Quantifying vegetation and canopy structural complexity from terrestrial LiDAR data using the forestr r package

Abstract

1. Terrestrial LiDAR (light detection and ranging) technologies have created new means of quantifying forest canopy structure, allowing not only the estimation of biomass, but also descriptions of the position and variability in canopy elements in space. Such measures provide novel structural information broadly useful to ecologists.
2. There is a growing need for both a detailed taxonomy of forest canopy structural complexity (CSC) and open, transparent, and flexible tools to quantify complexity in ways that will advance foundational ecological knowledge of structure‐function relationships.
3. The CSC taxonomy we present groups structural descriptors into five categories: leaf area and density, canopy height, canopy arrangement, canopy openness, and canopy variability. This paper also introduces the r package forestr, the first open‐source r package for the calculation of CSC metrics from terrestrial LiDAR data.
4. The r package forestr is an analysis toolbox that works with portable canopy LiDAR (PCL) data and other pixelated/voxelized point clouds derived from terrestrial LiDAR scanning (TLS) data to calculate CSC metrics of interest to ecologists, modellers, forest managers, and remote sensing scientists.

1 INTRODUCTION

The characterization of forest structure is a long‐standing (Watt, 1947; Whittaker & Woodwell, 1969) research area fundamental to interpreting, modelling, and improving the understanding of ecosystem functions. Light detection and ranging (LiDAR) has been used to characterize ecosystem structural features relevant to biogeochemical cycling (Antonarakis, Saatchi, Chazdon, & Moorcroft, 2011; Hardiman, Bohrer, Gough, Vogel, & Curtis, 2011; Hardiman et al., 2017), growth and carbon uptake (Stark et al., 2012), habitat suitability (Vierling, Vierling, Gould, Martinuzzi, & Clawges, 2008), food web stability (Barbosa et al., 2016), plant and canopy physiology (Asner & Mascaro, 2014; Atkins, Bohrer, et al., 2018; Atkins, Fahey, Hardiman, & Gough, 2018), ecosystem metaproperties (Paynter et al., 2017), forest relationships with hydrological networks (Detto, Muller‐Landau, Mascaro, & Asner, 2013), fire susceptibility (Hiers, O'Brien, Mitchell, Grego, & Loudermilk, 2009; Skowronski, Clark, Duveneck, & Hom, 2011) and community dynamics and competition (Rodríguez‐Ronderos, Bohrer, Sanchez‐Azofeifa, Powers, & Schnitzer, 2016). In terrestrial ecosystems, ground‐based, commercially available, and field portable LiDAR systems are revolutionizing the collection of quantitative ecosystem physical structural information, and providing an unprecedented view of structure (Asner et al., 2012; Calders, Armston, Newnham, Herold, & Goodwin, 2014; Calders et al., 2017; Eitel et al., 2016; Newnham et al., 2015; Paynter et al., 2016; Wilkes et al., 2017). The multidimensional data created by terrestrial LiDAR can be used to quantify the arrangement of canopy elements in space and describe the complexity of a canopy beyond estimates of biomass or leaf area alone (Hardiman et al., 2011). We refer to this heuristic as canopy structural complexity, or CSC. To expand the accessibility of LiDAR technology and the framework of CSC, open and flexible processing solutions for deriving CSC metrics are essential. In this paper, we present forestr (Atkins, Bohrer, et al., 2018; Atkins, Fahey, et al., 2018), a package for the R programming language (R Core Team, 2017), which uses pixelated (2‐D) or voxelized (3‐D) point‐cloud data from both portable canopy LiDAR (PCL) and terrestrial laser scanning (TLS) data, to calculate CSC metrics in five taxonomic categories (Table 1).

