Reducing tree volume overestimation in quantitative structure models using modeled branch topology and direct twig measurements (original) (raw)

Abstract

Quantitative Structure Models (QSMs) are fit to tree point clouds to represent the topology of trees as a network of cylinders. QSMs allow for the calculation of metrics difficult to measure without destructive sampling, including total tree volume. Current limitations in terrestrial laser scanning technology make small branches difficult to accurately resolve, causing overestimation of small branch volume in QSMs, which can translate into overestimating tree biomass. We present a new method called Real Twig to correct overestimated small branch and twig cylinders in QSMs. Real Twig differs from current methods by using twig diameters measured directly from corresponding tree species to model a unique taper for every path in the QSM, using the QSM’s inherent branching topology, but without relying on predefined mathematical or allometric relationships. To test Real Twig, we generated QSMs for different sets of trees that had detailed dry mass and density measurements obtained via felling after scanning. QSM-based biomass estimates were obtained by multiplying the tree’s QSM-based volume estimate by the tree’s specific basic density value. We trained our method with high-quality data consisting of five northern red oak (Quercus rubra L.) and five red maple (Acer rubrum L.) trees, using two different versions of TreeQSM, a widely used algorithm for generating QSMs. We further tested our method on three publicly available datasets, including managed forests and large tropical trees, collected with both phase-shift or time-of-flight sensors. QSMs corrected with our Real Twig method showed a very large improvement in tree biomass estimation, with a relative mean error of −1.2%, a relative root mean square error of 10.5%, and a concordance correlation coefficient of 0.999, compared to a relative mean error 76.8%, a relative root mean square error of 48.7%, and a concordance correlation coefficient of 0.982, when using the standard outputs of TreeQSM.

Introduction

Accurate estimates of total aboveground biomass (AGB) are important to understand how forests store carbon long term and respond to changes in atmospheric carbon dioxide (Houghton 2005). Since whole trees cannot be weighed while standing for AGB, allometric equations are used to estimate AGB from simple variables, such as the diameter at breast height (DBH) or total height of a tree (Vorster et al. 2020). The underlying data for allometric equations typically require destructive sampling, where trees are cut down and entirely weighed to fit a predictive equation covering a range of size classes and growing conditions (MacFarlane et al. 2014). However, destructive sampling is not only time consuming and expensive, but is often not feasible for rare, threatened, or endangered tree species (Frank et al. 2019).

While there are some nondestructive approaches to estimate AGB (MacFarlane et al. 2014; Montès et al. 2000), terrestrial laser scanning (TLS) has emerged as an efficient alternative to destructive sampling over the past decade (Arseniou et al. 2023; Calders et al. 2015a; Demol et al. 2022a; Disney et al. 2018; Holopainen et al. 2012; Stovall et al. 2017). With TLS, single trees or forest stands can be captured as a series of three-dimensional coordinates in space, known as a point cloud, enabling the computation of metrics traditionally difficult or impossible to capture otherwise (Calders et al. 2020). Point clouds capture a snapshot of a tree or forest stand at a specific point in time, making TLS well suited for forest inventory (Liang et al. 2016). Since the technical measurement biases and limitations unique to different laser scanning sensors are well documented and TLS can represent trees holistically with millions of unique data points, TLS may be less susceptible to errors when compared to traditional forest measurements (Calders et al. 2018, 2020). Moreover, because large trees are often missing from destructive sampling data (Weiskittel et al. 2015), TLS may be more suitable to develop allometric models across a wide range of tree sizes and forest types (Calders et al. 2022).

If the volume of a tree can be computed from a point cloud, AGB can be estimated nondestructively, by multiplying tree volume by a measured or published tree (wood and bark) density value (Arseniou et al. 2023). There are multiple approaches to calculate the volume of a tree from its point cloud. One approach well suited for conifers is the Outer Hull Model, where the point cloud is voxelized, woody material separated, and volume summed for the main stem and branch components (Stovall et al. 2017).

A common approach is to use a Quantitative Structure Model (QSM) (Fan et al. 2020; Hackenberg et al. 2015a; Raumonen et al. 2013; Yang et al. 2024), which uses geometric primitives to represent the tree’s topology from the point cloud. Using cylinders as a fundamental building block allows detailed branch structural metrics, surface area, volume, and other metrics to be easily calculated (Åkerblom et al. 2017; Arseniou et al. 2021b; Terryn et al. 2020), and individual main stem and branch volumes to be compared to reference measurements to assess QSM accuracy. One QSM approach is breaking the point cloud into small segments of points and using neighbor relationships to identify connected portions and bifurcations, where a new branch and branch order begin at each bifurcation, and cylinders are fit to the points with least squares iteration on a per branch basis (Raumonen et al. 2013). Alternate QSM approaches may define the tree’s topology with a sphere-based system to identify connected portions and bifurcations (Hackenberg et al. 2015a) or use the point cloud itself to create an underlying skeleton of nodes and internodes representing the tree’s branching structure (Yang et al. 2024). Regardless of the method used, attributes of trees can be described by the relationships between the geometric primitives. However, the accuracy of a QSM is always limited by the quality of the point cloud data. Higher-quality point clouds allow for better QSM topology and vice versa.

When carefully modeled with proper topology, QSMs can show good agreement with their reference destructive sampling data (Arseniou et al. 2023; Burt et al. 2021; Calders et al. 2015a; Demol et al. 2021b; Momo Takoudjou et al. 2018). However, current TLS technology struggles to accurately capture small branches and twigs in trees, due to beam divergence (the widening of the laser beam footprint with increasing distance from the scanner), occlusion, wind effects, and co-registration errors (Disney et al. 2018; Wilkes et al. 2017, 2021). QSMs typically reconstruct oversized small branches and twigs, leading to a large volume overestimation, often doubling the actual volume in branches <7 cm (Demol et al. 2021a, 2022b; Hackenberg et al. 2015b; Wilkes et al. 2021). These TLS sensor limitations are exacerbated as distance from the sensor increases, such that a decrease in point cloud quality and poor resolution of fine branching structures cause QSM volume and radii overestimation to increase drastically for small branches (Morhart et al. 2024). Any bias in QSM volume translates directly to inaccuracy in biomass estimation.

There are several current approaches to deal with this small branch overestimation problem. The first is to simply discard branches with a base cylinder diameter less than or equal to the error threshold (Demol et al. 2021a; Gonzalez de Tanago et al. 2018). This approach works well when only large branches are of interest, but necessarily omits part of the tree for total tree volume or AGB estimates. Another approach is an allometric statistical correction (Hackenberg et al. 2015a; Hackenberg and Bontemps 2023), where the cylinder radius is plotted against a strong independent predictor variable, and a power function is fit to identify overestimated cylinder radii with a user-defined confidence interval; any cylinder outside of this interval is considered an outlier and the overestimated cylinder radii are corrected by moving them to the predicted line. This generalized allometric correction approach assumes that the allometry of the tree is self-similar throughout all parts of the tree. This assumption is unlikely to be true, and it forces the tree to have a specific mathematical shape, regardless of whether this reflects the real taper in different parts of the tree. A more refined solution was developed by Raumonen et al. (2013), which adjusts the taper of each branch locally by constraining cylinders in branches to be smaller than those in their parent branches, usually combined with a parabolic model fit to cross-sections of the branch, which forces the branch to taper toward a fixed minimum constraint. This has been employed in other studies with varying minimum constraint sizes, with similar results (see e.g. Wilkes et al. 2021). This approach significantly improves branch tapering, but it does not constrain the branch to be realistic in size or consider the general allometry of the tree (unlike the allometric approach described above) and can sometimes modify the radii of larger cylinders that do not need correction.

