Spatial Analysis of Picea schrenkiana var. tianschanica: Biomass in the Tianshan Mountains, Xinjiang

Abstract

From a global ecological management perspective, as a core tree species in the mountain ecosystem of Xinjiang, the study of the spatial distribution characteristics of Picea schrenkiana var. tianschanica is crucial for maintaining the ecological balance in the Tianshan region. This study focuses on the western section of the Tianshan mountains in Xinjiang and employs the variogram analysis technique to explore the spatial heterogeneity of Picea schrenkiana var. tianschanica biomass. Successively, the study implements ordinary kriging, multivariate linear regression, the random forest algorithm, and an innovative random forest residual kriging method to conduct a spatial interpolation analysis of Picea schrenkiana var. tianschanica biomass in the target area. The results indicate that the biomass of Picea schrenkiana var. tianschanica exhibits moderate spatial autocorrelation, with its distribution pattern being influenced by a combination of topography, climate, and soil conditions. After comparing multiple spatial interpolation methods, it is found that the hybrid model combining regression analysis and kriging, delivers the best performance (R² = 0.642, RMSE = 40.18, RMSPE = 44.6). This model not only significantly improves the prediction accuracy, but also provides an intuitive and accurate spatial distribution map of Picea schrenkiana var. tianschanica biomass in the western section of the Tianshan mountains which reveals the global ecological importance of Picea schrenkiana var. tianschanica in an intuitive and accurate way, providing valuable scientific evidence and practical guidance for the field of international ecological protection and resource management.

1. Introduction

As the core of terrestrial ecosystems, forests play a crucial role in regulating climate, conserving water resources, and maintaining carbon balance, accounting for 90% of the biomass in terrestrial ecosystems [1]. The study of forest biomass allows for the quantification of changes in forest carbon storage and the analysis of its relationship with the carbon cycle, thereby helping evaluate the structure, function, and quality of forest ecosystems [2,3]. In the 18th century, Germany conducted the first statistical surveys of forest resources [4] to achieve sustainable management. Shortly after, the rise of industrialization led to environmental degradation, prompting a growing recognition of forests’ macroecological regulatory role. Subsequent forest resource surveys have incorporated environmental and remote sensing data to better analyze forest spatial structure, health status, and spatiotemporal changes. Since 1973, China has launched a national forest resource inventory, accumulating vast amounts of data that provide critical support for regional forest protection strategies [5]. Forest protection and sustainable management have remained central topics at international climate change conferences, including the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP), the World Economic Forum (WEF), and the Conference of the Parties to the Convention on Biological Diversity (CBD). These global forums offer a platform for international cooperation to promote forest protection, address climate change, and achieve carbon neutrality. The “carbon neutrality” and “carbon peak” goals proposed in 2021 further emphasize China’s commitment to forest protection. Therefore, studying the spatial distribution of forest biomass is essential for identifying constraints in forest ecological development, exploring the distribution patterns and changes in forest biomass, supporting sustainable management, and informing the research and development of global forestry resources.

Even at the age of 18 years, Picea schrenkiana var. tianschanica has a breast diameter of only 3 cm [6], underscoring the urgency of protecting and restoring this species. Additionally, the ban on commercial logging in the natural forests in the Tianshan mountains has been in effect for only 18 years, and the ecosystem is still in the process of gradual recovery, requiring more scientific guidance and careful management. In light of this, the present study focuses on exploring the spatial distribution patterns of Picea schrenkiana var. tianschanica biomass. The aim is to provide a scientific foundation for the effective restoration of Picea schrenkiana var. tianschanica and support the monitoring of the ecosystem’s sustainable development. By doing so, the study aims to contribute to the restoration and long-term stability of Picea schrenkiana var. tianschanica forest ecosystems.

The spatial heterogeneity of forest ecological factors is significant [7], influenced by natural factors, human intervention, the inherent characteristics of tree species, and the physical environment. Traditional biomass estimation [8,9] relies on manual field measurements, which are limited in coverage, produce discrete data, and consume significant human and material resources, often causing damage to the ecological environment [10]. With the development of remote sensing technology, the acquisition of forest biological and environmental data has become more diverse and real-time [11], making large-scale biomass distribution estimation possible. Remote sensing inversion models estimate regional biomass distribution by establishing relationships between remote sensing data and biomass data [12,13,14,15,16,17]; however, the accuracy of these models depends on the resolution of remote sensing images [18,19], making it challenging to analyze spatial heterogeneity and correlations within the forest. In recent years, the application of geostatistics in ecology has advanced rapidly [20]. Geostatistics is an effective method for studying spatial heterogeneity, capable of analyzing both the regularities and randomness of forest ecosystems [21], providing valuable insights into spatial patterns. When applied to biomass research, geostatistics can overcome some of the limitations of traditional methods and remote sensing models, particularly with respect to the utilization of spatial information. However, geostatistical methods face challenges in effectively handling complex environmental data. Machine learning, on the other hand, excels at constructing regression relationships between data and biomass but is limited in its ability to interpret spatial information. Thus, the study of spatial distribution in forests generally relies on three model frameworks: the spatial heterocorrelation model based on forest genesis theory, the spatial autocorrelation model grounded in the first law of geography, and hybrid models that combine the strengths of both approaches. Within the realm of spatial heterocorrelation models, researchers frequently use methods such as multivariate linear regression [22], geographically weighted regression [23], least squares [24], k-nearest neighbor [25], random forest [26,27], and artificial neural networks [28,29,30]. These technologies are effective in revealing the spatial distribution differences and complex relationships of forest biomass and other ecological factors. The spatial autocorrelation model, on the other hand, focuses on using variograms to analyze the mechanisms of spatial heterogeneity through the spatial coordinates of forest biomass. Techniques such as inverse distance weighting (IDW) [31], trend surface analysis [21], and geostatistics [32] have played an important role in this field, contributing significantly to our understanding of the spatial structure of forest ecosystems. With respect to combined models, these techniques consist, typically, of integrations of geostatistical and multivariate regression models, designed to overcome the limitations of single-model approaches. This hybrid modeling approach often involves using residuals from models such as polynomial regressions, random forests, and geographically weighted regressions, followed by methods like ordinary kriging (OK) for spatial interpolation and prediction [33,34,35,36]. These hybrid models are more effective at capturing the spatial variation characteristics of forest ecological factors and provide more accurate data to support the scientific management and protection of forest resources.

