Uncertainty Analysis of Remote Sensing Estimation of Chinese Fir (Cunninghamia lanceolata) Aboveground Biomass in Southern China

Abstract

Forest aboveground biomass (AGB) is not only the basis for forest carbon stock research, but also an important parameter for assessing the forest carbon cycle and ecological functions of forests. However, there are various uncertainties in the estimation process, limiting the accuracy of AGB estimation. Therefore, we extracted the spectral features, vegetation indices and texture factors from remote sensing images based on the field data and Landsat 8 OLI remote sensing images in Southern China to quantify the uncertainties. Then, we established three AGB estimation models, including K Nearest Neighbor Regression (KNN), Gradient Boosted Regression Tree (GBRT) and Random Forest (RF). Uncertainties at the plot scale and models were measured by using error equations to analyze the influences of uncertainties at different scales on AGB estimation. Results were as follows: (1) The R² of the per-tree biomass model for Cunninghamia lanceolata was 0.970, while the uncertainty of the residual and parameters for per-tree biomass model was 4.62% and 4.81%, respectively; and the uncertainty transferred to the plot scale was 3.23%. (2) The estimation methods had the most significant effects on the remote sensing models. RF was more accurate than other two methods, and had the highest accuracy (R² = 0.867, RMSE = 19.325 t/ha) and lowest uncertainty (5.93%), which outperformed both the KNN and GBRT models (KNN: R² = 0.368, RMSE = 42.314 t/ha, uncertainty = 14.88%; GBRT: R² = 0.636, RMSE = 32.056 t/ha, uncertainty = 6.3%). Compared to KNN and GBRT, the R² of RF was enhanced by 0.499 and 0.231, while the uncertainty was decreased by 8.95% and 0.37%, respectively. The uncertainty associated with the scale of remote sensing models remains the primary source of uncertainty when compared to the plot scale. On the remote sensing scale, RF is the model with the best estimation effect. This study examines the impact of both plot-scale and remote sensing model-scale methodologies on the estimation of AGB for Cunninghamia lanceolata. The findings aim to offer valuable insights and considerations for enhancing the accuracy of AGB estimations.

1. Introduction

Forests represent the most significant terrestrial ecosystems on the planet, accounting for 80% of terrestrial carbon reserves [1]. They play a crucial role in sustaining regional ecosystems and contributing to the global carbon equilibrium [2,3]. Forest biomass serves as a fundamental parameter within forest ecosystems and is a critical indicator for assessing both the structure and functionality of these ecosystems [4]. Total forest biomass is categorized into aboveground and belowground components, with aboveground biomass (AGB) constituting approximately 70% of the overall biomass [5], and has been acknowledged as a significant biodiversity metric that is effective for assessing ecosystem functionality [6].

Methods for estimating forest biomass mainly include traditional field survey methods and remote-sensing-based methods [7]; the traditional method is to obtain forest resource data through field measurements and data statistics, which has the disadvantages of being time-consuming and labor-intensive [8], and there are obvious limitations in the aspects of a large research scope and a long research cycle due to the limitations of time and cost. In contrast, remote-sensing-based methods are widely used in forest AGB estimation because of their rapid, low-cost, large-scale and low-destructive characteristics [9,10]. LiDAR, as an active remote sensing technique with strong penetration into vegetation, has been extensively utilized in the estimation of forest biomass [11,12]. However, due to its high data cost, complex data processing and susceptibility to the limitations of complex terrain, it is not widely used comparatively in regions with complex terrain [13,14]. In comparison, optical remote sensing images are extensively utilized for the estimation of AGB due to their benefits, which include accessibility, extensive spatial coverage and shorter revisit intervals [15,16]. Furthermore, optical remote sensing images exhibit varying spatial and temporal resolutions, as well as differing spectral bands [17], which can be fully utilized for texture features to reflect more accurate feature information [18]. The estimation of AGB at global, continental or national scales typically necessitates the use of medium-resolution data, exemplified by information acquired from the Moderate Resolution Imaging Spectroradiometer (MODIS), for AGB estimation [19]. In contrast, the estimation of AGB at localized scales typically relies on moderate-resolution data. Landsat 8 Operational Land Imager (OLI) data have been extensively utilized for AGB estimation at regional scales due to their extensive coverage, prolonged monitoring capabilities, moderate resolution, and time series analysis capability [20,21]. Previous studies have demonstrated a significant correlation between spectral bands, vegetation indices, transformed images (utilizing principal component analysis) and texture features with AGB. Consequently, these elements can be employed as effective indicators for estimating AGB [22,23]. A lot of scholars [24,25] have utilized Landsat 8 imagery for estimating forest AGB, and there is growing evidence that optical remote sensing techniques play an integral role in forest resource management [26].

