Aboveground Biomass Inversion Using DTM-Independent Crown Metrics from UAV Stereoscopic Imagery in the Greater and Lesser Khingan Mountains

Abstract

The utilization of photography imagery captured using cameras mounted on unmanned aerial vehicles (UAVs) for aboveground biomass (AGB) inventory has seen rapid growth in recent years. Existing research has predominantly focused on utilizing spectral and textural features for biomass inversion. However, estimating the AGB of trees remains a great challenge using stereoscopic imagery without the help of a digital terrain model (DTM). This study introduces five DTM-independent crown metrics using a digital surface model (DSM) and a canopy height model (CHM) derived from UAV stereoscopic imagery. The accuracy of the five metrics was evaluated against field measurements. The results indicate that the relationship between the crown cross-sectional area (CCSA) and AGB is stronger than that between tree height (TH) and AGB, with R² = 0.62 and RMSE = 69.22 (kg/tree) for Larix gmelinii and R² = 0.93 and RMSE = 142.06 (kg/tree) for Pinus sylvestris. Moreover, these DTM-independent crown metrics could be used to estimate the AGB of forests in the Greater and Lesser Khingan Mountain, with R² = 0.77 and RMSE = 77.10 (kg/tree) for coniferous trees and R² = 0.78 and RMSE = 72.46 (kg/tree) for all other trees. The results of this study demonstrate that UAV stereoscopic imagery can capture forest canopy information, and DTM-independent crown metrics can be used for AGB inversion where information on terrain under forest is unavailable.

1. Introduction

Forests constitute approximately 80% of the Earth’s total plant biomass and contribute 75% of the terrestrial Gross Primary Production (GPP) [1,2,3]. The distribution and density of forest AGB is critical for understanding the global carbon balance and climate change. Studies on large-scale forest AGB have attracted considerable attention from forest ecologists over the last three decades. Although we have gained a wealth of knowledge by spending an enormous amount of time and energy on field measurements for forest AGB estimation, traditional field surveys can be exhausting and costly. Consequently, a critical challenge persists in developing methods with which to collect forest attribute data in a more timely and cost-effective manner.

Small unmanned aircraft systems, also known as lightweight unmanned aerial vehicles (UAVs) or drones, are increasingly used to monitor vegetation structures such as carbon stocks, tree density, species distributions, and crown height [4,5,6]; map land cover change [7] and provide “a promising route to responsive, timely, and cost-effective monitoring of environmental phenomena” [8]. The UAV stereoscopic imagery acquired using off-the-shelf cameras onboard a UAV could be used to take three-dimensional measurements of trees. Because of the number of studies on the measurements of forest spatial structures using stereoscopic imagery and the rapid developments of UAV platforms and automatic tools for stereoscopic imagery processing in recent years, researchers are gradually paying more attention to the extraction of forest spatial structures using UAV stereoscopic imagery [5,9,10,11]. Stereoscopic images acquired with consumer-grade cameras on low-cost UAV platforms can be processed with structure-from-motion (SfM) algorithms to produce 3D data that can be used to estimate forest structure parameters [12,13,14,15].

However, significant challenges remain in estimating forest AGB using UAV stereoscopic imagery even for UAV Light Detection and Ranging (LiDAR), primarily due to the difficulty in measuring ground surface elevation accurately under dense and steep forest terrain. The DSM of the forest crown top was derived from UAV stereoscopic imagery, and a DTM of the ground surface under forest from other data sources is needed to extract the forest’s vertical structures. Many studies on the estimation of forest structure information have used UAV stereoscopic imageries with the help of a DTM from LiDAR data [16,17,18]. In this way, the application of UAV stereoscopic imagery is limited and does not work within a dense forest area, where a LiDAR DTM is unavailable. Therefore, some researchers have focused on point clouds of stereoscopic imagery acquired under leaf-off conditions, when the ground surface can be seen through the forest crown [19]. Ni evaluated the impact of forward overlaps and image resolutions for the mapping of three-dimensional forest structures using UAV stereoscopic imagery [20], and reported the estimation of the forest leaf area index using the height and crown cover extracted through the synthesis of the UAV stereoscopic imagery of two seasons, leaf-on and leaf-off, which lead to the time–cost acquisition of UAV stereoscopic imagery. Some studies have reported some progress using UAV stereoscopic imagery to extract forest AGB, as well as some constraints that hinder this imagery’s application, such as in dense forests and as two-season UAV stereoscopic imagery. It is necessary to study the estimation of forest structure information using a crown-top DSM from UAV stereoscopic imagery without the help of a LiDAR DTM.

However, the spatial structure of forest crown is a key determinant of forest ecosystem functions because of height-structured competitions for light [21,22]. Tree crowns serve as the primary sites for photosynthesis and respiration, representing one of the most critical determinants of tree growth; characteristics such as crown size, structure, shape, and spatial distribution indirectly influence growth vigor and productivity [23]. It could be inferred that the accuracy of stock volume and AGB can be improved using tree crown information captured via UAV stereoscopic imagery [24,25,26]. Shinozaki first proposed the pipe model theory, in which a truck cross-sectional area at the crown base is related to the total crown leaf mass, as well as to the total sapwood cross-sectional area of crown branches [27,28]. The pipe model theory was combined with the stem taper equation, and many researchers found a relationship between crown metrics and the truck cross-sectional area at the base of the crown, such as a good relationship with the diameter at breast height (DBH) [29] and a potential relationship between crown metrics and AGB.

