# Comparison of Statistical Modelling Approaches for Estimating Tropical Forest Aboveground Biomass Stock and Reporting Their Changes in Low-Intensity Logging Areas Using Multi-Temporal LiDAR Data

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## Abstract

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## 1. Introduction

_{2}emissions due to combustion in an Aleppo pine forest using LiDAR data. Here too, the best model for pre-fire AGB estimation was found to be MLR, and no significant statistical differences were observed among the high performing models. Latifi et al. [29] on the other hand, made use of a wide range of forest variables extracted from multiple remotely sensed data, such as orthorectified colour infrared (CIR) images, medium-resolution Thematic Mapper (TM) imagery, and high-density normalized LiDAR point clouds, for estimating the total volume and biomass in a mixed temperate forest landscape. When comparing the performance of various plot-level nonparametric predictions, which comprised of three distance measures of Euclidean, Mahalanobis, and Most Similar Neighbour, as well as RF, and multiple remotely sensed datasets, the authors showed the superior predictive capability of LiDAR-based metrics and RF combination. Application of evolutionary genetic algorithms was also tested to prune the original high dimensional dataset and improve the performance of modeling techniques; however, intercorrelation related issues proved to be a major hurdle causing unstable results during multiple runs. Meanwhile, Gagliasso et al. [30], on examination of the predictive performance of linear regression, geographic weighted regression (GWR), gradient nearest neighbor (GNN), most similar neighbor (MSN), random forest imputation, and k-nearest neighbor (k-nn), observed that the k-nn (k = 5) had the lowest RMSE and least amount of bias while predicting biomass across 19,000 acres on the Malheur National Forest. Notwithstanding the ever-increasing interest in modeling paradigms, comparative modeling studies for AGB change prediction in selectively logged tropical forests remains nominal.

- (i)
- Evaluate the performance of ordinary least squares (OLS) regression modelling and nine machine learning algorithms: random forest (RF), several variations of k-nearest neighbour (k-NN), support vector machine (SVM), and artificial neural networks (ANN)
- (ii)
- Estimate AGB stocks and report AGB change at the landscape level using the best model from the previous step and multi-temporal LiDAR datasets.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field Data

^{3}) per species, which is derived from a published database [36]; E is a compounded measure of environmental stresses—such as variability in temperature and precipitation—which improves estimation when field measurements of tree height are not available. For this, we retrieved a value of E = −0.104 for the location of this study area. Total live AGB (Mg/ha) was calculated by aggregation of individual tree biomass values and using plot appropriate hectare expansion factors. Table 1 presents a summary of the input data (dbh and AGB) in 2014, which were used for statistical analysis.

#### 2.3. Lidar Data and Processing

#### 2.4. Model Development and Assessment

- (i)
- Ordinary Least Squares (OLS) regression. This is a common method for modelling and predicting AGB from LiDAR metrics. The OLS model was implemented in R with the “lm” function.
- (ii)
- Random Forest (RF). The RF algorithm was implemented in R using the randomForest package [43]. In RF, ntree was set to 1000, and the other parameters (e.g. mtry) were left in RF default mode.
- (iii)
- k-Nearest Neighbour (k-NN) imputation. This is a non-parametric method used for regression and classification [44]. In this study, we conducted k-NN using the package yaImpute in R [45]. For each imputation, we set k = 1 neighbour to preserve the variance of the data [46]. Neighbour weighting methods used were the Euclidean (k-NN-EU), Mahalanobis (k-NN-MA), Most Similar Neighbour (k-NN-MSN), Independent Component Analysis (k-NN-ICA), Random Forest (k-NN-RF), and raw (unweighted) data (k-NN-RAW).
- (iv)
- Support Vector Machine (SVM). This is a non-parametric statistical method. The SVM algorithm was performed using the R package e1071 via an epsilon-regression with the default epsilon value of 0.1 [47].
- (v)
- Artificial neural network (ANN). Here, a simulation of a biological neural network system using mathematical modelling is performed [48]. Normally, three layers of neurons make up a neural network: an input layer, a hidden layer, and an output layer. The nnt package in R was used for the ANN [49]. The hidden layer neurons parameter was set to 40, and the input and hidden nodes were set to compute the logistic function, while the output node was set to compute a linear function. Before running ANN, the dataset was standardized.

