# Estimating Coarse Woody Debris Volume Using Image Analysis and Multispectral LiDAR

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}) across a 4300-hectare study area in the boreal forest of Alberta, Canada using optical imagery and an infra-canopy vegetation-index layer derived from multispectral aerial LiDAR. Our models predicted CWD volume with a coefficient of determination (R2) value of 0.62 compared to field data, and a root-mean square error (RMSE) of 0.224 m

^{3}/100 m

^{2}. Models using multispectral LiDAR data in addition to image-analysis data performed with up to 12% lower RMSE than models using exclusively image-analysis layers. Site managers and researchers requiring reliable and comprehensive maps of CWD volume may benefit from the presented workflow, which aims to streamline the process of CWD measurement. As multispectral LiDAR radiometric calibration routines are developed and standardized, we expect future studies to benefit increasingly more from such products for CWD detection underneath canopy cover.

## 1. Introduction

^{2}) on a small study area (~6 ha) in Hungary. Sumnall et al. [17] estimated various forest variables on plots located in a 2200-ha study area in southern England, containing semi-natural and plantation forests, by modelling LiDAR variables and considered their CWD (larger than 10cm at largest end) volume results to be moderately accurate (0.51 R2, 2.74 m

^{3}RMSE). These studies have proven the potential of LiDAR in aiding CWD estimates but have acknowledged that further studies are required to improve their results and have not been tested in boreal forests.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. CWD Survey

^{2}plots for sampling CWD volume. To obtain data in both natural and altered sites, while avoiding transitions between either, two plots were located on the seismic line and two plots were located in the surrounding forest. We call the plots in the seismic line “disturbance plots”, and they were designed to be rectangular areas limited by the footprint of the disturbance, with width equal to the seismic line’s width and variable length to obtain a 100 m

^{2}area. The plots in the surrounding natural environment were denominated “forest plots”, and they were circular areas with a radius of 5.64 meters. We positioned the disturbance plots systematically, one of them starting 15 meters away from the beginning of the line, and the other positioned starting 75 meters away from the end of the former disturbance plot. Finally, the forest plots were positioned randomly, with their center point located within a minimum distance of 12 meters and a maximum distance of 36 meters away from the center of the seismic line. By the end of the field season, we had sampled a total of 108 plots: 76 plots (19 sites) in the calibration area and 32 plots (8 sites) in the verification area.

_{L}is the diameter measured at the largest end, d

_{M}is the diameter at the middle, d

_{S}is the diameter at the smallest end, and L is the length of the stem.

#### 2.3. Remote Sensing and Pre-Processing

^{2}), and another during the summer of 2018, which captured multispectral LiDAR (ML) data with lower point density (raw 11 pts/m

^{2}). The data collected during the 2017 mission were used in a geographic object-based image analysis (GEOBIA) workflow to locate visible CWD objects (vCWD), and the 2018 ML data was used to generate infra-canopy vegetation indices useful as indicators for occluded CWD quantity. GEOBIA consists of subdividing georeferenced input images into segments denominated “image-objects”: relatively internally homogenous segments of the image usually defined by contrasts around their edges, which are intended to represent distinct parts of real-world objects [29]. We acknowledge the temporal disconnect between the dates of the field work and first LiDAR mission (2017) and second LiDAR mission. It is our assumption that any changes in CWD volume within that time period were minor and had no significant impact on our study.

#### 2.3.1. Orthomosaics and Dense LiDAR Point Cloud

^{2}, for noise removal and ground-point classification using Terrasolid software. Using ESRI (Environmental Systems Research Institute) ArcMAP (version 10.6.1; ESRI, Redlands, CA, USA), we gridded the elevation of the ground points into a 25cm GSD digital terrain model (DTM), and of the first return points into a 25 cm GSD digital surface model (DSM). A canopy height model (CHM) was obtained by subtracting the DSM by the DTM. We generated a 5 cm GSD orthomosaic of the study area by processing the air photos in Pix4Dmapper [30,31], using standard procedures for photo alignment, georeferencing and adjustments using a photogrammetric point cloud. A normalized difference vegetation index (NDVI) raster layer was generated using the near-infrared (NIR) and red bands of the orthomosaic.

