^{1}

^{*}

^{2}

^{1}

^{3}

^{2}

^{4}

^{5}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

A decomposition scheme was applied to ALOS/PALSAR data obtained from a fast-growing tree plantation in Sumatra, Indonesia to extract tree stem information and then estimate the forest stand volume. The scattering power decomposition of the polarimetric SAR data was performed both with and without a rotation matrix and compared to the following field-measured forest biometric parameters: tree diameter, tree height and stand volume. The analytical results involving the rotation matrix correlated better than those without the rotation matrix even for natural scattering surfaces within the forests. Our primary finding was that all of the decomposition powers from the rotated matrix correlated significantly to the forest biometric parameters when divided by the total power. The surface scattering ratio of the total power markedly decreased with the forest growth, whereas the canopy and double-bounce scattering ratios increased. The observations of the decomposition powers were consistent with the tree growth characteristics. Consequently, we found a significant logarithmic relationship between the decomposition powers and the forest biometric parameters that can potentially be used to estimate the forest stand volume.

In recent years, industrial plantations have been rapidly expanding in many parts of the world due to a number of factors: paper companies require a stable supply of pulp, electric power companies are interested in producing biofuel feed-stocks and other companies anticipate the expansion of carbon-trading. Plantation expansions seem inevitable because of the annually increasing global demand for paper. Therefore, it is becoming increasingly clear that the sustainable use of industrial plantations requires continuous investigation to monitor their land productivity and estimate the forest stand volume for commercial purposes.

Earth surface surveys currently take full advantage of remote satellite sensing technology. Both optical and microwave satellites provide key information on forest resources that are very important for the sustainable management of the environment. However, the persistent presence of water vapor and clouds makes continuous monitoring using optical satellite data unfeasible particularly over tropical regions.

Microwave radar imaging satellites are therefore expected to conduct periodic forest monitoring. Polarimetric synthetic aperture radar (POLSAR) is an advanced technology that provides image data with phase (scattering matrix) information, which has made it a center of attention in recent years as an effective instrument for identifying land cover and estimating forest biomass [

In POLSAR data analysis, the normalized radar cross section (^{0}) is used as a calculated parameter [

In this study, we examine the polarimetric SAR image decomposition scheme. A few studies have attempted to retrieve forest structural parameters, such as the tree diameter, tree height and timber volume, using polarimetric decomposition theorems. Garestier

It is well known that the accuracy of forest biometric parameter estimations is site-dependent [

In our previous work [^{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.

Therefore, the aim of this study was to extract tree trunk information for the planted

The study area is located in the southeastern part of the island of Sumatra, Indonesia (^{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).

The total plantation area covers 134.7 km^{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.

The plantation area consists of a single-layer forest of

Datasets containing the forest biometric parameters (hereafter forest parameters) for the period from 2006–2008 were made available by the Indonesian tree planting company. These forest parameters are obtained via regular ground-based observations performed at the permanent sample plots (PSPs) marked by the yellow colored circles in

The perimeter of each PSP is rhomb-shaped with 31.6 m diagonals within which individual trees are placed three meters apart in a triangular pattern. This arrangement provides 60 trees growing in each 0.05 ha PSP. The planting and harvesting of the trees are conducted once for each forest stand. Unit V is composed of 3,668 forest stands, which means that the PSPs only represent 0.87% of the total number of forest stands.

In addition to the numerical database mentioned above, the following geographical information, which is essential for GIS (Geographical Information System) analyses, was provided by the planting company: (i) the point vector data for the PSPs (

We used satellite imagery taken by the ALOS (Advanced Land Observing Satellite) provided by the JAXA (Japan Aerospace Exploration Agency). This satellite was loaded with PALSAR (Phased Array type L-band Synthetic Aperture Rader) microwave L-band sensors (wavelength: 23 cm) that enabled the acquisition of polarimetric radar data with a multi-polarization mode. The spatial resolution was 30 m in the range direction and 5 m in the azimuth direction. The full polarimetric data with four polarizations (HH + HV + VH + VV) used in this study were acquired on 20 May 2007 with an off-nadir angle of 21.5° in the ascending orbit. These are the only full-polarimetric PALSAR data available for the 2006–2008 period when the field observational data were also acquired. The precipitation on the data acquisition date reached 0.5 mm with a 3-day average (18–20 May) of 1.3 mm before the observation. Level 1.1 datasets consisting of complex scattering data were both utilized and analyzed with the ground-observed forest parameters using MATLAB, IDRISI and GIS software for image processing and Cartalinx for vector format editing.

