1. Introduction
Tree roots are estimated to comprise approximately 19%–28% of the total living tree biomass of boreal forests [
1,
2] and the ability to adequately estimate total root biomass is central to understanding the carbon dynamics and storage capacity of these forest ecosystems [
3,
4,
5,
6]. As illustrated by the reviews in Tobin
et al. [
7], Danjon and Reubens [
8], and Danjon
et al. [
9], knowledge of root system architecture is also of large importance in order to understand key ecosystem processes including tree stability, slope stabilization, erosion control, water and nutrient uptake through fine roots, and root competition. All of these processes affect a tree species’ competitive performance and aid in the understanding of observed shifts in intra- and interspecific competition and the resulting forest dynamics across resource gradients [
10]. Relative to the importance of adequately characterizing root systems, extensive studies of mature tree root systems are rare due to their high cost and labor-intensive nature [
8]. To the best of the authors’ knowledge, the only study that has made a detailed characterization of large root structures in the Fennoscandic boreal forests is Kalliokoski
et al. [
11]. The study sampled three of the most prevalent species in Finland—Norway spruce, Scots pine, and silver birch. In that study, 60 whole root systems were excavated from the tree bole to the first bifurcation of the root system and one to three sample roots were completely excavated to a diameter of 2 mm for each tree. The root diameters and lengths, azimuths, inclinations, and depths were manually measured, then the 3D coarse-root architecture of the root systems were modeled with software [
11].
Over time and in pace with technological advances, improved approaches for describing root and plant structure have been developed [
8,
12,
13,
14], often with the aim of making full 3D representations of root systems. A recent review from Danjon and Reubens [
8] outlines the progressive development from manual, to semi-automatic, to increasingly automated 3D descriptions. Manual methods have included: cross-sectional area descriptions of coarse root systems [
15]; the physical measurement of the
X,
Y, and
Z coordinates of root surfaces [
16]; dimensional measurements of root diameter, length, angle, and depth [
17]; and non-bulk methods that incorporate manual measurements into graphic depictions of simulated root systems [
18]. Semi-automatic methods have used digitized manual measurements in order to reconstruct whole 3D root systems with software. Digitizing methods have included the use of a digital compass, inclinometer, and caliper [
19] and a digitizing stylus device which records the
X,
Y, and
Z coordinates of the root surface [
20]. Digitized measurements can then be used in software to create 3D root system reconstructions [
20,
21,
22]; in fractal branching modeling, which simulates the growth of root systems utilizing statistical relationships among root parts [
12]; or for root-density based modeling [
23]. Automatic methods have focused on
in situ methods such as X-ray computed tomography (CT) scanning for small root systems [
24] and ground-penetrating radar (GPR) for large root systems [
25].
Recently, terrestrial laser scanning (TLS) systems have emerged as promising tools for a range of measurement tasks in forest ecosystems. The use of TLS has been proposed for measuring standard forest inventory variables such as stem volume and stem quality [
26,
27], forest canopy structure [
28], and aboveground tree biomass [
29]. Automated approaches for deriving 3D quantitative structure tree models from point cloud data have also emerged as promising approaches for the characterization of the aboveground components of individual trees [
30]. Other 3D reconstruction methods for deriving the aboveground biomass from TLS data include those developed by Bucksch and Fleck [
31], and Vonderach
et al. [
32]. The use of TLS to describe 3D root systems is in its infancy, but has been identified as the best available technique to describe the architecture of large root systems, although it requires further development [
8]. Early work has successfully represented the 3D structure of excavated individual root systems [
33,
34,
35], calculated whole stump volume using slices [
33,
35] or by modeling the root surface [
36,
37], and investigated potential sources of error associated with various scanned materials, scanners, and point cloud post-processing techniques [
35,
38,
39]. The volume of a root segment has been estimated from a triangulated root surface generated from a point cloud accurate to within ±50 μm as well as the feasibility of incorporating root growth ring data into the root reconstruction has also been investigated [
36]. Building on this methodology, the volume of a whole complex root system and successive year growth surfaces and root volumes have been modeled [
37]. Most recently, six Norway spruce stumps were mechanically pulled from the soil, scanned in the field, and the root architecture was recreated with a combination of a polyhedral grid for the stump and fit cylinders for the root portions of the root system [
40], following the modeling methodology developed by Raumonen
et al. [
30]. Whole root system and root size distribution volumes were estimated for each stump; however, soil was not removed from the root systems, resulting in some problems in the 3D reconstruction process. Further, no manual measurements were carried out to evaluate how well the root system model characterization actually represented the root systems.
The objectives of this study are twofold. First, we evaluate how well coarse root system architecture and volume can be estimated by applying 3D quantitative structure modeling to terrestrial laser point cloud data. Secondly, we utilize these 3D quantitative structure models (QSM) to derive key architectural and volumetric characteristics of mature Norway spruce tree root systems.
