A Concise Approach to Characterizing the Distribution of Canopy Leaf Mass per Area in Broad-Leaf Species Based on Crown Three-Dimensional Position and Vegetation Index

Abstract

Leaf mass per area (LMA) represents the allocation of carbon resources per unit leaf area, which is closely related to the photosynthetic capacity of tree leaves. Clarifying the distribution features of LMA is very useful in understanding nutrient and energy transmission and photosynthetic capacity in the canopy. To this aim, the leaf samples of varied forest types were collected, and LMA and related spectral data were measured. The Partial Least Squares (PLS), Linear Mixed Models (LMM), Support Vector Machine Regression (SVM), and Random Forest (RF) methods were used to establish a new model of three-dimension LMA prediction by using vegetation index, DBH, and the vertical and horizontal position of leaves in this study. The results found that the LMA varies significantly with the change in the spatial position of the leaves and horizontal distance to the tree trunk. Statistically speaking, changes in LMA were not significantly related to the direction where the leaves were located. The best model of 3D LMA estimation was RF with a 10-fold R² value of 0.939. Compared to the RF model, the maximum and minimum of R² of 10-fold testing of other models increased by 23.75% and 55.87%. The results indicated that RF has a strong generalization ability and can predict the LMA distribution in 3D with a high accuracy. This study showed a reference for LMA 3D feature distribution and is helpful in clarifying the photosynthetic capacity of the canopy.

1. Introduction

Recent scientific observations reveal a troubling rise in extreme weather phenomena [1], drawing unprecedented attention to the pressing issue of carbon sinks [2]. In this context, the Leaf Economic Spectrum (LES) of vegetation provides a clear reflection of the forest carbon sink, which plays a large role in terrestrial ecosystems [3]. LMA (Leaf Mass per Area) is a crucial component of the leaf economic spectrum, representing the amount of dry matter resources invested by plants per unit leaf area and describing the characteristics of the resource allocation strategies of the leaf. The plant LMA is a utilization pattern of carbon jointly determined by genes and environment, which can reflect the ecological niche of plants [4]. LMA has been proposed to determine the construction cost of a single leaf in the growth model, while biomass allocation has also be determined by leaf area and LMA in previous research [5]. LMA is defined by the leaf dry mass and the leaf area, which are significantly related to the photosynthetic process. Therefore, LMA is an important parameter for estimating plant leaf photosynthetic capacity and constructing vegetation nutrient budget models [6,7,8,9]. The LMA of plants can reflect the maximum photosynthetic rate and adaptive capacity of plants to their environment [7,10,11]. And it has been used to represent the responses of plants to stress in some studies [12,13]. LMA varies greatly among different vegetation types, and evergreen plants often have a larger LMA due to their thicker leaves compared with deciduous plants [9]. However, there is still a huge space for improvement in the accuracy of tree species identification for individual trees over larger areas. Even within the same species, LMA can be influenced by environmental factors such as soil composition, water availability, and CO₂ concentration [11,14,15]. Therefore, estimating the LMA distribution among a canopy at a large scale is significant.

Traditional analyses tend to consider the canopy as a big-leaf-structure and disregard the differential physiological and environmental resource gradients within the canopy. Consequently, more recent studies have attempted to explain within-canopy heterogeneity in leaf traits [16,17,18]. Thus, developing a new method to give a 3D estimate of LMA in canopy would be very useful for variations in three-dimensional LMA changes within the canopy. LMA is adjusted by plants according to the light gradient in the canopy, affecting the canopy nitrogen distribution [19]. According to prior investigations, the spatial distribution of leaf LMA exhibits a robust correlation with the distribution of leaf N per area (Narea) [20,21]. An accurate estimation of three-dimensional leaf mass per area (LMA) will enhance our understanding of nitrogen allocation strategies in plants, thereby allowing for a more precise assessment of photosynthetic efficiency. Results of previous research on the vertical distribution of LMA within the plant canopy showed that there was a notable decline in LMA from the upper to lower canopy parts [22]. This trend has been attributed to gradient fluctuations in light and water potential within the woody tissue in the canopy, and the water potential changes have even more of an effect on LMA variation than changes in light [23]. Besides this, seasonal variation is also an important factor affecting leaf traits [24]. Meanwhile, other studies have focused on the temporal and spatial dynamics of LMA within plant canopies, and results indicate that spatial correlations are more important than seasonal influences in LMA estimation [25]. It is beneficial that accurate three-dimensional (3D) LMA estimation is essential for assessing vegetation canopies.

