Tropical Peatland Forest Biomass Estimation Using Polarimetric Parameters Extracted from RadarSAT-2 Images

: This paper was aimed at estimating the forest aboveground biomass (AGB) in the Central Kalimantan tropical peatland forest, Indonesia, using polarimetric parameters extracted from RadarSAT-2 images. Six consecutive acquisitions of RadarSAT-2 full polarimetric data were acquired and polarimetric parameters were extracted. The backscattering coefﬁcient ( σ o ) for HH, HV, VH, and VV channels was computed respectively. Entropy (H) and alpha ( α ) were computed using eign decomposition. In order to understand the scattering behavior, Yamaguchi decomposition was performed to estimate surface scattering ( γ surf ) and volume scattering ( γ vol ) components. Similarly following polarimetric indices were computed; Biomass Index (BMI), Canopy Structure Index (CSI), Volume Scattering Index (VSI), Radar Vegetation Index (RVI) and Pedestal Height ( p h ). The PolSAR parameters were evaluated in terms of their temporal consistency, inter-dependence, and suitability for forest aboveground biomass estimation across rainy and dry conditions. Regression analysis was performed between referenced biomass measurements and polarimetric parameters; VSI, H, RVI, p h , and γ vol were found signiﬁcantly correlated with AGB. Biomass estimation was carried out using signiﬁcant models. Resultant models were validated using ﬁeld-based AGB measurements. Validation results show a signiﬁcant correlation between measured and referenced biomass measurements with temporal consistency over the acquisition time period.


Introduction
Aboveground biomass is an important biophysical describing all living biomass above the soil that includes stems, branches, leaves, barks, seeds and foliage in terrestrial ecosystems [1]. It plays an important role in maintaining the carbon cycle by removing CO 2 from the atmosphere by the process of photosynthesis and storing it in the components of trees. Due to rapid urbanization, forest regions are deforested and degraded especially in developing countries. The tropical rainforests are the most significant carbon reservoir. They are home to gigantic trees, world-famous plants, birds and a variety of fascinating mammals. Around 80% of the world's documented species can be found in tropical rainforests, although they cover only 6% of the Earth's land surface. Furthermore, tropical rainforests have the largest living biomass and home to the highest rate of terrestrial biodiversity However they are the most endangered habitat and vulnerable to deforestation and degradation. Annual deforestation

Study Area
The study site is located in tropical peat and kerangas forests around Palangkaraya, the capital city of Central Kalimantan Province, Indonesia ( Figure 1). Central Kalimantan lies within the Inter-Tropical Convergence Zone (ITCZ), and it falls under the wet tropical climate region. Central Kalimantan is hot and humid, the mean daily temperature ranges from 24 • C to 30 • C and annual rainfall varies between 2500 to 2800 mm [31][32][33]. Rainfall in the study area is common throughout the year, however, the rainy season is from October to February and the dry season is from March to September. The forest canopy has three strata with a maximum height of 35 m. The principal tree species of the upper canopy are Gonystylus Bancanus, Shorea spp. (Meranti), Cratoxylon Glaucum (Gerongang) and Dactylocladus Stenostachys (Mentibu). The mix swamp forest grades into the low-pole forest, which continues for a further 7 km from the Sebangau river or so. Low canopy forest has only two strata and very few trees of commercial value. The principal species of the upper canopy are Combretocarpus Rotundatus (Tumeh), Palaquium sp., Dyera Costulata, Ilex Cymosa, Dyospyros sp. and Calophyllum spp. [34,35]. The study site is relatively flat with an elevation that varies between 4 m to 157 m. Rainfall is common throughout the year, and varies from about 60 inches (150 cm) to over 180 inches (450 cm) per year. In most parts of Sabah the wettest months occur during the North-East Monsoon from October through February and the driest months during the South-West Monsoon from March to September.

SAR and Ancillary Data
RadarSAT-2 full polarimetric times series data were acquired from the Canadian Space Agency (CSA), in single look complex (SLC) format. A total of six acquisitions were acquired for study site during October 2018 to January 2019 (see Figure 2 at incident angle ranging form 22 • to 40 • (see Table 1). Each acquisition of the study area comprises of three adjust scenes. Land cover of the study site was obtained from CIFOR Atlast for Borneo Island (https://www.cifor.org/map/atlas/). SRTM 30 m DEM of study site was acquired from EarthExplorer (https://earthexplorer.usgs.gov/).  Daily maximum temperature ( • C) and precipitation measured from nearest meteorological weather station indicate the weather conditions during SAR data acquisition shown in Figure 3. The majority of the acquisitions were acquired under dry conditions, however, one acquisition was acquired under rainy conditions.

