# Estimating Forest Structural Parameters Using Canopy Metrics Derived from Airborne LiDAR Data in Subtropical Forests

^{*}

## Abstract

**:**

^{2}= 0.44–0.88) were relatively higher than general models (Adj-R

^{2}= 0.39–0.77). For forest structural parameters, the estimation accuracies of Lorey’s mean height (Adj-R

^{2}= 0.61–0.88) and aboveground biomass (Adj-R

^{2}= 0.54–0.81) models were the highest, followed by volume (Adj-R

^{2}= 0.42–0.78), DBH (Adj-R

^{2}= 0.48–0.74), basal area (Adj-R

^{2}= 0.41–0.69), whereas stem density (Adj-R

^{2}= 0.39–0.64) models were relatively lower. The combination models (Adj-R

^{2}= 0.45–0.88) had higher performance compared with models developed using standard metrics (only) (Adj-R

^{2}= 0.42–0.84) and canopy metrics (only) (Adj-R

^{2}= 0.39–0.83). The results also demonstrated that the optimal voxel size was 5 × 5 × 0.5 m

^{3}for estimating most of the parameters. This study demonstrated that canopy metrics based on canopy vertical profiles can be effectively used to enhance the estimation accuracies of forest structural parameters in subtropical forests.

## 1. Introduction

^{2}values of 0.93–0.98. The R

^{2}values were 0.94–0.95 and 0.95–0.97 for basal area and volume, which were predicted using the metrics of height percentiles and canopy densities as independent variables. Silva et al. (2016) [26] predicted and mapped volume using LiDAR metrics in Eucalyptus plantations in tropical forests (located in São Paulo, Brazil), and found that volume (Adj-R

^{2}= 0.84) was well predicted by the coefficient of variation of return height and the 99th height percentile from LiDAR. Tesfamichael and Beech (2016) [27] used height-related metrics (e.g., height percentiles, maximum height) and canopy density metrics to estimate plot-level structural attributes (i.e., mean height, maximum height, crown diameter and aboveground biomass) over a savanna ecosystem region located in the south western part of Zambia, and resulted in R

^{2}values of 0.48–0.95. However, these studies often include height and density predictors with little physical justification for model formulation. Moreover, they usually neglected a mechanism to summarize complex canopy characteristics into simple parameters, which can potentially be used for estimates of forest structural parameters in different forest conditions [14,28], and the standard metrics (i.e., height-based and density-based metrics) tend to be strongly inter-correlated, and depend on forest conditions, plot sizes, point cloud density and geometrical distributions of point clouds etc. [29,30,31,32,33], and a large subset of these metrics are linked to only a few forest stand characteristics. Thus, these metrics generally have a relatively low transferability and are limited in describing the vertical heterogeneity of forest structure [24].

^{2}= 0.52–0.91) for estimating forest structural parameters using the metrics derived from canopy vertical profiles (i.e., canopy volume profiles (CVP) and canopy height profiles (CHP)). Lovell et al. (2003) [37] used airborne and terrestrial LiDAR data to derive foliage profiles (FP) and estimated effective leaf area index (LAI) in temperate forests located in southern Australia. They found that results compared with LAI derived from classified hemispherical photographs with agreement within 8%. Coops et al. (2007) [38] refined the CVM approach to adapt discrete return LiDAR data. In addition, a Weibull fitting approach was conducted to fit FP profiles and further obtain relevant LiDAR metrics, and finally a number of forest structural parameters (i.e., mean height, basal area) (R

^{2}= 0.65–0.85) were estimated. Hilker et al. (2010) [39] assessed and compared canopy metrics derived from canopy vertical profiles using airborne and terrestrial LiDAR data. The results showed that airborne and terrestrial LiDAR were both able to accurately determine canopy height (absolute error of height was less than 2.5 m) and LAI (R

^{2}= 0.86–0.90). However, most previous studies that estimate forest structural parameters using canopy metrics derived from canopy vertical profiles were conducted in temperate, tropical and boreal forests, and published studies of the subtropical forests are few.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Acquisition and Pre-Processing

#### 2.2.1. LiDAR Data

^{−1}and a flight line side-lap of ≥60%. The sensor recorded returned waveforms of laser pulse with a temporal sample spacing of 1 ns (approximately 15 cm). The LiDAR system was configured to emit laser pulses in the near-infrared band (1550 nm) at a 360 kHz pulse repetition frequency and a 112 Hz scanning frequency, with a scanning angle of ±30° from nadir and a swath of 1040 m. The dataset had an average beam footprint size of 0.45 m (nadir) in diameter. The average ground point distances of the dataset were 0.49 m (flying direction) and 0.48 m (scanning direction) in a single strip, with pulse density of approximately 5.06 pulse m

^{−2}. The final extracted point clouds and associated waveforms were stored in LAS 1.3 format (American Society for Photogrammetry and Remote Sensing, Bethesda, MD, USA).

#### 2.2.2. Field Data

#### 2.3. Derived Metrics

#### 2.3.1. Canopy Volume Model Approach

^{3}), and these voxels were classified as either “filled” or “empty” volume depending on the presence or absence of LiDAR points within each voxel. “Filled” voxels were further classified as either “euphotic“ zone, if they were located in the uppermost 65% of all filled voxels, or as “oligophotic” zone if they were located below the point, whereas “empty” voxels were located either below (“closed gap”) or above the canopy (“open gap”) [38]. Open gap, euphotic, oligophotic and closed gap were determined as four canopy structure classes, with units defined as the volume of each class per unit area. All volume elements (Open gap, Oligophotic, Euphotic, Closed gap, Filled, Empty) were derived as canopy volume (CV) metrics using the CVM method and canopy volume profile (CVP) was visualized. Figure 4 shows the illustration of voxel-based CVM approach. Point clouds of a plot (30 × 30 m

^{2}) were voxelized, and divided into 36 vertical columns of voxels, and each column was further stratified with four canopy structure classes. All columns of a plot were expanded in a panel and the canopy volume distribution (CVD) was presented (Figure 4c). Finally, the volume percentages of canopy structure classes of each height interval (0.5 m) were calculated, resulting in CVP (Figure 4d).

^{−2}, horizontal resolutions of 1 m to 10 m were chosen (which were multiples of the footprint size and average ground point distances). Vertical resolutions of 0.5 m and 1 m were chosen to correspond to roughly three and six sampling intervals of the returned waveform. A sensitivity analysis was performed using CV-metrics (i.e., Open gap, Oligophotic, Euphotic, Closed gap, Filled, Empty).

#### 2.3.2. Weibull Fitting Approach

^{3}rectangular section) from the ground to canopy top [48,49]. In this study, a two-parameter Weibull density function (PDF) was used to describe CHD on each plot. As a Weibull model is highly adaptive, ranging from an inversed J-shape to unimodal skewed and unimodal symmetrical curve, the Weibull model has flexibility in characterizing distributions of a range of forest attributes [50,51]. The two parameters, i.e., Weibull scale (α

_{1}) and Weibull shape (β

_{1}), were derived by the maximum likelihood estimation method. Weibull scale determines the basic shape of the distribution density curve and Weibull shape controls the breadth of the distribution [52]. Foliage profile (FP) can delineate the vertical distribution of canopy phytoelement (e.g., leaf, stem, twig, etc.) density above the ground within a forest stand [37]. FP is defined as the total one-sided leaf area that is involved in photosynthesis per unit canopy volume at canopy height z, and describes changes in the leaf area distribution with increasing height [53]. FP is highly related to leaf area index (LAI), which was demonstrated in previous studies [35,54], and the relationship between FP and LAI is:

_{c}) from the ground to a given height z; FP(z) represents the foliage area volume density at height z (is the vertical foliage profile in a thin layer or “slice” through a canopy as a function of height z); z

_{1}and z

_{2}are different canopy height. A height interval or each vertical “slice” was 0.3 m. Meanwhile, we assumed that foliage elements in a thin “slice” were very small so that occlusion can be neglected, and leaves presented Poisson random distribution. Because airborne LiDAR is incapable of resolving foliage angle distribution, clumping and non-foliage elements, the foliage profiles derived from airborne LiDAR are referred to here as “apparent” foliage profiles and effective LAI [37]. In this study, LAI can be indirectly determined from LiDAR by estimating the derived gap probability in the canopy [37,38], and the gap probability be estimated as the total number of laser hits up to a height z relative to the total number of LiDAR shots as follows:

_{gap}(z) is a gap probability measurement at height z, #z is the number of hits down to a height z above the ground, and N is the total number of shots emitted up to the sky. Previous studies have showed that Weibull distribution function can also delineate vertical foliage profiles distributions [37,55]. In this study, the Weibull fitted scale parameter (α

_{2}) and shape parameter (β

_{2}) were derived from the apparent FP by linking Weibull cumulative function to cumulative projected foliage area index [37,38]:

_{2}and β

_{2}are fitted parameters, z is the height, and H is the maximum height in a plot.

_{25}, h

_{50}, h

_{75}, h

_{95}, h

_{mean}, h

_{cv}, h

_{skewness}and h

_{kurtosis}) and density-based (DB) metrics (d

_{1}, d

_{3}, d

_{5}, d

_{7}, d

_{9}, CC

_{2m}). A summary of these metrics with corresponding descriptions is shown in Table 2.

#### 2.4. Metrics Selection and Statistical Analysis

^{2}) improvement variable selection techniques were applied to select the metrics to be included in the models [59]. Independent variables were left in the model using an F-test with a p < 0.05 significance level. The standard least-squares method was used [60].

^{2}), Root-Mean-Square Error (RMSE), which has been transformed back to original scale, and relative RMSE (rRMSE), which are defined as the percentage of the ratio of RMSE and the observed mean values. In this study, dummy variables (or class variables) were added to the selected models as the dependent variables to assess whether these models differ between forest types [62]. Once the best models were chosen, leave-one-out cross-validation was performed to evaluate the predictive accuracies of the models [63].

## 3. Results

#### 3.1. Profile Analysis

_{c}for plots in different forest types and mean CVD.

#### 3.2. Accuracy Assessments

^{2}= 0.39–0.88, rRMSE = 5.13–29.86%). Overall, Lorey’s mean height (Adj-R

^{2}= 0.61–0.88, rRMSE = 5.13–12.79%) and AGB (Adj-R

^{2}= 0.54–0.81, rRMSE = 12.19–28.42%) was predicted most accurately. For volume, DBH and basal area, the R

^{2}values were slightly lower and ranged from 0.42 to 0.78, 0.48 to 0.74 and 0.41 to 0.69, respectively. The lowest accuracy was found for stem density (Adj-R

^{2}= 0.39–0.64, rRMSE = 18.68–29.86%). In comparison, most of forest structural parameters in type-specific models (Adj-R

^{2}= 0.44–0.88, rRMSE = 5.13–28.42%) had higher accuracies than in general models (Adj-R

^{2}= 0.39–0.77, rRMSE = 8.54–29.86%), indicating that the accuracies of forest type-specific models were generally improved rather than general models. Furthermore, the fitted models of the forest structural parameters were relatively more accurate for coniferous forests (Adj-R

^{2}= 0.54–0.81, rRMSE = 8.59–26.55%) than broad-leaved forests (Adj-R

^{2}= 0.50–0.88, rRMSE = 6.39–28.42%) and mixed forests (R

^{2}= 0.44–0.84, rRMSE = 5.13–29.52%). Compared with canopy metrics based models (Adj-R

^{2}= 0.39–0.83, rRMSE = 6.94–29.26%), standard metrics based models had a relatively higher performance (Adj-R

^{2}= 0.42–0.84, rRMSE = 5.60–29.86%) and the combination models performed best (Adj-R

^{2}= 0.45–0.88, rRMSE = 5.13–28.96%), indicating the inclusion of canopy metrics potentially improved the estimation performances of structural parameters.