In this study, to inverse forest AGB, we extracted crown metrics from a CHM and DSM derived from UAV stereoscopic imagery, such as crown volume (CV), crown surface area (CSA), crown cross-sectional area (CCSA), crown length (CL), and the ratio of crown surface area to crown volume (CSA/CV). Furthermore, the terrain influence for AGB inversion using DTM-independent crown metrics was analyzed considering the ground and slope. The main purpose of this study was to explore the potential ability to estimate AGB using DTM-independent crown metrics from UAV stereoscopic imagery without the assistance of tree height, aiming to advance multi-angle stereoscopic photogrammetry techniques for forest resource surveys.

2. Materials

2.1. Study Area

The study area is located in the Inner Mongolia Autonomous and Heilongjiang Region of China (46°–50° N, 119°–125° E) on the north slope of the Daxinganling Mountains. The area is about 770 km in length and 300 km in width, as shown in Figure 1a. This area is an important Chinese forestry base in the Daxinganling forest area and belongs to the frigid temperate zone of the coniferous forest vegetation. Its topography is mountainous, and elevation ranges between 587 m and 1265 m. This area belongs to the cold polar of China, and the annual mean temperature is −5.4 °C, with a minimum temperature of −52.6 °C. Most of the area is covered with forest. The dominant tree species is dahurian Larix gmelinii (Rupr.) Kuzen, followed by coniferous species such as Pinus sylvestris var. mongholica Litv. and broadleaf deciduous species such as Betula platyphylla Suk. and Populus davidiana Dode. Three measurement campaigns were carried out for the collection of leaf-off (late April and early May) and leaf-on (late June and Earth July) UAV stereoscopic imagery, as well as for field inventory based on UAV imagery (August).

2.2. Field Data

Field inventory was carried out between 1 and 15 August 2018, after the UAV imagery investigation. Based on the stand density characteristics within each UAV-sorted coverage area, two to three circular plots (15 m radius) were established, and 57 plots were measured. Each tree within a field sampling plot was matched to the corresponding tree on the printed digital orthophoto map (DOM) and labeled on both the printed DOM and the ground, as shown in the example in Figure 1c. In order to locate the field plot, a Trimble GeoXT6000 handheld (Trimble Inc., Sunnyvale, CA, USA) global positioning system (GPS) was used to navigate to the field plot center. Then, based on the GPS-located positions, the field plot center was further confirmed by matching trees on the printed DOM to the ground truth through tree attributes such as species, relative positions, sizes of trees, and obviously dead, fallen trees in order to minimize the mismatch between field measurements and the remote sensing dataset caused by geolocation uncertainties. The height and diameter at the breast height (DBH) of each tree, the height of the first live branch, and the contact height and crown widths of selected trees were measured and recorded. The DBH of each tree was measured using DBH tape, which is a specific measurement instrument for measuring DBH. Tree heights (THs) were measured with a laser range finder. The AGB of each tree was calculated using published allometric Equation (1) [30], and the parameters are shown in

Table 1. Allometric equations used in this study.

Species	Parameters of Allometric Equations
	c0	b0	r2	k2	r3	k3	r4	k4
Larix gmelinii	0.1081	2.5102	0.0303	0.42113	0.1625	−0.5624	0.02804	0.9016
Pinus sylvestris	0.1429	2.3177	0.0057	1.00894	0.0042	0.8969	0.65231	−0.3355
Betula platyphylla	0.2755	2.2358	0.0261	0.72790	0.0344	0.0686	0.15110	0.3442
Populus davidiana	0.2064	2.2646	0.0109	0.83649	0.0434	−0.1504	0.11583	0.2056

[30]. This field inventory process should guarantee that a tree measured in the field can be observed in the UAV DOM. The ranges of the maximum and minimum DBH, TH, and AGB of each tree and their mean value are shown in

Table 2. Accuracy of tree identification over field sampling plots.

Species	DBH (cm)		TH (m)		AGB (kg)		Number of Trees
	Mean Range		Mean Range		Mean Range
Larix gmelinii	21.3	6.5~39.3	16.5	6.5~24.4	184.8	10.5~625.2	378
Pinus sylvestris	31.0	4.9~54.7	17.6	5.6~22.8	414.1	4.2~1368.5	54
Betula platyphylla	11.6	4.7~17.7	12.0	6.1~17.5	56.0	7.1~128.4	40
Populus davidiana	13.7	6.7~19.2	14.2	7.2~20.9	68.6	13.2~140.5	58

Note: DBH: diameter at breast height; TH: tree height; AGB: aboveground biomass. “Range” refers to the interval between the maximum and minimum values of a measurement. “Mean” is the average of the measured values.

.

$$\left\{\begin{array}{l}{w}_s=c_0{D}^{b_0}/\left(1+r_2{D}^{k_2}+r_3{D}^{k_3}+r_4{D}^{k_4}\right)\\ w_b=c_0{r}_2{D}^{k_2+b_0}/\left(1+r_2{D}^{k_2}+r_3{D}^{k_3}+r_4{D}^{k_4}\right)\\ w_l=c_0{r}_3{D}^{k_3+b_0}/\left(1+r_2{D}^{k_2}+r_3{D}^{k_3}+r_4{D}^{k_4}\right)\end{array}\right\}$$

(1)

Here, $w_s$, $w_b$, and $w_l$ represent the biomass of the trunk, branches, and leaves, respectively. The correlation coefficients required for Equation (1) are shown in Table 1. The sum of $w_s$, $w_b$, and $w_l$ is denoted as the biomass (BIO).

