# Estimating Forest Canopy Cover in Black Locust (Robinia pseudoacacia L.) Plantations on the Loess Plateau Using Random Forest

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## Abstract

**:**

_{pan}) with a 15 × 15 window size, and textural variables calculated from spectral variables (T

_{B+VIs}) with a 9 × 9 window size. We compared different mtry and ntree values to find the most suitable parameters for the RF models. The results indicated that the RF model of spectral variables explained 57% (root mean square error (RMSE) = 0.06) of the variability in the field CC data. The soil-adjusted vegetation index (SAVI) and enhanced vegetation index (EVI) were more important than other spectral variables. The RF model of T

_{pan}obtained higher accuracy (R

^{2}= 0.69, RMSE = 0.05) than the spectral variables, and the grey level co-occurrence matrix-based texture measure—Correlation (COR) was the most important variable for T

_{pan}. The most accurate model was obtained from the T

_{B+VIs}(R

^{2}= 0.79, RMSE = 0.05), which combined spectral and textural information, thus providing a significant improvement in estimating CC. This model provided an effective approach for detecting the CC of black locust plantations on the Loess Plateau.

## 1. Introduction

_{pan}) and textural variables calculated from spectral variables (T

_{B+VIs}); and, (3) map the CC in the black locust plantations using the most accurate RF regression model. The results obtained in this study are conducive to efficiently estimating the CC. A CC map is an effective tool for detecting the state of forest areas and the associated forest health conditions, both of which can be used in developing forest management plans on the Loess Plateau of China.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field Data

#### 2.3. Remote Sensing Data

#### 2.4. Predictor Variables

#### 2.4.1. Spectral Variables

#### 2.4.2. Textural Variables Calculated from Panchromatic Image (T_{pan})

_{pan}, we compared the model accuracy of the eight GLCM measures with different moving window sizes ranging from 3 × 3 to 15 × 15 pixels (discussed below). As a result, eight T

_{pan}(each GLCM with optimal window size) variables were selected to analyze their relationships with CC.

#### 2.4.3. Textural Variables Calculated from Spectral Variables (T_{B+VIs})

_{B+VIs}), which included texture calculated from reflectance bands (T

_{B}) and texture calculated from VIs (T

_{VIs}), combines spectral and textural information. To find the optimal window size for T

_{B+VIs}, we compared the model accuracy of the eight GLCM measures with different moving window sizes ranging from 3 × 3 to 15 × 15 pixels based on B4 (T

_{B4}) (discussed below). Then, the optimal window size was applied to other spectral variables. The reason for choosing B4 as the deputation of spectral variables was that B4 was the most important and effective band to correlate with forest canopy [44]. Finally, 96 T

_{B+VIs}variables (12 spectral variables × 8 GLCM measures) were selected to analyze their relationships with CC.

#### 2.5. Random Forest (RF) Prediction of CC

- Model 1—spectral variables
- Model 2—textural variables calculated from the panchromatic image (T
_{pan}) - Model 3—textural variables calculated from the spectral variables (T
_{B+VIs})

^{2}) and the root mean square error (RMSE) were used to identify the best prediction model. The formulas of these statistical parameters are as follows:

## 3. Results

#### 3.1. Determining the Optimal Window Size

_{pan}and T

_{B4}in the selected seven window sizes. In T

_{pan}, the model accuracy increases as the window sizes increases and the optimal window size is 15 × 15. In T

_{B4}, the model accuracy increases from 3 × 3 to 9 × 9 and then a slight decrease is observed as the window size further increases. Therefore, we choose a window size of 15 × 15 as the optimal window size to calculate the texture from the panchromatic image and a window size of 9 × 9 as the optimal window size to calculate the texture from the spectral variables.

#### 3.2. Variable Selection and Parameter Tuning for the Final Three RF Models

_{pan}with a 15 × 15 window size. All the eight texture measures were selected as relevant variables, and the COR and MEAN hold higher importance values than other texture measures (Figure 3b). Model 3 was performed based on a 9 × 9 window size, and the optimal number of variables was 16. The top five variables in the variable importance were calculated based on the MEAN texture measure (Figure 3c). The MEAN measure calculated from SAVI (MEAN

_{SAVI}) and MSAVI (MEAN

_{MSAVI}) had higher importance values than that of the other variables.

#### 3.3. Model Comparison and CC Mapping

^{2}= 0.57, RMSE = 0.06, Figure 5a), and a higher accuracy was obtained when using T

_{pan}, (R

^{2}of 0.69 and RMSE of 0.05, Figure 5b). Model 3 with T

_{B+VIs}had the highest accuracy (R

^{2}= 0.79, RMSE = 0.05, Figure 5c). Therefore, Model 3 was used for the final estimation and mapping of the CC of black locust plantations.