Table 1. Detailed description of canopy structural complexity parameters with units and references, where available. The platform column indicates the current availability of each metric for each LiDAR platform, currently portable canopy LiDAR (PCL) and terrestrial laser scanning (TLS)

Area and density	Symbol	Units	Description	References	Platform
Mean VAI	VAI		Mean of column summed vegetation area index	Béland et al. (2011) and Hardiman, Bohrer, et al. (2013)	PCL, TLS
Maximum VAI	VAImax		Maximum x, z value of VAI	Hardiman, Bohrer, et al. (2013)	PCL, TLS
Mean height of VAImax	VAImode	m	Mean height of VAImax across a transect	Hardiman, Bohrer, et al. (2013)	PCL, TLS
Mean peak VAI	VAIpeak		Mean of VAImax	Hardiman, Bohrer, et al. (2013)	PCL, TLS
SD of height of max VAI	σZVAI		Standard deviation of the height of VAImax for each column		PCL
Height
Mean leaf height	H	m	Transect mean of column mean leaf height—mean of density‐adjusted vegetation heights per each column	Hardiman, Bohrer, et al. (2013)	PCL, TLS
Height^2	σH	m	Standard deviation of column mean leaf height	Hardiman, Bohrer, et al. (2013)	PCL, TLS
Root mean square height	H rms	M	The root mean square of column mean leaf height		PCL, TLS
Mean outer canopy height	MOCH	m	Mean of the column maximum canopy height	Parker et al. (2004)	PCL, TLS
Maximum canopy height	H max	m	Maximum canopy height	Hardiman et al. (2011)	PCL, TLS
Arrangement
Clumping index	Ω		Degree of foliar clumping	Hardiman, Bohrer, et al. (2013) and Zhao et al. (2012)	PCL
Canopy porosity	P C	Ratio	Ratio of bins with no leaf area to total bins	Hardiman, Bohrer, et al. (2013), Loeffler et al. (1992) and Zhu et al. (2003)	PCL
Cover and openness
Deep gaps	DG	Count	No. of columns with no LiDAR returns per metre of transect		PCL
Deep gap fraction	DGF	Ratio	Total number of deep gaps divided by length of transect		PCL
Gap fraction	Θ	Ratio	Transect mean of column ratio of sky hits relative to total leaf returns	Chen et al. (2005), Hardiman, Bohrer, et al. (2013), and Zhao et al. (2012)	PCL
Cover fraction	CF	Ratio	Transect mean of column ratio of canopy hits relative to total leaf returns	Hardiman, Bohrer, et al. (2013)	PCL
Heterogeneity
Canopy rugosity	R C	m	Transect variability of column variability of leaf density	Hardiman, Bohrer, et al. (2013) and Hardiman et al. (2011)	PCL, TLS
Top rugosity	R T	m	Transect variability of column maximum canopy height	Hardiman, Bohrer, et al. (2013) and Parker et al. (2004)	PCL
Rumple		Ratio	Ratio of the outer canopy surface to the ground surface	Kane et al. (2008, 2010) and Parker et al. (2004)	PCL
Mean of vertical SD	meanStd	m	Transect mean of column variability of mean leaf height	Hardiman, Bohrer, et al. (2013)	PCL
SD of vertical SD	StdStd	m	Standard deviation column variability of mean leaf height	Hardiman, Bohrer, et al. (2013)	PCL
Effective number of layers (ENL)	ENL	Count	A measure of occupation of 1 m wide layers by vegetation relative to total space occupation in a stand	Ehbercht et al. (2016)	PCL

