakest correlation of all the four-component scatterings to the stand volume (R = 0.582), and the standard error of estimate of 0.563 appeared to be sufficiently large for practical use in stand volume estimation. Moreover, it is apparent that some plots had higher volumes (log

_{10}V ≈ 2) at lower x-axis values. These plots commonly displayed lower P

_{d(θ)}and higher P

_{c(θ)}, which leads to a lower P

_{s(θ)}.

## 7. Concluding Remarks

## Acknowledgments

## References and Notes

- Garestier, F.; Dubois-Fernandez, P.C.; Guyon, D.; Le Toan, T. Forest biophysical parameter estimation using L-and P-band polarimetric SAR data. IEEE Trans. Geosci. Remote Sens
**2009**, 47, 3379–3388. [Google Scholar] - Gama, F.F.; Dos Santos, J.R.; Mura, J.C. Eucalyptus biomass and volume estimation using interferometric and polarimetric SAR data. Remote Sens
**2010**, 2, 939–956. [Google Scholar] - Lonnqvist, A.; Rauste, Y.; Molinier, M.; Hame, T. Polarimetric SAR data in land cover mapping in boreal zone. IEEE Trans. Geosci. Remote Sens
**2010**, 48, 3652–3662. [Google Scholar] - Goncalves, F.; Santos, J.; Treuhaft, R. Stem volume of tropical forests from polarimetric radar. Int. J. Remote Sens
**2011**, 32, 503–522. [Google Scholar] - He, Q.S.; Cao, C.X.; Chen, E.X.; Sun, G.Q.; Ling, F.L.; Pang, Y.; Zhang, H.; Ni, W.J.; Xu, M.; Li, Z.Y. Forest stand biomass estimation using ALOS PALSAR data based on LiDAR-derived prior knowledge in the Qilian Mountain, Western China. Int. J. Remote Sens
**2012**, 33, 710–729. [Google Scholar] - Neumann, M.; Saatchi, S.S.; Ulander, L.M.H.; Fransson, J.E.S. Assessing performance of L- and P-band polarimetric interferometric SAR data in estimating boreal forest above-ground biomass. IEEE Trans. Geosci. Remote Sens
**2012**, 50, 714–726. [Google Scholar] - Paradzayi, C.; Annegarn, H.J. Estimating potential woody biomass in communal savanna woodlands from synthetic aperture radar (SAR). Int. J. Appl. Geospat. Res
**2012**, 3, 53–62. [Google Scholar] - Santoro, M.; Fransson, J.E.S.; Eriksson, L.E.B.; Magnusson, M.; Ulander, L.M.H.; Olsson, H. Signatures of ALOS PALSAR L-band backscatter in Swedish forest. IEEE Trans. Geosci. Remote Sens
**2009**, 47, 4001–4019. [Google Scholar] - Clewley, D.; Lucas, R.; Accad, A.; Armston, J.; Bowen, M.; Dwyer, J.; Pollock, S.; Bunting, P.; McAlpine, C.; Eyre, T.; et al. An approach to mapping forest growth stages in Queensland, Australia through integration of ALOS PALSAR and Landsat sensor data. Remote Sens
**2012**, 4, 2236–2255. [Google Scholar] - Freeman, A.; Durden, S.L. A three-component scattering model for polarimetric SAR data. IEEE Trans. Geosci. Remote Sens
**1998**, 36, 963–973. [Google Scholar] - Cloude, S.R.; Pottier, E. An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geosci. Remote Sens
**1997**, 35, 68–78. [Google Scholar] - Yamaguchi, Y.; Moriyama, T.; Ishido, M.; Yamada, H. Four-component scattering model for polarimetric SAR image decomposition. IEEE Trans. Geosci. Remote Sens
**2005**, 43, 1699–1706. [Google Scholar] - Yamaguchi, Y.; Sato, A.; Boerner, W.M.; Sato, R.; Yamada, H. Four-component scattering power decomposition with rotation of coherency matrix. IEEE Trans. Geosci. Remote Sens
**2011**, 49, 2251–2258. [Google Scholar] - Cui, Y.; Yamaguchi, Y.; Yang, J.; Park, S.-E.; Kobayashi, H.; Singh, G. Three-component power decomposition for polarimetric SAR data based on adaptive volume scatter modeling. Remote Sens
**2012**, 4, 1559–1572. [Google Scholar] - Sugimoto, M.; Ouchi, K.; Nakamura, Y. Four-component scattering power decomposition algorithm with rotation of covariance matrix using ALOS-PALSAR polarimetric data. Remote Sens
**2012**, 4, 2199–2209. [Google Scholar] - Richards, J.A. Remote Sensing with Imaging Radar. Signals and Communication Technology Series; Springer-Verlag; Berlin/Heidelberg, Germany, 2009. Available online: http://www.springer.com/engineering/electronics/book/978-3-642-02019-3 (accessed on 3 September 2012).
- Austin, J.M.; Mackey, B.G.; Van Niel, K.P. Estimating forest biomass using satellite radar: An exploratory study in a temperate Australian Eucalyptus forest. For. Ecol. Manag
**2003**, 176, 575–583. [Google Scholar] - Hoekman, D.H.; Quiriones, M. Land cover type and biomass classification using AirSAR data for evaluation of monitoring scenarios in the Colombian Amazon. IEEE Trans. Geosci. Remote Sens
**2000**, 38, 685–696. [Google Scholar] - Balzter, H.; Baker, J.R.; Hallikainen, M.; Tomppo, E. Retrieval of timber volume and snow water equivalent over a Finnish boreal forest from airborne polarimetric synthetic aperture radar. Int. J. Remote Sens
**2002**, 23, 3185–3208. [Google Scholar] - Rowland, C.S.; Balzter, H.; Dawson, T.P.; Luckman, A.; Patenaude, G.; Skinner, L. Airborne SAR monitoring of tree growth in a coniferous plantation. Int. J. Remote Sens
**2008**, 29, 3873–3889. [Google Scholar] [Green Version] - Macelloni, G.; Paloscia, S.; Pampaloni, P.; Marliani, F.; Gai, M. The relationship between the backscattering coefficient and the biomass of narrow and broad leaf crops. IEEE Trans. Geosci. Remote Sens
**2001**, 39, 873–884. [Google Scholar] - Kobayashi, S.; Widyorini, R.; Kawai, S.; Omura, Y.; Sanga-Ngoie, K.; Supriadi, B. Backscattering characteristics of L-band polarimetric and optical satellite imagery over planted acacia forests in Sumatra, Indonesia. J. Appl. Remote Sens
**2012**, 6, 063525. [Google Scholar] - Kawai, S.; Widyorini, R. Sustainable Forest Management and Regional Environment in South-East Asia. Proceedings of the Second International Conference of Kyoto University Global COE Program in Search of Sustainable Humanosphere in Asia and Africa, Kyoto, Japan, 12–14 March 2008.
- Gunawan, R.; Wahyono, R. Faktor Bentuk (Form Factor) Acacia Mangium (in Indonesian); Technical Note of Research and Development Division; PT Musi Hutan Persada: South Sumatera, Indonesia, 2004; pp. 1–3. [Google Scholar]
- Yamaguchi, Y. Radar Polarimetry from Basic to Applications: Radar Remote Sensing Using Polarimetric Information (in Japanese); The Institute of Electrtonics, information and Communication Engineers Press: Tokyo, Japan, 2007; pp. 80–100. [Google Scholar]
- Lee, J.S.; Pottier, E. Polarimetric SAR Speckle Filtering. In Polarimetric Radar Imaging: from Basics to Applications; CRC Press: Boca Raton, FL, USA, 2009; pp. 143–178. [Google Scholar]
- McNeill, S.; Pairman, D. Stand age retrieval in production forest stands in New Zealand using C-and L-band polarimetric radar. IEEE Trans. Geosci. Remote Sens
**2005**, 43, 2503–2515. [Google Scholar]