_{95}(selected by four out of six models), d

_{7}(selected by four out of six models), d

_{3}, h

_{cv}and d

_{9}(each of them was selected by three out of six models) were the most frequently selected, indicating these metrics are more sensitive and representative to the forest structural parameters. For general CM models, all of CV metrics and WF metrics were selected for estimating forest structural parameters. Within CV metrics, the statistic of Oligophotic (all selected by six models), Empty (selected by four out of six models) and Open (selected by four out of six models) were sensitive to forest structural parameters and these metrics were selected both in the general models and forest type-specific models, suggesting that the three metrics have a strong ability to explain variations. Within WF metrics, α

_{1}was relatively sensitive to structural parameters (selected two out of six models). In six general combination models, most of standard metrics (nine out of 14) and canopy metrics (four out of total 10) were used in combination for parameter estimations. The metrics of Oligophotic, Empty, h

_{95}remained sensitive to structural parameters (selected by 2–4 out of six general combo models). Moreover, h

_{75}, d

_{1}and β

_{1}(selected by 2–3 out of 6) became more sensitive for DBH, Lorey’s mean height, and stem density in combination models than SM models.

^{2}values of 0.79 and 0.66, followed by DBH (R

^{2}= 0.60), volume (R

^{2}= 0.60) and basal area (R

^{2}= 0.52), whereas the accuracy of stem density model was the lowest (R

^{2}= 0.49). For Lorey’s mean height, AGB, DBH, and volume estimations, their relationships were close to the 1:1 line whereas basal area and stem density had a relationship that deviated from the 1:1 line, with a slightly larger deviation in broad-leaved forests.

#### 3.3. The Selection of Voxel Sizes

^{2}values of the models showed a trend of first increasing and then decreasing when horizontal resolutions of voxels were varied from 1 m to 10 m (Figure 10a,b), and the voxels in horizontal resolution of 5 m had the best performance. Figure 10a was subtracted from Figure 10b to calculate the result of Figure 10c, which demonstrated the difference of rRMSE values of forest structural parameters for various vertical resolutions (0.5 m and 1 m). The values presented were mostly positive, except for some of the differences were negative (e.g., G at 3 m horizontal resolution) (Figure 10c). In particular, DBH and stem density models had all positive values across 1 m to 10 m of horizontal resolutions, indicating the two parameters were strongly influenced by the vertical resolution of the voxels. As a result, the suitable voxel size in this study was 5 × 5 × 0.5 m

^{3}.

## 4. Discussion

#### 4.1. Canopy Vertical Profiles

_{c}. As mentioned above, the CVM approach provides a broad classification approach to categorize the canopy into photosynthetically active and less active zones [39]. Therefore, it can better reflect the spatial heterogeneity of forest structure, which is caused by the difference of light environment in the canopy. Furthermore, the CVP explicitly presented variation in the spatial arrangement of elements (i.e., open gap, euphotic, oligophotic, closed gap) within the vertical forest canopy [38]. As shown in Figure 5 and Figure 6, the broad-leaved forests had the largest closed gap volume and the smallest open gap volume when compared to coniferous forests and mixed forests. The explanations of these phenomena need to take into account the canopy geometry and tree architecture [36]. At our research site, coniferous forests are dominated by Masson pine and slash pine; these species usually consist of a regular and conical crown, demonstrating a heavily thinned upper canopy and a dense sub-canopy (Figure 3). Furthermore, more open upper canopies in coniferous stands allow more light to pass through to the lower canopy strata [69,70], so a shrubby understory may incrementally emerge, resulting in the most open gap and the lowest closed gap zones in coniferous forests. Conversely and notably, broadleaves with elliptical or spherical crown are very tall and have positively skewed canopies with a lower canopy transparency in this study area, as indicated by the large decrease in open gap zones. Additionally, the closed canopy volume generally increased with decreasing stand density [55], hence the broad-leaved forests with a lower stem density (1126.00 ha

^{−1}) also had a more closed canopy gap. Although with a much more shrubby understory, mixed conifer–broadleaf forests generally encompass median height broadleaved trees [65] with a high stem density (1431.78 ha

^{−1}) and canopy transparency, resulting in a higher amount of closed gap volume than coniferous forests and a slightly higher amount of open gap volume. On the other hand, as Yushan forest is in secondary succession, the forest canopy surface became more uneven, and the competitions among shade-intolerant species (e.g., Masson pine, Chinese sweet gum) were accelerated and further inhibited the establishment and growth of these species [71,72]. As a result, in late-successional stage, the shade-tolerant species (e.g., Oriental oak, camphorwood and Chinese holly) eventually dominated the canopy [69,72,73] and coexisted with other species. This process could cause the transmittance of light through the canopy to decline [74], which may result in an increase the spatial heterogeneity of the light environment [75,76] and a further enhancement of more microsite light availability in lower canopies [70,76,77,78,79]. Thus, for each forest type, the oligophotic zone, which represented a larger proportion of the total filled volume compared to the euphotic zone that represented photosynthetically active tissues (Figure 6). As mentioned above, the canopy architectures of the three forest types can help explain why the distributions of FP and CHD in coniferous forests and mixed forests inclined to the under canopy, whereas the curves of broad-leaved forests were distributed more towards the middle or upper canopy (Figure 7 and Figure 8b–d).

#### 4.2. Predictive Models

^{2}= 0.44–0.88, rRMSE = 5.13–28.42%) than the general models (Adj-R

^{2}= 0.39–0.77, rRMSE = 8.54–29.86%). Bouvier et al. (2015) [14] developed a separate model for coniferous, deciduous and mixed stands to estimate forest structural parameters in the Lorraine forests. The results demonstrated that the separate models reduce estimation errors (2.0–5.3%) compared to general models in some complex forests conditions, which was confirmed by our research results. Fu et al. (2011) [82] reported R

^{2}values for AGB of 0.37 of the general model and 0.43–0.68 of forest type-specific models in subtropical forests (located in southern Yunnan province, China). In our study site, the multi-layered forest conditions in subtropical forests contained greater species diversity, making the effects of tree-species composition (classified as forest types) significant. Overall, the models of the forest structural parameters were relatively more accurate for coniferous forests than broad-leaved forests and mixed forests. The relationships between stand structure and the forest structural parameters are species-dependent, and coniferous forests are usually characterized by relatively simple stand structures when compared with broad-leaved or mixed stands. So it is likely that the model prediction accuracy may decrease in multispecies stands [14]. Xu et al. (2015) [83] estimated forest structural parameters (i.e., Lorey’s mean height, stem density, basal area and volume) in the subtropical deciduous mixed forests (on Purple Mountain, located in eastern Nanjing), using canopy height metrics (i.e., height percentile, mean height, maximum height and minimal height) and canopy density metrics. Compared with our results (rRMSE = 5.13–22.28%), theirs showed a relatively lower rRMSE for Lorey’s mean height (6.47%), stem density (27.04%), basal area (16.38%), and volume (6.93%). Compared with canopy metrics-based models (Adj-R

^{2}= 0.39–0.83, rRMSE = 6.94–29.26%), standard metrics-based models had relatively higher performance (Adj-R

^{2}= 0.42–0.84, rRMSE = 5.60–29.86%), except for the volume and AGB (both in forest type-specific models). The combination models performed best (Adj-R

^{2}= 0.45–0.88, rRMSE = 5.13–28.96%), explaining a large amount of the variability for all forest structural parameters and indicating the increased utility of canopy metrics in capturing spatially explicit information describing a heterogeneous forest structure. For DBH, stem density, basal area, and AGB, Lefsky et al. (1999) [36] reported adjusted R

^{2}values of 0.61, 0.52, 0.87, and 0.91 in boreal forests, markedly higher than reported in this study. The cause of the lower performance in this research is likely the complex structure of the subtropical forests, which are typified by multi-layered forests which that encompass some stands with considerable variability in tree height and stem density, especially in old-growth stands, whereas boreal forests have a much higher homogeneous composition and more discernible canopy architecture.

_{1}and β

_{1}, indicating that both of them are suitable for estimating structure parameters in local forests. The capacity of the Weibull parameters to represent the key attributes of mean crown dimension is important, as it provides a mechanism to summarize complex canopy characteristics into simple parameters that can be empirically analyzed in relation to various forest stand characteristics. The two-parameter Weibull model was applied for characterizing many types of FPs and CHDs in this study. In general, these profiles of single layer canopies corresponded well (Figure 7). However, the unimodal Weibull distribution function applied to the profile is inadequate to describe properly multimodal structure, which may occur in multi-layered, multi-age, complex forest stands [52]. Thus, the relatively poor fit for multi-layered forests could result in errors in estimates of structural parameters, which may explain why the Weibull parameters are not statistically more significant predictors than CV metrics. In this regard, future work could focus on how to apply a multi curve fitting approach in order to further capture the full distributions of canopy vertical profiles. On the other hand, different plot selection strategies could influence the performance of predictive models [85]. The plot selection in this study was only according to forest type, thus our future work could also examine different plot selection strategies of field training plots (e.g., using LiDAR data or geographical factors as a prior information, etc.) and utilize a suitable strategy to improve the estimation accuracy of forest structural parameters.

#### 4.3. The Selection of Voxel Sizes

^{3}) or high (i.e., 10 × 10 × 1 m

^{3}) resolution conditions, the R

^{2}values showed a relatively lower performance. If voxels are too small, a voxel-based CVM approach may produce redundant unfilled voxels of empty volume containing few tree canopy elements, which may lead to the underestimation of forest structural parameters; however, too large voxels may lead to too few voxels and result in statistically insignificant descriptions of canopy features [90]. In these conditions, the voxel approach could become ineffective at characterizing the vertical distribution of various canopy structures and the capability to capture 3D heterogeneity of canopy structure for CV metrics could be constrained, hence resulting in relatively lower performances of the models. After taking into account factors of plot size (30 × 30 m

^{2}), point cloud densities (3.74 pts·m

^{−2}), etc., Hilker et al. (2010) [39] used a voxel size of 6 × 6 × 1 m

^{3}for discrete airborne LiDAR data to estimate the tree height and LAI in Douglas-fir-dominated forest stands with relatively high tree heights (30–35 m). Concerning a much higher point cloud density (5.06 pts·m

^{−2}) of LiDAR data and relatively lower tree heights (4.47–18.52 m) in this study site, a 1 m vertical resolution produced more coarse data than the vertical resolution of 0.5 m (approximately treble the temporal sample spacing of 1 ns (15 cm)), thus, constraining the ability of canopy volume metrics to describe the vertical variability of the forest canopy structures. Moreover, potential tree movement due to wind between laser acquisitions is also considered a source of uncertainty, as laser returns from the same target can be located in different voxels for different laser acquisitions. By using a voxel size larger than the pulse diameter, this issue can be slightly reduced [91]. Overall, the optimal voxel size is a key parameter to determine in order to improve characterizations of forest structure [92,93]. Consequently, the optimal voxel spatial resolution should be determined based on plot size, the characteristics of the LiDAR instrument used (e.g., beam diameter, footprint size, average point density and temporal sample spacing, etc.), and forest structure attributes (e.g., tree height, crown diameter, crown depth, etc.)