Spatial heterocorrelation models are effective at analyzing the complex relationships between forest ecosystem factors and environmental variables, including both linear and nonlinear relationships. However, these models are fundamentally non-spatial in nature. Forest resource distribution, by contrast, is inherently spatially dependent [37], and such models have limitations when it comes to capturing spatial information. As a result, they are unable to fully explain the dynamic changes in forest spatial patterns. In contrast, geostatistics is a mathematical method used to estimate unknown spatial data points based on known ones [38]. It excels at uncertainty assessments and spatial prediction [39], making it a powerful tool for exploring the randomness and regularity of forest spatial distribution [21]. However, the intrinsic variogram function of geostatistics is still unable to fully address the complex and variable environmental data encountered in forest surveys, limiting its scope of application. As the leading approach to research on the spatial distribution of forest resources, the combined model effectively integrates non-stationary spatial parameters with environmental variables [40]. By combining the strengths of geostatistics and regression models, this hybrid model not only enhances computational efficiency, but also significantly broadens its application scenarios and depth. This study follows this approach by employing four models—ordinary kriging, multiple linear regression, random forest, and regression kriging—along with Landsat 8 remote sensing images and forest inventory data. The study aims to identify variables that significantly influence the biomass of Picea schrenkiana var. tianschanica. These variables are then combined with forest field survey data for spatial analysis and modeling. Using the optimal prediction model, high-precision spatial interpolation of Picea schrenkiana var. tianschanica biomass is performed for the study area. The research process provides a scientific foundation for regional spatial analysis and offers valuable insights for practical applications and decision-making in related fields. Picea schrenkiana var. tianschanica is one of the most critical tree species in Xinjiang’s forest ecosystems, widely distributed across the Tianshan mountains and accounting for 59% of the province’s total natural forest area. As a globally significant coniferous species, Picea schrenkiana var. tianschanica plays a central role in ecological functions such as carbon sequestration, oxygen release, water conservation, and soil protection, underscoring its importance in addressing global climate change and maintaining ecological balance. In-depth analyses and monitoring of the spatial changes in the biomass of Picea schrenkiana var. tianschanica not only provide a scientific basis for the formulation and implementation of China’s ecological security strategy, but also offer a valuable regional case study for global forest ecosystem management and climate change adaptation strategies. This research is of significant importance for promoting the sustainable development of Xinjiang’s natural forest ecosystems and contributes new perspectives and data to the international discussion on ecological protection and resource management. The results of this study provide essential theoretical and practical guidance for the scientific management and operation of Picea schrenkiana var. tianschanica natural forests.

2. Materials and Methods

2.1. The Study Area

The study area is located in the western section of the Tianshan mountains in the Yili Kazakh Autonomous Prefecture of Xinjiang, with geographical coordinates spanning from 41°59′ to 44°31′ N (latitude) and from 79°58′ to 84°05′ E (longitude); the study area and sampling points are shown in Figure 1. The mountains in the area are divided into two wings, north and south, forming a trumpet-shaped pattern that opens to the west, with the central area naturally forming a winding river valley. In the mountains, Picea schrenkiana var. tianschanica, as a naturally growing treasure, is widely distributed on the shady and semi-shady slopes at altitudes of 1300 m to 2800 m on the northern slope of the Tianshan mountains. The growing environment of the Picea schrenkiana var. tianschanica is very unique. It has a temperate continental climate and the soil matrix is mainly gray–brown forest soil, but there is also dark brown soil and chestnut soil. In this fertile land, there are a small number of Betula sp., and, under the forest, there are a variety of vegetation types such as Berberis sp., Salix saposhnikovii A. Skv., Lonicera. sp., Sorbu sp., Cotoneastermelanocarpus sp., Geraniumdahuricum sp., Alchemilla sp., Aegopodiumpodagraria sp., etc.

2.2. Dataset Preparation

2.2.1. Biomass

The survey data of Picea schrenkiana var. tianschanica in the study area were obtained from the sample data of the 8th forest resources inventory (a type I forest resource survey). The data primarily include survey factors such as longitude and latitude, diameter at breast height, age group, canopy density, soil name, and humus layer thickness. The size of the sample plot for the survey was 28.28 m × 28.28 m (0.0799 hm⁻²) [41]. The sample tree was measured at a breast diameter of 5 cm (measured at a height of 130 cm from the ground). In the experiment, samples were categorized by age group, and the DBH data were standardized using the mean ± three times the standard deviation method to eliminate significant outliers caused by collection errors. Ultimately, 308 high-quality experimental samples were obtained.

