# Estimating Stand Volume and Above-Ground Biomass of Urban Forests Using LiDAR

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}were 0.81 (p < 0.01) for the stand volume model and 0.77 (p < 0.01) for the AGB model with a RMSE of 23.66 m

^{3}·ha

^{−1}(23.3%) and 19.59 Mg·ha

^{−1}(23.9%), respectively. We found that a combination of two LiDAR-derived variables (i.e., proxy of BA and proxy of H), which take the form of a forest allometric model, can be used to estimate stand volume and above-ground biomass in broadleaved urban forest areas. Our results can be compared to other studies conducted using LiDAR in broadleaved forests with similar methods.

## 1. Introduction

_{proxy}and H

_{proxy}are the LiDAR-derived variables representing, respectively, forest stand basal area (BA) and mean tree height (H).

## 2. Materials and Methods

#### 2.1. Study Area and Stand Delineation

^{2}) in September 2012 (Figure 1). The field plots were selected to represent the variety of species that were used in PNM upon its establishment (1983), e.g., Acer spp., Carpinus betulus, Fraxinus spp., Prunus avium, Quercus cerris, Quercus robur, Tilia spp., and Ulmus spp. (for more details see Marziliano et al. 2013; [10]). Moreover, plots were selected to represent three stages of forest stand development (i.e., stand age class): (1) <17 year; (2) 18–25 years; and (3) >25 years. Within each plot, all trees with a diameter equal or greater than 10 cm were identified by species and measured for their diameter at breast height (DBH), height, crown width at four cardinal directions, and crown depth (Figure S1). Field survey was undertaken using a Trimble GeoXT 6000 GPS. The GPS receiver had an estimated sub-meter accuracy after differential correction. From these measurements, we calculated the plot-level BA, mean DBH, and mean H. Stand VOL and AGB were calculated using the allometric equations of the Italian National Forest Inventory system [29]. For each tree, the following allometric equation was used:

_{i}is the forest stand characteristic for a tree (AGB or VOL), DBH

_{i}and H

_{i}are, respectively, the height and the diameter at breast height of the given tree. For each plot, total VOL and AGB were calculated by summing the values of all the trees belonging to the plot.

#### 2.2. LiDAR Data

^{2}, with a maximum of seven returns per impulse. This results in a relative position accuracy of ±10 cm and a relative height accuracy of ±7 cm (see Table 1). All the points with a scan angle greater than 10 degrees were excluded from the processing (Figure 2). After excluding the points, the average point density was 6 points/m

^{2}.

#### 2.3. LiDAR-Derived Basal Area (BA)

_{nofirst}0_10), 20th (A

_{nofirst}0_20), 30th (A

_{nofirst}0_30), 40th (A

_{nofirst}0_40), 50th (A

_{nofirst}0_50), 60th (A

_{nofirst}0_60) and 70th percentile (A

_{nofirst}0_70).

#### 2.4. LiDAR-Derived Mean Stand Height

_{first}90), 95th (Perc

_{first}95) and 99th (Perc

_{first}99) percentiles; and (2) area of the frequency histogram, i.e., from the 80th to the 90th percentile (A

_{first}80_90), from the 80th to the 99th percentile (A

_{first}80_99), from the 90th to the 95th percentile (A

_{first}90_95), from the 90th to the 99th percentile (A

_{first}90_99), and from the 95th to the 99th percentile (A

_{first}95_99).

#### 2.5. Model Development

_{proxy}is one of the LiDAR-derived variables for basal area (e.g., Weibull scale) and H

_{proxy}is one of the LiDAR-derived variables for mean stand height (e.g., Perc

_{first}90). The back-conversion to the multiplicative form introduces a bias that was corrected by adding half of the residual variance to the intercept before conversion [39]. The best-supported models were selected on the basis of the AIC (Akaike’s information criterion) value.

## 3. Results

#### 3.1. Basal Area (BA)

_{nofirst}), varied from 5.47 to 11.77, with a mean value of 8.36 and standard deviation (SD) of 2.08 (Figure 4). We tested the relationship between wb

_{nofirst}and ground measurements with correlation analysis. The wb

_{nofirst}values were highly related to field measurements of BA (Pearson = 0.78) and DBH (Pearson = 0.81) (Table 2). The MSEn of each Weibull distribution ranged from 6% to 32%, with the lowest MSEn found in the youngest plot, which were aged 12 years since plantation. The highest MSEn was found in one of the oldest plots (1A; 29 years old). Overall, the MSEn was lower in the five plots that were <25 years old (6.94%, 13.18%, 13.41%, 15.27%, and 15.82%) than the five plots of ≥25 years old (20.92%, 27.18%, 25.27%, 32.71%, and 23.7%). This is likely due to the characteristics of the height distributions that appeared to be bimodal as forests age increased.

