# Modeling Forest Aboveground Biomass and Volume Using Airborne LiDAR Metrics and Forest Inventory and Analysis Data in the Pacific Northwest

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2 }values of 0.83 and 0.81 for AGBM and gV, utilizing mean height and the 90th height percentile as predictors, respectively. Similar results were found for multiple regression models, where plot-level analysis produced models with R

^{2 }values of 0.87 and 0.88 for AGBM and gV, utilizing multiple height percentile metrics as predictor variables. Results suggest that the current FIA plot design can be used with dense airborne LiDAR data to produce area-based estimates of AGBM and gV, and that the increased spatial scale of hectare plots may be inappropriate for modeling AGBM of gV unless exhaustive tree tallies are available. Overall, this study demonstrates that ALS data can be used to create models that describe the AGBM and gV of Pacific Northwest FIA plots and highlights the potential of estimates derived from ALS data to augment current FIA data collection procedures by providing a temporary intermediate estimation of AGBM and gV for plots with outdated field measurements.

## 1. Introduction

^{2}= 0.83). Hyde et al. [34] used LiDAR, synthetic aperture radar (SAR), and interferometric synthetic aperture radar (InSAR) to individually and synergistically predict AGBM for a southwestern ponderosa pine forest, and found, through individual comparison, that LiDAR predicted AGBM best, accounting for almost 84% of the variability.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data

**Figure 1.**Malheur National Forest study area in eastern Oregon with slope depicted in degrees. Black squares represent locations of selected Forest Inventory and Analysis plots field-visited between 2007 and 2009. Actual plot locations have been obscured due to confidentiality constraints.

#### 2.2.1. Forest Inventory and Analysis Data

**Figure 2.**The location and dimensions of the subplots (r = 7.32 m) and one-hectare (r = 56.42 m) plot used by the Pacific Northwest Forest Inventory and Analysis region. Figure not drawn to scale.

Sample Year | |||||||||
---|---|---|---|---|---|---|---|---|---|

2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | |

Subplots | 36 | 76 | 120 | 20 | 80 | 88 | 104 | 84 | 100 |

Plot | 9 | 19 | 30 | 5 | 20 | 22 | 26 | 21 | 25 |

Hectare Plots | 9 | 19 | 30 | 5 | 20 | 22 | 26 | 21 | 25 |

#### 2.2.2. ALS Data

^{2}. Although the first data collection mission was performed during months where leaf-off conditions could be present, the majority of species within our study area do not lose their foliage during the winter months. Three hectare plots utilized in this study had LiDAR data acquired during both the leaf-on and leaf-off acquisitions. These plots were utilized to examine if major differences between LiDAR data collected during leaf-on and leaf-off conditions existed. Comparison of hectare plot-level metrics for these data did not identify large differences. For example, mean plot heights for leaf-off conditions were 7.6 m, 7.7 m, and 5.8 m. Corresponding mean heights from leaf-on conditions were 7.8 m, 7.8 m, and 5.9 m.

#### 2.3. Processing Approach

#### 2.3.1. Point Cloud-Based ALS Metrics

Crown Class | ||||||
---|---|---|---|---|---|---|

Og ^{b} | D ^{c} | CD ^{d} | I ^{e} | OT ^{f} | ||

Abies concolor | 34 | 0 | 6 | 19 | 6 | 3 |

Abies grandis | 331 | 1 | 52 | 111 | 121 | 46 |

Juniperus occidentalis | 24 | 0 | 3 | 12 | 7 | 2 |

Larix occidentalis | 79 | 0 | 23 | 32 | 23 | 1 |

Picea engelmannii | 5 | 0 | 0 | 3 | 2 | 0 |

Pinus contorta | 250 | 0 | 28 | 125 | 84 | 13 |

Pinus monticola | 1 | 0 | 1 | 0 | 0 | 0 |

Pinus ponderosa | 411 | 4 | 125 | 178 | 95 | 9 |

Pseudotsuga menziesii | 217 | 0 | 45 | 73 | 76 | 23 |

Cercocarpus ledifolius | 45 | 0 | 0 | 24 | 20 | 1 |

^{a}Number of trees;

^{b}Open grown crown class;

^{c}Dominant crown class;

^{d }Codominant crown class;

^{e}Intermediate crown class; and

^{ f}Overtopped crown class.