## 5. Conclusions

^{2}= 0.44–0.88, rRMSE = 5.13–28.42%) compared with the general models (Adj-R

^{2}= 0.39–0.77, rRMSE = 8.54–29.86%). The estimation accuracies of Lorey’s mean height and AGB were the highest, followed by volume, DBH and basal area, whereas stem density was relatively lower. Overall, metrics of Oligophotic, Empty, Open, α

_{1}were the most frequently selected, indicating their potential capability for predicting forest structural parameters in the forest stands within the study site. The results demonstrated the synergistic use of standard metrics and canopy metrics for better predicting forest structural parameters (∆Adj-R

^{2}= 0.01–0.20, ∆rRMSE = −5.71–1.39%), compared with models developed using standard metrics (only) and canopy metrics (only). In addition, the optimal voxel size for estimating forest structural parameters in this study is 5 × 5 × 0.5 m

^{3}, and the voxel vertical and horizontal resolutions should be determined based on plot size, the characteristics of the acquired LiDAR data (i.e., beam diameter, footprint size, average point density, and temporal sample spacing) and forest structure attributes (i.e., tree height, crown diameter, and crown depth).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Table A1.**Allometric equations for aboveground biomass components of dominant tree species and species group in the study site.

Tree Species | Component | a | b | R^{2} | References |
---|---|---|---|---|---|

Masson pine | Stem wood (W_{s}) | 0.141 | 1.092 | 0.9970 | Jiang et al. (1992) [42] |

Live branches (W_{b}) | 0.065 | 0.991 | 0.9871 | ||

Foliage (W_{f}) | 0.132 | 0.745 | 0.9827 | ||

Chinese fir | Stem wood (W_{s}) | 0.124 | 0.680 | 0.9704 | Ye and Jiang (1983) [43] |

Live branches (W_{b}) | 0.203 | 0.385 | 0.7223 | ||

Foliage (W_{f}) | 0.850 | 0.189 | 0.6567 | ||

Slash pine | Stem wood (W_{s}) | 0.235 | 0.900 | 0.9523 | Wang and Shi (1990) [44] |

Live branches (W_{b}) | 0.080 | 1.064 | 0.8520 | ||

Foliage (W_{f}) | 0.456 | 0.610 | 0.8802 | ||

Sawtooth oak | Stem wood (W_{s}) | 0.018 | 1.034 | 0.9864 | Xu et al. (2011) [46] |

Live branches (W_{b}) | 0.00008 | 1.468 | 0.9745 | ||

Foliage (W_{f}) | 0.004 | 0.769 | 0.8662 | ||

Sweet gum | Stem wood (W_{s}) | 0.093 | 0.801 | 0.9310 | Qian (2000) [45] |

Live branches (W_{b}) | 0.083 | 0.649 | 0.9890 | ||

Foliage (W_{f}) | 1.084 | 0.217 | 0.6940 | ||

Other broadleaves ^{a} | Stem wood (W_{s}) | 0.023 | 0.985 | 0.9903 | Sun et al. (1992) [47] |

Live branches (W_{b}) | 0.00004 | 3.785 | 0.9623 | ||

Foliage (W_{f}) | 0.00003 | 1.378 | 0.9456 |

^{2}H)

^{b}was used to calculate each biomass component. H = Tree height (m), D = DBH (cm) and a, b are the parameters.

^{a}The general equation of “Other broadleaves” includes tree species of Quercus variabilis, Quercus fabri, Quercus aliena, Quercus glandurifera var. brevipetiolata, Castanea sequinii, Liquidambar formasana and Pistacia chinensis.

Variables | Predictive Models | Adj-R^{2} | RMSE | rRMSE % |
---|---|---|---|---|

All plots | ||||

DBH/cm | $\mathrm{exp}(1.064+0.641\mathrm{ln}{h}_{95}-0.580\mathrm{ln}{d}_{1}+0.066\mathrm{ln}{d}_{7})\times 1.008$ | 0.60 *** | 1.72 | 12.33 |

h_{Lorey}/m | $\mathrm{exp}(-0.33-0.079\mathrm{ln}{h}_{\mathrm{cv}}+1.012\mathrm{ln}{h}_{95}-0.028\mathrm{ln}{d}_{7}-0.001\mathrm{ln}{d}_{9})\times 1.006$ | 0.75 *** | 0.97 | 9.15 |

N/(ha^{−1}) | $\mathrm{exp}(6.814-0.049\mathrm{ln}{h}_{\mathrm{cv}}+2.124\mathrm{ln}{d}_{1}-0.296\mathrm{ln}{d}_{7}-0.049\mathrm{ln}{d}_{9})\times 1.052$ | 0.42 *** | 423.75 | 29.86 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(0.899+0.851\mathrm{ln}{h}_{95}-0.819\mathrm{ln}{d}_{3}-0.177\mathrm{ln}{d}_{7})\times 1.019$ | 0.44 *** | 3.99 | 17.23 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(3.445-0.137\mathrm{ln}{h}_{\mathrm{cv}}+0.232\mathrm{ln}{h}_{25}+0.515\mathrm{ln}{h}_{50}+0.295\mathrm{ln}{d}_{3})\times 1.023$ | 0.46 *** | 22.34 | 17.46 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(-0.169-0.058\mathrm{ln}{h}_{\mathrm{kurtosis}}+1.817\mathrm{ln}{h}_{95}+0.627\mathrm{ln}{d}_{3}-0.048\mathrm{ln}{d}_{9})\times 1.037$ | 0.64 *** | 19.17 | 22.47 |

Coniferous forests | ||||

DBH/cm | $\mathrm{exp}(0.996+0.664\mathrm{ln}{h}_{95}-0.485\mathrm{ln}{d}_{1}+0.88\mathrm{ln}{d}_{7})\times 1.006$ | 0.67 ** | 1.20 | 9.50 |

h_{Lorey}/m | $\mathrm{exp}(-1.480-0.488\mathrm{ln}{h}_{\mathrm{cv}}+1.211\mathrm{ln}{h}_{95}-0.102\mathrm{ln}{d}_{7}-0.008\mathrm{ln}{d}_{9})\times 1.013$ | 0.66 | 1.09 | 11.47 |

N/(ha^{−1}) | $\mathrm{exp}(6.39-0.851\mathrm{ln}{h}_{\mathrm{cv}}+1.810\mathrm{ln}{d}_{1}-0.477\mathrm{ln}{d}_{7}+0.140\mathrm{ln}{d}_{9})\times 1.036$ | 0.60 | 315.78 | 18.68 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(-0.885+1.531\mathrm{ln}{h}_{95}+1.380\mathrm{ln}{d}_{3}-0.376\mathrm{ln}{d}_{7})\times 1.029$ | 0.62 ** | 4.53 | 19.63 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(3.459+0.633\mathrm{ln}{h}_{\mathrm{cv}}+3.732\mathrm{ln}{h}_{25}-2.335\mathrm{ln}{h}_{50}+0.491\mathrm{ln}{d}_{3})\times 1.029$ | 0.69 ** | 22.40 | 19.22 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(-2.216+0.565\mathrm{ln}{h}_{\mathrm{kurtosis}}+2.218\mathrm{ln}{h}_{95}+0.455\mathrm{ln}{d}_{3}-0.099\mathrm{ln}{d}_{9})\times 1.059$ | 0.72 ** | 16.86 | 24.17 |

Broad-leaved forests | ||||

DBH/cm | $\mathrm{exp}(0.949+0.680\mathrm{ln}{h}_{95}-0.654\mathrm{ln}{d}_{1}+0.028\mathrm{ln}{d}_{7})\times 1.009$ | 0.61 ** | 1.70 | 11.12 |

h_{Lorey}/m | $\mathrm{exp}(-0.296-0.149\mathrm{ln}{h}_{\mathrm{cv}}+0.981\mathrm{ln}{h}_{95}-0.082\mathrm{ln}{d}_{7}-0.031\mathrm{ln}{d}_{9})\times 1.004$ | 0.84 *** | 0.78 | 6.91 |

N/(ha^{−1}) | $\mathrm{exp}(7.663+0.602\mathrm{ln}{h}_{\mathrm{cv}}+2.500\mathrm{ln}{d}_{1}-0.144\mathrm{ln}{d}_{7}-0.071\mathrm{ln}{d}_{9})\times 1.056$ | 0.60 | 298.99 | 26.55 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(3.045+0.046\mathrm{ln}{h}_{95}+0.516\mathrm{ln}{d}_{3}-0.001\mathrm{ln}{d}_{7})\times 1.010$ | 0.54 | 2.62 | 11.96 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(3.459+0.633\mathrm{ln}{h}_{\mathrm{cv}}+3.732\mathrm{ln}{h}_{25}-2.335\mathrm{ln}{h}_{50}+0.491n{d}_{3})\times 1.029$ | 0.56 | 19.49 | 14.68 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(1.958-0.060\mathrm{ln}{h}_{\mathrm{kurtosis}}+1.150\mathrm{ln}{h}_{95}+0.579\mathrm{ln}{d}_{3}+0.057\mathrm{ln}{d}_{9})\times 1.063$ | 0.57 | 26.80 | 28.42 |

Mixed forests | ||||

DBH/cm | $\mathrm{exp}(1.184+0.360\mathrm{ln}{h}_{95}-1.116\mathrm{ln}{d}_{1}+0.110\mathrm{ln}{d}_{7})\times 1.008$ | 0.48 ** | 1.66 | 11.94 |

h_{Lorey}/m | $\mathrm{exp}(0.830+0.222\mathrm{ln}{h}_{\mathrm{cv}}+0.700\mathrm{ln}{h}_{95}+0.135\mathrm{ln}{d}_{7}-0.067\mathrm{ln}{d}_{9})\times 1.003$ | 0.81 *** | 0.60 | 5.60 |

