# Forest Growing Stock Volume Estimation in Subtropical Mountain Areas Using PALSAR-2 L-Band PolSAR Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}value was 0.612. The constructed multi-variable model produced a better inversion result, with a root mean square error (RMSE) of 70.965 m

^{3}/ha, which was improved by 22.08% in comparison to the single-variable models. Finally, the space distribution map of forest GSV was established using the multi-variable model. The range of estimated forest GSV was 0 to 450 m

^{3}/ha, and the mean value was 135.759 m

^{3}/ha. The study expands the application potential of PolSAR data in complex topographic areas; thus, it is helpful and valuable for the estimation of large-scale forest parameters.

## 1. Introduction

^{3}/ha) of the boles or stems of all living trees, and can be converted into above-ground biomass (AGB) by its density factor [2]. Therefore, the accurate quantification of forest biomass or GSV is essential for understanding the spatial distribution of carbon in vegetation areas, which can also provide effective predictions for the change trend of carbon stock [3]. In particular, large-scale forest GSV retrieval has become a research hotspot in recent years.

## 2. Materials

#### 2.1. Study Area

#### 2.2. Field Inventory Data

^{3}/ha to 434.42 m

^{3}/ha, with an average value of 194.75 m

^{3}/ha (Table 1). By random sampling, the plots were divided for the training (n = 44) and validation (n = 16) of models into two groups.

#### 2.3. Polarimetric SAR Data and Pre-Processing

_{3}] was generated and converted into the covariance matrix [C

_{3}], which could represent the full polarimetric data. Then, these data were multi-looked with 7 × 10 in the azimuth and range directions. A Lee filter with a 3 × 3 window was applied to reduce the speckle effects. Geocoding was performed using shuttle radar topography mission (SRTM) elevation data (30-m spatial resolution). Finally, the SAR images were re-sampled to 30-m spatial resolution. PolSARpro software (Version 5.1.3, European Space Agency, Paris, France) was used to pre-process the SAR data. Gamma software was used to perform geocoding and resampling.

#### 2.4. Ancillary Data

## 3. Methodology

#### 3.1. Terrain Correction

#### 3.1.1. Polarization Orientation Angle Correction

#### 3.1.2. Effective Scattering Area Correction

#### 3.1.3. Angular Variation Effect Correction

_{i}

_{,j}represents the elements of the corrected covariance matrix, z represents the different types of forest cover, and p and q represent different polarization channels. According to Equation (7), only the values of n corresponding to the primary diagonal elements of the covariance matrix need to be obtained. Considering the impact of forest characteristics on terrain correction, we try to calculate n corresponding to different types of forests in this paper in order to effectively reduce the topographic effect. The initial ranges of the n values are from zero to two. In addition, considering the computational complexity and accuracy of the n value, we set the interval of n to 0.01. The optimal n is determined by the absolute value of the correlation.

#### 3.2. Retrieval of GSV

## 4. Results

#### 4.1. Acquisition of Terrain Correction Factors

#### 4.2. Results of Terrain Correction

#### 4.3. Backscatter Sensitivity to Forest GSV

^{3}/ha) still have negative effects on the sensitivity between forest GSV and backscatter at the HH and VV channels.

#### 4.4. GSV Estimation and Mapping

^{2}values are 0.539 (Direct linear model, Figure 9a), 0.601 (Logarithmic model, Figure 9b), 0.603 (Quadratic model, Figure 9c), 0.579 (Exponential model, Figure 9d), and 0.612 (Water-Cloud analysis model, Figure 9e), respectively. The direct linear relationship (Figure 9a) between the backscatter coefficient and forest GSV is weak, but this phenomenon can be improved through the transformation of parameters, such as the natural logarithmic transformation of forest GSV (Figure 9b). In addition, the Water-Cloud analysis model is found to be the most reliable in the capacity of single-variable regression models, as it produces the highest coefficient of determination in the five models. Howeve, from Figure 9e, when the forest GSV is greater than 300 m

^{3}/ha, the change of the fitting curve tends to be gentle, which may limit its ability regarding estimation in higher GSV areas.