2.3. Collections of UAV Imagery

The UAV site was about 1 km × 1 km in size in order to meet the measurement requirements for large-scale permanent sample plots. UAV imagery was collected by flying along the same routes from 25 April to 1 May 2018 (leaf-off) and from 5 to 20 July 2018 (leaf-on), and UAV stereoscopic imagery was collected for 140 leaf-off and 123 leaf-on sites, with 121 sites in common, as shown in Figure 1a. The sites were determined according to the orbits of Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System (ICESat/GLAS) and the International Space Station (ISS), as well as the dynamics of forest stands. A six-rotor helicopter with a Sony NEX-5T camera (Sony Group Corporation, Tokyo, Japan) was used to acquire the UAV stereoscopic imagery, collecting images at 16.10 megapixels. The UAV can be automatically programmed with flying routes and positions to obtain photos associated with the ground station, as well as with appropriate UAV system settings, including the focal length of the camera, flying heights, forward overlaps, side overlaps, and flying speeds. In this study, a 16,000 mAh battery was used, providing about 18–20 min of flying at an above ground level (AGL) of about 300 m with a flying speed of 10 m/s; battery capacity determines flight duration. The forward and side overlaps along the fly path were about 90% and 60%, respectively. The focal length and shutter speed were 16 mm and 1/600 s for stereoscopic image collection, respectively. Images were stored in RGB format in this study, and the spatial resolution, or the ground sample distance (GSD), of the stereoscopic imagery was about 8.6 cm.

3. Method

3.1. UAV Stereoscopic Imagery Processing

The Agisoft Photoscan software package (version 1.2.2) was used to process the stereoscopic images, using the structure-from-motion (SfM) algorithm. The relative positions and orientations of the camera were used to create three-dimensional modeling equations in SfM, which can be calculated from identified matching points. The numerous overlapping stereoscopic images can be used to determine the number of point clouds with a local relative coordinate system, which was transformed into geo-referenced coordinates using GCP to produce a three-dimensional model.

Correspondingly, five basic steps were followed to process the UAV stereoscopic images: (a) Align photos. (b) Build dense point cloud. (c) Build digital elevation model (DEM): in this study, the leaf-on stereoscopic imagery was used to build dense point clouds, and a DSM was rasterized from the dense point cloud. (d) Build orthomosaic: orthomosaic export is normally used to generate high-resolution imagery based on source photos and the reconstructed model. (e) Transform coordinates: the geo-referenced coordinates of the point cloud were calculated from the relative coordinates using GCP, and 10–12 GCPs were placed as evenly as possible throughout each site.

3.2. Individual Tree Segmentation

Individual tree segmentation was performed using Liu’s algorithm, building upon two decades of methodological developments in this domain. The segmentation process followed a three-step approach. First, binary images of the DOM were generated using the Otsu’s Method (OTSU) algorithm, which is an adaptive threshold segmentation method that divides a gray image into the target and background by finding an alterable suitable threshold according to the image histogram. Second, the centers of each individual crown were identified with a morphological method for binary images (i.e., erosion and dilation operations). In this study, the window size used in the erosion and dilation operator (5.0) followed that established by Liu [31,32]. Third, watershed segmentation was used to first separate crowns and then extract the final individual crowns using the initial crown and binary images. The segmentation results are visualized in Figure 1, where red polygons demarcate crown boundaries of identified trees, with numerical identifiers corresponding to field inventory records.

3.3. DTM-Independent Crown Metrics

Accurate ground surface modeling presents significant challenges in dense forest environments when using aerospace remote sensing, requiring reliance on crown structure information obtained from the upper canopy and crown surfaces. Given this constraint, investigating the relationship between crown structure characteristics and tree growth status becomes crucial for forest biomass estimation. In this study, the UAV leaf-on stereoscopic imagery was used to build dense point clouds, and a DSM was rasterized from a dense point cloud in order to extract DTM-independent crown metrics, such as the crown volume (CV), crown surface area (CSA), crown cross-sectional area (CCSA), crown length (CL), and ratio of crown surface area to crown volume (CSA/CV).

Table 3. Definitions and equations of DTM-independent crown metrics.

DTM-Independent Crown Metrics	Descriptions
CV	Crown volume above the height of the tree boundary.
CSA	Crown surface area above the height of the tree boundary.
CCSA	Crown cross-sectional area above the height of the tree boundary.
CL	Crown length above the height of the tree boundary.
CSA/CV	Ratio of crown surface area to crown volume above the height of the tree boundary.

defines each metric, and Equations (2)–(5) show their calculation process. Because both the DOM and DSM were created using the same UAV stereoscopic imagery, the geometric coordinates of the DOM and DSM were matched to each other, and the boundary of each tree was extracted from the DOM through individual tree segmentation and then matched to the DSM. DTM-independent crown metrics were calculated by computing the pixels within the boundary polygon of each tree.

$$CV={\displaystyle \sum _{i\in N}^N{S}_{pixel}^i\cdot }{\overline{H}}_{pixel}^i$$

(2)

$$CSA={\displaystyle \sum _{i\in N}^N{C}_{pixel}^i}$$

(3)

$$CCSA={\displaystyle \sum _{i\in N}^N{S}_{pixel}^i}$$

(4)

$$CL=H_{top\text{–}canopy}-H_{bounder\text{–}canopy}$$

(5)

$$\begin{gathered} C_{pixel}^i=\sqrt{P\left(P-D_1\right)\left(P-D_2\right)\left(P-D_3\right)},P={\displaystyle \frac{1}{2}}\left(D_1+D_2+D_3\right), \\ D=\sqrt{\Delta X^2+\Delta Y^2+\Delta Z^2} \end{gathered}$$

(6)

A pixel of the DSM comprised two triangles; here, $D$ denotes the surface distance between two vertices of its i^th triangle; $X$, $Y$, and $Z$ are the coordinates of the vertices of a triangle; and $P$ is half the perimeter of a triangle. Moreover, $C_{pixel}^i$ denotes the surface area of the i^th pixel and can be calculated using Helen’s formula, Equation (6). $S_{pixel}^i$ and ${\overline{H}}_{pixel}^i$ are the horizontal area and average height of the i^th pixel from the DSM, respectively, and N is the number of pixels within the crown boundary. Finally, $H_{top\text{–}canopy}$, $H_{bounder\text{–}canopy}$, and $N$ denote the height of the crown top, height of the crown boundary, and number of pixels within the crown boundary, respectively.