#### 2.3.2. Multispectral LiDAR Acquisition and Processing

^{2}per channel. The raw LiDAR data were calibrated using LiDAR Mapping Suite [32] by the ARTEMiS lab, who reported 12 cm horizontal and 5 cm vertical RMSE strip-to-strip accuracy. The ML datasets for all three channels was supplied in 54 separate tiles of the study area.

^{2}, 4.49 pts/m

^{2}and 5.00 pts/m

^{2}for the Green, NIR and SWIR channels respectively. The percentage of single returns was of 99.7%, 33.5%, and 27.5% respectively for these channels. Rain previous to the flight and wet ground likely caused attenuation losses on all channels, most notably the green channel, which is obtained with a larger beam divergence and higher tilt angle than the other channels and is expected to have higher losses below the canopy [21]. Point height relative to ground was obtained on each channel with lasground (wilderness setting), which is a tool based on Axelsson’s [34] triangular irregular network filtering algorithm. Then, to avoid outliers, the maximum intensity of the ground points was set to three standard deviations plus the mean, according to the intensity distribution of each channel. Points with an estimated height smaller than 1 meter were exported in “shapefile” (SHP) format using las2shp. The point intensity of each SHP file was gridded into raster images using the inverse distance weighted (IDW) tool in ArcMap, with a cell-size of 50 cm, a fixed search radius of 1 meter and minimum of 2 sample points. IDW were used to reduce some of the bias of gridding and cell spatial attribution and was selected over simpler averaging methods because it preserved some of the variance of the raw datasets. IDW also was useful in reducing the effect of noise and banding, which was especially observed in the NIR channel, where the intensity distribution was offset between scanline directions due to internal hardware misalignment issues with the sensor (2.3%, 3.4%, and 0.2% average banding for the SWIR, NIR, and green channels respectively). Due to the small percentage of single returns, mostly observed in vegetated areas, all returns were considered in this study despite the fact that this introduces noise in the data [21]. Using the intensity raster images for each ML channel, active NDVI (aNDVI) and active NBR (aNBR) layers were calculated using the raster calculator tool in ArcMap. The green channel was used for aNDVI as a visible-spectrum substitute for the traditionally used red channel on passive NDVI calculations. Both aNDVI and aNBR layers were later used to derive vegetation-indices metrics per 100 m

^{2}plots, which were included in CWD volume models as predictor variables. The individual ML channels were not included in the analysis as it was assumed that active vegetation indices represented more parsimonious variables, likely to retain the information of multiple spectral layers.

#### 2.4. Geographic Object-Based Image Analysis

#### Classifier Training and Application

^{2}plots, which was included in CWD volume models as a predictor variable.

#### 2.5. Additional Layers

^{2}plots.

#### 2.6. Model Selection

#### 2.6.1. CWD Volume Modelling

^{2}plots to follow this pattern, as well as zero-inflated, CWD volume was modeled in two parts: a binomial distribution for the presence/absence of CWD, and a continuous distribution for volume on the plots where CWD was present. A binary response variable was created for the binomial models by treating all plots where CWD was absent as zero and all plots where CWD was present as one. The continuous model was trained on plots where CWD was present and used CWD volume as response variable. Candidate models were selected separately for the binomial and continuous parts, then combined into two-part CWD volume models. The final predicted CWD volume according to two-part models equals the predicted binomial component times the predicted continuous value. Given that the distribution of CWD volume in our study plots was positively skewed as well as zero-inflated, zero-adjusted gamma (ZAGA) distribution models were used to incorporate the best continuous and binomial models. We used the generalized additive models for location, scale and shape (GAMLSS) library in R to generate and test our ZAGA models [38,39]. Generalized additive models (GAMs) allow for the response variable to be modelled with Gaussian as well as numerous non-Gaussian distributions, as opposed to traditional linear modelling, and allow for link functions to model the relationship between the response variable and the predictors [40]. Additionally, GAMs are well suited for modeling non-linear relationships between the response and predictor variables because they are built based on the structure of the reference datasets instead of assuming a previously selected linear distribution [41]. The main assumptions of GAMs are that the samples are statistically independent, the variance and link functions are selected correctly, and that there are no outliers influencing the fit [42]. The stratified-random sampling strategy adopted in this study, as well as statistical tests and investigation performed with the raw data in R ensured the selected ZAGA models follow these assumptions.