Novel LiDAR methods are already enhancing the ways in which ecologists quantify, view, and characterize forest canopy structure (Eitel et al., 2016). Once made more broadly accessible, CSC may transform understanding of structure‐function relationships fundamental to contemporary ecology. LiDAR derived data describe the spatial two‐ or three‐dimensional (2‐D or 3‐D) location of vegetation elements and have been used to estimate ecosystem structural elements such as leaf area and density (Béland, Widlowski, Fournier, Côté, & Verstraete, 2011), forest canopy gap fraction (Danson, Hetherington, Morsdorf, Koetz, & Allgower, 2007; Jupp et al., 2008; Strahler et al., 2008), vegetation phenology (Calders et al., 2015; Sankey, Law, Breshears, Munson, & Webb, 2013), canopy moisture content (Gaulton, Danson, Ramirez, & Gunawan, 2013), foliar traits (Eitel, Vierling, & Long, 2010) and above‐ground biomass (Calders et al., 2015; Greaves et al., 2015; Stovall, Vorster, Anderson, Evangelista, & Shugart, 2017). LiDAR has also been used for more novel, functionally expressive descriptors of structure such as canopy rugosity, top rugosity, rumple, mean outer canopy height, and the effective number of layers (Ehbrecht, Schall, Ammer, & Seidel, 2017; Hardiman et al., 2011; Parker, Harding, & Berger, 2004). CSC metrics are useful to ecologists as they provide functionally meaningful and scalable information about structure–function relationships in ecosystems via terrestrial, air‐borne, and space‐borne LiDAR platforms (Asner & Mascaro, 2014; Atkins, Bohrer, et al., 2018; Atkins, Fahey, et al., 2018; Ehbrecht et al., 2017; Fahey, Fotis, & Woods, 2015; Fotis & Curtis, 2017; Hardiman, Bohrer, Gough, & Curtis, 2013; Hardiman et al., 2011; Hardiman, Gough, et al., 2013; LaRue et al., 2018; Lefsky, Cohen, Parker, & Harding, 2002; Lefsky, Harding, Cohen, Parker, & Shugart, 1999). Multidimensional, spatially integrated CSC measures that combine information about 2‐D and 3‐D structure may thus offer an advance over classical 2‐D structural variables, such as leaf area index (LAI), by enhancing the prediction, interpretation, and scaling of ecosystem functions (Gough, Curtis, Hardiman, Scheuermann, & Bond‐Lamberty, 2016; Gough, Vogel, Hardiman, & Curtis, 2010; Hardiman et al., 2011).

Though LiDAR approaches offer unprecedented possibilities for characterizing ecosystem structure, three challenges presently limit the ubiquitous use of this technology by the ecological community. First, a robust taxonomy is needed to guide the standardization of canopy structure terminology, and in turn, its mathematical derivation. Previous work has defined individual or small suites of CSC parameters (Fahey et al., 2015; Hardiman, Bohrer, et al., 2013; Hardiman et al., 2011; Parker et al., 2004); here, we detail a taxonomy of canopy structural characteristics using CSC and provide explicit, transparent, and detailed descriptions of their calculation in the supplementary material (see Supporting Information Appendix S1). Second, analytical software for deriving CSC metrics is limited and often proprietary. A final related challenge is that LiDAR measurements produce orders of magnitude more data than conventional canopy sampling approaches, thus requiring new, computationally efficient processing tools. For example, while optical approaches such as hemispherical imaging produce megabytes of data, a single terrestrial LiDAR scan may yield upwards of gigabytes of data, creating new challenges for data processing and interpretation. More tractable, transparent, and openly available data processing methods will make this powerful technology more accessible, useful, and practical to users not trained in remote sensing, while also providing a foundation upon which to further our ability to quantify ecosystem structure. To address these issues, we present forestr, an r package for calculating CSC metrics and graphics from terrestrial LiDAR (CRAN; https://cran.r-project.org/web/packages/forestr/index.html).

2 LIDAR DATA SOURCES AND NORMALIZATION

Terrestrial LiDAR data can be acquired from commercially available 2‐D (i.e., portable canopy LiDAR, PCL) and 3‐D terrestrial LiDAR scanners (TLS). Data from PCL and TLS systems can be visualized as “point clouds,” in which each LiDAR return corresponds to a data point with an x, y, z position in space (or in the case of PCL, an x, z position in space) (Figure 1). All CSC metrics calculated in the forestr package are based on the distribution of vegetation elements in space and are derived directly from the x, z, or x, y, z position of LiDAR hit density expressed as vegetation area index (VAI) (i.e., vegetation density). forestr generates canopy hit grids, 2‐D plots of horizontal and vertical distribution of VAI (Figure 2b) as well as canopy vegetation profiles (Figure 3).

