Effect of scan angle on ALS metrics and area-based predictions of forest attributes for balsam fir dominated stands


 In this study, we assessed the effect of airborne laser scanning (ALS) scan angle on point cloud metrics and the estimation of forest attributes in balsam fir (Abies balsamea (L.) Mill.) dominated forests of western Newfoundland, Canada. We collected calibration data from ground plot locations representing varying scan angles from two flight lines: within 4° of nadir in one flight line, and either 11–20° from nadir (low scan angle plots: L), or 21–30° from nadir (high scan angle plots: H) in an adjacent flight line. We computed three sets of ALS point cloud metrics for each ground plot using ALS data from: individual flight lines (near-nadir and off-nadir) and data from all available flight lines (up to 4) combined (aggregated, as commonly used in an operational inventory context). We generated three sets of models for each of the L and H plots using the ALS metric sets, and applied the models to independent validation data. We analysed the effect of scan angle on both the ALS metrics and performance statistics for area-based models generated using the L and H datasets. Our results demonstrate that off-nadir scan angles significantly affected (P < 0.05) specific metrics from both L (i.e. coefficient of variation (COVAR)) and H (i.e. maximum height, 95th percentile of height, mean height) plots, although the effects were trivial (mean absolute differences were ≤ 0.01 for COVAR and < 0.3 m for the height metrics). Forest attribute predictions using these and other metrics were also significantly affected (P < 0.05), namely gross merchantable volume (GMV), total volume (TVOL) and aboveground tree biomass (AGB) from L; and Lorey’s mean height (HGT), mean diameter at breast height (DBH), and GMV from H. We further demonstrated that combining ALS data from all available flight lines significantly increased errors for the predictions of HGT, GMV, and TVOL using L, and significantly reduced errors of HGT using H when compared to errors resulting from models developed with near-nadir data. While the differences in prediction errors were significant, they were small, with differences in mean absolute prediction errors all <1.3 per cent. Based on our results, we concluded that the effects of large scan angles, up to 30° off-nadir, on area-based forest attribute predictions were minimal in this study, which used ALS metrics calculated from ALS returns with a height above ground >2 m for balsam fir-dominated forests. This result may provide for operational efficiencies in implementing enhanced forest inventories in this particular forest environment.


Introduction
Over the last two decades, airborne laser scanning (ALS) has become an important technology for acquiring data in support of forest management in many jurisdictions (Hyyppä et al. 2008;Naesset 2014;Reutebuch et al. 2005;White et al. 2016). These data are being used operationally over large continuous areas due in part to the decreasing costs associated with data acquisition. These data provide precise and accurate measurements of tree heights and detailed characterizations of the forest's vertical structure with three-dimensional (3D) point clouds (Lim et al. 2003). Statistics generated from the ALS point cloud (ALS Forestry metrics) are used to describe the configuration of returned laser energy through the canopy's vertical profile. These metrics are subsequently used as predictor variables typically in conjunction with ground plot measurements to model forest inventory attributes with an area-based approach (ABA) (Naesset 2014;White et al. 2013White et al. , 2017. ALS acquisition parameters can determine the quality and usability of the ALS data for various applications, and ultimately can influence the derived forest attribute information (Hopkinson 2007;Montaghi 2013). Acquisition parameters directly influence the costs of ALS surveys and are therefore pragmatic considerations for forest managers (Reutebuch et al. 2005). As survey costs for ALS data are primarily a function of aircraft flight time, parameters that can be adjusted to increase spatial coverage and reduce flight time are of particular interest (Hopkinson et al. 2013). For example, comparable area coverage can be achieved either by increasing acquisition altitude using a narrower scan angle, or via a lower acquisition altitude and a wider scan angle (Keränen et al. 2016). However, there are complex interactions between acquisition parameters, as well as between the laser pulses and the nature and configuration of the forest target, that complicate investigations into these parameters (Disney et al. 2010;. For example, the influence of scan angle is linked to the penetration of the laser pulse into the canopy (Montaghi 2013). Holmgren et al. (2003a) observed an increase in canopy crown area visible to a laser pulse with increasing scan angles. The path length travelled by a laser pulse through the forest canopy therefore increases with larger scan angles, increasing the probability of canopy interception (Goodwin et al. 2007) and potentially introducing biases in derived ALS metrics (Roussel et al. 2018).
The ALS acquisition parameter scan angle has been the subject of extensive research in a forestry context (Table 1). The scan angle is defined as the angle at which the laser beam is directed away from the focal plane of the instrument (nadir) (Gatziolis and Andersen 2008). Acquisition guidelines for forest applications have been informed by this science (Gatziolis and Andersen 2008;Laes et al. 2008;White et al. 2013), although yet, no consensus can be drawn from studies attempting to quantify the effect of this parameter on ALS derived metrics and models (Roussel et al. 2018). Further, as technology continues to evolve rapidly, revisiting the state of knowledge associated with these parameters is warranted.
General statements about the influence of bias from scan angle on the accuracy of forest attribute predictions is highly dependent on which ALS metrics are used (Roussel et al. 2018). Montaghi (2013) demonstrated that the vegetation ratio and understory ratio from scanning angles >10 • off-nadir were significantly different from those derived from nadir, and hence would not be stable predictors in an ABA. Vegetation ratio, otherwise also referred to as canopy cover, is determined as the number of ALS returns above a certain height threshold (commonly 2 m above ground) divided by all returns, and is a measure of vertical vegetation density. Conversely, the understory ratio is calculated as the total number of returns below a specified height threshold (e.g. 2 m) that are not classified as ground, divided by all returns (including ground returns). Given that the calculation of these metrics includes ground returns, and as wider scan angles (i.e. > 15 • off-nadir) decrease the probability of obtaining returns from the ground (Ahokas et al. 2005) while also increasing the probability of vegetation returns (Hopkinson et al. 2005;Montaghi 2013), it is understandable that the vegetation and understory ratio metrics have been found to be unstable with increasing scan angles. Notably, it is common to exclude returns below a specified height threshold in calculating ALS metrics used in an ABA. For example, most metrics from an ABA excluding returns below a threshold value of 2 m have been demonstrated to be relatively unaffected by high scanning angles of up to 20 • offnadir for boreal and hemi-boreal forests of Sweden . However, it is not the case for density metrics and specific structural descriptor metrics when derived using all returns, including ground returns (Montaghi 2013). Moreover, Naesset (1997) found no significant effect from off-nadir scan angles ranging up to 20 • in using ALS metrics to determine mean tree height in Norway spruce (Picea abies Karst.) and Scots pine (Pinus sylvestris L.) dominated forests of southeast Norway.
The aforementioned studies provide substantial insight into the influence of various acquisition parameters on ALS data point distributions, derived metrics, and forest attribute predictions across a range of forest environments (Table 1). However, the majority of studies assessed the effects of a limited scan angle range and often used simulated forest environments and/or simulated ALS data (e.g. Holmgren et al. 2003a;Lovell et al. 2005;Disney et al. 2010;Yang et al. 2011;Qin et al. 2017). Commonly, the range of scan angles considered was limited to a maximum of 20 • off-nadir (e.g. Naesset 1997;Lovell et al. 2005;Leiterer et al. 2015;Keränen et al. 2016;) and focused on the impacts of scan angle on ALS point cloud metrics and not on forest attribute predictions derived using these metrics (e.g. Holmgren et al. 2003a;Ahokas et al. 2005;Bater et al. 2011;Montaghi 2013;Roussel et al. , 2018Dayal et al. 2020). The overall goal of this study was to investigate the effect of ALS acquisition scan angles up to 30 • off-nadir on ALS metrics and forest attribute predictions obtained from an ABA applied in a natural forest environment. Based on past research, we first hypothesized that larger scan angles would significantly affect some ALS metrics commonly used in an ABA. We tested this hypothesis by assessing differences in ALS metric values developed using ALS data acquired with near-nadir (nn) and off-nadir (on) scan angles, and also assessed ALS metric values when data from all available flight lines were combined (i.e. aggregated; agg) as commonly used in operational ALS-derived forest inventories. Our second hypothesis was that prediction errors for ABA models of forest attributes developed with on scan angles would differ from those developed with nn scan angles. We tested this hypothesis by comparing performance statistics of ABA models developed using ALS metrics derived with the different scan angle configurations. We developed the ABA models from single flight line metrics (nn or on), as well as from aggregated flight line metrics (agg), in order to assess if systematic bias or uncertainty would be offset when all flight lines were aggregated. We assumed that differences observed for derived ALS metrics or ABA model outcomes under these extreme-case controlled scenarios (nn or on) would inherently impact these metrics and models, relative to a scenario when there are a mix of scan angles, which is commonly the case when ALS acquisitions are used operationally in support of forest inventory applications. Quantifying the influence of scan angle on Effect of scan angle on ALS metrics and ABA predictions Riparian ecosystem (up to 33 different species) Max height and higher height percentiles were relatively more stable than the lower percentiles. Gap fraction and rumple index were affected more by increasing scan angle than sd.

