# Woody Biomass Estimation in a Southwestern U.S. Juniper Savanna Using LiDAR-Derived Clumped Tree Segmentation and Existing Allometries

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## Abstract

**:**

^{2}= 0.83, p < 0.001) to drive the allometry for J. monosperma on a per segment basis. Further, we showed that making use of the full 3D point cloud from LiDAR for the generation of canopy object statistics improved that relationship by including canopy segment point density as a covariate (R

^{2}= 0.91). This work suggests the potential for LiDAR-derived estimates of AGB in spatially-heterogeneous and highly-clumped ecosystems.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Description

#### 2.2. Field Measurements

#### 2.3. Airborne LiDAR Data

^{2}area situated along a 5-km north-south extent that included the 4-ha study area. Using an Optech Gemini with a laser pulse repetition rate of 125 kHz, 50% flight-line overlap, scan angle of ±16° and flying at an average altitude of 400 m above ground, LiDAR data were collected over the juniper savanna site. The LiDAR point cloud data had an average horizontal point spacing of 20 cm and a point density of 10 points·m

^{−2}. The mean horizontal relative accuracy was 25 cm RMSE, and vertical accuracy was approximately 10 cm RMSE or better for open surfaces. Figure 3A shows the full analysis extent.

#### 2.4. Canopy Segmentation and Statistics

^{2}), perimeter (m), canopy volume (m

^{3}), canopy density (points·m

^{−3}), canopy closure (unitless) and eccentricity (unitless). Canopy volume is defined as the projected canopy area multiplied by the maximum canopy height. Here, we define canopy closure as the ratio of canopy returns to ground returns within the projected area of each segment. If a segment has a well-defined major and minor axis, the eccentricity is computed for each segment. Trees and clumps with a near circular shape should have an eccentricity near zero, whereas more elliptically-shaped trees and clumps will have eccentricities near 0.5. The strength of these metrics is that they are computed on all of the points within the segmented point cloud rather than only the first reflective surface, as in a canopy height model.

#### 2.5. Validation of Clump Level Allometries

^{2}(R

^{2}

_{ADJ}) and root mean squared error (RMSE).

#### 2.6. Uncertainty Estimation

## 3. Results

#### 3.1. Field Measurements

^{2}, 70.6 m

^{3}and 32.5 cm, respectively (Figure 5), with an estimated stem density within our four-hectare analysis region of 135.1 stems·ha

^{−1}. The representativeness of the trees used to parametrize the LiDAR-based regressions of biomass was assessed by comparing field-measured canopy height with the mean local maximum canopy height within the LiDAR analysis extent, and the distribution of heights measured by our field plots was representative of the analysis extent (Figure 6). The mean estimated field biomass using the allometry from Grier et al. [32] was 15.6 megagrams per hectare (Mg·ha

^{−1}). The three ground-measured crown properties (height, area and volume) all performed well as predictors of single tree ESD, with adjusted R

^{2}

_{ADJ}values of 0.60, 0.77 and 0.80, respectively (p < 0.001). We chose to use canopy volume to drive our remote allometry (Figure 7), as it was the best predictor of ESD (R

^{2}

_{ADJ}= 0.79, RMSE = 1.23 cm

^{2}, p < 0.001). The resulting regression equation was:

#### 3.2. LiDAR Segmentation

#### 3.3. Segmentation-Derived Biomass and Uncertainty

_{CHM}and H

_{TEX}corresponding to maximum segment height derived via the surface height raster (2D) and the full point cloud (3D), respectively. The final three models were driven by TEXPERT-derived 3D point cloud statistics (Vol = volume only, Vol

_{D}= volume and point density, Vol

_{C}= volume and segment closure). Neither H

_{CHM}nor H

_{TEX}predictions of ESD showed relationships with ground-measured clumped ESD, which were commensurate with the ground-driven individual regressions (Figure 7A compared to Figure 8A,B), suggesting that the linearity imposed by log transforming the ground data is lost when scaling to multiple individuals. The 3D point cloud-derived height estimates from H

_{TEX}did show an improved fit relative to the raster-derived estimates from H

_{CHM}(R

^{2}

_{ADJ}= 0.22 vs. 0.24, p < 0.05), yet neither model showed correlations that were significantly improved relative to the volume-based models.