_{nofirst}0_10, Pearson = 0.23; A

_{nofirst}0_20, Pearson = 0.39) and DBH (range: A

_{nofirst}0_50, Pearson = 0.05; A

_{nofirst}0_60, Pearson = 0.13) (Table 2). In this case, correlation coefficients were significantly lower compared to the ones derived from the Weibull distribution.

#### 3.2. Mean Stand Height

_{first}90, Perc

_{first}95 and Perc

_{first}99 were highly correlated with the mean stand height (Pearson > 0.89) (Table 2). As for the relationship between the area of the frequency histogram of the point-cloud distribution (i.e., the first returns) and H, the Pearson coefficients ranged from −0.36 (A

_{first}80_90) to −0.68 (A

_{first}90_99). Considering that the purpose of the study was to select a LiDAR-based variable as a proxy of mean stand height, which is positively correlated with VOL and AGB, we did not include the variables associated with the area of the frequency histogram for mean stand height in our final models.

#### 3.3. Model Selection and Validation

^{2}ranged from 0.72 to 0.84 (Table 3). In general, models estimating VOL performed better than those estimating AGB. The lower performance of the AGB model is probably due to the presence of different tree species and consequently different wood densities, which are not delectable from LiDAR. The inclusion of the interaction term slightly increased the R

^{2}and AIC. Given the low degrees of freedom available for the analysis (n = 10), we selected the best models using the AIC to reduce overfitting effects. Therefore, models with the interaction term were not included in the final selection.

_{nofirst}is the “scale” parameter of the Weibull distribution fitted on all LiDAR points except the first returns; Perc

_{first}95 is the 95th percentile of the height distribution of LiDAR first returns. Both models were back-converted into their multiplicative form by adding half of the residual variance to the intercept (0.0297 and 0.030, respectively):

^{2}was 0.81 (p = 0.001383) for the VOL model and 0.77 (p = 0.001988) for the AGB model; the AIC was 4.59 and 4.8, respectively (Figure 6). The two models were then validated using the LOOCV procedure. The RMSE of the VOL model was 23.66 m

^{3}·ha

^{−1}(23.3%) and the RMSEcv was 32.86 m

^{3}·ha

^{−1}(32.3%). The RMSE of the AGB model was 19.59 Mg·ha

^{−1}(23.9%) and the RMSEcv was 26.89 Mg·ha

^{−1}(32.9%). For both VOL and AGB models, the close match between RMSEcv and RMSE suggested that the regressions had good predictive powers and that the models were not overfitting [41,42].

_{nofirst}increased by 1% and VOL increased by approx. 0.4% when Perc

_{first}95 increased by 1%. Similarly, in the AGB model, AGB increased by approx. 1.4% when wb

_{nofirst}increased by 1% and AGB increased by approx. 0.3% when Perc

_{first}95 increased by 1%. Similar ratios between coefficients can be found in forest allometric models based on field data measurements [43,44,45].

## 4. Discussion

^{−1}(19.2% of the mean) [46]. Popescu et al. (2004) used a tree-based approach to estimate stand volume and AGB in a deciduous forest in Virginia (USA), obtaining an R

^{2}of 0.39 (RMSE 52.84 Mg·ha

^{−1}) and 0.32 (RMSE 44 m

^{3}·ha

^{−1}) for stand volume and AGB, respectively [47]. More recently, Ioki et al. (2010) used an area based approach to estimate stand volume in an urban forest with an R

^{2}of 0.75 and an RMSE of 41.90 m

^{3}·ha

^{−1}(16.4% of the mean) [48].

