# Estimation of Individual Tree Stem Biomass in an Uneven-Aged Structured Coniferous Forest Using Multispectral LiDAR Data

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.78) and TSB (i.e., RMSE = 211.16 kg and R

^{2}= 0.65) cases. Our work demonstrates that BSB can be estimated with moderate to high accuracy using all the tested algorithms, contrary to the TSB, where only three algorithms (RF, SVR and GP) can adequately provide accurate TSB predictions due to bark irregularities along the stems. Overall, the multispectral LiDAR data provide accurate stem biomass estimates, the general applicability of which should be further tested in different biomes and ecosystems.

## 1. Introduction

_{2}removal from the atmosphere, storing more than 80% of the total aboveground carbon [3,4].

^{2}), although the RF provided more consistent results over the trials [74]. The stem volume and TSB of individual pines were also examined using full-waveform [1] and discrete-return LiDAR data [80]. As reported by [1], the full-waveform-derived metrics do not improve the volume and biomass estimates significantly compared to the discrete data, due to the limitations of single-tree delineation. In [80], the authors employed the crown geometric volume (CGV) method on LiDAR point cloud to estimate the TSB for three different tree density classes. According to the results, the low tree density sites provided the most accurate stem volume estimates (R

^{2}= 0.68) compared to the others (i.e., R

^{2}= 0.62 for the medium and R

^{2}= 0.44 for the dense), since the high tree density leads to large tree segmentation errors.

^{2}= 0.87 for the multispectral and R

^{2}= 0.72 for the single spectral). In 2020, [87] compared the suitability of monospectral and multispectral LiDAR for canopy fuel parameter estimations in a boreal forest. According to their findings, the multispectral LiDAR provided improved canopy fuel estimates compared to the monospectral LiDAR. Additionally, multispectral LiDAR data are more capable for individual tree detection compared to the monospectral data due to the spectral differentiation of the vegetation objects [88].

## 2. Study Area and Dataset Description

#### 2.1. Study Area

^{2}, and the altitude ranges between 900 and 2050 m, with an average of 1350 m. The climate is characterized as transitional Mediterranean/Mid-European with high variability among seasons. Uneven distribution of the annual precipitation is observed, ranging from 1213.9 mm of rainfall and 328.2 mm of snow in winters to 298.8 mm during the vegetative period. As for the geology, the area’s soil type is classified as Cambisol, and the main rocks are flysch and limestones which, along with the mountainous terrain, are quite vulnerable to weathering and erosion.

#### 2.2. Dataset Description

#### 2.2.1. Airborne LiDAR Data

^{2}) to discrete returns. As a result, the delivered data included a georeferenced point cloud in the Universal Transverse Mercator zone 34 coordinates system based on World Geodetic System 1984, along with trajectory files. The point cloud density for both channels was almost identical (i.e., 44.65 points/m

^{2}for the Near Infrared and 44.85 points/m

^{2}for the Green), with identical nominal pulse spacing of 0.15 m and 0.18 m, respectively, up to seven returns per pulse and a scan angle range from −32° to +32°. In addition, aerial photographs were acquired simultaneously with the LiDAR data, providing high resolution images of the entire forest.

#### 2.2.2. Field Survey

^{2}(40 m × 25 m). The distribution of the sampling plots across the study area was performed according to the different tree density, DBH distribution, and topographic features. This information was derived from the forest census data, of the 10-year forest management plan conducted in 2018. In each plot, only overstory trees that were detectable by the LiDAR sensor were measured. More specifically, DBH was recorded for each selected tree using a Haglof Mantax Blue caliper. Tree locations were determined using a Garmin eTrex 30x touch with an average horizontal position accuracy of 4 m. As a result, a set of 35 non-destructively sampled trees was recorded and correctly identified in the point cloud.

_{1}, r

_{2,}and r

_{3}are the radius of the first, second, and third disk, respectively, and r

_{s}is the radius at the end of the merchantable height. Eventually, the wood and bark density of the samples was multiplied with the volume of each stem partition for the TSB and BSB biomass calculation (Table 1 and Figure 3).

## 3. Methods

#### 3.1. LiDAR Data Processing

_{norm}) was calculated as according to the following equation (Equation (4)):

#### 3.2. Single-Tree Biomass Estimation Using Allometric Equations

^{2}, and Adjusted R

^{2}(adjR

^{2}).

#### 3.3. Single-Tree Biomass Estimation Using Regression Algorihtms

^{2}) in the k-fold cross-validation partitions [77]. The following sections (Section 3.3.1, Section 3.3.2, Section 3.3.3, Section 3.3.4, Section 3.3.5 and Section 3.3.6) present a brief description of each examined algorithm and the respective tuning parameters.

#### 3.3.1. Generalized Linear Models

#### 3.3.2. Gaussian Process

#### 3.3.3. Random Forest

#### 3.3.4. Support Vector Regression

#### 3.3.5. Extreme Gradient Boosting

#### 3.3.6. Model Performance and Evaluation

^{2}, and RMSE. The regression models were validated to an independent testing set (i.e., 30% of the total number of samples), which was randomly split from the training data (i.e., 32 destructively and 35 non-destructively in total), to obtain the predictive performance of each algorithm. In addition, the relative importance of individual predictors in each model was evaluated using the variable importance plots [140]. The variance importance, calculated using a model-agnostic procedure [141], provides a list of the ten most significant variables for each model, in descending order. The least important variable could potentially be excluded from the predictive models, decreasing the computational cost [77]. However, in the GLM case, the feature importance represents the percentage of GLMs containing each variable after the training procedure.

## 4. Results

#### 4.1. Allometric Equations

^{2}and adjR

^{2}for both models amounted to 0.96; however, the TSB one resulted in higher RSE.

#### 4.2. Barkless Stem Biomass

^{2}greater than 0.7 and RMSE lower than 195 kg, except for the GP with the linear kernel. More specifically, the developed GLM with three predictors achieved the highest performance in terms of MAE and RMSE, although the highest R

^{2}was obtained by the RF. The RF provided better results compared to the other algorithms (i.e., LR, GP, SVR, XGBoost), with a MAE of 152.65 kg, −5.08% rbias, RMSE of 175.76 kg, and R

^{2}of 0.78. The application of the GP algorithm with the rbf kernel led to the lowest MAE (162.23 kg) and RMSE (184.24 kg), while R

^{2}was higher (i.e., R

^{2}= 0.75) compared to the linear kernel. Both the SVR and the GLM resulted in similar estimation performance, as evidenced by the R

^{2}(0.73 and 0.72, respectively). The XGBoost model gave slightly lower results in terms of R

^{2}(0.69) compared to the RF, GP and GLM algorithms, with the second-highest RMSE (195.25 kg), an MAE of 157.29 kg, and an rbias of −5.08%. Additionally, Table 6 presents the best- and worst-performing linear models, according to the calculated statistical evaluation measures (i.e., MAE, MSE, rbias, RMSE and R

^{2}), and the correlation between the variables was examined, showing low correlation (<0.5) between selected predictors (Figure 7).

^{2}, followed by the int_std of the NIR channel. The p90 was considered as the most important variable for the XGBoost model as well. On the contrary to the ML algorithms, the int_std of the Green channel was identified as the most important variable presenting the highest frequency of occurrence, alongside the Hmax, p99 and p95 (Table 7). Overall, regarding the ML models, it is evident that the significance of the height-derived LiDAR metrics is considered higher compared to that of the intensity metrics (i.e., int_std_nir), as opposed to the GLM, where the intensity metrics (i.e., int_std_green and int_ske_green) are among the most valuable for the BSB estimation.

#### 4.3. Total Stem Biomass

^{2}and significantly higher RMSE and rbias metrics in comparison with the BSB models. More specifically, the RF model resulted in the highest R

^{2}(0.65) among the other algorithms, but with low MAE (152.65 kg) and RMSE (175.76 kg). The GP with the rbf kernel achieved marginally better R

^{2}over the linear kernel (0.62 and 0.6, respectively), although the latter resulted in lower rbias (−2.02%), RMSE (164.03 kg) and MAE (219.18 kg). The SVR model provided an R

^{2}of 0.57, with a MAE of 166.84 kg and high rbias (−6.15%). The GLM with three predictors achieved low performance in terms of RMSE and R

^{2}, although, it showed the lowest rbias (−1.12%). In addition, the best-performing linear model employed high correlated variables (i.e., Havg and p70), which is evidenced in Table 9. Finally, the XGBoost algorithm achieved the lowest R

^{2}(0.31) and the highest RMSE (290.89) compared to the rest of the employed algorithms.