#### 2.6.2. Keep-One-Out Cross-Validation and Verification Tests

^{2}) derived from the vCWD layer versus CWD measured ground cover per plot, without any additional modelling, to assess the potential and limitations of GEOBIA of CWD.

#### 2.7. Map Production

^{2}cells containing at least 50% coverage of the aNBR layer, which accounts for 99.3% of the study area (excluding water bodies and human-made features). On cells with less than 50% coverage on the aNBR layer (0.7% of the study area), we used the best model not containing ML variables.

^{3}/ha) on the entire 4300-hectare study area: one map dedicated to comprehensive CWD volume across all land cover types, and another dedicated to seismic line CWD density. Since the ML layers contained many gaps due to lower ground return density on closed canopy areas, the best-performing model using ML layers was used as a preferred model to generate these maps, and the best performing model without ML layers was used as a fallback model.

#### 2.7.1. Overall CWD Volume Layer

^{2}. Given that there were a few (less than 0.05% of the data) overpredictions well above the range of CWD volume observed in field plots, the maximum prediction value was set to the mean plus four standard deviations of the field sample distribution (~160 m

^{3}/ha). Predictions, along with their geo-locations, were imported into ArcMap as points and rasterized using the “point to raster” tool.

#### 2.7.2. Seismic Line CWD Volume Layer

^{3}/ha. A vector layer of all seismic lines on the study area was obtained via a seismic line mapper tool [44], which uses a least-cost path solution on a CHM to trace linear features on forested environments. The “generate points along lines” tool in ArcMap was used to both generate dense sampling points as well as sparse split points to segment each seismic line. Sampling points were attributed using the “extract values to points” tool, extracting values from the raster of overall volume. Lines were split into segments using the “split line at point” tool. Finally, segments were attributed with their mean CWD volume using the “spatial join” tool to link values of sampling points with each line segment.

## 3. Results

#### 3.1. Accuracy of Best Models

^{2}, 0.224 RMSE using ML data; 0.514 R

^{2}, 0.254 RMSE without ML) and on the verification area while training only on calibration area samples (0.721 R

^{2}, 0.198 RMSE using ML data; 0.628 R

^{2}, 0.203 RMSE without ML). Goodness of fit (R

^{2}) and root mean square error (RMSE) were comparable between cross-validation tests in the calibration area and tests in the verification area. Furthermore, these metrics were better in models including ML variables in relation to models without ML variables. The regression line of all models approximates the 1:1 relationship with a slightly gentler slope. The variance of CWD volume was greater in disturbance plots than in forest plots, and the former also displayed stronger zero-inflation in the calibration area plots (Figure 3).

#### 3.2. Map Products

^{3}/ha) was mapped over the 4300-hectare study area to generate two map products: a comprehensive map over all ground-cover types with 100m

^{2}raster cell-size (Figure 4), and a map of seismic line 100-m segments classified according to their average CWD density (Figure 5). High density CWD clusters were detected at the edges of previously harvested areas (Figure 4a) and in the southwestern portions of the study area in the form of partial windthrows (Figure 4c). Seismic lines with (Figure 5a) and without (Figure 5c) CWD treatment were identified in the maps. In Figure 4b, very low CWD quantities are observed in the interior of the harvested area (northwestern portion of Figure 4a), moderate CWD quantities in the natural forest (southeastern portion of Figure 4a), and very high CWD quantities in the transition between the two.