To ensure the accuracy and scientificity of Picea schrenkiana var. tianschanica biomass estimation, the allometric growth equation proposed by Zhang Huifang (2015) [42] was strictly followed when calculating the biomass of individual Picea schrenkiana var. tianschanica (R² = 0.981):

(1)$W_{AGB}=0.1661\ast D^{2.2528}$

In Equation (1), D represents the breast diameter (cm), while $W_{AGB}$ represents the aboveground biomass (kg).

By summarizing the biomass data of each tree in the sample plot, the total biomass of the entire sample plot was accurately calculated. To more effectively describe the biomass status of Picea schrenkiana var. tianschanica in the sample site, the total biomass was converted into biomass per hectare (t/hm⁻²), as show in Table 1 for the survey data and statistical analysis. It is worth noting that the biomass values across sample points exhibited a significant coefficient of variation, with the data displaying considerable variability. Therefore, further exploration of the spatial distribution variability of the biomass data is needed.

2.2.2. Climate

The environmental factors of the study area included three dimensions: climate, soil and topography. Climate data were obtained from the World Climate Website (https://www.worldclim.org/, accessed on 28 July 2024), which provides 19 types of bioclimatic data, including precipitation and temperature. Using the basic experimental data for the study area, these were clipped to generate a raster file (.tif format) with a spatial resolution of 30 arc seconds using the Terrain Factors in the Geospatial Data Cloud (https://www.gscloud.cn/, accessed on 28 July 2024). A digital elevation model (DEM) image with a resolution of 30 m was obtained for the study area. After image stitching and cropping, a 30 m resolution raster file was generated. Then, ArcGIS was used to extract the slope, aspect, and altitude information from the DEM. The soil factors were derived from the first-class forest survey data and included detailed information on the soil name, soil layer thickness, humus layer thickness, and dead branch and leaf thickness of the sample plot. In order to ensure the consistency and accuracy of the data, the above raster data were converted to the WGS_1984_UTM_Zone_45N projection coordinate system. Since the size of the sample plot was similar to the pixel size of the raster image (30 m × 30 m), the experiment used the spatial position of the sample point to extract the pixel value of the environmental factor as the environmental variable of the sample point.

2.2.3. Remote Sensing

Remote sensing data were obtained from 13 Landsat 8 OLI images taken in 2013 and 2014 between July and September, sourced from the United States Geological Survey (https://glovis.usgs.gov/, accessed on 28 July 2024). The ENVI 5.1 software was used to perform geometric correction, radiometric calibration, and atmospheric correction on the images one by one. After visual interpretation confirmed that the spectral characteristic curve of the forest area met the expectations, the images were spliced and cropped to finally generate a multispectral remote sensing image of the study area with a spatial resolution of 30 m and 7 bands. The image followed the WGS_1984_UTM_Zone_45N geographic coordinate system. In order to fully explore the potential variables highly correlated with Picea schrenkiana var. tianschanica biomass, this study focused on the in-depth analysis of remote sensing images and extracted key remote sensing vegetation factors commonly used in vegetation ecological assessment, such as the normalized difference vegetation index (NDVI) and the ratio vegetation index (RVI), the calculation methods of which are detailed in Table 2. The aim was to maximize the relevance of Picea schrenkiana var. tianschanica biomass through scientific calculations.

2.3. Collinearity Analysis

In order to identify the variables that significantly affected the biomass of Picea schrenkiana var. tianschanica biomass and exhibited certain correlations, a total of 34 variables—including forest survey factors, environmental factors, remote sensing factors, and biomass data—were subjected to Pearson’s correlation analyses using the SPSS 26.0 software. Highly significant variables in regression modeling are expected to improve model accuracy [43]. The study initially screened variables such as landform, soil name, soil layer thickness, humus layer thickness, litter thickness, canopy density, NDVI, RVI, and average temperature. Fourteen correlation coefficients were obtained, including daily temperature range (BIO2), isotherm (BIO3), seasonal temperature variation coefficient (BIO4), annual temperature range (BIO7), annual precipitation (BIO12), and driest quarter precipitation (BIO16). Variables that emerged as moderately (|p-value| < 0.5) and significantly correlated with Picea schrenkiana var. tianschanica biomass (r < 0.05) affected Picea schrenkiana var. tianschanica biomass. In order to further refine the model and ensure the validity of the parameters, the initially screened variables were subjected to multiple linear regression. The variance inflation factor (VIF) for each variable was calculated, and a strict VIF threshold (VIF > 15) was applied to identify and eliminate variables with multicollinearity, thereby avoiding bias and instability in the model estimation. After this optimization step, 10 variables that were both significant and independent of each other were selected, serving as the core parameters for constructing a high-precision regression model. Table 3 presents detailed statistical information on the variables screened in terms of correlation and VIF values, providing a solid data foundation for subsequent model development and validation.