**Figure 1.**(

**a**) The location of the study area in Sumatra, Indonesia (small black square). (

**b**) The area of Unit V (white line) superimposed on a true color composite image from ALOS AVNIR2 data.

**Figure 2.**Unit V represented using a true color composite image. Yellow circles mark the permanent sample plots (PSPs) where the field observations were conducted.

**Figure 3.**Composite images of the decomposition powers (RGB = double-bounce/canopy/surface scattering) for (

**a**) log

_{10}P, (

**b**) log

_{10}P

_{(θ)}and (

**c**) P

_{(θ)}/TP.

**Figure 4.**(

**a**) Enlarged portion of the composite P

_{(θ)}/TP image (Figure 3(c)) with the forest stand vector data, which are shown by a thin black line;

**(b**) forest stand polygons with a base 10 logarithm of the tree age (inflection point = −0.3). The transparent polygons have no tree age data.

**Figure 5.**Correlation analysis between the base 10 logarithms of the (

**a**) tree diameter at breast height (DBH). (

**b**) tree height and (

**c**) forest stand volume on the x-axis and the base 10 logarithms of the decomposition powers (P) (surface, double-bounce, canopy and helix scatterings) calculated from the covariance matrix (log

_{10}P

_{s}, log

_{10}P

_{d}, log

_{10}P

_{c}and log

_{10}P

_{h}) on the y-axis.