Uncertainty encompasses a broad range of concepts, including inaccuracy, fuzziness and ambiguity, among others. In the context of forest ecosystem productivity, which serves as a critical indicator, three primary categories of uncertainty are pertinent to the calculations associated with forest biomass: model uncertainty, measurement uncertainty and sampling uncertainty [27,28]. For example, Fareed and Numata believed that in a dense forest canopy, when the true height of trees exceeds 30 m, there will be an underestimation phenomenon that has an impact on the accurate estimation of AGB [29]. Shettles et al. [30] posited that model uncertainty constitutes the primary source of uncertainty, representing approximately 70% of the overall uncertainty. This study focuses exclusively on examining the uncertainty associated with the model, while measurement and sampling uncertainty were not considered. The uncertainties associated with the model can be categorized into four primary dimensions: the inherent uncertainty of the input variables, the inaccuracies arising from the specification of the model structure, the residual variance error of the model and the errors related to the model parameters. The uncertainty associated with the input variables primarily pertains to the measurement errors of these variables, specifically diameter at breast height (DBH) and tree height (H) [29]. Such errors may be influenced by the measurement instruments employed, the techniques utilized for measurement and the methodologies applied by the individual conducting the measurements. The inaccuracies in establishing the model framework primarily stem from an insufficient application of advanced modeling techniques [31] or validation data [32], meaning that the model form sets incorrectly. Compared with the first two types of errors, the residual variation and parameter errors of models are comparatively less studied. Therefore, we mainly analyzed the residual error of the model and the model parameter errors. The residual error of a model is indicative of its fitting accuracy, which can be quantitatively assessed using the coefficient of determination (R²). The value of R² approaching 1 signifies a superior fit of the model (overfitting cannot be excluded). Additionally, the uncertainty associated with the variation in residuals can be evaluated through the standard deviation of the residuals; however, the outcomes may exhibit variability contingent upon the specific study area and the data utilized. For example, Chen et al. [33] conducted an investigation into the uncertainty associated with spatial scales and emphasized the significance of accounting for the uncertainty in AGB estimates at the plot level when utilizing field plots for the calibration of remote-sensing-based biomass models. Silveira et al. [34] employed hierarchical and kriging interpolation techniques to mitigate uncertainty in the modeling process, utilizing both remote sensing data and forest inventory data. Zhang et al. [35] developed a random forest biomass estimation model utilizing remote sensing data in conjunction with forest inventory data, with the aim of examining the uncertainties present during the preprocessing phase of remote sensing images. Therefore, this paper builds on the existing research base and further quantifies two different types of uncertainty: the plot scale and the remote sensing model scale. However, regardless of the scale, there is always uncertainty in the process of estimating AGB, and ignoring it will produce more serious errors. Therefore, the question of how to reduce the uncertainty in the estimation process has become a hot topic in current research [36].

In this paper, we took Shaoguan, Heyuan and Huizhou in Guangdong Province as the study areas and Cunninghamia lanceolata as the study object. Utilizing Landsat 8 OLI remote sensing images in conjunction with field survey data, we developed estimation models employing K nearest neighbor regression (KNN), gradient-boosted regression tree (GBRT) and random forest (RF) methodologies. Additionally, error equations were applied to assess the uncertainty at both the plot scale and in remote sensing models. The aims of this study were as follows: (1) to examine the impact of plot scale and remote sensing models on the precision of AGB estimation; (2) to evaluate and compare the estimation accuracy and associated uncertainties of various remote sensing models; and (3) to identify the primary sources of uncertainty in the AGB estimation process, as well as to quantify the uncertainty arising from different scales.

2. Materials and Methods

2.1. Study Area

The study area is situated in the central and northern regions of Guangdong Province, China (20°13′–25°31′ N, 109°39′–117°19′ E; Figure 1), and includes Shaoguan, Huizhou and Heyuan, with an area of 48,700 square kilometers. Their climate type belongs to the East Asian monsoon zone, with an average precipitation of 1798.8 mm and an average annual temperature of 22.1 °C. These three regions exhibit a diverse topographical landscape characterized by a variety of landforms, including mountains, hills, plateaus, and plains. The region has a well-developed water system, including important rivers such as the Pearl River, the Xijiang River and the Beijiang River, as well as numerous tributaries, lakes and reservoirs, making it an important water resource base in Southern China. Vegetation types in this region mainly include tropical rainforests, evergreen broad-leaved forests and coniferous forests, which are distributed at different altitudes. According to the latest (9th) Forest Resources Inventory, Guangdong Province has a total forest area of 10,535,400 hectares, with a forest coverage rate of 58.59%, and Chinese Fir is the dominant tree species in this region.

