Developing nondestructive species‐specific tree allometry with terrestrial laser scanning

Allometric equations predict organism attributes from simple measurements and underlie many global‐scale estimates, from plant productivity to ecosystem carbon stocks. In forests, destructive harvesting of trees in common groups (e.g. plant functional type) or at the species level is necessary to develop allometry but, since sampling is extremely difficult, predictions from these equations have high uncertainty due to low sample size, spatial bias and unrepresentative sampling of tree size. Terrestrial laser scanning (TLS) is a promising remote sensing technology that enables efficient and nondestructive estimates of tree‐level structure for developing allometric equations. Here, we nondestructively estimated component biomass of three coniferous tree species (Pinus ponderosa, Pinus contorta and Pseudotsuga menziesii) in Colorado, USA using TLS. We evaluated the suitability for this nondestructive data to be supplanted for destructive data in the development of species‐specific allometric equations and compared the prediction accuracy against a commonly used national‐scale allometry. We found TLS biomass estimates were consistently more precise across species (RMSE = ~19%) than nation‐scale allometry (RMSE = ~39%). Nondestructive biomass estimates from TLS are a suitable addition to or replacement for traditional sampling methods, with indistinguishable biomass predictions across most of the tested diameter range. We further show how TLS can be used to develop allometric equations compatible with airborne LiDAR and other remote sensing variables (e.g. height and crown area), developing generalized biomass predictions from crown area and tree height (R2 = 0.87). The ability for TLS to support the development of nondestructive allometry at a global scale will enable a more nuanced understanding of the drivers of individual tree architecture, while supporting the next generation of biomass remote sensing.


| INTRODUC TI ON
Global forest carbon stock estimates (Friedlingstein et al., 2020) are directly dependent on indirect tree-level predictions of biomass carbon (Chave et al., 2014;Saatchi et al., 2011). Field measurements of tree diameter (and sometimes height) are used to predict tree-level standing biomass with predictive models created from a small number of destructively harvested trees (Chojnacky et al., 2014;Picard et al., 2012). The high cost of creating predictive biomass models, or allometric equations, may limit sample size and diameter range, both of which result in unreliable predictions (Chave et al., 2004;Duncanson, Rourke, et al., 2015;Vorster et al., 2020). The local-, national-and global-scale consequences of applying poorly constrained allometry to trees outside of the diameter range intended for forest carbon stock estimates is unclear but remains common practice due to a lack of alternative methods of predicting biomass in large trees. A more reliable method of developing allometric equations (Weiskittel et al., 2015), unrestricted by tree size and number of samples, is needed to update global-scale networks of plot biomass for improved estimates of global forest carbon storage.
Terrestrial laser scanners (TLS) are stationary ground-based light detection and ranging (LiDAR) instruments that collect millions of millimetre precision range estimates from multiple positions. Over the past decade, TLS has become an established method of nondestructively estimating tree-level and forest structure (Calders et al., 2020;Demol et al., 2022). Much of past work has focused on the development of algorithms to measure tree-level attributes such as diameter at breast height (DBH), height and tree-level biomass (Calders et al., 2015;Hopkinson et al., 2004;Lau, Calders, et al., 2019;Momo Takoudjou et al., 2017;Stovall et al., 2017). The most well-studied means of estimating tree volume (and biomass) using TLS relies on 3D cylinder fitting (e.g. quantitative structure models; QSMs; Raumonen et al., 2013). Many studies have highlighted the utility of cylinder fitting, but needleleaf trees consistently have high volume errors since QSM approaches are extremely sensitive to noise and dense foliage (Demol et al., 2021;Hackenberg et al., 2015). One method of estimating tree-level biomass, outer hull modelling (OHM), was developed to overcome errors in cylinder fitting for needleleaf trees and precisely estimated biomass of lodgepole pine trees for the whole tree, trunk, branch and needle components (Stovall et al., 2017). It remains unclear whether OHM can be applied to other needleleaf species and how errors in biomass estimates may vary by species.
TLS has only recently been proposed and assessed as a means of developing nondestructive biomass allometry (Demol et al., 2022;Momo Takoudjou et al., 2017;)-a critical step in improving airborne and spaceborne calibration and validation (Disney et al., 2019; for the highest precision estimates of global carbon stocks (CEOS, 2021). Here, we aim to determine if terrestrial laser scanning can improve or replace destructive calibration data for speciesspecific allometric biomass equations. We address this question with 41 destructively harvested trees from three species scanned with TLS prior to harvesting. Using a tested (Stovall et al., 2017) and recently improved TLS tree modelling algorithm (OHM), we nondestructively estimated biomass of the trunk and crown components, validating our estimates with field-measured biomass. We developed biomass allometry from both destructively harvested and TLS estimates, comparing the estimates and confidence interval of the scaling coefficients. In addition, we evaluated TLS for developing remote sensing-compatible allometric biomass equations, as described by Jucker et al. (2017). Finally, we evaluated the predictions from TLS allometry in comparison to the commonly used, national-scale Chojnacky et al. (2014) (Stovall et al., 2017;Vorster et al., 2020). We measured dry total above-ground biomass as well as the bole, bark, branch and foliage components. The bole and bark biomass components spanned the main stem from the 30.5 cm (1 foot) stump (excluded from total tree biomass) to where the bole becomes 10.2 cm (4 inch) in diameter. Branches included wood and bark of the main stem above this point and all branches. Foliage was all needles on the tree. In this study, we combined bole and bark components into a single trunk component, and branch and foliage biomass we combined into crown biomass.