^{3}/ha and in lowland was 3.4 m

^{3}/ha. Disturbance plots, most of which were located on treated seismic lines, had much higher volumes than the rest of the study area. This was expected given the practice of creating CWD piles as part of restoration treatments [7]. The population of seismic lines on the map products had slightly lower volumes than the rest of the upland areas, but treated lines had much higher volumes than untreated lines. Average volume on treated and untreated seismic lines was 18.2 m

^{3}/ha and 9.4 m

^{3}/ha respectively.

#### 3.3. Model Selection Tables

#### 3.4. Accuracy of Visible-CWD Layer

^{2}), RMSE, and slope of regression in plots with negative NDVI were all much superior than these metrics in all field plots.

## 4. Discussion

^{2}, 0.224 RMSE in cross-validation; 0.721 R

^{2}, 0.198 RMSE in the verification area) but required a sophisticated set of inputs, involving high-resolution aerial images, high density LiDAR point clouds as well as ML point clouds. The results presented in Figure 3 indicate that, even where ML data is not available, CWD volume can still be modeled with good predictive accuracy (0.514 R

^{2}, 0.254 RMSE in cross-validation; 0.628 R

^{2}, 0.203 RMSE in the verification area), with a mean decrease of 0.101 in R

^{2}and a mean increase of 0.0125 in RMSE in relation to ML-inclusive models. The final maps of CWD volume in the study area (Figure 4 and Figure 5) reveal that even though CWD distribution is largely controlled by the occurrence of wetlands, artificial piles of CWD on seismic lines and clear-cuts are exceptions which can cause CWD anomalies. Overall average CWD volume in the study area (9.78 m

^{3}/ha for the entire study area, 17.73 m

^{3}/ha for uplands and 3.14 m

^{3}/ha for lowlands) was small when compared to what Lee et al. [45] measured in aspen-dominated stands in Alberta (108.8 to 124.3 m

^{3}/ha), but upland volumes in the present study are comparable to several other studies [46,47,48] in boreal forests as presented in Table 6. It is not surprising that lowlands had a very low volume of CWD (3.14 m

^{3}/ha) since the lowland trees observed in the field were small (commonly close to 7 cm diameter at largest end) and since not all wetlands were densely populated by trees, especially bogs and marshes which were mostly shrubby. Additionally, the CWD distribution on the produced maps was very similar to the distribution in the reference data (Figure 6), with mean values from uplands and lowlands in the reference data (17.7 and 3.1 m

^{3}/ha respectively) close to the mean of uplands and lowlands in the final maps (13.7 and 3.4 m

^{3}/ha respectively).

^{3}/ha) is smaller than the distribution in the disturbance field plots (Figure 6; mean 36.2 m

^{3}/ha) which is likely due to the fact that field plots were constrained by the limits of disturbances. Artificial CWD piles are confined, while the map cells were not. It is also possible that overrepresentation of plots with large quantities of CWD in the reference data samples may be inflating this difference.

_{max}) was an important variable to model CWD volume in our study area likely due to the presence of deciduous, coniferous and mixed forest stands with great variance in tree size, and the fact that differently sized trees yield different volumes of CWD. Therefore, on homogenous forest stands it is likely that CHM

_{max}will not perform as well as a controlling factor for CWD volume. Finally, we predict that canopy cover and ML variables should be valuable indicators of occluded CWD volume in a variety of forest types, but their influence on model predictive power should decrease on areas with less canopy cover, such as forests recently affected by fires.

#### 4.1. Model Selection

#### 4.2. Importance of Multispectral LiDAR for Infra-Canopy Predictions

#### 4.3. Two-Part Models Versus Simple Models

^{2}values in relation to simple linear models when using either cross-validation or the verification area tests. Furthermore, AICc tests would place simple models well above the ΔAICc threshold of 2 and would only select two-part models as candidates.