3.4. Biomass Models and Estimation

The primary objective of model development was to estimate AGB for four tree species (Larix gmelinii, Pinus sylvestris, Betula platyphylla, and Populus davidiana) using crown structural information. Four models were constructed using the five DTM-independent crown metrics presented in Table 3. The first model was constructed using both TH and the five DTM-independent crown metrics; the second model employed stepwise linear regression using the six variables above; the third model was constructed using the five DTM-independent crown metrics; and the fourth model applied stepwise linear regression with five DTM-independent crown metrics. The comparison highlights that DTM-independent crown metrics can be used instead of TH for AGB inversion. The fundamental linear model structure is expressed in Equation (7):

$$\widehat{y}=f\left(x_i;\beta \right)+{\epsilon }_i$$

(7)

where ${\widehat{y}}_i$ is the tree biomass to be estimated and $f$ is a known function of known predictor variables and some unknown parameters $\beta$. The square correlation coefficient R² (Equation (8)) and RMSE (Root Mean Square Error) (Equation (9)) were used to assess the AGB models for Larix gmelinii, Pinus sylvestris, Betula platyphylla, and Populus davidiana trees. The methodological framework of this study is designed to systematically estimate aboveground biomass and is presented in Figure 2. This integrated workflow begins with the acquisition of UAV data, from which key crown metrics are derived. These metrics are then utilized for biomass inversion, ultimately supporting the development of allometric models for accurate AGB estimation.

$$R^2={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left(y_i-\overline{y}\right)\left({\widehat{y}}_i-\overline{\widehat{y}}\right)}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{\left({\widehat{y}}_i-\overline{\widehat{y}}\right)}^2}}}}$$

(8)

$$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}}{n-1}}}$$

(9)

where $y_i$ is the field-measured value for plot $i$; $\overline{y}$, the average value of all field-measured values; ${\widehat{y}}_i$, the model-estimated value for plot $i$; $\overline{\widehat{y}}$, the average value of all model-estimated values; and $n$, the number of plots.

4. Results

4.1. AGB Estimation Comparing DTM-Independent Crown Metrics with TH

The DTM-independent crown metrics and TH were used to estimate forest AGB for four tree species.

Table 4. Relationship between AGB and TH and DTM-independent crown metrics for four forest species.

	Model	Larix gmelinii	Pinus sylvestris	Betula platyphylla	Populus davidiana	Coniferous	Deciduous	All
Species
CSA		R2 = 0.46 RMSE = 83.29	R2 = 0.89 RMSE = 174.22	R2 = 0.22 RMSE = 26.72	R2 = 0.43 RMSE = 19.71	R2 = 0.64 RMSE = 94.72	R2 = 0.21 RMSE = 25.10	R2 = 0.67 RMSE = 89.08
CCSA		R2 = 0.62 RMSE = 69.22	R2 = 0.93 RMSE = 142.06	R2 = 0.26 RMSE = 26.07	R2 = 0.50 RMSE = 19.86	R2 = 0.76 RMSE = 78.65	R2 = 0.32 RMSE = 23.43	R2 = 0.78 RMSE = 73.57
CV		R2 = 0.49 RMSE = 81.30	R2 = 0.86 RMSE = 200.87	R2 = 0.16 RMSE = 27.62	R2 = 0.32 RMSE = 21.44	R2 = 0.61 RMSE = 95.52	R2 = 0.17 RMSE = 25.76	R2 = 0.61 RMSE = 90.65
CL		R2 = 0.22 RMSE = 97.36	R2 = 0.68 RMSE = 284.59	R2 = 0.08 RMSE = 28.93	R2 = 0.16 RMSE = 23.85	R2 = 0.40 RMSE=122.69	R2 = 0.04 RMSE = 27.71	R2 = 0.44 RMSE = 116.02
CSA/CV		R2 = 0.37 RMSE = 95.49	R2 = 0.77 RMSE = 206.96	R2 = 0.06 RMSE = 30.37	R2 = 0.15 RMSE = 23.98	R2 = 0.47 RMSE=125.37	R2 = 0.08 RMSE = 27.08	R2 = 0.47 RMSE = 118.86
TH		R2 = 0.56 RMSE = 87.24	R2 = 0.85 RMSE = 205.24	R2 = 0.63 RMSE = 18.36	R2 = 0.43 RMSE = 23.07	R2 = 0.58 RMSE=132.94	R2 = 0.57 RMSE = 21.79	R2 = 0.60 RMSE = 125.37

Note: The correlation coefficients in Table 4 are optimal, including nonlinear and linear values. The unit of the RMSE is (kg/tree).