3. Results
Visual inspection of the 3D QSM stump models and visualizations of the TLS point cloud data illustrate that the produced models appear to be realistic and complete representations of the coarse root systems (
Figure 2).
Our results indicate that root system volume can be estimated with relatively high precision using TLS data and the 3D QSMs (
Figure 7a). The root system volumes were estimated with a RMSE of 14.4 L (14.9% of the mean measured volume) and a mean prediction error (measured minus predicted values) of 4.3 L (4.4% of the mean measured volume) indicating an underestimation of the volumes (
Figure 7a). Overestimates ranged from 0.3 to 34.3% and underestimates from 3.9% to 17.6% of the measured volume. The two largest overestimates were stumps 12 (30.9%) and 8 (34.3%), which where the smallest volume stumps in the study (
Figure 7a). The two largest underestimates were stumps 1 (11.1%) and 3 (17.6%), which were the two largest volume stumps in the study (
Figure 7a). Most stump diameters estimated from the stump model showed high correlation to the manual measurement (
Figure 7b). Stump 9 produced the largest underestimate likely due to a large missing L-shaped section from the stump surface, which was more accurately measured during modeling (
Figure 7b). For the diameter estimates, full correlation was not expected as the TLS-based measurements were derived from the average of 27 diameter measurements from the opposite vertices taken from the stump model while the manual measurements were based on two perpendicular diameter measurements.
The results illustrate the ability of TLS data, combined with QSM, to estimate important root system architectural and volumetric variables. The root diameter distributions derived from the 3D models illustrate that an average of 55% of the total volume of the root system is comprised of the stump portion (data not shown). On average 16%, 34%, and 43% of the total volume is comprised of roots with a diameter of 5, 10, and 15 cm or less, respectively (data not shown). The frequency of breakpoints in a given diameter class varied between stumps (
Figure 8). All stumps had breakpoints less than 8 cm with increasingly more observations in the lower diameter classes (
Figure 8). Decreasingly fewer stumps were represented in each of the larger diameter classes by single observations (
Figure 8). The largest stump in the study (stump 3;
Figure 2a–c) also had the most breakpoints and was represented in all diameter classes up to 16 cm and as large as 21.5 cm (
Figure 8). For most of the sampled root systems, the volume of root system left in the soil was likely small in comparison to the extracted root system (
Figure 8).
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 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.
Estimated root system volume and linear root length were found to be correlated to the estimated stump diameter (
Figure 9) and simple linear regressions illustrate that stump diameter as the single predictor variable explained 86.8% of the variation in estimated root system volume and 72.1% of the variation in estimated linear root length of the sampled root systems (
Figure 9).
In a sensitivity analysis of the 165 models fitted on the stump portion of root system 2 (
Figure 2d), the standard deviation of the volume was 1.85 L or 7% of the average (25.9 L) with about 73% and 90% of the models between 24–28 L and 23–29 L, respectively (
Figure 10a). The standard deviation of the stump diameter was 1.3 mm or 0.6% of the average (20.1 cm) (
Figure 10b).
The average root portion volume increased from 22.5 to 27.5 L as
d increased with standard deviations of about 7%–10% of the average values (
Figure 11a), whereas the average linear root length decreased from 34 to 22 m with standard deviations of about 2.5%–6% (
Figure 11b). The average number of roots also decreased from 243 to 98 with increasing values of
d (data not shown). The average root portion volume was nearly the same for
l values between 2 and 6 with standard deviations of about 6%–9% of the averages (
Figure 11c). The average linear root length decreased from 30.5 to 28 m as
l increased with standard deviations of about 3%–4% of the averages (
Figure 11d).
The overall relationships of increasing root volume with increasing values of the
d and
l parameters (
Figure 11a,c, respectively) and decreasing linear root length with increasing values of the
d and
l parameters (
Figure 11b,d, respectively) held as root diameter increased (
Figure 12a–d).
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 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 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 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 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 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.
Stump volume, diameter, and height increased with larger cover set patch size
d for stump 3 (
Figure 13a–c). Stump volume and height increased (
Figure 13a,c) with the use of smaller cells, whereas modeled diameter decreased (
Figure 13b).
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.
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
Our results indicate that our scanning and stump modeling procedure is capable of rapidly and adequately representing root system architecture and root fraction volumes of multiple large root systems with minimal manual point cloud and modeling post-processing required. Our procedure was able to rapidly describe root variables relevant to the characterization of root volume, such as root diameter, linear root length, break point diameters, number of roots, root fraction counts, and cumulative percentages. Estimated root system volume and estimated linear root length could also be adequately predicted with estimated stump diameter. Taken together, the modeled root system characterizations and volumetric variables provide a highly detailed description of large root systems that can be readily utilized in various applications.