#### 4.4. Standardized Model Coefficients

_{sd}is similar to the information being supplied by pNDVI

_{sd}in the binomial model, namely that vegetated areas without CWD will have high aNBR without much variance, and that areas with CWD will have low aNBR pixels on CWD and high aNBR pixels on the surrounding vegetation, causing greater variance. In other words, the positive nature of the aNBR

_{sd}coefficient shows that an increase of CWD quantities can cause higher variance in aNBR captured with ML LiDAR. Finally, we believe that aNBR is not supplying substantial information about the variance of the response variable due to noise in the intensity values given that the intensity information available in LiDAR returns of the ground surface is very likely to have been affected by environmental factors such as target roughness, reflectance and wetness, as well as attenuation due to pulses being split into multiple returns [50].

_{max}at Table 5 indicate that an increase of tree size has a positive relationship with CWD volume, although it relates to a tapering curve given the negative CHM

_{max}

^{2}coefficient.

#### 4.5. Issues and Limitations

_{max}variable as an indicator for CWD volume. The presence of the canopy closure (CC) and height of tallest tree (CHM

_{max}) variables in all candidate models might be indicating that the ML data is not providing enough information about the occluded portions of the study area, and that the height of the tallest tree within each plot as well as the percentage of occluded area are supplementing that lack of information and improving the CWD volume estimates. If the ML datasets were more comprehensive and consistent, the value of CC and CHM

_{max}variables would likely diminish.

^{2}cells within the boundaries of seismic lines and CWD volume models could be applied to such cells for a more reliable prediction.

#### 4.6. Future Work

## 5. Conclusions

^{2}, 0.224 RMSE using ML data; 0.514 R

^{2}, 0.254 RMSE without ML) as well as in verification tests using independent samples from a spatially separated from the training area (0.721 R

^{2}, 0.198 RMSE using ML data; 0.628 R

^{2}, 0.203 RMSE without ML). The best model using ML performed better than the best model lacking ML variables. Our final CWD volume maps provide accurate, extensive, and high-resolution (10-m GSD) estimates for our study area and provide the foundation for a variety of management activities, including seismic line restoration and fire-hazard assessment.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{2}sampling plots were laid out (Figure A1): two circular forest plots randomly placed within a buffer from 12 to 36 meters away from the line, and two disturbance plots placed systematically starting 15 meters away from the beginning of the line and spaced 75 meters apart. Forest plots had a 5.645 m radius and disturbance plots had the same width as the seismic line and variable length to obtain a 100 m

^{2}area (Figure A2). Plots were located using a real-time kinematics (RTK) unit, by locating the center point of forest plots and the start and end points of disturbance plots. Volume was sampled for each CWD piece by obtaining three diameter measurements and one length measurement (Figure A3) exclusively within the sampling plots, while objects crossing the edge of the plots were measured as if they ended at the limits of the plot (Figure A4).

**Figure A1.**Examples of sampling areas for the collection of training and calibration CWD data. For each study site two (belt) disturbance plots are laid out on the seismic line and two (circle) forest plots are laid out off the seismic lines centered within a buffer from 12 to 36 meters away from the line.

**Figure A2.**Belt plot design for disturbance sampling. The belts have 100 m

^{2}area and the same width as the seismic line, the first belt starts 15 meters away from the start of the line, the second belt starts 75 meters away from the end of the first belt. A real-time kinematics (RTK) base-station is located somewhere close to the site for good signal with a rover sensor which was used to collect the coordinates of the start and end points.

