# Tree Biomass Equations from Terrestrial LiDAR: A Case Study in Guyana

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Tree Selection and Data Collection

#### 2.2.1. Tree Inventory

#### 2.2.2. TLS Data Acquisition

#### 2.2.3. Destructive Harvesting and Fresh Mass Sampling

#### 2.2.4. Laboratory Analysis

#### 2.3. Diameter, Tree Height and Crown Diameter from TLS Data

#### 2.4. Tree Volume and Biomass from TLS Data

#### 2.5. TLS-Derived Allometric Models

#### 2.6. Tree Aboveground Biomass Estimation from Pantropical Allometric Models

#### 2.7. Assessment of Allometric Models

## 3. Results

#### 3.1. Tree Attributes and Estimated Biomass

#### 3.2. Allometric Models Using TLS-Derived Measurements

#### 3.3. Evaluation of Allometric Models

## 4. Discussion

#### 4.1. Developing Allometric Models from TLS-Derived Attributes

#### 4.2. Choosing the Adequate Tree Attributes for Allometric Models

#### 4.3. Local or Pantropical Allometric Models?

#### 4.4. Challenges and Outlook

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AGB | Aboveground biomass |

adj-${R}^{2}$ | Adjusted R-square |

AICc | Akaike’s information criterion |

CCC | Concordance correlation coefficient |

CD | Crown diameter |

CF | Correction factor |

Ch05.I.5 | Chave et al. [12] Equation I.5 |

Ch05.II.3 | Chave et al. [12] Equation II.3 |

Ch14.E | Chave et al. [11] Equation (7) |

Ch14.H | Chave et al. [11] Equation (4) |

CV RMSE | Coefficient of variation of RMSE |

D | Diameter at breast height |

df | degrees of freedom |

dmf | dry mass fraction |

GWDD | Global wood density database [8] |

H | Height |

LiDAR | Light Detection And Ranging |

MMRV | Monitoring, measurement, reporting and verification |

POM | Point of measurement |

Rj17.E | Réjou-Méchain et al. [46] Equation (1) |

QSM | Quantitative structure models |

TLS | Terrestrial laser scanning |

RDVC | Reference Dummy Variable Correction |

REDD+ | Reducing emissions from deforestation and degradation |

RMSE | Root mean square error |

RSE | Residual standard error |

UAV | Unnamed aerial vehicle |

UAV-LS | Unnamed aerial vehicle laser scanning |

WD | Wood density |

## Appendix A

**Figure A1.**Relationship between pre-harvest against post-harvest values for D (

**a**) and H (

**b**), TLS-derived against post-harvest values for D (

**c**) and H (

**d**), TLS-derived against pre-harvest values for $CD$ (

**e**), and against harvested tree $AGB$ (

**f**), Solid line is 1:1 relationship.

**Table A1.**Summary of AGB estimates from TLS-derived and pantropical allometric models—${R}^{2}$, RMSE, CCC, sum of errors (sum, mean, standard deviation (SD)), mean percent error and relative error (n = 26) separated in small trees (D ≤ 70 $\mathrm{cm}$) and large trees (D > 70 $\mathrm{cm}$). Models are arranged based on the statistical parameters from the best model to the worst model.

Model | Type | ${\mathit{R}}^{2}$ | RMSE | CCC | Mean Error (Mg) | Sum Error (Mg) | SD Error (Mg) | Mean rel. Error (%) | SD. rel. Error (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Small | Large | Small | Large | Small | Large | Small | Large | Small | Large | Small | Large | Small | Large | Small | Large | ||

m5 | D.WD.CD | 0.83 | 0.84 | 1.27 | 2.69 | 0.87 | 0.90 | 0.03 | 0.06 | 0.50 | 0.53 | 1.31 | 2.86 | 44.08 | 0.11 | 70.75 | 22.73 |

m4 | D.WD.H.CD | 0.83 | 0.81 | 1.22 | 2.89 | 0.89 | 0.89 | 0.08 | 0.01 | 1.23 | 0.13 | 1.26 | 3.07 | 44.29 | −0.04 | 65.74 | 23.30 |

