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Volume 18
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10.3390/rs18010115
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Article

Modeling Moso Bamboo Tree Density and Aboveground Biomass Using Multi-Site UAV-LiDAR Data

by
Xinyao Liu
1,2,
Guiying Li
1,2,
Longwei Li
3 and
Dengsheng Lu
1,2,*
1
Key Laboratory for Humid Subtropical Eco-Geographical Processes of the Ministry of Education, Fujian Normal University, Fuzhou 350117, China
2
Institute of Geography, Fujian Normal University, Fuzhou 350117, China
3
School of Geographic Information and Tourism, Chuzhou University, Chuzhou 239000, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2026, 18(1), 115; https://doi.org/10.3390/rs18010115
Submission received: 25 November 2025 / Revised: 13 December 2025 / Accepted: 27 December 2025 / Published: 28 December 2025
(This article belongs to the Special Issue Applications of Artificial Intelligence Methods to Agroforestry Remote Sensing)
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Versions Notes

Highlights

What are the main findings?
  • The proposed layered texture metrics from UAV-LiDAR data are valuable for modeling tree density and aboveground biomass.
  • The tree density and aboveground biomass estimation models can be effectively developed through integrated sample plots and UAV-LiDAR data from multiple regions.
What is the implication of the main findings?
  • The selection of proper modeling methods that can effectively incorporate the features from multiple sites is needed for tree density and biomass estimation modeling.
  • The selection of variables and modeling methods should take the unique characteristics of Moso bamboo into account.

Abstract

Moso bamboo, widely distributed in subtropical regions of China, plays an important role in forest management and carbon cycle research. However, accurate estimation of tree density and aboveground biomass (AGB) remains challenging due to the unique characteristics of Moso bamboo forests in their growth and stand structure. This research aims to develop a new procedure for bamboo tree density and AGB estimation based on UAV-LiDAR and sample plots from multiple sites through comparative analysis of the incorporation of two groups of variables—regular point cloud metrics (e.g., height, point density) and layered texture metrics—and three modeling methods—multiple linear regression (MLR), mixed-effects modeling (MEM), and hierarchical Bayesian modeling (HBM). The results showed that incorporating layered texture metrics with regular variables substantially improved the estimation accuracy of both tree density and AGB. Among these models, HBM achieved the highest predictive performance, yielding coefficient of determination (R2) values of 0.54 for tree density and 0.59 for AGB, with corresponding relative root mean square errors (rRMSE) of 21.46% and 17.97%. This study presents a novel and effective method for estimating Moso bamboo tree density and AGB using multi-site UAV-LiDAR and sample plots, offering a scientific basis for precise management and carbon stock assessment.