N/(ha^{−1}) | $\mathrm{exp}(7.774+0.093\mathrm{ln}{h}_{\mathrm{cv}}+4.386\mathrm{ln}{d}_{1}-0.391\mathrm{ln}{d}_{7}+0.157\mathrm{ln}{d}_{9})\times 1.031$ | 0.48 ** | 336.73 | 28.52 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(1.308+0.772\mathrm{ln}{h}_{95}+1.036\mathrm{ln}{d}_{3}-0.046\mathrm{ln}{d}_{7})\times 1.009$ | 0.45 ** | 3.08 | 12.86 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(3.144+0.006\mathrm{ln}{h}_{\mathrm{cv}}-2.519\mathrm{ln}{h}_{25}+3.238\mathrm{ln}{h}_{50}+2.386n{d}_{3})\times 1.009$ | 0.60 *** | 16.76 | 12.70 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(-0.177-0.261\mathrm{ln}{h}_{\mathrm{kurtosis}}+1.917\mathrm{ln}{h}_{95}+1.380\mathrm{ln}{d}_{3}-0.081\mathrm{ln}{d}_{9})\times 1.016$ | 0.64 *** | 13.20 | 14.77 |

Variables | Predictive Models | Adj-R^{2} | RMSE | rRMSE % |
---|---|---|---|---|

All plots | ||||

DBH/cm | $\mathrm{exp}(2.852+0.169\mathrm{ln}OG-0.076\mathrm{ln}Oligo+0.081\mathrm{ln}Empty-0.576\mathrm{ln}\beta 2)\times 1.010$ | 0.50 *** | 1.86 | 13.31 |

h_{Lorey}/m | $\mathrm{exp}(-0.235-0.421\mathrm{ln}Oligo+1.010\mathrm{ln}F\mathrm{illed}-0.272\mathrm{ln}Empty-0.338\mathrm{ln}\mathsf{\beta}2)\times 1.009$ | 0.61 *** | 1.18 | 11.13 |

N/(ha^{−1}) | $\mathrm{exp}(5.545-0.508\mathrm{ln}OG+0.232\mathrm{ln}Eu+0.342\mathrm{ln}Oligo+1.332\mathrm{ln}\beta 1)\times 1.055$ | 0.39 *** | 415.17 | 29.26 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(2.119+0.579\mathrm{ln}Oligo+0.579\mathrm{ln}Empty+0.094\mathrm{ln}\alpha 2)\times 1.020$ | 0.41 *** | 3.67 | 15.82 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(3.063+0.249\mathrm{ln}OG+0.237\mathrm{ln}Eu+0.423\mathrm{ln}Oligo-0.694\mathrm{ln}\alpha 1)\times 1.025$ | 0.42 *** | 22.36 | 17.48 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(1.650-0.292\mathrm{ln}OG+1.021\mathrm{ln}Oligo-0.071\mathrm{ln}CG+0.717\mathrm{ln}Empty)\times 1.048$ | 0.54 *** | 19.84 | 23.25 |

Coniferous forests | ||||

DBH/cm | $\mathrm{exp}(1.455-0.535\mathrm{ln}OG+0.388\mathrm{ln}Oligo+0.622\mathrm{ln}Empty-0.052\mathrm{ln}\beta 2)\times 1.009$ | 0.54 | 1.40 | 11.09 |

h_{Lorey}/m | $\mathrm{exp}(-4.620-4.700\mathrm{ln}Oligo+5.948\mathrm{ln}Filled+0.281\mathrm{ln}Empty-2.952\mathrm{ln}\mathsf{\beta}2)\times 1.014$ | 0.64 | 1.21 | 12.79 |

N/(ha^{−1}) | $\mathrm{exp}(5.379-0.310\mathrm{ln}OG-0.726\mathrm{ln}Eu+1.019\mathrm{ln}Oligo+1.156\mathrm{ln}\beta 1)\times 1.042$ | 0.58 | 431.65 | 25.53 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(-1.378+1.535\mathrm{ln}Oligo+0.195\mathrm{ln}Empty-2.715\mathrm{ln}\alpha 2)\times 1.043$ | 0.55 | 4.73 | 20.48 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(-1.462+0.559\mathrm{ln}OG+2.869\mathrm{ln}Eu-0.765\mathrm{ln}Oligo-6.184\mathrm{ln}\alpha 1)\times 1.028$ | 0.72 ** | 18.32 | 15.72 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(-3.600-3.719\mathrm{ln}OG+2.238\mathrm{ln}Oligo-1.604\mathrm{ln}CG+5.287\mathrm{ln}Empty)\times 1.043$ | 0.74 ** | 18.51 | 26.55 |

Broad-leaved forests | ||||

DBH/cm | $\mathrm{exp}(3.562+0.454\mathrm{ln}OG-0.053\mathrm{ln}Oligo-0.099\mathrm{ln}Empty-0.958\mathrm{ln}\beta 2)\times 1.010$ | 0.51 | 1.81 | 11.79 |

h_{Lorey}/m | $\mathrm{exp}(1.030-0.149\mathrm{ln}Oligo+0.323\mathrm{ln}F\mathrm{illed}+0.250\mathrm{ln}Empty-0.613\mathrm{ln}\beta 2)\times 1.004$ | 0.83 *** | 0.88 | 7.72 |

N/(ha^{−1}) | $\mathrm{exp}(6.025-0.774\mathrm{ln}OG+1.103\mathrm{ln}Eu-0.015\mathrm{ln}Oligo+0.836\mathrm{ln}\beta 1)\times 1.078$ | 0.52 | 299.82 | 26.63 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(2.514+0.321\mathrm{ln}Oligo-0.040\mathrm{ln}Empty-0.032\mathrm{ln}\alpha 2)\times 1.013$ | 0.50 | 2.74 | 12.48 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(5.339-0.234\mathrm{ln}OG-0.981\mathrm{ln}Eu+0.588\mathrm{ln}Oligo+0.715\mathrm{ln}\alpha 1)\times 1.013$ | 0.58 | 18.97 | 14.28 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(4.009-0.188\mathrm{ln}OG+0.440\mathrm{ln}Oligo+0.615\mathrm{ln}CG-0.517\mathrm{ln}Empty)\times 1.055$ | 0.60 | 26.45 | 28.05 |

Mixed forests | ||||

DBH/cm | $\mathrm{exp}(3.172+0.169\mathrm{ln}OG+0.060\mathrm{ln}Oligo+0.002\mathrm{ln}Empty-0.724\mathrm{ln}\beta 2)\times 1.009$ | 0.48 | 1.78 | 12.79 |

h_{Lorey}/m | $\mathrm{exp}(0.481+0.318\mathrm{ln}Oligo+0.390\mathrm{ln}F\mathrm{illed}+0.210\mathrm{ln}Empty-0.109\mathrm{ln}\mathsf{\beta}2)\times 1.003$ | 0.75 *** | 0.75 | 6.94 |

N/(ha^{−1}) | $\mathrm{exp}(4.939-0.262\mathrm{ln}OG-0.997\mathrm{ln}Eu+0.965\mathrm{ln}Oligo+1.804\mathrm{ln}\beta 1)\times 1.034$ | 0.44 | 324.73 | 22.68 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(1.909+0.626\mathrm{ln}Oligo+0.080\mathrm{ln}Empty+0.153n\alpha 2)\times 1.009$ | 0.45 *** | 3.12 | 13.01 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(-0.871+0.626\mathrm{ln}OG+0.080\mathrm{ln}Eu+0.088\mathrm{ln}Oligo+0.744\mathrm{ln}\alpha 1)\times 1.008$ | 0.65 *** | 16.31 | 12.36 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(1.848+0.087\mathrm{ln}OG+1.195\mathrm{ln}Oligo+0.087\mathrm{ln}CG+0.119\mathrm{ln}Empty)\times 1.013$ | 0.71 *** | 13.00 | 14.55 |

**Table A4.**Predictive models and accuracy assessment results (using both standard metrics and canopy metrics).

Variables | Predictive Models | Adj-R^{2} | RMSE | rRMSE % |
---|---|---|---|---|

All forests | ||||

DBH/cm | $\mathrm{exp}(0.802-0.060\mathrm{ln}{h}_{\mathrm{cv}}-0.095\mathrm{ln}{h}_{75}+0.7401\mathrm{ln}{d}_{1}-0.548\mathrm{ln}Oligo)\times 1.008$ | 0.61 *** | 1.67 | 11.97 |

h_{Lorey}/m | $\mathrm{exp}(0.091-0.053\mathrm{ln}{h}_{50}+0.154\mathrm{ln}{d}_{1}+0.971\mathrm{ln}Empty-0.315\mathrm{ln}{\beta}_{1})\times 1.009$ | 0.77 *** | 0.90 | 8.54 |

N/(ha^{−1}) | $\mathrm{exp}(7.012+0.167\mathrm{ln}{d}_{1}+0.761\mathrm{ln}Oligo+0.741\mathrm{ln}{\alpha}_{1}+1.643\mathrm{ln}{\beta}_{1})\times 1.049$ | 0.45 *** | 410.02 | 28.90 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(1.576-0.255{h}_{\mathrm{kurtosis}}-0.304\mathrm{ln}{h}_{25}+1.031\mathrm{ln}{h}_{95}+0.073\mathrm{ln}Empty)\times 1.017$ | 0.50 *** | 3.47 | 14.96 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(0.201-0.463{h}_{75}-0.502\mathrm{ln}Oligo+0.845\mathrm{ln}Empty+2.343\mathrm{ln}{\alpha}_{1})\times 1.018$ | 0.58 *** | 21.07 | 16.47 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(0.519+0.193\mathrm{ln}{h}_{95}+1.458\mathrm{ln}{d}_{3}+1.300\mathrm{ln}CC{}_{2m}-1.348\mathrm{ln}Oligo)\times 1.036$ | 0.65 *** | 18.25 | 21.39 |

Coniferous forests | ||||

DBH/cm | $\mathrm{exp}(1.041-0.164\mathrm{ln}{h}_{\mathrm{cv}}+0.062\mathrm{ln}{h}_{75}+0.8131\mathrm{ln}{d}_{1}-0.182\mathrm{ln}Oligo)\times 1.006$ | 0.74 ** | 1.08 | 8.59 |

h_{Lorey}/m | $\mathrm{exp}(-1.207-0.196\mathrm{ln}{h}_{50}+0.582\mathrm{ln}{d}_{1}+1.441\mathrm{ln}Empty-0.661\mathrm{ln}{\beta}_{1})\times 1.010$ | 0.77** | 0.99 | 10.43 |

N/(ha^{−1}) | $\mathrm{exp}(1.881+0.573\mathrm{ln}{d}_{1}-3.703\mathrm{ln}Oligo+2.036\mathrm{ln}{\alpha}_{1}+0.029\mathrm{ln}{\beta}_{1})\times 1.033$ | 0.64 | 339.29 | 20.07 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(0.242-0.323{h}_{\mathrm{kurtosis}}-0.060\mathrm{ln}{h}_{25}+1.668\mathrm{ln}{h}_{95}+0.046\mathrm{ln}Empty)\times 1.029$ | 0.69 ** | 4.23 | 18.32 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(-1.585-0.537{h}_{75}-0.599\mathrm{ln}Oligo+1.392\mathrm{ln}Empty+3.014\mathrm{ln}{\alpha}_{1})\times 1.024$ | 0.78 ** | 18.21 | 15.63 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(-0.808+0.794\mathrm{ln}{h}_{95}+1.594\mathrm{ln}{d}_{3}+3.551\mathrm{ln}C{C}_{2m}-4.560\mathrm{ln}Oligo)\times 1.040$ | 0.81 ** | 14.53 | 20.83 |