Ch05.II.3 | WD.D.D${}^{2}$.D${}^{3}$ | 0.70 | 0.78 | 1.57 | 3.30 | 0.79 | 0.86 | −0.21 | −0.43 | −3.61 | −3.88 | 1.60 | 3.47 | 10.71 | −4.22 | 57.51 | 22.36 |

Ch05.I.5 | D${}^{2}$.WD.H | 0.76 | 0.67 | 1.40 | 4.25 | 0.84 | 0.79 | −0.11 | −0.88 | −1.95 | −7.91 | 1.44 | 4.42 | 15.26 | −7.57 | 47.45 | 24.95 |

Ch14.H | (D${}^{2}$.WD.H) | 0.75 | 0.67 | 1.41 | 4.11 | 0.84 | 0.79 | −0.09 | −1.16 | −1.45 | −10.44 | 1.45 | 4.19 | 19.54 | −9.21 | 48.42 | 23.74 |

m1 | D | 0.74 | 0.59 | 1.55 | 3.71 | 0.81 | 0.76 | 0.64 | 0.32 | 10.81 | 2.84 | 1.46 | 3.92 | 99.92 | 7.74 | 118.63 | 26.22 |

Rj17.E | D.D${}^{2}$.WD.E | 0.70 | 0.77 | 1.65 | 3.45 | 0.75 | 0.85 | −0.40 | −1.39 | −6.72 | −12.55 | 1.65 | 3.34 | 3.61 | −11.50 | 52.33 | 20.40 |

Ch14.E | D.D${}^{2}$.WD.E | 0.70 | 0.77 | 1.68 | 3.55 | 0.74 | 0.84 | −0.44 | −1.57 | −7.45 | −14.11 | 1.67 | 3.37 | 1.39 | −13.08 | 51.60 | 20.94 |

m3 | D.WD.H | 0.67 | 0.74 | 1.67 | 4.39 | 0.75 | 0.72 | −0.16 | −3.27 | −2.66 | −29.45 | 1.71 | 3.11 | 35.20 | −23.72 | 65.90 | 19.41 |

m2 | D.WD | 0.64 | 0.77 | 1.90 | 4.30 | 0.76 | 0.81 | 0.84 | 1.99 | 14.30 | 17.91 | 1.75 | 4.04 | 105.06 | 14.74 | 109.05 | 28.47 |

**Figure A2.**Mean error in estimates (estimated AGB minus reference AGB in $\mathrm{Mg}$) by DBH size class: small trees (D ≤ 70 $\mathrm{cm}$; n = 17) and large trees (D > 70 $\mathrm{cm}$; n = 9) for the TLS-derived allometric models and pantropical models.

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**Figure 2.**(

**a**) Vitex spp. tree point cloud (TLS-derived H = $51.8$ $\mathrm{m}$ and TLS-derived D = $114.6$ $\mathrm{c}$$\mathrm{m}$ with POM at $5.3$ $\mathrm{m}$), (

**b**) down-sampled tree point cloud ($0.026$ $\mathrm{m}$ point spacing, as in Calders et al. [42]), (

**c**) soft tissues (green) and hardwood (black) separated point cloud [43], and (

**d**) TreeQSM modelled after the hardwood point cloud.

**Figure 3.**Buttresses modelling of a Hymenolobium flavum tree. The bottom part of the stem was modelled with a triangular mesh instead of cylinders. The mesh volume replaced the volume of the cylinders.

**Figure 4.**Relationship between reference AGB (harvested trees; n = 26) and AGB estimated by TLS-derived and pantropical allometric models. Black solid line is 1:1 relationship; dashed coloured lines depict linear fit; and dotted grey lines indicate 95% confidence interval for the linear fit.

**Table 1.**Pantropical models from [11,12,46] included diameter at breast height (D, in $\mathrm{cm}$), specie-specific wood density values according to the GWDD ($WD$, in $\mathrm{g}\text{}{\mathrm{cm}}^{-3}$ or $\mathrm{kg}\text{}{\mathrm{m}}^{-3}$), total height (H, in $\mathrm{m}$), the environmental stress (E, calculated from the GPS average location of each tree

^{1}) to estimate aboveground biomass ($AGB$, in $\mathrm{k}\mathrm{g}$ dry mass) and $\epsilon $ is the model error.

Model | Form AGB = |
---|---|

Ch05.II.3 | $\begin{array}{c}\hfill WD\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}exp(-1.499+2.1481\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+0.207\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln{(D)}^{2}-0.0281\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln{(D)}^{3})+\epsilon \end{array}$ |

Ch05.I.5 | $\begin{array}{c}\hfill 0.0509\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}WD\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{D}^{2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}H+\epsilon \end{array}$ |

Ch14.H | $\begin{array}{c}\hfill 0.0673\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{(WD\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{D}^{2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}H\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}})}^{0.976}+\epsilon \end{array}$ |

Ch14.E | $\begin{array}{c}\hfill exp(-1.803-0.976\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}E+0.976\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+2.673\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)-0.0299\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln({D}^{2}))+\epsilon \end{array}$ |

Rj17.E | $\begin{array}{c}\hfill exp(-2.024-0.896\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}E+0.920\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+2.795\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)-0.0461\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln({D}^{2}))+\epsilon \end{array}$ |

**Table 2.**Pre- and post-harvested field measured attributes, and terrestrial laser scanning (TLS)-derived attributes range for: diameter (D), height (H), crown diameter ($CD$), wood density ($WD$; see note below) and aboveground biomass (AGB).

Attributes | Allometric Model Dataset (n = 72) | Validation Dataset (n = 26) | ||
---|---|---|---|---|

Measured_{pre} | TLS-Derived | Measured_{post} | TLS-Derived | |

Diameter (cm) | 12.9 − 134.0 | 13.3 − 126.2 | 16.7 − 128.7 | 16.7 − 130.2 |

Tree height (m) | 14 − 43.0 | 16.9 − 51.8 | 16.4 − 51.6 | 16.6 − 49.1 |

Crown diameter (m) | 4.4 − 42.6 | 2.5 − 42.9 | 3.4 − 30.8 _{pre} | 4.6 − 30.2 |

WD (g cm${}^{-3}$) | 0.4 − 1.0 | 0.4 − 1.0 | 0.4 − 0.9 | 0.4 − 1.0 |

AGB (Mg) | NA | 0.2 − 28.5 | 0.9 − 21.8 | 0.2 − 27.4 |

**Table 3.**Models description for the TLS-derived aboveground biomass estimations including diameter (D), wood density ($WD$), height (H), crown diameter ($CD$), Reference Dummy Variable Corrector ($RDVC$) and associated statistical parameters based on 72 trees.

Model | Type | Form | a | b | c | d | e | RDVC | df | RSE | adj-R${}^{2}$ | AICc |
---|---|---|---|---|---|---|---|---|---|---|---|---|

m1 | D | $ln(AGB)=\mathit{a}+\mathit{b}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+\epsilon $ | 0.6788 | 1.9337 | … | … | … | … | 70 | 0.360 | 0.90 | 61.52 |

m2 | D.WD | $ln(AGB)=\mathit{a}+\mathit{b}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+\mathit{c}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+RDVC+\epsilon $ | 0.6765 | 2.0246 | 1.0932 | … | … | −0.1968 | 69 | 0.274 | 0.94 | 23.61 |

m3 | D.WD.H | $ln(AGB)=\mathit{b}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+\mathit{c}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+\mathit{d}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(H)+RDVC+\epsilon $ | … | 1.9091 | 1.0978 | 0.3224 | … | −0.2138 | 69 | 0.266 | NA | 19.48 |

m4 | D.WD.H.CD | $ln(AGB)=\mathit{b}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+\mathit{c}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+\mathit{d}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(H)+\mathit{e}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(CD)+\epsilon $ | … | 1.7282 | 0.2603 | 1.1522 | 0.3698 | … | 68 | 0.240 | NA | 6.23 |

m5 | D.WD.CD | $ln(AGB)=\mathit{a}+\mathit{b}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(D)+\mathit{c}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(WD)+\mathit{e}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}ln(CD)+\epsilon $ | 0.5366 | 1.8124 | 1.1512 | … | 0.3878 | … | 68 | 0.246 | 0.96 | 9.28 |

