# Tree Root System Characterization and Volume Estimation by Terrestrial Laser Scanning and Quantitative Structure Modeling

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Root System Acquisition and Preparation

#### 2.2. Root System Volume Measurement

^{−1}). Total root system volume was calculated according to Equation (1):

_{air}= total mass of the root system in the air; MWm

_{air}= metal weight mass in the air; Tm

_{submerged}= total mass of the root system submerged in the water; MWm

_{submerged}= metal weight mass submerged in the water; and D

_{fluid}= density of the water. The few dislocated roots were attached to the main root system during the root system volume measurement and were consequently included in the estimated root system mass.

**Figure 1.**Images of the volume estimation method used for the root systems: (

**a**) Weighing the root system in the air; (

**b**) Weighing the root system in the water.

#### 2.3. TLS

**Figure 2.**Root system images: (

**a**) Root system 3 suspended at scanning; (

**b**) A 2D reprojection of the TLS point cloud data of root system 3, showing the effects of sensor obscuration (black shadow); (

**c**) Top view of the QSM of root system 3; (

**d**) Oblique bottom view of the QSM of root system 2.

#### 2.4. 3D Quantitative Structure Model (QSM)

#### 2.4.1. Outline of the Method

#### 2.4.2. Filtering

#### 2.4.3. Separation of the Stump and Roots

**Figure 3.**Determination of the cutting surface: (

**a**) Segmentation of the stump portion into planar regions (only regions with at least five cover sets are shown); (

**b**) Blue points show the initial cutting surface as defined by the selected large region; (

**c**) The final cutting surface (blue) and the normal line (red).

**Figure 4.**Determination of the stump portion of the point cloud: (

**a**) Different colors denote the patches closest to the normal line in their cell; (

**b**) The final stump portion is shown in blue.

#### 2.4.4. Modeling the Stump Portion with Cylindrical Triangulation

**Figure 5.**Construction of the closed surface stump model: (

**a**) Stump portion partitioned into cells formed by layers and sectors; (

**b**) Vertices of the triangles from the partition (blue) and interpolation (red); (

**c**) Final closed surface of the cylindrical triangulation model.

#### 2.4.5. Segmentation of the Roots

**Figure 6.**Determination of bases of the roots originating from the stump: (

**a**) The layer B (red) between the stump (blue) and the rest of the roots (green) forms the bases of the roots; (

**b**) Different colors show the final determined root bases. Notice that some small parts of layer B are not included in the root bases.

#### 2.4.6. Modeling the Root Portion with Cylinders

## 3. Results

**Figure 7.**(

**a**) Measured and estimated root system volume and (

**b**) stump diameter. Vertical bars are the standard deviations for the predicted values for 15 model fits for each root system.

**Figure 8.**Frequency of root breakpoint diameters. Each colored bar represents the mean frequency values in each diameter class for 15 model fits of an individual root system. The same dataset is presented at two different scales to improve legibility within each diameter class.

**Figure 9.**Estimated root system volume and linear root length vs. estimated stump diameter. The lines illustrate fitted regression lines: (

**a**) Root system volume = −69.5563 + 5.7511 × estimated diameter; (

**b**) Linear root length = −35.6380 + 4.6240 × estimated diameter.

**Figure 10.**(

**a**) Distributions of the estimated stump portion volumes (L) and (

**b**) diameters (cm) for 165 model fits of stump 2.

**Figure 11.**Sensitivity of QSMs for the d (the minimum distance between the centers of the balls and the maximum distance between any point and its nearest center) and l (relative cylinder length) parameters for the root portion. (

**a**,

**c**) Total root portion volume and (

**b**,

**d**) linear root length for different (

**a**,

**b**) d values and (

**c**,

**d**) l values. Blue lines are the averages, vertical blue bars are the standard deviations, and red lines are the minimum and maximum values for 15 model fits of stump 2.

**Figure 12.**Average sensitivity of QSMs for different values of the d (the minimum distance between the centers of the balls and the maximum distance between any point and its nearest center) and l (relative cylinder length) parameters and root diameters for 15 model fits of stump 2. (

**a**,

**c**) Root volume and (

**b**,

**d**) linear root length for different (

**a**,

**b**) d values and (

**c**,

**d**) l values.

**Figure 13.**Sensitivity of stump portion (

**a**) volume; (

**b**) diameter; and (

**c**) height to different cover set patch sizes d and cell sizes for 30 model fits of stump 3. Cell size determines the size of the triangles in the cylindrical triangulation model for the stump portion.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Smith, A.; Astrup, R.; Raumonen, P.; Liski, J.; Krooks, A.; Kaasalainen, S.; Åkerblom, M.; Kaasalainen, M.
Tree Root System Characterization and Volume Estimation by Terrestrial Laser Scanning and Quantitative Structure Modeling. *Forests* **2014**, *5*, 3274-3294.
https://doi.org/10.3390/f5123274

**AMA Style**

Smith A, Astrup R, Raumonen P, Liski J, Krooks A, Kaasalainen S, Åkerblom M, Kaasalainen M.
Tree Root System Characterization and Volume Estimation by Terrestrial Laser Scanning and Quantitative Structure Modeling. *Forests*. 2014; 5(12):3274-3294.
https://doi.org/10.3390/f5123274

**Chicago/Turabian Style**

Smith, Aaron, Rasmus Astrup, Pasi Raumonen, Jari Liski, Anssi Krooks, Sanna Kaasalainen, Markku Åkerblom, and Mikko Kaasalainen.
2014. "Tree Root System Characterization and Volume Estimation by Terrestrial Laser Scanning and Quantitative Structure Modeling" *Forests* 5, no. 12: 3274-3294.
https://doi.org/10.3390/f5123274