1. Introduction

Moso bamboo (Phyllostachys edulis) is one of the most important bamboo species and is widely distributed across southern and southeastern regions of China. It accounts for about 70% of the total bamboo forest area nationwide, according to a report from the National Forestry and Grassland Administration of China in 2023 [1]. Between the 9th Forest Resource Inventory (2014–2018) and 2021, the total bamboo forest area increased by 1.15 million hectares—a growth rate of 18% [2]. Moso bamboo exhibits unique growth characteristics and phenological rhythms. It grows rapidly from bamboo shoots to full height within 2 to 3 months and reaches the mature stage within 3 to 5 years [3]. A notable trait is its biennial shoot emergence pattern, with an “on-year” marked by prolific shoot growth in spring and an “off-year” characterized by little shoot development. Corresponding changes in canopy structure and leaf coloration are also observed between these two periods [4]. The growth cycle of Moso bamboo includes three stages—shoot emergence, rapid culm elongation, and leaf replacement [5]. Furthermore, the growth dynamics and structure attributes of Moso bamboo forests are strongly influenced by management practices. In intensively managed Moso bamboo stands, bamboo shoots are typically harvested in early spring, while mature culms are cut during autumn and winter [6]. In contrast, unmanaged stands, subject to less frequent human intervention, often retain a high proportion of half-mature and mature culms. Due to its biological characteristics, Moso bamboo possesses a strong capacity for carbon storage, making it an important contributor to the terrestrial carbon cycle [7]. Therefore, accurately quantifying aboveground biomass (AGB) in Moso bamboo forests is essential for understanding their roles in carbon sequestration and supporting their sustainable management [8]. Notably, Moso bamboo can accumulate substantial biomass in a short time, with annual biomass increases ranging from 10% to 30%, significantly higher than the 2% to 5% for typical woody species [9]. However, this rapid growth also presents management challenges. Without timely harvesting, overcrowding trees and roots can lead to self-thinning and, thus, reduced stand density and diminished ecological functions [10]. Precise estimation of culm density and AGB in Moso bamboo forests is critical for effective management and for evaluation of the carbon sink potential in the bamboo ecosystems [11].
Tree density, or culm density, in bamboo ecosystems is referred to as the number of trees or culms per unit area (i.e., culms/ha), serving as a key indicator of forest and community structures. It is closely related to ecological processes and plays a critical role in determining forest biomass. Tree density data provide essential scientific support for forest management and spatial planning [12]. In general, tree density is achieved through field surveys, but the time-consuming and labor-intensive nature of the feature limits its application to a large area [13]. Remote sensing provides an efficient alternative, offering high-resolution monitoring capability over broad extents. Remote sensing-based tree density estimation methods can be broadly categorized into two groups [14]: (1) rule-based methods—utilizing image binarization to identify green objects, following by geometric analysis to detect individual trees and estimate density by counting detected plants per unit area [15,16,17]; (2) machine learning-based methods—including deep learning and traditional machine learning approaches. Traditional machine learning-based regression modeling establishes the relationships between observed tree density and explanatory variables derived from remote sensing data [18,19]. The deep learning-based object detection approach employs convolutional neural networks or similar algorithms to automatically detect and count individual trees from high-resolution imagery [20,21,22,23]. The rule-based and deep learning–based methods depend on high-resolution imagery, which may be costly, computationally intensive, and difficult to generalize in large areas. Remote sensing inputs have included optical sensors and UAV-LiDAR data, and modeling techniques have spanned from multiple linear regression (MLR) and partial least squares regression (PLS) to random forest (RF) and artificial neural networks (ANN), demonstrating the feasibility of accurately estimating tree density across large areas [24].
The methods for estimating Moso bamboo AGB can be broadly classified into direct and indirect approaches. The direct observation method involves destructive sampling, whereby bamboo culms are cut, dried, and weighed to quantify AGB [25]. Indirect methods encompass allometric equation-based approaches and remote sensing techniques [26]. Allometric equations calculate AGB based on the relationships between AGB and measurable bamboo culm parameters such as diameter at breast height (DBH) and tree height [27]. Both direct and allometric methods provide high accuracy, but they are labor-intensive and time-consuming and thus are not practical for large-scale AGB estimation. In recent years, remote sensing-based approaches have become increasingly favored for Moso bamboo forest AGB estimation due to their nondestructive nature, broad spatial coverage, and temporal efficiency. These methods typically involve developing statistical or machine learning-based models, including parametric models (e.g., linear regressions) and machine learning algorithms like ANN, support vector regression (SVR), RF, and k-nearest neighbors (kNN) [24], that link field-measured AGB with remote sensing-derived variables such as vegetation indices and texture features from optical sensor data like Landsat, Sentinel-2, and WorldView-2 [28,29,30]. A major challenge arises from the intrinsic limitations of optical sensor data, notably its weak penetration and the phenomenon of spectral saturation in high AGB areas. These limitations often lead to substantial underestimation of AGB in dense Moso bamboo forests [31].
As an active remote sensing technology, LiDAR captures three-dimensional forest structural features by emitting laser pulses and recording their returns [32]. This capability enables accurate characterization of forest vertical structures, making it particularly effective for estimating AGB, even in dense forests [13]. With recent advancements in unmanned aerial vehicle (UAV) technology, UAV-based LiDAR systems have become increasingly prevalent in fine-scale forest monitoring. LiDAR-derived metrics, especially height-related (e.g., mean, maximum, and percentile height) and point density-related variables (e.g., canopy density at different height strata), are frequently used to build regression models for estimating forest structural parameters such as tree density and AGB [33,34,35,36]. For example, Cao et al. [37] demonstrated the strong potential of UAV-LiDAR data for estimating Moso bamboo forest AGB under varying management practices, reporting R2 values ranging from 0.59 to 0.87. However, compared with airborne or satellite LiDAR, UAV-LiDAR has a high point cloud density but relatively limited spatial coverage, implying a lack of representative forest types and sample plots, which makes it difficult to develop a robust AGB estimation model based on an individual study area alone [38,39,40].
This characteristic also poses challenges for developing models with strong generalization ability across broad regions. To address this, a potential solution is to integrate UAV-LiDAR data and field data from multiple sites to expand the sample size and improve the spatial representativeness of forest types and age groups [41]. This strategy introduces extra complexity, as regional variability, such as differences in terrain, soil properties, and management practices, can increase modeling uncertainty. Due to the unique growth characteristics of Moso bamboo, forests in different regions may exhibit similar average DBH or height while differing substantially in tree densities and AGB [5]. Such intra-species structural variability is often overlooked in previous studies, which typically rely on samples from a single region. As a result, conventional point cloud metrics and modeling approaches may be inadequate to capture the structural variability associated with differences in bamboo tree density and AGB across multiple regions. This underscores the need for modeling strategies that account for regional heterogeneity and the specific ecological characteristics of Moso bamboo forests.
Although LiDAR is regarded as the best data source for AGB estimation, the distinct characteristics of bamboo forest stand structure make AGB estimation a great challenge. Another difficulty is the limited sample size within a single study area, which constrains the development of robust and generalizable models. Directly combining samples across multiple sites can degrade modeling performance because of the substantial variability in physical features such as climate, terrain, and soil conditions, as well as forest management practices. These inter-site differences complicate the modeling process and reduce the transferability of tree density or AGB estimation models. To address these challenges, this study selected five sites from Fujian and Zhejiang provinces for developing a scalable and region-adaptive methodology for accurate tree density and AGB estimation of Moso bamboo forests. In this research, we proposed the layered texture variables, which were derived from UAV-LiDAR data, and integrated them with regular point cloud metrics. Three modeling approaches—multiple linear regression (MLR), mixed-effects modeling (MEM), and hierarchical Bayesian modeling (HBM)—were employed to construct estimation models for both tree density and AGB. Through this study, we attempt to develop a scalable and region-adaptive methodology for estimating bamboo tree density and AGB, demonstrating the advantages of combining layered texture metrics with hierarchical models. This research can improve our understanding of using multi-site UAV-LiDAR and a limited number of sample data in each site for developing robust bamboo tree density and AGB estimation models, which addresses the modeling dilemma caused by the lack of sufficient and representative sample plots in a single site.

2. Materials and Methods

2.1. Study Area

This study selected five sites, one in Zhejiang Province (i.e., Deqing County) and four in Fujian Province (i.e., Wuyishan National Park, Shunchang County, Yong’an County, and Shanghang County) (Figure 1). These sites span the northern, central, and southern subtropical zones. Both Zhejiang and Fujian Provinces are situated in southeastern China along the coastal region, characterized by mountainous and hilly terrain and a typical subtropical monsoon climate with four distinct seasons. The average annual temperature ranges from 15 °C to 20 °C, and annual precipitation generally falls between 1400 and 1800 mm. These warm and humid conditions are ideal for bamboo growth, resulting in extensive bamboo resources across both provinces. The major characteristics of each study area are provided in Table 1.

2.2. Framework

The overall framework for modeling bamboo tree density and AGB is illustrated in Figure 2, consisting of five main steps: (1) collection and preprocessing of UAV-LiDAR and Moso bamboo field survey data; (2) delineation of spatial distributions of Moso bamboo forests within the UAV flight coverage; (3) extraction of various variables, including commonly used variables and newly proposed variables from UAV-LiDAR point clouds, followed by selection of modeling variables; (4) development of estimation models for bamboo tree density and AGB using different approaches; (5) model evaluation and application to predict bamboo tree density and AGB across the study areas.