## 5. Discussion

^{2}compared to the ones using only the height information, especially in a study area like the Pertouli University Forest, which is characterized by complex structure, high canopy cover and intense topography [106]. Overall, the results demonstrate that BSB can be reliably estimated using the GLM and the ML algorithms (i.e., RF, SVR, GP and XGBoost) in an uneven-aged structured coniferous forest, while TSB estimations are more reliable using the RF, SVR and GP (with both kernels), with the RF providing the best results in both cases (i.e., BSB and TSB).

^{2}(i.e., MAE = 121.71 kg, MSE = 35585.08 kg, rbias = 1.89%, RMSE = 167.09 kg, R

^{2}= 0.72). However, the GLM severely underperformed (MAE = 174.55 kg, MSE = 45549.33 kg and R

^{2}= 0.44) in the case of the TSB estimation compared to the rest of the examined algorithms (i.e., RF, GP and SVR). Even though the Green channel presents lower sensitivity in canopy returns registration, due to its large beam divergence [142], the int_std was the most frequently selected variable in both BSB and TSB linear models (Table 6 and Table 9). It is noteworthy that the int_std of the Green channel is the variable selected in the best performing linear models, which indicates the significance of the LiDAR intensity information for stem biomass estimation. In general, height metrics were selected in every GLM but, contrary to the intensity metrics, the best performing BSB model consisted of the least frequent height-related variables (i.e., p10 and p70). These two variables are highly correlated, with a Pearson’s correlation coefficient greater than 0.5. Moreover, in the TSB GLM, both the p70 and the b50 were rated as the second and third most frequently selected variables in the best- and worst-performing regression models, respectively (Table 10). A comparison of the BSB and the TSB GLM accuracy reveals that the former performs significantly better. The low predictive performance of the GLM in the TSB estimations can be attributed to the fact that bark volume and biomass variation do not only depend on the tree species but also on the growth rate, the environmental conditions and the genetic constitutions of trees [137]. In addition, allometric equations can introduce uncertainty in the estimated biomass results mainly due to measurement errors, transect size, the fraction of the AGB and the characteristics of the study area [143]. As a result, although the linear models performed well in the BSB predictions, they proved to be inadequate for TSB estimations (i.e., MAE = 173.92 kg, and R

^{2}= 0.32), and new bark biomass ones need to be developed with the use of a large sample size (e.g., sample size >100).

^{2}). As opposed to the GLM, all the ML models identified only height-related LiDAR-derived metrics as the most important features for the prediction of BSB, such as p99, p90, p95, and Hmax. With respect to TSB estimations, the RF algorithm resulted in an R

^{2}of 0.65 with among the lowest MAE and RMSE (i.e., MAE = 152.65 kg and RMSE = 175.76 kg), and identified the Hstd, the p80 and int_ske of both the Green and NIR channels as the most important variables of the regression model. On the contrary, the XGBoost algorithm was found to be prone to overfitting due to the small sample size (i.e., MAE = 236.67 kg, RMSE = 290.89 kg and R

^{2}= 0.31) [146]. According to the literature, the RF algorithm has a significant advantage over the other ML algorithms in terms of its accuracy and its ability to perform with small sample sizes [131]. The RF and GLM-related findings of this work are similar to other studies (e.g., [44,77,146]), although none of them have been conducted in an uneven-aged structured forest.

^{2}in all of the tested algorithms (i.e., RF, SVR, XGBoost and GLM). In 2020, [147] tested the RF, SVR, and GLM in plantations, resulting in a higher performance compared to ours in terms of R

^{2}, but much higher rbias values as well. In addition, [60] used linear models with logarithmic transformations for stem volume estimation in a boreal forest, using primarily height metrics and reported superior results compared to the ones of the present study. This variation in the results can be attributed to the significant difference between the study sites, as the one in our work is a naturally regenerated uneven-aged forest with complex topography, contrary to semi-natural regenerated and hilly forest in Finland.