Here, we present a new method called “Real Twig” to correct inherent QSM small branch and twig overestimation biases. The motivation behind Real Twig is to provide QSMs that are not only realistic looking, but also have precise and accurate tree metrics. If the QSM closely resembles its real-life counterpart, accurate tree metrics, such as volume, surface area, length, and biomass, will naturally follow. We designed Real Twig with only one assumption about tree architecture, namely that the twig is the smallest aboveground woody building block of any tree species. To this end, Real Twig improves upon previous approaches by correcting every cylinder in a QSM using an allometric taper model uniquely fit to each path in a tree’s branching network, constrained by the actual twig diameter measurement specific to the given tree species. Once the twig diameter is given, our method is entirely automated, adaptable for different workflows, and can be run on any QSM that provides topological relationships between cylinders. This study tested the effectiveness of combining species-specific, direct twig measurements and dynamic taper models throughout a QSM, to overcome deficiencies in current TLS sensor technology for use in tree modeling.

Methods

Real Twig

Real Twig differs from other QSM correction methods (described above) by using parts of a QSM that are well modeled and adequately covered with laser points (e.g. large branches and their cylinders) to inform the taper of poorly modeled parts (e.g. small branches and twigs) down to the twig level. Unlike the approach of Hackenberg et al. (2015a), this approach does not assume that every part of the tree tapers in the same way. Unlike the approach of Raumonen et al. (2013), which uses only local information to adjust the taper of each branch, Real Twig models every “path” in a QSM from the base cylinder to each twig tip (Fig. 1b), where the largest part of the tree is its base, and the smallest part is a twig that ends a path. Real Twig uses a monotonic generalized additive model (GAM), which allows it to automatically incorporate species-specific twig allometry into its corrected QSMs. The total number of paths is always equal to the total number of twigs in the QSM, which can range from a few hundred for small trees to thousands in large trees. For any given tree, a subset of twig diameters can be measured manually from the ground using calipers or from small branch samples cut from the canopy. These twig measurements provide tree or species-specific information to correct poorly modeled cylinder radii in a QSM. Detailed step-by-step instructions for applying the Real Twig method and visualized results are outlined in Fig. 1.

Figure 1

(a) Flowchart of the Real Twig processing steps and (b) an illustration of a Quantitative Structural Model (QSM) for a European ash tree with a single “path” highlighted in black. A path starts at the basal cylinder in the QSM and proceeds to a terminal twig; the number of paths in the tree is equal to the number of twigs. (c, f) QSM cylinders without modifications for a sessile oak and northern red oak tree. (d, g) QSM cylinders with TreeQSM’s standard parent–child and parabolic tapering correction. (e, h) TreeQSM cylinders corrected with Real Twig.

The first step of the Real Twig method (see flowchart in Fig. 1a) is to ensure that all parent–child cylinder relationships are consecutively defined. This ensures that all paths in the tree, from the base to each branch tip, can be successfully traced without gaps caused by missing cylinder indices. Starting from the base of the tree, we assign cylinders an index in consecutive order based on their parent–child relationships. The result is a QSM where all cylinders have a unique index. The first cylinder index is always the base of the main stem and the last cylinder index is equal to the total number of cylinders in the QSM. We follow a similar procedure for the branches, where the main stem is defined as branch “one,” and the rest of the branches are numbered consecutively until the last branch is reached. Our definition of orders and branches follows the approach of TreeQSM, where a new branch begins at a new branch order and ends at a twig tip (Raumonen et al. 2013).

Next, we calculate the “growth length” of each cylinder, which is the length of a given parent cylinder, plus the length of every child cylinder supported by the parent cylinder (Hackenberg et al. 2015a; Hackenberg and Bontemps, 2023). We use the growth length parameter because it can be matched to real measurements on a tree and does not contain any of the cylinder radii errors we are trying to correct, unlike the “growth volume” employed by Hackenberg et al. (2015a). Growth length also identifies all twigs in a QSM, which will always have a growth length equal to their cylinder length. We calculate growth length recursively for each cylinder using the R (R Core Team 2023) implementation of the igraph software package (Csárdi et al. 2023). For every cylinder, we recursively identify all its child cylinders and sum the length of these cylinders to get each cylinder’s growth length.

Next, we identify all paths in the QSM, from the base of the tree to each branch tip (Fig. 1b), using the igraph software package. The total number of paths in a QSM is always equal to the number of twig cylinders. Before we can model the path taper, we need to remove all poorly modeled cylinders (e.g. Fig. 1c, f), whose radii will influence the GAM taper. For every cylinder in each branch order in the path, we use the following filter:

Y_1=a/b/left(c+1right){Y}_1=a/b/\left(c+1\right)Y_1=a/b/left(c+1right)

Y_2=fraclog(b)a2{Y}_2=\frac{\log (b)}{a^2}Y_2=fraclog(b)a2

Y_3=fraca2log(b){Y}_3=\frac{a^2}{\log (b)}Y_3=fraca2log(b)

lower=IQRleft(Yxright)ast1.5−Q1lower= IQR\left({Y}_x\right)\ast 1.5-Q1lower=IQRleft(Yxright)ast1.5−Q1

upper=IQRleft(Yxright)ast1.5+Q3upper= IQR\left({Y}_x\right)\ast 1.5+Q3upper=IQRleft(Yxright)ast1.5+Q3

I=0,mathrmifYxgelowermathrmandYxleupper,mathrmelseI=1I=0,\mathrm{if}\ {Y}_x\ge lower\ \mathrm{and}\ {Y}_x\le upper,\mathrm{else}\ I=1I=0,mathrmifYxgelowermathrmandYxleupper,mathrmelseI=1

where a is the cylinder radius, b is the cylinder growth length, c is the branch order, _Y_1 is the general cylinder pass, _Y_2 is the small cylinder pass, _Y_3 is the large cylinder pass, IQR is the interquartile range, _Q_1 is the first quartile, _Q_3 is the third quartile, and I is a binary index, where 0 is a good fit and 1 is a poor fit, and all poor fits are removed before the next Yx filter. Only the cylinders that remain after this filter are used in the next step. _Y_2 and _Y_3 are done separately for each branch order along the path, while _Y_1 is done along the entire path.

Next, we run all the remaining good fit cylinders through a recursive taper filter, where the _i_th cylinder in the path can only be 1/sqrt(i) larger than all cylinders before it in the path. This allows for greater radii variation at the base of the path and a very tight taper as we approach the twig. The cylinders that remain following the taper filter are used to fit a monotonic GAM.