Remote sensing technology has the ability for estimation at a local or large scale. As a part of remote sensing, the UVA platform has also been widely used for parameter estimation or monitoring environmental features. UAV-derived canopy height models (CHMs) using RGB imagery to estimate solar radiation showed a high consistency with hemispherical photography with an R² of 0.7. And UAV photogrammetry has been proposed as an alternative for forest light environment assessment [26]. This information was then merged with regularly obtained LMA data from imaging spectroscopy, ultimately yielding a higher-precision estimation of canopy LMA [27]. In other studies, the vertical canopy was divided into nine equal parts, resulting in three layers: upper, middle, and bottom. Leaves are randomly collected from each layer. The result was basically consistent with those of previous studies [18]. Nonetheless, research delving into the 3D distribution of LMA within vegetation canopies has been limited, with most studies solely focused on vertical shifts. Previous research on specific leaf area (SLA), the reciprocal of LMA, has investigated leaf area’s vertical and horizontal distribution [28]. A model of LMA for a specific layer at the top of the canopy has been established, which allows us to consider the model as based on the vegetation index related with LMA [29]. Hence, this paper offers an approach based on vertical and horizontal parameters. By incorporating leaf position within the canopy, description of the tree size (DBH and tree height) and vegetation index related to LMA, we generate 3D LMA data which accurately reflect the LMA distribution throughout the canopy.

This study aims to develop an LMA inversion model applicable to most broad-leaf tree species within the vegetation canopy in the region by deploying Hs (the height of the sample point), HD (horizontal distance from the sample point to the trunk), tree height and DBH (diameter at breast height), which represent the 3D position within the canopy and tree size as reference indicators respectively. This study used the normalized parameter RDINC (relative depth into the crown)—based on tree height, subbranch height, and sampling height—and mHD (mean relative horizontal distance)—based on the E-W diameter or N-S diameter. By combining the acquired vegetation index related with LMA data from remote sensing with the LMA distribution in this study, a more precise prediction of LMA values at various positions within the canopy could be generated. Such an approach might increase the accuracy of models that utilize LMA as a parameter for vegetation assessment.

2. Materials and Methods

2.1. Study Area

Maoershan Forest Farm (45°02′20″–45°18′16″ N, 127°18′00″–127°41′06″ E), located in the northwest of Shangzhi City, Heilongjiang Province (Figure 1), in the northeast of China, was founded in 1958. This region is mostly mountainous and hilly, with slopes ranging between 10 and 15°. The highest altitude can reach 799 m, the lowest can reach 246 m, and the mean altitude is around 426 m. The climate of this region belongs to the middle temperate continental monsoon climate zone. January is the coldest month, with an average temperature of −20.2 °C, while July records the highest average temperature of 21.6 °C. The mean annual temperature stands at 2.5 °C. The mean annual precipitation is around 400~650 mm. The annual sunshine duration is around 2300 h. The vegetation cover is mainly the natural secondary forest formed after the destruction of the Primitive Korean pine forest. The main tree species include the following: Pinus koraiensis Siebold et Zuccarini, Pinus sylvestris var. mongolica Litv., Picea koraiensis Nakai, Fraxinus mandschurica Rupr., Juglans mandshurica Maxim, Quercus mongolica Fisch. ex Ledeb., Tilia amurensis Rupr., Ulmus davidiana Planch. var. japonica (Rehd.) Nakai, and Betula platyphylla Sukaczev, along with more than 10 additional species.

2.2. Data Acquisition

The experiment was carried out in the Maoershan Forest Farm from July to August 2021. During field sampling, eight rectangular plots (each 0.06 ha, 20 m × 30 m) were established, with each plot representing a single target species. For each species, several samples were collected to ensure that all target species were represented across the study plots. The eight sample plots share similar stand density (1200–1500 stems per hectare) and tree species composition (mainly broad-leaf trees), and the main soil type across all plots is dark brown forest soil. Based on the team’s previous tree-by-tree survey results of multiple plots, we determined the dominant broad-leaf species by counting the number of trees with DBH (diameter at breast height) > 5 cm in the inventory data. Then, two~three upper, healthy dominant trees were selected from the dominant species as the test trees: those with symmetrical growth (leaf direction balanced distribution), healthy growth, and those free of diseases and pests. For eight species, we collected and analyzed two or three samples per species and 10 leaves at each of the 12 sampling positions to allocate the data. In order to reduce the error caused by the relief of the terrain, the sample plots were all selected in an area with a small slope, and the four corners of each plot were located and recorded by the SOUTH RTK (SOUTH Inc., Guangzhou, China) instrument.