Figure 1
Overview of the study using low (L) and high (H) scan angle plots combined with ALS metrics derived from near-nadir (nn), off-nadir (on), and aggregated (agg) flight line data to create model sets: MS_L nn , MS_L on , MS_L agg , MS_H nn , MS_H on , MS_H agg . The model sets are used to make predictions on independent validation data.
area-based inventory model outcomes in this forest environment can inform operational ALS-based forest inventory programs.

Material and methods
Figure 1 provides an overview of the methodological approach of the study. We collected ground plot data to develop area-based models of six forest inventory attributes: Lorey's mean height (HGT), diameter at breast height (DBH), basal area (BA), total volume (TVOL), gross merchantable volume (GMV), and aboveground tree biomass (AGB). We selected calibration plot locations to represent varying scan angles from two flight lines: within 4 • of nadir in one flight line, and either 11-20 • from nadir (low scan angle plots: L), or 21-30 • from nadir (high scan angle plots: H) in the second flight line. We computed three sets of ALS point cloud metrics for each ground plot using points from: each flight line (nn and on) and all flight lines combined (agg). We generated three sets of models for each of the L and H plots using the ALS metrics sets, and applied the models to independent validation data. We analysed the effect of scan angle on both the ALS metrics (Experiment 1) and model performance statistics (Experiment 2) from both the L and H datasets.

Study area
Centred at 48.77 • N and 58.19 • W, the study area is approximately 950 km 2 and is located in western Newfoundland, Canada ( Figure 2). Located in the eastern extent of the Boreal Shield Ecozone (Marshall et al. 1999), the landscape has a gently undulating to hilly surface, segmented by numerous ponds, lakes and streams. Elevation ranges from 28 m to 638 m above sea level. Forested land is naturally fragmented with bog, barren and ponds. The area is characterized by balsam fir (Abies balsamea (L.) Mill.), black spruce (Picea mariana (Mill.) BSP), eastern larch (Larix laricina (Du Roi) K. Koch), white birch (Betula papyrifera Marsh.), white spruce (Picea glauca (Moench) Voss) and yellow birch (Betula alleghaniensis Britton). The dominant species by volume is balsam fir, which represents more than 90 per cent of the growing stock. Growth conditions are favourable due to the orthic and gleyed podzols; however, the growth season is relatively short from mid-June to the end of September. The forest understory varies with stand density and age, soil conditions, status of regeneration, and silvicultural treatments such as pre-commercial thinning. Understory vegetation can be composed of tree saplings and seedlings, ferns (e.g. Dryopteris carthusiana (Vill.) HP Fuchs) and to a lesser extent ericaceous shrubs (e.g. Kalmia angustifolia L., Rhododendron groenlandicum (Oeder) Kron and Judd, Vaccinium spp.).

ALS data
Full waveform ALS data were acquired for the extent of the study area in 2016 (August 15 through September 24) using a RIEGL LMS-Q680i sensor. This sensor has a beam divergence of 0.5 mrad, yielding a footprint of approximately 0.5 m. Flight altitude averaged 1000 m above ground level with an approximate aircraft speed of 100 knots. Data were collected with a field of view of 60 • and a minimum 50 per cent overlap between flight trajectories. The ALS acquisition was extended beyond all study area borders to ensure necessary over-edge coverage. A total of 153 flight lines were acquired in a series of parallel flight lines, oriented in a southwest to northeast direction ( Figure 2) and distributed to accommodate changes in ground elevation. Less than 2 per cent of the study area was sampled only once (i.e. covered by one flight line) due to variability in terrain, while the remainder of the study area was covered by at least two flight lines. The waveforms were discretized by the data provider (Leading Edge Geomatics, Canada) using the Gaussian pulse estimation computation method (Jutzi and Stilla 2006). Depending on the individual pulse's target and associated returned energy, the processing yielded a maximum of four discretized returns from each pulse.
Effect of scan angle on ALS metrics and ABA predictions Not excluding waterbodies, we calculated the resulting average point density to be 7.3 points m −2 with a standard deviation of 2.4 points m −2 . ALS returns were classified according to standard LAS specification classes (ASPRS 2013) by the data provider and delivered in LAS 1.2 format.