Referenced Data
Referenced data were collected both from referenced biomass map [36] and a 30-day field visit in the study site. A total of 300 referenced measurements were taken from referenced map uniformally distributed throughout the study area and 54 plots of 20 m × 20 m dimensions were sampled during the field survey. Distribution of referenced biomass measurements taken from referenced biomass map and field plots are shown in Figure 1. In each field plot, the diameter at breast height (DBH), tree species, and plot center GPS location was measured. Due to the existence of wildlife in the study site and limited available resources, field data was only collected over easily accessible forest patches. A locally developed generic allometric equation [37] was used to calculate the stand level aboveground biomass. Table 2 listed locally developed generic allometric equations for the study site. The histograms for referenced AGB data are shown in Figure 4. Sample points collected from referenced biomass maps ranged from 0.04 Mg ha −1 to 636 Mg ha −1 and field data collected from field visit ranged from 28.36 Mg ha −1 to 530.25 Mg ha −1 . Sampled data collected from referenced biomass map was used as training data and data collected from field survey was used as validation data.

Main PolSAR Concepts in the Context of This Study
Fully polarimetric SAR measurements can be represented by scattering matrix shown in equation below: where S xy is the complex backscattering term associated with x and y being the transmitted and received polarization respectively. Equation (1) can be rewritten in the Pauli basis: In space-born SAR polarimetry, after polarimetric calibration, Faraday rotation compensation need to be applied by rotating it an angle θ around the radar line of sight leading to: The corresponding covariance matrix is positive semi-definite Hermitian: The covariance matrix is fundamental to characterizing the SAR image to corresponding scattering components, e.g., surface, double-bounce, and volume scattering. Cloude and Pottier have proposed a polarimetric coherence matrix, reformulating the covariance matrix in the Pauli basis, with the target vector in the reciprocal mono-static case given by Equation (2). Then, the coherence matrix can be expressed as follows:

Yamaguchi Decomposition Parameters
Yamaguchi proposed a four-component decomposition scheme [43], which can decompose a coherency matrix to the surface, double-bounce, volume and helix scattering. Mathematical expressions to compute volumetric scattering coefficients are listed below: Corresponding volumetric scattering power can be obtained by: Biomass Index (BMI) is an indicator of the relative amount of woody compared to leafy biomass. As BMI is not a ratio, and therefore is influenced by slope.
Canopy Structure Index (CSI) is a measure of relative importance of vertical versus horizontal structure in the vegetation. Ecosystems dominated by nearly vertical trunks or stems will have higher CSI values than will ecosystems dominated by horizontal or near-horizontal branches. As the chosen study area for this research is intact forest, CSI can be an important indicator of tree density.
Volume scattering index (VSI) is a measure of depolarization of the linearly polarized incident radar signal. High values of result when the cross-polarized bacscatter is dominating if compared to co-polarized backscatter.
The radar vegetation index (RVI) measures the randomness of scattering and can be written as: This assumption is valid when the interaction between the soil and vegetation is negligible. Thus equation for RVI reduced to the form of: Durden et al. (1990) [44] put forward a pedestal height (h p ) as the ratio of minimum eigenvalue to maximum eigenvalue (Lee and Pottier, 2009) [45]: As a measure of the unpolarized backscattered energy, the pedestal height is expected to be high in the case of an forest area.

Eigen Decomposition Parameters
Cloude and Pottier (1996) proposed the following description for the eigenvectors of the covariance matrix in the Pauli basis [46]: The average angle α can be calculated using where Entropy is the measure of target randomness or disorder, which is defined as:

Backscattering Coefficient
The radar backscattering coefficient σ o provides information about the imaging surface, and it is the function of radar observation parameters: frequency, polarization, incident angle, and surface parameters: roughness, geometric shape and dielectric constant of the target.