2.3. Data Collection and Preprocessing

Field surveys and UAV-LiDAR data were collected at typical sites in Zhejiang and Fujian Provinces between 2022 and 2024. The number of sample plots collected at each site is summarized in Table 2. A total of 50 sample plots were surveyed. The standard plot size was 20 m × 20 m, except in Yong’an, where plots were measured with a size of 30 m × 30 m. The coordinates of the plot corners were recorded using a real-time-kinematic (RTK) positioning system. Within each plot, culms with a diameter at breast height (DBH) greater than 5 cm were measured, and their DBH values were recorded. The AGB of individual bamboo culms was calculated using Equation (1) [42]. The total AGB for each plot was obtained by summing the AGB of all measured bamboo culms, expressed in megagrams per hectare (Mg/ha). In addition, the number of bamboo culms per plot was counted to determine plot-level tree density.
A = 0.386 D1.658
where A and D are the AGB (kg) and DBH (cm) of a Moso bamboo culm.
The LiDAR data for typical sites were acquired using a DL-160 multi-rotor UAV equipped with a GL-54 LiDAR sensor. Flights were conducted in terrain-following mode at an altitude of approximately 100 m, yielding an average point density exceeding 100 points/m2. The UAV-LiDAR point clouds provided by the data provider were subsequently processed through noise removal, classification, and normalization. The resulting normalized point clouds served as the basis for extracting structural metrics, which were used in the development of bamboo tree density and AGB estimation models.

2.4. Moso Bamboo Forest Distributions in Typical Sites

The spatial distribution of Moso bamboo forests within typical sites (i.e., UAV flight areas) was manually delineated through visual interpretation based on UAV high-resolution RGB images, historical imagery from Google Earth (Google LLC, Mountain View, CA, USA), and field survey data. These products were used for tree density and AGB prediction using the developed models, respectively.

2.5. Extraction and Selection of Variables from UAV-LiDAR Point Clouds

A total of 116 variables were extracted from LiDAR point clouds based on the sample plots. These variables were categorized into two main groups: regular variables and layered texture variables (Table 3). The regular variables comprise 26 commonly used LiDAR-derived metrics characterizing vegetation structure (e.g., canopy cover, gap fraction), height distribution (e.g., height percentiles), and point density within specific canopy height strata. These metrics were calculated using the “Forest Parameters Calculation based on Polygon” function in LiDAR360 software 8.0 (GreenValley International, Beijing, China), with normalized LiDAR point clouds and plot polygons as inputs.
The layered texture variables, introduced as novel features in this study, were derived from layered canopy height models (CHMs) generated from the LiDAR data. Unlike traditional textural metrics, layered textures capture fine-scale structural variation of the forest canopy across vertical strata. The layered texture metrics are essentially texture features that primarily reflect the spatial structure within or across the bamboo canopy, but they are limited in capturing other key characteristics related to tree density or AGB, such as tree height. In previous research, the modeling was mainly based on height-related variables for AGB estimation without taking the textural features into account. Here, we aim to explore the role of incorporating layered texture metrics into regular point cloud variables (e.g., height- and density-related metrics) in improving the modeling performance, and to understand how the addition of the complementary information contained in different types of metrics can improve modeling performance. The procedure for calculating layered texture variables involved the following steps:
(1)
LiDAR points with heights below 2 m were excluded to reduce the influence of the understory on the extraction of variables [43]. The remaining points were stratified into 10-layer bins based on height percentiles (10th, 20th, …, 100th), representing vertical segments from the forest floor to the canopy top. These strata were labeled from 0 to 9.
(2)
For each sample plot, a fishnet grid with a resolution of 1 m × 1 m was created. LiDAR points within each height bin were projected onto the grid to form CHM layers. For each grid cell, the maximum height value among all points falling within the cell was retained; if no points were present, the cell was assigned a NoData value. This process yielded 10 CHM layers corresponding to distinct vertical strata.
(3)
For each CHM layer, the gray-level co-occurrence matrix (GLCM) based textural metrics were computed at the plot scale. A total of 90 texture features were extracted, including contrast, energy, correlation, mean, variance, standard deviation, entropy, dissimilarity, and homogeneity.
Given the large number of LiDAR-derived variables and the potential for multicollinearity among them, it is necessary to reduce redundancy and identify key predictors that are significantly associated with bamboo tree density and AGB. Previous studies have shown that multiplicative models are particularly effective for estimating forest parameters such as mean height, timber volume, and tree density [44,45]. These multiplicative relationships can be linearized by applying natural logarithmic transformations to both response and explanatory variables, thus allowing for the use of multiple linear regression (MLR). Accordingly, all LiDAR-derived variables, along with bamboo tree density and AGB, were transformed into their natural logarithmic forms prior to analysis.
The variable selection process for the model is as follows: A bivariate correlation analysis was performed for all log-transformed independent variables (i.e., LiDAR-derived variables) and log-transformed response variables (tree density and AGB) across all sample plots. For each pair of significantly correlated variables, only those variables that showed statistically significant correlation with the response variables were retained as the initial predictor set for modeling. This reduced set of predictors was then input into stepwise regression to construct the MLR model. Variables were iteratively included or excluded based on an F-test threshold of 0.1 and a significance level of 0.05. The model with the highest adjusted R2 and the smallest number of predictors was selected as the optimal MLR model. The variables retained in this model were subsequently used as fixed-effect variables in the development of both the mixed-effects models (MEM) and the hierarchical Bayesian models (HBM). To identify appropriate random-effect variables for MEM and HBM, the stepwise regression procedure was repeated independently for each study area, using only the sample plots from that site. This allowed for the incorporation of site-specific variability in the hierarchical modeling framework.

2.6. Development of Bamboo Tree Density and AGB Estimation Models

Tree density and AGB estimation models were developed using different combinations of LiDAR-derived predictors and modeling approaches. Two groups of predictor variables—a regular set and a hybrid set—were tested. The regular set included only regular LiDAR-derived variables such as canopy cover (CC), gap fraction (GF), height percentiles, and point density metrics, while the hybrid set included all variables from the regular set, with the addition of layered texture variables derived from layered CHMs. Three modeling approaches were applied: MLR, MEM, and HBM. These combinations resulted in a total of six modeling scenarios for both tree density and AGB.