## 6. Conclusions

- BSB can be adequately estimated from all the tested algorithms, contrary to the TSB where only a portion of the selected algorithms (i.e., RF, GP and SVR) provided accurate estimations.
- All the algorithms provided more accurate BSB estimations compared to the TSB ones.
- The RF algorithm resulted in the most precise BSB and TSB estimates in terms of R
^{2}MAE and RMSE, compared to the rest of the examined algorithms. - The intensity metrics significantly contribute to accurate BSB and TSB estimation, being among the most important variables in the best performing algorithms.
- The ML regression algorithms outperformed the GLM in the TSB estimation, which can be credited to the better generalization capacity and ability of the former to model complex relationships.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Allouis, T.; Durrieu, S.; Vega, C.; Couteron, P. Stem Volume and Above-Ground Biomass Estimation of Individual Pine Trees From LiDAR Data: Contribution of Full-Waveform Signals. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2013**, 6, 924–934. [Google Scholar] [CrossRef] - Eggleston, S.; Buendia, L.; Miwa, K.; Ngara, T.; Tanabe, K. IPCC Guidelines for National Greenhouse Gas Inventories; IPCC: Geneva, Switzerland, 2006. [Google Scholar]
- Węgiel, A.; Polowy, K. Aboveground Carbon Content and Storage in Mature Scots Pine Stands of Different Densities. Forests
**2020**, 11, 240. [Google Scholar] [CrossRef] [Green Version] - Jandl, R.; Lindner, M.; Vesterdal, L.; Bauwens, B.; Baritz, R.; Hagedorn, F.; Johnson, D.W.; Minkkinen, K.; Byrne, K.A. How strongly can forest management influence soil carbon sequestration? Geoderma
**2007**, 137, 253–268. [Google Scholar] [CrossRef] - Kajimoto, T.; Matsuura, Y.; Sofronov, M.A.; Volokitina, A.V.; Mori, S.; Osawa, A.; Abaimov, A.P. Above- and belowground biomass and net primary productivity of a Larix gmelinii stand near Tura, central Siberia. Tree Physiol.
**1999**, 19, 815–822. [Google Scholar] [CrossRef] - Luo, S.; Wang, C.; Xi, X.; Pan, F.; Peng, D.; Zou, J.; Nie, S.; Qin, H. Fusion of airborne LiDAR data and hyperspectral imagery for aboveground and belowground forest biomass estimation. Ecol. Indic.
**2017**, 73, 378–387. [Google Scholar] [CrossRef] - Duncanson, L.; Armston, J.; Disney, M.; Avitabile, V.; Barbier, N.; Calders, K.; Carter, S.; Chave, J.; Herold, M.; MacBean, N.; et al. Aboveground Woody Biomass Product Validation Good Practices Protocol. Land Product Validation Subgroup (Working Group on Calibration and Validation, Committee on Earth Observation Satellites), 2021, 236. Available online: https://lpvs.gsfc.nasa.gov/PDF/CEOS_WGCV_LPV_Biomass_Protocol_2021_V1.0.pdf (accessed on 3 November 2021).
- Zhang, L.; Deng, X.; Lei, X.; Xiang, W.; Peng, C.; Lei, P.; Yan, W. Determining stem biomass of Pinus massoniana L. through variations in basic density. Forestry
**2012**, 85, 601–609. [Google Scholar] [CrossRef] - García, M.; Riaño, D.; Chuvieco, E.; Danson, F.M. Estimating biomass carbon stocks for a Mediterranean forest in central Spain using LiDAR height and intensity data. Remote Sens. Environ.
**2010**, 114, 816–830. [Google Scholar] [CrossRef] - Dutcă, I.; Zianis, D.; Petrițan, I.C.; Bragă, C.I.; Ștefan, G.; Yuste, J.C.; Petrițan, A.M. Allometric Biomass Models for European Beech and Silver Fir: Testing Approaches to Minimize the Demand for Site-Specific Biomass Observations. Forests
**2020**, 11, 1136. [Google Scholar] [CrossRef] - Shearman, T.M.; Varner, J.M.; Robertson, K.; Hiers, J.K. Allometry of the pyrophytic Aristida in fire-maintained longleaf pine–wiregrass ecosystems. Am. J. Bot.
**2019**, 106, 18–28. [Google Scholar] [CrossRef] - Xu, Q.; Man, A.; Fredrickson, M.; Hou, Z.; Pitkänen, J.; Wing, B.; Ramirez, C.; Li, B.; Greenberg, J.A. Quantification of uncertainty in aboveground biomass estimates derived from small-footprint airborne LiDAR. Remote Sens. Environ.
**2018**, 216, 514–528. [Google Scholar] [CrossRef] - Zianis, D.; Mencuccini, M. On simplifying allometric analyses of forest biomass. For. Ecol. Manag.
**2004**, 187, 311–332. [Google Scholar] [CrossRef] - Migolet, P.; Goïta, K.; Ngomanda, A.; Biyogo, A.P.M. Estimation of Aboveground Oil Palm Biomass in a Mature Plantation in the Congo Basin. Forests
**2020**, 11, 544. [Google Scholar] [CrossRef] - Djomo, A.N. Allometric equations for biomass estimations in Cameroon and pan moist tropical equations including biomass data from Africa. For. Ecol. Manag.
**2010**, 260, 1873–1885. [Google Scholar] [CrossRef] - Chave, J.; Andalo, C.; Brown, S.; Cairns, M.A.; Chambers, J.Q.; Eamus, D.; Fölster, H.; Fromard, F.; Higuchi, N.; Kira, T.; et al. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia
**2005**, 145, 87–99. [Google Scholar] [CrossRef] - Nogueira, E.M.; Fearnside, P.M.; Nelson, B.W.; Barbosa, R.I.; Keizer, E.W.H. Estimates of forest biomass in the Brazilian Amazon: New allometric equations and adjustments to biomass from wood-volume inventories. For. Ecol. Manag.
**2008**, 256, 1853–1867. [Google Scholar] [CrossRef] - Fehrmann, L.; Kleinn, C. General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe. For. Ecol. Manag.
**2006**, 236, 412–421. [Google Scholar] [CrossRef] - Basuki, T.M.; van Laake, P.E.; Skidmore, A.K.; Hussin, Y.A. Allometric equations for estimating the above-ground biomass in tropical lowland Dipterocarp forests. For. Ecol. Manag.
**2009**, 257, 1684–1694. [Google Scholar] [CrossRef] - Martin, F.S.; Navarro-Cerrillo, R.M.; Mulia, R.; van Noordwijk, M. Allometric equations based on a fractal branching model for estimating aboveground biomass of four native tree species in the Philippines. Agrofor. Syst.
**2010**, 78, 193–202. [Google Scholar] [CrossRef] - Wang, X.; Jiao, H. Spatial Scaling of Forest Aboveground Biomass Using Multi-Source Remote Sensing Data; IEEE: Piscataway, NJ, USA, 2020. [Google Scholar]
- Ota, T.; Ogawa, M.; Shimizu, K.; Kajisa, T.; Mizoue, N.; Yoshida, S.; Takao, G.; Hirata, Y.; Furuya, N.; Sano, T.; et al. Aboveground Biomass Estimation Using Structure from Motion Approach with Aerial Photographs in a Seasonal Tropical Forest. Forests
**2015**, 6, 3882–3898. [Google Scholar] [CrossRef] [Green Version] - Lin, J.; Wang, M.; Ma, M.; Lin, Y. Aboveground Tree Biomass Estimation of Sparse Subalpine Coniferous Forest with UAV Oblique Photography. Remote Sens.
**2018**, 10, 1849. [Google Scholar] [CrossRef] [Green Version] - Ota, T.; Ahmed, O.S.; Minn, S.T.; Khai, T.C.; Mizoue, N.; Yoshida, S. Estimating selective logging impacts on aboveground biomass in tropical forests using digital aerial photography obtained before and after a logging event from an unmanned aerial vehicle. For. Ecol. Manag.
**2019**, 433, 162–169. [Google Scholar] [CrossRef] - Jannoura, R.; Brinkmann, K.; Uteau, D.; Bruns, C.; Joergensen, R.G. Monitoring of crop biomass using true colour aerial photographs taken from a remote controlled hexacopter. Biosyst. Eng.
**2015**, 129, 341–351. [Google Scholar] [CrossRef] - Fensham, R.J.; Fairfax, R.J.; Holman, J.E.; Whitehead, P.J. Quantitative assessment of vegetation structural attributes from aerial photography. Int. J. Remote Sens.
**2002**, 23, 2293–2317. [Google Scholar] [CrossRef] - Singh, M.; Malhi, Y.; Bhagwat, S. Biomass estimation of mixed forest landscape using a Fourier transform texture-based approach on very-high-resolution optical satellite imagery. Int. J. Remote Sens.