**Figure A4.**Measuring strategy for CWD partly outside the sampling area. Only the (blue) segment within the area is measured, as if it ended at the edge of the sampling area. The dashed red lines represent tape used in (

**a**) disturbance plots or biodegradable paint used in (

**b**) forest plots to mark the edges of the plots.

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**Figure 1.**Workflow chart of this study with the sub-section numbers where each step is explained in this document. We mapped non-occluded coarse woody debris (CWD) via a geographic object-based image analysis (GEOBIA) workflow. Occluded CWD quantities were estimated using multispectral LiDAR (ML) vegetation indices from underneath the canopy. We selected potential models for CWD volume using the small sample Akaike information criterion (AICc) as an indicator for model predictive power.

**Figure 2.**Location of the calibration and verification areas within the 4300-hectare study area as well as the location of the field plots where CWD volume was surveyed. The background image is a false-color image using near infrared, red and green spectral bands. Upland broadleaf stands dominated by trembling aspen appear as lighter shades of red; conifer-dominated lowlands and mixed-wood uplands appear as darker tones. Roads, seismic lines (petroleum-exploration corridors), and petroleum well pads appear as lines and geometric features.

**Figure 3.**Scatter plots of actual versus predicted coarse woody debris (CWD) volume in m

^{3}. The best model with multispectral LiDAR (ML) data was used to estimate CWD volume on (

**a**) the calibration area plots using keep-one-out cross-validation, and on (

**b**) the verification area plots using the calibration plots to train the model. Similarly, the best model without ML data was also applied to the (

**c**) calibration and (

**d**) verification areas. Goodness-of-fit (R

^{2}), root mean square error (RMSE) and sample size (S) are indicated on each plot.

**Figure 4.**Map of coarse woody debris (CWD) volume per hectare (m

^{3}/ha) over the study area. High quantities of CWD are displayed in red, medium quantities in yellow and low quantities in blue. Roads and water bodies are excluded from the CWD volume model and are presented as dark blue. Insets (

**a**) and (

**c**) showcase hotspots of CWD in false-color imagery. Insets (

**b**) and (

**d**) showcase the CWD volume map over (

**a**) and (

**c**) respectively.

**Figure 5.**Map of coarse woody debris (CWD) volume per hectare (m

^{3}/ha) over seismic lines on the study area. The gray-scale background image presents volume per hectare for the entire study area, while the seismic lines are classified as high (red) medium (yellow) and low (blue) CWD quantities. (

**a**) and (

**c**) are false-color aerial images showing examples of high and low CWD densities respectively. (

**b**) and (

**d**) are field photos of (

**a**) and (

**c**) respectively.

**Figure 6.**Box and whisker diagram for coarse woody debris (CWD) volume on reference data (green, total of 108 field plots) on the CWD map for the entire application area (blue, total of 379,025 cells) and on seismic lines (red, 63,816 sampling points). All reference data (

**a**) are divided into (

**b**) disturbance plots (54 plots) and (

**c**) forest plots (54 plots). Forest plots are divided into (

**d**) lowland plots (14 plots) and (

**e**) upland plots (40 plots). All map predictions (

**f**) are divided into (

**g**) lowland (38% of cells) and (

**h**) upland (62% of cells) predictions. Seismic line predictions (

**i**) are divided into (

**j**) untreated lines (90% of samples) and (

**k**) treated lines (10% of samples). Original values were in m

^{3}/100m and were projected to m

^{3}/ha. Box-plot outliers are presented in gray.

**Figure 7.**Scatter plots of actual versus predicted coarse woody debris (CWD) ground cover in m

^{2}. Predicted ground cover presented here is the area sum of CWD objects detected via image-analysis. A weak relationship is observed when (