2.6.1. Multiple Linear Regression Model (MLR)

MLR uses several explanatory variables to predict the value of the response variable. It provides the contributions of each explanatory variable to the response variable. The formula of MLR is expressed as Equation (2). This study used a stepwise regression process to identify key modeling variables.
y = β 0 + β 1 x 1 + β 2 x 2 + ⋯ + β p x p + ε
where y is the response variable (log-transformed tree density or AGB), x 1 , x 2 , … , x p are explanatory variables (log-transformed LiDAR-derived variables), β0 is the intercept, β1, β2, …, βp are coefficients associated with x 1 , x 2 , … , x p , and ε is the model error.

2.6.2. Mixed-Effects Model (MEM)

MEM is different from traditional MLR; it contains a parameter of random effect, which enables it to handle various types of data, demonstrating great flexibility and effectiveness when dealing with abnormal distribution data [46,47]. It can be expressed as Equation (3):
y = β 0 + ∑ j X j β j + ∑ k Z k b k + ε  
where y is the response variable (log-transformed density and biomass), β0 is the fixed intercept, x 1 , x 2 , … , x p are explanatory variables (log-transformed LiDAR-derived variables), β1, β2, …, βp are coefficients associated with x 1 , x 2 , … , x p , ∑ j X j β j is the fixed effect, representing the joint influence of all explanatory variables X j on the response variable y under an assumption of equal effect in all observations; ∑ k Z k b k is the random effect, representing the differences between groups or individual observations, exhibited by variations in intercept and coefficients among groups; and ε is the model error. In this study, the “sites” were used as groups in MEM, and MEM was implemented using the package “lmer” in the R software 4.4.1 (R Core Team, Vienna, Austria).

2.6.3. Hierarchical Bayesian Model (HBM)

HBM is a statistical modeling method suitable for multilevel or nested structure data. It integrates the likelihood of the observed data with prior distributions of the parameters to derive posterior distributions through Bayes’ theorem [48]. Within the Bayesian framework, priors can be classified into non-informative and informative types [49,50]. Informative priors can enhance model performance [51]. Therefore, obtaining reasonable prior information from external knowledge (such as literature or measured data) is particularly crucial [52]. The fundamental equation of Bayesian inference is as follows:
p θ y = p y θ p θ p ( y )
where p(θ|y) is the posterior distribution of the parameters given the observed data; p(y|θ) is the likelihood function; p(θ) is the prior distribution of the parameters; y denotes the observed data; and θ represents the unknown model parameters.
Compared to traditional Bayesian models, HBM introduces a multilevel structure that allows for parameter sharing across groups. In this study, the “sites” were used as a grouping factor in the HBM. To construct informative prior distributions, model parameters were first estimated using MEM, and the HBM was then fitted using the “brm” package in the R software (R Core Team, Austria). To ensure the stability of the Markov Chain Monte Carlo (MCMC) sampling process and model convergence, the model was run for 10,000 iterations with a burn-in period of 1000 steps, sample chains of 4, and a thinning parameter of 4.

2.7. Evaluation of Model Performances and Prediction of Tree Density and AGB in Typical Sites

The predicted values of tree density and AGB from the developed models were in natural logarithmic form. Therefore, they were transformed back to their original units using the inverse function first. The leave-one-out cross-validation (LOOCV) approach was conducted to evaluate model performance. LOOCV is a special case of k-fold cross-validation [53]. In this method, if there are n samples, n − 1 samples are used to train the model, and the remaining one is used for validation. This process is repeated n times so that each sample is used once for validation. Finally, the evaluation metrics, including the coefficient of determination (R2), root mean square error (RMSE), relative RMSE (rRMSE), and bias (Bias), were calculated to assess the predictive performance of each model developed under different scenarios. A higher R2 along with lower RMSE and rRMSE indicates better model performance, while a Bias closer to zero suggests minimal systematic error.
Based on the model evaluations, the optimal models were identified and then used to predict tree density and AGB in the typical sites. The required input variables were derived from UAV-LiDAR data using a 20 m × 20 m grid (matching the plot size) and were transformed into natural logarithmic form and fed into the selected models to produce spatial estimates of tree density and AGB on a logarithmic scale. The outputs were subsequently transformed back to obtain final estimates of tree density and AGB in their original units across the typical sites.

3. Results

3.1. Analysis of Selected Modeling Variables

The selected variables based on the regular set and the hybrid set (Table 4) indicate that for bamboo tree density modeling, height metrics and structural variables—particularly gap fraction (GF) and the 90th percentile height (H90)—emerged as the most influential predictors when using the regular set. After incorporating layered texture variables, H90 remained a dominant predictor in the MLR and continued to serve as a fixed effect with dissimilarity in the mid-canopy (Diss5) in both the MEM and HBM. Notably, the layered texture metrics contributed substantially as random effect variables in both MEM and HBM, highlighting their values in capturing spatial heterogeneity and fine-scale structural variability in bamboo stands.
The selected modeling variables for AGB were markedly different from those for tree density, with a strong emphasis on density metrics and layered texture features. Within the regular set, the MLR retained only the structural variable GF as a predictor, whereas the MEM and HBM, in addition to incorporating GF as a fixed effect, further identified CC, D2, and D5 as random effects. In the hybrid set, several layered texture metrics, such as Diss5 and the standard deviation in the lowest layer (Std0), emerged as key predictors in the MLR model and were retained as fixed effects in MEM and HBM. The corresponding random-effect variables included CC, the mean from the mid-canopy (Mean6), and homogeneity in the lowest canopy (Hom0). Unlike the tree density model, the AGB model did not select any height-related metrics, suggesting that structural, density, and texture metrics provide more informative features for estimating AGB.
Across both tree density and AGB models developed using the hybrid set, the selected predictors were predominantly drawn from layered texture metrics, and the total number of selected variables was greater than in the models based solely on the regular set. This result highlights the enhanced descriptive power of the hybrid set. Furthermore, most of the informative texture metrics originated from the lower and mid-canopy layers (e.g., Con3, Hom0, and Diss5) emphasized the crucial role of canopy texture features from these vertical strata in accurately modeling bamboo tree density and AGB.