2.4. Model Evaluation Metrics

The evaluation indicators used in this study are mainly based on the determination coefficient (R-squared, R²), root mean square error (Root Mean Square Error, RMSE) and root mean square error percentage (Root Mean Square Percentage Error, RMSPE) to comprehensively evaluate the effectiveness of the biomass model and the accuracy of the prediction results [44]. The equations for the calculation of the evaluation indicators are as follows:

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

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

(4)$RMSPE=RMSE/\overline{y}\times 100$

In Equations (2)–(4), $y_i$ is the observed biomass value, ${\hat{y}}_i$ is the predicted biomass value, $\overline{y}$ is the average of the observed biomass values, and $n$ is the number of samples. The larger the R² and the lower the RMSE and RMSPE, the better the estimation performance of the model. RMSPE can reflect the change of RMSE relative to the sample mean and can effectively express the relative accuracy of the model compared to RMSE [45].

2.5. Models Comparison

2.5.1. Ordinary Kriging

The study used the GS+ 9.0 software to conduct a semivariance analysis on the biomass of Picea schrenkiana var. tianschanica and explore its spatial variation characteristics. Subsequently, the gstat package in RStudio was employed to construct an ordinary kriging model for further analysis of the spatial distribution of Picea schrenkiana var. tianschanica biomass. During the semivariogram analysis, the study focused on three core parameters of the semivariogram model: still, nugget, and range, all of which are crucial for understanding the structure of the spatial variation of biomass. At the same time, the spatial autocorrelation of Picea schrenkiana var. tianschanica biomass was investigated in depth, as it is a prerequisite for geostatistical modeling analysis. The ordinary kriging modeling analysis is only meaningful when the spatial autocorrelation is at a medium or high level [46]. The GS+ 9.0 software offers four theoretical variogram models: linear, exponential, spherical, and Gaussian. To ensure the accuracy and reliability of the model fitting, this study evaluated the fitting accuracy of the theoretical variogram models based on the residual minimization principle and the maximization of the coefficient of determination (R²). It is worth noting that the original data for Picea schrenkiana var. tianschanica biomass exhibited some skewness (skewness = 0.79, kurtosis = 0.06), indicating non-normality. To improve the distribution shape, a square root transformation was applied, which effectively reduced the skewness (skewness = −0.08, kurtosis = 0.85). The normality of the transformed data was verified using the Kolmogorov−Smirnov (K−S) test (p = 0.32 > 0.05). Table 4 presents the parameters of the four variograms fitted using GS+ 9.0 and their corresponding accuracy evaluation results. These experimental data provide a solid foundation for selecting appropriate models for subsequent spatial interpolation and prediction.

The analysis of the block-to-base ratio (i.e., the difference between the sill value and the nugget value divided by the sill value) can clearly determine the spatial correlation characteristics of the biomass of Picea schrenkiana var. tianschanica. When the block-to-base ratio is lower than 0.25, it indicates a strong spatial correlation, when it is between 0.25 and 0.75, it indicates a moderate spatial correlation, and, when it is greater than 0.75, it suggests that randomness dominates and that the spatial correlation is weak. The results revealed a significant spatial correlation in the biomass of Picea schrenkiana var. tianschanica. After comparing the models using objective data, the exponential function model showed the lowest residual value and the highest determination coefficient in the fitting process, indicating the best fit. Therefore, the parameters obtained from the exponential function model were used to construct the ordinary kriging (OK) model, providing a more accurate reflection of the spatial distribution characteristics of Picea schrenkiana var. tianschanica biomass.

2.5.2. Multiple Linear Regression

The multiple linear regression method was used in Rstudio to construct a quantitative relationship model between Picea schrenkiana var. tianschanica biomass and environmental variables. The specific equation is as follows:

Biomass = (−25.58 × NDVI) + (0.48 × RVI) − (15.25 × BIO2) − (7.58 × BIO3) + (45.10 × Land forms) − (1.11 × Name) + (1.30 × layer Thickness) + (0.51 × Humus layer) + (4.20 × Fallen Leaves) + (2.08 × Canopy density) + 409(5)

Equation (5) was obtained by fitting the training sample data. Its coefficient of determination (R²) was 0.45, the adjusted coefficient of determination (adjust. R²) was 0.423, and the F value statistic was 16.72 (p < 0.01), indicating high statistical significance. This result confirms the overall reliability of the model. Notably, all 10 variables included in the model made significant contributions. Variables such as NDVI, RVI, BIO2, BIO3, landforms, soil name, and soil layer thickness carried greater weights in the regression model, revealing that the growth of Picea schrenkiana var. tianschanica is profoundly influenced by climate, terrain, soil, and other environmental factors. Furthermore, the incorporation of remote sensing factors (e.g., NDVI and RVI) not only enriched the model’s input data, but also significantly enhanced the accuracy and performance of the biomass modeling for Picea schrenkiana var. tianschanica. This underscores the potential of remote sensing technology in forest resource monitoring and management.