_{2012}= f (LiDAR metrics 2012; AGB in 2014)

_{2014}= f (LiDAR metrics 2014; AGB in 2014)

_{2017}= f (LiDAR metrics 2017; AGB in 2014)

_{(2012–2014)}= AGB

_{2014}− AGB

_{2012}

_{(2014–2017)}= AGB

_{2017}− AGB

_{2014}

_{(2012–2017)}= AGB

_{2017}− AGB

_{2012}

_{t}is the AGB stock for year t and ΔAGB

_{t1-t2}is the AGB change between years t1 and t2, both expressed in Mg/ha. Leave-one-out cross-validation (LOOCV) was employed to assess accuracy. This is done by iteratively removing a single plot i from the total number of plots n, then using the remaining plots to fit a separate model and predict a value for the removed plot (${\widehat{y}}_{i}$), the prediction is then compared to the observed value (${y}_{i}$). We calculated, in Mg/ha, absolute root mean squared error (RMSE), mean difference (MD), and the coefficient of determination (R

^{2}), in order to respectively evaluate model precision, accuracy, and agreement between the predicted and observed estimates (Equations (8)–(10)).

## 3. Results

#### 3.1. Principal Component Analysis (PCA) and Variable Selection

#### 3.2. Model Performance

#### 3.3. Aboveground Biomass Change Mapping and Uncertainty

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Location map of the study area at Fazenda Cauaxi located in the eastern Brazilian Amazon; (

**b**) LiDAR-derived canopy height model within the unlogged and reduced impact logging (RIL) work units (UT) of 100-ha each with colour ramp; and (

**c**,

**d**) LiDAR-derived point clouds across areas logged (

**c1**–

**c3**) by RIL or unlogged (

**d1**–

**d3**) in 2012 (

**c1**,

**d1**), 2014 (

**c2**,

**d2**), and 2017 (

**c3**,

**d3**) corresponding to the zoomed areas denoted in 1b and sharing the same colour ramp. Grid size in (

**c1**–

**c3)**and (

**d1**–

**d3**) is 10 m. The coordinate reference system for the study area is EPSG:4674.

**Figure 2.**Procedure for estimating aboveground biomass (AGB) stocks and AGB change using LiDAR data and statistical modelling approaches.

**Figure 3.**Principal Components (PC1 and PC2) and LiDAR metrics (

**a**); The percentage of variation explained by the six first PCs (

**b**).

**Figure 4.**Aboveground biomass stock (AGB) within the unlogged and reduced impact logging (RIL) work units of 100-ha each in 2012 (

**a**), 2014 (

**b**), and 2017 (

**c**). Zoom view of the AGB stock maps in areas unlogged and logged by RIL in 2012 (

**a1**), 2014 (

**b1**), and 2017 (

**c1**).

**Figure 5.**Map of aboveground biomass (AGB) change within the unlogged and reduced impact logging (RIL) work units of 100-ha each from 2012 to 2014 (

**a**), 2014 to 2017 (

**b**), and 2012 to 2017 (

**c**). Zoom view of the AGB change maps in areas unlogged and logged by RIL (

**a1**–

**c1**).

Attributes | Min | Max | Mean | sd |
---|---|---|---|---|

dbh (cm) | 10 | 186.00 | 32.70 | 20.16 |

ρ (g/cm^{3}) | 0.26 | 0.99 | 0.73 | 0.14 |

AGB (kg·tree^{−1}) | 22.46 | 73.70 | 18.04 | 36.84 |

AGB ( Mg·ha^{−1}) | 65.34 | 525.79 | 238.11 | 86.48 |

Specifications | 2012 | 2014 | 2017 |
---|---|---|---|

LiDAR system | ALTM 3100 | ALTM 300 | ALTM 3100 |

Acquisition date | 27–29 July | 26–27 December | 12 December |

Datum | Sirgas 2000 | Sirgas 2000 | Sirgas 2000 |

Pulse density (pulses/m^{2}) | 13.89 | 37.5 | 22.61 |

Flying height (m) | 850 m | 850 m | 850 m |

Field of view (°) | 11 | 12 | 15 |

Scanning Frequency (Hz) | 59.8 | 83.0 | 40 |

Overlap Percentage (%) | 65 | 65 | 70 |

Variable | Description |
---|---|

HMAX | Maximum height |

HMEAN | Mean height |

HMODE | Modal height |

HSD | Height standard deviation |

HVAR | Height variance |

HCV | Height coefficient of variation |

HIQ | Height interquartile distance |

HSKE | Height skewness |

HKUR | Height kurtosis |

H20TH | Height 20th percentile |

H25TH | Height 25th percentile |

H30TH | Height 30th percentile |

H40TH | Height 40th percentile |

H50TH | Height 50th percentile |

H60TH | Height 60th percentile |

H70TH | Height 70th percentile |

H75TH | Height 75th percentile |

H80TH | Height 80th percentile |

H90TH | Height 90th percentile |

H95TH | Height 95th percentile |

H99TH | Height 99th percentile |

CR | Canopy relief ratio ((HMEAN − HMIN)/(HMAX − HMIN)) |

COV | Canopy cover (percentage of first return above 2.00 m) |

**Table 4.**Eigenvalues and eigenvectors for the first six principal components and selected LiDAR metrics.

PCs | Ev | Eigenvectors (Eg) | |||||
---|---|---|---|---|---|---|---|

HMEAN | HCV | HKUR | COV | HMODE | HSKEW | ||

PC1 | 3.27 | −0.30 | 0.11 | −0.05 | 0.02 | −0.17 | 0.13 |

PC2 | 2.50 | −0.04 | 0.36 | −0.17 | −0.10 | −0.17 | 0.27 |

PC3 | 1.67 | 0.05 | −0.09 | 0.45 | 0.33 | 0.02 | 0.31 |

PC4 | 0.89 | 0.03 | −0.05 | −0.38 | 0.85 | 0.14 | 0.09 |

PC5 | 0.77 | 0.09 | −0.10 | 0.05 | 0.05 | −0.88 | 0.07 |

PC6 | 0.60 | −0.05 | 0.12 | 0.29 | 0.35 | −0.30 | −0.38 |

**Table 5.**Aboveground biomass (AGB) model precision and accuracy derived from the LOOCV procedure. Average and standard deviation of predicted AGB (Mg/ha) stocks at plot level in 2014.

Method | R^{2} | RMSE | MD | LiDAR-Derived AGB (Mg/ha) Stock in 2014 | ||
---|---|---|---|---|---|---|

Mg/ha | % | Mg/ha | % | |||

OLS | 0.70 | 46.94 | 19.71 | −0.57 | −0.24 | 237.54 ± 74.56 |

RF | 0.59 | 55.44 | 23.29 | −0.16 | −0.07 | 237.94 ± 57.77 |

k–NN-RAW | 0.35 | 75.90 | 31.87 | −1.54 | −0.65 | 236.56 ± 81.97 |

k-NN-EU | 0.48 | 66.90 | 28.09 | −4.09 | −1.72 | 234.01 ± 84.29 |

k–NN-MA | 0.39 | 73.01 | 30.66 | −4.66 | −1.96 | 233.44 ± 81.64 |

k-NN-MSN | 0.53 | 64.61 | 27.09 | −4.39 | −1.94 | 233.71 ± 89.04 |

k-NN-ICA | 0.38 | 73.01 | 30.66 | −4.66 | −1.96 | 233.44 ± 81.64 |

k-NN-RF | 0.40 | 74.71 | 31.21 | −3.43 | −1.44 | 234.67 ± 88.50 |

SVM | 0.57 | 56.24 | 23.62 | 1.59 | 0.67 | 239.69 ± 60.93 |

ANN | 0.61 | 54.48 | 22.89 | 0.09 | 0.03 | 238.20 ± 76.72 |

**Table 6.**Aboveground biomass stocks and changes estimates at landscape level derived from the OLS model for the unlogged and reduced impact logging (RIL) work units (UT) within each year of logging. Std Error is the estimated standard error of the estimator for the mean aboveground biomass (AGB) stock and AGB changes derived from the uncertainty analysis.