3.2. Comparative Analysis of Modeling Results

3.2.1. Tree Density Modeling Results

Comparative analysis of tree density modeling results (Figure 3) revealed that hierarchical-based modeling approaches, i.e., MEM and HBM, combined with the hybrid set yielded the highest accuracy, significantly outperforming other model-variable combinations. For the regular set, the MLR showed relatively poor performance with R2 and rRMSE values of 0.15 and 29.08%. In contrast, all three models (MLR, MEM, and HBM) demonstrated notable improvements after incorporating layered texture variables, reducing rRMSE by 5.9%, 2.67%, and 2.98%, respectively. As illustrated in the scatterplots between measured and predicted tree density across sample plots, models using the hybrid set showed predictions more tightly aligned with the 1:1 reference line. These results highlight the limited predictive capability of traditional LiDAR-derived variables alone in modeling tree density. The inclusion of layered textural metrics substantially improved model performance by better capturing the complex canopy structures. Specifically, MEM and HBM using the hybrid sets achieved R2 values of 0.51 and 0.54, and rRMSE values of 22.03% and 21.46%, respectively.

3.2.2. AGB Modeling Results

The AGB estimation models using the regular set consistently yielded poor results regardless of the modeling approaches employed (Figure 4). Specifically, the MLR model exhibited a low R2 value of 0.08 and a high rRMSE value of 27.03%. Both MEM and HBM performed poorly with R2 values of 0.25 and 0.31 and rRMSE values of 24.41% and 23.36%. However, the inclusion of layered textural variables substantially improved the modeling performance across all modeling approaches. As shown in Figure 4, when the hybrid set was used, the MLR model’s R2 increased to 0.17, and its rRMSE value decreased to 25.63%, demonstrating the important role of incorporating layered texture metrics into the regular set in improving AGB modeling. The most significant improvements were observed in the HBM, with the R2 increasing to 0.59 and the rRMSE reducing to 17.97%. Compared to the HBM based solely on the regular set, the HBM based on the hybrid set showed an increase in R2 by 0.28 and a reduction in rRMSE by 5.39%. These results highlighted the substantial contribution of layered texture variables in capturing the complex structural attributes that influence AGB variation in Moso bamboo forests. Furthermore, they demonstrated that integrating advanced structural variables with a hierarchical-based modeling framework leads to the most accurate AGB estimation.

3.2.3. The Performances of Tree Density and AGB Estimation Models in Individual Sites

The above results indicate that HBM utilizing the hybrid set demonstrated superior performance for both tree density and AGB estimation. To further evaluate their spatial generalization, model performance was evaluated across different sites (Table 5, Figure 5). The results revealed that the AGB estimation model exhibited more consistent accuracy across sites than the tree density estimation model, with rRMSE ranging from 13.43% to 21.30%, indicating stable generalization ability. Among the sites, Yong’an stood out with R2 values of 0.62 and 0.80 and rRMSE values of 19.38% and 15.41%, followed by Shunchang with R2 values of 0.79 and 0.53 and rRMSE values of 18.09% and 21.30% for the tree density and AGB models, respectively (Table 5), indicating strong model fit and robust generalizability for these two sites. In contrast, model performances in Deqing and Shanghang varied significantly between the two target variables. The tree density model performed poorly in both sites, with R2 values of only 0.30 and 0.12. Additionally, for the plots with high tree density, the estimation showed certain fluctuations, with both overestimation and underestimation observed (Figure 5(a2,a3)). However, the AGB model showed improvement in the same sites. Both models achieved an R2 of 0.69 and an rRMSE of approximately 14%, which were substantially better than the corresponding tree density estimates. In the Wuyishan region, both the tree density model and the AGB model exhibited notably low accuracy with R2 values of 0.23 and 0.38 and rRMSE values of 24.64% and 20.66%. These findings suggest that tree density and AGB may exhibit different sensitivities to structural variables and modeling approaches, depending on site-specific conditions, such as stand structure complexity, management practices, and environmental heterogeneity. Notably, AGB estimation models appear more reliable than tree density estimation models across sites, potentially due to their broader integration of structural indicators captured by layered texture metrics.

3.3. Spatial Patterns of Tree Density and AGB of Moso Bamboo Forests in Typical Sites

Since the HBMs based on the hybrid set yielded the best prediction performance for both bamboo tree density and AGB, they were applied to estimate tree density and AGB for all typical sites, as illustrated in Figure 6. The predicted tree density and AGB distributions indicated noticeably different patterns among these sites. Shunchang (Figure 6(a1,b1)) and Wuyishan (Figure 6(a4,b4)) exhibited similar spatial patterns with clearly defined high-density/high-AGB zones and strong spatial clustering; Deqing (Figure 6(a2,b2)) exhibited relatively homogeneous patterns with low to moderate values in both tree density and AGB; in contrast, Shanghang and Yong’an had mismatched patterns between tree density and AGB. Shanghang (Figure 6(a3,b3)) showed relatively low tree density but high AGB, whereas Yong’an had the opposite pattern—high tree density and lower AGB, with a relatively uniform spatial distribution pattern (Figure 6(a5,b5)).