Next, we check if the current path contains a broken branch (Fig. 1a). We need to check for broken branches, because if we do not, the GAM will treat the last cylinder in the path as a twig, which will unrealistically taper the broken branch, resulting in a volume underestimation of the broken branch. We define a broken branch as a first-order branch with at most one second-order branch attached to it. If the criteria are met, we set the minimum cylinder size of the path to be the last well-fit first-order branch cylinder. If there are not any well-fit first-order branch cylinders, the minimum cylinder branch size is 25% smaller than the last first-order cylinder along the path.

Next, we fit a monotonic GAM to each path using the cobs R package (Ng and Maechler 2007) and force the intercept of the model to be equal to our species-specific twig radius, or minimum cylinder radius in the case of broken branches. For the model parameters, we set lambda equal to 0.01, degree to 1, constraint to increase, and nknots to the number of good fit cylinders minus one. If there are ≤ 3 well-fit cylinders in the path to model, we set the radius equal to the species-specific twig radius.

Finally, we take the mean radius for each cylinder using a weighted mean, where the weight is the cylinder radius. We use a weighted mean because the same cylinder can be in multiple paths. For example, the base of the tree appears in every path, while an individual twig is only in one path. The weighted mean considers the natural allometry and taper throughout the tree, where longer paths with more volume contribute more to the final radii than shorter paths with less volume. Optionally, we can model the main stem as its own unique path without the weighting influence of the other paths, as the main stem is generally modeled well in QSMs, assuming that the main stem is roughly circular in cross-section and does not contain large buttress flares (Arseniou et al. 2023; Demol et al. 2021b; Disney et al. 2018; Momo Takoudjou et al. 2018).

Calibration data for Real Twig—Harvard Forest trees

We selected five northern red oak (Quercus rubra L.) and five red maple (Acer rubrum L.) trees from a 2017 study in Harvard Forest (Petersham, MA, USA) to compare aboveground woody biomass from destructive sampling with estimates of aboveground woody biomass from TLS-based approaches (Arseniou et al. 2023). The trees were healthy, covering a range of size classes and canopy positions. The 10 trees were in two separate plots called the “main” and “north” plots, respectively, with the north plot located 30 m NNE from the northeast corner of the main plot. The main plot was a 50 × 50 m square delineated using a measuring tape and compass, with each edge aligned with the four main cardinal directions. The north plot was a 30 × 30 m square delineated in the same way as the main plot. The 10 trees were laser scanned in leaf-off conditions, and then destructively sampled in leaf-on conditions for detailed main stem mass, branch mass, and density measurements (Table 1).

Table 1

Tree variables from destructively sampled trees from Harvard Forest in 2017.

The main stem basic density is an average of the wood and bark density taken from multiple disks cut every four feet along the main stem. The branch basic density is an average of the wood and bark density taken from disks cut at the midpoint of all first-order branches. All mass and density measurements are expressed on an oven-dry basis.

Table 1

Tree variables from destructively sampled trees from Harvard Forest in 2017.

The main stem basic density is an average of the wood and bark density taken from multiple disks cut every four feet along the main stem. The branch basic density is an average of the wood and bark density taken from disks cut at the midpoint of all first-order branches. All mass and density measurements are expressed on an oven-dry basis.

Harvard Forest terrestrial laser scanning and data processing

Each plot was systematically scanned with a Riegl VZ-400 (a time-of-flight sensor) in April 2017 during leaf-off conditions to minimize occlusion and maximize capture of the upper canopy branches. All scans were taken at a wavelength of 1550 nm, pulse rates of 100 or 300 kHz, and an angular resolution of 0.04 mrad, with multiple discrete returns and waveform output enabled. Given the sensor’s beam divergence of 0.35 mrad, the spacing between individual points at 10 m was ~6 mm. The main plot consisted of 48 scans in total. Thirty-six scans were taken inside the plot spaced 10 m apart. Outside of the plot boundary, two scans were taken 10 m from the plot corners spaced 20 m apart. Four additional scans were taken 25 m from the plot edges along the four ordinal directions. The north plot consisted of nine scans total. One scan was taken in the plot center. Four scans were taken 10 m from the plot center in the four cardinal directions, while four scans were taken 21.2 m from the plot center along the four ordinal directions. The individual scans from all plots were co-registered into a single point cloud using the Riegl RiSCAN PRO software with reference points being retroreflective targets placed in the field. The individual trees were manually extracted from the forest stand point cloud and downsampled to a final resolution of 1.0–1.5 cm.

Harvard Forest tree measurements and destructive sampling

The 10 trees were measured and destructively sampled in August 2017 during leaf-on conditions (Table 1). DBH was measured on each tree at 1.37 m from the highest point on the ground with a diameter tape to the nearest 0.1 cm. After the trees were felled, the total tree height was measured from the base of the tree to the highest twig with a measuring tape. The trees were divided into the main stem and branch components, where the main stem progresses from the base of the tree and is the largest branch at each branching junction until the top of the tree is reached. The remaining parts of the tree were classified as branches. The mass of the main stem and branch components were immediately measured with a crane scale to capture their green mass. Disks were systematically cut along the main stem every 4 ft and from the midpoint of every branch >2.54 cm in diameter. The disks were immediately weighed to capture their green mass. The disks were peeled into wood and bark in the laboratory and then oven dried to estimate dry mass and basic density for the wood and bark. The basic density of each disk was calculated by averaging the basic density of the wood and bark. Finally, the basic density of main stem and branches was calculated by averaging the basic densities of their corresponding disks. See Arseniou et al. (2023) for more details on the destructive sampling protocol. Table 1 summarizes the tree measurements.

Other data for additional validation of Real Twig

To validate our Real Twig method outside of our training dataset, we opted to use publicly available datasets. These datasets were chosen to reflect how different processing workflows can affect the generation of QSMs of trees from TLS point clouds, given varying scanning conditions, point cloud quality, growing conditions, and tree size. The goal was to show that Real Twig could be applied to a variety of tree data sets, without a priori knowledge of destructive reference values.

The first dataset consists of 15 European ash (Fraxinus excelsior L.) trees, which were destructively sampled in 2017, in Belgium, with detailed green main stem density measurements, total green mass, total volume, and laser scanned in leaf-off conditions with a Riegl VZ-1000 or VZ-400 scanner, which are both time-of-flight sensors (Demol et al. 2021a). These trees represent high-quality point clouds, laser scanned under near-optimal conditions, to test our Real Twig method. These trees represent a European even-aged management system, so tree variation and form were significantly impacted by management (Fig. 1b).

The second dataset consists of 12 sessile oak (Quercus petraea L.) trees (Hackenberg et al. 2015b). These trees were laser scanned in 2013 during leaf-off conditions in Germany, with a Z+F IMAGER 5010c scanner, which is a phase-shift sensor. These trees were destructively sampled to get basic main stem density and total dry mass. These trees represent poor-form trees, with an abundance of epicormic sprouts, growing in a natural stand (Fig. 1c, d, e). The trees were also scanned under poor weather conditions, so the point clouds were observed to be affected by wind and rain noise. These trees represent lower-quality point clouds, with quality destructive sampling reference data, to test our Real Twig method. We did not use the already filtered point clouds in our analysis, but instead used the raw plot data, and manually segmented and filtered the 12 trees using CloudCompare (CloudCompare 2023). We downsampled the final point clouds to a resolution of 1.0 cm.