The sensitivity analysis revealed that the standard deviations for estimated stump volume and diameter were in good agreement with the average values (
Figure 10). Furthermore, the overall performance of the QSM was shown to be quite stable and predictable against small changes in the
d and
l parameter values (
Figure 10,
Figure 11 and
Figure 12), as well as changes to the patch sizes (
Figure 13). As expected, as
d increased root volume increased (
Figure 11a and
Figure 12a), while linear root length (
Figure 11b and
Figure 12b) and the average number of roots decreased. This is because smaller cover sets are able to separate smaller roots better and bigger roots more accurately. Also as expected, as
l increased root volume increased (
Figure 11c and
Figure 12c), linear root lengths shortened (
Figure 11d and
Figure 12d). The linear root lengths shortened because of less accurate curvature approximations. Increasing the patch size
d caused the point clouds used for cylindrical triangulation of the stump portion to become larger, increasing modeled stump portion volume and height (
Figure 13a,c). Diameter increased because the boundary of the cutting surface became less accurate (
Figure 13b). Decreasing the cell size (defining smaller triangles) increased the stump volume and height estimate and decreased the diameter estimate because small curved details are best modeled with smaller triangles. The effect of varying patch and cell size was predictable and relatively small.
The QSM root modeling procedure is capable of describing more topological and volumetric characteristics of whole large root systems than the few examples presented here. Further post-processing of the root models could obtain other root topological and size information previously identified as important by various authors for a wide range of applications [
42], such as branching angle, segment length, number of forks, root depth, horizontal spread, root external surface area, and root taper.
The modeling procedures presented here further advance the 3D description of large root systems, best characterizing larger-diameter root architecture. Many of the root measurements that can be made using developed manual analog and digitized measurements can be produced more quickly from TLS point cloud data provided the estimated surfaces are within view of the scanner. Manually digitizing root systems is still superior to TLS in that it is possible to accurately describe all root surfaces regardless of position, but can be much more time consuming. As an example, Danjon and co-workers accurately and completely manually digitized structurally complex large pine trees (mean DBH of 38 cm) to a minimum diameter of 5 mm, taking as many as 10 days per root system [
8,
21]. In our procedure, each root system was scanned three times within 1.5 h (average 30 min automated scanning and manual scanner set-up each). The point cloud co-registration and post-processing work together with the reconstruction of the QSMs took about 10–20 min per root system. The total scanning and modeling time was about 2 h per root system.
Other scanning methods have been successfully applied to various systems, but each has limitations and presents further challenges. Data acquisition times using CT scanning are very fast and capable of describing root architecture down to <0.5 mm
in situ, but so far have only been used to describe root systems of small plants. GPR can describe large coarse root systems
in situ under suitable conditions, but reliable accurate reconstructions of root systems in commonly encountered unsuitable conditions are still not possible [
25]. Highly accurate (± 50 μm) laser scanning arms have been used to describe a whole root system (pine tree with an 8-cm DBH) down to a diameter of 0.5 mm, but scanning must be done by hand and post-processing times can be demanding with the methodology used by Wagner
et al. [
37].
Our models underestimated observed root system volume by about 4.4% across all root systems with the overestimates ranging from 0.3% to 34.3% and underestimates ranging from 3.9% to 17.6%. The magnitude of the prediction error is very similar to tree stem QSMs consisting of cylinders (1.36% ± 7.33%) or triangulated meshes (−4.62% ± 2.32%) found by Åkerblom
et al. [
41]. The exact reasons for the modeled volume underestimate are unclear, but several contributing factors are possible. Occlusion occurs when data for the whole or parts of roots are not captured in the point cloud due to shadowing from the perspective of the scanner. Other studies have shown that the frequency of occlusion can increase with increasing structural root complexity [
39] and decreasing number of different scan angles used to generate the point cloud [
35]. This study only used three scanning positions per root system and it is likely that any occlusion problems would have been reduced by introducing more scanning positions. However, for most root systems in this study, both structurally simple and complex root systems produced good volume estimates (
Figure 7a).
Another contributing factor to the modeled volume underestimate may be that for some root systems, broken root pieces that were separated from but scanned with the root system were not included in the modeled volume estimates. Based on the relatively small size of these pieces for most of the root systems in the study, we do not expect that their inclusion would have drastically reduced the modeled underestimates; however, this could have contributed to the underestimate observed in stumps 1 and 3 (
Figure 2a–c;
Figure 7a). The reason for the overestimates observed in the small-volume stumps 8 and 12 (
Figure 7a) is not clear.
Finally, the question of how well the cylinder model actually fits the roots can be raised. The surface of the root is a reflected sampled surface in TLS point cloud data and is therefore subject to errors related to accuracy of the scanner, reflective properties of the root surface, and the angle of incidence of the laser beam. The modeled cylinder fits of the roots are least squares fits of the sample points closest to the sampled surface and the angle of a longitudinally central vector the length of the defined root segment. In highly crooked root portions, this procedure can yield a proportion of cylinders that are fit incorrectly, that partially overlap, or where “gaps” in portions of roots are not accounted for, leading to an overall underestimate. In other less structurally complex root systems, this same fitting procedure may lead to an overall overestimate.