2.2. Data Sources and Processing

2.2.1. Field Survey Data

Forest reference data play a vital role in the estimation of biomass. The sample plot data utilized in this research were derived from field surveys conducted in Guangdong Province, spanning from November 2023 to March 2024. Each plot measured 30 m by 30 m, resulting in a total of 87 plots surveyed. Among them, 40 sample plots are in Shaoguan, 25 sample plots are in Heyuan and 22 sample plots are in Huizhou. The field survey was conducted utilizing portable global positioning system (GPS) technology as well as static differential GPS methodologies. Since the DBH, H and biomass measured by the sample plot data are related to the spectral, radiometric and other characteristics of the forest vegetation information from remote sensing data [37], we needed to investigate Cunninghamia lanceolata species with DBH > 5 cm; attributes such as DBH, H, coordinates of the sample plot center, elevation, slope and slope position of every plot were recorded [38], and the biomass of each tree within the plot was determined using the anisotropic growth equation specific to the Cunninghamia lanceolata species [39]. The biomass of each sample plot can be obtained by summing the biomass of each species.

The Cunninghamia lanceolata per-tree biomass model is as follows:

$$W=0.06539\times D^{2.01735}\times H^{0.49425}$$

(1)

where $W$ is the dry biomass of the individual tree, $D$ is DBH of the individual tree and $H$ is H of the individual tree.

2.2.2. The Collection and Analysis of Remote Sensing Data

The Landsat 8 OLI images utilized in this research can be accessed via the official website of the United States Geological Survey (USGS) (https://earthexplorer.usgs.gov (accessed on 18 November 2023)); the images were acquired in November and December 2023, and their image resolution is 30 m (

Table 1. Images of the study area.

Survey Year	ID	Acquisition Date	Cloudy/%
2023	LC08_L2SP_121044_20231118_20231122_02_T1	18 November 2023	0.02%
	LC08_L2SP_121043_20231118_20231122_02_T1	18 November 2023	0.02%
	LC08_L2SP_122044_20231125_20231129_02_T1	25 November 2023	1.28%
	LC08_L2SP_122043_20231227_20240104_02_T1	27 December 2023	4.76%

). The images were preprocessed using ENVI 5.3 software [40], using radiometric calibration and atmospheric correction to eliminate the effects of terrain and aerosol reflections on ground objects, followed by terrain correction of the image using the slope matching method, by which the mean values of terrain shadows on the north and south slopes were made similar. Finally, the images were mosaicked and cropped by the software to obtain the image.

2.2.3. The Process of Extracting and Selecting Remote Sensing Variables

The images were pre-processed utilizing ENVI 5.3, from which three categories of remote sensing variables were derived from Landsat 8 OLI images: spectral features, vegetation indices and texture features. Spectral features represent the fundamental and most straightforward characteristics in remote sensing imagery. Nonetheless, the occurrence of “different spectra for identical objects and identical spectra for disparate objects” is prevalent in remote sensing data, which complicates the attainment of accurate estimation outcomes when solely depending on spectral features [41,42]. Vegetation index is essentially a multi-band reflectance transformation, which can make the transformed data highlight the vegetation information and weaken the non-vegetation feature information, so it can better reflect the growth conditions of the vegetation and spatial distribution of the location compared to the spectral features. Texture features take into account the spatial relationships among pixels, which can effectively represent variations in grayscale within an image and enhance the recognition of spatial information. Consequently, the integrated application of the three categories of remote sensing factors can more accurately capture the characteristics of features and their transformations [43,44]. In the present study, we identified a total of 121 remote sensing factors, comprising 7 spectral features, 7 vegetation indices, 3 information enhancement factors, and 104 texture features (

Table 2. Variables obtained from the remote sensing images.

Sensor	Feature Type	Feature Name	Definition
Landsat 8	Spectral bands	B2, B3, B4, B5, B6, B7	Blue, Green, Red, NIR, SWIR1, SWIR2
	Information enhancement	PCA1, PCA2, PCA3	Principal component analysis [45]
	Vegetation indices	DVI	NIR-Red
		RVI	NIR/Red
		NDVI	(NIR − Red)/(NIR + Red)
		NDVI2	(NIR − Green)/(NIR + Green)
		LCI	(NIR + Red)/2
		SAVI	1.5 × (NIR − Red)/8 × (NIR + Red + 0.5)
		EVI	2.5 × ((NIR − Red)/(NIR + 6 × Red − 7.5 × Blue + 1))
	Textural features	Contrast (CON), Dissimilarity (DIS), Angular second moment (ASM), Entropy (ENT), Variance (VAR), Correlation (COR), Homogeneity (HOM), Mean (ME)	Gray level co-occurrence matrix [46]

Note: BX refers to a specific single band within the image.

). Subsequently, we employed RF to filter the importance of remote sensing factors. Finally, we selected the factors exhibiting high significance for model construction, which primarily included 1 spectral feature and 14 texture features (Figure 2).

2.3. Remote Sensing Models

In this research, remote sensing variables were utilized to develop a model for estimating the AGB of Cunninghamia lanceolata. The modeling methods mainly include KNN, GBRT and RF.