**2014**, 35, 3331–3349. [Google Scholar] [CrossRef] - Muukkonen, P.; Heiskanen, J. Biomass estimation over a large area based on standwise forest inventory data and ASTER and MODIS satellite data: A possibility to verify carbon inventories. Remote Sens. Environ.
**2007**, 107, 217–624. [Google Scholar] [CrossRef] - Roy, P.S.; Ravan, S.A. Biomass estimation using satellite remote sensing data—An investigation on possible approaches for natural forest. J. Biosci.
**1996**, 21, 535–561. [Google Scholar] [CrossRef] - Sousa, A.M.O.; Gonçalves, A.C.; Mesquita, P.; Marques da Silva, J.R. Biomass estimation with high resolution satellite images: A case study of Quercus rotundifolia. ISPRS J. Photogramm. Remote Sens.
**2015**, 101, 69–79. [Google Scholar] [CrossRef] [Green Version] - Muukkonen, P.; Heiskanen, J. Estimating biomass for boreal forests using ASTER satellite data combined with standwise forest inventory data. Remote Sens. Environ.
**2005**, 99, 434–447. [Google Scholar] [CrossRef] - Baloloy, A.B.; Blanco, A.C.; Candido, C.G.; Argamosa, R.J.L.; Dumalag, J.B.L.C.; Dimapilis, L.L.C.; Paringit, E.C. Estimation of mangrove forest aboveground biomass using multispectral bands, vegetation indices and biophysical variables derived from optical satellite imageries: Rapideye, Planetscope and sentinel-2. ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci.
**2018**, IV-3, 29–36. [Google Scholar] - Steininger, M.K. Satellite estimation of tropical secondary forest above-ground biomass: Data from Brazil and Bolivia. Int. J. Remote Sens.
**2000**, 21, 1139–1157. [Google Scholar] [CrossRef] - Schlund, M.; Davidson, M.W.J. Aboveground Forest Biomass Estimation Combining L- and P-Band SAR Acquisitions. Remote Sens.
**2018**, 210, 1151. [Google Scholar] [CrossRef] [Green Version] - van Yunjin Kim, J. Zyl Comparison of forest parameter estimation techniques using SAR data. In IGARSS 2001. Scanning the Present and Resolving the Future, Proceedings of the IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat.No.01CH37217), Sydney, Australia, 9–13 July 2001; IEEE: Piscataway, NJ, USA, 2001; Volume 3, pp. 1395–1397. [Google Scholar]
- Solberg, S.; Astrup, R.; Gobakken, T.; Næsset, E.; Weydahl, D.J. Estimating spruce and pine biomass with interferometric X-band SAR. Remote Sens. Environ.
**2010**, 114, 2353–2360. [Google Scholar] [CrossRef] - Debastiani, A.B.; Sanquetta, C.R.; Corte, A.P.D.; Rex, F.E.; Pinto, N.S. Evaluating SAR-optical sensor fusion for aboveground biomass estimation in a Brazilian tropical forest. Ann. For. Res.
**2019**, 62, 109–122. [Google Scholar] [CrossRef] - Hamdan, O.; Aziz, H.K.; Rahman, K.A. Remotely sensed l-band sar data for tropical forest biomass estimation. J. Trop. For. Sci.
**2021**, 11, 318–327. [Google Scholar] - Santoro, M.; Cartus, O. Research Pathways of Forest Above-Ground Biomass Estimation Based on SAR Backscatter and Interferometric SAR Observations. Remote Sens.
**2018**, 10, 608. [Google Scholar] [CrossRef] [Green Version] - Kronseder, K.; Ballhorn, U.; Böhm, V.; Siegert, F. Above ground biomass estimation across forest types at different degradation levels in Central Kalimantan using LiDAR data. Int. J. Appl. Earth Obs. Geoinf.
**2012**, 18, 37–48. [Google Scholar] [CrossRef] - Drake, J.B.; Knox, R.G.; Dubayah, R.O.; Clark, D.B.; Condit, R.; Blair, J.B.; Hofton, M. Above-ground biomass estimation in closed canopy Neotropical forests using lidar remote sensing: Factors affecting the generality of relationships. Glob. Ecol.
**2003**, 12, 147–159. [Google Scholar] [CrossRef] - Ene, L.T.; Næsset, E.; Gobakken, T.; Gregoire, T.G.; Ståhl, G.; Nelson, R. Assessing the accuracy of regional LiDAR-based biomass estimation using a simulation approach. Remote Sens. Environ.
**2012**, 123, 579–592. [Google Scholar] [CrossRef] - Popescu, S.C. Estimating biomass of individual pine trees using airborne lidar. Biomass Bioenergy
**2007**, 31, 646–655. [Google Scholar] [CrossRef] - Gleason, C.J.; Im, J. Forest biomass estimation from airborne LiDAR data using machine learning approaches. Remote Sens. Environ.
**2012**, 125, 80–91. [Google Scholar] [CrossRef] - Popescu, S.C.; Wynne, R.H.; Nelson, R.F. Measuring individual tree crown diameter with lidar and assessing its influence on estimating forest volume and biomass. Can. J. Remote Sens.
**2003**, 29, 564–577. [Google Scholar] [CrossRef] - Ståhl, G.; Holm, S.; Gregoire, T.G.; Gobakken, T.; Næsset, E.; Nelson, R. Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, NorwayThis article is one of a selection of papers from Extending Forest Inventory and Monitoring over Space and Time. Can. J. For. Res.
**2011**, 41, 96–107. [Google Scholar] [CrossRef] [Green Version] - Stovall, A.E.; Vorster, A.G.; Anderson, R.S.; Evangelista, P.H.; Shugart, H.H. Non-destructive aboveground biomass estimation of coniferous trees using terrestrial LiDAR. Remote Sens. Environ.
**2017**, 200, 31–42. [Google Scholar] [CrossRef] - Næsset, E.; Gobakken, T.; Solberg, S.; Gregoire, T.G.; Nelson, R.; Ståhl, G.; Weydahl, D. Model-assisted regional forest biomass estimation using LiDAR and InSAR as auxiliary data: A case study from a boreal forest area. Remote Sens. Environ.
**2011**, 115, 3599–3614. [Google Scholar] [CrossRef] - Ghosh, S.M.; Behera, M. Aboveground biomass estimation using multi-sensor data synergy and machine learning algorithms in a dense tropical forest. Appl. Geogr.
**2018**, 96, 29–40. [Google Scholar] [CrossRef] - Huang, X.; Ziniti, B.; Torbick, N.; Ducey, M.J. Assessment of Forest above Ground Biomass Estimation Using Multi-Temporal C-band Sentinel-1 and Polarimetric L-band PALSAR-2 Data. Remote Sens.
**2018**, 150, 1424. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Li, M.; Li, C.; Liu, Z. Forest aboveground biomass estimation using Landsat 8 and Sentinel-1A data with machine learning algorithms. Sci. Rep.
**2020**, 10, 9952. [Google Scholar] [CrossRef] - He, Q.-S.; Cao, C.-X.; Chen, E.-X.; Sun, G.-Q.; Ling, F.-L.; Pang, Y.; Zhang, H.; Ni, W.-J.; Xu, M.; Li, Z.-Y.; et al. Forest stand biomass estimation using ALOS PALSAR data based on LiDAR-derived prior knowledge in the Qilian Mountain, western China. Int. J. Remote Sens.
**2011**, 33, 710–729. [Google Scholar] [CrossRef] - Chang, J.; Shoshany, M. Mediterranean shrublands biomass estimation using Sentinel-1 and Sentinel-2. In Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 10–15 July 2016. [Google Scholar]
- Naik, P.; Dalponte, M.; Bruzzone, L. Prediction of Forest Aboveground Biomass Using Multitemporal Multispectral Remote Sensing Data. Remote Sens.