The last dataset consisted of four large, old-growth, tropical trees from Brazil, which were laser scanned with a Riegl VZ-400 (a time-of-flight sensor) in 2018 (Burt et al. 2021), in leaf-on conditions. The leaves were virtually removed from the point cloud using the TLSeparation algorithm (Vicari et al. 2019). The trees were also destructively sampled with detailed volumes, total dry mass, and basic main stem density values. This dataset represents high-quality point clouds and reference data for very large trees, with the added uncertainty of virtual leaf removal, to test our Real Twig method.

Tree measurement data for the public data sets are shown in Table 2.

Table 2

Tree variables from publicly available datasets.

Each dataset represents different growing conditions and point cloud quality to test our Real Twig method. Main stem basic density and AGB are on a dry-mass basis, except for those trees indicated with awhich are on a green-mass basis. All density values are an average of multiple disks collected along the main stem.

Table 2

Tree variables from publicly available datasets.

Each dataset represents different growing conditions and point cloud quality to test our Real Twig method. Main stem basic density and AGB are on a dry-mass basis, except for those trees indicated with awhich are on a green-mass basis. All density values are an average of multiple disks collected along the main stem.

Twig measurements

Our search of the literature revealed that measurements of tree twig diameters are not common. So, we selected trees planted on the Michigan State University campus of varied sizes and ages, of the appropriate species, and measured twig diameters using a Pittsburgh 6″ Dial Caliper (Model #92437). We measured one to four unique twigs on each tree in perpendicular directions depending on the accessibility of the twigs from the ground. To find an unbiased direction to measure the first twig on a tree, we recorded the number on the second hand of a watch and multiplied this number by 60 to convert it into an azimuth. We used a Suunto MC-2 hand compass to find the starting azimuth and ensure that subsequent measurements were perpendicular to each other. We measured the diameter of the twig to the nearest hundredth of an inch at the midpoint of the twig, between the current year’s growth and the previous year’s terminal bud scar, being careful to avoid any swelling from lateral buds. Next, we averaged the twig diameters, converted diameters to radii by dividing the diameters in half, and converted the units from inches to millimeters. Finally, we calculated the minimum, maximum, standard deviation (SD) and coefficient of variation (CV) values for each species. All of the twig measurements used in this study are shown in Table 3.

Table 3

Twig radii measurements in millimeters (mm)

Table 3

Twig radii measurements in millimeters (mm)

Sessile oak has not been planted on Michigan State University’s campus and is not naturalized in Michigan, USA. To test our method on the sessile oak trees from the publicly available dataset by Hackenberg et al. (2015b), we used twig measurements from another publicly available dataset from the Altitudinal Vicariants dataset collected in northern Spain (Milla and Reich 2011), accessed from the TRY plant trait database (Kattge et al. 2020). Milla and Reich measured their twig diameters to the nearest hundredth of a millimeter at the base of the twig. We also used the Bridge dataset (Baraloto et al. 2010), available from the TRY plant trait database (Kattge et al. 2020), containing stem and leaf traits from French Guiana for the four large tropical trees (Burt et al. 2021), which were also not present on Michigan State University’s campus.

Nondestructive volume estimation

For the Harvard data, we generated QSMs for the 10 trees using two versions of TreeQSM (v2.4.1 and v2.3.0). We used two different versions of TreeQSM to ensure that our training method was not overfit to a single version of TreeQSM or individual QSMs. We also wanted to compare the drastic volume differences we observed between different versions of TreeQSM and understand its cause. For the other datasets, we used only the latest version of TreeQSM (v2.4.1 at the time of writing) for validating our Real Twig method, as new users are most likely to download the latest version.

We started by generating 40 unique QSMs for each tree using unique combinations of input parameters with the define_inputs function from TreeQSM v2.4.1. We generated two values for PatchDiam1, 10 values for PatchDiam2Min, and two values for PatchDiam2Max. We chose to generate 10 values for PatchDiam2Min, as it has the greatest impact on small branch reconstruction during the cylinder fitting process (Demol et al. 2022b). TreeQSM’s input combinations are multiplicative, giving us a total of 40 unique input parameter combinations. From the 40 models, we chose the optimal input parameters with a custom metric. For our custom metric, we maximized the average SurfCov parameter (the percentage of a cylinder’s surface covered by points) and minimized the mad parameter (the mean absolute distance from a cylinder’s surface to the underlying points).

Using the optimal input parameters, we generated 30 additional QSMs using both TreeQSM v2.3.0 and v2.4.1 to account for underlying stochasticity inherent to QSM generation (Calders et al. 2015b; Disney et al. 2018), and volume differences between the two versions. From the 30 new models with the optimal input parameters, we let TreeQSM choose the optimal model with the lowest mad, which is the default optimal QSM selection metric. For all the QSMs generated, we enabled the parabolic branch tapering and parent child corrections, which are the default settings for TreeQSM. TreeQSM returns both the original, unmodified cylinder data and the modified cylinder data, so we did not need to generate additional QSMs to test our Real Twig method since it works on the unmodified cylinder data. For the European ash trees, we followed the same procedure described above for the Harvard data, but using only TreeQSM 2.4.1.

For the sessile oak and large tropical trees, like the European ash data, we wanted to test our Real Twig method for different use cases of TreeQSM (v2.4.1) without any a priori knowledge about the measured mass and volumes of the trees. For our QSM input parameters for these two data sets, we used the define_inputs function to automatically select a single best PatchDiam1, PatchDiam2Min, and PatchDiam2Max. Using these parameters, we generated 30 QSMs to account for any stochasticity in QSM generation and had TreeQSM automatically select the best model with the lowest mad. We left all other input parameters as the defaults to best represent a typical use case of TreeQSM.

For the large tropical trees, we opted to use TreeQSM’s (v2.4.1) triangulation mesh for estimating the volume of the main stem up until the first branch. These trees contained large buttress flares which TreeQSM was unable to properly reconstruct, leading to oversized cylinders, with circular diameters the width of the buttress. We could have manually removed the buttress flares from the point cloud as was done by Burt et al. (2021); however, we found that a triangulation mesh better captures the main stem volume and has proven effective for estimating the total mass of tropical trees in similar studies (Momo Takoudjou et al. 2018).

Comparisons of biomass and volume outputs from TreeQSM and Real Twig

TreeQSM returns volume estimates for both the main stem and branch components. Our analyses of the training data showed that the best, currently available correction for incorrectly sized cylinders is the local taper correction method of Raumonen et al. (2013) described in the introduction. We wanted to compare the Real Twig method of correcting QSMs to the best, currently available approach, using independent reference data.

The best reference data we had in each data set were total tree biomass estimates, with separate branch and stem biomass estimates available for the Harvard Forest trees. Since we had tree density measurements and mass estimates from the destructive sampling, we compared differences in biomass generated by different versions of TreeQSM with and without the Real Twig method employed against reference destructive sampling data. Since all biomass estimates were generated by multiplying QSM volume by the same tree’s density estimates, the only differences in biomass were due to differences in the volume estimates from the QSMs.