Work Unit (UT) | $\mathbf{A}\mathbf{G}{\mathbf{B}}_{2012}(\mathbf{Mg}/\mathbf{ha})$ | $\mathbf{A}\mathbf{G}{\mathbf{B}}_{2014}(\mathbf{Mg}/\mathbf{ha})$ | $\mathbf{A}\mathbf{G}{\mathbf{B}}_{2017}(\mathbf{Mg}/\mathbf{ha})$ | $\mathbf{\u2206}\mathbf{A}\mathbf{G}{\mathbf{B}}_{\left(2012\u20132014\right)}(\mathbf{Mg}/\mathbf{ha})$ | $\mathbf{\u2206}\mathbf{A}\mathbf{G}{\mathbf{B}}_{\left(2014\u20132017\right)}(\mathbf{Mg}/\mathbf{ha})$ | $\mathbf{\u2206}\mathbf{A}\mathbf{G}{\mathbf{B}}_{\left(2012\u20132017\right)}(\mathbf{Mg}/\mathbf{ha})$ | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | sd | std Error | Mean | sd | std Error | Mean | sd | std Error | Mean | sd | std Error | Mean | sd | std Error | Mean | sd | std Error | ||

RIL | 2006 | 112.85 | 683.75 | 4.94 | 220.69 | 104.75 | 5.04 | 193.11 | 252.29 | 5.07 | 107.84 | 665.07 | 2.38 | −27.58 | 225.25 | 1.88 | 80.26 | 703.70 | 2.90 |

2007 | 224.11 | 95.58 | 4.28 | 263.18 | 93.90 | 4.37 | 232.94 | 171.30 | 4.38 | 39.07 | 38.03 | 2.70 | −30.24 | 146.12 | 2.43 | 8.83 | 148.94 | 2.97 | |

2008 | 198.68 | 109.30 | 4.94 | 234.89 | 108.52 | 5.16 | 230.90 | 103.03 | 4.90 | 36.21 | 39.63 | 1.92 | −3.99 | 40.88 | 2.01 | 32.22 | 55.41 | 2.68 | |

2010 | 202.97 | 101.22 | 4.61 | 244.05 | 93.87 | 4.53 | 218.99 | 314.21 | 4.40 | 41.08 | 36.17 | 1.71 | −25.07 | 299.06 | 1.92 | 16.02 | 300.80 | 2.59 | |

2012 | 264.54 | 239.32 | 4.60 | 252.27 | 111.26 | 5.24 | 242.47 | 100.24 | 4.75 | −12.27 | 229.46 | 3.73 | −9.80 | 55.19 | 2.60 | −22.07 | 228.75 | 3.85 | |

2013 | 289.88 | 82.47 | 3.92 | 275.22 | 95.75 | 4.75 | 259.74 | 92.83 | 4.58 | −14.66 | 71.37 | 3.53 | −15.47 | 38.58 | 1.90 | −30.14 | 69.93 | 3.48 | |

Unlogged | 284.58 | 71.48 | 3.44 | 312.09 | 74.58 | 3.59 | 294.29 | 74.25 | 3.60 | 27.51 | 32.16 | 2.68 | −17.80 | 38.08 | 1.86 | 9.71 | 46.76 | 2.29 |

© 2020 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**

Rex, F.E.; Silva, C.A.; Dalla Corte, A.P.; Klauberg, C.; Mohan, M.; Cardil, A.; Silva, V.S.d.; Almeida, D.R.A.d.; Garcia, M.; Broadbent, E.N.;
et al. Comparison of Statistical Modelling Approaches for Estimating Tropical Forest Aboveground Biomass Stock and Reporting Their Changes in Low-Intensity Logging Areas Using Multi-Temporal LiDAR Data. *Remote Sens.* **2020**, *12*, 1498.
https://doi.org/10.3390/rs12091498

**AMA Style**

Rex FE, Silva CA, Dalla Corte AP, Klauberg C, Mohan M, Cardil A, Silva VSd, Almeida DRAd, Garcia M, Broadbent EN,
et al. Comparison of Statistical Modelling Approaches for Estimating Tropical Forest Aboveground Biomass Stock and Reporting Their Changes in Low-Intensity Logging Areas Using Multi-Temporal LiDAR Data. *Remote Sensing*. 2020; 12(9):1498.
https://doi.org/10.3390/rs12091498

**Chicago/Turabian Style**

Rex, Franciel Eduardo, Carlos Alberto Silva, Ana Paula Dalla Corte, Carine Klauberg, Midhun Mohan, Adrián Cardil, Vanessa Sousa da Silva, Danilo Roberti Alves de Almeida, Mariano Garcia, Eben North Broadbent,
and et al. 2020. "Comparison of Statistical Modelling Approaches for Estimating Tropical Forest Aboveground Biomass Stock and Reporting Their Changes in Low-Intensity Logging Areas Using Multi-Temporal LiDAR Data" *Remote Sensing* 12, no. 9: 1498.
https://doi.org/10.3390/rs12091498