**2021**, 13, 1282. [Google Scholar] [CrossRef] - Kaasalainen, S.; Holopainen, M.; Karjalainen, M.; Vastaranta, M.; Kankare, V.; Karila, K.; Osmanoglu, B. Combining Lidar and Synthetic Aperture Radar Data to Estimate Forest Biomass: Status and Prospects. Forests
**2015**, 6, 252–270. [Google Scholar] [CrossRef] - Sinha, S.; Jeganathan, C.; Sharma, L.K.; Nathawat, M.S. A review of radar remote sensing for biomass estimation. Int. J. Environ. Sci. Technol.
**2015**, 142, 1779–1792. [Google Scholar] [CrossRef] [Green Version] - Laurin, G.V.; Puletti, N.; Grotti, M.; Stereńczak, K.; Modzelewska, A.; Lisiewicz, M.; Sadkowski, R.; Kuberski, Ł.; Chirici, G.; Papale, D. Species dominance and above ground biomass in the Białowieża Forest, Poland, described by airborne hyperspectral and lidar data. Int. J. Appl. Earth Obs. Geoinf.
**2020**, 92, 102178. [Google Scholar] [CrossRef] - Jiang, X.; Li, G.; Lu, D.; Chen, E.; Wei, X. Stratification-Based Forest Aboveground Biomass Estimation in a Subtropical Region Using Airborne Lidar Data. Remote Sens.
**2020**, 12, 1101. [Google Scholar] [CrossRef] [Green Version] - Silva, C.A.; Saatchi, S.; Garcia, M.; Labriere, N.; Klauberg, C.; Ferraz, A.; Meyer, V.; Jeffery, K.J.; Abernethy, K.; White, L.; et al. Comparison of Small- and Large-Footprint Lidar Characterization of Tropical Forest Aboveground Structure and Biomass: A Case Study From Central Gabon. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2018**, 11, 3512–3526. [Google Scholar] [CrossRef] [Green Version] - Maltamo, M.; Eerikäinen, K.; Packalén, P.; Hyyppä, J. Estimation of stem volume using laser scanning-based canopy height metrics. For. Int. J. For. Res.
**2006**, 79, 217–229. [Google Scholar] [CrossRef] [Green Version] - Næsset, E. Practical large-scale forest stand inventory using a small-footprint airborne scanning laser. Scand. J. For. Res.
**2004**, 19, 164–179. [Google Scholar] [CrossRef] - Kelley, J.; Bone, C. Use of Multi-Temporal LiDAR to Quantify Fertilization Effects on Stand Volume and Biomass in Late-Rotation Coastal Douglas-Fir Forests. Forests
**2021**, 12, 517. [Google Scholar] [CrossRef] - Yu, X.; Hyyppä, J.; Holopainen, M.; Vastaranta, M. Comparison of Area-Based and Individual Tree-Based Methods for Predicting Plot-Level Forest Attributes. Remote Sens.
**2010**, 2, 1481–1495. [Google Scholar] [CrossRef] [Green Version] - Goldbergs, G.; Levick, S.R.; Lawes, M.; Edwards, A. Hierarchical integration of individual tree and area-based approaches for savanna biomass uncertainty estimation from airborne LiDAR. Remote Sens. Environ.
**2018**, 205, 141–150. [Google Scholar] [CrossRef] - Latella, M.; Sola, F.; Camporeale, C. A Density-Based Algorithm for the Detection of Individual Trees from LiDAR Data. Remote Sens.
**2021**, 13, 322. [Google Scholar] [CrossRef] - Vauhkonen, J.; Ene, L.; Gupta, S.; Heinzel, J.; Holmgren, J.; Pitkanen, J.; Solberg, S.; Wang, Y.; Weinacker, H.; Hauglin, K.M.; et al. Comparative testing of single-tree detection algorithms under different types of forest. Forestry
**2012**, 85, 27–40. [Google Scholar] [CrossRef] [Green Version] - Li, W.; Guo, Q.; Jakubowski, M.K.; Kelly, M. A New Method for Segmenting Individual Trees from the Lidar Point Cloud. Photogramm. Eng. Remote Sens.
**2012**, 78, 75–84. [Google Scholar] [CrossRef] [Green Version] - Vega, C.; Hamrouni, A.; El Mokhtari, S.; Morel, J.; Bock, J.; Renaud, J.-P.; Bouvier, M.; Durrieu, S. PTrees: A point-based approach to forest tree extraction from lidar data. Int. J. Appl. Earth Obs. Geoinf.
**2014**, 33, 98–108. [Google Scholar] [CrossRef] - Silva, C.A.; Hudak, A.T.; Vierling, L.A.; Loudermilk, E.L.; O’Brien, J.J.; Hiers, J.K.; Jack, S.B.; Gonzalez-Benecke, C.; Lee, H.; Falkowski, M.J.; et al. Imputation of Individual Longleaf Pine (Pinus palustris Mill.) Tree Attributes from Field and LiDAR Data. Can. J. Remote Sens.
**2016**, 42, 554–573. [Google Scholar] [CrossRef] - Koch, B.; Heyder, U.; Weinacker, H. Detection of individual tree crowns in airborne lidar data. Photogramm. Eng. Remote Sens.
**2006**, 72, 357–363. [Google Scholar] [CrossRef] [Green Version] - Yao, W.; Krzystek, P.; Heurich, M. Tree species classification and estimation of stem volume and DBH based on single tree extraction by exploiting airborne full-waveform LiDAR data. Remote Sens. Environ.
**2012**, 123, 368–380. [Google Scholar] [CrossRef] - Kaartinen, H.; Hyyppä, J.; Yu, X.; Vastaranta, M.; Hyyppä, H.; Kukko, A.; Holopainen, M.; Heipke, C.; Hirschmugl, M.; Morsdorf, F.; et al. An International Comparison of Individual Tree Detection and Extraction Using Airborne Laser Scanning. Remote Sens.
**2012**, 4, 950–974. [Google Scholar] [CrossRef] [Green Version] - De Almeida, C.T.; Galvão, L.S.; Aragão, L.E.d.O.C.E.; Ometto, J.P.H.B.; Jacon, A.D.; Pereira, F.R.d.S.; Sato, L.Y.; Lopes, A.P.; Graça, P.M.L.d.A.; Silva, C.V.d.J.; et al. Combining LiDAR and hyperspectral data for aboveground biomass modeling in the Brazilian Amazon using different regression algorithms. Remote Sens. Environ.
**2019**, 232, 111323. [Google Scholar] [CrossRef] - Yu, X.; Hyyppä, J.; Vastaranta, M.; Holopainen, M.; Viitala, R. Predicting individual tree attributes from airborne laser point clouds based on the random forests technique. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, 28–37. [Google Scholar] [CrossRef] - Räty, J.; Varvia, P.; Korhonen, L.; Savolainen, P.; Maltamo, M.; Packalen, P. A Comparison of Linear-Mode and Single-Photon Airborne LiDAR in Species-Specific Forest Inventories. IEEE Trans. Geosci. Remote Sens.
**2021**, 1–14. [Google Scholar] [CrossRef] - Packalen, P.; Maltamo, M. Predicting the Plot Volume by Tree Species Using Airborne Laser Scanning and Aerial Photographs. For. Sci.
**2006**, 52, 611–622. [Google Scholar] - Corte, A.P.D.; Souza, D.V.; Rex, F.E.; Sanquetta, C.R.; Mohan, M.; Silva, C.A.; Zambrano, A.M.A.; Prata, G.; de Almeida, D.R.A.; Trautenmüller, J.W.; et al. Forest inventory with high-density UAV-Lidar: Machine learning approaches for predicting individual tree attributes. Comput. Electron. Agric.
**2020**, 179, 105815. [Google Scholar] [CrossRef] - Kankare, V.; Vastaranta, M.; Holopainen, M.; Räty, M.; Yu, X.; Hyyppä, J.; Hyyppä, H.; Alho, P.; Viitala, R. Retrieval of Forest Aboveground Biomass and Stem Volume with Airborne Scanning LiDAR. Remote Sens.
**2013**, 5, 2257–2274. [Google Scholar] [CrossRef] [Green Version] - Neumann, M.; Lawes, M.J. Quantifying carbon in tree bark: The importance of bark morphology and tree size. Methods Ecol. Evol.
**2021**, 12, 646–654. [Google Scholar] [CrossRef] - Kwak, D.-A.; Lee, W.-K.; Cho, H.-K.; Lee, S.-H.; Son, Y.; Kafatos, M.; Kim, S.-R. Estimating stem volume and biomass of Pinus koraiensis using LiDAR data. J. Plant Res.
**2010**, 123, 421–432. [Google Scholar] [CrossRef] - Wallace, A.; Nichol, C.; Woodhouse, I. Recovery of Forest Canopy Parameters by Inversion of Multispectral LiDAR Data. Remote Sens.
**2012**, 4, 509–531. [Google Scholar] [CrossRef] [Green Version] - Hopkinson, C.; Chasmer, L.; Gynan, C.; Mahoney, C.; Sitar, M. Multisensor and Multispectral LiDAR Characterization and Classification of a Forest Environment. Can. J. Remote Sens.
**2016**, 42, 501–520. [Google Scholar] [CrossRef] - Budei, B.C.; St-Onge, B.; Hopkinson, C.; Audet, F.-A. Identifying the genus or species of individual trees using a three-wavelength airborne lidar system. Remote Sens. Environ.
**2018**, 204, 632–647. [Google Scholar] [CrossRef] - Lindberg, E.; Holmgren, J.; Olsson, H. Classification of tree species classes in a hemi-boreal forest from multispectral airborne laser scanning data using a mini raster cell method. Int. J. Appl. Earth Obs. Geoinf.
**2021**, 100, 102334. [Google Scholar] [CrossRef] - Ekhtari, N.; Glennie, C.; Fernandez-Diaz, J.C. Classification of Airborne Multispectral Lidar Point Clouds for Land Cover Mapping. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2018**, 11, 2068–2078. [Google Scholar] [CrossRef] - Dalponte, M.; Ene, L.; Gobakken, T.; Næsset, E.; Gianelle, D. Predicting Selected Forest Stand Characteristics with Multispectral ALS Data. Remote Sens.
**2018**, 10, 586. [Google Scholar] [CrossRef] [Green Version] - Maltamo, M.; Räty, J.; Korhonen, L.; Kotivuori, E.; Kukkonen, M.; Peltola, H.; Kangas, J.; Packalen, P. Prediction of forest canopy fuel parameters in managed boreal forests using multispectral and unispectral airborne laser scanning data and aerial images. Eur. J. Remote Sens.
**2020**, 53, 245–257. [Google Scholar] [CrossRef] - Dai, W.; Yang, B.; Dong, Z.; Shaker, A. A new method for 3D individual tree extraction using multispectral airborne LiDAR point clouds. ISPRS J. Photogramm. Remote Sens.
**2018**, 144, 400–411. [Google Scholar] [CrossRef] - Chen, Q. Modeling aboveground tree woody biomass using national-scale allometric methods and airborne lidar. ISPRS J. Photogramm. Remote Sens.
**2015**, 106, 95–106. [Google Scholar] [CrossRef] - Tinkham, W.T.; Smith, A.M.S.; Affleck, D.L.R.; Saralecos, J.D.; Falkowski, M.J.; Hoffman, C.M.; Hudak, A.T.; Wulder, M.A. Development of Height-Volume Relationships in Second Growth Abies grandis for Use with Aerial LiDAR. Can. J. Remote Sens.
**2016**, 42, 400–410. [Google Scholar] [CrossRef] - Edson, C.; Wing, M.G. Airborne Light Detection and Ranging (LiDAR) for Individual Tree Stem Location, Height, and Biomass Measurements. Remote Sens.
**2011**, 3, 2494–2528. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.; Cao, L.; She, G. Estimating Forest Structural Parameters Using Canopy Metrics Derived from Airborne LiDAR Data in Subtropical Forests. Remote Sens.
**2017**, 9, 940. [Google Scholar] [CrossRef] [Green Version] - Clark, M.L.; Roberts, D.A.; Ewel, J.J.; Clark, D.B. Estimation of tropical rain forest aboveground biomass with small-footprint lidar and hyperspectral sensors. Remote Sens. Environ.
**2011**, 115, 2931–2942. [Google Scholar] [CrossRef] - Dalponte, M.; Coomes, D.A. Tree-centric mapping of forest carbon density from airborne laser scanning and hyperspectral data. Methods Ecol. Evol.
**2016**, 7, 1236–1245. [Google Scholar] [CrossRef] [Green Version] - Coomes, D.A.; Dalponte, M.; Jucker, T.; Asner, G.P.; Banin, L.F.; Burslem, D.F.R.P.; Lewis, S.L.; Nilus, R.; Phillips, O.L.; Phua, M.-H.; et al. Area-based vs tree-centric approaches to mapping forest carbon in Southeast Asian forests from airborne laser scanning data. Remote Sens. Environ.
**2017**, 194, 77–88. [Google Scholar] [CrossRef] [Green Version] - Harrison, D.; Hunter, M.C.; Lewis, A.C.; Seakins, P.W.; Nunes, T.V.; Pio, C.A. Isoprene and monoterpene emission from the coniferous species Abies Borisii-regis—implications for regional air chemistry in Greece. Atmos. Environ.
**2001**, 35, 4687–4698. [Google Scholar] [CrossRef] - Burkhart, H.E.; Tomé, M. Modeling Forest Trees and Stands; Springer: Dordrecht, The Netherlands, 2012; ISBN 978-94-007-1597-4. [Google Scholar]
- Miguel, E.; Péllico Netto, S.; Azevedo, G.; Azevedo, G.; Rezende, A.; Pereira, R. Alternative methods of scaling Eucalyptus urophylla trees in forest stands: Compatibility and accuracy of volume equations. IForest-Biogeosci. For.
**2018**, 11, 275–283. [Google Scholar] [CrossRef] [Green Version] - Morgenroth, J.; Gomez, C. Assessment of tree structure using a 3D image analysis technique—A proof of concept. Urban For. Urban Green.
**2014**, 13, 198–203. [Google Scholar] [CrossRef] - Dumitru, M.C.; Constantin, N. Tree trunk shape analysis-classical geometry approach. Nat. Resour. Sustain. Dev.
**2016**, 6, 108–115. [Google Scholar] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2017. [Google Scholar]
- Raybaut, P. Spyder-Documentation. Available online: Pythonhosted.org (accessed on 19 November 2021).
- Liu, J.; Skidmore, A.K.; Jones, S.; Wang, T.; Heurich, M.; Zhu, X.; Shi, Y. Large off-nadir scan angle of airborne LiDAR can severely affect the estimates of forest structure metrics. ISPRS J. Photogramm. Remote Sens.
**2018**, 136, 13–25. [Google Scholar] [CrossRef] - Donoghue, D.; Watt, P.; Cox, N.; Wilson, J. Remote sensing of species mixtures in conifer plantations using LiDAR height and intensity data. Remote Sens. Environ.
**2007**, 110, 509–522. [Google Scholar] [CrossRef] - Stefanidou, A.Z.; Gitas, I.; Korhonen, L.; Georgopoulos, N.; Stavrakoudis, D. Multispectral LiDAR-Based Estimation of Surface Fuel Load in a Dense Coniferous Forest. Remote Sens.
**2020**, 12, 3333. [Google Scholar] [CrossRef] - Gatziolis, D. Dynamic Range-based Intensity Normalization for Airborne, Discrete Return Lidar Data of Forest Canopies. Photogramm. Eng. Remote Sens.
**2011**, 77, 251–259. [Google Scholar] [CrossRef] - Hopkinson, C.; Chasmer, L. Using discrete laser pulse return intensity to model canopy transmittance. Photogramm. J. Finland
**2007**, 20, 16–26. [Google Scholar] - You, H.; Wang, T.; Skidmore, A.; Xing, Y. Quantifying the Effects of Normalisation of Airborne LiDAR Intensity on Coniferous Forest Leaf Area Index Estimations. Remote Sens.
**2017**, 9, 163. [Google Scholar] [CrossRef] [Green Version] - Korpela, I.; Ørka, H.O.; Hyyppä, J.; Heikkinen, V.; Tokola, T. Range and AGC normalization in airborne discrete-return LiDAR intensity data for forest canopies. ISPRS J. Photogramm. Remote Sens.
**2010**, 65, 369–379. [Google Scholar] [CrossRef] - Ahokas, E.; Kaasalainen, S.; Hyyppä, J.; Suomalainen, J. Calibration of the optech altm 3100 laser scanner intensity data using brightness targets. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2006**, 36, 1–6. [Google Scholar] - Baltsavias, E.P. Airborne laser scanning: Basic relations and formulas. ISPRS J. Photogramm. Remote Sens.
**1999**, 54, 199–214. [Google Scholar] [CrossRef] - Korpela, I.; Hovi, A.; Morsdorf, F. Understory trees in airborne LiDAR data—Selective mapping due to transmission losses and echo-triggering mechanisms. Remote Sens. Environ.
**2012**, 119, 92–104. [Google Scholar] [CrossRef] - Carrilho, A.C.; Galo, M.; Santos, R.C. Statistical outlier detection method for airborne lidar data. ISPRS-Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2018**, XLII-1, 87–92. [Google Scholar] [CrossRef] [Green Version] - Zhang, W.; Qi, J.; Wan, P.; Wang, H.; Xie, D.; Wang, X.; Yan, G. An Easy-to-Use Airborne LiDAR Data Filtering Method Based on Cloth Simulation. Remote Sens.
**2016**, 8, 501. [Google Scholar] [CrossRef] - Chen, Z.; Gao, B.; Devereux, B. State-of-the-Art: DTM Generation Using Airborne LIDAR Data. Sensors
**2017**, 17, 150. [Google Scholar] [CrossRef] [Green Version] - Khosravipour, A.; Skidmore, A.K.; Isenburg, M.; Wang, T.; Hussin, Y.A. Generating Pit-free Canopy Height Models from Airborne Lidar. Photogramm. Eng. Remote Sens.
**2014**, 80, 863–872. [Google Scholar] [CrossRef] - Kodors, S. Point Distribution as True Quality of LiDAR Point Cloud. Balt. J. Mod. Comput.
**2017**, 5, 362–378. [Google Scholar] [CrossRef] - Wu, Y.; Peng, X.; Ruan, K.; Hu, Z. Improved image segmentation method based on morphological reconstruction. Multimed. Tools Appl.
**2017**, 76, 19781–19793. [Google Scholar] [CrossRef] - Duan, Z.; Zhao, D.; Zeng, Y.; Zhao, Y.; Wu, B.; Zhu, J. Assessing and Correcting Topographic Effects on Forest Canopy Height Retrieval Using Airborne LiDAR Data. Sensors
**2015**, 15, 12133–12155. [Google Scholar] [CrossRef] - Zianis, D.; Xanthopoulos, G.; Kalabokidis, K.; Kazakis, G.; Ghosn, D.; Roussou, O. Allometric equations for aboveground biomass estimation by size class for Pinus brutia Ten. trees growing in North and South Aegean Islands, Greece. Eur. J. For. Res.