PolSAR Data Pre-Processing
The acquired time series RadarSAT-2 full polarimetric data were multi-looked to 20 m square pixel. Backscattering coefficient (σ o ) for HH, HV, VH and VV channels were calculated using Equation (21). Eigen-decomposition parameters, i.e., alpha (α) and entropy (H) were computed using Equations (16) and (20) respectively. Volumetric scattering behaviour was estimated using Yamaguchi decomposition (Equation (8)). Similarly polarimetric indices that include Canopy Structure Index (CSI), Volume Scattering Index (VSI), Radar Vegetation Index (RVI), Pedestal Height (p h ) were calculated using Equations (10), (11), (13) and (14) respectively. The whole processing was done using PCI Geomatica and open source SNAP software package provided by the European Space Agency (ESA). All of the computed parameters were terrain-corrected using SRTM 30 m DEM. Lee sigma filter 7 × 7 was performed to smooth the speckles in the resultant images. The same processing was applied on all RadarSAT-2 acquisitions as listed in Table 1. All of the polarimetric parameters extracted and used for further analysis are listed in Table 3. Correlation analysis was performed among all polarimetric parameters listed in Table 3, and results are shown in Figure 5. As can be seen from the Figure 5 mostly the correlation among polarimetric parameters is not significantly high except few exceptions; e.g., α is correlated to σ V H with R 2 of 0.60; entropy (E) is significantly correlated with VSI, RVI and p h with R 2 of 0.60, 0.78 and 0.79 and σ V H is moderately correlated with VSI.

Modeling AGB vs. Polarimetric Parameters
As the referenced biomass measurements (training data) was made available at the 1 hectare scale. To match this, all polarimetric parameters were upscaled to 1 hectare (100 m × 100 m) resolution. Regression analysis was performed between referenced biomass measurements and polarimetric parameters. Logarithmic regression was chosen based on plotting results. In logarithmic regression saturation often occurs beyond a certain point. Hence, the accuracy such relationship significantly influenced beyond the saturation point. If X is the independent variable and Y is dependent variable, then the logarithmic regression equation can be written as: where X is the forest aboveground biomass in Mg ha −1 , Y is the polarimetric parameter extracted from RadarSAT-2 image, ln is the natural log and x o , x 1 are regression coefficients. In case regression modeling, coefficient of determination (R 2 ) is of utter most significance. R 2 describes the proportion of variance in the dependent variable that is predictable from the independent variable.
In the best case, if the relationship between dependent and independent variable is perfectly linear then SS res = 0 and R 2 = 1.
Similarly, the resultant root mean square error can be estimated using equation written as under: where x o − x 1 is the residual and N is the number of sample points. The resultant regression analysis is discussed in Section 3. The same approach was adopted for all RadarSAT-2 acquisitions, regression results are summarized in Table 4. In order to get AGB as a function of polarimetric parameter, the resultant regression models were inverted. Using inverted regression biomass maps were generated for all acquisitions and using validation data, these maps were validated. The complete methodological framework is shown in Figure 6.

Results and Discussions
First of all, temporal consistency and inter-dependency of polarimetric parameters and their suitability for AGB estimation is discussed. We also described the results of regression between polarimetric parameters and reference biomass measurements. Next, the validation results are described in detail.

Temporal Dependence of Polarimetric Parameters
As PolSAR images were acquired under different weather conditions (see Figure 3). It is important analyze the impact caused by different weather conditions. For this, the PolSAR parameters extracted from temporal images were evaluated in terms of their temporal consistency, inter-dependence and suitability for forest aboveground biomass estimation across rainy and dry conditions. Figure 7 shows the correlation graph of each polarimetric parameter for all PolSAR acquisitions. It can be seen that α and CSI are not temporally correlated, however H, σ V H , p h , RVI, γ vol and VSI are temporally correlated at scale of moderate to high. Based on this temporal correlation, it is expected that the AGB vs polariemtric parameters modeling results will be temporally consistent except for α and CSI. The suitability of selected polarimetric parameters (listed in Table 3) for AGB estimation can be validated by modeling referenced AGB vs. polarimetric parameters using regression. For this, all selected polarimetric parameters (listed in Table 3) were chosen for further analysis.