shows the R² and RMSE values for the AGB estimation models. For Larix gmelinii, crown cross-sectional area (CCSA) demonstrated the strongest correlation with AGB (R² = 0.62, RMSE = 69.22 kg/tree), followed by tree height (R² = 0.56, RMSE = 87.24 kg/tree). For Pinus sylvestris, CCSA showed the highest correlation (R² = 0.93, RMSE = 142.06 kg/tree), while tree height ranked fourth in predictive power (R² = 0.85, RMSE = 205.24 kg/tree) after CSA, CCSA, and CV. The relationships differed notably for deciduous species. The AGB of Betula platyphylla correlated strongly with TH (R² = 0.63, RMSE = 18.36 kg/tree), while CCSA provided the second strongest relationship (R² = 0.26, RMSE = 26.07 kg). For Populus davidiana, CCSA again emerged as the optimal predictor (R² = 0.50, RMSE = 19.86 kg/tree), with tree height ranking third (R² = 0.43, RMSE = 23.07 kg/tree) after CSA and CCSA. These results indicate that the relationship between AGB and CCSA was superior to that between AGB and TH for three species except Betula platyphylla. With regard to the forest stand, similar patterns emerged between AGB and crown metrics. For coniferous trees, CCSA provided the strongest correlation (R² = 0.76, RMSE = 78.65 kg/tree), while tree height ranked fourth (R² = 0.58, RMSE = 132.94 kg/tree), following CSA, CCSA, and CV.

In Table 4, all three revealed consistent patterns in the relationships between AGB and crown metrics. The correlations between AGB and three metrics—crown surface area (CSA), crown cross-sectional area (CCSA), and crown volume (CV)—demonstrated comparable strength to the traditional TH relationship. CCSA emerged as the optimal predictor of all tree AGB, achieving an R² value of 0.78 with an RMSE of 73.57 (kg/tree). In comparison, TH ranked fourth after CSA, CCSA, and CV, with an R² value of 0.60 and RMSE of 125.37 (kg/tree). Notably, the DTM-independent crown metrics showed stronger correlations with AGB for coniferous trees compared to deciduous trees, suggesting that crown architectural characteristics are more reliable for estimating the AGB of coniferous trees than that of deciduous trees.

4.2. Influence of Terrain on DTM-Independent Crown Metrics for AGB Estimation

In order to analyze the influence of terrain on DTM-independent crown metrics for AGB estimation, the crown metrics from the CHM and DSM were calculated to analyze the correlation with AGB. Because the Canopy Height Model (CHM) is derived by removing the influence of terrain from the Digital Surface Model (DSM), the crown metrics from the CHM and DSM eliminate the influence of terrain, and the relationships between AGB and the five DTM-independent crown metrics from the CHM and DSM for ground and slope were calculated, with the results shown in

Table 5. Relationships between AGB and TH and DTM-independent crown metrics from CHM for ground and gentle slope.

	Species	Coniferous	Deciduous	All
Slope
Ground	CSA	R2 = 0.52	R2 = 0.39	R2 = 0.54
		RMSE = 88.14	RMSE = 67.27	RMSE = 90.99
	CCSA	R2 = 0.70	R2 = 0.40	R2 = 0.73
		RMSE = 62.77	RMSE = 22.42	RMSE = 63.95
	CV	R2 = 0.58	R2 = 0.31	R2 = 0.55
		RMSE = 82.66	RMSE = 24.18	RMSE = 90.24
	CL	R2 = 0.25	R2 = 0.18	R2 = 0.29
		RMSE = 111.56	RMSE = 26.34	RMSE = 116.72
	CSA/CV	R2 = 0.49	R2 = 0.15	R2 = 0.42
		RMSE = 179.27	RMSE = 26.74	RMSE = 178.20
	TH	R2 = 0.60	R2 = 0.56	R2 = 0.55
		RMSE = 89.52	RMSE = 22.72	RMSE = 83.04
Slope	CSA	R2 = 0.71	R2 = 0.14	R2 = 0.71
		RMSE = 93.23	RMSE = 18.60	RMSE = 93.71
	CCSA	R2 = 0.79	R2 = 0.15	R2 = 0.80
		RMSE = 79.04	RMSE = 18.57	RMSE = 78.30
	CV	R2 = 0.62	R2 = 0.04	R2 = 0.63
		RMSE = 107.34	RMSE = 19.72	RMSE = 107.27
	CL	R2 = 0.51	R2 = 0.02	R2 = 0.51
		RMSE = 121.68	RMSE = 19.89	RMSE = 122.89
	CSA/CV	R2 = 0.43	R2 = 0.03	R2 = 0.44
		RMSE = 131.70	RMSE = 20.34	RMSE = 131.08
	TH	R2 = 0.46	R2 = 0.63	R2 = 0.52
		RMSE = 155.14	RMSE = 12.22	RMSE = 152.94

and

Table 6. Relationships between AGB and TH and DTM-independent crown metrics from DSM for ground and gentle slope.

	Species	Coniferous	Deciduous	All
Slope
Ground	CSA	R2 = 0.53	R2 = 0.24	R2 = 0.54
		RMSE = 84.26	RMSE = 24.81	RMSE = 71.33
	CCSA	R2 = 0.70	R2 = 0.32	R2 = 0.73
		RMSE = 63.11	RMSE = 23.46	RMSE = 55.26
	CV	R2 = 0.58	R2 = 0.20	R2 = 0.55
		RMSE = 81.26	RMSE = 25.44	RMSE = 70.44
	CL	R2 = 0.30	R2 = 0.08	R2 = 0.30
		RMSE = 106.90	RMSE = 27.27	RMSE = 93.60
	CSA/CV	R2 = 0.49	R2 = 0.11	R2 = 0.42
		RMSE = 95.58	RMSE = 26.87	RMSE = 88.30
	TH	R2 = 0.60	R2 = 0.56	R2 = 0.55
		RMSE = 89.52	RMSE = 22.72	RMSE = 83.04
Slope	CSA	R2 = 0.70	R2 = 0.11	R2 = 0.70
		RMSE = 93.95	RMSE = 19.01	RMSE = 94.07
	CCSA	R2 = 0.77	R2 = 0.14	R2 = 0.78
		RMSE = 81.70	RMSE = 18.65	RMSE = 80.82
	CV	R2 = 0.60	R2 = 0.03	R2 = 0.60
		RMSE = 99.98	RMSE = 19.79	RMSE = 100.84
	CL	R2 = 0.46	R2 = 0.005	R2 = 0.46
		RMSE = 125.90	RMSE = 20.04	RMSE = 126.718
	CSA/CV	R2 = 0.38	R2 = 0.09	R2 = 0.41
		RMSE = 135.30	RMSE = 19.55	RMSE = 132.79
	TH	R2 = 0.46	R2 = 0.63	R2 = 0.52
		RMSE = 155.14	RMSE = 12.22	RMSE = 152.94