| Field TLS methods
Terrestrial laser scans were collected using the same procedure outlined in Stovall et al. (2017) with a phase-shift FARO Focus3D 120 unit (ranging error ~2 mm) at a resolution of 6 mm at 10 m distance (~0.6 mrad). Three to four scans were collected per tree from multiple angles to limit occlusion, requiring approximately 3 min per scan or ~15-20 min per tree. Stovall et al. (2017) estimated that the required field and processing time required for the nondestructive TLS approach was on average ~16 times less per tree than destructive sampling. The latter approach is especially time consuming for large trees. Scan distance from the target tree was approximately 10 m, varying depending on tree size and stand openings. Styrofoam spheres were placed near the target tree as reference objects for scan registration. Near-windless conditions were required for collecting each scan position to ensure errors in the point cloud were minimized.

| TLS preprocessing
Preprocessing of the TLS data was identical to that described in Stovall et al. (2017). In short, we processed all TLS data in Faro SCENE (2015), where registration of multiple scan positions was completed, and the trees of interest were manually segmented from the point cloud ( Figure 1). Stray points were filtered in SCENE using the parameters in Stovall et al. (2017; allocation threshold = 10%, distance threshold = 5 mm, grid size = 3 × 3). Following Stovall et al. (2017), rather than using automated methods, we manually isolated tree point clouds (clipping trees approximately 30.5 cm above-ground) and separated trunk and crown points in Cloud Compare (version 2.11.1) using the segment tool. During this process we visually inspected the point clouds and focused on isolating obvious trunk points. The remaining points were attributed to the crown of the tree. Each tree took 5-10 min to manually preprocess. Finally, each component was exported in ASCII format to be used in the OHM algorithm. (Stovall et al., 2017) The OHM method, developed and applied using the R programming language (R Core Team, 2022), was used to nondestructively estimate tree-level volume from TLS data (Stovall et al., 2017). The approach is completed in two stages: (i) trunk modelling and (ii) crown modelling.

| Tree modelling approach
The trunk modelling method originally used convex hull peeling (see Stovall et al. (2017) for details) to 'peel' the outer noisy  has ~10 independent measurements from which a single diameter value is based. Second, the multiple subsection diameters enable confidence intervals for the diameter estimates of individual trunk segments. Next, a linear outlier exclusion method is implemented as described in Stovall et al. (2017), with a plus or minus 20% buffer. Finally, with the remaining diameter values, a median estimate is computed per trunk segment, further reducing the impact of outliers.
The voxel-based branch modelling algorithm is also updated and simplified from the previous version (Stovall et al., 2017). The branch modelling approach is directly dependent on the diameter measurements estimated using OHM. The TLS crown point cloud is voxelized and segmented into 10 cm sections corresponding to the trunk segments. For a given section of crown points the voxel size distribution is adjusted as a log function (B model ) based on the OHM estimated trunk segment radius (r): where D is the distance of the voxel from the trunk and D max is the maximum value of D. Voxels with values of B model less than 1 mm are assumed to be 1 mm in size. For an individual crown subsection, the B model is multiplied by the normalized voxel distribution (total voxels per distance interval from crown normalized by the total number of voxels per crown segment). The approach produces a volumetric distribution of crown points based on adjusted voxel size, which is summed for total crown biomass estimates. The approach differs from the original implementation of the voxel crown modelling in that foliage and branches are not separated from each other.
Instead, the modelling is simplified as a single 'crown' volume and biomass. For Douglas fir trees, we found a substantial proportion of TLS returns were attributed to needles along the woody branch structure, dramatically distorting voxel volumes due to an exceptionally high density of returns throughout the crown. The structure of Douglas fir branches is such that the needles account for nearly all branch volume on the exterior portion of the crown. In addition, the beam divergence of laser scanners sets a lower limit of measurable detail at a specific distance (5 mm objects at 10 m distance for the TLS in this study). As a result, the TLS will return near-solid surfaces when measuring these dense needleleaf canopies. To account for these combined measurement challenges, we referenced our available destructive measurements, finding the average ratio between branch and foliage biomass (~0.4 ± 0.1). We applied a simple correction factor of 0.4 times the crown voxel volume, assuming the proportion of returns attributed to needles was 2.5 times more than the returns from branches. We expect a similar approach will be necessary in other high crown density species, requiring further coincident harvest and TLS acquisition. As in Stovall et al. (2017),