^{2}value of 0.417, whose root mean square error (RMSE) is 91.075 m

^{3}/ha. For the multi-variable model, the correlation coefficient R

^{2}value is 0.630, whose RMSE is 70.965 m

^{3}/ha. Obviously, the accuracy of the multi-variable model inversion is higher than that of the Water-Cloud analysis model inversion. Therefore, the multi-variable model is used to estimate the forest GSV for the whole study region. The results are shown in Figure 11. Figure 11a is the schematic diagram for the spatial distribution of the forest GSV at the pixel scale, which shows that the range of the estimated forest GSV is 0 to 450 m

^{3}/ha. Figure 11b is the histogram of the GSV map. The mean and standard deviation of the GSV in the region are 135.759 m

^{3}/ha and 47.255 m

^{3}/ha. Furthermore, we also calculated the GSV of different land-cover types. The mean GSV of woodland, shrubbery, sparse woodland, and other forest were 137.701 m

^{3}/ha, 130.541 m

^{3}/ha, 125.991 m

^{3}/ha, and 113.759 m

^{3}/ha, respectively. The standard deviations were 45.906 m

^{3}/ha, 42.172 m

^{3}/ha, 56.274 m

^{3}/ha, and 62.051 m

^{3}/ha, respectively.

## 5. Discussion

^{2}values of the two models only differ by 0.062, but the former has a higher accuracy of GSV estimation than the latter in the model test. This indicates that co-polarization can also make a certain contribution in GSV estimation. Therefore, our study recommends using the multi-variable model to map the GSV in the study area.

## 6. Conclusions

^{3}/ha. Therefore, our study recommended using the multi-variable model to map the GSV in the study area. The range of estimated forest GSV was 0 to 450 m

^{3}/ha. The mean value and stander deviation were 135.759 m

^{3}/ha and 47.255 m

^{3}/ha, respectively. The study expands the application potential of PolSAR data in complex topographic areas; thus, it is helpful and valuable for the large-scale (e.g., national or global scale) estimation of forest parameters.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The test site: phased array-type L-band synthetic aperture radar (PALSAR-2) image in the Pauli basis. The yellow circles are field sampling plots.

**Figure 4.**The geocoded angular factors for terrain correction. (

**a**) Polarization orientation angle (POA) shift angle; (

**b**) Project angle; (

**c**) Incidence angle; and (

**d**) Local incidence angle.

**Figure 5.**Distribution of correlation coefficients for various values of n and the positons of the optimum n values at four forest cover types (based on data obtained on 14 July 2016): (

**a**) Woodland; (

**b**) Shrubbery area; (

**c**) Sparse woodland; and (

**d**) Other forest.

**Figure 6.**Backscatter coefficient variation of the original data and each correction stage in different polarization channels (HH, HV, and VV). Original data:

**a1**,

**b1**,

**c1**; POA correction stage:

**a2**,

**b2**,

**c2**; Effective scattering area (ESA) correction stage:

**a3**,

**b3**,

**c3**; Angular variation effect (AVE) correction stage:

**a4**,

**b4**,

**c4**.

**Figure 7.**The relationship between backscatter coefficients of different polarization channels and local incidence angles at different correction stages: POA correction stage (HH:

**a**, HV:

**b**, VV:

**c**); ESA correction stage (HH:

**d**, HV:

**e**, VV:

**f**); AVE correction stage (HH:

**g**, HV:

**h**, VV:

**i**).

**Figure 8.**The relationship between forest growing stock volume (GSV) and backscatter coefficents of different polarzation channels. Original data: (