#### 2.3.2. Extraction of Subplot and Hectare Plot Point Clouds

DBH (cm) | Height (m) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Min | Max | SD ^{b} | CV(%) ^{c} | Mean | Min | Max | SD ^{b} | CV(%) ^{c} | ||

Abies concolor | 34 | 38.2 | 3.3 | 99.1 | 25.8 | 67.5 | 18.8 | 2.7 | 42.1 | 10.9 | 57.8 |

Abies grandis | 331 | 27.9 | 2.5 | 97.8 | 18.9 | 67.7 | 15.3 | 1.5 | 42.7 | 8.1 | 53.0 |

Juniperus occidentalis | 24 | 27.3 | 12.7 | 63.5 | 13.9 | 50.8 | 10.4 | 6.1 | 16.2 | 3.2 | 30.5 |

Larix occidentalis | 79 | 27.2 | 2.5 | 65.8 | 15.5 | 56.9 | 20.8 | 3.0 | 39.6 | 8.8 | 42.4 |

Picea engelmannii | 5 | 24.4 | 17.8 | 35.8 | 7.5 | 30.8 | 16.9 | 11.6 | 24.1 | 5.0 | 29.7 |

Pinus contorta | 250 | 14.9 | 2.5 | 35.1 | 8.0 | 53.3 | 12.5 | 2.1 | 27.1 | 6.6 | 53.1 |

Pinus monticola | 1 | NA | 45.0 | 45.0 | NA | NA | NA | 33.5 | 33.5 | NA | NA |

Pinus ponderosa | 411 | 38.2 | 2.5 | 111.3 | 24.6 | 64.3 | 18.5 | 1.8 | 42.7 | 10.0 | 54.2 |

Pseudotsuga menziesii | 217 | 28.5 | 2.8 | 108.0 | 21.4 | 75.2 | 16.5 | 2.1 | 41.8 | 8.9 | 53.8 |

Cercocarpus ledifolius | 45 | 21.2 | 4.1 | 120.7 | 16.3 | 77.1 | 5.6 | 1.2 | 7.9 | 1.3 | 23.0 |

^{a}number of trees;

^{b }standard deviation; and

^{c}coefficient of variation percentage.

**Table 4.**Subplot and hectare plot descriptive statistics for mean estimated biomass and volume. Descriptive statistics for subplot and hectare plot aboveground biomass (AGBM) and gross volume (gV) were calculated excluding subplots and hectare plots with no Forest Inventory and Analysis reported ABGM or gV.

n ^{a} | n_{r }^{b} | Mean | Min | Max | SD ^{c} | CV(%) ^{d} | |
---|---|---|---|---|---|---|---|

Subplot AGBM (Mg∙ha^{−1}) | 232 | 197 | 90.30 | 2.09 | 564.35 | 91.02 | 101 |

Hectare Plot AGBM (Mg∙ha^{−1}) | 58 | 55 | 81.04 | 0.92 | 235.00 | 58.25 | 72 |

Subplot gV (m^{3}∙ha^{−1}) | 232 | 197 | 150.04 | 1.56 | 1059.49 | 163.25 | 109 |

Hectare Plot gV (m^{3}∙ha^{−1}) | 58 | 55 | 134.53 | 0.39 | 381.78 | 100.20 | 74 |

^{a}number of plots;

^{b }reduced number of plots;

^{c}standard deviation; and

^{d}coefficient of variation percentage.

n ^{a} | Mean | Min | Max | SD ^{b} | CV(%) ^{c} |
---|---|---|---|---|---|

197 | 1.25 | 0.38 | 3.72 | 0.67 | 54.02 |

^{a}Number of FIA subplots;

^{b}Standard deviation; and

^{c}Coefficient of variation percentage.

**Figure 3.**Light detection and ranging (LiDAR) analysis levels. Point clouds were extracted for individual subplots, clusters of four subplots, and hectare plots.