, respectively. First, the results show that the correlations between AGB and the CCSA, CSA, and CV from the CHM and DSM were superior to that between AGB and TH for coniferous trees in ground and slope plots. Table 6 shows R² = 0.77 and RMSE = 81.70 (kg/tree) for conifer CCSA and R² = 0.46 and RMSE = 155.14 (kg/tree) for conifer TH. These results prove that DTM-independent crown metrics can be used to estimate coniferous forest AGB, even in cases where TH cannot be accurately measured without DTM assistance.

Second, the relationships between AGB and the five DTM-independent crown metrics from the CHM and DSM were similar in the ground and slope plots. Take the optimal CCSA as an example, as shown in Table 5, the R² and RMSE values from the CHM are 0.79 and 79.04 (kg/tree) for coniferous trees, respectively, and R² = 0.80 and RMSE = 78.30 (kg/tree) for all trees in slope. Accordingly, in Table 6, the R² and RMSE values from the DSM are consistent with those of the CHM: R² = 0.77 and RMSE = 81.70 (kg/tree) for coniferous trees and R² = 0.78 and RMSE = 80.82 (kg/tree) for all trees in slope. The results show that the accuracy of the DTM-independent crown metrics for estimating AGB was not affected by terrain. Third, in comparing the contents of Table 6 and Table 5, the changing trend of the relationship between AGB and the five DTM-independent crown metrics from the DSM in ground and slope is similar to that from the CHM in ground and slope. This proves that the accuracy of AGB inversion using five DTM-independent crown metrics is not affected by terrain.

4.3. Stepwise Linear Regression Model Using Five DTM-Independent Crown Metrics and TH

To evaluate the ability of DTM-independent crown metrics in estimating forest AGB, four regression models were developed, as shown in

Table 7. Estimation models of forest AGB developed using TH and DTM-independent crown metrics.

	Species	Larix gmelinii	Pinus sylvestris	Betula platyphylla	Populus davidiana	Coniferous	Deciduous	All
Model
Model using TH and five DTM-independent crown metrics		R2 = 0.75 RMSE = 56.09	R2 = 0.83 RMSE = 115.55	R2 = 0.80 RMSE = 14.55	R2 = 0.55 RMSE = 18.50	R2 = 0.83 RMSE = 66.57	R2 = 0.61 RMSE = 18.11	R2 = 0.84 RMSE = 62.51
Stepwise linear regression model using TH and DTM-independent crown metrics		R2 = 0.75 RMSE = 55.97	R2 = 0.82 RMSE = 116.97	R2 = 0.78 RMSE = 14.52	R2 = 0.52 RMSE = 18.60	R2 = 0.83 RMSE = 66.59	R2 = 0.59 RMSE = 18.17	R2 = 0.84 RMSE = 62.46
Model using five DTM-independent crown metrics		R2 = 0.63 RMSE = 67.92	R2 = 0.79 RMSE = 127.62	R2 = 0.27 RMSE = 27.22	R2 = 0.52 RMSE = 18.98	R2 = 0.77 RMSE = 77.11	R2 = 0.35 RMSE = 23.29	R2 = 0.78 RMSE = 72.51
Stepwise linear regression model using DTM-independent crown metrics		R2 = 0.63 RMSE = 67.88	R2 = 0.79 RMSE = 125.27	R2 = 0.26 RMSE = 26.07	R2 = 0.51 RMSE = 18.68	R2 = 0.77 RMSE = 77.10	R2 = 0.35 RMSE = 23.01	R2 = 0.78 RMSE = 72.46

: multivariate linear regression incorporating both TH and the five DTM-independent crown metrics, stepwise linear regression using TH and the five DTM-independent crown metrics, linear regression utilizing only the five DTM-independent crown metrics, and stepwise linear regression based on the five DTM-independent crown metrics. For Larix gmelinii, the stepwise linear regression combining TH with crown metrics achieved optimal performance (R² = 0.75, RMSE = 55.97 kg/tree), though the model using only crown metrics also demonstrated strong predictive capability (R² = 0.63, RMSE = 67.88 kg/tree). Pinus sylvestris models showed good accuracy for TH-inclusive (R² = 0.82, RMSE = 116.97 kg/tree) and TH-exclusive approaches (R² = 0.79, RMSE = 125.27 kg/tree). Similarly, Populus davidiana models maintained consistent performance by including TH (R² = 0.52, RMSE = 18.60 kg/tree) and excluding TH (R² = 0.51, RMSE = 18.68 kg/tree). This pattern extends to broader species groupings, with coniferous species models showing strong performance both with TH (R² = 0.83, RMSE = 66.59 kg/tree) and without TH (R² = 0.77, RMSE = 77.10 kg/tree). In an analysis including all tree species, the TH-inclusive model achieved an R² = 0.84 and RMSE = 62.46 (kg/tree), compared to the R² = 0.78 and RMSE = 72.46 (kg/tree) for the five DTM-independent crown metrics.