Figure 1

Panels (a–c) show the progression for portable canopy LiDAR (PCL) from data collection (a) through preprocessing (b) to the normalized hit‐grid, or matrix of VAI (c) from which higher‐order statistics are calculated. Panels (d–f) show progression for terrestrial scanning LiDAR from data collection (d) to voxelization based on the 3‐D point cloud (e) to pixelated hit grids of VAI, sliced from the point cloud. The dataset presented is from a mixed vegetation forest in Virginia, outlined further in Supporting Information Appendix S2. Tree images from IAN/UMCES Symbol and Image Libraries and are for conceptual representation of vegetation position only (ian.umces.edu/imagelibrary/)

Figure 2

Comparison of a side‐profile of a red pine (Pinus resinosa) plantation in Michigan (a) from a picture taken with a standard DSLR camera with a canopy hit‐grid (b) derived from a single PCL transect. The distribution of VAI, shown in (b) corresponds with the actual canopy in (a)

Calculating CSC metrics from terrestrial LiDAR requires the normalization of raw point‐cloud data to account for occlusion and saturation, problems ubiquitous to all optical canopy mensuration methods of canopy mensuration. PCL data are normalized for light attenuation and occlusion, using the Beer–Lambert Law of light attenuation (Beer, 1852; Lambert, 1760) using the formulation for LiDAR measurements from Richardson, Moskal, and Kim (2009). Unsaturated areas of the canopy (i.e., area of the canopy where the PCL is able to detect sky) do not require normalization, while saturated areas of the canopy (i.e., areas where the PCL does not detect sky) are corrected based on maximum VAI (Supporting Information Appendix S1). Custom‐built PCL units are user‐mounted, upward facing, single‐return LiDAR systems that create 2‐D undercanopy profiles along sampling transects (Hardiman, Bohrer, et al., 2013; Hardiman et al., 2011). A full description and use of PCL is outlined in Parker et al. (2004). As an example, we show data from a red pine plantation stand in northern Michigan, notable for the distinct canopy layer with virtually no understory vegetation, allowing for clear canopy delineation. This data file can be found in the forestr GitHub directory, or directly at the URL: https://raw.githubusercontent.com/atkinsjeff/forestr/master/data-raw/red_pine_plain1.CSV. A complete worked example of PCL data is in Supporting Information Appendix S2, and additional examples are included in vignettes included the package and in readme files found in the GitHub repository.

Figure 3

PAVD profile showing the proportional density of vegetation distributed across the red pine transect (same as for Figure 2). The distinct lack of subcanopy is well demonstrated in the PAVD profile. At left (a), the spline curve includes the histogram, while at right (b) the histogram is omitted. See Supporting Information Appendix S1 for more details

Increasingly popular, off‐the‐shelf TLS systems collect spherically projected images from stationary scan locations. Occlusion of vegetation is minimized when multiple scan locations are aligned and combined with artificial registration targets (Cifuentes, Van der Zande, Salas, Farifteh, & Coppin, 2014). TLS data are commonly converted into x, y, z or ASCII format with each row representing the Cartesian coordinates and return intensity of a single LiDAR return. TLS data require corrections based on topography and scan density, as outlined in Supporting Information Appendix S1. A worked example using 3‐D TLS data can be found in Supporting Information Appendix S2, in which a slice from a TLS scan of a mixed hardwood forest in Virginia is analysed. These data are included in the forstr package and in the GitHub repository and in the TLS vignette included in forestr.