Broad-leaved forests | ||||

DBH/cm | $\mathrm{exp}(0.876-0.095\mathrm{ln}{h}_{\mathrm{cv}}-0.325\mathrm{ln}{h}_{75}+0.5881\mathrm{ln}{d}_{1}-0.797\mathrm{ln}Oligo)\times 1.008$ | 0.68 | 1.54 | 10.06 |

h_{Lorey}/m | $\mathrm{exp}(1.020+0.047\mathrm{ln}{h}_{50}-0.226\mathrm{ln}{d}_{1}+0.633\mathrm{ln}Empty-0.255\mathrm{ln}{\beta}_{1})\times 1.003$ | 0.88 *** | 0.72 | 6.39 |

N/(ha^{−1}) | $\mathrm{exp}(7.281+0.074\mathrm{ln}{d}_{1}+0.8081\mathrm{ln}Oligo+0.583\mathrm{ln}{\alpha}_{1}+2.132\mathrm{ln}{\beta}_{1})\times 1.055$ | 0.62 | 273.49 | 24.29 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(3.404-0.100{h}_{\mathrm{kurtosis}}-0.166\mathrm{ln}{h}_{25}+1.109\mathrm{ln}{h}_{95}-0.902\mathrm{ln}Empty)\times 1.009$ | 0.63 | 2.49 | 11.34 |

V/( m^{3}·ha^{−1}) | $\mathrm{exp}(9.533+2.028{h}_{75}+1.027\mathrm{ln}Oligo-1.599\mathrm{ln}Empty-3.683\mathrm{ln}{\alpha}_{1})\times 1.011$ | 0.67 | 16.65 | 12.54 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(2.376-0.395\mathrm{ln}{h}_{95}+1.210\mathrm{ln}{d}_{3}+3.440\mathrm{ln}C{C}_{2m}-4.200\mathrm{ln}Oligo)\times 1.051$ | 0.66 | 26.67 | 28.29 |

Mixed forests | ||||

DBH/cm | $\mathrm{exp}(0.615+0.012\mathrm{ln}{h}_{\mathrm{cv}}-0.331\mathrm{ln}{h}_{75}+0.5901\mathrm{ln}{d}_{1}-1.911\mathrm{ln}Oligo)\times 1.008$ | 0.55 ** | 1.58 | 11.34 |

h_{Lorey}/m | $\mathrm{exp}(0.089-0.136\mathrm{ln}{h}_{50}+0.295\mathrm{ln}{d}_{1}+1.043\mathrm{ln}Empty-0.969\mathrm{ln}{\beta}_{1})\times 1.002$ | 0.84 *** | 0.55 | 5.13 |

N/(ha^{−1}) | $\mathrm{exp}(8.121+0.135\mathrm{ln}{d}_{1}+1.246\mathrm{ln}Oligo+0.120\mathrm{ln}{\alpha}_{1}+4.921\mathrm{ln}{\beta}_{1})\times 1.029$ | 0.50 *** | 319.05 | 22.28 |

G/(m^{2}·ha^{−1}) | $\mathrm{exp}(-0.179-0.069{h}_{\mathrm{kurtosis}}+0.361\mathrm{ln}{h}_{25}-1.140\mathrm{ln}{h}_{95}+1.927\mathrm{ln}Empty)\times 1.009$ | 0.56 ** | 2.77 | 11.56 |

V/(m^{3}·ha^{−1}) | $\mathrm{exp}(0.201-0.463{h}_{75}-0.502\mathrm{ln}Oligo+0.845\mathrm{ln}Empty+2.343\mathrm{ln}{\mathsf{\alpha}}_{1})\times 1.018$ | 0.71 *** | 15.87 | 12.02 |

AGB/(Mg·ha^{−1}) | $\mathrm{exp}(0.519+0.630\mathrm{ln}{h}_{95}+1.113\mathrm{ln}{d}_{3}+0.073\mathrm{ln}C{C}_{2m}+1.788\mathrm{ln}Oligo)\times 1.009$ | 0.79 *** | 10.89 | 12.19 |