Table 8. Calculated coefficients of two stepwise linear models.

Model	TH	CSA	CCSA	CV	CL	CSA/CV	$\mathit{\epsilon }$	R2	RMSE
① TH and DTM-independent crown metrics
Larix gmelinii	10.80		9.74	1.02	−10.71		−92.96	0.75	55.97
Pinus sylvestris	15.62		10.71	0.29			−174.81	0.82	116.97
Betula platyphylla	7.60		4.71				−61.59	0.78	14.52
Populus davidiana	3.76	5.04		−1.67			−11.54	0.52	18.60
Coniferous	11.04		11.60	0.47	−6.08		−116.72	0.83	66.59
Deciduous	6.36	1.71					−36.70	0.59	18.17
All	10.78	−0.74	13.17	0.39		8.68	−148.21	0.84	62.46
② DTM-independent crown metrics
Larix gmelinii	\		12.36	1.00	−14.69	−19.13	89.91	0.63	67.88
Pinus sylvestris	\		13.90	0.25			26.36	0.79	125.27
Betula platyphylla	\		6.18				21.46	0.26	26.07
Populus davidiana	\	3.17	8.22	−2.51			15.93	0.51	18.68
Coniferous	\	−1.47	16.35	0.39			20.27	0.77	77.10
Deciduous	\		8.90	−0.83			20.44	0.35	23.01
All	\	−1.31	16.73	0.35			6.46	0.78	72.46

① Features selected from TH and five DTM-independent crown metrics using stepwise procedure; ② features selected from five DTM-independent crown metrics using stepwise procedure.

shows the features selected for each tree species using ① the stepwise linear regression model based on TH and the five DTM-independent crown metrics and ② the stepwise linear regression model based on only the five DTM-independent crown metrics. Analysis of feature selection frequency revealed CCSA as the most consistently selected variable, appearing twelve times across both model types. CV demonstrated similar importance with eleven selections, while CSA was selected six times. CL and CSA/CV showed lower selection frequencies, chosen three and two times, respectively, across the models. Table 8 shows the calculated coefficient of TH and the five DTM-independent crown metrics in the two stepwise linear models (TH, CSA, CCSA, CV, CL, CSA/CV), as well as the intercept ($\epsilon$) and their accuracy using validation data (R², RMSE). The validation accuracy of the regression model using TH is close to that of the model using TH for Larix gmelinii, Pinus sylvestris, and Populus davidiana.

The AGB estimation accuracy was determined using scatter plots to compare field-measured AGB against AGB estimated using the stepwise linear regression with five DTM-independent crown metrics. The analysis revealed distinct patterns across species groups. For Larix gmelinii (red line) and Pinus sylvestris (blue line) in Figure 3a, the estimated AGB was closer to the 1:1 line (black line), indicating a high estimation accuracy. In contrast, Betula platyphylla (red line) and Populus davidiana (blue line) in Figure 3b, estimated AGB is more discretely distributed around line A 1:1 line, suggesting a lower prediction accuracy. In Figure 3c, the estimated AGB of coniferous shows a relatively good fit with the 1:1 line than deciduous tree, which indicated that DTM-independent crown metrics is more suitable to estimate AGB of coniferous tree comparing with deciduous tree.

5. Discussion

5.1. Relationships Between Five DTM-Independent Crown-Metrics and AGB

Tree growth fundamentally depends on light interception capacity, with crown structures intercepting approximately 80% of solar radiation [33,34]. Crown morphological traits, particularly size characteristics, are shaped by competition for light and space resources [35]. The crown distribution may be applied to the analysis of physiological processes, principally photosynthesis, respiration, and transpiration, to estimate light interception within the crown and explain the tree growth situation [36]. Consequently, the derived crown metric is considered one of the most important traits that affects tree growth; however, this knowledge is crucial for forest biomass prediction [37].

Analysis of the relationships between forest AGB and DTM-independent crown metrics revealed that three parameters, CSA, CCSA, and CV, were superior compared to CL and the CSA/CV ratio across all four species. This finding was reinforced by the frequent selection of CSA and CV in stepwise regression models. For aspects of light interactions within the tree crown: CSA and CCSA indicate light interception capacity, while CV represents the internal light transmission pathway, thus reflecting the radiation utilization efficiency of the trees. The metrics differ in dimensional information: CSA and CCSA capture a two-dimensional horizontal structure of the tree canopy, and CV provides three-dimensional information in both the horizontal and vertical directions. The relationship between forest biomass and CV is supposed to be superior to that with CSA and CCSA; however, the results indicate the opposite, because CV is the sum of the crown pixel area times ${\overline{H}}_{pixel}^i$. If the tree segmentation boundary is larger than the crown, ${\overline{H}}_{pixel}^i$ is the crown height and it becomes larger and CV increases rapidly. Luckily, the accuracy of CV will gradually improve with future improvements in the accuracy of single-tree segmentation.

From the results, CCSA is the optimal parameter for estimating AGB. Based on pipe model theory, the sapwood cross-sectional area at the base of a crown is positively related to the total cross-sectional area of the crown branches, while that of crown branches has good correlation with DBH and forest AGB, which has good correlation with CCSA. This explains why the relationship between forest AGB and CCSA is stronger compared to other DTM-independent crown metrics. However, from Table 4, we also found that the R² between biomass and CL is under 0.5 and lower than the R² of CSA, CCSA, and CV for four tree species, because CL can only reflect information in the vertical direction [38]. The results show that the relationship between forest AGB and CSA/CV is close to that with CL. CSA/CV could be called the relative surface area of the crown, which determines the shape of the tree crown.