However, 3‐D TLS systems differ notably from PCL and airborne LiDAR scanning (ALS) systems in how they “see” the canopy. TLS systems provide orders of magnitude greater spatial resolution than PCL and ALS systems, but variations in the vertical distribution of leaf angle introduces issues with complex and nonuniform occlusion effects in multiple zenith angles rather than single nadir point of view typical of PCL and ALS acquisitions (Jupp et al., 2008). Multiangle TLS occlusion is minimized with standardized sampling schemes (Wilkes et al., 2017) and by stitching together multiple scan locations for a more complete 3‐D representation of the upper canopy. A distinct advantage to the aggregation approach we have outlined is the creation of a common analytical framework across TLS and PCL with strong potential to apply to ALS systems (LaRue et al., 2018). The approach we outline below is not meant to supplant existing analytical frameworks for any format of TLS or ALS, but rather to present a framework to derive CSC metrics of interest. A taxonomy of canopy structural complexity.

Canopy structural complexity metrics distill whole‐system complexity into descriptors of ecosystem structure. Here, we present a taxonomy of CSC in five categories (Table 1), with detailed mathematical derivations found in Supporting Information Appendix S1. Not all CSC metrics are as yet available for both PCL and TLS via forestr (see Table 1), though efforts are underway to expand package capabilities.

1. Area and Density metrics describe the number of leaf or vegetation surface area layers overlaying the ground surface area and are therefore dimensionless. These include leaf area and vegetation area indexes (LAI and VAI, respectively). LAI varies through space and time and is a crucial structural variable in modelling interactions between the land surface and the atmosphere through effects on canopy light interception, aerodynamic drag (Maurer, Bohrer, Kenny, & Ivanov, 2015; Schaudt & Dickinson, 2000; Weligepolage, Gieske, & Su, 2012; Zhao et al., 2012) and surface resistance to heat and mass transport, and, consequently, photosynthesis (Béland et al., 2011; Sellers et al., 1997). Because the discrimination of leaves from nonleaf vegetation elements in the canopy (branches, fruiting bodies, etc.) is difficult using LiDAR alone, we use the term VAI, which includes all vegetative tissues. An advantage to using LiDAR to estimate VAI is its ability to locate the relative position and density of vegetation within a canopy, and to derive characteristics that describe where maximum VAI occurs in the canopy (where VAI_max is the maximum VAI of any x, z position in the canopy and VAI_peak is the average of maximum VAI across each x‐column in a transect) or the mean height at which maximum VAI occurs across a horizontal transect, VAI_mode.

2. Height metrics summarize the vertical patterns of vegetation distribution through the canopy, including the above‐ground elevation of vegetation that forms the outer (uppermost) canopy surface. Accurate measures of tree and canopy height are important for estimating wood production (Jenkins, Birdsey, & Pan, 2001), light interception (King, 1990), canopy hydraulic conductance (McDowell et al., 2002), and biodiversity (Goetz, Steinberg, Dubayah, & Blair, 2007). This CSC grouping includes mean leaf height (H), maximum canopy height (H_max), and mean outer canopy height (MOCH) as well as other related measures.

3. Canopy Cover and Openness metrics describe openness of the outer surface of the canopy as a two dimensional (x, y) horizontal plane. This is an important distinction from metrics in the canopy arrangement grouping (below) that are calculated in two dimensions from the distribution of VAI along the horizontal (x) and the vertical (z) axes. Cover and openness metrics include gap fraction (θ), cover fraction (CF), and deep gap fraction (DGF). Here, θ is a measure of the canopy gap area (i.e., fraction of the horizontal area not occupied by vegetation) and is a well‐established forest structural metric used to infer LAI following the Beer–Lambert Law's assumption that the attenuation of light from the top to bottom of the canopy is a function of leaf area (i.e., LAI) (Martens, Ustin, & Rousseau, 1993). Both CF and DGF are related to θ as CF is the inverse of θ. We define a “deep gap” or DG, as a vertical, 1 m wide column in which canopy elements are not present (i.e., detected via LiDAR)—column width in forestr is mutable, acknowledging that the grid size of interest to a user may be scale, system, or instrument dependent. DGF is the ratio of the number of deep gaps to transect length.