Eight species of broad-leaved tree species in Northeast China were selected for the experiment: Betula platyphylla Suk., Tilia amurensis Rupr., Juglans mandshurica Maxim., Phellodendron amurense Rupr., Quercus mongolica Fischer. ex Ledebour., Fraxinus mandschurica Rupr., Populus davidiana Dode, and Ulmus davidiana Planch var. japonica (Rehd.) Nakai. These samples were kindly provided by Maoershan Forest Farm.

During sampling, the canopy of each sample tree was divided into three equal layers according to the canopy thickness, and a number of healthy and pest-free leaves were selected from four directions of east, south, west, and north in each layer. We used an averruncator to collect the branch; filled a form with the name of the plot, tree species, the height of the tree, the height of the sample, the height of the lowest branch, the horizontal distance from the sample point to the trunk, the diameter at breast height, the East–West crown diameter, the North–South crown diameter, and the coordinates of the tree; and named them according to the species–number–layer–orientation format. The twelve samples were collected from each tree and the branches were placed in plastic bags marked according to the species–number–layer–orientation format (Figure 2).

After finishing the collection and marking work, we returned to the laboratory as quickly as possible. We dipped the ends of the collected branches into water, chose 10 randomly sized leaves from the collected branches and placed them into a plastic bag, and then placed them in an ice-chilled styrofoam container after naming them in the same format. Subsequently, spectral measurements of these leaves were conducted using the SVC HR-1024i spectrometer (Spectra Vista Corporation, Poughkeepsie, NY, USA) (Figure 3).

During spectral measurements, the indoor environment was carefully controlled to ensure the absence of ambient light sources and the HLG-150 fiber optic light source (Nanjing Chunhui Science Technology Industrial Co., Ltd., Nanjing, China) was fixed as the unique incident light source. Each leaf’s reflection spectrum was measured after using a whiteboard placed on a black substrate to reference the radiation (Figure 4). The leaf reflectance spectrum was measured within the wavelength range of 400 nm to 2500 nm. Five measurements were taken for each leaf and an average was taken, with 5 to 10 repeated experiments conducted for each combination of layer and direction. Following spectral measurement, data were exported and resampled to a 10 nm spectral resolution using the built-in software of SVC HR1024i (version 1.21.14, Spectra Vista Corporation, Poughkeepsie, NY, USA). The output was formatted as ‘*.csv’ files for subsequent statistical analysis.

After the steps mentioned above, the Li-3000c was used to count leaf area and record the leaf area of the samples. Then, the leaves were put in envelopes and named according to the species–number–layer–orientation format, before being put in a 70 °C oven for at least 24 h until they reached a constant weight.

$$\mathrm{LMA}={\displaystyle \frac{DW}{A}}$$

(1)

where DW is the weight of the dry leaf (g), and A is the leaf area (m²).

The weight of the dry leaf of each envelope was measured by electronic scales, and the LMA (Leaf Mass per Area, g/m²) was obtained according to the ratio of the dry weight to the leaf area.

2.3. Data Analysis

To delineate the spatial distribution of leaf blades within the canopy, we employed the mean relative depth into the crown (RDINC) with 10% relative depth increments for every layer (the 80%~100% range was allocated to one piece to balance the data volume) and divided the mean relative horizontal distance from the sample point to the trunk (mHD) into three equally sized segments.

To estimate LMA (Leaf Mass per Area), we chose RDINC, mHD, DBH, and vegetation index as the candidates; we chose tree size and layer as the dummy variables; and four methods were chosen to estimate LMA: PLS (Partial Least Squares Regression), LMM (Linear Mixed Model), SVM (Support Vector Machine), and RF (Random Forest).

The Partial Least Squares (PLS) Regression method represents an advanced approach in multivariate statistical analysis, adept at performing both multivariate linear regression and principal component analysis concurrently. When confronted with challenges such as multicollinearity among variables, a large number of variables with a limited sample size, or heteroscedasticity, using PLS regression confers unmatched advantages over traditional linear regression methodologies. However, the PLS regression model cannot perform variable selection, resulting in an overly complex model when incorporating all variables. Therefore, this study performed a preliminary variable-importance ranking using the random forest algorithm before model construction. By including only the variables with higher importance in the model, the study aimed to enhance the usability and accuracy of the model.

Linear Mixed Model (LMM): This extension of Generalized Linear Models encompasses both fixed and random effects. By modeling fixed effects across different levels of random effects, an LMM can offer improved explanatory power for analyzing data. In this study, diameter at breast height (DBH) was classified into 5 cm intervals as a random effect, while vegetation indices and the three-dimensional positions of leaves within the canopy were used as fixed effects in constructing the Linear Mixed Model (LMM). This approach aimed to capture the differences in three-dimensional LMA prediction models across different DBH classes, thereby enhancing the predictive capability of the model.