Ground plot sample designs
We collected two independent datasets of ground plots for calibrating and validating models of forest attributes within the study area (Figure 1), each with their respective sample design.
The calibration data were collected in 2018 to represent low scan angle plots (up to 20 • , the extent examined by most past studies; dataset L) and high scan angle plots (up to 30 • , a novelty of our study; dataset H). We selected potential plot locations using a stratified random sampling design guided by ALS predictions of total volume (further described in Section 2.6 of Luther et al. 2019). Of the five forest attributes mapped, total volume (predicted with regression; R 2 = 0.91; RMSD% = 17.57 per cent; Bias% = −6.27 per cent) best characterized the complete 3D structure of the forest as the computation of total volume was based on all trees and not limited to merchantable trees having a diameter at breast height (DBH) ≥ 9 cm. In order to capture the full range of variability in total volume (3.6-439.9 m 3 ha −1 ), we divided the range of volume values into 20 equal strata. We randomly selected two plot locations per strata, one from each scan angle group, L and H. We only established plots at locations where ALS data from two different flight lines were available such that the first was scanned from near nadir (average absolute scan angle of 0 • to 4 • ), and the second was scanned with an absolute off-nadir average scan angle ranging from 11 • to 19 • for dataset L, and 21 • to 30 • for dataset H ( Figure 3). Furthermore, to ensure plots were sampled with a similar density of pulses, we only included plots that had a point density difference that was less than 1 point m −2 between the nadir and off-nadir ALS data from first returns classified as vegetation and having heights between 2 and 30 m (min. diff. = 0; max. diff. = 30.9; mean diff. = 10.3; sd diff. = 7.5 per cent relative to the greater total number of points from either nn or on). Additionally, we used photo-interpreted species composition (delineated from 25 per cent classes of basal area) to restrict sample selection to balsam fir dominated stands. The field sampling resulted in 40 balsam fir dominated plots, 20 for each of the L and H calibration datasets used in both experiments. Through this sample design, we targeted extremecase scenarios with respect to scan angle in order to test our hypotheses for both L and H (first and second flight line, Figure 4). We collected the ground plot data used for validation in 2016 and 2017, following a structurally-guided sampling approach without consideration of scanning angles. This design yielded a more heterogeneous mix of angles in the agg validation ALS data than for agg from both L and H (aggregated flight lines, Figure 4) and is typical of an operational ABA scenario. To guide our design, we used principal components of ALS metrics as a basis for stratification. We constructed a covariance matrix using a suite of 29 ALS metrics consisting of height, density and structural statistics and submitted it to a principal component analysis (PCA) (Frazer et al. 2011;White et al. 2017). As for the calibration data, we restricted the analysis to areas dominated by balsam fir according to photo-interpreted forest inventory stand polygons. We used the first two principal components extracted as a basis for stratification as they accounted for 82.8 per cent of the total variance found within the ALS data. The first component explained 67.9 per cent of the total variance and was positively correlated (r = 0.98) with median ALS canopy height as expected per established guidelines (White et al. 2017). Similarly, the second component accounted for 14.8 per cent of the total variance, and was positively correlated (r = 0.80) with the coefficient of variation of ALS canopy height. We selected plot locations by dividing the range of values for each PCA component into 10 equal strata and randomly selecting a sample plot location from each combination of PCA strata. In total, we sampled 41 balsam fir dominated plots and used these as independent validation data for our second experiment.

Ground plot positioning
We positioned all ground plots used in our study using a Trimble GeoExplorer 6000 series GeoXH™ decimeter system with Floodlight satellite shadow reduction technology in order to maximize under canopy GPS accuracy (Trimble Navigation Limited 2011). In order to secure proper initialization, the unit was receiving positions from a minimum of four satellites for a minimum of 5 minutes prior to data capture. We surveyed plot centre locations by averaging 1000 GPS positions collected during a time interval of 25-40 minutes, and post-processed these for differential correction. Base station observation data for post-processing were obtained from the closest reference station which was within 60 kilometres from all plot locations. We observed a mean vertical precision of 1.1 m and 1.0 m, a mean horizontal precision of 0.9 m and 0.9 m, and a mean standard deviation of 1.5 m and 1.2 m from the post-processing of the respective plot locations from the calibration and validation datasets, respectively. We deemed the positional errors to be less than 5 m, which has been shown to not substantially affect ALS-based predictions of forest attributes using plots ranging in size from 300 to 400 m 2 (Gobakken and Naesset 2008).

Tree measurements and forest attribute calculations
We followed plot measurement guidelines established for Canada's National Forest Inventory (NRCan 2008). We established fixed-area circular plots with 11.28 m radius (area of 400 m 2 ) using the ultrasound's horizontal distance feature of the Postex ® instrument (Haglöf Sweden AB, Långsele, Sweden). We recorded species, living status, DBH and height for all merchantable trees on all calibration plots. In addition, we recorded these same attributes on all plots for all trees with a minimum height of 1.3 m for a centred subplot of radius 3.99 m (area of 50 m 2 ). We measured diameters at 1.3 m using a diameter tape and heights using the height vertex feature of the Postex ® . We sampled validation plots with the same prescription as the calibration plots with the exception of 18 plots, where we measured heights only for a sample of trees and predicted the remainder. We predicted heights by developing species-specific relationships between DBH and height using Forestry Figure 3 Simplified schematic representing sample design for plot selection of the calibration data with: a) swath breakdown by scan angle for flight line (fl) 3, and location of b) a low scan angle plot, and c) a high scan angle plot. ALS point cloud metrics were computed for each ground plot using points from: each flight line independently (near-nadir (nn) and off-nadir (on)) and all available flight lines combined (aggregated (agg)). Note: schematic is not to scale; flight altitude was consistent for all flight lines averaging 1000 m above ground level with a minimum of 50 per cent overlap between swaths.

Figure 4
Violin plots illustrating the distribution of mean absolute scan angles obtained from first (nn, Val sfl ) and second (on) single, and aggregated (agg, Val agg ), flight line ALS data observed for the calibration (L and H) and validation datasets. Mean (point) and standard deviation (line) are illustrated in red, while the median, interquartile range, percentiles (25 th and 75 th ), minimum, maximum, and outliers are depicted in black by the overlaid boxplots.
the Gomprez function for plot-specific mixed-effects models per Mehtätalo et al. (2015). Height-diameter curves were developed with the lmfor package (Mehtätalo 2018) in the R programming environment (R Core Team 2019).
From these standard measurements, we derived a suite of structural attributes for all plots from all the live tree measurements. As the subplot was 1/8 of the area of the plot, we replicated these measurements seven times (8 repetitions in total) in order to be representative of the plot area. We computed Lorey's mean height (HGT, in m) as the weighted average of tree heights, weighted by their respective basal areas; DBH (cm), simply as the mean diameter at breast height. We calculated basal area (BA) by summing all individual merchantable tree basal areas within a plot. Similarly, we estimated gross merchantable volume (GMV, in m 3 ha −1 ), total volume (TVOL, in m 3 ha −1 ) and aboveground tree biomass (AGB, in t ha −1 ) by summing individual tree values estimated with species-specific allometric equations. Regional volume and biomass equations were available from Warren and Meades (1986). For species and cases where coefficients were not available, we used equations from Ker (1974). For AGB, we used national equations from Lambert et al. (2005). We scaled plot estimates for BA, GMV, TVOL and AGB to per hectare estimates based on plot size. The ranges of these structural forest attributes are summarized in Figure 5.