## 4. Discussion

_{B+VIs}with 9 × 9 windows obtained higher accuracy than T

_{pan}with 15 × 15 windows. Kamal et al. [60] observed that a pixel window size corresponding to the field plot size or slightly larger could generate high accuracies in LAI estimation. Chen et al. [61] concluded that images at a finer spatial resolution needed a larger window size than at a coarse resolution. In our study, the 15 × 15 window size of T

_{pan}(equivalent to 9 m × 9 m) was still smaller than the sample plot size (20 m × 20 m). For T

_{B+VIs}, the window size of 9 × 9 (equivalent to 21.6 m × 21.6 m), which corresponded to the extent of the field plots, produced higher accuracy than T

_{pan}. This result was consistent with that of Wood et al. [29] and Gomez et al. [59], who suggested that the window size should match the sample plot size to achieve high accuracy.

_{pan}presented a significant improvement. All of the texture measures were selected as relevant to the response variables. The eight texture measures explained the variation of CC from different aspects, and only one type of texture measure contained insufficient information to explain the CC variance. Kim [67] demonstrated that adding individual texture measure to spectral bands did not improve forest classification accuracy. However, when incorporated multiple texture measures, the forest classification accuracy increased to 83% in overall accuracy. St.-Louis et al. [6] also found that multiple texture measures explained a higher proportion of the variability in bird species richness than single measures. The higher accuracy of Model 2 was consistent with numerous prior studies, which indicated that T

_{pan}was particularly useful in measuring complex structures, such as tropical forests [29,59]. The usefulness of T

_{pan}may be due to the high resolution of the panchromatic image used for the texture analysis, which increased the scope for distinguishing specific forest structure parameters, especially crown attributes (e.g., CC, crown diameter, etc.) [5,26,27,66].

_{B+VIs}yielded the highest accuracy in estimating forest CC compared with the spectral variables and T

_{pan}. The improved performance may be related to their combination of spatial and spectral information, which is consistent with the findings of many previous studies [6,12,27,44,52]. Gu et al. [16], Pfeifer et al. [68], and Pu and Cheng [28] demonstrated that by including texture information into spectral data models, the models’ predictive capacity could be improved, especially for the canopy structure at the stand level, which is mainly because the information associated with spectral and textural signatures is complementary in the estimation of forest parameters [59]. In addition, texture was credible in detecting varying forest canopy structural characteristics and is efficient in addressing saturation problems that are associated with vegetation indices when mapping CC, especially in dense canopies [26].

## 5. Conclusions

_{pan}and T

_{B+VIs}to estimate black locust plantation CC based on RF regression models. The optimal window size for T

_{pan}and T

_{B+VIs}were 15 × 15 and 9 × 9, respectively. The experimental results demonstrated that both T

_{pan}and T

_{B+VIs}performed better than spectral variables. The RF model of T

_{B+VIs}, which reflected the complementary relationship between spectral and textural information, provided the most useful approach to investigating and characterizing black locust plantations CC. This model can be applied for mapping black locust plantations CC on the Loess Plateau of China.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the study area and the field sample plots identified from the multispectral (

**a**) and panchromatic (

**b**) data of QuickBird imagery.

**Figure 2.**Illustration of the window size effect on the prediction of the forest CC (based on texture calculated from panchromatic image and Band 4).

**Figure 3.**Number of explanatory variables selected by the Boruta algorithm and their importance values: (

**a**) spectral variables; (

**b**) T

_{pan}; (

**c**) T

_{B+VIs}. (VImp represent the variable’s importance values).

**Figure 4.**Effect of mtry and ntree on the random forest (RF) models of (

**a**) spectral variables; (

**b**) T

_{pan}; (

**c**) T

_{B+VIs}.

**Figure 5.**Plots of the observed and predicted CC using RF with (

**a**) Model 1; (

**b**) Model 2; and, (

**c**) Model 3.

**Figure 6.**Predicted CC map of the black locust plantations based on Model 3 using QuickBird imagery.

Variable (Unit) | Minimum | Maximum | Mean | Standard Deviation |
---|---|---|---|---|

CC | 0.28 | 0.88 | 0.67 | 0.10 |

DBH (cm) | 5.38 | 26.41 | 12.58 | 4.80 |

Crown Diameter (m) | 2.02 | 5.81 | 3.51 | 0.88 |

Density (N/ha) | 250 | 2775 | 1228 | 676 |

Height (m) | 5.38 | 19.98 | 11.98 | 3.03 |

**Table 2.**Selected vegetation indices (VIs) used for canopy cover (CC) estimation [11].

Spectral Vegetation Indices |
---|

1. Simple Ratio (SR) = $\frac{\mathrm{NIR}}{\mathrm{R}}$ |

2. Soil Adjusted Vegetation Index (SAVI) = $(1+\mathrm{L})\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}+\mathrm{L}}$ |

3. Enhanced Vegetation index (EVI) = $\mathrm{G}\frac{\mathrm{NIR}-\mathrm{R}}{{\mathrm{NIR}+\mathrm{C}}_{1}{\mathrm{R}-\mathrm{C}}_{2}\mathrm{B}+\mathrm{L}}$ |