**a**) all field plots are used in regression, and a much stronger relationship is observed in (

**b**) plots with negative average normalized-difference vegetation index (NDVI).

Type | Area % | Mean Canopy Closure | |
---|---|---|---|

Upland Forest | Broadleaf | 7% | 87% |

Mixed | 19% | 74% | |

Coniferous | 33% | 61% | |

Lowland | Swamp | 5% | 38% |

Fen | 35% | 27% | |

Bog | 1% | 11% | |

Marsh | 1% | 1% |

**Table 2.**Description and summary statistics of all variables used in model selection, each variable summarized with: mean, standard deviation (Std Dev), minimum (Min) and maximum (Max). The response variable was coarse woody debris (CWD) volume measured in the field, and the predictor variables were derived from a variety of remote sensing products. Visible CWD (vCWD) and water (vWater) area were derived from the results of geographical object-based image analysis (GEOBIA) on aerial orthophotos obtained over the study area. A wetland probability raster was obtained from ABMI [37]. Canopy closure (CC) was derived from a canopy height model (CHM). Passive normalized difference vegetation index (NDVI) was derived from the orthophotos used in GEOBIA, while active NDVI and normalized burn ratio (NBR) were derived from multispectral LiDAR datasets.

Variable | Definition | Mean | Std Dev | Min | Max |
---|---|---|---|---|---|

Response | Response variable: total ground-truth CWD volume (m^{3}). | 0.25 | 0.34 | 0.00 | 1.50 |

vCWD | Total visible CWD area (m^{2}) on orthophotos, obtained with GEOBIA. | 1.50 | 2.63 | 0.00 | 11.89 |

vWater | Total visible water area (m^{2}) on orthophotos obtained with GEOBIA. | 1.31 | 3.00 | 0.00 | 14.40 |

Brightness | Average visible-spectrum reflectance on orthophotos. Scaled 0–255. | 99.06 | 10.24 | 75.33 | 122.11 |

WP | Average wetland probability, scaled from 0 to 1. | 0.28 | 0.30 | 0.02 | 0.92 |

CC | Canopy closure, obtained as proportion of cells with CHM > 2 m. | 0.45 | 0.31 | 0.01 | 0.96 |

CHM_{max} | Maximum CHM value within plot (i.e. height of tallest tree). | 14.97 | 5.47 | 2.72 | 30.82 |

pNDVI_{r} | Passive NDVI range within plot. | 0.99 | 0.17 | 0.57 | 1.37 |

pNDVI_{sd} | Passive NDVI standard deviation within plot. | 0.14 | 0.04 | 0.06 | 0.27 |

aNDVI_{r} | Active NDVI range within plot. | 0.95 | 0.24 | 0.00 | 1.72 |

aNBR_{r} | Active NBR range within plot. | 1.49 | 0.18 | 0.51 | 1.82 |

aNBR_{sd} | Active NDVI standard deviation within plot. | 0.26 | 0.07 | 0.09 | 0.43 |

**Table 3.**Candidate two-part models for coarse woody debris (CWD) volume according to small sample Akaike information criterion (AICc). The rank (r), degrees of freedom (df) and delta AICc (ΔAICc) are provided for each model. The following variables were selected in all continuous models: area of detected CWD objects via image-analysis (vCWD); canopy closure (CC); and height of the tallest tree (CHM

_{max}). The following were selected in some continuous models: standard deviation of the active normalized burn ratio (aNBR

_{sd}) and range of passive NDVI (pNDVI

_{r}). Finally, all logistic models included: vCWD, standard deviation of passive NDVI (pNDVI

_{sd}), visible water area (vWater) and wetland probability (WP).

r | Continuous Model | Logistic Model | df | AICc | ΔAICc |
---|---|---|---|---|---|

1 | vCWD^{2} + CC + CHM_{max} + CHM_{max}^{2} + aNBR_{sd}^{2} | vCWD + pNDVI_{sd} + vWater + WP | 12 | −2.08 | 0.00 |

2 | vCWD^{2} + CC + CHM_{max} + CHM_{max}^{2} + aNBR_{sd}^{2} + pNDVI_{r} | vCWD + pNDVI_{sd} + vWater + WP | 13 | −1.98 | 0.09 |

3 | vCWD^{2} + CC + CHM_{max} + CHM_{max}^{2} + pNDVI_{r} | vCWD + pNDVI_{sd} + vWater + WP | 12 | −1.43 | 0.64 |

4 | vCWD^{2} + CC + CHM_{max} + CHM_{max}^{2} | vCWD + pNDVI_{sd} + vWater + WP | 11 | −0.43 | 1.65 |

**Table 4.**Intercept and coefficients for binomial part of the best zero-adjusted gamma model. Values are presented for models created with the original training data and models using standardized predictor variables (mean of zero and standard deviation of one). Variables include visible coarse woody debris area (vCWD), standard deviation of passive normalized difference vegetation index (pNDVI

_{sd}), visible water (vWater) and wetland probability (WP).