## 5. Conclusions

## Supplementary Materials

**a**) plot 28C (12 years); (

**b**) 25A (16); (

**c**) 23b (17); (

**d**) 18C (20); (

**e**) 14A (21); (

**f**) 9A (25); (

**g**) 2A (28); (

**h**) 2AND (28); (

**i**) 1A (29); (

**j**) 1D (29).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AGB | Above-ground biomass |

AIC | Akaike information criterion |

BA | Basal area |

DBH | Diameter at breast height |

DTM | Digital Terrain Model |

ESS | Ecosystem services |

H | Mean stand height |

LiDAR | Light detection and ranging |

LOOCV | Leave-One-Out Cross-Validation |

MSE | Mean square error |

MSEn | Normalized mean square error |

PNM | Parco Nord Milano |

RMSE | Root mean square error |

RMSEcv | Root mean square error from cross validation |

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**Figure 1.**Location of the study area (Parco Nord Milano, PNM) in the Lombardy region, Northern Italy. The 10 sample plots from which the ground-field data were obtained are shown as red dots.

**Figure 2.**LiDAR profiles and 3D Views of a forested area of Parco Nord Milano (

**a**); (

**b**) and (

**c**) are respectively the profile and 3D View of Plot 1A, 29 years old; (

**d**) and (

**e**) are respectively the profile and 3D View of Plot 23B, 17 years old.

**Figure 3.**LiDAR points height distributions for two plots with different stand age. (

**a**) Plot 1A, 29 years old; (

**b**) Plot 23B, 17 years old. Dotted line: distribution of points belonging to the first return; solid line: distribution of points belonging to all returns; dashed line: belonging to all returns except the first.

**Figure 4.**Fitted Weibull distribution for each plot: (

**a**) plot 28C (12 years); (

**b**) 25A (16); (

**c**) 23b (17); (

**d**) 18C (20); (

**e**) 14A (21); (

**f**) 9A (25); (

**g**) 2A (28); (

**h**) 2AND (28); (

**i**) 1A (29); (

**j**) 1D (29). Solid lines represent the height distribution of LiDAR points belonging to all return except the first. Dashed lines represent the fitted Weibull distribution. Parameters and Mean Squared Error are shown for each fit.

**Figure 5.**R

^{2}and AIC values of the best model for each couple of predictors. (

**a**) Panel shows VOL model; (

**b**) panel shows AGB model.

**Figure 6.**Scatterplot of predicted values as a function of observed values for the VOL model (

**a**) and for the AGB model (

**b**). The line shows a 1:1 relationship.

**Table 1.**Characteristics of the Airborne LiDAR scanner and flight specification of the acquisition survey conducted for this study.

Characteristic | Specifications |
---|---|

Laser scanner | Riegl LMS-Q680i |

Point density | ±10/m^{2} |

Laser pulse rate | 290 kHz |

Wavelength | Near infrared |

Position accuracy | ±10 cm |

Height accuracy | ±7 cm |

Field of View | 60° |

Number of returns | ≤7 |

**Table 2.**Pearson correlation coefficient between LiDAR derived variables and ground measurements. BA is basal area; DBH is mean diameter at breast height; H is Height mean; A

_{nofirst}0_10, A

_{nofirst}0_20, A

_{nofirst}0_30, A

_{nofirst}0_40, A

_{nofirst}0_50, A

_{nofirst}0_60 and A

_{nofirst}0_70 are the areas calculated from the height distribution of the LiDAR points of all returns except the first between 0 and the 10th percentile, 0 and the 20th percentile, 0 and the 30th percentile, 0 and the 40th percentile, 0 and the 50th percentile, 0 and the 60th percentile and 0 and the 70th percentile, respectively; A

_{first}80_90, A

_{first}80_99, A

_{first}90_95, A

_{first}90_99, A

_{first}95_99 are the areas calculated from the height distribution of the LiDAR points belonging to the first return between the 80th and the 90th percentile; the 80th and the 99th percentile, the 90th and the 95th percentile, the 90th and the 99th percentile and the 95th and the 99th percentile, respectively.