| Developing and comparing Nondestructive
Allometry to traditional methods

| Developing Allometric equations
Species-specific allometric equations were developed from both destructive biomass measurements and TLS modelling. We used the nls function in R programming language to fit nonlinear models relating DBH (D) in centimetres to total above-ground biomass (AGB) in kilograms using the form: where a is the normalizing coefficient and b is the scaling exponent.
We also tested log-log least squares regression (see Supporting Information), but, apart from the error structure, the predictions were not dramatically different from the nls model.
In addition, we tested the potential for TLS to aid in the development of remote sensing-compatible allometric relationships as discussed by Jucker et al. (2017). We specifically focused on variables easily derived using high-resolution optical or LiDAR remote sensing methods: (i) crown area and (ii) tree height. We tested the following equation forms as we expected them to be linear in nature, improving prediction stability: where 1 , 0 and 2 are coefficients, A crown is tree crown projected area, and H is tree height. Given the similar wood density across trees in the study, we expected crown structure would explain most of the variation in total biomass. To confirm this expectation, we tested for a species effect in our allometric models but found no significant difference in slope or intercept. We reported the equation coefficients and fit statistics for the final models for Equations (3)-(5).

| Validation and allometric error statistics
The TLS-based tree-level biomass estimates and allometric equation predictions were evaluated using established statistical measures consistent with other similar studies. For all assessments in this study, we derived root mean square error (RMSE; kg and per cent of mean), bias (kg and per cent of mean) and mean absolute error (MAE; kg and per cent of mean). The absolute and relative forms of these statistics allow us to compare within a single species and across species, highlighting differences in error for each category evaluated. For the tree-level validation, we derived these error statistics for comparisons of whole tree biomass, trunk (bole We highlighted size-dependent differences in errors from our validation of tree-level TLS biomass estimates using one-to-one and residual plots. We highlight the differences in allometry by compar-

| Whole Tree and component biomass validation
Overall, TLS closely estimated destructive estimates of whole tree, trunk and crown biomass (Table 1; Figure 2). Across the study species, whole tree biomass estimates had relatively low RMSE (13% to 25%) and bias (−4% to 11%). Trunk biomass RMSE ranged from 9% to 32% while bias was −1% to 22%. Crown biomass relative RMSE was higher (17% to 86%) but had low bias (−8% to 4%). Errors in component biomass estimates were dependent on species, with trunk errors lowest in lodgepole pine and highest in Douglas fir, while crown biomass errors were highest in lodgepole pine and lowest in Douglas fir. Ponderosa pine performed well in all whole tree and component estimates (RMSE: 13% to 17%).