Support Vector Machine Regression (SVM): The Support Vector Machine (SVM) model represents a relatively recent machine learning technique that has been extensively employed to address classification and regression problems. The fundamental principle of SVM involves the use of nonlinear mapping to project the original data into a high-dimensional space, wherein a hyperplane is identified. This hyperplane, supported by several vectors known as support vectors, maximizes the distance from the data points in the training set. By fine-tuning various hyperparameters, SVM achieves a balance between model generalization and overfitting. In the SVM model constructed for this experiment, R was utilized to perform a grid search for the cost and epsilon hyperparameters, aiming to minimize the Mean Absolute Error (MAE). The optimal hyperparameters, corresponding to the grid points where the MAE is lowest, were selected. The cost parameter controls the penalty factor, determining the tolerance for misclassification in the SVM model; a high cost may lead to overfitting by overemphasizing the correct classification of each sample, whereas a low cost may reduce model accuracy. The epsilon parameter defines the tolerance margin within which prediction errors are permitted; a large epsilon includes more points within the tolerance margin, potentially decreasing model accuracy, while a small epsilon reduces tolerance for errors, which may also result in overfitting. Thus, these hyperparameters are crucial for adjusting the complexity and generalization ability of the model to achieve optimal performance.

Random Forest Model (RF): The core concept of random forests involves aggregating the classification results of several weak classifiers through voting to generate a robust classifier. By employing bootstrapped random sampling with replacement for training data selection, each tree within the forest is trained on a different subset of the data. This ensemble machine learning algorithm is suitable for analyzing nonlinear relationships among complex variables. The aforementioned four methods were all subjected to cross-validation for accuracy assessment, aiming to identify the optimal model for predicting the three-dimensional distribution of LMA.

In this study, we constructed models for Leaf Mass per Area (LMA) using H (sampling height), HD (horizontal distance from leaf to trunk), and DBH (diameter at breast height), along with vegetation indices, which are listed in the variable ranking for correlation with LMA (importance ranking was integrated using random forest). The top 15 vegetation indices were selected for model construction (

Table 1. The vegetation index used in this study.

Name	Formula *	Ref
Red Edge	Max first derivative in (R680~R760)	[30]
Yellow Edge	Max first derivative in (R560~R640)	[30]
Blue Edge	Max first derivative in (R490~R530)	[30]
ReMSR	${\displaystyle \frac{\frac{R_{750}}{R_{705}}-1}{\frac{R_{750}}{R_{705}}+1}}$	[31]
RDVI	${\displaystyle \frac{R_{800}-R_{670}}{\sqrt{R_{800}+R_{670}}}}$	[32]
TVI	${\displaystyle \frac{120\times \left(R_{750}-R_{550}\right)-200\times \left(R_{670}-R_{550}\right)}{2}}$	[33]
RVSI	${\displaystyle \frac{\left(R_{750}+R_{710}\right)}{2}}-R_{730}$	[34]
MCARI1	$1.5\times \left[1.2\times \left(R_{712}-R_{670}\right)-0.5\times \left(R_{712}-R_{550}\right)\right]\times {\displaystyle \frac{R_{712}}{R_{670}}}$	[35]
MCARI2	${\displaystyle \frac{1.5\times \left[1.2\times \left(R_{712}-R_{670}\right)-0.5\times \left(R_{712}-R_{550}\right)\right]}{0.5\times \left[2\times R_{800}+1-\sqrt{{\left(2\times R_{800}+1\right)}^2-8\times \left(R_{800}-R_{670}\right)}\right]}}\times {\displaystyle \frac{R_{712}}{R_{670}}}$	[35]
MTVI1	$1.5\times \left[1.2\times \left(R_{712}-R_{550}\right)-2.1\times \left(R_{670}-R_{550}\right)\right]$	[35]
MTVI2	${\displaystyle \frac{1.5\times \left[1.2\times \left(R_{712}-R_{550}\right)-0.5\times \left(R_{670}-R_{550}\right)\right]}{0.5\times \left[2\times R_{800}+1-\sqrt{{\left(2\times R_{800}+1\right)}^2-8\times \left(R_{800}-R_{670}\right)}\right]}}$	[35]
ARSIs	${\displaystyle \frac{R_{660}-R_{650}}{R_{520}-R_{650}}}$	[36]
NDVI(a,b)	${\displaystyle \frac{R_a-R_b}{R_a+R_b}}$	/
RVI(a,b)	${\displaystyle \frac{R_a}{R_b}}$	/
SR(a,b)	$R_a-R_b$	/

* The result based on SVC HR 1024i, Excel 2016 (Microsoft Corporation, Redmond, WA, USA), R (version 4.2.2, R Foundation for Statistical Computing, Vienna, Austria).