## References

- Pan, Y.; Birdsey, R.A.; Phillips, O.L.; Jackson, R.B. The Structure, Distribution, and Biomass of the World’s Forests. Ann. Rev. Ecol. Evol. Syst.
**2013**, 44, 593–622. [Google Scholar] [CrossRef] - Hill, S.; Lati, H.; Heurich, M.; Müller, J. Individual-tree-and stand-based development following natural disturbance in a heterogeneously structured forest: A LiDAR-based approach. Ecol. Inform.
**2017**, 38, 12–25. [Google Scholar] [CrossRef] - Franklin, J.F.; Spies, T.A.; Pelt, R.V.; Carey, A.B.; Thornburgh, D.A.; Rae, D.; Lindenmayer, D.B.; Harmon, M.E.; Keeton, W.S.; Shaw, D.C.; et al. Disturbances and structural development of nsatural forest ecosystems with silvicultural implications, using Douglas-fir forests as an example. For. Ecol. Manag.
**2002**, 155, 399–423. [Google Scholar] [CrossRef] - Palace, M.W.; Sullivan, F.B.; Ducey, M.J.; Treuhaft, R.N.; Herrick, C.; Shimbo, J.Z.; Mota-E-Silva, J. Estimating forest structure in a tropical forest using field measurements, a synthetic model and discrete return lidar data. Remote Sens. Environ.
**2015**, 161, 1–11. [Google Scholar] [CrossRef] - McElhinny, C.; Gibbons, P.; Brack, C.; Bauhus, J. Forest and woodland stand structural complexity: Its definition and measurement. For. Ecol. Manag.
**2005**, 218, 1–24. [Google Scholar] [CrossRef] - Spies, T.A. Forest Structure: A Key to the Ecosystem. Northwest Sci.
**1998**, 72, 34–39. [Google Scholar] - Zimble, D.A.; Evans, D.L.; Carlson, G.C.; Parker, R.C.; Grado, S.C.; Gerard, P.D. Characterizing vertical forest structure using small-footprint airborne LiDAR. Remote Sens. Environ.
**2003**, 87, 171–182. [Google Scholar] [CrossRef] - Miura, N.; Jones, S.D. Characterizing forest ecological structure using pulse types and heights of airborne laser scanning. Remote Sens. Environ. J.
**2010**, 114, 1069–1076. [Google Scholar] [CrossRef] - Pasher, J.; King, D.J. Multivariate forest structure modelling and mapping using high resolution airborne imagery and topographic information. Remote Sens. Environ.
**2010**, 114, 1718–1732. [Google Scholar] [CrossRef] - Corlett, R.T. Where are the Subtropics? Biotropica
**2013**, 45, 273–275. [Google Scholar] [CrossRef] - Zhang, Y.J.; Cristiano, P.M.; Zhang, Y.F.; Campanello, P.I.; Tan, Z.H.; Zhang, Y.P.; Goldstein, G.; Cao, K.F. Carbon Economy of Subtropical Forests. Trop. Tree Physiol.
**2016**, 6, 337–355. [Google Scholar] - Global Forest Resources Assessment 2015. Available online: http://www.fao.org/3/a-i4808e.pdf (accessed on 14 June 2017).
- Ouyang, S.; Xiang, W.; Wang, X.; Zeng, Y.; Lei, P.; Deng, X.; Peng, C. Significant effects of biodiversity on forest biomass during the succession of subtropical forest in south China. For. Ecol. Manag.
**2016**, 372, 291–302. [Google Scholar] [CrossRef] - Bouvier, M.; De, M.; Renaud, J. Generalizing predictive models of forest inventory attributes using an area-based approach with airborne LiDAR data area-based approach with airborne LiDAR data. Remote Sens. Environ.
**2015**, 156, 322–334. [Google Scholar] [CrossRef] - White, J.C.; Coops, N.C.; Wulder, M.A.; Vastaranta, M.; Hilker, T.; Tompalski, P.; White, J.C.; Coops, N.C.; Wulder, M.A.; Vastaranta, M.; et al. Remote Sensing Technologies for Enhancing Forest Inventories: A Review Remote Sensing Technologies for Enhancing Forest Inventories: A Review. Can. J. Remote Sens.
**2016**, 42, 619–641. [Google Scholar] [CrossRef] - Mcroberts, R.E.; Tomppo, E.O. Remote sensing support for national forest inventories. Remote Sens. Environ.
**2007**, 110, 412–419. [Google Scholar] [CrossRef] - Wulder, M.A.; White, J.C.; Nelson, R.F.; Næsset, E.; Ørka, H.O.; Coops, N.C.; Hilker, T.; Bater, C.W.; Gobakken, T. Lidar sampling for large-area forest characterization: A review. Remote Sens. Environ.
**2012**, 121, 196–209. [Google Scholar] [CrossRef] - Wulder, M. Optical remote-sensing techniques for the assessment of forest inventory and biophysical parameters. Prog. Phys. Geogr.
**1998**, 22, 449–476. [Google Scholar] [CrossRef] - Duncanson, L.I.; Niemann, K.O.; Wulder, M.A. Integration of GLAS and Landsat TM data for aboveground biomass estimation. Carbon
**2010**, 36, 129–141. [Google Scholar] [CrossRef] - Lu, D.; Chen, Q.; Wang, G.; Moran, E.; Batistella, M.; Zhang, M.; Laurin, G.V.; Saah, D. Aboveground Forest Biomass Estimation with Landsat and LiDAR Data and Uncertainty Analysis of the Estimates. Int. J. For. Res.
**2012**, 2012. [Google Scholar] [CrossRef] - Rosenqvist, Å.; Milne, A.; Lucas, R.; Imhoff, M.; Dobson, C. A review of remote sensing technology in support of the Kyoto Protocol. Environ. Sci. Policy
**2003**, 6, 441–455. [Google Scholar] [CrossRef] - Yu, Y.; Yang, X.; Fan, W. Estimates of forest structure parameters from GLAS data and multi-angle imaging spectrometer data. Int. J. Appl. Earth Obs. Geoinf.
**2015**, 38, 65–71. [Google Scholar] [CrossRef] - Li, W.; Niu, Z.; Chen, H.; Li, D.; Wu, M.; Zhao, W. Remote estimation of canopy height and aboveground biomass of maize using high-resolution stereo images from a low-cost unmanned aerial vehicle system. Ecol. Indic.
**2016**, 67, 637–648. [Google Scholar] [CrossRef] - Véga, C.; Renaud, J.; Durrieu, S.; Bouvier, M. On the interest of penetration depth, canopy area and volume metrics to improve Lidar-based models of forest parameters. Remote Sens. Environ.
**2016**, 175, 32–42. [Google Scholar] [CrossRef] - Means, J.E.; Acker, S.A.; Fitt, B.J.; Renslow, M.; Emerson, L.; Abstract, C.J.H. Predicting Forest Stand Characteristics with Airborne Scanning Lidar. Photogramm. Eng. Remote Sens.
**2000**, 66, 1367–1371. [Google Scholar] - Silva, C.A.; Klauberg, C.; Hudak, A.T.; Vierling, L.A.; Liesenberg, V.; Carvalho, S.P.C.E.; Rodriguez, L.C.E. A principal component approach for predicting the stem volume in Eucalyptus plantations in Brazil using airborne LiDAR data. Forestry
**2016**, 89, 422–433. [Google Scholar] [CrossRef] - Tesfamichael, S.G.; Beech, C. Combining Akaike’s Information Criterion and discrete return LiDAR data to estimate structural attributes of savanna woody vegetation. J. Arid Environ.
**2016**, 129, 25–34. [Google Scholar] [CrossRef] - Sabol, J.; Procházka, D.; Patočka, Z. Development of models for forest variable estimation from airborne laser scanning data using an area-based approach at a plot level. J. For. Sci.
**2016**, 62, 137–142. [Google Scholar] [CrossRef] - Frazer, G.W.; Magnussen, S.; Wulder, M.A.; Niemann, K.O. Simulated impact of sample plot size and co-registration error on the accuracy and uncertainty of LiDAR-derived estimates of forest stand biomass. Remote Sens. Environ. J.
**2011**, 115, 636–649. [Google Scholar] [CrossRef] - Montealegre, A.L.; Riva, J.D.; García-martín, A. Use of low point density ALS data to estimate stand-level structural variables in Mediterranean Aleppo pine forest. Forestry
**2016**, 1–10. [Google Scholar] [CrossRef] - Zolkos, S.G.; Goetz, S.J.; Dubayah, R. A meta-analysis of terrestrial aboveground biomass estimation using lidar remote sensing. Remote Sens. Environ.
**2013**, 128, 289–298. [Google Scholar] [CrossRef] - Magnussen, S.; Næsset, E.; Gobakken, T. Reliability of LiDAR derived predictors of forest inventory attributes: A case study with Norway spruce. Remote Sens. Environ.
**2010**, 114, 700–712. [Google Scholar] [CrossRef] - Magnussen, S.; Næsset, E.; Gobakken, T. Prediction of tree-size distributions and inventory variables from cumulants of canopy height distributions. Forestry
**2013**, 86, 583–595. [Google Scholar] [CrossRef] - MacArthur, R.; MacArthur, J.W. On bird species diversity. Ecology
**1961**, 42, 594–598. [Google Scholar] - Aber, J.D. A method for estimating foliage-height profiles in broad-leaved forests. Ecology
**1979**, 67, 35–40. [Google Scholar] [CrossRef] - Lefsky, M.A.; Cohen, W.B.; Acker, S.A.; Parker, G.G. Lidar Remote Sensing of the Canopy Structure and Biophysical Properties of Douglas-Fir Western Hemlock Forests. Remote Sens. Environ.
**1999**, 361, 339–361. [Google Scholar] [CrossRef] - Lovell, J.L.; Jupp, D.L.B.; Culvenor, D.S.; Coops, N.C.; Les, R. Using airborne and ground-based ranging lidar to measure canopy structure in Australian forests. Can. J. Remote Sens.
**2003**, 29, 607–622. [Google Scholar] [CrossRef] - Coops, N.C.; Hilker, T.; Wulder, M.A.; St-Onge, B.; Newnham, G.; Siggins, A.; Trofymow, J.A. Estimating canopy structure of Douglas-fir forest stands from discrete-return LiDAR. Trees
**2007**, 21, 295–310. [Google Scholar] [CrossRef] - Hilker, T.; Leeuwen, M.V.; Coops, N.C. Comparing canopy metrics derived from terrestrial and airborne laser scanning in a Douglas-fir dominated forest stand. Trees
**2010**, 24, 819–832. [Google Scholar] [CrossRef] - Kraus, K.; Pfeifer, N. Determination of terrain models in wooded areas with airborne laser scanner data. ISPRS J. Photogramm. Remote Sens.
**1998**, 53, 193–203. [Google Scholar] [CrossRef] - Song, Y.B.; Ding, Y.P. The development and latest progress of JSCORS. Bull. Surv. Mapp.
**2009**, 2, 73–74. [Google Scholar] - Jiang, B.; Yuan, W.; Zhu, G. A preliminary study on the plantation biomass and produce structure of Pinus massoniana, Pinus elliottii and Pinus taeda. J. Zhejiang For. Sci. Technol.
**1992**, 12, 1–9. [Google Scholar] - Ye, J.; Yang, Z. Biomass structure of planted Chinese fir in Southern Jiangsu province, China. Acta Ecol. Sin.
**1983**, 3, 7–14. [Google Scholar] - Wang, Q.; Shi, Y. A preliminary study on the biomass and production of slash pine plantation in Jiangsu province. Acta Phytoecol. Geobot. Sin.
**1990**, 14, 2–12. [Google Scholar] - Xu, J.; Wang, M.; Huang, Q.; Gong, S. Study on aboveground biomass model of natural individual trees of Quercus acutissima. Anhui For. Sci. Technol.
**2011**, 37, 3–6. [Google Scholar] - Qian, G. Studies on the dynamic change of the net production quantity of liquidambar formosana plantation. Acta Agric. Univ. Jiangxiensis
**2000**, 22, 399–404. [Google Scholar] - Sun, D.; Ruan, H.; Ye, J. Biomass Structure of Oak-Dominated Secondary Forest in Kongqingshan. Available online: http://refhub.elsevier.com/S0034-4257(16)30106-7/rf0260 (accessed on 14 June 2017).
- Zhao, K.; Popescu, S.; Nelson, R. Lidar remote sensing of forest biomass: A scale-invariant estimation approach using airborne lasers. Remote Sens. Environ.
**2009**, 113, 182–196. [Google Scholar] [CrossRef] - Weishampel, J.F.; Drake, J.B.; Cooper, A.; Blair, J.B.; Hofton, M. Forest canopy recovery from the 1938 hurricane and subsequent salvage damage measured with airborne LiDAR. Remote Sens. Environ.
**2007**, 109, 142–153. [Google Scholar] [CrossRef] - Bailey, R.; Dell, T. Quantifying diameter distributions with the Weibull function. For. Sci.
**1973**, 19, 97–104. [Google Scholar] - Penner, M.; Woods, M.; Pitt, D.G. A comparison of airborne laser scanning and image point cloud derived tree size class distribution models in Boreal Ontario. Forests
**2015**, 6, 4034–4054. [Google Scholar] [CrossRef] - Tompalski, P.; Coops, N.C.; White, J.C.; Wulder, M.A. Enriching ALS-derived area-based estimates of volume through tree-level downscaling. Forests
**2015**, 6, 2608–2630. [Google Scholar] [CrossRef] - Zhao, J.; LI, J.; Liu, Q. Review of forest vertical structure parameter inversion based on remote sensing technology. J. Remote Sens.
**2013**, 17, 697. [Google Scholar] - Jupp, D.L.B.; Culvenor, D.S.; Lovell, J.L.; Newnham, G.J.; Strahler, A.H.; Woodcock, C.E. Estimating forest LAI profiles and structural parameters using a ground-based laser called ‘Echidna
^{®}. Tree Physiol.**2008**, 29, 171–181. [Google Scholar] [CrossRef] [PubMed] - Hilker, T.; Coops, N.C.; Newnham, G.J.; Leeuwen, M.V.; Wulder, M.A.; Stewart, J.; Culvenor, D.S. Comparison of Terrestrial and Airborne LiDAR in Describing Stand Structure of a Thinned Lodgepole Pine Forest. J. For.
**2012**, 10, 97–104. [Google Scholar] - Sprugel, D. Correcting for Bias in Log-Transformed Allometric Equations. Ecology
**1983**, 64, 209–210. [Google Scholar] [CrossRef] - Næsset, E. Predicting forest stand characteristics with airborne scanning laser using a practical two-stage procedure and field data. Remote Sens. Environ.
**2002**, 80, 88–99. [Google Scholar] [CrossRef] - Næsset, E.; Bollandsås, O.M.; Gobakken, T. Comparing regression methods in estimation of biophysical properties of forest stands from two different inventories using laser scanner data. Remote Sens. Environ.
**2005**, 94, 541–553. [Google Scholar] [CrossRef] - García-gutiérrez, J.; Martínez-Álvarez, F.; Troncoso, A.; Riquelme, J.C. A comparison of machine learning regression techniques for LiDAR-derived estimation of forest variables. Neurocomputing
**2015**, 167, 24–31. [Google Scholar] [CrossRef] - Naesset, E.; Okland, T. Estimating tree height and tree crown properties using airborne scanning laser in a boreal. Remote Sens. Environ.
**2002**, 79, 105–115. [Google Scholar] [CrossRef] - Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Kutner, M.; Nachtsheim, C.; Neter, J.; Li, W. Applied Linear Statistical Models, 5th ed.; McGraw-Hill/Irwin: New York, NY, USA, 2004. [Google Scholar]
- Bengio, Y. No Unbiased Estimator of the Variance of K-Fold Cross-Validation. J. Mach. Learn. Res.
**2004**, 5, 1089–1105. [Google Scholar] - Parker, G.G. Structure and Microclimate of Forest Canopies. In Forest Canopies; Lowman, M.D., Nadkarni, N.M., Eds.; Academic Press: San Diego, CA, USA, 1995; pp. 73–106. [Google Scholar]
- Wilkes, P.; Suarez, L.; Andrew, H.; Andrew, M.; William, W.; Mariela, S.-B.; Skidmore, A.K. Using discrete-return ALS to quantify number of canopy strata across diverse forest types Using discrete-return airborne laser scanning to quantify number of canopy strata across diverse forest types. Methods Ecol. Evol.
**2015**, 1–13. [Google Scholar] [CrossRef] - Lefsky, M.A.; Harding, D.; Cohen, W.B.; Parker, G.; Shugart, H.H. Surface Lidar Remote Sensing of Basal Area and Biomass in Deciduous Forests of Eastern Maryland, USA. Remote Sens. Environ.
**1999**, 67, 83–98. [Google Scholar] [CrossRef] - Leiterer, R.; Torabzadeh, H.; Furrer, R.; Schaepman, M.E.; Morsdorf, F. Towards Automated Characterization of Canopy Layering in Mixed Temperate Forests Using Airborne Laser Scanning. Forests
**2015**, 6, 4146–4167. [Google Scholar] [CrossRef] - Van Leeuwen, M.; Nieuwenhuis, M. Retrieval of forest structural parameters using LiDAR remote sensing. Eur. J. For. Res.
**2010**, 129, 749–770. [Google Scholar] [CrossRef] - Ishii, H. The role of crown architecture, leaf phenology and photosynthetic activity in promoting complementary use of light among coexisting species in temperate forests. Ecol. Res.
**2010**, 25, 715–722. [Google Scholar] [CrossRef] - He, J.; Zhu, S. The Preliminary Study on the Law of the Crown Structure of Massons Pine in Mid-Subtropical Region. J. Mt. Agric. Biol.
**1990**, 9, 61–72. [Google Scholar] - Liang, X.; Ye, W. Advances in Study of Forest Gaps. J. Trop. Subtrop. Bot.
**2001**, 9, 355–364. [Google Scholar] - Kneeshaw, D.D.; Bergeron, Y. Canopy Gap Characteristics and Tree Replacement in the Southeastern Boreal Forest. Ecology
**1998**, 79, 783–794. [Google Scholar] [CrossRef] - An, S.; Zhao, R. Analysis of Characteristics of Secondary Forest Vegetation in the North Subtropical Zone of China. J. Nanjing Univ. Sci.
**1991**, 27, 324–331. [Google Scholar] - Spies, T.A.; Frankli, J.F. Gap Characteristics and Vegetation Response in Coniferous Forests of the Pacific Northwest. Ecology
**1989**, 70, 543–545. [Google Scholar] [CrossRef] - Yang, J.; Liu, X.; Yang, X. Forest canopy structure, light environment and their effects on the vegetation pattern and growth of understory in forests. J. Sci. Teach. Univ.
**2015**, 35, 57–62. [Google Scholar] - Montgomery, R.A.; Chazdon, R.L. Forest structure, canopy architectura, and light transmittance in old-growth and second-growth tropical rain forests. Ecology
**2001**, 82, 2707–2718. [Google Scholar] [CrossRef] - Zhu, S.; He, J. The Preliminary Study on the Law of the Crown Structure of Masson’s pine in South-subtropcial. J. Mt. Agric. Biol.
**1993**, 12, 36–44. [Google Scholar] - Messier, C.; Sylvain, P.; Bergeron, Y. Effects of Overstory and Understory Vegetation on the Understory Light Environment in Mixed Boreal Forests. J. Veg. Sci.
**1998**, 9, 511–520. [Google Scholar] [CrossRef] - Parent, S.; Messier, C. A simple and efficient method to estimate microsite light availability under a forest canopy. Can. J. For. Res.
**1996**, 26, 151–154. [Google Scholar] [CrossRef] - Zhao, F.; Yang, X.; Schull, M.A.; Román-colón, M.O.; Yao, T.; Wang, Z.; Zhang, Q.; Jupp, D.L.B.; Lovell, J.L.; Culvenor, D.S.; et al. Measuring effective leaf area index, foliage profile, and stand height in New England forest stands using a full-waveform ground-based lidar. Remote Sens. Environ.
**2011**, 115, 2954–2964. [Google Scholar] [CrossRef] - Tang, H.; Dubayah, R.; Brolly, M.; Ganguly, S.; Zhang, G. Large-scale retrieval of leaf area index and vertical foliage profile from the spaceborne waveform lidar (GLAS/ICESat). Remote Sens. Environ.
**2014**, 154, 8–18. [Google Scholar] [CrossRef] - Fu, T.; Pang, Y.; Huang, Q.F.; Liu, Q.W.; Xu, G.C. Prediction of Subtropical Forest Parameters Using Airborne Laser Scanner. J. Remote Sens.
**2011**, 15, 1092–1104. [Google Scholar] - Xu, Z.; Cao, L.; Ruan, H.; Li, W.; Jiang, S. Inversion of subtropical forest stand characteristics by integrating very high resolution imagery acquired from UAV and LiDAR point-cloud. Chin. J. Plant Ecol.
**2015**, 39, 849–856. [Google Scholar] - Wilkes, P.; Jones, S.; Suarez, L.; Haywood, A.; Mellora, A.; Soto-Berelov, M.; Woodgate, W. MAUP and LiDAR derived canopy structure. Int. Geosci. Remote Sens. Symp.
**2013**, 173–175. [Google Scholar] - Maltamo, M.; Bollandsås, O.M.; Næsset, E.; Gobakken, T.; Packalén, P. Different plot selection strategies for field training data in ALS-assisted forest inventory. Forestry
**2011**, 84, 23–31. [Google Scholar] [CrossRef] - Van der Zande, D.; Stuckens, J.; Verstraeten, W.W.; Mereu, S.; Muys, B.; Coppin, P. 3D modeling of light interception in heterogeneous forest canopies using ground-based LiDAR data. Int. J. Appl. Earth Obs. Geoinf.
**2011**, 13, 792–800. [Google Scholar] [CrossRef] - Stoker, J. Volumetric Visualization of multiple-return Lidar Data: Using Voxels. Photogramm. Eng. Remote Sens.
**2009**, 75, 109–112. [Google Scholar] - Zheng, G.; Moskal, L.M. Computational-Geometry-Based Retrieval of Computational-Geometry-Based Retrieval of Effective Leaf Area Index Using Terrestrial Laser Scanning. IEEE Geosci. Remote Sens. Soc.
**2015**, 50, 3958–3969. [Google Scholar] [CrossRef] - Grau, E.; Durrieu, S.; Fournier, R.; Gastellu-etchegorry, J.; Yin, T. Estimation of 3D vegetation density with Terrestrial Laser Scanning data using voxels. A sensitivity analysis of influencing parameters. Remote Sens. Environ.
**2017**, 191, 373–388. [Google Scholar] [CrossRef] - Li, J.; Hu, B.; Noland, T.L. Classification of tree species based on structural features derived from high density LiDAR data. Agric. For. Meteorol.
**2013**, 171–172, 104–114. [Google Scholar] [CrossRef] - Kükenbrink, D.; Schneider, F.D.; Leiterer, R.; Schaepman, M.E.; Morsdorf, F. Quantification of hidden canopy volume of airborne laser scanning data using a voxel traversal algorithm. Remote Sens. Environ.
**2017**, 194, 424–436. [Google Scholar] [CrossRef] - Oshio, H.; Asawa, T.; Hoyano, A.; Miyasaka, S. Estimation of the leaf area density distribution of individual trees using high-resolution and multi-return airborne LiDAR data. Remote Sens. Environ.
**2015**, 166, 116–125. [Google Scholar] [CrossRef] - Béland, M.; Widlowski, J.; Fournier, R.A. A model for deriving voxel-level tree leaf area density estimates from ground-based LiDAR. Environ. Model. Softw.
**2014**, 51, 184–189. [Google Scholar] [CrossRef]