4. Atmospherically Resistant Vegetation Index (ARVI) = $\frac{\mathrm{NIR}-\mathrm{RB}}{\mathrm{NIR}+\mathrm{RB}}$, RB = $\mathrm{R}-\mathsf{\gamma}(\mathrm{B}-\mathrm{R})$ |

5. Modified Soil Adjusted Vegetation Index (MSAVI) = $\left[\left(2\mathrm{NIR}+1\right)-\sqrt{{\left(2\mathrm{NIR}+1\right)}^{2}-8\left(\mathrm{NIR}-\mathrm{R}\right)}\right]/2$ |

6. Non-linear Vegetation index (NLI) = $\frac{{\mathrm{NIR}}^{2}-\mathrm{R}}{{\mathrm{NIR}}^{2}+\mathrm{R}}$ |

7. Difference Vegetation index (DVI) = $\mathrm{NIR}-\mathrm{R}$ |

8. Normalized Difference Vegetation Index (NDVI) = $\frac{\mathrm{NIR}-\mathrm{R}}{\mathrm{NIR}+\mathrm{R}}$ |

_{1}= 6.0, C

_{2}= 7.5, and G (gain factor) = 2.5 [51].

**Table 3.**Formulas for the texture measurements used in this study [52].

Grey Level Co-occurrence Matrix (GLCM) Based Texture Parameter Estimation |
---|

1. Mean (MEAN) = ${\sum}_{i,j=0}^{N-1}p\left(i,j\right)$ |

2. Homogeneity (HOM) = ${\sum}_{i}{\sum}_{j}\frac{p\left(i,j\right)}{1+{\left(i-j\right)}^{2}}$ |

3. Contrast (CON) = ${\sum}_{n=0}^{N-1}{n}^{2}\{{\sum}_{i=1}^{N}{\sum}_{j=1}^{N}p(i,j)\}$ |

4. Dissimilarity (DIS) = ${\sum}_{n=0}^{N-1}n\{{\sum}_{i=1}^{N}{\sum}_{j=1}^{N}p(i,j)\}$ |

5. Entropy (ENT) = $-{\sum}_{i}{\sum}_{j}p\left(i,j\right)\mathrm{log}\left(p\left(i,j\right)\right)$ |

6. Variance (VAR) = ${p}_{i,j}{\left({i-u}_{i}\right)}^{2}$ |

7. Angular Second Moment (ASM) = ${\sum}_{i}{\sum}_{j}{\left\{p\left(i,j\right)\right\}}^{2}$ |

8. Correlation (COR) = $\frac{{\sum}_{i}{\sum}_{j}\left(ij\right)p\left(i,j\right)-{\mu}_{x}{\mu}_{y}}{{\sigma}_{x}{\sigma}_{y}}$ |

${\mu}_{x}$ = ${\sum}_{i=0}^{N-1}i{\sum}_{j=0}^{N-1}\text{}{P}_{i,j}$ |

${\mu}_{y}$ = ${\sum}_{i=0}^{N-1}j{\sum}_{j=0}^{N-1}\text{}{P}_{i,j}$ |

${{\sigma}_{x}}^{2}$ = ${\sum}_{i=0}^{N-1}\text{}{\left(i-{\mu}_{x}\right)}^{2}{\sum}_{j=0}^{N-1}\text{}{P}_{i,j}$ |

${{\sigma}_{y}}^{2}$ = ${\sum}_{j=0}^{N-1}\text{}{\left(j-{\mu}_{y}\right)}^{2}{\sum}_{i=0}^{N-1}\text{}{P}_{i,j}$ |

Here, P(i,j) is the normalized co-occurrence matrix. |

CC | Percent (%) |
---|---|

<0.4 | 0.75 |

0.4–0.6 | 40.38 |

0.6–0.8 | 58.82 |

0.8–1.0 | 0.05 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, Q.; Wang, F.; Zhao, J.; Zhou, J.; Yu, S.; Zhao, Z.
Estimating Forest Canopy Cover in Black Locust (*Robinia pseudoacacia* L.) Plantations on the Loess Plateau Using Random Forest. *Forests* **2018**, *9*, 623.
https://doi.org/10.3390/f9100623

**AMA Style**

Zhao Q, Wang F, Zhao J, Zhou J, Yu S, Zhao Z.
Estimating Forest Canopy Cover in Black Locust (*Robinia pseudoacacia* L.) Plantations on the Loess Plateau Using Random Forest. *Forests*. 2018; 9(10):623.
https://doi.org/10.3390/f9100623

**Chicago/Turabian Style**

Zhao, Qingxia, Fei Wang, Jun Zhao, Jingjing Zhou, Shichuan Yu, and Zhong Zhao.
2018. "Estimating Forest Canopy Cover in Black Locust (*Robinia pseudoacacia* L.) Plantations on the Loess Plateau Using Random Forest" *Forests* 9, no. 10: 623.
https://doi.org/10.3390/f9100623