**2011**, 130, 145–160. [Google Scholar] [CrossRef] - Romero, F.M.B.; Jacovine, L.A.G.; Ribeiro, S.C.; Torres, C.M.M.E.; da Silva, L.F.; Gaspar, R.d.O.; da Rocha, S.J.S.S.; Staudhammer, C.L.; Fearnside, P.M. Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study. Forests
**2020**, 11, 874. [Google Scholar] [CrossRef] - Stovall, A.E.L.; Anderson-Teixeira, K.J.; Shugart, H.H. Assessing terrestrial laser scanning for developing non-destructive biomass allometry. For. Ecol. Manag.
**2018**, 427, 217–229. [Google Scholar] [CrossRef] - Nelder, J.A.; Wedderburn, R.W.M. Generalized Linear Models. J. R. Stat. Soc. Ser. Gen.
**1972**, 135, 370. [Google Scholar] [CrossRef] - Zheng, B.; Agresti, A. Summarizing the predictive power of a generalized linear model. Stat. Med.
**2000**, 19, 1771–1781. [Google Scholar] [CrossRef] - Brewer, M.J.; Butler, A.; Cooksley, S.L. The relative performance of AIC, AIC
_{C}and BIC in the presence of unobserved heterogeneity. Methods Ecol. Evol.**2016**, 7, 679–692. [Google Scholar] [CrossRef] - Perez-Cruz, F.; Van Vaerenbergh, S.; Murillo-Fuentes, J.J.; Lazaro-Gredilla, M.; Santamaria, I. Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances. IEEE Signal Process. Mag.
**2013**, 30, 40–50. [Google Scholar] [CrossRef] [Green Version] - Bousquet, O.; von Luxburg, U.; Rätsch, G. (Eds.) Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, 2–14 February 2003 and Tübingen, Germany, 4–16 August 2003: Revised Lectures; Lecture Notes in Computer Science, Lecture Notes in Artificial Intelligence; Springer: Berlin, Germany; New York, NY, USA, 2004. [Google Scholar]
- Pham, T.D.; Le, N.N.; Ha, N.T.; Nguyen, L.V.; Xia, J.; Yokoya, N.; To, T.T.; Trinh, H.X.; Kieu, L.Q.; Takeuchi, W. Estimating Mangrove Above-Ground Biomass Using Extreme Gradient Boosting Decision Trees Algorithm with Fused Sentinel-2 and ALOS-2 PALSAR-2 Data in Can Gio Biosphere Reserve, Vietnam. Remote Sens.
**2020**, 12, 777. [Google Scholar] [CrossRef] [Green Version] - Breiman, L. Random Forests; Machine Learning Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001; Volume 45, pp. 5–32. Available online: https://link.springer.com/article/10.1023/A:1010933404324#citeas (accessed on 2 November 2021).
- Biau, G.; Scornet, E. A random forest guided tour. Test
**2016**, 25, 197–227. [Google Scholar] [CrossRef] [Green Version] - Silveira, E.M.O.; Silva, S.H.G.; Acerbi-Junior, F.W.; Carvalho, M.C.; Carvalho, L.M.T.; Scolforo, J.R.S.; Wulder, M.A. Object-based random forest modelling of aboveground forest biomass outperforms a pixel-based approach in a heterogeneous and mountain tropical environment. Int. J. Appl. Earth Obs. Geoinf.
**2019**, 78, 175–188. [Google Scholar] [CrossRef] - Strobl, C.; Malley, J.; Tutz, G. An introduction to recursive partitioning: Rationale, application, and characteristics of classification and regression trees, bagging, and random forests. Psychol. Methods
**2009**, 14, 323–348. [Google Scholar] [CrossRef] [Green Version] - Marabel, M.; Alvarez-Taboada, F. Spectroscopic Determination of Aboveground Biomass in Grasslands Using Spectral Transformations, Support Vector Machine and Partial Least Squares Regression. Sensors
**2013**, 13, 10027–10051. [Google Scholar] [CrossRef] [Green Version] - Awad, M.; Khanna, R. Efficient Learning Machines: Theories, Concepts, and Applications for Engineers and System Designers; Springer Nature: Berkeley, CA, USA, 2015; Available online: https://library.oapen.org/viewer/web/viewer.html?file=/bitstream/handle/20.500.12657/28170/1001824.pdf?sequence=1&isAllowed=y (accessed on 2 November 2021).
- Ahmed, K.T.; Park, S.; Jiang, Q.; Yeu, Y.; Hwang, T.; Zhang, W. Network-based drug sensitivity prediction. BMC Med. Genom.
**2020**, 13, 193. [Google Scholar] [CrossRef] - Diamantopoulou, M.J.; Özçelik, R.; Yavuz, H. Tree-bark volume prediction via machine learning: A case study based on black alder’s tree-bark production. Comput. Electron. Agric.
**2018**, 151, 431–440. [Google Scholar] [CrossRef] - Friedman, J.H. Greedy function approximation: A gradient boosting machine. Ann. Stat.
**2001**, 29, 1189–1232. [Google Scholar] [CrossRef] - Biau, G.; Cadre, B. Optimization by gradient boosting. In Advances in Contemporary Statistics and Econometrics; Springer: Cham, Switzerland, 2021. [Google Scholar]
- Errousso, H.; Malhene, N.; Benhadou, S.; Medromi, H. Predicting car park availability for a better delivery bay management. Procedia Comput. Sci.
**2020**, 170, 203–210. [Google Scholar] [CrossRef] - Cade, B.S. Model averaging and muddled multimodel inferences. Ecology
**2015**, 96, 2370–2382. [Google Scholar] [CrossRef] - Biecek, P. DALEX: Explainers for Complex Predictive Models in R. J. Mach. Learn. Res.
**2018**, 19, 3245–3249. [Google Scholar] - Kukkonen, M.; Maltamo, M.; Korhonen, L.; Packalen, P. Multispectral Airborne LiDAR Data in the Prediction of Boreal Tree Species Composition. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 10. [Google Scholar] [CrossRef] - Ketterings, Q.M.; Coe, R.; van Noordwijk, M.; Ambagau’, Y.; Palm, C.A. Reducing uncertainty in the use of allometric biomass equations for predicting above-ground tree biomass in mixed secondary forests. For. Ecol. Manag.
**2001**, 146, 199–209. [Google Scholar] [CrossRef] - Wu, J.; Yao, W.; Choi, S.; Park, T.; Myneni, R.B. A Comparative Study of Predicting DBH and Stem Volume of Individual Trees in a Temperate Forest Using Airborne Waveform LiDAR. IEEE Geosci. Remote Sens. Lett.
**2015**, 12, 2267–2271. [Google Scholar] [CrossRef] - Liu, J.; Hyyppa, J.; Yu, X.; Jaakkola, A.; Kukko, A.; Kaartinen, H.; Zhu, L.; Liang, X.; Wang, Y.; Hyyppa, H. A Novel GNSS Technique for Predicting Boreal Forest Attributes at Low Cost. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 4855–4867. [Google Scholar] [CrossRef] - Vauhkonen, J.; Korpela, I.; Maltamo, M.; Tokola, T. Imputation of single-tree attributes using airborne laser scanning-based height, intensity, and alpha shape metrics. Remote Sens. Environ.
**2010**, 114, 1263–1276. [Google Scholar] [CrossRef] - Leite, R.V.; do Amaral, C.H.; Pires, R.d.P.; Silva, C.A.; Soares, C.P.B.; Macedo, R.P.; da Silva, A.A.L.; Broadbent, E.N.; Mohan, M.; Leite, H.G. Estimating Stem Volume in Eucalyptus Plantations Using Airborne LiDAR: A Comparison of Area- and Individual Tree-Based Approaches. Remote Sens.
**2020**, 12, 1513. [Google Scholar] [CrossRef] - Eysn, L.; Hollaus, M.; Lindberg, E.; Berger, F.; Monnet, J.-M.; Dalponte, M.; Kobal, M.; Pellegrini, M.; Lingua, E.; Mongus, D.; et al. A Benchmark of Lidar-Based Single Tree Detection Methods Using Heterogeneous Forest Data from the Alpine Space. Forests
**2015**, 6, 1721–1747. [Google Scholar] [CrossRef] [Green Version] - Wang, X.-H.; Zhang, Y.-Z.; Xu, M.-M. A Multi-Threshold Segmentation for Tree-Level Parameter Extraction in a Deciduous Forest Using Small-Footprint Airborne LiDAR Data. Remote Sens.
**2019**, 11, 2109. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**ALS-generated canopy height model of Pertouli University Forest, showing the sampled trees; (