**Figure 1.**An overview of the workflow for forest structural parameters estimation. DTM: Digital Terrain Model.

**Figure 3.**Examples of the three main forest types in study site. (

**a**) Coniferous forest; (

**b**) broad-leaved forest; (

**c**) mixed forest.

**Figure 4.**The illustration of voxel-based canopy volume model. (

**a**) A plot (30 × 30 m

^{2}) was stratified with voxelization and height bin is 0.5 m; (

**b**) a voxel column was stratified in four structure classes (open gap, euphotic, oligophotic, closed gap) with canopy volume model approach; (

**c**) canopy volume distribution, which shows the distribution of canopy structure classes after all columns were expanded in a panel; (

**d**) the canopy volume profile, which was transformed from the canopy volume distribution diagram, shows the volume percentage of each class of total volume in each height interval.

**Figure 5.**Canopy volume distributions for the plots in different forest types. (

**a**–

**c**) Three typical plots of coniferous forest; (

**d**–

**f**) three typical plots of mixed forest; (

**g**–

**i**) three typical plots of broad-leaved forest.

**Figure 6.**Canopy volume profiles for the plots in different forest types. (

**a**–

**c**) Three typical plots of coniferous forest; (

**e**–

**g**) three typical plots of mixed forest; (

**i**–

**k**) three typical plots of broad-leaved forest; (

**d**,

**h**,

**l**) the mean canopy volume profiles in each forest.

**Figure 7.**Foliage profiles for the plots in different forest types. (

**a**–

**c**) Three typical plots of coniferous forest; (

**e**–

**g**) three typical plots of mixed forest; (

**i**–

**k**) three typical plots of broad-leaved forest; (

**d**,

**h**,

**l**) the mean foliage profiles in each forest type.

**Figure 8.**The mean cumulative leaf area index profiles for plots in different forest types (

**a**) and mean canopy height distribution: (

**b**) coniferous forest; (

**c**) mixed forest; (

**d**) broad-leaved forest.

**Figure 9.**Scatter plots of field-measured and LiDAR estimated mean diameter at breast height (

**a**), lorey’s mean height (

**b**), stem density (

**c**), basal area (

**d**), volume (

**e**) and aboveground biomass (

**f**) for cross-validation in combination models.

**Figure 10.**Comparison of the forest structural parameters estimation accuracies for different voxel sizes. (

**a**) The vertical resolution of voxel sizes is 0.5 m and the horizontal resolutions range from 1 m to 10 m; (

**b**) the vertical resolution of voxel sizes is 1 m and the horizontal resolution range from 1 m to 10 m; (

**c**) comparison of the difference of rRMSE values (∆rRMSE) of model accuracies between vertical resolution 0.5 m and vertical resolution 1 m. DBH: mean diameter at breast height; h

_{Lorey}: Lorey’s mean height; N: Stem density; G: Basal area.

Parameters | Coniferous Forest (n = 14) | Broad-Leaved Forest (n = 14) | Mixed Forest (n = 23) | ||||||
---|---|---|---|---|---|---|---|---|---|

Range | Mean | SD | Range | Mean | SD | Range | Mean | SD | |

DBH/cm | 8.08–19.22 | 12.62 | 2.53 | 11.63–20.99 | 15.32 | 3.29 | 10.58–19.69 | 13.90 | 2.51 |

h_{Lorey}/m | 4.47–12.97 | 9.50 | 2.00 | 7.70–18.52 | 11.35 | 2.75 | 7.79–14.18 | 10.79 | 1.71 |

N/(ha^{−1}) | 656–3167 | 1690.64 | 643.15 | 322.00–1833.00 | 1126.00 | 428.55 | 689.00–2344.00 | 1431.78 | 438.40 |

G/(m^{2}·ha^{−1}) | 6.97–34.07 | 23.08 | 6.79 | 12.11–28.10 | 21.92 | 3.89 | 16.84–35.37 | 23.98 | 4.46 |

V/(m^{3}·ha^{−1}) | 32.19–178.08 | 116.53 | 34.75 | 90.62–212.45 | 132.77 | 32.30 | 82.78–187.91 | 131.98 | 28.67 |

AGB/(Mg·ha^{−1}) | 11.02–127.39 | 69.74 | 27.76 | 32.03–219.67 | 94.28 | 44.93 | 49.65–141.73 | 89.36 | 25.95 |

_{Lorey}: Lorey’s mean height; N: Stem density; G: Basal area; V: Volume; AGB: Aboveground biomass.