).

The ARSIs vegetation index is extracted based on Figure 5. The bands with a correlation value more than 0.1 are taken as the biochemical significant wavelength (Figure 5a blue shadow), the highest R² increment in the biochemical insignificant wavelength is taken as R_spec (Figure 5b red dashed line), the lowest R² in the biochemical insignificant wavelength is taken as the reference wavelength R_ref (Figure 5c red dashed line), and the wavelength corresponding to the maximum value of R_index² in the biochemical significant wavelength (Figure 5d red dashed line) is calculated according to the formula as the reference wavelength R_indi [36].

$${R_{\mathit{Index}}}^2={\left[Correlation\left(\frac{R_{ref}-R_{spec}}{R_{indi}-R_{spec}},Y\right)\right]}^2$$

(2)

Due to the spectral range of the hyperspectral data, a range of 400–1000 nm was selected in this study. A value of 660 nm was chosen as the R_ref, 520 nm was chosen as the R_indi, and 650 nm was chosen as the R_spec.

$$ARSI\mathrm{s}={\displaystyle \frac{R_{\mathrm{ref}}-R_{\mathrm{spec}}}{{{\displaystyle R}}_{\mathrm{indi}}-{{\displaystyle R}}_{\mathrm{spec}}}}={\displaystyle \frac{R_{660}-R_{650}}{R_{520}-R_{650}}}$$

(3)

For the purpose of the article, an additional attribute of ‘tree size’ was created based on the package ‘mclust’ in R to cluster the original trees into ‘big’, ‘medium’, and ‘small’ by Cluster.

$$C\mathrm{luster}={\displaystyle \frac{DB{H}^2\times heigh{t}_{tree}}{4}}$$

(4)

2.4. Validation

The accuracy of the model was evaluated by the parameters below: determination coefficient (R²), root mean squared error (RMSE), and mean absolute error (MAE).

Determination coefficient (R²)

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

(5)

Root mean squared error (RMSE)

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

(6)

Mean absolute error (MAE)

$$MAE={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left|y_i-{\hat{y}}_i\right|}}{\mathrm{n}}}$$

(7)

where $\widehat{y_i}$ is the predicted value, $y_i$ is the observed value, ${\overline{y}}_i$ is the average of observed value, and $n$ is the number of samples.

3. Results

3.1. One-Way ANOVA of LMA for Layers and Directions in Canopy

3.1.1. One-Way ANOVA Between Different Layers Inside Canopy

This research analyzed the spatial distribution features of LMA (Leaf Mass per Area) in the canopy and the results are shown the in table and figures.

Table 2. The distribution of original LMA data for the layers inside the canopy.

	Layer	Max	Min	Average	Std. *
LMA (g/m2)	High	193.72	41.17	87.18	28.17
	Middle	148.75	41.24	78.60	23.71
	Low	135.72	24.75	75.17	22.67

* Standard deviation.

shows the range of LMA for different layers and Figure 6A shows the distribution in different layers of leaf mass per area (LMA); the pairwise comparison (Figure 6B) shows that the mean relative LMA has a significant difference between the high group and the low group, and between the middle group and the low group at the level of p < 0.001 (p = 1.28 × 10⁻⁸ < 0.001).

3.1.2. One-Way ANOVA for Different Directions Inside Canopy

Table 3. The distribution of original LMA data in the directions inside the canopy.

	Direction	Max	Min	Average	Std. *
LMA (g/m2)	E	153.63	41.17	79.63	23.49
	S	157.30	41.24	80.61	25.56
	W	193.72	24.75	83.60	30.57
	N	143.93	32.92	78.23	22.89

* Standard deviation.

shows the range of LMA for different directions and Figure 7A shows the distribution for different directions of leaf mass per area (LMA); the pairwise comparison (Figure 7B) of the mean relative LMA shows an insignificant difference between the directions (p = 0.272 > 0.05). After one-way analysis of variance with the direction and layer data, we concluded that the direction has little relationship with the leaf mLMA.

This demonstrates that leaf mass per area (LMA) at a given canopy position can be sufficiently characterized by its three-dimensional coordinates alone, without requiring consideration of directional effects.

3.2. Frequency Distribution of Data

We divided the canopy vertically into nine sections and horizontally into several segments to describe the trends of LMA (leaf mass per area) with positional blocks. The original data were divided into eight equal parts for the 0%~80% section of RDINC in 10% increments, and into one bigger part for the 80%~100% section (because the points in 80%~90% and the 90%~100% are both far less than other equal parts respectively), after removing errors and fewer than three observations in each group from the box-plot (Figure 8).