**a**–

**f**) plots employed for non-destructive sampling (i.e., measurement of DBH for stem biomass estimation using allometric equations); (

**g**) area of interest for destructive sampling.

**Figure 3.**The barkless stem biomass (BSB) (

**a**) and the total stem biomass (TSB) (

**b**) calculated for each tree based on the destructive sampling implementation.

**Figure 4.**Workflow of the barkless and total stem biomass (BSB and TSB, respectively) estimation using destructive sampling and ALS data in an uneven-aged structured coniferous forest.

**Figure 5.**Effects of the simple DTM-based normalization on the crown structure and the derived parameters. (

**a**) An illustration of the unnormalized tree as it is registered by the LiDAR sensor, where D is the height difference from a specific canopy point to the treetop. (

**b**) The normalized tree using the typical DTM-based normalization procedure, resulting in irregularities in the canopy representation (D > D’) and false detected treetops (red point). (

**c**) The normalized tree using the tree-based normalization procedure, eliminating the effects of the normalization procedure in the canopy structure (Dnorm = D).

**Figure 6.**Pearson’s correlation matrix between predictor variables derived from multispectral LiDAR data.

**Figure 7.**Scatterplots (

**a**–

**f**) of the observed versus the predicted barkless stem biomass (BSB) for the testing set (i.e., 20 samples). The blue line represents the fitted line, and the red line represents the 1:1 line.

**Figure 8.**Demonstration of the relative importance of the predictors for each tested ML algorithm (BSB).

**Figure 9.**Scatterplots (

**a**–

**f**) of the observed versus the predicted total stem biomass (TSB) for the testing set (i.e., 20 samples). The blue line represents the fitted line, and the red line represents the 1:1 line.

**Figure 10.**Demonstration of the relative importance of the predictors employed for each examined algorithm (i.e., RF, SVR, GP, and XGBoost) for the total stem biomass (TSB).

Biomass | Mean (kg) | Standard Deviation (kg) | Minimum (kg) | Maximum (kg) |
---|---|---|---|---|

Barkless Stem Biomass | 556.02 | 311.79 | 3.25 | 1088.66 |

Total Stem Biomass | 642.37 | 355.45 | 4.23 | 1260.59 |

**Table 2.**LiDAR-derived metrics calculated for the stem biomass estimation. All the height metrics were calculated using all the echoes of each point cloud (Green and NIR channels), and the intensity-related metrics were obtained using only first-of-many and single returns.

LiDAR Metrics | Description |
---|---|

p10, p20… p95, p99 | Height Percentiles |

b10, b20… b95, b99 | Height Bicentiles |

Hmax | Max Height |

Havg | Average Height |

Hstd | Height Standard Deviation |

int_skew | Intensity Skewness |

int_std | Intensity Standard Deviation |

int_avg | Average Intensity |

Hyperparameter | Values |
---|---|

Number of boosting iterations | 50 to 1000, with 50 step |

Maximum depth of the tree | 1 to 5 |

Step size of each boosting step | 0.01 to 0.07, with 0.01 step |

Minimum loss reduction (gamma) | 1 to 10 |

Subsample ratio of columns when constructing each tree | 0 to 1, with 0.1 step |

Minimum sum of instance weight needed in a child | 5 to 30, with 5 step |

Subsample ratio of the training instance | 0 to 1, with 0.1 step |

**Table 4.**Parameter values, residual standard error, R

^{2}and adjusted R

^{2}for total, and woody stem biomass estimation based on DBH.

Equation | Parameter | RSE | R^{2} | adjR^{2} |
---|---|---|---|---|

Total Stem Biomass | a = 8.3488 | 0.3014 | 0.9597 | 0.9584 |

b = 2.5691 | ||||

Barkless Stem Biomass | a = 8.2480 | 0.1317 | 0.9612 | 0.9599 |

b = 2.6342 |

**Table 5.**Average testing performance of the employed algorithms for barkless stem biomass (BSB) estimation using multispectral LiDAR data (i.e., 20 testing samples).

Model | MAE | MSE | rbias | RMSE | R^{2} |
---|---|---|---|---|---|

Generalized Linear Model | 121.71 | 35,585.08 | 1.89 | 167.09 | 0.72 |

Gaussian Process (linear) | 195.44 | 64,833.22 | –5.3 | 254.26 | 0.56 |

Gaussian Process (rbf) | 162.23 | 33,970.03 | –6.47 | 184.24 | 0.75 |

Random Forest | 152.65 | 30,911.8 | –5.08 | 175.76 | 0.78 |

Support Vector Regression | 161.87 | 35,494.6 | –6.43 | 188.32 | 0.73 |

XGBoost | 157.29 | 38,154.86 | –5.08 | 195.25 | 0.69 |

**Table 6.**The best- and worst-performing GLMs selected for the barkless stem biomass (BSB) estimations, using the exhaustive screening variable selection (described in Section 3.3.1).

Model | MAE | MSE | rbias | RMSE | R^{2} |
---|---|---|---|---|---|

p10 + p70 + int_std_green | 74.34 | 9443.85 | 0.83 | 97.10 | 0.85 |

p95 + b95 + int_ske_green | 190.68 | 115,204.1 | 2.09 | 336.79 | 0.43 |

**Table 7.**Demonstration of feature importance for the GLM for the barkless stem biomass (BSB) estimation. In this table, the frequency represents the percentage of linear models containing each variable after the testing procedure.

Variable | Frequency (%) |
---|---|

int_std_green | 35.71 |

Hmax | 10.71 |

p99 | 10.71 |

p95 | 10.71 |

int_ske_green | 7.14 |

b95 | 7.14 |

p10 | 7.14 |

p70 | 3.57 |

b80 | 3.57 |

**Table 8.**Average testing performance of the employed algorithms for the total stem biomass (TSB) estimation using multispectral LiDAR data (i.e., 20 testing samples).

Model | MAE | MSE | rbias | RMSE | R^{2} |
---|---|---|---|---|---|

Generalized Linear Model | 174.55 | 45,549.33 | –1.12 | 220.37 | 0.44 |

Gaussian Process (linear) | 164.03 | 48,150.58 | –2.02 | 219.18 | 0.60 |

Gaussian Process (rbf) | 169.16 | 48,717.19 | –7.02 | 220.58 | 0.62 |

Random Forest | 175.05 | 44,622.09 | –4.94 | 211.16 | 0.65 |

Support Vector Regression | 166.84 | 51,173.42 | –6.15 | 226.00 | 0.57 |

XGBoost | 236.67 | 84,701.11 | –4.91 | 290.89 | 0.31 |

**Table 9.**The best- and worst-performing GLMs selected for the total stem biomass (TSB) estimations, using the exhaustive screening variable selection (described in Section 3.3.1).

Model | MAE | MSE | rbias | RMSE | R^{2} |
---|---|---|---|---|---|

Havg + p70 + int_std_green | 158.50 | 40,721.83 | −0.05 | 201.79 | 0.57 |

p70 + b50 + int_std_green | 178.80 | 46,749.84 | −1.45 | 226.23 | 0.31 |

**Table 10.**Demonstration of feature importance for the GLM for the total stem biomass (TSB) estimation. In this table, the frequency represents the percentage of linear models containing each variable after the testing procedure.

Variable | Frequency (%) |
---|---|

int_std_green | 34.48 |

p70 | 31.03 |

b50 | 27.58 |

Havg | 3.44 |

p80 | 3.44 |

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## Share and Cite

**MDPI and ACS Style**

Georgopoulos, N.; Gitas, I.Z.; Stefanidou, A.; Korhonen, L.; Stavrakoudis, D.
Estimation of Individual Tree Stem Biomass in an Uneven-Aged Structured Coniferous Forest Using Multispectral LiDAR Data. *Remote Sens.* **2021**, *13*, 4827.
https://doi.org/10.3390/rs13234827

**AMA Style**

Georgopoulos N, Gitas IZ, Stefanidou A, Korhonen L, Stavrakoudis D.
Estimation of Individual Tree Stem Biomass in an Uneven-Aged Structured Coniferous Forest Using Multispectral LiDAR Data. *Remote Sensing*. 2021; 13(23):4827.
https://doi.org/10.3390/rs13234827

**Chicago/Turabian Style**

Georgopoulos, Nikos, Ioannis Z. Gitas, Alexandra Stefanidou, Lauri Korhonen, and Dimitris Stavrakoudis.
2021. "Estimation of Individual Tree Stem Biomass in an Uneven-Aged Structured Coniferous Forest Using Multispectral LiDAR Data" *Remote Sensing* 13, no. 23: 4827.
https://doi.org/10.3390/rs13234827