ALS plot metrics
We first processed the ALS data to generate a digital terrain model (DTM) with spatial resolutions of 1 m × 1 m using the LTK™ extension (Lim Geomatics 2016) for ArcGIS (ESRI 2016). To do so, we generated a triangular irregular network (TIN) using returns classified as ground obtained from all available flight lines and interpolated a raster surface from the TIN using natural neighbor interpolation. To avoid introducing potential noise throughout our experiments and isolate for an effect of scan angle, we normalized all ALS data (nn, on, agg) to the common DTM. We calculated individual flight line and aggregated ALS metrics for each plot, with a precision of 11 and a scale of 9, with the lidR package (Roussel and Auty 2017) in the R programming environment (R Core Team 2019). For each calibration plot of dataset L and H, we computed three sets of ALS metrics (i.e. predictor variables): i) using ALS points from a single flight line acquired at nearnadir (nn); ii) using ALS points from a second single flight line acquired off-nadir (on), and iii) using aggregated (agg) points from all available flight lines, resulting in three sets of metrics for each of the L (L nn , L on , L agg ) and H (H nn , H on , H agg ) datasets (b), c) in Figure 3). Absolute off-nadir scan angle averages ranged from 11 • to 19 • for dataset L, and 21 • to 30 • for dataset H (Figure 4). Similarly, for each validation plot used in our second experiment, we computed ALS metrics: i) from single flight line ALS data (dataset Val sfl ) and ii) from aggregated ALS data obtained from all overlapping flight lines (Val agg ) (Figure 4). The standard deviation of scan angles was higher for the validation data set compared to the calibration data set. The higher standard deviation is due to the fact that we did not target specific scan angles in the sample design for the validation data. However, since all models were applied to the same set of validation data, comparisons of the associated prediction errors are possible, regardless of the higher standard deviation of scan angles found in the validation data. As suggested by White et al. (2013), we first applied a threshold of 2 m to separate canopy returns from ground and low vegetation returns, which has been demonstrated to be appropriate for the mature boreal forest conditions of our study site (Luther et al. 2019). Further, we applied an upper threshold of 30 m in order to Forestry limit erroneous returns that exceeded the maximum tree height in the region (Government of Newfoundland and Labrador 2020). We calculated the average point densities of the first returns (i.e. pulse densities) within these thresholds from the single flight line data to be 2.9 (sd = 1.0) and 3.1 (sd = 1.1) points m −2 from the calibration and validation plot locations, respectively. The corresponding average point densities from the agg points were 6.1 (sd = 1.9) and 6.4 (sd = 1.8) points m −2 . The total number of individual flight lines contributing to agg averaged 3.1 (sd = 0.2), 2.9 (sd = 0.6), and 3.0 (sd = 0.6) flight lines for L agg , H agg , and Val agg , respectively.
We divided the metrics into four groups commonly used in area-based forest inventory approaches (White et al. 2013): canopy height, vertical structure, density, and cover metrics. The height metrics included minimum, maximum, mean, median, standard deviation and percentiles of return heights (i.e. the height below which a proportion of ALS returns are found, e.g. 95 th percentile implies that 95 per cent of ALS returns are lower than this height). The vertical structure metrics comprised statistical measures of skewness, kurtosis, coefficient of variation, vertical distribution ratio (Goetz et al. 2006) and a vertical complexity index (van Ewijk et al. 2011). We calculated the density metrics, by dividing the range of heights from ALS for each plot into 10 equal intervals and calculated the cumulative proportion of returns found in the first nine intervals per Woods et al. (2008). We computed cover metrics by first deriving a canopy height model (CHM) of 1 m × 1 m resolution where each cell was assigned to the maximum height value. Then, at 2 m height intervals, and for heights (z) up to 18 m, we returned the number cells found in the CHM with a height value > z m and divided it by the number of nonvoid cells (Penner et al. 2013). We manually selected a reduced set of metrics from each metric group by first avoiding very highly correlated metrics within each group (Pearson correlation coefficient, r > 0.95) and assessed variable importance during the initial model development. Finally, we retained 13 metrics with a mean decrease accuracy (%IncMSE) > 3 per cent for the final models (Table 2). Figure 6 illustrates the mean and standard deviation of each ALS plot metric grouped by ALS configuration (nn, on, agg) from both L and H datasets.

Forest attribute models
We modelled the relationship between the aforementioned six forest attributes and the ALS metrics obtained from the different ALS configurations (nn, on, agg) within each scan angle group (L, H) using random forest regression. The non-parametric approach is well known (White et al. 2017) and its application in ALSbased inventories is well established (e.g. Luther et al. 2019). We built random forest models (Breiman 2001) in R (R Core Team 2019) with ModelMap (Freeman and Frescino 2009). ModelMap automates the process of model building by calling upon the randomForest package (Liaw and Wiener 2002). Each random forest model consisted of 500 trees with infinite tree depth. Each tree was developed with a bootstrapped random subset of the calibration data and a random selection of predictors at each node of the tree to determine the split. We then used tuneRF to determine the optimal number of predictor variables to retain at each node (mtry) for each model. The tuneRF algorithm's default value for mtry is the number of predictors divided by three. The algorithm then searches for the optimal mtry value according to out-of-bag error estimates which varied by attribute. We evaluated the random forest models according to out-of-bag errors during model development.
To evaluate the predictive performance of the forest attribute models, we calculated the coefficient of determination (R 2 ; Equation (1)), root mean square error (RMSE, absolute and relative; Equations (2) and (3), respectively) as a measure of error spread and the average bias (absolute and relative; Equations (4) and (5), respectively): where n is the number of validation plots, y i is the observed value for plot i,ŷ i is the predicted value for plot i, andȳ is the mean of the observed variable, i.e. HGT, DBH, BA, GMV, TVOL, or AGB. We repeated the forest attribute modelling with five seeds, generated pseudorandomly, whereby the seeds influenced the selection of samples and predictors for the random forest models.