#### 2.3.3. Calculation of Above Ground Level Elevations and Removal of Ground Points

#### 2.3.4. Height Percentiles

#### 2.3.5. Height Bins

**Figure 4.**Conceptual illustration of the separation of vertical space (

**left**), and example of the vertical distribution and separation (by metric type) of light detection and ranging (LiDAR) returns in a hectare plot (

**right**).

**Figure 5.**Cross sectional plot of one subplot point cloud visualizing the minimum height thresholds for density metrics, with subfigures a through f highlighting all points above the minimum height thresholds of 0 m (

**a**), 5 m (

**b**), 10 m (

**c**), 15 m (

**d**), 20 m (

**e**), and 25 m (

**f**), respectively.

#### 2.3.6. Density Metrics

#### 2.3.7. Regression Analysis

Independent Variables (Light Detection and Ranging Area-Based Metrics) | Predicted Variables (FIA Field Measurements) |
---|---|

Height Percentiles (p) | AGBM (Mg∙ha^{−1}) |

p25, p50, p75, p90, p95, max, mean | gV (m^{3}∙ha^{−1}) |

Height Bins (hb) | |

hb0-5, hb5-10, hb10-15, hb15-20, hb20-25, hbgt25 | |

Density (d) | |

d1, d2, d3, d4, d5, d6 |

## 3. Results

_{sqrt}and gV

_{sqrt}) was most appropriate for these data.

**Figure 7.**Scatter plot of simple linear regression results for the best simple linear regression aboveground biomass models (transformed and non-transformed) for individual subplots (

**a**,

**b**), plots (

**c**,

**d**), and hectare plots (

**e**,

**f**). * indicates p-values of less than 0.05.

**Figure 8.**Scatter plot of simple linear regression results for the best simple linear regression gross volume models (transformed and non-transformed) for individual subplots (

**a**,

**b**), plots (

**c**,

**d**), and hectare plots (

**e**,

**f**). * indicates p-values of less than 0.05.

**Table 7.**Summary of the best subplot-level aboveground biomass and gross volume simple linear regression models for each point cloud metric set. * indicate p-values of less than 0.05.

Subplot-Level | ||||||||
---|---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | PRESS | |

AGBM_{sqrt} | mean | 0.77 | 0.77 | 2.03 | 2.21 * | 1.08 * | 819.56 | |

AGBM_{sqrt} | hb20-25 | 0.52 | 0.52 | 2.94 | 6.11 * | 51.28 * | 1725.46 | |

AGBM_{sqrt} | d3 | 0.67 | 0.67 | 2.45 | 1.70 * | 24.60 * | 1198.80 | |

gV_{sqrt} | mean | 0.73 | 0.73 | 3.01 | 2.39 * | 1.44 * | 1812.01 | |

gV_{sqrt} | hb20-25 | 0.49 | 0.49 | 4.16 | 7.61 * | 67.88 * | 3469.53 | |

gV_{sqrt} | d3 | 0.62 | 0.62 | 3.57 | 1.77 * | 32.54 * | 2548.38 |

**Table 8.**Summary of the best clustered subplot-level aboveground biomass and gross volume simple linear regression models for each point cloud metric set. * indicates p-values of less than 0.05.

Plot-Level | |||||||
---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | PRESS |

AGBM_{sqrt} | mean | 0.83 | 0.83 | 1.45 | 1.96* | 1.18* | 119.73 |

AGBM_{sqrt} | hb20-25 | 0.56 | 0.56 | 2.31 | 5.57* | 63.59* | 305.42 |

AGBM_{sqrt} | d3 | 0.76 | 0.76 | 1.71 | 3.12* | 21.54* | 168.47 |

gV_{sqrt} | p90 | 0.81 | 0.81 | 2.05 | 0.49 | 0.65* | 237.39 |

gV_{sqrt} | mean | 0.80 | 0.79 | 2.12 | 2.26* | 1.15* | 258.30 |

gV_{sqrt} | hb20-25 | 0.54 | 0.54 | 3.18 | 7.01* | 83.90* | 578.31 |

gV_{sqrt} | d3 | 0.74 | 0.73 | 2.4 | 3.75* | 28.53* | 332.59 |

**Table 9.**Summary of the best hectare plot-level aboveground biomass and gross volume simple linear regression models for each point cloud metric set. * indicates p-values of less than 0.05.