4. Canopy Arrangement metrics are derived from second‐order structural statistics of horizontal and vertical distribution of vegetation. As such, canopy arrangement measures summarize multidimensional, 2‐D or 3‐D, relationships among vegetation elements in canopy space. While the 3‐D arrangement of the canopy can be used directly to study specific changes to canopy structure, usually as a result of disturbance (Fotis et al., 2018; Rodríguez‐Ronderos et al., 2016). Clumping index (Ω) is a measure of how grouped vegetation is relative to a random distribution that describes the relationship between canopy gap fraction and VAI—with a more clumped canopy having a higher gap fraction for the same measure of VAI (Chen, Menges, & Leblanc, 2005) and in turn is useful in describing light interception/transmission through the canopy. Canopy porosity (P_C) is the ratio of filled to void space in the canopy along the x, z vertical plane of a transect and affects how wind, light, energy, and water move through a canopy (Loeffler, Gordon, & Gillespie, 1992; Zhu, Matsuzaki, & Gonda, 2003).

5. Canopy Heterogeneity metrics describe variation in the heterogeneity of vegetation position in canopy space. Canopy rugosity (R_C) describes the horizontal and vertical variance of VAI throughout the canopy. R_C has been shown to be stronger than VAI as a predictor of ecosystem‐scale light and nitrogen use efficiency (LUE, NUE respectively) and primary production (Hardiman et al., 2011). R_C has also been shown to continue increasing as a forest ages, even after leaf area saturates (Hardiman, Bohrer, et al., 2013; Hardiman, Gough, et al., 2013), making it a useful descriptor of canopy structural change in mature forests with stable LAI. Top rugosity (R_T), or surface rugosity, is the standard deviation of maximum canopy height (i.e., final LiDAR returns) and has been used to characterize differences in canopy heterogeneity during forest stand development (Parker et al., 2004; Parker & Russ, 2004). Rumple is the ratio of the outer canopy surface to the ground and correlates with canopy closure, tree density and mean diameter at breast height (DBH) (Kane et al., 2010), and varies with stand plant community structure and age (Kane, Varner, & Hiers, 2008; Parker et al., 2004). Effective number of layers (ENL), a descriptor of vertical structure based on the proportion of filled 1 m² bins of canopy throughout the vertical axis of the canopy, strongly correlates with stand age, showing a logarithmic increase with advancing stand age (Ehbrecht, Schall, Juchheim, Ammer, & Seidel, 2016). Ehbrecht et al. (2017) uses ENL derived from TLS, along with fractal dimension, to calculate the stand structural complexity index (SSCI), an index correlated with tree spacing and size differentiation with applications in forest management.

3 DISCUSSION

Canopy structural complexity metrics provide a detailed whole‐system view of structure with the potential for broad and far‐reaching applications in ecology. There is substantial evidence that open‐source solutions foster and catalyse ecological research (e.g., AmeriFlux, PalEON, and the abundance of ecology‐based r packages) and are particularly advantageous for applications that involve large datasets and multiple‐collaborators. Previously, the algorithms to calculate these CSC metrics have been dispersed across the literature, proprietary, or finely tuned to a specific site or single ecosystem type—all limitations to access, transparency, and transferability. Open‐source data processing algorithms invite innovation, and dramatically lower the effort required to utilize emerging technologies, facilitating otherwise intractable or proprietary data analysis that can lead to significant advances. Our goal is to accelerate the adoption of ground‐based LiDAR methods by providing a standardized, quantitatively defined suite of functionally meaningful CSC metrics and an open‐source, transparent package, forestr, to calculate them.