**Figure 6.**(

**a**–

**c**) Same as in Figure 5(a–c), except the decomposition powers are calculated from the rotated covariance matrix of log

_{10}P

_{s(θ)}, log

_{10}P

_{d(θ)}, log

_{10}P

_{c(θ)}and log

_{10}P

_{h(θ)}on the y-axis.

**Figure 7.**Correlational analysis (

**a**) between the base 10 logarithms of DBH (log

_{10}DBH) and the ratios of the decomposition powers to the total power (P

_{(θ)}/TP), (

**b**) between log

_{10}H and P

_{(θ)}/TP, (

**c**) between log

_{10}V and P

_{(θ)}/TP, including P

_{s(θ)}/TP, P

_{d(θ)}/TP, P

_{c(θ)}/TP and P

_{h(θ)}/TP.

**Figure 8.**Scatterplot and logarithmic regression (thick line) of the parameters with the decomposition powers divided by the total power (P

_{(θ)}/TP) on the x-axis and the base 10 logarithm of the stand volume (log

_{10}V) on the y-axis. The 95% confidence band is shown by thin lines.

**Table 1.**Correlation coefficients (R) between the base 10 logarithms of the forest parameters and the base 10 logarithms of the decomposition powers: (

**a**) P calculated from the covariance matrix and (

**b**) P

_{(θ)}from the rotated covariance matrix.

(a) | (b) | |||||
---|---|---|---|---|---|---|

Decomposition Power | log_{10}DBH | log_{10}H | log_{10}V | log_{10}DBH | log_{10}H | log_{10}V |

Surface | −0.691 | −0.674 | −0.698 | −0.724 | −0.718 | −0.723 |

Double-bounce | 0.104 | 0.050 | 0.116 | −0.107 | −0.157 | −0.083 |

Canopy | 0.488 | 0.513 | 0.443 | 0.520 | 0.546 | 0.473 |

Helix | 0.363 | 0.402 | 0.338 | 0.334 | 0.374 | 0.312 |

**Table 2.**Correlation coefficients (R) and P-values between the base 10 logarithms of the forest parameters DBH (log

_{10}DBH), height (log

_{10}H) and stand volume (log

_{10}V) and the P

_{(θ)}/TP; ratios of the decomposition powers to the total power.

log_{10}DBH | log_{10}H | log_{10}V | ||||
---|---|---|---|---|---|---|

Decomposition power | R | P-value | R | P-value | R | P-value |

Surface | −0.778 | <0.001 | −0.769 | <0.001 | −0.758 | <0.001 |

Double-bounce | 0.572 | 0.002 | 0.516 | 0.007 | 0.582 | 0.002 |

Canopy | 0.719 | <0.001 | 0.730 | <0.001 | 0.677 | <0.001 |

Helix | 0.676 | <0.001 | 0.698 | <0.001 | 0.687 | <0.001 |

**Table 3.**Statistical test of the logarithmic regression shown in Figure 8. The degrees of freedom are displayed in the DF column, the calculated sum of the square terms is displayed in the SS column, and the mean square terms are displayed in the MS column. The corresponding F statistics and P-values are also provided.

R^{2} = 0.557, Standard Error of Estimate = 0.563 | |||||
---|---|---|---|---|---|

DF | SS | MS | F | P-value | |

Regression | 1 | 9.552 | 9.552 | 30.164 | <0.001 |

Residual | 24 | 7.600 | 0.317 | ||

Total | 25 | 17.152 | 0.686 |

## Share and Cite

**MDPI and ACS Style**

Kobayashi, S.; Omura, Y.; Sanga-Ngoie, K.; Widyorini, R.; Kawai, S.; Supriadi, B.; Yamaguchi, Y.
Characteristics of Decomposition Powers of L-Band Multi-Polarimetric SAR in Assessing Tree Growth of Industrial Plantation Forests in the Tropics. *Remote Sens.* **2012**, *4*, 3058-3077.
https://doi.org/10.3390/rs4103058

**AMA Style**

Kobayashi S, Omura Y, Sanga-Ngoie K, Widyorini R, Kawai S, Supriadi B, Yamaguchi Y.
Characteristics of Decomposition Powers of L-Band Multi-Polarimetric SAR in Assessing Tree Growth of Industrial Plantation Forests in the Tropics. *Remote Sensing*. 2012; 4(10):3058-3077.
https://doi.org/10.3390/rs4103058

**Chicago/Turabian Style**

Kobayashi, Shoko, Yoshiharu Omura, Kazadi Sanga-Ngoie, Ragil Widyorini, Shuichi Kawai, Bambang Supriadi, and Yoshio Yamaguchi.
2012. "Characteristics of Decomposition Powers of L-Band Multi-Polarimetric SAR in Assessing Tree Growth of Industrial Plantation Forests in the Tropics" *Remote Sensing* 4, no. 10: 3058-3077.
https://doi.org/10.3390/rs4103058