^{2}

_{ADJ}= 0.89, p < 0.001), yet when segment point density was included as a covariate in the regression, the correlation between predicted and measured ESD increased and the RMSE decreased, in spite of the increasing model complexity (Vol

_{D}R

^{2}

_{ADJ}= 0.91, p < 0.001; Figure 8C). Canopy closure did not show a significant improvement over the volume-only model (Table 2). Using the Vol

_{D}model structure, the resulting 95th percentile confidence interval for the estimated total biomass over the field measurement extent was calculated as 14.7 ± 0.13 Mg·ha

^{−1}compared to the field-measured mean of 15.6 Mg·ha

^{−1}, where uncertainty is expressed as the mean standard deviation from each segment’s AGB estimate output from the Monte Carlo approach described in Section 2.6. On a per-segment basis, the AGB estimates and corresponding segment standard deviations from the Vol

_{D}model were well distributed and reasonable given our knowledge of the site (Figure 9).

_{D}(Figure 10A,B), as well as the difference between the Vol and Vol

_{D}outputs (Figure 10C), which corresponds to roughly 2.6 Mg·ha

^{−1}across the analysis extent.

## 4. Discussion

^{2}

_{ADJ}= 0.91).

^{2}of 0.79, p < 0.001), consistent with the good agreement seen in previous studies (e.g., [35,36]). Potential sources of error between field-measured crown parameters and those derived from LiDAR are potentially due to the horizontal resolution of the LiDAR data (1 m), effectively smoothing maximum heights and canopy edges, and to errors in the ground data collection. Higher resolution data may constrain the absolute error associated with measuring canopy heights, but agreement with field measurements may not improve unless the sophistication of the field height estimates increases (e.g., with the use of a laser hypsometer rather than a collapsible height stick). Our sample size for the regressions used to assess the goodness of fit at the segmentation level was greatly reduced relative to our ground validation sample size (n = 52 for field regressions, n = 15 for segmentation-based regressions) given that in most cases, single canopy objects derived from LiDAR were actually comprised of multiple individuals. Further, our circle plot-based validation approach poorly accommodated segmented canopy objects, which spanned the circle plot perimeter, reducing the number of segments we were able to include in the predictive models. This small sample size may reduce our ability to scale these results to areas further reaching than our immediate analysis area. However, we believe the method we employed is scalable and that the general results of increasing explanatory power by leveraging the full point cloud data would not fall apart had we increased our sampling number.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Extent of piñon juniper woodlands (PJ, dark green) and juniper savanna (JSAV, light green) ecosystems across the four corner states. (Right) Location and layout of the field site, with tree crown locations bounded by the four 17.5-m radius circle plots.

**Figure 2.**Typical branching patterns of Juniperus monosperma across the study area. Some individuals branch below the ground (

**A**), while others branch above (

**B**). Due to the woody mass that sometimes forms at the base of these trees, we measured equivalent stem diameters (ESD; Equation (1)) as illustrated in (

**B**), using an ~30-cm radius from the woody mass to each stem diameter measurement.

**Figure 3.**LiDAR canopy height acquisition extent (

**A**) displayed as a canopy height raster. The corresponding TEXPERT segmentation (

**B**) represents the delineated isolated and clumped crowns, used to generate canopy statistics on the raw height and volume data (

**C**).

**Figure 4.**(

**A**) The automatic delineation of ground and vegetation from the TEXAS model, resulting in (

**B**) clumped crown segmentation, which was then (

**C**) vectorized and overlaid on ground-measured stem maps within our study area for segment statistic generation.

**Figure 7.**Ground-derived relationships between canopy parameters and equivalent stem diameter (ESD; see Equation (1)). Both axes have been log transformed to establish linear fits.