KNN is a typical nonparametric regression model, and its basic principle is to predict variables based on the spatial similarity between observation and prediction points, and this method can solve the problem of parameter estimation for remote sensing data whose probability density distribution function is not normally distributed or is unknown [47]. Consequently, it has been extensively utilized in the assessment of biomass and carbon stock. The parameter range of the K value (number of neighbors) of the KNN model is 2–10, the equidistant spacing is 1, the distance metric is Euclidean distance, the weights are set to mean weights, and the algorithm is chosen as the approximate nearest neighbor algorithm.

GBRT is an iterative algorithm for regression tree modeling introduced by Friedman [48]. In this framework, all regression trees are interconnected, with each subsequent tree being constructed based on the residuals and outcomes of the preceding tree [49]. The fundamental approach involves the creation of multiple weak classifiers, which collectively yield a robust classifier following numerous iterations. The application of the GBRT model in this research is grounded in the “Gradient Boosting Regressor” algorithm available within the “Scikit-learn” library for the Python programming language. In this study, based on the best combination of parameters for goodness-of-fit, the maximum number of iterations was chosen to be 60, subsampling to be 0.5, learning rate to be 0.05, the maximum depth of the decision tree to be 7 and the minimum sample of leaf nodes to be 3.

RF is an ensemble learning model introduced by Breiman [50], characterized by the aggregation of multiple randomly generated decision trees. This methodology effectively mitigates the risk of overfitting through the combination of diverse trees, resulting in superior performance in both classification and regression tasks. Consequently, RF has been widely adopted across various research domains [51,52]. In the present study, the RF model is implemented utilizing the “Random Forest Regression” algorithm available in the “Scikit-learn” library for the Python programming language. The RF model decision tree has a parameter range of 20–200, an aliquot spacing of 10, a minimum sampling spacing of 2, a maximum depth of the decision tree of 10, and a minimum sample of leaf nodes of 1.

In this research, the aforementioned three methodologies were employed independently to develop the AGB estimation model for Cunninghamia lanceolata, after which the uncertainties caused by the residual variance errors of the three remote sensing models were analyzed and quantified.

2.4. Accuracy Assessment

Approximately seventy percent (60 groups) of the dataset was randomly allocated for the purpose of model fitting, while the remaining thirty percent (27 groups) was designated for accuracy validation and cross-validation throughout the model fitting process. The performance of the model was assessed using the metrics R², RMSE and rRMSE. RMSE is the average degree of deviation between the estimated value and the true value. The smaller the RMSE value, the smaller the difference between the estimated value and the actual value, and the higher the accuracy of the model estimation. And rRMSE is the ratio of RMSE to the mean of the actual observed values; the smaller its value, the smaller the proportion of the size of the estimation error relative to the observed values. To enhance the objectivity of the model outcomes, this study conducted ten iterations for each model and subsequently calculated the average of the evaluation metrics for comparative analysis. The relevant formulas are presented as follows:

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

(2)

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

(3)

$$rRMSE={\displaystyle \frac{RMSE}{\overline{y}}}\times 100\%$$

(4)

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

2.5. Analysis of the Uncertainty

2.5.1. Calculation of the Plot Scale Uncertainty

(1)

Calculation of the Residual Uncertainty in the Per-tree Biomass Model

To determine the residual uncertainty associated with the per-tree biomass model, it is essential to calibrate the model utilizing the observed biomass values of Cunninghamia lanceolata. Subsequently, the uncertainty associated with the residual variation can be determined by evaluating the discrepancy between the predicted values and the observed values. Let the observed biomass be denoted as $A$, and the biomass prediction model be represented as $f (g,\widehat{\alpha })$. Therefore, $A$ can be articulated using the following equation:

$$A=f\left(g,\widehat{\alpha }\right)+\epsilon$$

(5)

where $\widehat{\alpha }$ is the predicted value of the parameter in the biomass model, $g$ is the variable (DBH, H) and $\epsilon$ is the difference between the predicted and measured values. The form of $f (g,a)$ used in this paper is $f \left(g,a\right)=a{D}^b{H}^c$. The equation of residual $\epsilon$ was as follows:

$$\epsilon =A-f\left(g,\widehat{\alpha }\right)$$

(6)

where $\epsilon$ is the difference between the predicted and measured values, $A$ is the observed biomass value and $f (g,\widehat{\alpha })$ is the biomass prediction model. The uncertainty associated with the variation in model residuals can be quantified through the standard deviation of the residuals. According to the relevant study [53], the standard deviation of the residuals exhibits a linear correlation with biomass. Consequently, the uncertainty associated with the variation in model residuals can be determined by establishing a linear relationship between the standard deviation of the residuals and biomass. The corresponding formula is presented below:

$${\sigma }_{\epsilon }=\delta (g,\widehat{a})$$

(7)