4. Discussion

4.1. The Need to Identify Key Variables Representing Bamboo Forest Stand Structure Characteristics

In estimating AGB using LiDAR data, regular metrics such as height, point density, and intensity are commonly employed to build predictive models. These variables have proven effective in capturing AGB variations across different tree species [54,55,56,57], but are not effective for bamboo forests due to similar canopy height features among different sites. This research examined a set of regular metrics, including height percentiles and point density, to construct bamboo tree density and AGB estimation models using MLR, MEM, and HBM, and found generally low predictive performance, with R2 values ranging from 0.15 to 0.40 for bamboo tree density models and from 0.08 to 0.31 for AGB models, which is significantly lower than that for other forest types [58,59,60,61,62]. These findings suggest that the common LiDAR variables have limitations in capturing bamboo forest stand features, and there is a need to identify variables suitable for specific targets.
When utilizing only the regular set, the AGB model built with MLR relied solely on GF, whereas in the MEM and HBM models, GF was selected as a fixed effect, and CC, D2, and D3 were selected as random effects. These variable selection outcomes suggest that height metrics offer limited information for AGB estimation, while point density metrics demonstrate relatively strong explanatory power. This observation may be attributed to the unique growth characteristics of Moso bamboo forests; that is, most Moso bamboo forests have similar heights between 15 and 20 m [63], making it challenging to differentiate AGB variations based solely on height metrics. Conversely, point density metrics, which represent the proportion of point cloud data within various height strata, can effectively capture the structural attributes of bamboo forests, including spatial distribution, culm density, and size. This research found that point density metrics were more significant than height metrics in tree density and AGB modeling, a similar conclusion to that of Cao et al. [37]. Compared to height metrics, the point density metrics accurately reflect the morphological and spatial distribution features of bamboo forests, providing high explanatory power in AGB estimation.
To enhance the bamboo tree density and AGB estimation performance, this study introduced layered texture variables that were derived from point cloud data. Unlike traditional 2D texture metrics, these layered textures capture the vertical structural variations from the ground to the canopy top, offering a comprehensive representation of the forest’s 3D architecture. The concept of layered texture variables aligns with prior research utilizing TomoSAR data, which demonstrated that vertical structural features enhanced AGB estimation accuracy [64]. After incorporating layered texture variables, the prediction accuracy of both the tree density and AGB models improved considerably. Layered texture variables dominated the set of selected predictors, highlighting their effectiveness. Notably, the selected specific variables differed between the two models, reflecting their distinct target characteristics. In the AGB models using MEM and HBM methods, the layered texture variables were mainly derived from the lower layer (Std0, Hom0) and the middle layer (Diss5, Mean6), which can capture the growth status and spatial distribution of bamboo culms. Given that Moso bamboo stem biomass accounts for approximately 75% of total AGB [65], these variables are particularly informative, enhancing the precision of AGB estimation. In contrast, the tree density model selected layered texture variables not only from the lower and middle layers (Con3, Diss5) but also from the upper layer (Cor8). The upper-layer texture variables primarily reflect the bamboo canopy, providing information on canopy structure, thereby improving tree density estimation. Overall, layered texture variables serve distinct functions in the two models: the AGB model places greater emphasis on bamboo culms, while the tree density model captures both culm distribution and canopy characteristics, illustrating the value of multiscale structural information in forest modeling.

4.2. The Importance of Selecting an Appropriate Modeling Approach

When modeling variables are determined, another concern is selecting a suitable modeling algorithm to establish bamboo tree density and AGB estimation models. The comparative analysis of employing MLR, MEM, and HBM methods indicates that both MEM and HBM consistently outperformed MLR in terms of modeling performance. When using only the regular variable set for modeling, the prediction accuracy of MLR was very poor, with R2 values of 0.15 and 0.08 for the tree density and AGB models, respectively. After incorporating the layered texture variables, the accuracy exhibited limited improvement. This indicates that, as a simple regression model, although the layered texture variables contain valuable information about the internal structure of Moso bamboo forests, MLR lacks the capability to effectively capture their complex and nonlinear interactions. Consequently, its ability to leverage these advanced features for improving estimation is constrained.
The hierarchical structure of MEM and HBM allowed both models to improve estimation accuracy with the addition of layered texture variables. Notably, HBM outperformed MEM in both tree density and AGB. The fundamental distinction between HBM and MEM lies in their treatment of model parameters: MEM treats the fixed effects as deterministic constants, while the random effects follow a specified probability distribution. Bayesian methods treat all parameters as random variables and assign corresponding probability distributions [66,67]. The key strength of the HBM framework is its use of prior distributions for parameters, which allows the model to incorporate prior knowledge during estimation [68,69]. This probabilistic formulation likely contributes to HBM’s superior performance. The Bayesian framework has advantages over MEM: the incorporation of priors provides an additional layer of regularization, which is particularly beneficial when modeling complex and diverse ecological systems where predictor variables (e.g., layered texture metrics) may exhibit nonlinear relationships. These priors help prevent overfitting to noise. As highlighted by Zapata et al. [69], Bayesian methods are particularly beneficial in situations with small sample sizes, as prior information can help mitigate the uncertainty caused by limited data. The findings of this study confirm the value of HBMs in enhancing model robustness and performance under such conditions. By providing posterior distributions for small-area parameters, HBM enables parameter inference without relying on potentially unrealistic asymptotic assumptions, which can yield more stable and precise estimates, thereby reducing the risk of extreme predictions for atypical plots [70].
Compared with previous studies, the HBMs in this research demonstrated superior performance in estimating both tree density and AGB. For example, Pearse et al. [71] reported an R2 of 0.48 and an rRMSE of 34.2% for tree density using LiDAR data, and an R2 of 0.42 and an rRMSE of 36.1% using optical satellite data with elastic net regression in New Zealand forests. In contrast, the HBM for AGB in this research achieved an R2 of 0.59 and an rRMSE of 17.97%, outperforming models that relied solely on spectral data [72]. While the model’s accuracy was slightly lower than that reported by Zhang et al. [50], who achieved an R2 of 0.89 for Moso bamboo AGB estimation using a random forest (RF) model through the combination of LiDAR and Sentinel-2 data, their model included 36 predictor variables, which may limit its interpretability and transferability. In comparison, the HBM employed only five key variables, achieving competitive accuracy while maintaining simplicity, robustness, and greater potential for application across different sites.