Intercept | vCWD | pNDVI_{sd} | vWater | WP | |
---|---|---|---|---|---|

Original | −0.137 | −1.823 | −17.701 | 0.559 | 4.687 |

Standardized | −3.674 | −5.059 | −0.819 | 1.874 | 1.333 |

**Table 5.**Intercept and coefficients for continuous part of the best zero-adjusted gamma model. Values are presented for models created with the original training data and models using standardized predictor variables (mean of zero and standard deviation of one). Variables include squared area of visible coarse woody debris (vCWD), canopy closure (CC), height of tallest tree (CHM

_{max}), squared height of tallest tree (CHM

_{max}

^{2}) and squared standard deviation of active normalized burn ratio (aNBR

_{sd}

^{2}).

Intercept | vCWD^{2} | CC | CHM_{max} | CHM_{max}^{2} | aNBR_{sd}^{2} | |
---|---|---|---|---|---|---|

Original | −6.956 | 0.012 | −3.070 | 0.581 | −0.012 | 11.284 |

Standardized | −1.547 | 0.133 | −0.662 | 1.161 | −0.369 | 0.061 |

**Table 6.**Minimum and maximum average coarse woody debris volume (m

^{3}/ha) over varied boreal forest types presented in other studies. Note that the present study estimated volumes in 100 m

^{2}plots and upscaled the values for an estimate per hectare. Minimum value from Pedlar et al. [48] includes snags. Sturtevant et al. [46] values are for individual stands, while all other studies present averages.

Citation | Forest Types (Min/Max) | Location | Min | Max |
---|---|---|---|---|

Lee et al., 1997 [45] | 20–30 yr. aspen stands/120 + yr. aspen stands | AB, Canada | 108.8 | 124.3 |

Linder et al., 1997 [49] | Natural pine, spruce and deciduous stands | Sweden | 62 | - |

Sturtevant et al., 1997 [46] | 58 yr. fir stand/80 yr. fir stand | NL, Canada | 15.2 | 78.1 |

Sippola et al., 1998 [47] | Managed 15 yr. spruce stands/Natural mixed stands | Finland | 6.6 | 47.2 |

Pedlar et al., 2002 [48] | Spruce stands/mixed stands | ON, Canada | <17.8 | 131.5 |

Present study | Black spruce dominated wetlands/Upland coniferous, deciduous and mixed forests | AB, Canada | 3.14 | 17.73 |

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**MDPI and ACS Style**

Lopes Queiroz, G.; McDermid, G.J.; Linke, J.; Hopkinson, C.; Kariyeva, J.
Estimating Coarse Woody Debris Volume Using Image Analysis and Multispectral LiDAR. *Forests* **2020**, *11*, 141.
https://doi.org/10.3390/f11020141

**AMA Style**

Lopes Queiroz G, McDermid GJ, Linke J, Hopkinson C, Kariyeva J.
Estimating Coarse Woody Debris Volume Using Image Analysis and Multispectral LiDAR. *Forests*. 2020; 11(2):141.
https://doi.org/10.3390/f11020141

**Chicago/Turabian Style**

Lopes Queiroz, Gustavo, Gregory J. McDermid, Julia Linke, Christopher Hopkinson, and Jahan Kariyeva.
2020. "Estimating Coarse Woody Debris Volume Using Image Analysis and Multispectral LiDAR" *Forests* 11, no. 2: 141.
https://doi.org/10.3390/f11020141