2.5.3. Random Forest

Random forests are a powerful tool for solving classification and regression problems in forest resource analysis [47,48]. This study utilized random forests to address the regression problem between Picea schrenkiana var. tianschanica biomass and the various environmental variables. While the prediction performance of random forest algorithms is relatively insensitive to the number of sample points, the numerical settings of mtry and ntree have a more significant impact on the model’s performance [49]. In order to optimize the model performance, the study systematically adjusted these two parameters. Specifically, the mtry parameter was set based on a rule of thumb: its value was approximately equal to or slightly lower than one-third of the total number of variables used in the modeling process and did not exceed the total number of variables [50]. In the experiment, the initial value of mtry was set to 1, with an upper limit of 10 and a step size of 1. The grid optimization method was used to compare the coefficient of determination (R²) of the model under different mtry values. It was determined that the model achieved the highest accuracy when mtry was set to 7. Table 5 presents the results of the mtry optimization process, showing that the model’s R² was maximized at this value. The parameter ntree refers to the number of decision trees in the random forest (RF) model [51]. The number of trees (ntree) was optimized using a step size of 100, ranging from an initial value of 500 to 1000, through the grid optimization method. The goal was to find the optimal value that would ensure model stability while avoiding overfitting. After verification, the model performed best when ntree was set to 800.

In summary, this study used the combination of the parameters mtry = 7 and ntree = 800 (R² = 0.57, RMSPE = 49.74) to construct the Picea schrenkiana var. tianschanica biomass random forest model. The fitting results of each hyperparameter are shown in Table 5.

2.5.4. Random Forest Residual Kriging

The regression kriging model achieves significant improvements in prediction accuracy by combining the regression model with classic kriging interpolation techniques. In this study, RStudio was used to construct a residual kriging interpolation model (random forest residual kriging, RFRK) based on the random forest (RF) algorithm which effectively integrated the prediction power of RF with the spatial interpolation advantages of ordinary kriging (OK). Specifically, the RFRK model first applied an RF regression model to the training dataset to explore the complex relationship between biomass and a set of auxiliary variables. Through this process, preliminary biomass predictions and their corresponding residuals were obtained. These residuals exhibited specific statistical properties, including a skewness of 0.42 and a kurtosis of 3.7. The Kolmogorov−Smirnov (K−S) test (p = 0.098 > 0.05) further confirmed the validity of the normality assumption of their distribution, providing a foundation for subsequent analyses. Next, an exponential model was used to fit the variation function of the residuals in order to capture their spatial structure. The model parameters included: nugget = 6030, sill = 8749, range = 20.06 km, and nugget-to-sill ratio = 0.31. The model fitting was good, with an R² value of 0.35, indicating that the residual data were suitable for kriging interpolation. Finally, by adding the kriging interpolation results of the residuals to the RF model’s predictions, a more accurate biomass regression kriging prediction map was obtained. The modeling process is summarized in the following equation:

(6)$RFK\left(Biomass\right)=RF\left(Biomass\right)+OK\left({\epsilon }_{RF}\right)$

In Equation (6), $RFK\left(Biomass\right)$ represents the prediction result of RFRK, $RF\left(Biomass\right)$ represents the residual, and $OK\left({\epsilon }_{RF}\right)$ represents the OK interpolation of the residual. This equation succinctly summarizes the core ideas and workflow of the RFRK model.

3. Results

3.1. Accuracy Evaluation

The 93 test samples were input into the four constructed models and key evaluation metrics, including the coefficient of determination (R²), root mean square error (RMSE), and root mean square percentage error (RMSPE), were calculated to assess each model’s performance with respect to the prediction of Picea schrenkiana var. tianschanica biomass. The results are summarized in Table 6. To further explore the relationship between model performance and prediction results, a quadratic equation was fitted to each model, and the corresponding regression plots were created (see Figure 2). As shown in Table 6, the OK model delivered the worst performance in terms of R². This is primarily due to the smoothness and continuity of its predictions, which tend to average out extreme biomass values (both maximum and minimum). Consequently, the regression curve in Figure 2 shows a clear averaging trend [52]. In comparison, the MLR and RF models performed adequately, but the RFRK model outperformed the other three. Its R² value was 0.13, 0.58, and 1.73 times higher than those of the OK, MLR, and RF models, respectively. The RFRK model also demonstrated clear advantages in terms of RMSPE, with values 0.118, 0.134, and 0.086 lower than those of the OK, MLR, and RF models, respectively. Notably, although the OK model performed worse than the MLR model in terms of R², it showed a better performance with respect to RMSE. This is visually reflected in the measured−predicted scatter plot in Figure 2. While the MLR model exhibited a better fit, its predicted values included negative values, which are illogical for biomass prediction and lead to a higher RMSE. In summary, this study not only compares the performance of each model through quantitative evaluation indicators, but also illustrates the advantages and limitations of different models with respect to predicting Picea schrenkiana var. tianschanica biomass through intuitive charts. This highlights the importance of considering multiple evaluation indicators when selecting the most suitable model.

3.2. Spatial Analysis

This study innovatively employed the random forest residual kriging (RFRK) method for spatial interpolation to accurately predict the biomass of Picea schrenkiana var. tianschanica in the western section of the Tianshan mountains. The prediction results not only revealed the spatial variation characteristics of Picea schrenkiana var. tianschanica biomass in the region, but also highlight the critical role of environmental factors in shaping the forest biomass distribution pattern.