Hectare Plot-Level | |||||||
---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | PRESS |

AGBM_{sqrt} | mean | 0.73 | 0.73 | 1.81 | 1.47 * | 1.23 * | 186.49 |

AGBM_{sqrt} | hb15-20 | 0.63 | 0.63 | 2.12 | 3.16 * | 65.55 * | 254.03 |

AGBM_{sqrt} | d3 | 0.73 | 0.72 | 1.83 | 2.39 * | 23.65 * | 190.55 |

gV_{sqrt} | p90 | 0.73 | 0.72 | 2.45 | −0.47 | 0.68 * | 336.96 |

gV_{sqrt} | mean | 0.71 | 0.71 | 2.51 | 1.55 | 1.63 * | 364.11 |

gV_{sqrt} | hb15-20 | 0.62 | 0.61 | 2.92 | 3.81 * | 86.77 * | 482.64 |

gV_{sqrt} | d3 | 0.71 | 0.71 | 2.52 | 2.74 * | 31.51 * | 361.20 |

^{2}value and higher RMSE than the SLR models developed for AGBM and gV SLR. The initial height bin-based MR model for AGBM (utilizing the square root transformation) utilized hb5-10, hb10-15, and hb15-20 as independent variables. This model showed no multicollinearity issues (VIFs below 10). All independent variables utilized were significant at the α = 0.05 level. The height bin-based model for gV (utilizing the square root transformation) employed hb10-15 and hb20-25, and showed no indication of multicollinearity (VIFs below 10). All independent variables were significant at the α = 0.05 level. The height bin-based MR models for AGBM and gV accounted for 74% and 73% of the variability in field estimated AGBM and gV, respectively. Analysis of the VIFs for the initial density-based MR models for the square root transformed AGBM and square root transformed gV did not indicate multicollinearity issues. All selected independent variables (d2 and d4 for AGBM and d2 and d5 for gV) were significant at the α = 0.05 level. Density-based MR models for AGBM and gV accounted for 75% and 73% of the variability in the field estimated AGBM and gV, respectively.

^{2 }values improved from models based on individual subplots to models based on plots. When the scale of the analysis level is increased to the hectare plot-level, a decrease in model R

^{2 }values was observed. This pattern was visible in both SLR models and MR models (Table 7, Table 8 and Table 9 and Table 10, Table 11 and Table 12, respectively). Overall, the best R

^{2 }values were obtained when using plot-level analysis.

**Table 10.**Subplot-level multiple regression analysis results. * indicates p-values of less than 0.05.

Subplot MR Models | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | β_{2} | β_{3} | β_{4} | β_{5} | PRESS |

AGBM_{sqrt} | p90, mean | 0.78 | 0.78 | 1.99 | 1.58 * | 0.13 * | 0.85 * | NA | NA | NA | 802.77 |

AGBM_{sqrt} | hb5-10, hb10-15, hb15-20, hb20-25, hbgt25 | 0.78 | 0.77 | 2.02 | 2.85 * | 8.72 * | 11.47 * | 18.45 * | 17.81 * | 39.00 * | 832.19 |

AGBM_{sqrt} | d2,, d3, d5, d6 | 0.78 | 0.77 | 2.02 | 2.85 * | 11.58 * | 6.61 * | 20.64 * | −30.14 * | NA | 821.39 |

gV_{sqrt} | p95, max, mean | 0.75 | 0.75 | 2.93 | 2.83 * | 0.32 * | −0.21 * | 1.22 * | NA | NA | 1771.70 |

gV_{sqrt} | hb5-10, hb10-15, hb15-20, hb20-25, hbgt25 | 0.75 | 0.74 | 2.97 | 3.38 * | 9.77 * | 15.90 * | 26.42 * | 19.56 * | 54.08 * | 1789.31 |

gV_{sqrt} | d2, d5, d6 | 0.74 | 0.74 | 2.97 | 3.45 * | 21.18 * | 32.91 * | −46.42 * | NA | NA | 1775.36 |

Plot MR Models | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | β_{2} | β_{3} | β_{4} | PRESS |

AGBM_{sqrt} | p75, p95 | 0.87 | 0.87 | 1.26 | 1.03 | 0.32* | 0.23* | NA | NA | 97.33 |

AGBM_{sqrt} | hb5-10, hb15-20, hbgt25 | 0.86 | 0.85 | 1.32 | 2.09* | 19.91* | 33.74* | 58.81* | NA | 102.27 |