where ${\sigma }_{\epsilon }$ is the standard deviation of the residuals and $\delta$ is the fitting parameter. In this study, the six-step methodology outlined in reference [54] was employed to compute the value of ${\sigma }_{\epsilon }$. The procedure is delineated as follows: (1) The measured biomass values of Cunninghamia lanceolata ($y$) were organized in ascending order. (2) The residuals ($M_{\epsilon }$) were determined by subtracting the predicted values from the biomass model ($\widehat{y}$), with the residuals representing the discrepancies between the measured and predicted values. (3) The plots were categorized into groups, with each group containing $n$ blocks, and any final group with fewer than $n$ blocks was amalgamated with the preceding group. (4) The mean values of the predicted carbon stock ($\overline{\widehat{y}}$) and the standard deviations of the residuals (${\sigma }_{\epsilon }$) were computed for each group. The calculations for the mean value, residuals and standard deviation of the residuals were conducted as follows:

$$\overline{\widehat{y}}={\displaystyle \frac{1}{n}}\sum _{j=1}^n{\widehat{y}}_j$$

(8)

$$M_{\epsilon }=y-\widehat{y}$$

(9)

$${\sigma }_{\epsilon }={\displaystyle \frac{1}{n-1}}\sqrt{\sum _{j=1}^n{\left(M_{{\epsilon }_j}-{\overline{M}}_{{\epsilon }_j}\right)}^2}$$

(10)

where $y$ is the measured biomass values, $\widehat{y}$ is the predicted values, ${\widehat{y}}_j$ is the predicted value of AGB in the $j$th plot, $M_{{\epsilon }_j}$, ${\overline{M}}_{{\epsilon }_j}$ are the residual and residual standard deviation of the $j$th plot, respectively, and $n$ is the number of plots.

(5) The predicted mean value $\overline{\widehat{y}}$ and standard deviation of the residuals ${\sigma }_{\epsilon }$ should be fitted accordingly. The corresponding equation for this fitting can be articulated as follows:

$${\sigma }_{\epsilon }=\theta \left(\overline{\widehat{y}}\right)$$

(11)

(6) To calculate the residual uncertainty of the model, substitute the predicted AGB for each plot into the fitted equation. Subsequently, compute the total of the residual standard deviations across all plots and divide this sum by the aggregate of the measured AGB values.

(2)

Calculation of the Parameter Uncertainty in the Per-tree Biomass Model

To assess the uncertainty associated with the model parameters, we can employ the first-order Taylor series expansion. If the function possesses an $n$th order derivative at $x_0$, as $x$ approaches $x_0$, the function can be represented as follows:

$$f\left(x\right)\approx f\left(x_0\right)+f^{\prime }\left(x_0\right)\left(x-x_0\right)+{\displaystyle \frac{f^{\prime \prime }\left(x_0\right)}{2!}}({x-x_0)}^2+\dots +{\displaystyle \frac{f^{\left(n\right)}\left(x_0\right)}{n!}}{(x-x_0)}^n$$

(12)

Then, the biomass model $A=f \left(g,\widehat{a}\right)$ can be expressed after a Taylor series first order expansion as

$$A=f(g,\widehat{a})\approx f(g,a)+{\displaystyle \frac{\partial f\left(g,\alpha \right)}{{\partial }_{a_j}}}(\widehat{\alpha }-\alpha )$$

(13)

where $f(g,\widehat{a})$ is the predicted value of the per-tree biomass model, $x$ is the variable in the biomass model, $\widehat{\alpha }$ is the simulated value of parameters, ${\displaystyle \frac{\partial f\left(g,\alpha \right)}{{\partial }_{a_j}}}$ is the partial derivative of the parameters and ${\displaystyle \frac{\partial f\left(g,\alpha \right)}{{\partial }_{a_j}}}(\widehat{\alpha }-\alpha )$ reflects the parametrically induced modeling error ${\sigma }_{\lambda }$, which can be approximated as

$${\sigma }_{\lambda }^2\approx Z_{jk}var\left(a\right)Z_{jk}^T$$

(14)

where $Z_{jk}$ represents the matrix with $Z$ designated as $j\times k$, $Z_{jk}^T$ signifies the transpose matrix of $Z_{jk}$ and $var\left(\alpha \right)$ denotes the covariance matrix associated with the estimated parameter $\alpha$ within the biomass equation.