First, the averaged DBH and H values for each PSP were calculated. Second, the basic forest biometric parameters (DBH, H and N) for the date the satellite image was taken were interpolated using linear regression analysis between two known points, that is, the anterior and posterior ground observation values. The above procedure is necessary because the ground observations are conducted all year round throughout the entire plantation area, which means the observations were not all made at the same time for all of the PSPs in Unit V and not on the same day as the satellite data. The initial DBH, H and N values on the planted date were used for the interpolation of PSPs with young trees and only a single ground measurement. These initial values were estimated using sigmoidal growth curves, which yield 1.91 cm and 1.07 m for DBH and H, respectively [

These interpolated DBH, H and N values were used with a stem volume form factor of 0.48 [^{3}/ha) as follows:

The covariance matrix ([C]) and coherency matrix ([T]) of the second order statistics were first calculated [_{VH} = _{HV}, the covariance matrix is given as the following:
_{HH}, _{VV} and _{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

The following radiometric and geometric corrections were performed because the level 1.1 PALSAR datasets were calibrated by JAXA. First, for the speckle filtering of the radiometric correction, a boxcar filter (^{2}, where Δ^{2}. The filtered covariance and coherency matrices are denoted as 〈[

For the geometric corrections, the slant to ground range conversion was applied in order to both correct the incidence angle of the radar beam and to register the remotely sensed imagery to a reference system grid (the Universal Transverse Mercator (UTM) coordinate system). Considering that the study area is almost flat, it was assumed that the relief influence was small, and the local topographic effects were therefore not accounted for. The inverse distance weighted (IDW) interpolation method was then applied with a weighting factor of one. The pixel spacing was consequently set to 30 m in the range direction and 15 m in the azimuth direction based on the speckle filtering size.

We used the four-component scattering model for image decompositions both with and without the matrix rotation developed by Yamaguchi

The rotated coherency matrix 〈[_{p}(

The rotation angle (

Yamaguchi _{s}, _{d}, _{c} as well as _{h}, and _{s(θ)}, _{d(θ)}, _{c(θ)} and _{h(θ)} are the expansion coefficients (_{s}, 〈[_{d}, 〈[_{c} and 〈[_{h} are the scattering models for the surface, double-bounce, canopy and helix scatterings, respectively. Each of the four-component powers, _{s}, _{d}, _{c}, _{h}) from 〈[_{(θ)} (_{s(θ)}, _{d(θ)}, _{c(θ)}, _{h(θ)}) from the rotated 〈[_{s}〈[_{s}, _{d}〈[_{d}, _{c}〈[_{c} and _{h}〈[_{h} and _{s(θ)}〈[_{s}, _{d(θ)}〈[_{d}, _{c(θ)}〈[_{c} and _{h(θ)}〈[_{h}, respectively.

It is worth mentioning that the third parameter in

The polarimetric SAR information was statistically compared to the ground observations of the forest parameters (DBH: diameter at breast height, H: height and V: stand stem volume). Statistical comparisons were first performed between the base 10 logarithms of the forest parameters (log_{10}DBH, log_{10}H and log_{10}V) and (i) the base 10 logarithms of the decomposition powers, _{10}_{(θ)} (log_{10}_{(θ)}) from the rotated covariance matrix 〈[

The decadic logarithm is often used to investigate the relationship between microwave backscattering and forest parameters [

The forest parameters were then compared to the decomposition power, _{(θ)}, normalized by the total power (TP), namely, _{(θ)}/_{s(θ)}/_{d(θ)}/_{c(θ)}/_{h(θ)}/

A linear correlation analysis was performed between the PSP forest parameters and the average decomposition powers from the forest stands. This approach is based on the assumption that each forest stand is a uniform entity because it is managed as a whole as mentioned above. Such analyses based on forest stand information are common in other studies as well [

The vector data of the PSPs and forest stands were geo-referenced with the satellite raster data using ground control points (GCPs), which yielded a total RMS (root mean square) error of 8.27 m. The polygon boundary of the forest stands were rasterized and optimized with edge treatment to extract the satellite data. To obtain an edge-eroded forest stand, any pixels within the forest stand boundary and designated buffer zones, which are approximately 15 m from the boundary line, were eliminated from the area. Moreover, forest stands less than 0.0144 km^{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.

_{10}_{10}_{(θ)} and _{(θ)}/_{(θ)}/_{10}_{10}_{(θ)}.

Notably, each forest stand had similar color tones. The portions where the blue color dominates in

The decomposition powers were separately extracted from and averaged over each of the forest stands containing a PSP for the comparison to the ground-based observation data of the forest parameters. Details of the field-measured data used in this study were given in [_{10}DBH (_{10}H (_{10}V (_{10}

The decomposition power shown in _{s}, the surface scattering (the blue colored squares), (2) _{d}, the double-bounce scattering (red colored triangles), (3) _{c}, the canopy scattering (green colored circles) and (4) _{h}, the helix scattering (cross marks). The same symbols and colors are also used in

Similarly, _{(θ)}. A Pearson’s correlation coefficient (_{10}_{10}_{(θ)} on the forest parameters (

The trends in the relationship between log_{10}_{10}_{(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 _{(θ)} correlation (

_{(θ)}/_{(θ)} (

According to the results discussed in Section 5.2, the _{s}(_{d}(_{c}(

The nonlinear regression line was as follows:

_{10}^{2}) is 0.557 for a

Comparing _{(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 (_{(θ)}, which is derived from the rotated matrix, showed a slightly higher correlation than

Combining the power decomposition scheme with the matrix rotation method [

Our approach is based on calculating the ratio of the decomposition powers to the total power (^{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.

Furthermore, a comparison between the composite _{(θ)}/

Gonçalves

Because the physical characteristics of the double bounce scattering model are dependent on the tree trunk and surface interactions [

The plots in

Gonçalves _{(θ)}/^{2} = 0.557,

The double-bounce scattering showed a statistically significant increase in the correlation analysis with the forest stand volume (_{(θ)}/_{10}V ≈ 2) at lower x-axis values. These plots commonly displayed lower _{d(θ)} and higher _{c(θ)}, which leads to a lower _{s(θ)}.

We think that these uncertainties in the relationship between the decomposition powers and forest structural parameters are associated with some vestigial canopy effects, which seem to be persistent, especially for the double-bounce scattering, and are difficult to model. The scattering model developed accounting for the Acacia forest structure yields a more accurate estimation result.

In many parts of the world, the number and size of industrial plantations have increased in recent years and especially in the tropics, where fast-growing trees are cultivated to supply paper materials that are currently under increasing global demand. We aimed to estimate the forest stand volume of Acacia plantations located in Sumatra, Indonesia. The 4-component power decomposition scheme was applied to the ALOS/PALSAR data to compare the decomposition powers to the field-measured biometric parameters, such as the tree diameter, height and stand volume.

Our findings are as follows: (i) the decomposition powers derived from the rotated matrix were better correlated to the forest parameters than those derived from the non-rotated matrix; (ii) all of the decomposition powers had more significant correlations with the forest parameters when divided by the total power (

These outcomes, especially (iii), are consistent with both forest and backscattering characteristics: (1) the surface scattering decreases as the exposure of the bare ground decreases, (2) the canopy scattering increases as the canopy layer grows thicker and expands and (3) the double-bounce scattering, which is supposed to physically reflect the stem or stand volume, increases as the tree diameter and height increase.

Our future research goal is to improve stand volume and biomass estimation to increase the practical application of the present methodology to industrial plantations of fast-growing trees and to investigate the effects of the forest structure on the microwave SAR data by comparing decomposition power characteristics for other tree types.

This work was supported by the Coordination Funds for Promoting Space Utilization of the Ministry of Education, Culture, Sports, Science and Technology in Japan, the research grant for Mission Research on Sustainable Humanosphere from Research Institute for Sustainable Humanosphere (RISH), Kyoto University and by the APU Academic Research Subsidy from Ritsumeikan Asia Pacific University. We gratefully acknowledge the MHP Plantation Company, Sumatra, Indonesia, for their kind cooperation in providing the field observational data. We are also deeply grateful to the staff of the R&D and Planning Sections of the MHP Company for their kind and continuous support during our field surveys.

(

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

Composite images of the decomposition powers (RGB = double-bounce/canopy/surface scattering) for (_{10}_{10}_{(θ)} and (_{(θ)}/

(_{(θ)}/

Correlation analysis between the base 10 logarithms of the (_{10}_{s}, log_{10}_{d}, log_{10}_{c} and log_{10}_{h}) on the y-axis.

(_{10}_{s(θ)}, log_{10}_{d(θ)}, log_{10}_{c(θ)} and log_{10}_{h(θ)} on the y-axis.

Correlational analysis (_{10}DBH) and the ratios of the decomposition powers to the total power (_{(θ)}/_{10}H and _{(θ)}/_{10}V and _{(θ)}/_{s(θ)}/_{d(θ)}/_{c(θ)}/_{h(θ)}/

Scatterplot and logarithmic regression (thick line) of the parameters with the decomposition powers divided by the total power (_{(θ)}/_{10}

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

| ||||||
---|---|---|---|---|---|---|

_{10}DBH |
_{10}H |
_{10}V |
_{10}DBH |
_{10}H |
_{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 |

Correlation coefficients (_{10}DBH), height (log_{10}H) and stand volume (log_{10}V) and the _{(θ)}/

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

| ||||||

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 |

Statistical test of the logarithmic regression shown in

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

| |||||

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

Residual | 24 | 7.600 | 0.317 | ||

Total | 25 | 17.152 | 0.686 |