# Predicting Stem Total and Assortment Volumes in an Industrial Pinus taeda L. Forest Plantation Using Airborne Laser Scanning Data and Random Forest

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

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## Abstract

**:**

^{2}equal to 0.98, 0.98 and 0.96, with unbiased predictions of −0.17%, −0.12% and −0.23%, and Root Mean Square Error (RMSE) values of 7.83%, 7.71% and 8.63%. Our methodology makes use of commercially available airborne lidar and widely used mathematical tools to provide solutions for increasing the industry efficiency in monitoring and managing wood volume.

## 1. Introduction

^{3}·ha

^{−1}·year

^{−1}[2]. Moreover, P. taeda is commonly managed for production of multiple types of wood such as stem total, saw logs, pulpwood and small-diameter logs and branches, which are used for energy. Saw logs and pulpwood can be further divided into different assortments that differ in size and therefore in economic value [3].

## 2. Methods

#### 2.1. Study Area Description

^{−1}, respectively. The climate of the region is characterized as warm and temperate [28], with annual average precipitation of approximately 1378 mm and an annual average temperature of 18.4 °C. The P. taeda stands are situated on a plateau where the topography is relatively flat. The plantations are managed by Klabin S.A., a pulp and paper company.

#### 2.2. Field Data Collection

^{2}(i.e., 20 m × 30 m) were randomly established and measured across 50 stands distributed in four plantations. As such, the sample plots well represent the study area, and they capture the entire structural variability in these stands with ages ranging from three to nine years old. All plots were geo-referenced with a geodetic GPS with differential correction capability (Trimble Pro-XR, Trimble, Sunnyvale, CA, USA) ensuring a location error lower than 10 cm. In each sample plot, individual trees were measured for dbh (diameter at breast height) at 1.30 m and a random subsample (15%) of trees for tree height (Ht). For those trees in the plots that were not directly measured for Ht, the inventory team of Klabin S.A. predicted heights from hypsometric equations [29], employing dbh as the independent variable, and Ht as the dependent variable, following the model below:

^{2}) and standard error of estimate in percentage (SEE%) of the models ranged from 0.96 to 0.98 and 5.1 to 6.5, respectively.

_{i}= stem diameter (cm) at the ith position; dbh = diameter (cm) at breast height (1.30 m); h = total height (m); h

_{i}= height (m) at the ith position; and K = π/40,000 is an adjustment factor to estimate volume as m

^{3}·ha

^{−1}.

^{2}and standard error of the estimate (SEE; given in %) for the polynomial models used in this study are presented in Table 1.

^{3}·ha

^{−1}for each class of stand ages is presented in Table 2. SEE (%) is the standard error of the estimate, expressed as a percentage.

#### 2.3. Lidar Data Acquisition and Data Processing

#### 2.4. Predictor Variables Selection

#### 2.5. Random Forest Model Development

^{2}, Root Mean Square Error (RMSE), and Bias (both absolute and relative) by the linear relationship between predicted (output from RF) and observed stem volumes:

_{i}is the observed value for plot i, and ${\widehat{y}}_{i}$ is the predicted value for plot i. Moreover, relative RMSE (%) and biases (%) were calculated by dividing the absolute values (Equations (5) and (6)) by the mean of the observed stem volume. Based on earlier experiences and recommendations from literature [4,5], we defined acceptable model accuracy as a relative RMSE and Bias of <15%.

^{2}, absolute and relative RMSE and Bias were computed based on the linear relationship between observed and predicted volumes using the holdout samples. We used also two-sided Kolmogorov-Smirnov (KS) in R [38] and a statistical equivalence test [41] to compare the field- and lidar-based stem volume estimates in each iteration.

#### 2.6. Predictive Stem Volumes Maps

## 3. Results

#### 3.1. Predictor Variable Selection

#### 3.2. Model Performances

^{2}, RMSE and Bias for all 500 bootstrap runs (Table 8). Observed and predicted stem volumes in each bootstrap iteration did not differ significantly by the statistical KS and equivalence test (p-values > 0.05) as well. Overall, all models using H99TH and HSKEW performed very well, with relative RMSE and Bias <15% in the bootstrap procedure. The observed and the average of the predicted stem volumes from the 500 bootstrap runs were also compared and according to the KS and equivalence tests those values did not differ significantly (p-values > 0.05) too (Figure 5).

#### 3.3. Prediction Maps

## 4. Discussion

^{2}of ~0.65 for estimating both saw log and pulpwood volumes. While those authors have showed the great potential of lidar in retrieving assortment volumes, this specific application is still relatively novel and further studies, such as presented herein, still need to be carried out.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Location of study area in Telêmaco Borba, Paraná, Brazil. The black dotes indicate the location of the Pinus teada stands.

**Figure 2.**Process of forest volume mesurement. (

**A**) Pinus plantation; (

**B**) Timber harvester and (

**C**) Log segmentation for classes of volume mesurements.

**Figure 3.**Procedure for predicting stem total and assortment volumes in an industrial P. taeda forest plantation using airborne laser scanning data and random forest.