4.3. The Need to Combine Multi-Site UAV-LiDAR and Sample Plots

Previous studies on estimating forest structural parameters such as AGB typically relied on sample data from a single region. The models developed in this way often achieve good accuracy within a specific study area; however, their applicability to other regions was unclear. In reality, it is often difficult to collect a large number of sample plots within a single site, especially when UAV flight coverage is limited, making it challenging to construct a reliable estimation model. To overcome this limitation, integrating sample data from multiple regions can be an effective strategy to expand the training dataset [41]. This strategy increases the overall sample size, but it introduces new challenges; for instance, variations in topography, climate, and management types across regions introduce heterogeneity into the data. Simple regression methods struggle to account for both interregional differences and shared patterns, potentially resulting in poor model performance for certain regions and a decline in overall prediction accuracy. Hierarchical-based modeling methods such as MEM and HBM provide effective solutions to this problem [41]. These models can account for both overall trends and region-specific variations by allowing parameters to vary across regions. HBM can leverage information from other regions to improve prediction stability and address the issue of sample imbalance, which is especially useful when certain regions have a limited number of samples [67].
This research examined modeling methods based on samples from five typical regions in Fujian and Zhejiang Provinces, covering three climatic zones: northern, central, and southern subtropical zones. The significant variations in climate, ecological conditions, and management practices among these regions introduced strong heterogeneity, posing substantial challenges for unified modeling. The results demonstrate that hierarchical-based modeling methods outperformed traditional MLR in terms of estimation accuracy (Figure 3 and Figure 4), underscoring the importance of adopting a hierarchical-based modeling strategy when dealing with multi-site data. Among the hierarchical-based methods, HBM not only achieved higher overall accuracy than MEM but also exhibited greater robustness and stability across different sites. This highlights HBM’s strong generalizability, particularly in the presence of sample imbalance. In addition, as mentioned above, different regions are characterized by distinct climatic conditions, topography, and management practices, all of which may affect the growth of Moso bamboo forests. Although such factors were not considered in the modeling in this study, it is undeniable that they may exert a certain degree of influence on the estimation results of bamboo tree density and AGB. Therefore, incorporating these variables in future studies may help further explain inter-site differences and improve the accuracy of UAV-LiDAR–based estimation of bamboo forest structural parameters.

5. Conclusions

Tree density and AGB estimation using UAV-LiDAR data is typically conducted at the individual site. However, the limited number of sample plots within the relatively small extent of a study area poses a great challenge to the development of a robust and reliable estimation model, especially for bamboo forests, which exhibit uniform tree height and unique stand structures. This research examined the integration of samples from five typical sites across Fujian and Zhejiang Provinces and evaluated three modeling approaches (MLR, MEM, and HBM) under two data scenarios: the regular set and the hybrid set. The results showed that (1) the incorporation of layered texture variables and regular set improved modeling performance; (2) the HBM delivered the highest predictive performance, particularly for AGB estimation, achieving an R2 of 0.59 and an rRMSE of 17.97%, with strong generalizability across sites (rRMSE between 13.43% and 21.30%); and (3) hierarchical-based modeling methods proved effective for integrating multi-site samples, expanding the training dataset and improving model representativeness and transferability, thereby demonstrating their feasibility and robustness as a modeling strategy. These findings highlight the potential of using hierarchical-based approaches based on the hybrid set to address limitations in sample size and forest heterogeneity, offering new insights into accurate tree density and AGB estimation for Moso bamboo forests.

Author Contributions

X.L.: data curation; formal analysis; methodology; resources; software; validation; writing—original draft. G.L.: formal analysis; methodology; project administration; writing—review and editing. L.L.: data curation; resources; writing—review and editing. D.L.: conceptualization; data curation; formal analysis; funding acquisition; investigation; methodology; project administration; resources; supervision; visualization; writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Key R&D Program of China [#2021YFD2200400102].