**a**) HH, (

**b**) HV, and (

**c**) VV; After POA compensation: (

**d**) HH, (

**e**) HV, and (

**f**) VV. After ESA correction: (

**g**) HH, (

**h**) HV, and (

**i**) VV; After AVE correction: (

**j**) HH, (

**k**) HV, and (

**l**) VV.

**Figure 9.**Fitting curves of the single-variable models: (

**a**) Direct linear model; (

**b**) Logarithmic model; (

**c**) Quadratic model; (

**d**) Exponential model; and (

**e**) Water-Cloud analysis model.

**Figure 10.**The relationship between predicated GSV and reference GSV using test sample dataset: (

**a**) Water-Cloud analysis model; and (

**b**) Multi-variable model.

**Figure 11.**Forest GSV estimation results of the whole study region: (

**a**) Spatial distribution of forest GSV at pixel scale; (

**b**) Histogram of GSV map.

Range | Mean | |
---|---|---|

DBH | 4.06 to 30.10 cm | 17.84 cm |

Height | 4.60 to 20.20 m | 13.24 m |

Number of Stems | 30 to 350 | 96 |

Growing Stock Volume | 6.88 to 434.42 m^{3}/ha | 194.75 m^{3}/ha |

Data | Woodland | Shrubbery | S-Woodland | O-Forest | |
---|---|---|---|---|---|

HH | 16 June 2016 | 1.31 | 1.27 | 1.60 | 1.48 |

30 June 2016 | 1.20 | 1.41 | 1.50 | 1.37 | |

14 July 2016 | 1.24 | 1.23 | 1.52 | 1.42 | |

11 August 2016 | 1.11 | 1.09 | 1.30 | 1.22 | |

25 August 2016 | 1.13 | 1.06 | 1.36 | 1.25 | |

22 September 2016 | 1.16 | 1.12 | 1.37 | 1.24 | |

6 October 2016 | 1.32 | 1.35 | 1.58 | 1.46 | |

HV | 16 June 2016 | 0.91 | 0.83 | 0.93 | 0.77 |

30 June 2016 | 0.76 | 0.67 | 0.79 | 0.57 | |

14 July 2016 | 0.82 | 0.74 | 0.82 | 0.63 | |

11 August 2016 | 0.74 | 0.65 | 0.65 | 0.48 | |

25 August 2016 | 0.74 | 0.63 | 0.67 | 0.47 | |

22 September 2016 | 0.70 | 0.56 | 0.65 | 0.44 | |

6 October 2016 | 0.85 | 0.79 | 0.83 | 0.64 | |

VV | 16 June 2016 | 1.14 | 1.24 | 1.44 | 1.38 |

30 June 2016 | 1.04 | 1.14 | 1.36 | 1.26 | |

14 July 2016 | 1.09 | 1.20 | 1.39 | 1.29 | |

11 August 2016 | 1.01 | 1.11 | 1.20 | 1.14 | |

25 August 2016 | 1.01 | 1.06 | 1.22 | 1.11 | |

22 September 2016 | 1.01 | 1.10 | 1.23 | 1.13 | |

6 October 2016 | 1.13 | 1.29 | 1.42 | 1.34 |

Acquisition Time | HH | HV | VV |
---|---|---|---|

16 June 2016 | 0.418 | 0.495 | 0.370 |

30 June 2016 | 0374 | 0.561 | 0.216 |

14 July 2016 | 0.489 | 0.643 | 0.473 |

11 August 2016 | 0.435 | 0.564 | 0.377 |

25 August 2016 | 0.469 | 0.563 | 0.428 |

22 September 2016 | 0.182 | 0.545 | 0.123 |

6 October 2016 | 0.381 | 0.487 | 0.349 |

Model | Regression Equation | R^{2} |
---|---|---|

Direct linear | ${\sigma}_{HV}^{0}=-17.525+0.013GSV$ | 0.529 |

Logarithmic | ${\sigma}_{HV}^{0}=-26.608+2.296ln\left(GSV\right)$ | 0.601 |

Quadratic | ${\sigma}_{HV}^{0}=-28.155+2.941ln\left(GSV\right)-0.066{\left(ln\left(\mathrm{GSV}\right)\right)}^{2}$ | 0.603 |

Exponential | ${\sigma}_{HV}^{0}=-19.914+0.377sqrt\left(GSV\right)$ | 0.579 |

Water-Cloud analysis | ${\sigma}_{HV}^{0}=-12.932-7.163\mathrm{exp}\left(-0.008GSV\right)$ | 0.612 |

Multi-variable | $ln\left(GSV\right)=-2.611+0.531{\sigma}_{HH}^{0}+0.031{\left({\sigma}_{HH}^{0}\right)}^{2}-1.693{\sigma}_{HV}^{0}-0.063{\left({\sigma}_{HV}^{0}\right)}^{2}$ $+0.255{\sigma}_{VV}^{0}+0.01{\left({\sigma}_{VV}^{0}\right)}^{2}$ | 0.674 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, H.; Zhu, J.; Wang, C.; Lin, H.; Long, J.; Zhao, L.; Fu, H.; Liu, Z.
Forest Growing Stock Volume Estimation in Subtropical Mountain Areas Using PALSAR-2 L-Band PolSAR Data. *Forests* **2019**, *10*, 276.
https://doi.org/10.3390/f10030276

**AMA Style**

Zhang H, Zhu J, Wang C, Lin H, Long J, Zhao L, Fu H, Liu Z.
Forest Growing Stock Volume Estimation in Subtropical Mountain Areas Using PALSAR-2 L-Band PolSAR Data. *Forests*. 2019; 10(3):276.
https://doi.org/10.3390/f10030276

**Chicago/Turabian Style**

Zhang, Haibo, Jianjun Zhu, Changcheng Wang, Hui Lin, Jiangping Long, Lei Zhao, Haiqiang Fu, and Zhiwei Liu.
2019. "Forest Growing Stock Volume Estimation in Subtropical Mountain Areas Using PALSAR-2 L-Band PolSAR Data" *Forests* 10, no. 3: 276.
https://doi.org/10.3390/f10030276