**Figure 4.**Distribution of observed (black line) and predicted (red line)

**s**tem volume from RF. The gray histograms is based from field data. (

**A**) Total volume (Vt) (

**B**) Commercial volume (Vc) and (

**C**) Pulpwood volume (Vp).

**Figure 5.**Equivalence plots of the observed and the mean of predicted Vt (

**A**), Vc (

**B**) and Vp (

**C**) obtained from the 500 bootstrapped RF model runs. (N = 50). The equivalence plot design presented herein is an adaptation of the original equivalence plots presented by [41]. The grey polygon represents the ±25% region of equivalence for the intercept, and the green vertical bar represents a 95% of confidence interval for the intercept. The predicted stem volumes from the RF models are equivalent with reference to the intercept and slope since the green bar is completely within the grey polygon. If the grey polygon is lower than the green vertical bar, the predicted stem volumes are negatively biased; and if it is higher than the green vertical bar, the predicted stem volumes are positively biased. Moreover, the grey dashed line represents the ±25% region of equivalence for the slope, the fit line is within the dotted lines and the black vertical bar is within the gray rectangle, indicating that the pairwise measurements are equivalent. A green bar that is wider than the region outlined by the grey dashed lines indicates highly variable predictions. The white dots are the pairwise measurements, and the solid line is a best-fit linear model for the pairwise measurements. The light grey dashed line represented the relationship 1:1. The horizontal red bars represent the standard deviation of the 500 bootstraping predictions.

**Figure 6.**Predicted Vt, Vc and Vp of P. taeda at stand-level for the studied stands. (

**A**) 3–5 years; (

**B**) 5–7 years and (

**C**) 7–9 years. The thick line in the box indicates the median value of the predicted stem volume. Boxes extend from the 25th to the 75th percentile, whiskers extend 1.5 times the length of the interquartile range above and below the 75th and 25th percentiles. The white dote is the mean of the predicted stem volume, and the vertical read lines represents the standard deviation around the mean (Mean ± SD).

**Figure 7.**Predicted Vt (

**A1**–

**C1**), Vc (

**A2**–

**C2**) and Vp (

**A3**–

**C3**) of P. taeda at stand-level obtained from the RF models. Representative stand of early (i.e., 3–5 years) (

**A1**–

**3**), intermediate (i.e., 5–7 years) (

**B1**–

**3**) and advanced-stages of development (i.e., 7–9 years) (

**C1**–

**3**).

**Figure 8.**Coefficient of variation (CV) maps in percentage (%) of Vt (

**A1**–

**C1**), Vc (

**A2**–

**C2**) and Vp (

**A3**–

**C3**) of P. taeda at stand-level obtained from the 500 RF bootstrapped runs. Representative stand of early (i.e., 3–5 years) (

**A1**–

**3**), intermediate (i.e., 5–7 years) (

**B1**–

**3**) and advanced stages of development (i.e., 7–9 years) (

**C1**–

**3**).

DBH (cm) Range | Adj. R^{2} | SEE (%) | |
---|---|---|---|

dbh | Volume | ||

0.0–17.9 | 0.96 | 9.58 | 11.55 |

18.0–29.9 | 0.98 | 7.99 | 9.33 |

30.0–70.0 | 0.98 | 7.52 | 8.21 |

Ages (I) | Stem Total and Assortment Volumes (m^{3}·ha^{−1}) | N | ||
---|---|---|---|---|

Vt | Vc | Vp | ||

3 ≤ I < 5 | 56.25 ± 10.98 | 47.53 ± 12.15 | 45.67 ± 11.14 | 19 |

5 ≤ I < 7 | 134.20 ± 30.77 | 124.67 ± 30.3 | 114.20 ± 23.41 | 22 |

7 ≤ I < 9 | 169.50 ± 22.86 | 160.2 ± 22.20 | 129.50 ± 24.83 | 13 |

Mean ± Sd | 113.70 ± 52.53 | 103.86 ± 52.99 | 92.13 ± 42.11 | Total = 50 |

Parameter | Value |
---|---|

Scan angle (°) | +/−30° |

Footprint (m) | 0.33 m |

Flight speed (km/h) | 234.0 km/h |

Horizontal accuracy | 10 cm |

Elevation accuracy | 15 cm |

Operating altitude | 666.17 m |

Scan frequency | 300 kHz |

Pulse density | 4 pulse m^{−2} |

**Table 4.**Lidar-derived canopy height metrics considered as candidate variables for predictive V models [31].

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

HMIN | Height Minimum |

HMAX | Height Maximum |

HMEAN | Height Mean |

HMAD | Height median absolute deviation |

HSD | Height standard deviation |

HSKEW | Height skewness |

HKURT | Height kurtosis |

HCV | Height coefficient of variation |

HIQ | Height interquartile range |

HMODE | Height mode |

H01TH | Height 1th percentile |

H05TH | Height 5th percentile |

H10TH | Height 10th percentile |

H15TH | Height 15th percentile |

H20TH | Height 20th percentile |

H25TH | Height 25th percentile |

H30TH | Height 30th percentile |

H35TH | Height 35th percentile |

H40TH | Height 40th percentile |

H45TH | Height 45th percentile |

H50TH | Height 50th percentile |

H55TH | Height 55th percentile |

H60TH | Height 60th percentile |

H65TH | Height 65th 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 1.30 m) |