Regression Analysis-Modeling AGB vs. Polarimetric Parameters
Regression results for AGB vs. polarimetric parameters for 31 December 2018 acquisition is shown in Figure 8. Similarly, regression results for selected polarimetric parameters for all PolSAR acquisitions are listed in Table 4. As it can be seen from the Figure 8, all polarimetric parameters were normalized between 0 and 1. This makes it easy to compare results from different polarimetric parameters having a different dynamic range. It can be seen from Figure 8; VSI, H, RVI, p h , and α are significantly correlated with referenced biomass measurements. Similarly, CSI and σ V H are moderately correlated with referenced biomass measurements. Similar consistent results were found for other PolSAR acquisitions (see Table 4). Similarly it can be seen from Table 4; regression results for 13 November 2018 acquisition are least correlated if compared to other acquisitions. This can be easily correlated with moist weather conditions during acquisition (see Figure 3). Among selected polarimetric parameters, VSI was found to be the most correlated with R 2 ranging from 0.45 (under moist conditions) to 0.62 (under dry conditions). Similarly, σ V H found the least correlated with R 2 ranging from 0.27 (under moist conditions) to 0.42 (under dry conditions). Regression results for 24 December 2018 acquisition are also moderately affected by moist conditions caused by rainfall few days before acquisition. The regression results for all selected variables are temporally consistent except of those affected by moist conditions caused by heavy precipitation.
As PolSAR-based AGB estimation at a higher level of forest biomass experiences saturation of PolSAR signal [5,28,29], in this study SAR signal saturation was observed mainly at stand level 300 Mg ha −1 . However, for few polarimetric parameters e.g., RVI, p h , and CSI saturation was observed at stand level 400 Mg ha −1 .

Model Validation-Reference Biomass vs Observed Biomass
Based on regression analysis, models for VSI, H, RVI, p h and γ vol are selected for biomass mapping. To do so, these models were inverted and from resultant models, the AGB of study site was estimated.
To get a more realistic outcome, a low pass filter was applied to get relatively smooth AGB maps. Resultant biomass maps were validated using validation set (field based referenced biomass measurements). Validation results are shown in Figure 9. The resultant R 2 and RMSE are summarized in Table 5.   45 Mg ha −1 respectively during dry and wet conditions. These results are consistent with other published research for forest AGB estimation [47,48]. However it can be seen from Figure 9, the estimated AGB is lower than referenced AGB. As C-band mostly interacts with leaves, main branches and under perfectly dry conditions can penetrate to the stem of tree, hence C-band is good to estimate AGB over low biomass regions.

Limitations
In this research, forest AGB was accurately estimated with the following limitations:

1.
Referenced biomass data collected through the field is not uniformally distributed throughout the study area. With more field data that are uniformally distributed throughput the study site cover major tree species can comprehensive understanding of true biomass conditions. However it is extremely difficult due to existence of wild-life.

2.
As region specific tree species allometric equations are not available for tree species in study site. Generic region specific allometric was used to calculate AGB using field data. Species specific allometric can give more accurate AGB estimates.

3.
As C-band is mostly sensitive to leaves and main branches, more precise AGB estimation can be done by developing synergy of polarimetric parameters extracted from Cand L-band PolSAR data.

Conclusions
This study presents tropical peatland forest biomass estimation using polarimetric parameters extracted from RadarSAT-2 images. Polarimetric parameters includes backscattering coefficient (σ o ), eign-decomposition parameters (H, α), Yamaguchi decomposition parameters (γ sur f , γ vol ) and polarimetric indices (VSI, RVI, p h , CSI) were used to modeled AGB. A detailed methodology for pro-processing of PolSAR images and AGB modeling is presented in this paper. Non-linear regression was used to model AGB as a function of polarimetric parameters. The regression result shows significant correlation between polarimetric parameters and referenced AGB. Selected regression models based on polarimetric parameters (VSI, H, RVI, p h , γ vol ) were further used to generate biomass maps. Resultant biomass maps were validated with strong correlated was found between referenced AGB and predicted AGB with R 2 ranging from 0.77 to 0.58 ranging from 33.21 Mg ha −1 to 37.53 under dry conditions, R 2 ranging from 0.63 to 0.55 and RMSE ranging from 41.44 to 54.45 under moist conditions. PolSAR images acquired under perfectly dry conditions perform better than the ones acquired under moist conditions. A saturation point was observed at 300 Mg ha −1 for VSI, H, γ vol , α and σ V H . However, the saturation point for models developed using RVI, p h , CSI was observed at 400 Mg ha −1 . The selected models also shown temporally consistent behavior.

Conflicts of Interest:
The authors do not report any conflict of interest. The funding sponsors did not have any role in study design, data collection, analysis, data interpretation, manuscript writing and paper publication.

Abbreviations
The following abbreviations are used in this manuscript: