# Improving Forest Aboveground Biomass (AGB) Estimation by Incorporating Crown Density and Using Landsat 8 OLI Images of a Subtropical Forest in Western Hunan in Central China

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}

_{adj}) and root mean square error (RMSE) of the linear dummy model and linear mixed-effects model were significantly better than those of the linear model; the R

^{2}

_{adj}increased more than 0.16 and the RMSE decreased more than 2.12 for each vegetation type, and the F-test also showed significant differences between the linear model and linear dummy variable model and between the linear model and linear mixed-effects model. The accuracies of the AGB estimations of the linear dummy variable model and the linear mixed-effects model were significantly better than those of linear model in the thin and dense crown density classes. There were no significant differences in the AGB estimation performance between the linear dummy variable model and linear mixed-effects model; these two models were more flexible and more suitable than the linear model for remote-sensing-based AGB estimation. The results of this study provide a new approach for solving the low-accuracy estimations of linear models.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{3}. However, the distribution of the forest resources in this region is extremely uneven, the forest biomass in different stand ages is heterogeneous, and forest productivity is low [29,30].

#### 2.2. Field Survey Data

#### 2.3. Remote Sensing Data

#### 2.4. Statistical Model

#### 2.5. Model Fitting and Evaluating

^{2}

_{adj}) and the root mean square error (RMSE). The difference between model 1 and model 2 and between model 1 and model 3 were evaluated using the F-test. The residuals were analyzed to determine the AGB estimation performance of the three models in the different crown density classes. In order to compare the performance improvement of the linear model by the linear dummy variable model (model 2) and linear mixed-effects model (model 3) for AGB estimation, the accuracy of the model 1, model 2, and model 3 were assessed using the percentage root mean square error (RMSE%) and percentage mean residual deviation (Bias%) of the different crown density classes (thin, medium, dense, and total). The difference between model 2 and model 3 was also assessed.

## 3. Results

^{2}and R

^{2}

_{adj}of model 2 and model 3 were larger than those of model 1, and the RMSE values were smaller than those of model 1. These results indicate that the performances of model 2 and model 3 were better than that of model 1. The R

^{2}

_{adj}of model 2 and model 3 for pine forest had the smallest increase compared with model 1; the value of R

^{2}

_{adj}increased by 0.16, and the RMSE values were smaller for model 2 and model 3 than for model 1. For the fir forest, model 2 and model 3 had the largest R

^{2}

_{adj}values, and compared with model 1, the values increased more than 0.39. For the mixed forest and total vegetation, the R

^{2}

_{adj}and RMSE values of model 2 and model 3 were better than those of model 1. These results show that model 2 and model 3, which were considered the crown density classes, had higher accuracies of AGB estimation than model 1.

## 4. Discussion

^{2}of the linear model (model 1) for the four vegetation types ranged from 0.1 to 0.3, indicating that the model had low accuracy. In addition, model 1 exhibited overestimation in the low crown density class and underestimation in the high crown density class of all vegetation types. The overestimations and underestimations of AGB were also investigated by Zhao et al., who determined that they were caused by the “global model (stepwise regression)” [40]. In addition, overestimations and underestimations have been observed when AGB was estimated using nonparametric models such as random forest, decision tree, and K-nearest neighbor methods [41,42,43]. In this study, the significant overestimations and underestimations of the linear model occurred in the thin (crown density < 0.4) and dense (crown density ≥ 0.7) plots, respectively. There were no significant overestimations or underestimations for model 2 and model 3 in the thin and dense plots. In addition, there were no significant differences between the linear dummy variable model (model 2) and linear mixed-effects model (model 3) except for the mixed forests (Table 8). However, in comparison with the model 1, model 2 and model 3 performed significantly better, and the results of the F-test and residuals verified the significant differences. The AGB estimation results of the three models were evaluated in the crown density classes and the results showed that the overestimation in the thin plots and underestimation in the dense plots of model 1 were not observed in model 2 and model 3.

^{2}

_{adj}and RMSE of the three models indicated that the performances of model 2 and model 3 were better than that of model 1. The dummy variable model considered the group differences as special fixed parameters. The purpose of using the dummy variable model in this study was to introduce the parameter of crown density class into the intercept of the model so that the degree of freedom of the error was increased and the variance of the error was decreased, thereby improving the precision of the model [45]. The linear mixed-effects model considered the group differences as two parts: One part was the difference caused by different groups, and the other was the difference caused by random effects. Since the error and the random effect of the variance-covariance structures was considered, the model had high precision. Some studies compared dummy variable models with mixed-effects models for the estimation of large-scale forest growth models and the determination of biomass allometric growth equations. The linear mixed-effects model was a compromise between the dummy variable model and the linear model; in most cases, the dummy variable model was slightly better than the mixed-effects model, but this often depended on the sample size [45,46]. In this study, the sample plots were divided into the three categories of thin, medium, and dense crown density. The overall RMSE% and Bias% of model 2 were better than model 3, which supported the aforementioned results. In the past, the application of dummy variable models and mixed-effects models focused on the determination of allometric growth equations, whereas in this study, we considered whether the partition of the crown density classes improved the estimation accuracy of AGB using remote sensing data.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The location of study area: (

**a**) The study area location in China; (

**b**) the western Hunan in Hunan province; and (

**c**) a false color composite of Landsat 8 OLI band 6 in red, band 5 in green, and band 4 in blue.

**Figure 2.**Spatial distribution of sampling plots corresponding to plots of aboveground biomass (AGB) values and crown density class across the western Hunan.

**Figure 3.**The relationships between predicted AGB from different models in different crown density against observed AGB for different vegetation types.

**Figure 4.**Residual boxplots of AGB of model 1, model 2, and model 3 for different vegetation types among different crown density classes: (

**A**–

**D**) represents pine forest, fir forest, mixed forest, and total vegetation, respectively (model 1—linear regression model; model 2—linear dummy variable model; model 3—linear mixed-effects model; ** indicates that the residuals were significantly different from 0 at the 0.01 level; * indicates that the residuals were significantly different from 0 at the 0.05 level).

**Figure 5.**Comparison of root mean square error percent (RMSE%) and Bias percent (Bias%) results at different crown density classes of models 1–3 for pine forest, fir forest, mixed forest, and total vegetation. The significant differences between model 1 and model 2, and model 1 and model 3 for RMSE% and Bias% are expressed in capital letters (AA), and the lowercase letter (a) represents significant differences between model 2 and model 3.

Vegetation Type | Crown Density | AGB (Mg/ha) | ||||
---|---|---|---|---|---|---|

No. | Minimum | Mean | Maximum | Standard Deviation | ||

Pine | Thin | 41 | 1.05 | 16.40 | 47.33 | 10.61 |

Middle | 70 | 3.61 | 33.60 | 83.58 | 17.06 | |

Dense | 14 | 6.16 | 51.17 | 118.07 | 35.57 | |

Total | 125 | 1.05 | 29.65 | 118.07 | 20.94 | |

Fir | Thin | 54 | 22.76 | 31.11 | 57.46 | 8.70 |

Middle | 77 | 24.72 | 51.18 | 130.87 | 18.37 | |

Dense | 31 | 55.55 | 92.55 | 154.48 | 30.65 | |

Total | 162 | 22.76 | 52.41 | 154.48 | 28.68 | |

Mixed | Thin | 18 | 24.52 | 37.70 | 65.42 | 10.53 |

Middle | 53 | 31.74 | 62.13 | 131.03 | 24.02 | |

Dense | 19 | 41.28 | 92.57 | 171.53 | 37.06 | |

Total | 90 | 24.56 | 63.67 | 171.53 | 30.86 | |

Total | Thin | 113 | 1.05 | 26.65 | 65.42 | 12.77 |

Middle | 200 | 3.61 | 48.11 | 131.03 | 22.68 | |

Dense | 64 | 6.16 | 83.26 | 171.53 | 37.39 | |

Total | 377 | 1.05 | 47.70 | 171.53 | 30.06 |

Spectral Variables | Definitions of Spectral Variables | No. |
---|---|---|

Original Band | b_{1}—coastal, b_{2}—blue, b_{3}—green (GRN), b_{4}—red (RED), b_{5}—near infrared (NIR), b_{6}—shortwave infrared1 (SWIR1), b_{7}—shortwave infrared2 (SWIR2) | 7 |

Inversions of band_{i} | $I{B}_{i}=1/{b}_{i}$, i = 1,…,7 | 7 |

Simple two-band ratios ($S{R}_{i,j}$) | $S{R}_{i,j}={b}_{i}/{b}_{j}$, i, j = 1,…7; i ≠ j | 42 |

Three-band ratios | $S{R}_{i,j,k}={b}_{i}/\left({b}_{j}+{b}_{k}\right)$, i, j, k = 1,…,7; i ≠ j ≠ k, j < k | 106 |

Vegetation indices | Normalized difference vegetation index (NDVI), atmospherically resistant vegetation index (ARVI), soil adjusted vegetation index (${\mathrm{SAVI}}_{l}=\text{}\left({b}_{5}-{b}_{4}\right)\left(1+l\right)/\left({b}_{5}+{b}_{4}+l\right),$ l = 0.1), atmospherically resistant vegetation index (ARVI), enhance vegetation index (EVI), albedo, sum of three visible bands ($VI{S}_{234}$, $VI{S}_{234}={b}_{2}+{b}_{3}+{b}_{4}$) | 7 |

Principal component analysis | The first 3 PCs from principal component analysis (PCA1, PCA2, PCA3) | 3 |

Texture measures | Grey-level co-occurrence matrix-based texture measures of original bands (${b}_{i}$), including contrast (${b}_{iCONj}$), correlation (${b}_{iCORj}$), dissimilarity (${b}_{iDISj}$), entropy (${b}_{iENj}$), homogeneity (${b}_{iHOj}$), angular second moment (${b}_{iSEMj}$), mean (${b}_{iMEj}$), and variance(${b}_{iVAj}$) with different window sizes j (3 × 3, 5 × 5, 7 × 7) | 168 |

**Table 3.**Pearson correlation coefficients between remote sensing factors and aboveground biomass (AGB).

Variables | Correlation Coefficients | Variables | Correlation Coefficients | Variables | Correlation Coefficients | Variables | Correlation Coefficients |
---|---|---|---|---|---|---|---|

b3 | −0.254 ** | $S{R}_{37}$ | −0.236 ** | $S{R}_{416}$ | −0.210 ** | ${b}_{4ME5}$ | −0.276 ** |

b4 | −0.233 ** | $S{R}_{46}$ | −0.207 ** | $S{R}_{417}$ | −0.215 ** | ${b}_{7COR7}$ | 0.258 ** |

$VI{S}_{234}$ | −0.260 ** | $S{R}_{47}$ | −0.227 ** | $S{R}_{426}$ | −0.206 ** | ${b}_{3ME7}$ | −0.251 ** |

ARVI | 0.162 * | $S{R}_{64}$ | 0.227 ** | ${b}_{3ME3}$ | −0.265 ** | ${b}_{4ME7}$ | −0.242 ** |

$I{B}_{4}$ | 0.247 ** | $S{R}_{73}$ | 0.236 ** | ${b}_{4ME3}$ | −0.247 ** | ${b}_{2SEM5}$ | 0.251 ** |

$I{B}_{2}$ | 0.232 ** | $S{R}_{124}$ | 0.210 ** | ${b}_{5VA3}$ | 0.272 ** | ${b}_{2SEM7}$ | 0.230 ** |

$S{R}_{14}$ | 0.228 ** | $S{R}_{134}$ | 0.204 * | ${b}_{2COR5}$ | 0.260 ** | —— | —— |

$S{R}_{41}$ | −0.244 * | $S{R}_{327}$ | −0.229 ** | ${b}_{3ME5}$ | −0.279 ** | —— | —— |

Vegetation Type | Parameter | Estimate | Std.coef | p-Value | Vegetation Type | Parameter | Estimate | Std.coef | p-Value |
---|---|---|---|---|---|---|---|---|---|

Pine | ${b}_{2COR5}$ | 24.14 | 0.33 | <0.01 | Fir | ${b}_{5VA3}$ | 1.14 | 0.25 | <0.01 |

$S{R}_{327}$ | −165.54 | −0.27 | <0.01 | $I{B}_{2}$ | 1061.00 | 0.61 | <0.01 | ||

${b}_{2SEM5}$ | 19.47 | 0.17 | <0.01 | ${b}_{2SEM7}$ | 36.49 | 0.24 | <0.01 | ||

${b}_{3ME5}$ | 6.90 | 0.40 | <0.01 | ||||||

Mixed | ${b}_{7COR7}$ | 30.55 | 0.30 | <0.01 | Total vegetation | ${b}_{3ME7}$ | −3.62 | −0.25 | <0.01 |

${b}_{4ME7}$ | −10.05 | −0.60 | <0.01 | ${b}_{5VA3}$ | 0.83 | 0.14 | <0.01 | ||

$VI{S}_{234}$ | 9.00 | 0.36 | <0.01 | ${b}_{2SEM5}$ | 15.36 | 0.09 | <0.05 |

**Table 5.**Parameter estimates of the linear dummy variable model (model 2) and linear mixed-effects model (model 3).

Vegetation Type | Model 2 | Vegetation Type | Model 3 | ||||||
---|---|---|---|---|---|---|---|---|---|

Parameter | Estimate | S.D. | p-Value | Parameter | Estimate | S.D. | p-Value | ||

Pine | ${b}_{2COR5}$ | 16.70 | 4.77 | <0.01 | Pine | ${b}_{2COR5}$ | 13.35 | 3.77 | <0.01 |

$S{R}_{327}$ | −113.52 | 48.43 | <0.05 | $S{R}_{327}$ | −118.00 | 21.87 | <0.01 | ||

${b}_{2SEM5}$ | 16.85 | 6.86 | <0.05 | ${b}_{2SEM5}$ | 12.67 | 6.15 | <0.05 | ||

Fir | ${b}_{5VA3}$ | 0.62 | 0.22 | <0.01 | Fir | ${b}_{5VA3}$ | 0.16 | 0.20 | <0.05 |

$I{B}_{2}$ | 732.08 | 208.43 | <0.01 | $I{B}_{2}$ | 515.01 | 172.84 | <0.01 | ||

${b}_{2SEM7}$ | 17.18 | 7.68 | <0.05 | ${b}_{2SEM7}$ | 5.74 | 6.06 | <0.05 | ||

${b}_{3ME5}$ | 5.29 | 2.08 | <0.01 | ${b}_{3ME5}$ | 4.44 | 1.69 | <0.01 | ||

Mixed | ${b}_{7COR7}$ | 23.65 | 7.636 | <0.01 | Mixed | ${b}_{7COR7}$ | 10.55 | 6.79 | <0.05 |

${b}_{4ME7}$ | −4.80 | 3.665 | <0.05 | ${b}_{4ME7}$ | −1.42 | 2.86 | <0.05 | ||

$VI{S}_{234}$ | 6.28 | 5.165 | <0.05 | $VI{S}_{234}$ | 0.74 | 4.09 | <0.05 | ||

Total vegetation | ${b}_{3ME7}$ | −2.20 | 0.66 | <0.01 | Total vegetation | ${b}_{3ME7}$ | −1.60 | 0.50 | <0.01 |

${b}_{5VA3}$ | 0.48 | 0.21 | <0.05 | ${b}_{5VA3}$ | 0.25 | 0.20 | <0.05 | ||

${b}_{2SEM5}$ | 8.05 | 5.49 | <0.05 | ${b}_{2SEM5}$ | 1.07 | 4.56 | <0.05 |

Vegetation Type | R^{2} | R^{2}_{adj} | RMSE | Predict Mean |
---|---|---|---|---|

Pine | 0.23 | 0.21 | 18.41 | 29.64 |

Fir | 0.22 | 0.22 | 25.57 | 52.43 |

Mixed | 0.21 | 0.19 | 27.28 | 63.67 |

Total vegetation | 0.11 | 0.10 | 28.47 | 47.40 |

**Table 7.**The model fitting results of model 2 (linear dummy variable model) and model 3 (linear mixed-effects model) for different vegetation types.

Vegetation Type | Model# | R^{2} | R^{2}_{adj} | RMSE | Predict Mean |
---|---|---|---|---|---|

Pine | 2 | 0.41 | 0.40 | 16.05 | 29.65 |

3 | 0.39 | 0.38 | 16.29 | 29.36 | |

Fir | 2 | 0.61 | 0.61 | 17.88 | 52.39 |

3 | 0.61 | 0.61 | 17.92 | 51.95 | |

Mixed | 2 | 0.46 | 0.44 | 22.56 | 63.64 |

3 | 0.43 | 0.42 | 23.12 | 62.41 | |

Total vegetation | 2 | 0.41 | 0.41 | 22.99 | 47.70 |

3 | 0.41 | 0.41 | 23.07 | 47.51 |

**Table 8.**The comparisons of linear models (model 1), linear dummy variable models (model 2), and linear mixed-effects models (model 3). p-Value is from the F-test used to compare the similarity of models 1–3 against the null hypothesis of no significant difference.

Vegetation Type | Model# | Models 1–3 | Model 2 and Model 3 | ||
---|---|---|---|---|---|

F-Value | p-Value | F-Value | p-Value | ||

Pine | 1 | ||||

2 | 11.76 | <0.01 | |||

3 | 4.12 | <0.05 | 2.44 | 0.12 | |

Fir | 1 | ||||

2 | 29.58 | <0.01 | |||

3 | 17.31 | <0.01 | 1.28 | 0.26 | |

Mixed | 1 | ||||

2 | 9.37 | <0.01 | |||

3 | 0.77 | 0.38 | 4.69 | 0.03 | |

Total vegetation | 1 | ||||

2 | 111.48 | <0.01 | |||

3 | 66.03 | <0.01 | 2.95 | 0.09 |

© 2019 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**

Li, C.; Li, Y.; Li, M.
Improving Forest Aboveground Biomass (AGB) Estimation by Incorporating Crown Density and Using Landsat 8 OLI Images of a Subtropical Forest in Western Hunan in Central China. *Forests* **2019**, *10*, 104.
https://doi.org/10.3390/f10020104

**AMA Style**

Li C, Li Y, Li M.
Improving Forest Aboveground Biomass (AGB) Estimation by Incorporating Crown Density and Using Landsat 8 OLI Images of a Subtropical Forest in Western Hunan in Central China. *Forests*. 2019; 10(2):104.
https://doi.org/10.3390/f10020104

**Chicago/Turabian Style**

Li, Chao, Yingchang Li, and Mingyang Li.
2019. "Improving Forest Aboveground Biomass (AGB) Estimation by Incorporating Crown Density and Using Landsat 8 OLI Images of a Subtropical Forest in Western Hunan in Central China" *Forests* 10, no. 2: 104.
https://doi.org/10.3390/f10020104