r | HMIN | HCV | HIQ | HSKEW | HKUR | H99TH | COV |
---|---|---|---|---|---|---|---|

HCV | −0.45 ** | ||||||

HIQ | 0.14 | −0.09 | |||||

HSKEW | −0.30 ** | 0.83 *** | −0.36 * | ||||

HKUR | 0.27 | −0.81 *** | 0.07 | −0.82 *** | |||

H99TH | 0.39 ** | −0.80 *** | 0.61 *** | −0.81 *** | 0.77 *** | ||

COV | 0.23 | −0.74 *** | 0.12 | −0.67 *** | 0.53 *** | 0.58 *** |

**Table 6.**Mean of the model improvement ratio (MIR) among the remained lidar-derived metrics not highly correlated. The bold represents the highest MIR values.

Atributes | LiDAR-Derived Metrics | ||||||
---|---|---|---|---|---|---|---|

HMIN | HCV | HIQ | HSKEW | HKUR | H99TH | COV | |

Vt | 0.16 | 0.40 | 0.18 | 0.75 | 0.31 | 0.99 | 0.12 |

Vc | 0.15 | 0.39 | 0.17 | 0.77 | 0.30 | 0.99 | 0.10 |

Vp | 0.16 | 0.65 | 0.20 | 0.74 | 0.38 | 0.98 | 0.11 |

**Table 7.**Model accuracies of random forest (RF) models per stem volume in terms of Adj. R

^{2}, Root Mean Square Error (RMSE) and bias calculated by the relationship between predicted and observed stem volumes.

Volume | LiDAR Derived Metrics | Adj. R^{2} | RMSE | Bias | ||
---|---|---|---|---|---|---|

m^{3}·ha^{−1} | % | m^{3}·ha^{−1} | % | |||

Vt | 0.97 | 8.91 | 7.83 | −0.19 | −0.17 | |

Vc | H99TH + HSKEW | 0.98 | 8.00 | 7.71 | −0.12 | −0.12 |

Vp | 0.96 | 7.96 | 8.63 | −0.22 | −0.24 |

**Table 8.**Model accuracies per stem volume type. The average and standard deviation of Adj. R

^{2}, RMSE and bias derived from the 500 bootstrap runs are displayed.

Volume | Adj. R^{2} | RMSE | Bias | ||
---|---|---|---|---|---|

m^{3}·ha^{−1} | % | m^{3}·ha^{−1} | % | ||

Vt | 0.94 ± 0.02 | 12.02 ± 2.78 | 9.80 ± 2.18 | −0.58 ± 2.85 | −0.45 ± 2.30 |

Vc | 0.95 ± 0.02 | 11.67 ± 2.76 | 10.31 ± 2.76 | −0.95 ± 2.80 | −0.82 ± 2.45 |

Vp | 0.91 ± 0.04 | 11.83 ± 2.56 | 12.10 ± 2.57 | −0.49 ± 2.73 | −0.54 ± 2.77 |

© 2017 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**

Silva, C.A.; Klauberg, C.; Hudak, A.T.; Vierling, L.A.; Jaafar, W.S.W.M.; Mohan, M.; Garcia, M.; Ferraz, A.; Cardil, A.; Saatchi, S. Predicting Stem Total and Assortment Volumes in an Industrial *Pinus taeda* L. Forest Plantation Using Airborne Laser Scanning Data and Random Forest. *Forests* **2017**, *8*, 254.
https://doi.org/10.3390/f8070254

**AMA Style**

Silva CA, Klauberg C, Hudak AT, Vierling LA, Jaafar WSWM, Mohan M, Garcia M, Ferraz A, Cardil A, Saatchi S. Predicting Stem Total and Assortment Volumes in an Industrial *Pinus taeda* L. Forest Plantation Using Airborne Laser Scanning Data and Random Forest. *Forests*. 2017; 8(7):254.
https://doi.org/10.3390/f8070254

**Chicago/Turabian Style**

Silva, Carlos Alberto, Carine Klauberg, Andrew Thomas Hudak, Lee Alexander Vierling, Wan Shafrina Wan Mohd Jaafar, Midhun Mohan, Mariano Garcia, António Ferraz, Adrián Cardil, and Sassan Saatchi. 2017. "Predicting Stem Total and Assortment Volumes in an Industrial *Pinus taeda* L. Forest Plantation Using Airborne Laser Scanning Data and Random Forest" *Forests* 8, no. 7: 254.
https://doi.org/10.3390/f8070254