Experimental design to assess the effects of scan angle
We partitioned our analyses of scan angle effects into two experiments ( Figure 1). We first assessed whether effects of scan angle could be observed directly on the stability of the ALS metrics obtained from the different ALS configurations (nn, on, agg) within each group of calibration plots (L, H) (Experiment 1). We performed an Anderson-Darling test of normality on the metric distributions using the nortest package (Gross and Ligges 2015) in the R programming environment (R Core Team 2019). Since this test indicated that the majority of data did not fit the normal distribution, we used a nonparametric two sample (i.e. paired ALS configurations for each plot within L and H) Wilcoxon signedrank test (WSRT) (Hollander and Wolfe 1999) to assess our null hypothesis (H 0 ) that ALS metrics derived from the three ALS configurations originate from the same population. We further conducted a post-hoc power analysis for the Wilcoxon signedrank test in G * Power (Faul et al. 2013) to determine the sensitivity of our analysis. We based this analysis on accepting a 5 per cent probability of incorrectly rejecting H 0 (i.e. probability of Type I error/false positive) and similarly, accepting a 5 per cent probability of incorrectly failing to reject H 0 (i.e. probability of Type II error/false negative). We proceeded to analyse the observed difference in values using statistics of mean difference Effect of scan angle on ALS metrics and ABA predictions (MD; Equation (6)), a measure of bias, and mean absolute difference (MAD; Equation (8)). We further calculated values relative to the observed mean value for each group (MD% and MAD%; Equations (7) and (9), respectively).
where y (nn|on|agg),j is the ALS metric (y) derived from either nn, on or agg for plot j, and y (nn|agg),j is the ALS metric (y) derived from nn or agg for plot j, where n is the number of plots andȳ is the mean for each ALS metric (i.e. MAX, P95, MEAN, SKEW, COVAR, VDR, VCI, D2, D5, D8, CC2, CC6, or CC14), as derived from nn, and from on, when considering the nn vs. on and nn vs. agg comparisons and the on vs. agg comparison, respectively. In order to assess the effect of scan angle on forest attribute predictions (Experiment 2), we first made comparisons of on and agg derived random forest model performance measures with those obtained from a nn ALS configuration within each scan angle group. We assessed models developed from single flight line data (models within MS_L nn , MS_L on , MS_H nn , and MS_H on ) using the single flight line validation dataset (Val sfl ). Similarly, we assessed models developed from aggregated flight line data (models within MS_L agg and MS_H agg ) using the aggregated flight line validation dataset (Val agg ). We assessed the final model performances by comparing measures (R 2 , RMSE%, Bias%) commonly used to evaluate area-based model performance (Piñeiro et al. 2008;White et al. 2017). Furthermore, we calculated prediction errors (PE = observedpredicted) for each forest attribute at each plot location by comparing predicted values from the models constructed for the different ALS configurations to respective observed values. We then subjected prediction errors to repeated measures analyses of variance (RMANOVA) treating the different scan angle groups (L, H) as fixed effects, and making comparisons of the different ALS configurations (nn, on, agg) with multivariate tests (Wilks lambda). We calculated effect sizes as generalized eta squared (ŋ 2 G; Olejnik and Algina 2003) and performed post-hoc tests on the effected groups. We used post-hoc analyses using univariate tests (pairwise paired t-test) with a Bonferroni adjustment (Bonferroni 1936) to reveal pairwise differences, between ALS configurations, that were statistically significantly different (P < 0.05). We tested whether the mean prediction error for each attribute among the ALS configurations was significantly different. In order to determine whether each set of prediction errors met the normality assumptions of RMANOVA, we used the Shapiro-Wilk Test for normality of residuals (Royston 1982) and normal QQ plots. These analyses indicated that all prediction errors fit the normal. The assumption of sphericity was automatically checked and corrected for eventual deviation during the computation of the RMANOVA test. Sphericity is the condition where the variances of the differences between all combinations of the within-subject groups (nn, on, agg) are equal, where a violation would cause the RMANOVA test to become too liberal (i.e. increase in Type I error) (Howell, 2009). The Greenhouse-Geisser sphericity correction (Greenhouse and Geisser 1959) was automatically applied only to within-subject factors violating the sphericity assumption (i.e. where Mauchly's test (Mauchly 1940) p-value is significant, P < 0.05). We performed all analyses of variance using the R-package rstatix (Kassambara 2019). We computed mean prediction errors (MPE; Equation (10)) and mean absolute prediction errors (MAPE; Equation (12)), and further calculated values relative to the observed values Forestry Figure 6 Boxplots illustrating the distribution of ALS metrics observed from the calibration (for both L and H) plots grouped by ALS configuration (nn, on, agg). Mean (point) is illustrated in red, while the median, interquartile range, percentiles (25 th and 75 th ), minimum, maximum, and outliers are depicted in black by the boxplots.
Effect of scan angle on ALS metrics and ABA predictions Table 3 Mean and relative mean difference (MD, MD%), mean and relative mean absolute difference (MAD, MAD%) and results of the Wilcoxon signed rank test (WSRT) in comparing ALS metrics derived from near-nadir and off-nadir single flight line, and aggregated, ALS data. Values are presented in the units of their respective metric. Significance levels: * * * P < 0.001; * * P < 0.01; * P < 0.05; blank = not significant.
where y j is the observed value (y) derived from our tree measurements and forest attribute calculations for plot j,ŷ (nn|on|agg),j Forestry  Similarly, in order to assess the magnitude of differences between predicted forest attributes relative to one another, we assessed the differences in MPE% and MAPE%. Finally, we highlighted which of these interactions were statistically significant with the results from RMANOVA post-hoc tests.

Scan angle effects on ALS metrics
The results of the Wilcoxon signed-rank test (  H plots. Although not always significant throughout the comparisons, the maximum height of the canopy (MAX) was always more accurately sampled from either on or agg, than from nn, for both L and H (i.e. positive MD). Based on the assumptions of the post-hoc power analysis, using an alpha of 0.05, a power of 0.95, a sample size of 20 and two tails, we computed the effect size (d) to be 0.87, which was determined to be large according to Cohen (1988).

Assessment of area-based forest attribute models
The model performance measures according to out-of-bag errors for the six model sets are shown in Table 4. Overall, the results indicated high correspondence between predicted and observed values for L plots (R 2 > 0.80), with lower correspondence for H plots (R 2 > 0.69, with the exception of DBH, which had R 2 > 0.43). Errors in prediction were lower for L plots (RMSE% < 24; Bias% < 1.5) and higher for H plots (RMSE% < 35; Bias% < 3). Of particular relevance for this study, we observed minimal variation in model performance for each attribute among the ALS configurations (differences in R 2 < 0.05, RMSD% < 2.3 and Bias% ≤ 1.6) ( Table 3). From these results, we deemed the ALS-based models were sufficiently accurate to be applied to the independent validation data to allow for a meaningful comparison of error statistics between ALS configurations within each calibration dataset (Experiment 2).

Scan angle effects on area-based model performance
We applied the L and H models fitted with ALS metrics derived independently from the ALS configurations to all 41 validation plots. Figure 7 illustrates the model performance measures of MS_L and MS_H for all ALS configurations assessed with the independent validation plots. Model performance measures showed minimal variation by ALS configuration within each attribute and model set (differences in R 2 < 0.03, RMSE% < 2 per cent, Bias% < 3.5 per cent from MS_L; differences in R 2 ≤ 0.07, RMSE% < 1.7 per cent, Bias% ≤ 2.9 per cent from MS_H). Although, coefficients of determination were particularly stable for each attribute regardless of the ALS configuration or model set, we observed consistently lower R 2 from models developed Effect of scan angle on ALS metrics and ABA predictions with on ALS metrics in comparison with those developed from nn ALS metrics, with the exception of BA from MS_L on . We observed slightly higher RMSE% (increases ≤2 per cent) for most attributes derived from on in comparison to those derived from nn with the exception of HGT from MS_L, and HGT, GMV and TVOL from MS_H, for which we observed slight decreases (decreases <0.5 per cent). Associated Bias% were variable for MS_L on and was consistently lower from all attributes predicted from MS_H on . Similarly, when comparing the model performance measures derived from agg with those derived from nn, R 2 remained very stable (differences in R 2 ≤ 0.03). We observed marginally higher RMSE% (decreases <1.5 per cent) for most attributes predicted from both MS_L agg and MS_H agg and Bias% (decreases <3.5 per cent). Associated Bias% were all higher from MS_L agg , and variable by attribute predicted from MS_H agg . In summary, R 2 s remained very stable regardless of the ALS configuration or model set, while values for bias and RMSE were generally lower for nn than for on or agg for L plots. Similarly, for H plots, values for RMSE were marginally lowest when derived from nn; however, in contrast, biases were lowest when derived from on. Figure 8 illustrates the distribution of prediction errors resulting from the different ALS configurations within each forest attribute of each model set. Except for DBH and BA from MS_L, and BA from MS_H, the RMANOVA indicated that the mean prediction errors were significantly different for all other attributes (Table 5; P < 0.05) and hence an effect of ALS configuration was observed, albeit for very small effect sizes (ŋ 2 G ≤ 0.01). Table 6 denotes the differences in relative and absolute MPE and MAPE when derived from either on and agg compared to nn, and from agg compared to on ALS configurations, as well as the results of the pairwise comparison post-hoc analysis. Although no trend was apparent in significance of the pairwise comparisons from either modelset (MS_L or MS_H), the relationship between on and nn prediction errors were significantly different (P < 0.05) for GMV, TVOL and AGB from MS_L, and HGT, DBH and GMV from MS_H. From the agg and nn comparison, we observed prediction errors from half of the six predicted attributes from MS_L (HGT, GMV, TVOL) to be significantly different (P < 0.05), while surprisingly, only HGT from MS_H. As for the agg and on comparison, we found prediction errors from HGT from MS_L, and from GMV, TVOL and AGB from MS_H to significantly differ (P < 0.05 and P < 0.01, respectively). Of note, differences in mean absolute prediction errors relative to the ground measurements (MAPE% diff ) from models developed from L agg plots, in comparison with those derived from L nn plots, were slightly higher than from H plots (≤ 1 per cent) (based on |MAPE% diff |).