With structure–function relationships, a ubiquitous ecological theme that underlies numerous theories and observations, the novel application of LiDAR‐based CSC measures to fundamental and applied ecosystem science could fill critical knowledge gaps requiring quantitative understanding of structural complexity. Though the research areas that could benefit are many, we suggest three may particularly profit. First, mounting evidence from observational studies suggests that in many cases structural complexity, rather than broadly used indices of biological diversity, are superior predictors of an array of ecosystem functions, including primary production and animal species abundance (Dănescu, Albrecht, & Bauhus, 2016; Malumbres‐Olarte, Vink, Ross, Cruickshank, & Paterson, 2013; Silva Pedro, Rammer, & Seidl, 2017; Stevens & Tello, 2011). However, studies evaluating the effect of structural complexity on ecosystem functioning generally incorporate semi‐quantitative or descriptive, rather than quantitative, measures of CSC in their analysis. Secondly, empirical understanding and model representation of canopy light distribution and energy balance stands to benefit greatly from quantitative assessments of 2‐ and 3‐D structural complexity. Assumptions about how vegetation arrangement affects light and energy balance form the mathematical foundation of ecosystem to Earth system models that simulate biogeochemical cycling, albedo, and other energy‐sensitive processes, and, yet, models incorporating spatially explicit representation of canopy structure lack multidimensional observational data for parameterization and validation (Bonan, Levis, Sitch, Vertenstein, & Oleson, 2003; Medvigy, Wofsy, Munger, Hollinger, & Moorcroft, 2009; Vierling et al., 2008). Lastly, quantitative measures of structural complexity could aid in identifying vegetation arrangements that enhance resilience and stability following disturbance and extreme weather events (Stuart‐Haëntjens, Curtis, Fahey, Vogel, & Gough, 2015), and restore ecosystem functions to predisturbance levels (Stanturf, Palik, & Dumroese, 2014). Advances in this research area would greatly improve foundational understanding of CSC–function relationships, and inform ecosystem management (Fahey et al., 2018).

Open‐source solutions such as the R and Python programming languages, along with community‐contributed packages for these languages including forestr (Atkins, Bohrer, et al., 2018; Atkins, Fahey, et al., 2018), lidR (Roussel, Caspersen, Béland, Thomas, & Achim, 2017), rLiDAR (Silva Pedro et al., 2017), and VoxR (Lecigne, Delagrange, & Messier, 2014) create new opportunities for exploration of structure‐function relationships not only from terrestrial LiDAR, but from air‐ and space‐borne LiDAR as well. We welcome and invite additions, revisions, expansions, and innovations from the community to forestr to further catalyse research in this area. Work is needed to expand that capability of the package to analyse terrestrial LiDAR and potential to derive CSC metrics from airborne LiDAR as well—though issues of point cloud density and scale are important considerations.

The full development* version of forestr is available on GitHub: https://github.com/atkinsjeff/forestr.

ACKNOWLEDGEMENTS

This work was supported by U.S. National Science Foundation Emerging Frontiers Awards 1550657 (Virginia Commonwealth University), 1550650 (University of Connecticut), and 1550639 (Purdue University), NSF Hydrology Award 1521238 (Ohio State University), and by the U.S. Department of Energy's Office of Science, Office of Biological and Environmental Research, Terrestrial Ecosystem Sciences program under award DE‐SC0007041 and DE‐SC0006708, and the Ameriflux Management project under Flux Core Site agreement 7096915 through Lawrence Berkeley National Laboratory. Thanks to Chris Black for some last minute testing.

AUTHORS’ CONTRIBUTIONS

J.W.A. wrote and prepared the manuscript and served as chief author of forestr. G.B., T.H.M. and B.S.H. developed algorithms that forestr is based on. J.W.A., B.S.H., R.T.F. and C.M.G. developed the theoretical framework of CSC, with input from the other authors. A.E.L.S. and N.Z. wrote key sections of forestr. All authors made significant contributions to the preparation, planning, and revision of the manuscript and contributed intellectually and/or practically to the development of the forestr.

DATA ACCESSIBILITY

Both an archived version of forestr used in this manuscript (https://doi.org/10.5281/zenodo.1305095) as well as the most‐up‐to‐date development version (https://github.com/atkinsjeff/forestr) are freely available online.