Figure 9 shows that in the same layer of RDINC, the mLMA tends to increase with the increase in mHD; in the same layer of mHD, the mLMA tends to decrease with the increase in RDINC. Detail are shown in

Table 4. The mLMA and mHD distribution for the values of RDINC.

Group	RDINC *	mLMA *	mHD *
0%~10%	0.06417	1.0000	0.6544
	0.1458	0.9724	0.5679
10%~20%	0.1613	1.0149	0.8098
	0.2653	0.9625	0.5926
20%~30%	0.2607	1.0413	0.7740
	0.3550	0.8748	0.5206
30%~40%	0.3587	0.9295	0.8634
	0.4278	0.8773	0.3010
	0.4343	0.9559	0.5771
40%~50%	0.4465	0.9096	0.7999
	0.5841	0.9697	0.2849
	0.5462	0.9231	0.5189
50%~60%	0.5432	0.9435	0.8210
	0.6440	0.8861	0.5390
60%~70%	0.6518	0.9230	0.8672
	0.7387	0.8270	0.5687
70%~80%	0.7401	0.8910	0.8596
80%~100%	0.8436	0.7469	0.8045

* RDINC: Relative depth into crown; mLMA: mean relative LMA; mHD: mean relative horizontal distance from point to trunk.

. Each ‘Group’ is divided into 3 parts by mHD in 0%~33%, 33%~66%, and 66%~100%, and remove the fewer than three observations parts.

Figure 9 illustrates that mLMA tends to increase with the increase in mHD, and mLMA tends to decrease with the increase in RDINC. In addition to this, the line in Figure 9a shows a low slope, and p > 0.05 for the relation between mHD and mLMA; the simple linear regression is not significant, so we attempt to use machine learning models and nonlinear models. Nevertheless, the R² value and fact that p < 0.05 show a good result in linear regression in Figure 9b. The blue points and lines correspond to the mean value of each RDINC and mHD group. Therefore, we speculate that mLMA might have some functional relationship with RDINC and mHD.

3.3. Model Establish and Evaluation

In this experiment, four modeling methods were used. Variable selection was performed by conducting correlation tests to rank the independent variables (Figure 10).

The top 15 vegetation indices, along with sampling height (Hs), horizontal distance from sample leaf to the trunk (HD), and diameter at breast height (DBH), were chosen for modeling.

Two models are established in the data preprocessing step: first, we trained a layer categorizer based on tree height, DBH, and sample height; second, we trained a subbranch position prediction model based on tree height and DBH. The two model accuracies are 98.40% (Figure 11a) and 96.39% (Figure 11b).

The Random Forest model consists of two sub-models: 1. a model to estimate the top-layer LMA (leaf mass per area) with the vegetation index and tree height, tree size, and DBH; 2. a model to estimate the distribution of nLMA which is normalized by the top-layer LMA. The final LMA prediction is the product of 1 and 2.

Model accuracy evaluation was conducted using 10-fold cross-validation to find the highest prediction accuracy and the best model was selected for constructing the three-dimensional distribution of LMA.

In this experiment, we are going to select a coefficient of determination R², root mean square error RMSE, and residual analysis p-Value as indicators to evaluate the fitting effect and prediction accuracy of the model. The significance of the RF model in

Table 5. The results of each model.

Method *	Test Max R2	Test Min R2	Test Min RMSE (g/m2)	p-Value
LMM ***	0.649	0.316	11.249	2.544 × 10−6
PLS **	0.448	0.261	17.387	4.036 × 10−3
SVM ***	0.716	0.238	11.689	3.322 × 10−5
RF ***	0.939	0.716	6.325	7.889 × 10 −12

* Significance values: ‘***’ p < 0.001; ‘**’ p < 0.01; ‘*’ p < 0.05.

shows the best test with a cross-validation R² between 0.716 and 0.939 and the lowest RMSE. The test min R² of the LMM model (cross-validation R² 0.316~0.649) is better than that of the PLS model (cross-validation R² 0.261~0.448), and SVM has the lowest test min R² (cross-validation R² 0.238~0.716). The result shows that the LMA prediction based on 3D position and the vegetation index with Random Forest model can describe LMA with a higher accuracy (Figure 12).

3.4. The Result of Prediction

In this study, a crown-like scatter plot was simulated, and interpolation based on the corresponding LMA (Leaf Mass per Area) values of the collected sample points’ relative spatial positions was performed to describe the LMA distribution within the canopy (Figure 13).