**Table 4.**Summary of AGB estimates from TLS-derived and pantropical allometric models—${R}^{2}$, root mean square error (RMSE), concordance correlation coefficient (CCC), sum of errors (sum, mean, standard deviation (SD)), mean percent error and relative error (n = 26). Models are arranged based on the statistical parameters from the best model to the worst model.

Model | Type | ${\mathit{R}}^{2}$ | RMSE | CCC | Error (Mg) | Relative Error (%) | |||
---|---|---|---|---|---|---|---|---|---|

Sum | Mean | SD | Mean | SD | |||||

m5 | D.WD.CD | 0.93 | 1.91 | 0.96 | 1.03 | 0.04 | 1.95 | 28.25 | 61.35 |

m4 | D.WD.H.CD | 0.92 | 1.99 | 0.96 | 1.36 | 0.05 | 2.03 | 28.33 | 57.91 |

Ch05.II.3 | WD.D.D${}^{2}$.D${}^{3}$ | 0.89 | 2.32 | 0.94 | −7.49 | −0.29 | 2.35 | 5.54 | 48.26 |

Ch05.I.5 | D${}^{2}$.WD.H | 0.85 | 2.75 | 0.92 | −9.86 | −0.38 | 2.78 | 7.35 | 41.98 |

Ch14.H | (D${}^{2}$.WD.H) | 0.85 | 2.67 | 0.92 | −11.89 | −0.46 | 2.69 | 9.59 | 43.31 |

m1 | D | 0.87 | 2.52 | 0.93 | 13.65 | 0.53 | 2.51 | 68.01 | 105.95 |

Rj17.E | D.WD.E | 0.88 | 2.43 | 0.93 | −19.28 | −0.74 | 2.36 | −1.62 | 44.04 |

Ch14.E | D.WD.E | 0.88 | 2.49 | 0.93 | −21.56 | −0.83 | 2.39 | −3.62 | 43.52 |

m3 | D.WD.H | 0.88 | 2.92 | 0.89 | −32.11 | −1.23 | 2.69 | 14.80 | 60.97 |

m2 | D.WD | 0.89 | 2.96 | 0.92 | 32.21 | 1.24 | 2.74 | 73.80 | 98.95 |

© 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**

Lau, A.; Calders, K.; Bartholomeus, H.; Martius, C.; Raumonen, P.; Herold, M.; Vicari, M.; Sukhdeo, H.; Singh, J.; Goodman, R.C. Tree Biomass Equations from Terrestrial LiDAR: A Case Study in Guyana. *Forests* **2019**, *10*, 527.
https://doi.org/10.3390/f10060527

**AMA Style**

Lau A, Calders K, Bartholomeus H, Martius C, Raumonen P, Herold M, Vicari M, Sukhdeo H, Singh J, Goodman RC. Tree Biomass Equations from Terrestrial LiDAR: A Case Study in Guyana. *Forests*. 2019; 10(6):527.
https://doi.org/10.3390/f10060527

**Chicago/Turabian Style**

Lau, Alvaro, Kim Calders, Harm Bartholomeus, Christopher Martius, Pasi Raumonen, Martin Herold, Matheus Vicari, Hansrajie Sukhdeo, Jeremy Singh, and Rosa C. Goodman. 2019. "Tree Biomass Equations from Terrestrial LiDAR: A Case Study in Guyana" *Forests* 10, no. 6: 527.
https://doi.org/10.3390/f10060527