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

Standard metrics | ||

Height-based | Percentile heights (h_{25}, h_{50}, h_{75} and h_{95}) | The percentiles of the canopy height distributions (25th, 50th, 75th and 95th) of first returns. |

Mean height (h_{mean}) | Mean height above ground of all first returns. | |

Coefficient of variation of heights (h_{cv}) | Coefficient of variation of heights of all first returns. | |

Skewness and Kurtosis of heights (i.e., h _{skewness} and h_{kurtosis}) | The skewness and kurtosis of the heights of all points. | |

Density-based | Canopy return density (d_{1}, d_{3}, d_{5}, d_{7} and d_{9}) | The proportion of points above the quantiles (10th, 30th, 50th, 70th and 80th) to total number of points. |

Canopy cover above 2 m (CC_{2m}) | Percentages of first returns above 2 m. | |

Canopy metrics | ||

Canopy volume | Filled and Empty zones of CVM (i.e., Filled and Empty) | The voxels contained point clouds and voxels contained no point clouds within canopy spaces. |

Open and Closed gap zones of CVM (i.e., Open gap (OG) and Closed gap (CG)) | The empty voxels located above and below the canopy respectively. | |

Euphotic and Oligophotic zones of CVM (i.e., Euphotic (Eu) and Oligophotic (Oligo)) | The voxels located within an uppermost percentile (65%) of all filled grid cells of that column, and voxels located below the point in the profile | |

Weibull-fitted | α_{1} and β_{1} parameter of Weibull distribution | The scale parameter α and shape parameter β of the Weibull density distribution fitted to CHD. |

α_{2} and β_{2} parameter of Weibull distribution | The scale parameter α and shape parameter β of the Weibull density distribution fitted to FP. |

Forest Types | Parameters | SM Models | CM Models | Combination Models | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Standard Metrics | Adj-R^{2} | RMSE | rRMSE % | Canopy Metrics | Adj-R^{2} | RMSE | rRMSE % | All Metrics | Adj-R^{2} | RMSE | rRMSE % | ||

All plots | DBH/cm | h_{95}, d_{1}, d_{7} | 0.60 *** | 1.72 | 12.33 | OG, Oligo, Empty, β_{2} | 0.50 *** | 1.86 | 13.31 | h_{cv}, h_{75}, d_{1}, Oligo | 0.61 *** | 1.67 | 11.97 |

h_{Lorey}/m | h_{cv}, h_{95}, d_{7}, d_{9} | 0.75 *** | 0.97 | 9.15 | Oligo, Filled, Empty, α_{1} | 0.61 *** | 1.18 | 11.13 | h_{50}, d_{1}, Empty, β_{1} | 0.77 *** | 0.90 | 8.54 | |

N/(ha^{−1}) | h_{cv}, d_{1}, d_{7}, d_{9} | 0.42 *** | 423.75 | 29.86 | OG, Eu, Oligo, β_{1} | 0.39 *** | 415.17 | 29.26 | d_{1}, Oligo, α1, β_{1} | 0.45 *** | 410.02 | 28.90 | |

G/(m^{2}·ha^{−1}) | h_{95}, d_{3}, d_{7} | 0.44 *** | 3.99 | 17.23 | Oligo, Empty, α_{2} | 0.41 *** | 3.67 | 15.82 | h_{kurtosis}, h_{25}, h_{95}, Empty | 0.50 *** | 3.47 | 14.96 | |

V/(m^{3}·ha^{−1}) | h_{cv}, h_{25}, h_{50}, d_{3} | 0.46 *** | 22.34 | 17.46 | OG, Eu, Oligo, α_{1} | 0.42 *** | 22.36 | 17.48 | h_{75}, Oligo, Empty, β_{1} | 0.58 *** | 21.07 | 16.47 | |

AGB/(Mg·ha^{−1}) | h_{kurtosis}, h_{95}, d_{3}, d_{9} | 0.64 *** | 19.17 | 22.47 | OG, Oligo, CG, Empty | 0.54 *** | 19.84 | 23.25 | h_{95}, d_{3}, CC_{2m}, Oligo | 0.66 *** | 18.25 | 21.39 | |

Coniferous forest | DBH/cm | h_{95}, d_{1}, d_{7} | 0.67 ** | 1.20 | 9.50 | OG, Oligo, Empty, β_{2} | 0.54 | 1.40 | 11.09 | h_{cv}, h_{75}, d_{1}, Oligo | 0.74 ** | 1.08 | 8.59 |

h_{Lorey}/m | h_{cv}, h_{95}, d_{7}, d_{9} | 0.66 | 1.09 | 11.47 | Oligo, Filled, Empty, α_{1} | 0.64 | 1.21 | 12.79 | h_{50}, d_{1}, Empty, β_{1} | 0.77 ** | 0.99 | 10.43 | |

N/(ha^{−1}) | h_{cv}, d_{1}, d_{7}, d_{9} | 0.60 | 315.78 | 18.68 | OG, Eu, Oligo, β_{1} | 0.58 | 431.65 | 25.53 | d_{1}, Oligo, α_{1}, β_{1} | 0.64 | 339.29 | 20.07 | |

G/(m^{2}·ha^{−1}) | h_{95}, d_{3}, d_{7} | 0.62 ** | 4.53 | 19.63 | Oligo, Empty, α_{2} | 0.55 | 4.73 | 20.48 | h_{kurtosis}, h_{25}, h_{95}, Empty | 0.69 ** | 4.23 | 18.32 | |

V/(m^{3}·ha^{−1}) | h_{cv}, h_{25}, h_{50}, d_{3} | 0.69 ** | 22.40 | 19.22 | OG, Eu, Oligo, α_{1} | 0.72 ** | 18.32 | 15.72 | h_{75}, Oligo, Empty, β_{1} | 0.78 ** | 18.21 | 15.63 | |

AGB/(Mg·ha^{−1}) | h_{kurtosis}, h_{95}, d_{3}, d_{9} | 0.72 ** | 16.86 | 24.17 | OG, Oligo, CG, Empty | 0.74 ** | 18.51 | 26.55 | h_{95}, d_{3}, CC_{2m}, Oligo | 0.81 ** | 14.53 | 20.83 | |

Broad-leaved forest | DBH/cm | h_{95}, d_{1}, d_{7} | 0.61 ** | 1.70 | 11.12 | OG, Oligo, Empty, β_{2} | 0.51 | 1.81 | 11.79 | h_{cv}, h_{75}, d_{1}, Oligo | 0.68 | 1.54 | 10.06 |

h_{Lorey}/m | h_{cv}, h_{95}, d_{7}, d_{9} | 0.84 *** | 0.78 | 6.91 | Oligo, Filled, Empty, α_{1} | 0.83 *** | 0.88 | 7.72 | h_{50}, d_{1}, Empty, β_{1} | 0.88 *** | 0.72 | 6.39 | |

N/(ha^{−1}) | h_{cv}, d_{1}, d_{7}, d_{9} | 0.60 | 298.99 | 26.55 | OG, Eu, Oligo, β_{1} | 0.52 | 299.82 | 26.63 | d_{1}, Oligo, α_{1}, β_{1} | 0.62 | 273.49 | 24.29 | |

G/(m^{2}·ha^{−1}) | h_{95}, d_{3}, d_{7} | 0.54 | 2.62 | 11.96 | Oligo, Empty, α_{2} | 0.50 | 2.74 | 12.48 | h_{kurtosis}, h_{25}, h_{95}, Empty | 0.63 | 2.49 | 11.34 | |

V/(m^{3}·ha^{−1}) | h_{cv}, h_{25}, h_{50}, d_{3} | 0.56 | 19.49 | 14.68 | OG, Eu, Oligo, α_{1} | 0.58 | 18.97 | 14.28 | h_{75}, Oligo, Empty, β_{1} | 0.67 | 16.65 | 12.54 | |

AGB/(Mg·ha^{−1}) | h_{kurtosis}, h_{95}, d_{3}, d_{9} | 0.57 | 26.80 | 28.42 | OG, Oligo, CG, Empty | 0.60 | 26.45 | 28.05 | h_{95}, d_{3}, CC_{2m}, Oligo | 0.66 | 26.67 | 28.29 | |

Mixed forest | DBH/cm | h_{95}, d_{1}, d_{7} | 0.48 ** | 1.66 | 11.94 | OG, Oligo, Empty, β_{2} | 0.48 | 1.78 | 12.79 | h_{cv}, h_{75}, d_{1}, Oligo | 0.55 ** | 1.58 | 11.34 |

h_{Lorey}/m | h_{cv}, h_{95}, d_{7}, d_{9} | 0.81 *** | 0.60 | 5.60 | Oligo, Filled, Empty, α_{1} | 0.75 *** | 0.75 | 6.94 | h_{50}, d_{1}, Empty, β_{1} | 0.84 *** | 0.55 | 5.13 | |

N/(ha^{−1}) | h_{cv}, d_{1}, d_{7}, d_{9} | 0.48 ** | 336.73 | 28.52 | OG, Eu, Oligo, β_{1} | 0.44 | 324.73 | 22.68 | d_{1}, Oligo, α_{1}, β_{1} | 0.50 *** | 319.05 | 22.28 | |

G/(m^{2}·ha^{−1}) | h_{95}, d_{3}, d_{7} | 0.45 ** | 3.08 | 12.86 | Oligo, Empty, α_{2} | 0.45 *** | 3.12 | 13.01 | h_{kurtosis}, h_{25}, h_{95}, Empty | 0.56 ** | 2.77 | 11.56 | |

V/(m^{3}·ha^{−1}) | h_{cv}, h_{25}, h_{50}, d_{3} | 0.60 *** | 16.76 | 12.70 | OG, Eu, Oligo, α_{1} | 0.65 *** | 16.31 | 12.36 | h_{75}, Oligo, Empty, β_{1} | 0.71 *** | 15.87 | 12.02 | |

AGB/(Mg·ha^{−1}) | h_{kurtosis}, h_{95}, d_{3}, d_{9} | 0.64 *** | 13.20 | 14.77 | OG, Oligo, CG, Empty | 0.71 *** | 13.00 | 14.55 | h_{95}, d_{3}, CC_{2m}, Oligo | 0.79 *** | 10.89 | 12.19 |

_{Lorey}: Lorey’s mean height; N: Stem density; G: Basal area; V: Volume; AGB: Aboveground biomass. OG: Open gap; Oligo: Oligophotic; Eu: Euphotic; CG: Closed gap.

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/rs9090940

**AMA Style**

Zhang Z, Cao L, She G. Estimating Forest Structural Parameters Using Canopy Metrics Derived from Airborne LiDAR Data in Subtropical Forests. *Remote Sensing*. 2017; 9(9):940.
https://doi.org/10.3390/rs9090940

**Chicago/Turabian Style**

Zhang, Zhengnan, Lin Cao, and Guanghui She. 2017. "Estimating Forest Structural Parameters Using Canopy Metrics Derived from Airborne LiDAR Data in Subtropical Forests" *Remote Sensing* 9, no. 9: 940.
https://doi.org/10.3390/rs9090940