(3)

Synthesis of Uncertainty

When the indirectly measured quantity is derived from individual measurements obtained through direct measurements, the uncertainty associated with the indirect measurements can be articulated as a composite uncertainty that encompasses the uncertainties of each direct measurement [55]. Consequently, the overall error can be represented as

$$K_Z=\sqrt{K_{j_1}^2+K_{j_2}^2+K_{j_3}^2+\dots +K_{j_i}^2}$$

(15)

where $K_Z$ is the total error and $K_{j_i}$ is the error of the $i$th variable. According to this equation, the overall uncertainty (${\sigma }_z$) is determined as follows:

$${\sigma }_z=\sqrt{{\sigma }_{\epsilon }^2+{\sigma }_{\lambda }^2}$$

(16)

where ${\sigma }_{\epsilon }$ represents the residual uncertainty associated with the per-tree biomass model, while ${\sigma }_{\lambda }$ denotes the uncertainty pertaining to the model parameters. The propagation of error from the per-tree biomass model to the uncertainty at the plot scale, denoted as ${\sigma }_p$, is computed using the following methodology:

$${\sigma }_p=\sqrt{\sum _{i=1}^N{\sigma }_{ti}^2/S}$$

(17)

where $N$ represents the quantity of sampled wood, ${\sigma }_{ti}$ denotes the overall uncertainty associated with the per-tree biomass model for the $i$th plot of wood plants and $S$ signifies the area of the plot.

2.5.2. Calculation of Uncertainty for Remote Sensing Models

The six-step methodology [54] was employed to determine the uncertainty associated with the residual variance of the remote sensing estimation model. The detailed procedures and formulas utilized in this process are outlined in the six-step section of the initial point in Section 2.5.1. Consequently, the uncertainty of the remote sensing model (${\sigma }_R$) can be articulated as follows:

$${\sigma }_R={\sum }_{i=1}^n{\sigma }_{\epsilon }/y_z$$

(18)

where ${\sum }_{i=1}^n{\sigma }_{\epsilon }$ represents the cumulative sum of the standard deviations of the residuals across all plots, while $y_z$ signifies the total of the measured values of AGB.

2.5.3. Calculation of Total Uncertainty from Different Sources

The total uncertainty ($\sigma$) of the Cunninghamia lanceolata AGB was calculated as follows:

$$\sigma =\sqrt{{\sigma }_p^2+{\sigma }_R^2}$$

(19)

where ${\sigma }_p$ is the plot scale uncertainty and ${\sigma }_R$ is the remote sensing model uncertainty.

3. Results and Analysis

3.1. Accuracy of Different Remote Sensing Models

Scatter plots illustrating the predictive accuracy of AGB estimation models utilizing the KNN, GBRT and RF methodologies are shown in Figure 3. The data presented in the Figure indicate that, under identical modeling conditions, the KNN model exhibited the least favorable performance, achieving an R² of 0.368 and a RMSE of 42.314 t/ha. The GBRT model ranked second, with an R² of 0.636 and an RMSE of 32.056 t/ha. In contrast, the RF model demonstrated superior performance, attaining an R² of 0.867 and an RMSE of 19.325 t/ha. When compared to the KNN and GBRT models, the RF model showed an improvement in R² of 0.499 and 0.231, respectively, while the RMSE was reduced by 22.989 t/ha and 12.731 t/ha, respectively. Furthermore, an analysis of the predicted and observed values across various models reveals a notable tendency for KNN and GBRT to exhibit a significant overestimation of low values and underestimation of high values. The lowest measured value is 21.942 t/ha, while the highest is 277.09 t/ha. The lowest prediction value based on the KNN model is 70.487 t/ha and the highest is 143.022 t/ha, with a large range, and there are obvious saturation characteristics. While the corresponding GBRT model-predicted values are 60.368 t/ha and 189.963 t/ha, these two models of the relative error between the groups of data are larger. The issue of low values associated with the overestimation and underestimation of high values in the RF model has been notably enhanced, yielding predicted values of 50.946 t/ha and 223.989 t/ha, respectively. The relative errors among the various data groups are minimal, indicating that the RF model demonstrates superior estimation accuracy.

3.2. Calculation of Plot Scale Uncertainty

3.2.1. Uncertainty of the Per-Tree Biomass Model

The parameters of the binary biomass model were determined using the measured AGB of Cunninghamia lanceolata, and the fitted binary biomass model was $A=0.077D^{1.844} H^{0.654}$; the R² of the model was 0.970 (Figure 4a). Figure 4b presents a scatter plot illustrating the error equation associated with the per-tree biomass model. The Figure indicates that the standard deviations of the residuals exhibit an upward trend corresponding to the increase in the predicted biomass values. The fitted model, which accounts for the uncertainty of the model residuals, is expressed as $y=0.0479x-0.3275.$ Then, the predicted values of biomass were substituted into the fitted formula to determine the uncertainty of the residual variance for the binary biomass model, which was 4.62%. To assess the uncertainty associated with the model parameters, we can calculate it by estimating the variance–covariance matrix of the parameters and integrating this information with Equation (14). Through this calculation, it can be determined that the variance–covariance matrix for the parameters of the binary biomass model can be represented as $\left(\begin{array}{ccc}0.000000012& -0.00000047& -0.00000250\\ -0.00000047& 0.00036000& -0.00058000\\ -0.00000250& -0.00058000& 0.00200000\end{array}\right)$, which was substituted into Equation (14), with the result that the value of parameter uncertainty was 4.81%, 6%. Synthesizing the two uncertainties, the total uncertainty of the binary biomass model was 6.67%.