We employed a random forest model to predict the three-dimensional LMA of the canopy. The results indicated that relative spatial position could explain at least 30% of the within-canopy LMA variability. By estimating the three-dimensional distribution and multiplying it with the estimated top LMA, we obtained an estimate of the actual LMA, with a ten-fold cross-validated R² value of 0.7387 for the test set. The images of the LMA interpolation and predicted values are shown in Figure 14.

The results of the stratified accuracy validation are presented in Figure 14. The model predictions slightly overestimate LMA for the upper and middle layer, while slightly underestimating it for the lower layer. Overall, the prediction accuracy of the model is highest for the upper layer (R² = 0.888), followed by the lower layer (R² = 0.789) and the middle layer (R² = 0.560). The mean differences between layers are significant, following the distribution pattern of upper > middle > lower, consistent with trends reported in previous studies, thereby lending credibility to the results. To represent the distribution patterns of predicted LMA across different layers visually, each layer was sliced and the corresponding LMA values were normalized to three ranges of 0–0.33, 0.33–0.66, and 0.66–1. This normalization facilitated the clear visualization of the three layers within the z-axis range of 0 to 1. As shown in Figure 15, there is a noticeable increase in LMA with increasing HD (|x|,|y|) across all three layers, with the upper and middle layer exhibiting more pronounced trends. When the predicted LMA at the top layer is high, the model’s estimation accuracy fluctuates, the impact of random errors in the observed values increases, and the confidence in the estimated results decreases.

When the top-layer LMA is less than 125 g/m², the model exhibits relatively stable prediction variability. Additionally, the predicted LMA values for the lower layer are generally lower than the observed values. The overall trend aligns with findings from previous studies, indicating that the model can be effectively used for large-scale predictions.

4. Discussion

In this study, a three-dimension estimation of canopy LMA (Leaf Mass per Area) for broad-leaved tree species in the study area was developed, which offered a possibility for improving the three-dimension accuracy of various vegetation biophysical parameter models with LMA as the parameter in this area. The number of articles on stratification analysis of vertical changes in tree canopy has been increasing in recent years. This study shows a trend that mLMA inside the canopy follows the following trend: upper layer > middle layer > lower layer, which has been found by previous studies [37]. Some studies have shown that considering the three-dimensional differences inside the canopy can offer a better prediction of the canopy NPP [38]. There are many studies on the vertical gradient changes in vegetation canopy parameters. For example, the vertical distribution of vegetation canopy leaves [37], biomass [39], the distribution of forest canopy leaf area [40], the change trend of leaf traits between different layers in the canopy [18], and the distribution of canopy nitrogen and LMA, as affected by the change in vertical ecological factors in the canopy, have been studied [41,42]. Scholars have gradually realized that the spatial structure of the canopy can be an important factor affecting canopy vegetation parameters. In order to improve the utilization rate of light energy, plants will enhance the complexity of canopy structure spontaneously to achieve more light interception and maintain canopy NPP [43,44,45]. The allocation of biomass can also be determined by leaf area and LMA [5]. Obviously, LMA plays an important role and is linked to other vegetation parameters. And its three-dimensional prediction has gradually become more important in the study of the three-dimensional structure of tree canopy; it shows great significance for improving the accuracy of canopy photosynthesis capacity prediction.

It is now generally believed that the photosynthetic capacity of trees is related to the LMA and to the nitrogen distribution of leaves, which are considered important parameters in vegetation photosynthesis [21,46]. Leaf nitrogen content is a probably function of LMA [42]. However, some studies have shown that, unlike LMA, which is simple to measure and has significant changes in canopy position, there is no definite relationship between leaf nitrogen content and changes in canopy position [47]. Moreover, LMA shows a significant light dependence in the canopy, which has also been proved to be one of the important reasons for the three-dimensional variation in LMA in the canopy [48]. The reason for selecting LMA as the prediction target in this study is that LMA can better reflect leaf structure across variations in the plant canopy environment such as light and water gradients, and it is possible for us to predict with a simplified three-dimensional position. The model in this study may significantly streamline the LMA measurement process in regions with intricate terrain features, including those with varied exposure and undulating surfaces.

In a previous study, people used LVA (leaf volume per area) × LD (leaf density) to calculate LMA, but these are leaf structure parameters based on leaf scale, which is difficult to apply when predicting large quantities. Hence, our model uses simple positional parameters and can be used for the estimation of large quantities of LMA with a high accuracy.