Scan angle effects on ALS metrics
In the context of previous research, we hypothesized that some ALS metrics derived from data acquired with off-nadir scan angles would be significantly different from metrics derived using ALS data acquired with near-nadir scan angles (within 4 • of nadir). The literature demonstrates contrasting findings with respect to the effect of scan angle and specific ALS metrics. Consistent with the work of Montaghi (2013), we found no significant difference in ALS metrics generated using ALS data with nn or on L scan angles (|11-19| • ), with the exception of COVAR from the vertical structure metrics group. Contrary to our results, Yang et al. (2011) demonstrated that the error for the vegetation height metric RH100 (i.e. MAX) ranged from 2 m to >12 m for a 20 • off-nadir scan angle for simulated waveform data in simulated deciduous forests. Consistent with our results, and contrary to Yang et al. (2011, using discrete return ALS in real deciduous forests, found no significant effects of scan angle on MAX for scan angles up to 16 • . Disney et al. (2010) found that MAX and MEAN generally increased with increasing scan angle from nadir to 30 • , by 0 per cent and 8 per cent, respectively, for simulated birch canopies; and by 17 per cent and 19 per cent, respectively, for simulated pine canopies. In our study, we found MAX, P95, and MEAN increased significantly from values for nn observations when generated using ALS data with on H scan angles (21-30 • ), albeit for a minimal amount (MAD <0.3 m).
These results highlight the dependency of scan angle effects on site specific forest structure. It is known that crown shape affects the interception of laser pulses within forest canopies (e.g. Lovell et al. 2005). Nelson (1997) demonstrated that as canopy shape progressed from a conic form to a more spheric structure, average canopy height, canopy profile area, and canopy volume increased, canopy height variation decreased, and coefficients of variability remained stable or decreased. Similarly, in assessing the effect of scan angle on height percentiles, Holmgren et al. (2003a) simulated pine and spruce stands with digitally reconstructed solid trees (i.e. impermeable to pulse beam penetration) and found more variation associated with species that have longer crowns (i.e. spruce) and sparse forests. Plots in our study were sampled in natural, predominantly single-layered, balsam fir stands. Balsam fir trees have symmetrical spike-like crowns, which taper gradually to a narrow conical spire-like top, allowing for more penetration of the laser pulse through the canopy. Further, the natural forest environment (i.e. non-simulated; permeable to pulse beam penetration) increased the probability of penetration of laser beams through openings in the forest canopy, hence facilitating sampling by the ALS.
Broader scan angles (i.e. >15 • ) increase the probability of upper canopy vegetation returns and decrease the likelihood of obtaining ground returns (Hopkinson et al. 2005;Montaghi 2013). Research has demonstrated patterns relating bias to scan angle to be most prominent for point density and structural descriptor metrics that are calculated with ground returns (e.g. understory ratio, vegetation ratio (Montaghi 2013); gap fraction, vertical gap fraction profile (Liu et al. 2018)). In our study, all structural and density metrics from both L and H, with the exception of COVAR from L, were not significantly different when generated from nn or on ALS data; the computation of the ALS metrics used in our analysis excluded returns below 2 m, and hence, excluded ground returns.
Any potential effects associated with larger scan angles are frequently offset by maintaining sufficient overlap between flight lines and using aggregated flight line data (Evans et al. 2009). When we compared ALS metrics from H, we found that height metrics P95 and MEAN were significantly different not only for the Forestry Table 6 Differences in relative and absolute mean prediction errors (MPE) and mean absolute prediction errors (MAPE) when derived from either on and agg compared to nn, and from agg compared to on ALS configurations, as well as the results of the pairwise comparison (pwc) RMANOVA posthoc analysis. Forest attributes for which differences in mean prediction error among the ALS configurations, within L or H, were deemed significant from pwc are indicated with asterisks ( * * * P < 0.001; * * P < 0.01; * P < 0.05; blank = not significant; n/a = not applicable). . Surprisingly, we observed all metrics with the exception of SKEW, CC2, and CC14 were significantly different when derived using nn versus agg ALS configurations from L, whereas this same trend was not apparent from H. Possibly this is because the distribution of angles within L agg were more mixed (i.e. less clustered at the extremes of the range assessed (|0-20| • )) when compared to those in H agg (i.e. clustered around 0 • and 25 • ) (Figure 4). The probability of canopy interception is known to increase with larger scan angles (Goodwin et al. 2007), and it was not surprising that we observed consistently, for both L and H, more accurate sampling Effect of scan angle on ALS metrics and ABA predictions of maximum height by combining all available flight lines (agg) in comparison with ALS data acquired from nn (MD = 0.22-0.24 m). Post-hoc power analysis determined an associated large effect size of 0.87, indicating that if the means of the metrics being compared do not differ by 0.87 standard deviations or more, the difference in metric values is considered inconsequential, even if it is statistically significant. In our analysis, all metrics from the various ALS configurations differed by <0.87 standard deviations and hence, all significant differences found between metrics can be considered inconsequential. Nonetheless, differences that were deemed as significant from the WSRT provide evidence that the distribution of median values for that given ALS metric is shifted to the left or right from the other. It is therefore important to consider not only whether there was a shift in the population's distribution, but also the magnitude of differences being observed (absolute and relative MD, MAD) in the interpretation of the results. Given this, we confirmed our stated hypothesis that larger scan angles would significantly affect some ALS metrics commonly used in an ABA. We found that specific ALS metrics derived from on scan angles (as well as some metrics derived with agg), differed significantly, albeit minimally, from those derived with nn scan angles.