LiDAR Derived Variables | Forest Stand Measurements | |
---|---|---|

BA | DBH | |

wb_{nofirst} | 0.78 | 0.81 |

A_{nofirst}0_10 | 0.23 | −0.08 |

A_{nofirst}0_20 | 0.39 | 0.13 |

A_{nofirst}0_30 | 0.38 | 0.08 |

A_{nofirst}0_40 | 0.36 | 0.08 |

A_{nofirst}0_50 | 0.33 | 0.05 |

A_{nofirst}0_60 | 0.33 | 0.05 |

A_{nofirst}0_70 | 0.36 | 0.09 |

H | ||

A_{first}80_90 | −0.36 | |

A_{first}80_95 | −0.47 | |

A_{first}80_99 | −0.51 | |

A_{first}90_95 | −0.57 | |

A_{first}90_99 | −0.68 | |

A_{first}95_99 | −0.62 | |

Perc_{first}90 | 0.92 | |

Perc_{first}95 | 0.91 | |

Perc_{first}99 | 0.89 |

**Table 3.**R

^{2}, Akaike information criterion (AIC), Root mean square error (RMSE) and Root mean square error from cross validation (RMSEcv) of the best models for selected models. RMSE is expressed in m

^{3}·ha

^{−1}for forest stand volume (VOL) and in (Mg·ha

^{−1}) for above-ground biomass (AGB). (i) Indicates the presence of an interaction term and bold characters indicates the best models.

Response Variable | Model | R^{2} | AIC | RMSE | RMSEcv |
---|---|---|---|---|---|

ln VOL (m^{3}·ha^{−1}) | ln wb_{nofirst} + ln Perc_{first}95 | 0.81 | 4.59 | 23.66 (23.3%) | 32.86 (32.3%) |

ln A_{nofirst}0_10 + ln Perc_{first}90 | 0.76 | 6.81 | 26.19 (25.7%) | 35.64 (35%) | |

ln wb_{nofirst} + ln Perc_{first}95 (i) | 0.81 | 6.58 | 23.67 (23.3%) | 34.1 (33.5%) | |

ln A_{nofirst}0_20 + ln Perc_{first}95 (i) | 0.84 | 4.71 | 20.18 (19.8%) | 33.9 (33.3%) | |

ln AGB (Mg·ha^{−1}) | ln wb_{nofirst} + ln Perc_{first}95 | 0.77 | 4.8 | 19.59 (23.9%) | 26.89 (32.9%) |

ln A_{nofirst}0_10 + ln Perc_{first}90 | 0.72 | 6.81 | 21.52 (26.3%) | 28.76 (35.1%) | |

ln wb_{nofirst} + ln Perc_{first}95 (i) | 0.77 | 6.79 | 19.63 (24%) | 27.81 (34%) | |

ln A_{nofirst}0_20 + ln Perc_{first}95 (i) | 0.80 | 5.31 | 17.97 (22%) | 31.11 (38%) |

**Table 4.**Selected models with estimated coefficients for predicting stand volume (VOL) and above-ground biomass (AGB).

Response Variable | Model | β0 | β1 | β2 |
---|---|---|---|---|

lnVOL | ${\mathsf{\beta}}_{0}+{\mathsf{\beta}}_{1}\mathrm{ln}\left({\text{wb}}_{\text{nofirst}}\right)\text{}+{\mathsf{\beta}}_{2}\text{ln}\left({\text{Perc}}_{\text{first}}95\right)$ | 0.38 | 1.49 | 0.37 |

lnAGB | ${\mathsf{\beta}}_{0}+{\mathsf{\beta}}_{1}\text{ln}\left({\text{wb}}_{\text{nofirst}}\right)+{\mathsf{\beta}}_{2}\text{ln}\left({\text{Perc}}_{\text{first}}95\right)$ | 0.78 | 1.44 | 0.19 |

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**MDPI and ACS Style**

Giannico, V.; Lafortezza, R.; John, R.; Sanesi, G.; Pesola, L.; Chen, J.
Estimating Stand Volume and Above-Ground Biomass of Urban Forests Using LiDAR. *Remote Sens.* **2016**, *8*, 339.
https://doi.org/10.3390/rs8040339

**AMA Style**

Giannico V, Lafortezza R, John R, Sanesi G, Pesola L, Chen J.
Estimating Stand Volume and Above-Ground Biomass of Urban Forests Using LiDAR. *Remote Sensing*. 2016; 8(4):339.
https://doi.org/10.3390/rs8040339

**Chicago/Turabian Style**

Giannico, Vincenzo, Raffaele Lafortezza, Ranjeet John, Giovanni Sanesi, Lucia Pesola, and Jiquan Chen.
2016. "Estimating Stand Volume and Above-Ground Biomass of Urban Forests Using LiDAR" *Remote Sensing* 8, no. 4: 339.
https://doi.org/10.3390/rs8040339