However, for the same vertical layer of the canopy, the light and water fluxes at different horizontal positions can be totally different, which is likely to lead to variation in vegetation parameters within the same layer, but there are relatively few relevant studies on this. In our experiment, not only the vertical canopy and environmental changes, but also the horizontal changes in each canopy layer were considered as influencing factors. Leaves in different layers, or even leaves at different horizontal positions in the same layer, have different coping strategies against the changes in light and water flux received. Leaves change their resource allocation strategy, which is then reflected in the vegetation parameters. Although different species respond differently to different environmental factors [11], the accuracy of tree species identification for individual trees over larger areas needs to improve; this paper has constructed a distribution logic that is applicable to a larger range and applicable to all broad-leaved tree species in the area, and the model has a decent prediction accuracy (min 10-fold R² = 0.716).

Recent studies have been conducted on the spatial differences in photosynthetic parameters in different layers and their contribution to the net photosynthetic rate at different positions in the canopy (the canopy has been divided into three layers in the vertical direction—upper, middle, and lower—and two parts in the horizontal direction—inner and outer). After qualitative comparison, the photosynthetic parameters show clear vertical and horizontal gradient distribution [49]. Similar results are shown with this study.

The model obtained in this paper describes the changes in different 3D positions as follows: The LMA increases with the increase in vertical height of the sample point in the canopy and the horizontal distance from the sample point to the trunk. Due to the stronger illumination at higher positions within the canopy and further away from the trunk in the same layer, plants allocate more resources towards building the mechanical tissue of leaves to cope with the water stress caused by intense light at the top of the canopy. The height of the top canopy and the distance from the trunk causes it greater resistance to get water to these places. Therefore, the transpiration pull required by plants to transport water to these places is relatively high. In order to prevent the water potential becoming too low, which may also cause high xylem tension, the plant closes its stomata in advance, which leads to a decrease in photosynthetic capacity in these positions. Previous studies have suggested that the photosynthetic capacity of leaves with a larger LMA tends to be lower [50].

The results obtained in this study are consistent with previous research hypotheses: light and hydraulic gradient affect the three-dimensional distribution of LMA; light and hydraulic power restrict the change in LMA. The higher the sample point is and the farther it is from the trunk, the higher the LMA will be [28]. Previous review articles have summarized plant LMA under environmental stress, showing that plants with a high LMA are more tolerant to stress, which is similar to this study.

It has been proposed that a combination of accurate LiDAR and optical remote sensing can be used for three-dimension estimation of vegetation parameters [51]. The three-dimensional structure of the tree crown was accurately extracted by laser point cloud data in a recent paper, enabling the height of the lowest branches to be located and the layer-wise extraction of the crown radius inside the canopy within different RDINC parts. Notably, an impressive prediction accuracy of 91% was achieved within the RDINC range of 0.15~1, suggesting its potential as a viable alternative method of traditional field measurement [52]. This paper quantitatively estimates the three-dimensional variations in LMA at different canopy positions for dominant broad-leaved tree species in Maoershan Mountain. Combining the LMA of a certain position at the top of the canopy obtained by remote sensing image, the sample point height and distance from the trunk were obtained by LiDAR. Then, the three-dimensional distribution of LMA of the canopy can be estimated by the model obtained in this study. We use the following parameters: sample height and sample distance from the trunk, which could be measured easily to estimate the three-dimensional LMA distribution as accurately and conveniently as possible. In this way, it can be possible to obtain the three-dimensional changes in other important vegetation parameters coupled with LMA, such as light and efficiency, biomass estimation, etc., so as to improve the estimation accuracy of the corresponding parameters.

In addition, some studies have considered the seasonal variation in leaf parameters [24]. Temperature changes also have a great effect on the LMA of plants because of the variation in leaf LVA and LD in response to the transformation of the environment temperature [53]. And only the spatial dimension of LMA was analyzed in this study. However, the level of the response of leaves at different locations to season, age [54], and temperature is not always consistent, which is also a challenge for us in the future.

5. Conclusions

In this study, the 3D LMA (Leaf Mass per Area) estimating method was mentioned. The results showed that LMA decreases with increasing depth and increases with increasing distance between the sample point and the trunk. This research established four methods to estimate LAM and the Random Forest model (RF) achieved the highest accuracy. The R² of 10-fold cross-validation ranged from 0.716 to 0.939. Then, a point cloud simulating the canopy shape was created and interpolated the LMA observations and top-layer LMA to the corresponding points. The LMA distribution of the point cloud was predicted based on its position by the RF model and the corresponding top-layer LMA with an R² of 0.7387. This model effectively describes the LMA distribution of an unknown broad-leaf tree canopy and can be extended to larger scales using LiDAR and optical remote sensing for broader data acquisition, enabling the observation of the three-dimensional distribution of canopy LMA on a larger scale.

The 3D model has a decent accuracy and can be used in more cases of data prediction. However, the tree age, temperature, and the season variation might be variable in different canopy locations; the model might be optimized for this in the future studies.