We chose to use the Harvard trees to train our Real Twig method because of the detailed stem and branch density values. This allowed us to convert the QSM branch and stem volumes into aboveground biomass by multiplying the individual volume components (main stem and branch volumes) by their corresponding basic density values from destructive sampling. We needed to calculate separate stem and branch masses to ensure there were not any compensating errors in total biomass estimates that masked the effectiveness of using Real Twig for correcting any branch mass and volume overestimation in the QSMs. The total mass was the sum of the mass of a tree’s branches and its main stem.

None of the public datasets had separate branch density values, so we were only able to assess the accuracy of total mass and were unable to check for any compensating errors between the main stem and branches. For the Demol et al. (2021a) European ash trees, only green density was taken from disks along the main stem, so only total green biomass could be compared. All other calculations were on a dry-mass basis, as were the mass validation metrics described in the next section. See Table 2 for a summary of the public datasets used in this analysis.

Statistical analysis

We calculated the following standard validation metrics for each dataset (Arseniou et al. 2023; Burt et al. 2021; Calders et al. 2015b) comparing different TLS-based mass estimates to the reference destructive data.

Individual tree error:

beginequationmathcalE=mathrmMassmathrmTLS−mathrmMassmathrmRefendequation\begin{equation} \mathcal{E}={\mathrm{Mass}}_{\mathrm{TLS}}-{\mathrm{Mass}}_{\mathrm{Ref}} \end{equation}beginequationmathcalE=mathrmMassmathrmTLS−mathrmMassmathrmRefendequation

(1)

Individual tree relative error:

beginequationmathrmRE=fracleft∣mathcalEright∣mathrmMassmathrmRefendequation\begin{equation} \mathrm{RE}=\frac{\left|\mathcal{E}\right|}{{\mathrm{Mass}}_{\mathrm{Ref}}} \end{equation}beginequationmathrmRE=fracleft∣mathcalEright∣mathrmMassmathrmRefendequation

(2)

Mean relative error (%) across all trees:

beginequationmathrmMRE\begin{equation} \mathrm{MRE}\%=\frac{1}{n}\sum_{i=1}^n{\mathrm{RE}}_i\times 100\% \end{equation}beginequationmathrmMRE

(3)

Root mean square error across all trees:

beginequationmathrmRMSE=sqrtfrac1nsumi=1nmathcalEi2endequation\begin{equation} \mathrm{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^n{\mathcal{E}}_i^2} \end{equation}beginequationmathrmRMSE=sqrtfrac1nsumi=1nmathcalEi2endequation

(4)

Relative root mean square error (%) across all trees:

beginequationmathrmRMSE\begin{equation} \mathrm{RMSE}\%=\frac{\mathrm{RMSE}}{\ \mathrm{Mean}\_{\mathrm{Mass}}_{\mathrm{Ref}}} \end{equation}beginequationmathrmRMSE

(5)

In the above equations, MassTLS is the TLS mass estimate of a single tree by converting QSM volume to mass with the tree’s unique density values. MassTLS is either, total, stem, or branch mass depending on if the dataset has branch specific density values for a tree. MassRef is the reference mass from destructive sampling. It is the tree’s corresponding total, stem, or branch mass depending on the dataset. i refers to a single tree, while n refers to all trees in the dataset. Mean_MassRef is the mean mass for either the total, stem, or branch mass in the dataset. Finally, we quantified the difference between the MassTLS and MassRef using the concordance correlation coefficient (CCC) (Lin 1989). All statistical analyses, tables, and figures were created using R (R Core Team 2023).

Results

Comparisons of Real Twig and different TreeQSM versions for the Harvard trees

All methods used to generate volumes and masses from the Harvard trees were precise and accurate for modeling the main stems of the trees with CCC values close to 1, though there was a general bias toward overestimating main stem biomass by 15%–30% for stems <150 kg. For both versions of TreeQSM, main stem biomass estimates were close to the reference main stem mass, with a RMSE% of 7.0% and a CCC of 0.997 for v2.3.0, while v2.4.1 had a RMSE% of 6.7% and a CCC of 0.998 (Table 4). With Real Twig applied, the main stem biomass estimates were similar to TreeQSM, with a RMSE% of 6.9% and a CCC of 0.997 with Real Twig applied to v2.3.0, and a RMSE% of 7.2% and a CCC of 0.997 with Real Twig applied to v2.4.1. For v2.4.1, Real Twig slightly reduced the MRE% of the main stem biomass but slightly increased the RMSE% across the 10 trees, with the opposite pattern being true when Real Twig was applied to v2.3.0.

Table 4

Accuracy statistics for the Harvard Forest trees broken down into total, main stem, and branch components.

Table 4

Accuracy statistics for the Harvard Forest trees broken down into total, main stem, and branch components.

For the branch biomass of the Harvard Forest trees, there were significant differences between all methods. TreeQSM v2.3.0 performed better than v2.4.1, with v2.4.1 at least doubling mass estimation errors for all statistics (Table 4). TreeQSM v2.3.0 overestimated branch biomass with an MRE% of 363%, a RMSE% of 160%, and a CCC value of 0.654. TreeQSM v2.4.1 severely overestimated branch biomass with an MRE% of 949%, a RMSE% of 346%, and a CCC value of 0.381. By contrast, Real Twig with TreeQSM v2.4.1 had highly accurate branch biomass estimates, with an MRE% of −0.7%, a RMSE% of 8.4%, and a CCC value of 0.997. Real Twig with TreeQSM v2.3.0 showed a modest underestimation of branch biomass, with an MRE% of −9.1%, a RMSE% of 16.5%, and a CCC value of 0.989. Overall, Real Twig dramatically improved branch biomass estimates when compared to the current, best-available corrections in either version of TreeQSM, reducing the average error in total AGB estimates by three orders of magnitude for v2.4.1 and with a 36-fold reduction in error for v2.3.0.

For the total biomass, the total error is the sum of the main stem and branch components. The results show that errors in the total mass estimates are mostly the result of branch biomass overestimation (Fig. 2). TreeQSM v2.4.1 had the largest overestimation, with an MRE% of 126%, a RMSE% of 77.6%, and a CCC value of 0.831. TreeQSM v2.3.0 overestimated the total mass less, with an MRE% of 50%, a RMSE% of 37.2%, and a CCC value of 0.947. Real Twig applied to TreeQSM v2.4.1 performed the best, with an MRE% of 0.02%, a RMSE% of 6.7%, and a CCC value of 0.998. Real Twig applied to TreeQSM v2.3.0 also performed very well with an MRE% of 2.2%, a RMSE% of 5.7%, and a CCC value of 0.998. Overall, Real Twig dramatically improved total biomass estimates compared to the current, best-available corrections in either version of TreeQSM, dropping the average error total AGB estimates by two orders of magnitude for v2.4.1 and with a 25-fold reduction in error for v2.3.0.

Figure 2

Mass estimates for the Harvard Forest trees using two different versions of TreeQSM with and without Real Twig. The horizontal dashed lines are the ±10% error lines. The solid black line is the identity line.

Validation of Real Twig with European ash trees

For the 12 European ash trees studied (Fig. 3), Real Twig dramatically increased the accuracy and precision of the total green mass estimates, with only one tree falling outside ±10% of the reference mass (Fig. 3). TreeQSM v2.4.1 overestimated total mass by 60.8% on average, with a RMSE% of 107% and a CCC of 0.645 (Table 5), while Real Twig showed very high accuracy in total mass: MRE = −0.26%, with a RMSE% of 6.3% and a CCC of 0.996.