Scan angle effects on area-based model performance
Our second hypothesis was that prediction errors for ABA models of forest attributes developed with on scan angles, including agg, would differ from those developed solely with nn scan angles. We expected that the use of ALS metrics developed with large on scan angles would significantly affect predictions of forest attributes derived from an ABA. This expectation was based on previous studies and guidelines that cautioned the use of ALS data acquired with large on scan angles (> 15 • ) for forest characterization (Ahokas et al. 2005;Disney et al. 2010;Laes et al. 2008). In our study, we found significant variations, albeit trivial, in ALS metrics derived from the three ALS configurations. The variations in ALS metrics did have an effect on prediction errors associated to certain attributes; however, significant differences in mean absolute prediction errors were all <1.3 per cent.
Interestingly, although the observed biases in the ALS metrics were all deemed trivial, we found them to be inherent in the area-based prediction errors. The RMANOVA indicated that the mean prediction errors were significantly different for all attributes (P < 0.05) for a very small effect size (ŋ 2 G ≤ 0.006) with few exceptions, and hence an effect of ALS configuration was observed for most predicted attributes. Naesset (1997) reported no significant effect of scan angle using regression to estimate stand height (i.e. mean height) for boreal forests using ALS data acquired with scan angles up to 20 • off-nadir. Surprisingly, we found smaller prediction errors when we predicted HGT (MS_L) from on relative to when predicted from nn, with an associated bias of 0.05 m (MPE diff ). The latter reported bias is however consistent with findings of Lovell et al. (2005), who similarly observed a slightly larger bias of 0.12 m in predicting stand height using simulated ALS data acquired at 20 • off-nadir. Moreover, Keränen et al. (2016) demonstrated that the narrower scan angle range, 15 • compared to 20 • , resulted in slightly more accurate predictions of mean height (RMSE%: 8.5-11 vs. 9-12 per cent) and plot volume . This trend was consistent with our results in predicting TVOL from MS_L, |0-4| • compared to |11-19| • , with RMSE% of 21.36 vs. 22.59 per cent respectively, and contradictory in predicting HGT with RMSE% of 11.36 vs. 11.27 per cent, respectively. The innovative aspects of our study, namely the larger range of scan angles we assessed and the diversity of forest attributes included in our analyses, make direct comparisons with past research challenging. Nonetheless, consistent with our findings in predicting HGT from MS_H, Holmgren et al. (2003b) found no significant effect on the prediction of height from both nadir (|0-10| • ) and off-nadir (|10-30| • ) simulated ALS datasets.
Finally, and of practical interest, we found no significant evidence that using aggregated flight line metrics would offset any potential systematic bias or uncertainty introduced by using wider scan angles in the forest attributes we assessed. In fact, we found significantly larger prediction errors in the predictions of HGT GMV, and TVOL from MS_L agg than MS_L nn , although these differences were minimal (MAPE% diff ≤ 1.25 per cent). We observed the same for HGT from MS_H, albeit for a difference in MAPE of only 0.04 m (MAPE% diff 0.34 per cent). We also found significant differences in prediction errors associated to HGT predicted from MS_L, and GMV, TVOL and AGB from MS_H, in comparing observations from agg with those obtained from on, albeit for a maximum MAPE% diff of <1 per cent. We therefore confirmed our hypothesis that prediction errors for ABA models of specific forest attributes developed with on scan angles, including models developed with agg, differed, although minimally, from those developed with nn scan angles.

Experimental considerations
Throughout our experiments, we assumed that if we observed no or minimal impact on derived ALS metrics or ABA model outcomes under our extreme scan angle scenarios (nn, on), we would not expect there to be an impact when we have a mix of scan angles, which manifest in typical ALS acquisitions in support of forest inventory applications. In real-world ABA applications, ALS metrics are commonly derived from ALS data obtained with 2 overlapping flight lines. For our plot dataset, ALS metric were generated using data from up to 4 overlapping flight lines. Since these data were acquired at varying scan angles, it is difficult, if not impossible, to isolate the effects of scan angle when using aggregated flight line data. We therefore attempted to isolate the impact of scan angle by deriving metrics using only a single flight line of data (nn, on) and keeping all other experimental considerations constant, including height normalization of the point clouds. We normalized all data to a common DTM, derived from aggregated flight line data, which would be the case for an operational EFI using an ABA. We therefore assessed the effect of scan angle with respect to how ALS sampled the canopy only from the varying angle groups, and further assessed whether these effects, if any, would be inherent in the ABA predictions of forest attributes.
In order to assess the effect of scan angle on the stability of ALS metrics, the target must be sampled in the same manner from all the various ALS configurations. Commonly used oscillating mirror mechanisms yield a seesaw scanning pattern and tend Forestry to accumulate points at the swath boundaries, the end of a laser system's arc, as it reverses direction (Balsa-Barreiro and Lerma 2014). Ultimately, it is the spatial point distribution on the target area that provides information about the real quality of the data: a uniform point pattern will yield reliable sampling of the target, while an irregular point pattern produces inconsistent sampling and hence less stable information and derived ALS metrics. Lovell et al. (2005) confirmed this by simulating ALS data with a seesaw scanning pattern and demonstrated that maximum tree height retrieval is less accurate at the scanned swaths edges due to uneven spacing in sampling. ALS systems which uses a rotating mirror, as is the case with the RIEGL LMS-Q680i sensor used in this study, yield uniform parallel sampling patterns throughout the sampled swath (RIEGL Laser Measurement Systems 2012) and hence minimize uneven spacing in sampling at the swath's edge. Nonetheless, when considering establishing a plot representing an on scan angle of 30 • , we had to ensure that the full extent of tree heights were sampled for all trees within the plot. Theoretically, the pulses would potentially not sample the height extent of trees at this extreme angle. In our dataset, one plot represented an average on scan angle of −30 • . At this location, we observed 42 per cent of points acquired from −29 • , and the remainder from −30 • , hence not sampling the extreme swath boundary but rather sampling the extremity of data acquired at ∼ − 29 • . Using trigonometry, we calculated the swath width to be 1154.7 m, of which 23 m is associated to data acquired at −30 • . Given the proportion of the plot sampled from −30 • (58 per cent) and the plot radius, the minimum distance from the swath's edge to the plot's perimeter was calculated to be 10 m. We determined the theoretical maximum height at this location to be 17.3 m. As the ground measured maximum tree height for this plot was 15.5 m (i.e. < 17.3 m), we can assume that despite this plot's position near the edge of the swath, the ALS uniformly sampled the height extent of all trees in the plot representing an on scan angle of −30 • . This demonstrates that the scanning mechanism of the ALS instrument and uniformity in horizontal sampling must also be considered when examining the effects of scan angle.
In establishing ground plot locations, it was also important to consider proximity to the nearest base station. Ten ground plots exceeded national guidelines (Donahue et al. 2013) which suggest establishing control points within 50 km of survey locations; nonetheless all plots were within 60 km from the nearest reference base station. We did not consider the potential positional errors to be a limiting factor in our study as the ALS metric pairs being compared, and associated forest attribute prediction errors, were derived from the same location, slightly miss-positioned or not.
Although Goodwin et al. (2007) demonstrated that the effects of topography on the probability of interception in the canopy and ground surface were most evident at scan angle ranges greater than 15 • , Ørka et al. (2018) concluded that terrain effects, including slope and aspect, were negligible in operational ALSderived forest inventories for slopes ranging up to 43 • . As with our analysis, the latter study derived ALS metrics from returns with a height threshold >2 m. For that reason, we did not consider topography in our sample designs and did not consider slope to be a limiting factor in our study because our ground plot data consisted of slopes ranging from 0-26 • (mean = 7.7, 3.9, 9.1; min. = 2.3, 0, 0.5; max. = 20.6, 24.1, 26.5; sd = 5.0, 5.1, 6.5 degrees for L, H, and validation datasets, respectively).
Finally, we also considered the possible effects of the time lag between the ALS data acquisition and ground plot sampling which were of 1-2 growing seasons. In our study area, the growing season is relatively short from mid-June to the end of September and growth rates are slow. As long as growth is similar across our study area, we would not expect the time lag to affect the results. However, since growth is dependent on site productivity, non-uniform increases in growth between plots may be present. Since we calibrated the 2016 acquired ALS data with measurements sampled in 2018 and applied the developed models to ground plots sampled in 2016-2017, we would expect a slight bias in predicted attributes from growth alone. Therefore, it is possible that a portion of the observed prediction errors could be attributed to the aforementioned temporal discrepancies between ALS acquisition and ground sampling. However, at the plot level, error associated with growth would be uniform across all predicted attributes, regardless of the model set or ALS configuration, thus permitting assessments of the effect of scan angle on ALS metrics and model predictions.