Based on this model, we created a biomass distribution map of Picea schrenkiana var. tianschanica in the western Tianshan mountains (see Figure 3) which provides essential insights into the region’s ecosystem structure and function. Through detailed analysis of biomass sample points and environmental data, we identified several areas—such as ZhaoSu, Tekes, Gongliu, and Xinyuan—that are key natural forest reserves in the Yili region. These areas are located in a unique geographical zone, a trumpet-shaped valley formed by the convergence of the Ili and the Tekes rivers, surrounded by both the northern and southern mountain ranges, which creates a distinct ecological environment. Notably, the high-altitude barrier effect in the northern section of the mountains blocks the northern cold air currents, resulting in a favorable climate with adequate precipitation and mild conditions, free from extreme weather disruptions. Additionally, the soil in these areas is primarily fertile gray−brown forest soil, which provides ideal growing conditions for Picea schrenkiana var. tianschanica. Based on the comprehensive prediction model and environmental factors, the study suggests that future management and conservation strategies for the natural Picea schrenkiana var. tianschanica forests in the western Tianshan mountains should prioritize the region’s unique environmental characteristics. Special attention should be given to shady and semi-shady slopes at altitudes around 2300 m. Active intervention measures, such as the improvement of soil conditions (e.g., enhancing soil thickness and nutrients), along with artificial seeding and breeding programs, should be implemented in areas where the growth of Picea schrenkiana var. tianschanica is scarse or absent. This process should continue until the newly established forests are stable enough to contribute to water conservation and ecological balance, ultimately improving forest productivity and the region’s ecological services.

4. Discussion

This study innovatively used the random forest residual kriging method for the spatial interpolation of Picea schrenkiana var. tianschanica biomass to accurately predict the biomass of Picea schrenkiana var. tianschanica in the western section of the Tianshan mountains. The prediction results not only reveal the spatial variation characteristics of Picea schrenkiana var. tianschanica biomass in the region, but also intuitively demonstrate the key role of environmental factors in shaping the distribution pattern of forest biomass. Through in-depth analyses of Picea schrenkiana var. tianschanica sample points and environmental data, it can be concluded that Picea schrenkiana var. tianschanica grows best in mid-mountain locations, at altitudes of 1300 m to 2900 m, mainly growing on gentle slopes, slopes, and steep slopes, while the number of Picea schrenkiana var. tianschanica growing on flat slopes and steep slopes is relatively small. The above analyses reached similar conclusions to those drawn by Liu Yufeng [53] and Liu Guanglu [6] in their study on the changes in the terrain of Tianshan with respect to Picea schrenkiana var. tianschanica. According to the research by Wei Kun [54], the water conservation capacity of the Tianshan mountains is relatively high at altitudes of 1500 m to 3500 m. This is consistent with our experimental analysis, showing that Picea schrenkiana var. tianschanica prefers to grow in moist and warm mid-mountain areas. Picea schrenkiana var. tianschanica is suitable for growth in soils with a thickness of about 70 cm and which contain mainly gray−brown soil. This is because gray−brown forest soil is the most concentrated and most abundant mountain forest soil type in the Tianshan mountains. As the most fertile soil in the western section of the Tianshan mountains, it can ensure the nutrient acquisition of Picea schrenkiana var. tianschanica [55]. Excessively thin soil has an insufficient nutrient accumulation capacity and the water evaporates too quickly, while excessively thick soil is characterized by poor air permeability which would affect the root growth of Picea schrenkiana var. tianschanica; as the soil layer deepens, the soil nutrients decrease. The above conclusions are similar to those drawn by Zheng Shuanli [55] and Chen Tingjian [56] in their studies on the impact of soil on Picea schrenkiana var. tianschanica biomass and can be used as the analysis results of this study. Through the analysis of the interpolation results of the Picea schrenkiana var. tianschanica scale, it can be concluded that the areas with high Picea schrenkiana var. tianschanica biomass are concentrated along the northern slope of the southern mountain range at the trumpet mouth. Its administrative area planning includes Tekes, Gongliu, Xinyuan, etc. These areas are scattered with forest farms, which are affiliated with the western-state-owned Forest Management Bureau of Yili. From the perspective of topography and climate, the terrain characteristics of the western section of Tianshan are that the mountain is open to the west in a trumpet shape. Under the influence of the terrain uplift, it is easy to intercept a large amount of warm and humid air currents from the Atlantic Ocean, making the mid-mountain forest belt rich in rainfall, and the snowmelt and rainwater are gathered in the Yili River and Tekes River, making the river distribution network in the region abundant in water resources. Secondly, the northern mountain range blocks the Siberian cold current in the north, rendering the northern slope of the southern mountain range mild and free from extreme environmental changes. From the perspective of the soil, the areas with high Picea schrenkiana var. tianschanica biomass clusters are dominated by gray–brown forest soil with the best fertility which ensures the nutrient supply for the growth of Picea schrenkiana var. tianschanica. Therefore, high-value clusters are concentrated along the northern slope of the southern mountain range. The carbon storage of the Picea schrenkiana var. tianschanica ecosystem in this area is the largest. In addition, from 2000 to 2015, the western-state-owned Forest Management Bureau implemented the “Tianshan Forest Protection Project” in the naturally growing forest areas of the western Tianshan mountains, so that the growth process of the Picea schrenkiana var. tianschanica is well protected and its biomass can continue to increase year by year [57]. Conversely, the sunny slope area of the southern mountain range is adjacent to the Taklamakan Desert. Unlike the warm and humid environment of the northern slope, it belongs to an arid and semi-arid area with little precipitation, resulting in poor growth of Picea schrenkiana var. tianschanica and low average biomass.