3.2.2. Uncertainty at the Plot Scale

The overall uncertainty was determined to be 6.67% by integrating the uncertainty associated with the per-tree biomass model, as outlined in Equation (17). When this uncertainty is applied to the plot scale, it can be quantified using Equation (17), yielding a resultant uncertainty of 3.23%.

Table 3. Results of each uncertainty source at the plot scale.

Model	Parameter Error/%	Residual Variation Error/%	Plot Scale Uncertainty/%
$\mathrm{A}=0.077{\mathrm{D}}^{1.844}{\mathrm{H}}^{0.654}$	4.81	4.62	3.23

presents the various sources of uncertainty involved in biomass estimation at the plot scale.

3.3. Uncertainty of Remote Sensing Estimation Models

Figure 5 illustrates the correlation between the standard deviation of the residuals for each model and the mean values of the predicted biomass, and we can find that the uncertainties of the KNN, GBRT and RF models are 14.88%, 6.3% and 5.93%, respectively, by substituting the predicted values of each model into the fitting formula. In order to more intuitively reflect the differences between the predicted and measured values of each model, we compared the data of 87 sample plots with the corresponding results in Figure 6; as can be seen from the Figure, there are large differences between the predicted values of the KNN model and the measured values of the plots, with a maximum absolute difference between the two of 134.067 t/ha, and the same phenomenon exists in the GBRT model, with a maximum absolute difference between the two of 87.126 t/ha. For RF, compared to the first two models, the phenomenon of the difference between the predicted value and the measured value has been greatly improved, the maximum absolute difference is 53.1 t/ha, and the minimum absolute difference is only 0.03 t/ha, of which most of the absolute difference is within 20 t/ha, which indicates that the predicted value of the model and the measured value is more consistent with the predicted value, and has a good prediction accuracy, and its uncertainty is also the highest among the three models.

3.4. Total Uncertainty in Biomass Estimation

Table 4. Total uncertainty of AGB estimation based on Landsat 8 data.

Model	Uncertainty of Remote Sensing-Based Estimation Models/%	Uncertainties at the Plot Scale			Total Uncertainty/%
		Model Parameter Errors/%	Model Residual Variance/%	Uncertainty at the Plot Scale/%
KNN	14.88	4.81	4.62	3.23	15.22
GBRT	6.3				7.08
RF	5.93				6.75

presents the comprehensive uncertainty associated with the remote-sensing-based estimation of AGB for Cunninghamia lanceolata. By integrating the plot scale uncertainty with the uncertainty derived from the remote sensing model, as outlined in Equation (19), we determined the total uncertainties to be 15.22%, 7.08% and 6.75% for the KNN, GBRT and RF models, respectively.

4. Discussion

4.1. Analysis of Plot Scale Uncertainty

Despite the extensive research undertaken to quantify AGB in forest ecosystems, significant uncertainties persist in the estimation methodologies [35,56]. In this paper, we constructed KNN, GBRT and RF models based on remote sensing data, and the error equations were used to analyze the uncertainty at the plot scale and remote sensing model scale. Our analysis indicates that the uncertainty associated with the remote sensing estimation model constitutes the primary source of uncertainty, surpassing that of plot scale uncertainty. Among the models evaluated, the KNN model exhibited the highest level of uncertainty at 14.88%, while the RF model demonstrated the lowest uncertainty at 5.93%. Within the context of plot-scale uncertainties, the predominant source of uncertainty was identified as the parameter error associated with the per-tree biomass model. In comparison, the uncertainty attributed to residual variance was marginally lower. This observation aligns with the findings of Huang et al. [57]. However, it is noteworthy that the parameter error of the model in this study was found to be greater than that reported by Chen et al. [33] and Wang et al. [58]. The discrepancy may be attributed to the fact that Chen et al. [33] employed larger modeling plots compared to the present study, suggesting that the parameter error of the model approaches zero as the plot number increases. In contrast, Wang et al. [58] utilized a grouping approach and assessed the errors of both univariate and bivariate biomass models through the Taylor series method. This indicates that grouping can significantly mitigate the variability of the parameter covariance matrices, thereby yielding a more precise estimation of parameter error. This study focuses solely on the uncertainty associated with the binary biomass model, while the uncertainty of the univariate biomass model warrants further investigation in future research.