Implications of scan angle on area-based forest inventory
Understanding and quantifying scan angle effects can aid in guiding acquisition efforts and refining forest attribute predictions by identifying those metrics that are sensitive to scan angle. Large off-nadir scan angles can reduce acquisition costs because more area can be sampled in a single flight line, and flying time is reduced. However, acquisition parameters are related, and no single factor can be considered in isolation (Montaghi 2013). Previously, and based on technology available at the time, recommendations from the literature often limited scan angle for forest applications to <15 • (Ahokas et al. 2005;Disney et al. 2010;Laes et al. 2008). ALS technology has evolved rapidly over the past two decades, as have other associated technologies that are integral to ALS data acquisition and processing (e.g. global positioning systems, inertial measurement unit, gyro-stabilized mount, etcetera). These advancements in technology have contributed to acquisition efficiencies and higher point densities (Jakubowski et al. 2013). Nonetheless, researchers have used ALS data acquired at scan angles exceeding these recommendations to successfully predict forest attributes from these data. Luther et al. (2019) predicted Lorey's mean height, basal area, volume and AGB explaining over 83 per cent of the variability of the response data (RMSD% < 26 per cent) using the ALS data analyzed in this study. Similarly, Cao et al. (2016) used ALS data acquired within 30 • of nadir to predict Lorey's mean height (R 2 0.84; RMSE% 8.28 per cent) and AGB (R 2 0.74; RMSE% 15.21 per cent) in secondary subtropical dominated forests. Guerra-Hernández et al. (2016) modelled a set of forest stand variables for 4 different forest types (pure stone pine, mixed, maritime pine, and Pyrenean oak) using ALS data acquired at scan angles up to 50 • from nadir and explained 61-85 per cent, 67-98 per cent and 74-98 per cent of the variability in ground-truth stand height, basal area and volume, respectively (associated range in RMSE% of 6.01-20.42 per cent, 7.95-32.62 per cent and 8.9-31.95 per cent, respectively). The success of Effect of scan angle on ALS metrics and ABA predictions more recent studies using scan angles >15 • could be partially due to the advancements in ALS and associated technologies.
Although single flight line ALS metrics have previously been demonstrated to support model development of forest attributes (e.g. Luther et al. 2014), for the purpose of calibrating satellite imagery (e.g. McInerney et al. 2010), and/or upscaling to a largearea inventory (e.g. Wulder et al. 2012), it is more common practice to use ALS metrics derived from multiple adjacent flight lines for predicting forest attributes in support of operational forest inventories (White et al. 2013). Maintaining overlap between flight lines not only prevents data gaps and enables higher pulse densities from multiple look angles (providing a more complete 3D sampling of any given object), it also increases the likelihood of ground returns in dense forest canopy (Ahokas et al. 2005) or in steep topography (Lin et al. 2013). Adjoining flight lines also enable co-registration to remove swath biases. Our analysis demonstrated a benefit in aggregating ALS data from overlapping flight lines as we observed the maximum canopy height to be best captured from off-nadir scan angles, further supporting established guidelines (e.g. White et al. 2013) of maintaining >50 per cent overlap between flight lines. Negative values of MPE diff from MS_L agg indicate the prediction errors are less when the attributes are predicted with agg obtained from scan angles up to 20 • off-nadir than from MS_L nn (significant for HGT, GMV, TVOL) or MS_L on (significant for GMV, TVOL, AGB) for the majority of attributes (Table 6). Similarly, we observed smaller prediction errors by including the large off-nadir scan angles up to 30 • from MS_H agg than from MS_H on (significant for GMV, TVOL, AGB). When comparing prediction errors from MS_H agg with those from MS_H nn , the trend is consistent for TVOL and AGB; however, these relationships were not deemed significant from the pairwise comparison tests. Although not always deemed significant, prediction errors were actually larger for HGT, DBH and GMV when derived from MS_H agg than from MS_H nn , which is indicative of no improvement in model predictions for these attributes by including large off-nadir (> 20 • ) acquired ALS data.

Conclusion
In this study, we hypothesized that specific ALS metrics derived from data acquired with large off-nadir scan angles up to 30 • would be significantly different from ALS metrics derived using data acquired with near-nadir scan angles and that these differences would inherently affect ABA predictions of forest attributes. A major finding of this study is that the ALS acquisition parameter scan angle significantly affected (P < 0.05) specific single flight line metrics from both |11-19| • (L; namely COVAR) and |21-30| • (H; namely MAX, P95, MEAN) off-nadir scan angles but that the effects, although statistically significant, were inconsequential. Forest attribute predictions using these and other metrics were also significantly affected (P < 0.05), namely GMV, TVOL and AGB from L, and HGT, DBH and GMV from H. We further demonstrated that combining ALS data from all available adjacent flight lines significantly (P < 0.05) increased accurate measurement of maximum canopy height from both L and H relative to measurements derived from single flight line data. Although prediction errors increased when derived from aggregate ALS data in comparison to those derived from single flight line near-nadir ALS data for the predictions of HGT, GMV and TVOL from L, and significantly reduced errors for HGT from H, the significant differences in mean absolute prediction errors were all <1.3 per cent. Based on these findings, we conclude that the influence of large scan angles, up to 30 • off-nadir, on area-based forest attribute predictions were minimal in this study which used ALS metrics based exclusively on ALS returns >2 m for balsam fir dominated forests. These results suggest that larger ALS acquisition scan angles could be used in these forest types with minimal impacts on area-based model outcomes, enabling operational efficiencies for implementing enhanced forest inventories in these forest environments.

Data availability statement
The data underlying this article will be shared on reasonable request to the corresponding author.