Based on the above data analysis, the biomass data from the interpolated surface of the Picea schrenkiana var. tianschanica distribution area were statistically analyzed, and the average biomass of the Picea schrenkiana var. tianschanica growing area in the western Tianshan mountains was found to be 123.64 t/hm⁻². In the study of the biomass of Picea schrenkiana var. tianschanica in the western Tianshan mountains, Liu Yufeng [53] obtained the estimated biomass of Picea schrenkiana var. tianschanica in each age group in the Nileke area based on the second-class forest resource survey data from 1996. By converting the research results, the average biomass of the area was found to be about 114 t/hm⁻², only about 7% different from the conclusion of this study. Although the results are relatively close, due to the inconsistencies in scale and time across the study area, these comparison results are only used as reference, not as verification. Li Hu [58] used the remote sensing vegetation index inversion model (model R² was around 0.75) to obtain the unit biomass of Picea schrenkiana var. tianschanica in the western Tianshan mountains (Tekes River, Kashgar River, Gongnaisi River, Ili River basin) from 1986 to 2007, which was 142.73 t/hm⁻². The study area and scale were similar to those used in this study, and there was a 13.37% difference with the results from this study. The root mean square error percentage of the random forest residual model in this study was 32%; therefore, it can be concluded that the result of 123.64 t/hm² for the biomass obtained by regression kriging of random forest residual interpolation is more reasonable. This study successfully quantifies the spatial variability of Picea schrenkiana var. tianschanica biomass by introducing regression kriging of random forest residuals and reveals the significant impact of environmental factors on Picea schrenkiana var. tianschanica biomass. This method is not only suitable for describing the spatial distribution pattern of Picea schrenkiana var. tianschanica biomass, but also provides a powerful tool for forest productivity assessments in the study area. During the experiment, the combined model was carefully selected based on the principles of maximizing the R² value and minimizing the RMSPE to ensure the accuracy and reliability of the final interpolation results. With respect to the process of exploring the spatial heterogeneity of Picea schrenkiana var. tianschanica biomass, although significant spatial variability in Picea schrenkiana var. tianschanica biomass in the western Tianshan mountains was revealed by constructing a semivariogram, challenges remain in relation to the fitting of the semivariogram. The GS+ software, combined with the variogram fitting method in the gstat package, uses the least squares method to fit the parameters; however, a small change in the initial parameters may lead to poor convergence of the results. Future research is expected to introduce more advanced curve-fitting techniques, such as genetic algorithms, particle swarm algorithms [59], and artificial fish swarm algorithms [60]. By comparing and analyzing the fitting effects of these algorithms, we can seek the optimal semivariogram function parameters to further improve the fitting accuracy. Given the widespread distribution of Picea schrenkiana var. tianschanica forests in the Tianshan mountains, this study effectively reflects the spatial variability of forest biomass in the western Tianshan mountains through evenly distributed sample plot surveys and a rich data collection. Looking ahead, we plan to integrate data from multiple forest surveys and incorporate more dimensional remote sensing factors (such as texture information, band combination information, etc.) to deepen the analysis and improve the prediction of the spatiotemporal heterogeneity of Picea schrenkiana var. tianschanica biomass in the Tianshan region. This strategy aims to achieve real-time monitoring of forest biomass in the western section of the Tianshan mountains and provide solid data support and theoretical guidance for long-term scientific forest operation and management.

5. Conclusions

From the macro perspective of global ecological protection, this study proposes an internationally forward-looking recommendation for the future management and protection of the natural forest of Picea schrenkiana var. tianschanica in the western section of the Tianshan mountains after comprehensive model prediction and in-depth analyses of multidimensional environmental factors. The strategy focuses on using the unique ecological and environmental factors in the region as scientific guidance, with particular emphasis on the mid-mountain shady and semi-shady slopes at an altitude of about 2300 m, which is the key ecological location for the optimal growth of Picea schrenkiana var. tianschanica. In view of the low-biomass areas in the current distribution of Picea schrenkiana var. tianschanica forests, we advocate the adoption of active and precise artificial intervention strategies to promote the combination of natural recovery and artificial restoration. Specific measures include the following. First, the use of refined soil improvement techniques, such as the thickening of the soil layer and the use of scientific proportions to increase soil organic matter and key nutrients, should be considered to optimize the base conditions for the growth of Picea schrenkiana var. tianschanica. Second, through the implementation of precise artificial sowing and genetic improvement plans and the use of advanced forestry science and technology means, Picea schrenkiana var. tianschanica seed sources with strong adaptability and great growth potential should be selected, gradually filling the ecological gap and promoting the natural regeneration of Picea schrenkiana var. tianschanica forests and the reconstruction of the ecosystem. This continuous ecological restoration process requires not only meticulous on-site management, but also long-term planning and monitoring to ensure that the newly planted Picea schrenkiana var. tianschanica forests can grow steadily until they can independently conserve water resources and maintain biodiversity and regional ecological balance. In order to more comprehensively evaluate the performance of the model and capture the dynamic changes in the biomass of Tianshan spruce, future studies need to incorporate timeseries data into the experiment and conduct synchronous analyses by integrating the results of multiple experiments. In the long run, this series of measures will greatly enhance the productivity of the forest ecosystem in the western Tianshan region, strengthen its key service function as Earth’s life support system, make important contributions to global biodiversity conservation and climate regulation, and demonstrate China’s international responsibility and commitment in the field of ecological civilization construction.