**Figure 8.**Modeled equivalent stem diameter (ESD; Equation (1)) versus measured stem diameter. Here, the modeled stem diameter was generated using max height from the raster canopy height model (CHM) (

**A**); max height from the TEXPERT height model (

**B**); segment volume from TEXPERT (

**C**); volume and density (

**D**); and volume and closure (

**E**). RMSE is expressed in units of cm.

**Figure 9.**Overview map of the study extent, displaying Mg AGB binned into roughly 0.08-ha hexels, highlighted by the red extent marker (

**A**); the individual segment calculations of kg AGB driven by the best performing model (VolD) are shown in (

**B**); with the corresponding segment standard deviation in kg shown in (

**C**).

**Figure 10.**Mapped mean biomass (Mg AGB) binned into roughly 0.08-ha hexels across the analysis extent derived from the best predictors of equivalent stem diameter, volume and density (

**A**) and the corresponding mean standard deviation for the mean AGB in each hex (

**B**); (

**C**) highlights the difference between biomass predictions using ESD as a function of volume only, vs. ESD derived from volume and density, calculated as Vol—Vol

_{D}, where the resulting difference is expressed in terms of Mg AGB.

**Table 1.**Summary of the clumped segmentation statistics generated from the full 3D point cloud for all of the canopy objects within the analysis extent. Abbreviations: Standard Deviation (Std), Average (Avg).

Segment Statistic | Min | Max | Mean | Std |
---|---|---|---|---|

Max Elevation (m) | 1.55 | 8.31 | 4.14 | 0.76 |

Min Elevation (m) | 0 | 3.44 | 0.3 | 0.09 |

Avg Elevation (m) | 0.57 | 5.67 | 2.12 | 0.37 |

Med Elevation (m) | 0.22 | 7.36 | 2.28 | 1.06 |

Std Elevation (m) | 0.28 | 2.38 | 1.02 | 0.23 |

RMS Elevation (m) | 0.64 | 5.77 | 2.36 | 0.4 |

Perimeter (m) | 10.97 | 290.45 | 42.08 | 24.43 |

Projected Area (m^{2}) | 12.67 | 2158.13 | 94.35 | 117.73 |

Volume (m^{3}) | 41.33 | 5302.16 | 399.52 | 611.66 |

Density (unitless) | 0.08 | 0.99 | 0.44 | 0.21 |

Closure (unitless) | 0.17 | 1 | 0.75 | 0.15 |

**Table 2.**Predictive model structures tested in the study. Models driven by height or volume alone contain only a slope (α) and intercept (b) as parameters, whereas models with two inputs (Vol

_{D}and Vol

_{C}) contain an additional primary and interaction term (β and γ). ESD, equivalent stem diameter.

ESD = b + α (x_{1}) + β (x_{2}) + γ (x_{1} × x_{2}) | ||||||||
---|---|---|---|---|---|---|---|---|

Model | x_{1} | x_{2} | b | α | β | γ | R^{2}_{ADJ} | p |

H_{CHM} | CHM Height | - | −3.05 | 14.04 | - | - | 0.22 | 0.046 |

H_{TEX} | TEX Height | - | −10.07 | 15.73 | - | - | 0.24 | 0.038 |

Vol | Volume | - | 31.43 | 0.08 | - | - | 0.89 | <0.0001 |

Vol_{D} | Volume | Density | 6.41 | 0.16 | 42.17 | −0.15 | 0.91 | <0.0001 |

Vol_{C} | Volume | Closure | 11.21 | 11.21 | 26.65 | −0.18 | 0.89 | <0.0001 |

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## Share and Cite

**MDPI and ACS Style**

Krofcheck, D.J.; Litvak, M.E.; Lippitt, C.D.; Neuenschwander, A. Woody Biomass Estimation in a Southwestern U.S. Juniper Savanna Using LiDAR-Derived Clumped Tree Segmentation and Existing Allometries. *Remote Sens.* **2016**, *8*, 453.
https://doi.org/10.3390/rs8060453

**AMA Style**

Krofcheck DJ, Litvak ME, Lippitt CD, Neuenschwander A. Woody Biomass Estimation in a Southwestern U.S. Juniper Savanna Using LiDAR-Derived Clumped Tree Segmentation and Existing Allometries. *Remote Sensing*. 2016; 8(6):453.
https://doi.org/10.3390/rs8060453

**Chicago/Turabian Style**

Krofcheck, Dan J., Marcy E. Litvak, Christopher D. Lippitt, and Amy Neuenschwander. 2016. "Woody Biomass Estimation in a Southwestern U.S. Juniper Savanna Using LiDAR-Derived Clumped Tree Segmentation and Existing Allometries" *Remote Sensing* 8, no. 6: 453.
https://doi.org/10.3390/rs8060453