4.2. Uncertainty in Different Remote Sensing Estimation Models

In comparison to conventional parametric regression techniques, machine learning approaches offer distinct advantages in the estimation of AGB in forests [59,60]. Consequently, we developed a remote sensing model for estimating the AGB of Cunninghamia lanceolata utilizing Landsat 8 OLI data in conjunction with three different machine learning methodologies. The assessment of AGB in forests utilizing the KNN and GBRT models results in significant overestimations of lower biomass values and underestimations of higher biomass values. Furthermore, the fitting accuracies of both KNN and GBRT models are inferior to those achieved by the RF model. While the inaccuracies in estimating AGB within the RF model have shown considerable improvement, this issue persists. This persistence may be attributed to the substantial variability in measured forest AGB values within the study area, which renders the RF model more susceptible to the influence of outliers [61]. Furthermore, the study area exhibits heterogeneity in its characteristics, which contributes to its diversity. In regions characterized by low AGB in forests, the forest pixels are influenced by the spectral signatures of other non-forest elements, leading to an overestimation of AGB when utilizing the model. Conversely, in areas with elevated forest AGB values, the reflectance spectra of the vegetation tend to become saturated, resulting in estimated AGB values that exceed the actual measured values. For instance, Suwanlee et al. [62] developed support vector machine (SVM) and RF models to map forest AGB utilizing Sentinel-1 and Sentinel-2 data, respectively. Their findings indicated that the RF model demonstrated superior efficiency and consistency in comparison to the SVR model over the two-year period analyzed. Similarly, Zhuo et al. [63] created various remote sensing models to estimate forest AGB using measured biomass data and UAV hyperspectral imagery. Their results further corroborated the RF model’s preeminence, achieving an R² of 0.82 and a RMSE of 116.14 g/m², outperforming three other estimation models during the same timeframe. Numerous studies have concluded that the RF model possesses distinct advantages over alternative models in the estimation of forest AGB.

4.3. Limitations and Future Research

In the context of plot scale analysis, it is essential to account for the influences of measurement errors, sampling variability, plot size and plot positioning inaccuracies, alongside the uncertainty introduced by the per-tree biomass model. Notably, several researchers have investigated the uncertainty associated with sample plot size and positioning errors. Mayamanikandan et al. [64] conducted a study examining the uncertainty associated with plot size, shape and location errors utilizing Sentinel data. Their findings indicated that model uncertainty was reduced by approximately 50% when the plot size was increased from 0.01 ha to 0.64 ha. Similarly, Frazer et al. [65] explored the impact of plot size and alignment errors on the uncertainty of LiDAR-derived canopy metrics and AGB estimation models. Their results demonstrated a significant enhancement in AGB predictions and a considerable reduction in model uncertainty when the plot size was expanded from 314 m² (10 m radius) to 1964 m² (25 m radius). Persson et al. [66] used continuous forest inventory data to investigate the uncertainty of field survey data due to measurement error, model error and sample location error. By taking these errors into account, the prediction uncertainty based on remote sensing was reduced by 6–18%, and the residuals of the anisotropic growth model and the location error were the main sources of error. All of the above results showed that the plot size showed an inverse relationship with uncertainty, and the model uncertainty decreased with the increase in plot size. In addition, for Cunninghamia lanceolata, as a fast-growing coniferous timber species endemic to subtropical regions in China, the degree of growth adaptation in different regions was not consistent, and its stand biomass also had large differences; the prediction accuracy of the same model at different regional scales will produce large differences, and if regional differences are ignored, this will inevitably lead to inaccurate model estimation results [67]. Therefore, in subsequent studies we should explore the effects of uncertainty in biomass estimation at different scales and regions, and also consider the effects of plot size and positioning errors.

5. Conclusions

In this paper, Shaoguan, Heyuan and Huizhou in Guangdong Province were taken as the study area, and Cunninghamia lanceolata was used as the research object. Biomass estimation models utilizing KNN, GBRT and RF were developed using Landsat 8 OLI remote sensing imagery in conjunction with field survey data. Error equations were employed to assess the uncertainties associated with both plot scale and remote sensing model scale, facilitating an analysis of how variations in scale influence the estimation of AGB. (1) The primary source of uncertainty at the plot scale in the per-tree biomass model was identified as parameter uncertainty, while the residual uncertainty of the model was relatively minor. (2) In contrast, at the plot scale, the uncertainty associated with the remote sensing model emerged as the predominant factor influencing biomass estimation. Among the models evaluated, the KNN model exhibited the lowest estimation accuracy (R² = 0.368) and the highest uncertainty (14.88%). The GBRT model followed, with an R² of 0.636 and an uncertainty of 6.3%. Conversely, the RF model demonstrated the highest precision, achieving an R² of 0.867 and the lowest uncertainty at 5.93%. When compared to the KNN and GBRT models, the RF model’s R² improved by 0.499 and 0.231, respectively, while its uncertainty decreased by 8.95% and 0.37%. This study analyzed the uncertainties at both the plot scale and the remote sensing model scale to identify the key factors influencing the accuracy of biomass estimation, thereby providing insights that may enhance estimation accuracy and mitigate uncertainty in the estimation process.