Author Contributions

Conceptualization, methodology, validation, and manuscript (original draft) writing were performed by C.C. Data collection and analyses were conducted by W.S. The financial support for the project leading to this publication was acquired by T.B. The study materials were provided by Q.L. Project administration, management, and coordination efforts for the research activity planning were conducted by S.C. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

All participants in this study were fully informed of the research objectives, procedures, potential risks, and benefits before participating, and they all gave their informed consent.

Data Availability Statement

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Sampling point location map of the western section of Tianshan Mountain in Xinjiang.

Figure 2. Regression relationship between the predicted and measured values of different models: (a) ordinary kriging; (b) random forest;(c) multiple linear regression; (d) random forest residual kriging.

Figure 3. Biomass distribution of Picea schrenkiana var. tianschanica growth clusters.

Table 1

Survey data and biomass statistical analysis of Picea schrenkiana var. tianschanica.

Survey Data of Picea schrenkiana var. tianschanica
Data Types	Name		Data Range				Data Unit
Forest survey	DBH		5.0~101.5				Centimeter (cm)
	Canopy density		0~80				Percentage (%)
	Age group		Young, nearly mature, middle-aged, mature, over-mature				Five categories
	Altitude range		1400~3054				Meter (m)
	Slope range		2~51				Degrees (°)
	Slope aspect		North, northeast, east, southeast, south, southwest, west, northwest				Eight categories
	Slope position		Valley, ridge, upslope, mid-slope, downslope				Five categories
	Topography		High mountain, mid-mountain				Two categories
	Soil name		Chestnut brown soil, chestnut calcium soil, dark brown soil, brown soil, lime soil				Five categories
	Soil layer thickness		10~120				Centimeter (cm)
	Humus layer thickness		0~30				Centimeter (cm)
Statistical analysis of Picea schrenkiana var. tianschanica biomass
Title 1	Category	Quantity	Minimum	Maximum	Standard	Mean	Variation (%)
Forest survey	Biomass (t/hm−2)	308	0.103	411.47	97.30	123.73	78

Table 2

Calculation equation of vegetation indexes.

Vegetation Index	Equation	Pixel Value Range	Vegetation Display Range
Normalization	$NDVI=\left({\displaystyle \frac{B5-B4}{B5+B4}}\right)$	−1~1	0.2~0.8
Ratio	$RVI=B5/B4$ 1	0~30	2.0~12.0

¹ B5 represents the near-infrared band, B4 represents the red band.

Table 3

Statistical analysis of the variables used in this work.

Data Type	Factor	Min Value	Max Value	Mean	StandardDeviation	VIF	Relevance
Climate	BIO2	10.88	13.83	11.94	0.55	4.42	−0.172 **
	BIO3	23.95	35.20	29.00	1.68	4.35	−0.173 **
Elevation	Landforms	—	—	—	—	1.03	0.122 *
Soil	Name	—	—	—	—	1.16	−0.243 **
	Layer thickness	6.00	120.00	53.74	19.18	1.09	0.211 **
	Humus layer	0.00	30.00	6.52	6.00	1.52	0.298 **
	Fallen leaves	0.00	15.00	2.58	2.42	1.11	0.306 **
Tree	Canopy density	0.00	0.80	0.32	0.21	1.13	0.156 **
Remote sensing	NDVI	0.14	0.97	0.64	0.13	2.10	0.140 *
	RVI	1.16	14.00	5.41	2.98	2.09	0.139 *

* represents a significant correlation at the 0.05 level, ** represents a significant correlation at the 0.01 level.

Table 4

Fitting parameters of the biomass variograms of Cunninghamia lanceolata.

Model	Nugget	Sill	Block-to-Base	Ratio Range (km)	Residual	R2
Linear	21.24	22.53	0.94	21.30	11.7	0.158
Spherical	14.50	21.01	0.67	11.70	8.36	0.477
Exponential	15.69	23.02	0.68	30.80	6.55	0.520
Gaussian	13.66	22.01	0.62	17.87	7.89	0.486

Table 5

Random forest hyperparameter optimization.

Hyperparameter Mtry Optimization
Mtry	R2	RMSPE	Mtry	R2	RMSPE
1	0.320	54.1	6	0.564	54.8
2	0.427	55.8	7	0.591	53.7
3	0.475	55.7	8	0.586	54.4
4	0.518	55.7	9	0.589	54.2
5	0.541	55.2	10	0.585	54.1
Hyperparameter Ntree optimization
Ntree	R2	RMSPE	Ntree	R2	RMSPE
100	0.580	54.2	600	0.577	54.6
200	0.579	54.6	700	0.583	54.2
300	0.573	54.1	800	0.585	54.1
400	0.578	54.3	900	0.582	54.7
500	0.571	54.9	1000	0.575	54.6

Table 6

Fitting accuracy of different models.

Model	R2	RMSE	RMSE% RMSPE
Ordinary kriging	0.235	53.37 t/hm−2	47.8
Multiple linear regression	0.339	55.06 t/hm−2	49.4
Random forest	0.565	49.74 t/hm−2	44.6
Random forest residual kriging	0.642	40.18 t/hm−2	36.0

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