Figure 3

Sixteen European ash trees with mass estimates from TreeQSM and Real Twig. The horizontal dashed lines are the ±10% error lines. The solid black line is the identity line.

Validation of Real Twig for sessile oak trees

Compared to the Harvard and European ash trees, the Real Twig results showed far less improvement for the sessile oak trees, with a CCC value of 0.897. However, the Real Twig results were still drastically more accurate than TreeQSM v2.4.1, with the latter having a CCC value of only 0.173. Real Twig was able to improve the accuracy of nearly all the trees, with most of them falling within ±10% of the reference mass after correction (Fig. 4). TreeQSM had an MRE of 74.7% on average, with a RMSE of 78.7%, while Real Twig had an MRE of −1.5% on average, with an RMSE of 9.2% (Table 6). Both TreeQSM and Real Twig showed little correlation between mass overestimation and tree size, over the size range of these trees.

Validation of Real Twig for large tropical trees

The large tropical trees showed an overall error difference between TreeQSM and Real Twig that was lower than that seen for the other data sets (Fig. 5). In both cases, the total mass estimates are roughly parallel to the reference line, but TreeQSM v2.4.1 generally overestimated total mass, while Real Twig generally underestimated total mass, with MRE% values of 18% and −6.5%, respectively (Table 7). For TreeQSM, the RMSE% and CCC values are 17 and 0.973, respectively, while Real Twig has RMSE% and CCC values of 4.7 and 0.998, respectively. Nonetheless, Real Twig increased the precision of the total mass estimates, with an absolute bias reduced by 3-fold compared to the current, best-available correction for TreeQSM (Fig. 5 and Table 7).

Table 5

Accuracy statistics for the European ash trees.

Table 5

Accuracy statistics for the European ash trees.

Overall performance of Real Twig for all study trees

When all the study trees are combined, Real Twig greatly outperforms TreeQSM v2.4.1, the current best algorithm. TreeQSM consistently overestimates total mass over a wide range of tree sizes, while Real Twig showed highly accurate mass estimates (Table 8, Fig. 6). For TreeQSM, the RMSE% and CCC values were 48.7% and 0.982, respectively, while Real Twig had RMSE% and CCC values of 10.5% and 0.999, respectively. Looking at all trees together (Fig. 6), we can see that Real Twig’s error correction exponentially decreases compared to TreeQSM v2.4.1 as the size of the trees increases because there is a smaller proportion of total mass in small branches. One of the smallest trees in the study had a %MRE of >400%, which was corrected to a little over 10% error with the Real Twig method (Fig. 6). On the other hand, all the study trees had %MRE >10% when not corrected with the Real Twig method.

Figure 4

Twelve sessile oak trees with mass estimates from TreeQSM and Real Twig. The horizontal dashed lines are the ±10% error lines. The solid black line is the identity line.

Table 6

Accuracy statistics for the sessile oak trees.

Table 6

Accuracy statistics for the sessile oak trees.

Discussion

Improved tree volume and biomass estimation from QSMs with Real Twig

TLS has emerged as a legitimate, nondestructive way to estimate total tree aboveground woody biomass or volume with a reasonable degree of precision and accuracy, as many studies have now demonstrated (Arseniou et al. 2023; Calders et al. 2015b; Demol et al. 2022a; Gonzalez de Tanago et al. 2018; Lau et al. 2019; Momo Takoudjou et al. 2018). However, Demol et al. (2022b) recently cautioned that significant volume overestimations will likely be a problem until there are further advances in laser scanning technology, data processing, and QSM software that can solve the problem of overestimation of smaller portions of the tree (i.e. small branches and twigs). This study shows that the Real Twig method can greatly improve the precision and accuracy of tree volume and biomass estimation, by dramatically improving the volume estimates of smaller portions of trees modeled with a QSM, in this case TreeQSM. Out of the 41 trees of different species, obtained from the multiple, independent datasets examined, every tree showed a large increase in mass accuracy and precision with Real Twig applied, with most falling within our target goal of ±10% of the reference mass, and with total mass errors as low as 0.04%. In contrast, the current version of TreeQSM (v2.4.1) with its most advanced cylinder fitting and segmentation routine always overestimated mass by >10% when compared to reference values from destructive sampling, with some small trees exceeding >400% overestimation.

Figure 5

Four large tropical trees with mass estimates from TreeQSM and Real Twig. The horizontal dashed lines are the ±10% error lines. The solid black line is the identity line.

The Real Twig method was successful because it improves upon previous approaches to deal with the small branch overestimation issue. We were not satisfied with the practice of not attempting to model smaller parts of the tree, by discarding branches below a given diameter threshold. Our results show that this could only be a viable solution when trees are very large (Fig. 6) and smaller branches and twigs are not a significant component of total mass; it is an incomplete solution in any event. Such an approach also does not allow for estimating the volume or mass of smaller trees, composed of smaller parts. Since planting new trees is a significant strategy within forest carbon offset projects that help remove carbon dioxide from the atmosphere to mitigate climate change (Nilsson and Schopfhauser 1995; Pacala and Socolow 2004), it is important to be able to estimate the change in tree biomass over time for younger, faster-growing trees (McMahon et al. 2010; Yang et al. 2023).

A major improvement with Real Twig is the rescaling of every cylinder in the tree by incorporating ideas from both the local tapering approach of Raumonen et al. (2013) and the existence of a whole-tree allometry from Hackenberg et al. (2015a). Real Twig does not assume that every part of a tree shares the same allometry. Real Twig models every path in the tree with its own, distinct taper. By averaging across paths, Real Twig allows the local allometry of individual parts of the tree to contribute to the architecture of the whole tree, producing a visually realistic QSM.

Another major innovation was recognizing that it is not only possible, but likely, that none of the cylinders in the smaller parts of a tree will be correctly modeled by the QSM. The allometric modeling approach of Hackenberg et al. (2015a) uses the whole population of cylinders to fit an allometric model to determine outliers and correct them. However, if the QSM data do not contain many correctly modeled small cylinders, then coefficients of the model fit to the QSM data will be biased, specifically toward overestimation of small parts of the tree. Our solution was to measure actual twig diameters for the species of interest, or to use published values, to force the taper model to taper to the appropriate twig size and rescale the taper of each branch path to be realistic.

Table 7

Accuracy statistics for the large tropical trees.

Table 7

Accuracy statistics for the large tropical trees.

Table 8

Accuracy statistics across all trees in the study.

Table 8

Accuracy statistics across all trees in the study.

Differences in volume estimation between different versions of TreeQSM

There were large differences in the two versions of TreeQSM software used to generate tree volume (and mass) estimates in this study, with and without the Real Twig correction. This is the first study to show such large version differences, and an important finding, because the same data could produce very different estimates of tree volume and biomass. This would be particularly problematic if changes in forest volume or biomass over time were computed with different versions of the software. It is also notable that the difference between the different versions of TreeQSM is reduced when the Real Twig correction method is applied. Examining these differences helped us to better understand the results of the study and potential improvements to TreeQSM, other QSM methods, and Real Twig.