| Comparing destructive, TLS and Chojnacky et al. (2014) Allometry
The TLS-based allometry closely approximated the destructive allometry, with species-specific prediction errors substantially lower than the Chojnacky et al. allometry (Figure 3a; Table 2). The TLS allometry had 4% to 42% lower RMSE and 12% to 30% lower bias than the Chojnacky et al. predictions. TLS allometry predictions were within 3% of the RMSE of the tree-level estimates, except for ponderosa pine, which had ~8% higher RMSE than the tree-level modelling ( Table 2)   considered should be reliable, assuming the crown structure is open enough to reduce trunk occlusion in the TLS scans. We expect further improvements to trunk biomass estimates when applying the method to higher-quality multiple-return TLS data that reduces occlusion in the interior crown.
Crown biomass errors were dependent on species-specific crown structure. Ponderosa pine crowns had the lowest noise in the TLS data of any species due to the openness of the crown and relatively heterogeneous clumped needle structure. As a result, these trees had remarkably low errors across all components. In contrast,  lodgepole pine crowns had a high density of needles on the external portion of the crown structure, occluding the internal branching structure. Although crown biomass RMSE was high in this species, estimates were nearly unbiased, suggesting whole tree biomass estimates should remain unbiased if the method were applied to nondestructively measured trees. Douglas fir crowns had a crown structure with a high density of needles covering all branches, resulting in nearly 2.5 times higher than expected crown volume using the voxel-based algorithm and requiring a correction factor derived from the average ratio of needle to branch biomass (~0.4). The deviation was consistent throughout the range of observed crown biomass, suggesting a simple species-specific correction factor can appropriately adjust these estimates and be applied to other trees within this species. We expect laser scanners with larger beam divergence (e.g. handheld and mobile LiDAR) will suffer greatest from this issue and care should be taken if applying the OHM algorithm.
Future studies should not only investigate the consistency of this correction factor for Douglas fir trees but also evaluate the need for correction factors in other species displaying similar high-density needle structure along branches of the tree. Although we did not test quantitative structure models in this study, we expect poor performance in line with Stovall et al. (2017). TLS campaigns targeting single trees (multiple scans around a single individual) should still be paired with destructive sampling as species-specific TLS algorithms continue to be developed and refined to better estimate crown biomass.
The TLS allometric coefficients closely approximated those developed from destructive data, suggesting this method can soon be applied operationally for developing high sample-size biomass allometry including large trees. In contrast, the Chojnacky et al. equations both under (lodgepole and ponderosa pine) and overestimated (Douglas fir) tree-level biomass, with bias increasing with tree diameter and ranging from −16% to 42% (Figure 3; Table 2). The trend of bias in allometric estimates is consistent with past work that found a ~25% underestimate in broadleaf species in comparison to TLS . For context, the tree species evaluated here are well characterized since they have commercial forestry value.
Prediction errors in species that are less well studied are likely to be substantially higher. For example, a recent study found allometric equations for redwood Sequoia sempervirens had ~30% to 40% underestimate in biomass in comparison to TLS .
We expect these trends of biased allometry to continue to emerge with additional TLS-based studies. The detailed 3D tree-level measurements collected from TLS helps support the development of a new class of remote sensingcompatible allometry. Here, we derived simple attributes directly from the TLS data (e.g. crown diameter and tree height), developing biomass estimates across species with 150 kg or 40% RMSE.
Expanding this approach to larger trees will help characterize the uncertainty of these equations, but we expect-like other TLS measures-prediction errors will not be strongly dependent on tree size (Calders et al., 2015;. Tree-level remote sensing-centric allometry (Jucker et al., 2017), such as this, can be directly applied to optical data using deep learning methods (Weinstein et al., 2021) or to airborne LiDAR data using crown TA B L E 2 Statistics comparing direct tree-level TLS biomass, TLS nondestructive allometric predictions, and Chojnacky et al. allometric predictions to tree-level destructive biomass estimates. Error estimates from independent fivefold cross-validation shown in parentheses for TLS allometry Although optical and airborne LiDAR are unable to fully capture understorey trees due to occlusion, the easily measured canopy trees dominate the biomass of many conifer forests (Brown et al., 1997;Stephenson et al., 2014) which is explained primarily by the dominance of stand-replacing disturbance (Lutz et al., 2012). TLS should continue to be integrated into destructive sampling campaigns and leveraged for next generation allometric equations that will allow for precise tree-level biomass predictions, directly relevant to the scale of forest management decisions (i.e. the individual tree).
A key aspect of tree growth is adaptation to environmental conditions, but most species-specific tree-level biomass allometry is unable to incorporate such factors due to a low number of tree observations. Here, adding an additional 19 scanned ponderosa pine trees produced similar biomass predictions, but the increased sample size provided more representative estimates of species-specific variation ( Figure S3). Tree-level biomass samples commonly represent a small area and a narrow range of a species' environmental conditions. Past work has investigated environmental drivers of tree allometry

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interest.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/2041-210X.14027.

DATA AVA I L A B I L I T Y S TAT E M E N T
All code for the OHM algorithm is available on GitHub (https:// github.com/aesto vall/OHM) or Zenodo (Stovall, 2022 (Stovall, 2021).