AGBM_{sqrt} | d2, d6 | 0.86 | 0.86 | 1.30 | 1.98* | 15.57* | 36.97* | NA | NA | 96.65 |

gV_{sqrt} | p25, p75, p95 | 0.88 | 0.88 | 1.63 | 0.93 | −3.25* | 0.46* | 0.06* | NA | 165.70 |

gV_{sqrt} | hb0-5, hb5-10, hb15-20, hbgt25 | 0.85 | 0.84 | 1.87 | 5.10* | −3.43* | 20.28* | 39.32* | 76.50* | 208.26 |

gV_{sqrt} | d2, d6 | 0.84 | 0.83 | 1.91 | 2.31* | 20.35* | 50.08* | NA | NA | 211.99 |

**Table 12.**Hectare plot-level multiple regression analysis results. * indicates p-values of less than 0.05.

Hectare Plot MR Models | |||||||||
---|---|---|---|---|---|---|---|---|---|

DV | IV | R^{2} | Adj-R^{2} | RMSE | β_{0} | β_{1} | β_{2} | β_{3} | PRESS |

AGBM_{sqrt} | hb5-10, hb15-20, hbgt25 | 0.74 | 0.73 | 1.82 | 1.83 * | 14.04 * | 48.68 * | 42.35 * | 189.49 |

AGBM_{sqrt} | d2, d4 | 0.75 | 0.74 | 1.77 | 1.67 * | 11.92 * | 15.67 * | NA | 178.87 |

gV_{sqrt} | hb10-15, hb20-25 | 0.71 | 0.71 | 2.53 | 2.55 * | 43.08 * | 83.40 * | NA | 365.18 |

gV_{sqrt} | d2, d5 | 0.73 | 0.72 | 2.45 | 1.38 | 21.16 * | 22.93 * | NA | 343.98 |

## 4. Discussion

**Figure 9.**Cross-sectional plots of two subplot point clouds displaying the location of the best aboveground biomass and gross volume predictor variables. The

**left**subfigures identify the mean height for each example subplot. The

**middle**subfigures identify the location of height bin 20-25 for each example subplot. The

**right**subfigures identify the location of density 3 for each example subplot.

**Figure 10.**A visual comparison of height bin 15-20 and height bin 20-25 metrics for a hectare plot. Height bin15-20 provides more information about the conditions present on the hectare plot than height bin 20-25. (

**a**) Cross sectional plot of one hectare plot and the location of height bin 15-20 and height bin 20-25; (

**b**) Top-down representation of all points within the hectare plot; (

**c**) Top-down representation of the points falling within height bin 15-20; and (

**d**) Top-down representation of the points falling within height bin 20-25.

^{2}values ranging from 0.74 to 0.78. AGBM and gV models utilizing height bin metrics always required more predictor variables than models utilizing density metrics, in part due to the compartmentalized nature of height bin metrics. Density metrics exhibit strong spatial correlation, and as such the inclusion of a large number of density bins leads to multicollinearity issues.

^{2 }values are a result of the discrepancies in the population distribution between hectare plots and plots. Such discrepancies would not be an issue if exhaustive tree tallies were available for the hectare plots. Overall, this finding provides evidence that the current FIA plot design can be used with dense airborne LiDAR data to produce area-based estimates of AGBM and gV.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Sheridan, R.D.; Popescu, S.C.; Gatziolis, D.; Morgan, C.L.S.; Ku, N.-W.
Modeling Forest Aboveground Biomass and Volume Using Airborne LiDAR Metrics and Forest Inventory and Analysis Data in the Pacific Northwest. *Remote Sens.* **2015**, *7*, 229-255.
https://doi.org/10.3390/rs70100229

**AMA Style**

Sheridan RD, Popescu SC, Gatziolis D, Morgan CLS, Ku N-W.
Modeling Forest Aboveground Biomass and Volume Using Airborne LiDAR Metrics and Forest Inventory and Analysis Data in the Pacific Northwest. *Remote Sensing*. 2015; 7(1):229-255.
https://doi.org/10.3390/rs70100229

**Chicago/Turabian Style**

Sheridan, Ryan D., Sorin C. Popescu, Demetrios Gatziolis, Cristine L. S. Morgan, and Nian-Wei Ku.
2015. "Modeling Forest Aboveground Biomass and Volume Using Airborne LiDAR Metrics and Forest Inventory and Analysis Data in the Pacific Northwest" *Remote Sensing* 7, no. 1: 229-255.
https://doi.org/10.3390/rs70100229