Figure 6

Mean relative error (%) of total aboveground biomass estimated from QSM-generated volumes, using two different approaches, applied to trees of different size (stem diameter at breast height, DBH, cm) from different datasets (symbols).

Our analysis suggests that TreeQSM has evolved toward an improved ability to reconstruct branches and correctly represent the tree’s topology in later versions, with the consequence of exacerbating the small branch overestimation problem inherent in the input point clouds (Fig. 7). The oldest version of TreeQSM (v2.0) does not successfully reconstruct the higher-order branches of the input point cloud and has visible issues with branch topology, leading to branch volume omission. Version 2.3.x improves the branching topology and reconstructs more, higher-order branches, leading to a more realistic QSM, and therefore more branch volume. Finally, version 2.4.x reconstructs even more higher-order branches and improves on the tree topology, but has a more relaxed taper constraint, leading to a substantial increase in high-order branch volume.

Figure 7

Top-down view of a northern red oak from Harvard Forest showing the difference in tapering, topology, branch connectivity, and cylinder radii between different versions of TreeQSM and Real Twig. The QSM cylinders colored in black are overlaid on top of the input point cloud colored in light gray. All QSMs have the same input parameters where both exist in the different versions and have the same input point cloud. The Real Twig corrected QSM uses the raw cylinder fits from v2.4.1 shown here.

TreeQSM version 2.4.x overestimates total tree volume because it fits better to the input point cloud, finding more branches and providing a more realistic topology of the tree, at the expense of including more point cloud–related errors, caused by beam divergence, wind noise, and co-registration errors. Older versions (2.0–2.3.x) omit some branches and have a strictly enforced taper, regardless of the underlying point cloud data, leading to volume omission (Pasi Raumonen, personal communication, 13 June 2023). This explains why post-processing tree point clouds after the initial registration can reduce QSM volume overestimation when wind and occlusion errors are not factors (Demol et al. 2022b; Wilkes et al. 2021). Additionally, TreeQSM v2.3.x reconstructs fewer branches than v2.4.x, and the branches that are reconstructed are ~10% shorter than v2.4.x (Pasi Raumonen, personal communication, 13 June 2023). This means that earlier versions of TreeQSM could have produced seemingly more accurate estimates of tree volume and biomass, due to compensating errors, i.e. omitting small branches that are actually present in the real tree, while overestimating the volume of smaller branches that are included. Because the smaller twigs are missing, the path lengths are reduced, and smaller branches abruptly end before reaching actual twigs, but are modeled as twigs in the QSM. This is a likely explanation for the significant (−9%) average underestimation of branch biomass when Real Twig was applied to TreeQSM v2.3.x (Table 3). This is also a likely explanation of the results of previous validation studies using older versions of TreeQSM, with an overestimation bias of 9.68% to 21% (Calders et al. 2015b; Demol et al. 2021b) compared to more recent studies that found tree volumes more than doubled in their overestimation at 52%, with most of the error occurring in the small branches when using TreeQSM v2.4.x (Demol et al. 2022b).

Implications of size-dependent error in tree volume and biomass estimation with QSM-based approaches

Our results clearly show that the relative error in AGB estimated from QSMs can be very high for small trees, which are composed of only small parts, without the Real Twig correction. We also showed that this error declines asymptotically toward smaller and smaller estimation errors, when applied to trees of increasing size (Fig. 6). In contrast, Calders et al. (2015b) reported that error in AGB estimates from QSMs were independent of DBH. We suspect that our results differ from theirs because they examined error over a more limited size range of trees from ~10 to 65 cm DBH, whereas we included much smaller and much larger trees. Other studies validating TLS with destructive sampling reference also show that for larger trees (>1500 kg) TLS mass is closer to the reference destructive mass, and vice versa for smaller trees (<1500 kg) (Burt et al. 2021; Calders et al. 2015b; Demol et al. 2021b, 2022b; Hackenberg et al. 2015b; Momo Takoudjou et al. 2018). We believe that the source of this pattern lies in the proportion of twigs and small branches in a tree. The larger the tree’s total volume, the less twig volume contributes to total tree volume. In contrast, the smaller the tree’s total volume, the more twigs and small branches contribute to the total tree volume.

Twig size also plays a role, as the smaller the actual twig diameter, the harder it is for TLS to accurately resolve, leading to oversized twigs in point clouds and QSMs. In the case of large tropical trees, most of their mass is in the main stem and large branches, while their twigs are stout with diameters approaching 1 cm (Table 3). This is an ideal situation for TLS, where most twigs can be captured, and their volume contributes little to the total tree volume. This explains the pattern in our own results, where total mass overestimation systematically decreases as total tree size increases (Fig. 6).

Tree size and its effect on AGB estimation using remote sensing and QSMs have important implications for building allometric equations to predict AGB from DBH. Databases of destructive sampling measurements of AGB are often missing large trees (Weiskittel et al. 2015) because of the difficulty in finding, or justifying the felling of, very large trees. Our results show that the best case for obtaining good estimates with QSM-based estimation approaches may be for large trees. In contrast, it is very easy and cost-efficient to destructively sample small trees, which currently represent the worst-case scenario for QSM-based estimation approaches. Our results show that carbon sequestration rates could be drastically overestimated if QSM-based approaches are employed, without correction with a method such as Real Twig. In general, QSM-based solutions for estimating mass of volume of small trees and small parts of trees need more scrutiny.

Considerations for improved tree volume and biomass estimation from QSMs

Our Real Twig method can correct QSM volume overestimation in small branches and twigs, resulting in dramatic increases in accuracy of branch and total tree volume and mass estimation from TLS-QSM-based approaches. For the best total tree volume estimates, we recommend starting with the highest possible quality point cloud. “Quality” is a subjective term, but for this purpose, we refer to quality as the best topological representation of the tree with minimal occlusion and a well-defined woody skeleton. We recommend, if possible, using point clouds in the “leaf-off” condition to achieve this. Burt et al. (2021) showed that removing the leaves from a “leaf-on” point cloud is a necessity for accurate AGB estimates; otherwise, AGB will be overestimated upwards of 40%. This is because leaves are modeled as wood in the point cloud, magnifying the overestimation error.

Our results showed a lower level of accuracy improvements from Real Twig for large tropical trees, which could have been the result of removing leaf points from point clouds (these were the only trees we examined that were scanned in a “leaf-on” condition). Arseniou et al. (2021a) showed that artificial leaf removal from point clouds with the TLSeparation algorithm (Vicari et al. 2019) can result in the accidental removal of twigs and small, higher-order branches. So, it is possible that some of the underestimation of total tropical tree biomass by Real Twig came from assuming that the twigs were slightly larger parent branches because actual twigs in the point cloud were removed by the leaf removal algorithm, along with the leaves. This error could be even larger if Real Twig is applied to QSMs constructed from point clouds of smaller trees with their leaf points removed. To minimize this problem, we recommend using Real Twig with TreeQSM v2.4.1, as it reconstructs more high-order branch cylinders from the point cloud and, when corrected with Real Twig, gives the most realistic models of the trees (see Figs. 2 and 6). We also recommend visually inspecting each optimal QSM against its input point cloud to ensure that the QSM with the best topology is selected.