Table 4 shows that five DTM-independent crown metrics are more suitable for the AGB inversion of coniferous trees. Because coniferous trees have more regular crown shapes that are typically conical, more structure information about the coniferous tree canopy can be observed through UAV imagery. In contrast, deciduous species exhibit more complex ellipsoidal structures with irregular shapes and branch crossings, increasing the challenge of accurately observing crown parameters. However, the correlation for deciduous species is lower compared to conifer species, especially birch. This is because the density of birch plots is higher than for other species, and the intersection part of the canopy is greater and near the top of the canopy. A point cloud simulated from UAV stereoscopic imagery only contains information above the intersection of the canopy, and this part of the canopy fails to reflect the growth condition of the trees. However, the range of birch biomass (7.1–128.4 kg) is the lowest compared to that of other three species, which could also cause the correlation to be lower. Under normal circumstances, the crown size increases as the trees grow in low-density and short-term stands. However, this relationship becomes more complex in denser and long-term stands where crown recession can occur.

5.2. The Potential of DTM-Independent Crown-Metrics for AGB Estimation

The results indicate that the accuracy of AGB inversion using only crown metrics is similar to that using TH, and even for some parameters, such as CCSA, the accuracy is higher. This suggests that the crown metrics contain growth information of the trees, and the DTM-independent crown-metrics have the potential to be used for AGB inversion without the assistance of TH. Five DTM-independent crown metrics were calculated using a CHM and DSM, the correlation with AGB was analyzed, and no drastic change in accuracy was observed. This proves that in the absence of a DTM, which makes it impossible to obtain TH, DTM-independent crown metrics can be used for AGB inversion. The R² and RMSE were calculated for AGB inversion in different terrain conditions, proving that the accuracy is not affected by terrain when using the five DTM-independent crown metrics to estimate AGB.

Crown size serves as a key indicator of tree growth through its reflection of continuous tree-to-tree interactions, particularly niche differentiation. These interactions shape crown space occupancy patterns and competitive dynamics, which directly influence radial tree growth [39]. This relationship carries particular significance as changes in tree allometry that can affect tree structure along both vertical and horizontal light gradients over time [40]. Crown space occupancy patterns effectively capture growth competition through multi-dimensional crown forms, with different metrics capturing distinct aspects of the crown architecture: CSA, CCSA, and CSA/CV characterize horizontal growth patterns, CL represents vertical development, and CV encompasses both horizontal and vertical space utilization. The DTM-independent crown metrics developed in this study capture specific aspects of crown structure information. However, DTM-independent crown metrics provide a more complete representation of the three-dimensional crown structure across both the horizontal and vertical directions, enhancing AGB estimation accuracy [41]. This improvement is shown in Table 4 and Table 7; the models using the five DTM-independent crown metrics demonstrated lower RMSE values compared to models using a single crown metric for four tree species.

However, the tree crown is an important indicator for tree growth, and TH is an indicator for radial tree growth. Our analysis revealed that the correlations of CSA, CCSA, and CV with biomass were superior to that with TH for coniferous trees. Also, in Table 4 and Table 7, the results show that the integration of crown metrics with TH improved AGB estimation accuracy, with R² values increasing from 0.77 to 0.83 and RMSE values decreasing from 77.10 (kg/tree) to 66.59 (kg/tree). While there was only a 0.05 difference for R², our research demonstrates the potential of DTM-independent crown metrics for forest AGB estimation, even in cases where TH cannot be accurately measured without DTM assistance using UAV technology.

6. Conclusions

This study demonstrates that the potential of drone-derived DTM-independent crown metrics for estimating forest AGB in the case of TH cannot be measured. UAV technology offers unprecedented capabilities for forest monitoring, combining ultra-high-spatial-resolution photogrammetric imagery (approximately 8 cm in our study) with cost-effective three-dimensional data acquisition through stereoscopic imagery. This approach enables detailed measurements of key stand attributes, as validated by recent drone-based forest studies. Specially, this paper assesses the following: (1) the feasibility of using UAV technology for mapping the 3D forest crown structure, (2) how UAV-derived crown attributes respond to tree growth environmental variables, and (3) to what extent UAV-derived crown metrics contribute to our understanding of AGB estimation. The tree crown is considered an important aspect, both in terms of the biological ecology and physiological mechanisms of trees; not only does the crown include important components of photosynthesis and respiration (branches, twigs, and leaves), but the size of the crown also directly reflects tees’ ability to compete for and possess growth space. Crown size also affects the radial growth of the trunk, which will further affect tree growth. Consequently, there is an inevitable relationship between crown characteristics and forest AGB according to forest phenotyping theory and pipe model theory.

However, the demand for accurate and cost-efficient methods for estimating forest AGB is increasing. LiDAR UAVs can measure the height of the ground surface with correct measurement settings, requiring high-echo intensity and high-cost Lidar sensors. However, it is important to note that a DTM from ALS may be affected by errors, depending on terrain characteristics and vegetation cover. We aim to use low-cost and easily accessible UAV photogrammetric images to obtain the main canopy parameters for improving the accuracy of AGB inversion. In this study, DTM-independent crown metrics were calculated from UAV photogrammetric imagery to estimate forest AGB based on the understanding how the crown affects tree growth according to forest phenotyping theory and pipe model theory. We hope that the developed DTM-independent crown metrics can potentially meet the accuracy of AGB measurements in areas where DTMs are not available, such as stands with dense crowns. Moreover, we believe that UAV stereophotogrammetry, as a complementary tool for traditional field surveys, can be used to obtain three-dimensional information of tree crowns for AGB estimation at low costs. Future research efforts should focus on how spaceborne crown metrics could also be used for the AGB estimation of large-scale forests.