Data Availability Statement

Due to confidentiality agreements, sample plots and LiDAR data used in this research can only be made available to bona fide researchers subject to a nondisclosure agreement. For details of these data and how to request access, please directly contact Professor Dengsheng Lu at Fujian Normal University.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Location of the five selected sites in Fujian and Zhejiang Provinces.
Figure 1. Location of the five selected sites in Fujian and Zhejiang Provinces.
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Figure 2. Flowchart of modeling Moso bamboo tree density and aboveground biomass (MBF—Moso bamboo forest; CHM—canopy height model; GLCM—gray level co-occurrence matrix).
Figure 2. Flowchart of modeling Moso bamboo tree density and aboveground biomass (MBF—Moso bamboo forest; CHM—canopy height model; GLCM—gray level co-occurrence matrix).
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Figure 3. Scatterplots between measured and predicted tree density based on models constructed using different scenarios. (a,b) represent the modeling results using the regular set and the hybrid set, respectively; 1, 2, and 3 represent MLR, MEM, and HBM, respectively. R2 stands for the coefficient of determination, RMSE stands for the root mean square error with a unit of culms/ha, rRMSE stands for relative RMSE; the unit of Bias is culms/ha.
Figure 3. Scatterplots between measured and predicted tree density based on models constructed using different scenarios. (a,b) represent the modeling results using the regular set and the hybrid set, respectively; 1, 2, and 3 represent MLR, MEM, and HBM, respectively. R2 stands for the coefficient of determination, RMSE stands for the root mean square error with a unit of culms/ha, rRMSE stands for relative RMSE; the unit of Bias is culms/ha.
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Figure 4. Scatterplots between measured and predicted aboveground biomass of Moso bamboo forest plots from the models based on different variable sets and modeling approaches. (a,b) represent the models using the regular set and the hybrid set, respectively; 1, 2, and 3 represent MLR, MEM, and HBM, respectively. R2 stands for the coefficient of determination, RMSE stands for the root mean square error with a unit of Mg/ha, rRMSE stands for relative RMSE; the unit of Bias is Mg/ha.
Figure 4. Scatterplots between measured and predicted aboveground biomass of Moso bamboo forest plots from the models based on different variable sets and modeling approaches. (a,b) represent the models using the regular set and the hybrid set, respectively; 1, 2, and 3 represent MLR, MEM, and HBM, respectively. R2 stands for the coefficient of determination, RMSE stands for the root mean square error with a unit of Mg/ha, rRMSE stands for relative RMSE; the unit of Bias is Mg/ha.
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Figure 5. Performance of the hierarchical Bayesian models using the hybrid set for estimating Moso bamboo tree density and aboveground biomass (AGB) across different sites. (a,b) represent the tree density model and the AGB model; 1–5 represent Shunchang County, Deqing County, Shanghang County, Wuyishan National Park, and Yong’an County, respectively.
Figure 5. Performance of the hierarchical Bayesian models using the hybrid set for estimating Moso bamboo tree density and aboveground biomass (AGB) across different sites. (a,b) represent the tree density model and the AGB model; 1–5 represent Shunchang County, Deqing County, Shanghang County, Wuyishan National Park, and Yong’an County, respectively.
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Figure 6. Estimated Moso bamboo tree density and aboveground biomass using a hierarchical Bayesian model based on the hybrid set in the selected typical sites. (a,b) represent the estimated tree density (culms/ha) and estimated aboveground biomass (Mg/ha). 1–5 represent Shunchang County, Deqing County, Shanghang County, Wuyishan National Park, and Yong’an County, respectively.
Figure 6. Estimated Moso bamboo tree density and aboveground biomass using a hierarchical Bayesian model based on the hybrid set in the selected typical sites. (a,b) represent the estimated tree density (culms/ha) and estimated aboveground biomass (Mg/ha). 1–5 represent Shunchang County, Deqing County, Shanghang County, Wuyishan National Park, and Yong’an County, respectively.
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Table 1. Characteristics of the five selected sites.
Table 1. Characteristics of the five selected sites.
Study AreasLocationsTerrains
Deqing
County		Northwest of Zhejiang ProvinceThe terrain slants from west to east, transitioning from mountains to plains
Wuyishan
National Park		Junction of Fujian and Jiangxi ProvincesUndulating terrain with elevation ranging from 350 to 2158 m
Shunchang
County		Northwest Fujian ProvinceDominated by mountains and hills, with an average elevation of 800 m
Yong’an
County		Central Fujian ProvinceDominated by mountains and hills, with an elevation difference as high as 1500 m
Shanghang
County		Southwest Fujian Province, a transitional zone from the central to the south subtropical regionDominated by medium and low mountains
Table 2. Summary of collected sample plots and UAV-LiDAR data.
Table 2. Summary of collected sample plots and UAV-LiDAR data.
Study AreasNo. of Sample PlotsPlot Collection DatesTree Density
(Culms/ha)		Aboveground Biomass
(Mg/ha)		UAV-LiDAR Data
MeanStandard DeviationMeanStandard DeviationAcquisition DatesPoint Density (ps/m2)
Deqing62024.053816.71083.465.2615.832024.05890
Wuyishan122023.012683.3765.060.7415.532022.12170
Shunchang122024.082727.11102.756.7917.362024.08166
Yong’an132024.083176.9973.557.3820.202024.081076
Shanghang72022.093548.11083.365.2615.782022.1098
Table 3. Features derived from LiDAR point clouds.
Table 3. Features derived from LiDAR point clouds.
Variable TypesNo.VariablesDescription
Regular
variables		26GF (gap fraction)The ratio of the number of points with a z value lower than 2 m to the total number of points within a plot.
CC (canopy cover)The ratio of the number of first return points from vegetation to the total first return points within a plot.
H1, H5, H10, H20, H25, H30, H40, H50, H60, H70, H75, H80, H90, H95Ranking all points from the low to the high, x% is the height position where x% points are located with a plot.
D0, D1, D2, D3, D4,
D5, D6, D7, D8, D9		Dividing point clouds within a plot into 10-layer bins with an equal height, the ratio of the number of points in a particular bin to the total number of points
Layered
textural variables		90Coni, Enei, Cori, Meani, Vari, Stdi, Enti, Dissi, HomiDividing point clouds within a plot into 10-layer bins based on height percentiles, creating corresponding layered CHMs, from which textural features—contrast, energy, correlation, mean, variance, standard deviation, entropy, dissimilarity, and homogeneity—were calculated.
Note: i represents the i-th layer from the bottom to the top according to CHM percentiles (10, 20, …, 100), ranging from 0 to 9.
Table 4. Summary of selected modeling variables for tree density and AGB estimation.
Table 4. Summary of selected modeling variables for tree density and AGB estimation.
DataModelsTree DensityAGB
Regular variable
set		MLRGF, H90GF
MEM, HBMFixed effect: GF, H90
Random effect: CC, D1, H50		Fixed effect: GF
Random effect: CC, D2, D5
Hybrid variable
set		MLRDiss5, H90Diss5, Std0
MEM, HBMFixed effect: Diss5, H90
Random effect: Con3, CC, Cor8		Fixed effect: Diss5, Std0
Random effect: CC, Mean6, Hom0
Notes: The regular set includes metrics directly derived from LiDAR point clouds; the hybrid set includes the regular set and layered textural metrics.
Table 5. Comparative analysis of HBMs for tree density and AGB estimation across sites.
Table 5. Comparative analysis of HBMs for tree density and AGB estimation across sites.
Study AreasShunchangDeqingShanghangWuyishanYong’an
TD
(Culms/ha)		AGB
(Mg/ha)		TD
(Culms/ha)		AGB
(Mg/ha)		TD
(Culms/ha)		AGB
(Mg/ha)		TD
(Culms/ha)		AGB
(Mg/ha)		TD
(Culms/ha)		AGB
(Mg/ha)
R20.790.530.300.690.120.690.230.380.620.80
RMSE493.3312.101024.348.76589.868.58661.3112.55615.848.84
rRMSE (%)18.0921.3026.8413.4316.6214.7724.6420.6619.3815.41
Bias−45.57−0.2469.31−2.20−38.12−0.91−22.760.07−132.82−1.16
Notes: R2—coefficients of determination; RMSE—root mean square error; rRMSE—relative RMSE; TD—tree density; AGB—aboveground biomass; the unit of RMSE and Bias for TD is culms/ha, and the unit of RMSE and Bias for AGB is Mg/ha.
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Liu, X.; Li, G.; Li, L.; Lu, D. Modeling Moso Bamboo Tree Density and Aboveground Biomass Using Multi-Site UAV-LiDAR Data. Remote Sens. 2026, 18, 115. https://doi.org/10.3390/rs18010115

AMA Style

Liu X, Li G, Li L, Lu D. Modeling Moso Bamboo Tree Density and Aboveground Biomass Using Multi-Site UAV-LiDAR Data. Remote Sensing. 2026; 18(1):115. https://doi.org/10.3390/rs18010115

Chicago/Turabian Style

Liu, Xinyao, Guiying Li, Longwei Li, and Dengsheng Lu. 2026. "Modeling Moso Bamboo Tree Density and Aboveground Biomass Using Multi-Site UAV-LiDAR Data" Remote Sensing 18, no. 1: 115. https://doi.org/10.3390/rs18010115

APA Style

Liu, X., Li, G., Li, L., & Lu, D. (2026). Modeling Moso Bamboo Tree Density and Aboveground Biomass Using Multi-Site UAV-LiDAR Data. Remote Sensing, 18(1), 115. https://doi.org/10.3390/rs18010115

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