It is important to understand that Real Twig was trained only with realistic twig diameter measurements and not with actual measurements along the main stem and branches of the trees. As a result, what our method determines to be a good or bad cylinder fit may occasionally exclude correctly modeled cylinders, especially in smaller diameter branches, which could lead to overaggressive tapering in smaller parts of the tree. Our method could also artificially increase the diameter of branch bases, especially if the branch base cylinder was determined to be a poor fit. This is a side effect of using growth length as the radius predictor variable in the GAM, as every time there is a fork in a tree, the growth length of a cylinder decreases. Without enough well-fit cylinders with similar growth lengths, the GAM predicts the radius based on the closest well-fit cylinders, which could inflate the branch base and decrease the smaller branches, as the closest well-fit cylinder for small branches is the measured twig diameter. This could create a path that is inflated at the path base and too narrow as growth length decreases. These small errors could cancel out and still yield accurate branch volumes, but at the expense of correctness of path tapering relative to the real tree. As a general principle, the best total tree volume estimates will have QSMs that are visually close to the actual tree, with the input parameters determined either visually or automatically (Calders et al. 2015a). Regarding input parameters, we recommend using a semi-automated approach, where the starting input parameters are chosen automatically, before being manually reduced gradually, until the maximum amount of small branch detail is achieved while still maintaining proper topology.

Another consideration is the accuracy and generality of tree density estimates, which convert QSM volumes to tree mass. While we were able to generate precise and accurate estimates of total tree mass with only main stem density values from the public datasets, we had the lowest total mass estimate error when we used tree-specific main stem and branch densities (i.e. the Harvard data). Using separate tree-specific main stem and branch densities is important for the accurate conversion of volume to woody mass because there can be a large density variation within a tree between its main stem and branch components (Demol et al. 2021a; Disney et al. 2018; MacFarlane 2020). If the main stem and branch density are not equal, using the incorrect density for either may lead to systematic bias when converting to total tree mass even if the total tree volume from the QSM is correct. Another little-discussed issue is bark density, as TLS scans the tree’s outside bark volume, and bark differs in density from wood and occupies a variable portion of total tree volume (Neumann and Lawes 2021). Future validation studies should consider how to accurately separate wood and bark components of volume or both branches and stem and include detailed measurements of both wood and bark density of stems and branches (MacFarlane 2024).

Finally, our results show that Real Twig can overcome well-known deficiencies in both time-of-flight and phase-shift sensor technologies and their ability to resolve fine details in trees, such as beam divergence and co-registration errors. However, the end goal is not merely to correct known errors, but to better understand the errors inherent to specific TLS sensors and mitigate them as much as possible in the field, by matching the appropriate sensor and parameters to the trees being scanned. While studies have investigated some of these sensor deficiencies and their effect on QSMs, they do so with only one sensor and fixed sets of input parameters (Morhart et al. 2024; Wilkes et al. 2021). Future studies should consider multiple laser scanning sensor technologies, with varying input parameters, such as the effect of angular resolution and distance or scan numbers, on trees in situ and controlled environments, relating the results back to the species’ measured twig diameter, and Real Twig’s ability to overcome these deficiencies. Until TLS sensor technology can resolve these fine details efficiently and accurately, Real Twig or similar corrections must serve as the final step in the data processing pipeline to ensure precise and accurate metrics from QSMs.

Conclusion and next steps for Real Twig

Real Twig was shown to provide greatly improved estimates of tree volume and mass and more realistic looking tree models when applied to the outputs of TreeQSM. However, Real Twig is dependent on QSMs with accurate topology and species-specific twig diameter measurements for the best results. We see three next steps for further calibration and validation of the Real Twig method.

First, more intelligent cylinder radii and broken branch filters need to be developed. The filters should identify good and bad fit cylinders based on their taper within the QSM itself, their growth length or relative position in the tree or path, and their relationship to the measured twig diameter. The filter should be dynamic, retaining more small cylinders for higher-quality QSMs and fewer small cylinders for lesser-quality QSMs. Identifying correctly modeled cylinders will allow for better modeling between different tree growth forms, especially excurrent growth forms that retain multiple broken lower branches. Our future work will focus on testing Real Twig for a broader range of species and tree architectures, especially excurrent growth forms, such as those of pines, which have whorls of branches attached to a dominant main stem, and more abrupt tapering along paths. Here, we only look at tree species with a deliquescent branching architecture.

Second, the method relies on having measured twig diameters for a specific tree species. While reviewing the literature of this paper and searching for already published datasets, we were surprised how few studies of trees and forests have included measurements of tree twigs. Thus, the twig measurements published here add much-needed data to fill this data gap. Collaboration in the research community is needed to measure more twig diameters across different countries and tree species. While our results show that a genus-average twig diameter is a reasonable substitute for a specific species’ twig diameter, if the genus average is not available, or the species is unknown, the twig diameter will be uncertain. Given the time it takes to measure a few twigs on a tree, we recommend tree-specific measurements on every tree scanned, unless time or cost prohibitive. These measurements will not only improve the accessibility of Real Twig but will also provide valuable reference data for future tree modeling using remote sensing data.

Finally, work is underway to allow Real Twig to be updated to support other QSM modeling programs to help make accurate and precise tree volume estimates more accessible to the remote sensing community. The Real Twig method currently supports the cylinder-based approaches of TreeQSM (Raumonen et al. 2013) and SimpleForest (Hackenberg et al. 2014), but the method can be implemented for any geometric primitive-based approach that provides information on parent–child relationships.

Acknowledgements

We want to acknowledge the Michigan State University W.J. Beal Botanical Gardens and Campus Arboretum for the collection of trees on which (real) twigs were measured. We want to thank the research staff of Harvard Forest (David Orwig, Audrey Barker Plotkin), Alan Strahler, and UNAVCO for coordinating the Harvard Forest TLS experiment. We would also like to thank Samuel Clark, Garret Dettmann, and Georgios Arseniou of Michigan State University, Jereme Frank (University of Maine), David Walker, and Phil Radtke (Virginia Tech University) for their contribution to the collection of destructive tree measurements in Harvard Forest. We also want to thank Dr Kim Calders at Ghent University for sharing his point clouds of the Harvard Forest trees for this research. We would also like to thank Dr Pasi Raumonen for helping us to understand the differences between TreeQSM versions.

Author contributions

Aidan Morales (Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing—original draft) and David MacFarlane (Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing—review & editing).

Conflict of interest

None declared.

Funding

This work was partially supported with funds from a joint venture agreement between Michigan State University (MSU) and the United States Department of Agriculture Forest Service, Forest Inventory and Analysis Program, Northern Research Station. Part of D.W.M.’s time was paid for with funds from Michigan AgBioResearch, the USDA National Institute of Food and Agriculture. Part of A.M.’s time was supported by an Academic Achievement Graduate Assistantship from MSU.

Data availability

The code underlying the Real Twig method and a database of twig measurements are available in an R package called rTwig: https://github.com/aidanmorales/rTwig. Additional documentation and examples can be found at the rTwig package website: https://aidanmorales.github.io/rTwig. The primary data underlying this article are available in the article. Other data will be shared on reasonable request to the corresponding author.

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© The Author(s) 2024. Published by Oxford University Press on behalf of Institute of Chartered Foresters.

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