Research on the construction of growth models for dominant tree species in the Manas River Basin, Xinjiang

Forest resource inventory data

Forest resource survey data are obtained by conducting repeated surveys of the same area of forest resources on a regular basis, in order to grasp the quantity, quality, and growth changes of the forest resources. They serve as an important basis for understanding the current status and dynamic changes of forest resources and are essential data for establishing forest growth models (Chen et al., 2023). The data used in this study include the forest resource survey data of Xinjiang (abbreviated as “Class I Inventory”, with a survey cycle of 5 years). In 2011, Xinjiang conducted the 8th Class I Inventory, employing a systematic sampling method to lay out tree measurement plots on topographic maps at intervals of 4 km × 6 km in mountainous and 2 km × 3 km in plain areas. Within these plots, fixed sample plots were established as squares measuring 28.28  ×  28.28 m, covering an area of 0.07 ha. The “Class I Inventory” field data meticulously documented information such as forest type, tree height, stand age, and plot area, possessing advantages of high accuracy and strong timeliness (Du, Chen & Li, 2023). In this paper, the data were randomly divided into modeling samples and validation samples, accounting for 70% and 30% of the total samples, respectively. Statistical analysis of the sample data was conducted using relative professional software, with detailed statistical results presented in Tables 1 and 2. Tables 1 and 2 show the descriptive statistics of key variables in the modeling sample and the testing sample respectively.

Other related data

The vector boundary data for the study area used in this paper were obtained from the Resource and Environment Science and Data Platform (https://www.resdc.cn/Default.aspx). ArcGIS was employed to perform tasks such as clipping and projection transformation for the study area. The Digital Elevation Model (DEM) data originated from the Geospatial Data Cloud Platform (https://www.gscloud.cn/). With an annual temporal resolution and a spatial resolution of one km, this data exhibits strong reality and other advantages (Wang, 2022). The climate factor data used in this study were sourced from the Global Change Science Data Publishing & Repository (https://www.geodoi.ac.cn/WebCn/doi.aspx?Id=3582), which provides daily temperature data from all stations in China. The daily temperature grid data nationwide were interpolated using the inverse distance weighting (IDW) method. Annual temperature data were then obtained by averaging the daily temperature grid data within the administrative boundaries of prefecture-level cities, with a spatial resolution of 1km for all scales. For the raster datasets of annual precipitation (P), vapor pressure deficit (VPD), and minimum of daily maximum temperature (TXn) for the year 2011, obtained through the ArcGIS software, coordinate system transformations were conducted to ensure that the input raster layers and point layers shared the same coordinate system. Subsequently, the point value extraction method in spatial analysis, using the center value of the sampled pixel as the default option, was employed to extract corresponding climate and topographic data for the forest modeling sample points. The extracted data were then statistically analyzed and organized using Excel, ultimately generating corresponding vector data results for various climate and topographic factors. These data were primarily used for parameter selection and model construction in the multiple nonlinear forest growth model.

Establishment of basic models

In this study, SPSS 27.0 (IBM Corp., Armonk, NY, USA) and Matlab R2023a (The MathWorks, Natick, MA, USA) software were used to establish basic forest growth models such as diameter at breast height (DBH)—tree height and stand age—DBH based on sample plot observation data, with specific forms shown in Table 3. During the construction of the classic Logistic model describing forest growth, the nlinfit function was employed to optimize the relevant parameters (Wang, 2019), resulting in optimal theoretical models for the relationships between DBH and tree height, as well as stand age and DBH for each tree types. The model used can be found in Table 3.

Establishment of multivariate nonlinear forest growth models

Apart from being influenced by the intrinsic characteristics of tree types, factors such as competition, site quality, and climate also have significant impacts on tree growth. To further improve the accuracy of the forest growth model in the study area, this article first conducted correlation analysis between annual precipitation, elevation, maximum temperature, minimum temperature, and other factors with diameter at breast height (DBH). Variables strongly correlated with DBH were selected to enter the optimal basic model. Then, a multiple nonlinear forest growth model was constructed (Wu, 2022). The specific form of the multiple nonlinear forest growth model is shown in Table 4. This provides theoretical basis and data support for tree growth research and management in the region.

To further improve the prediction accuracy of the model, this article conducts point-to-point extraction of raster data and forest resource modeling data. In order to quantify the strength of the association between these factors and the diameter at breast height (DBH), we perform statistical correlation analysis between the extracted geoclimatic factors, such as annual precipitation (P), vapor pressure deficit (VPD), maximum temperature extreme (TXx), minimum temperature extreme (TXn), maximum of minimum daily temperature (TNx), minimum of minimum daily temperature (TNn), as well as topographic factors like DEM data, and the DBH. Statistical analysis of the relationship between site factors and climate factors. Using correlation analysis techniques in statistics and we calculate the correlation coefficients between each of the aforementioned geoclimatic and topographic factors and the tree DBH one by one. This step aims to assess the linear association strength between each factor and DBH size. The various factors are summarized in Table 5. Through comparative analysis of the correlation coefficients between the geoclimatic and topographic factors and DBH, we select the three variables with the strongest correlation with DBH and include them as core independent variables in the basic model. Based on this, we further develop a multivariate nonlinear forest growth model, which can more comprehensively reflect the complex influence of geoclimatic and topographic conditions on forest growth dynamics.

Deep learning model

Machine learning methods are a class of intelligent data analysis techniques based on big data. Compared to traditional modeling methods, machine learning methods can achieve more accurate simulations and predictions. Deep learning methods, as an important branch of machine learning, are advanced machine learning techniques based on neural networks. They mimic the working manner of human brain neural networks, performing high-level abstractions of data through multiple layers of nonlinear transformations to discover complex patterns within the data (Niu, 2009). This paper employs deep learning methods to calculate the correlation coefficients for the basic models of diameter at breast height (DBH)—tree height and age—DBH for dominant tree types in the Manas River Basin of Xinjiang. We adopted a feedforward neural network with a single hidden layer containing 10 neurons, using the hyperbolic tangent function as the activation function. The output layer employed a linear activation function. The model was trained using the Levenberg–Marquardt algorithm with a learning rate of 0.01. In order to effectively prevent overfitting, we introduce L2 regularization (weight decay coefficient is 0.001), and monitor early stopping through the verification set during the training process to retain the model with the best generalization performance. To ensure the independence and reliability of the evaluation, we strictly divided the dataset into a training set (70%), a validation set (15%), and a test set (15%). All reported accuracy metrics are based on results from the test set, thereby avoiding overfitting-induced performance overestimation. Based on the introduction of variables such as climatic factors, the same method is used to calculate the correlation coefficients of the models. Compared to basic models and multiple nonlinear forest growth models, deep learning methods exhibit higher accuracy in establishing forest growth models. By utilizing a fully connected neural network constructed within the deep learning framework, combined with environmental factors, highly accurate predictions of DBH can be obtained. Many studies have demonstrated the feasibility of deep learning models in predicting tree growth (Zhang, Gu & Dong, 2014).

Model validation

The optimal models for DBH-tree height and age-DBH for each dominant tree types are obtained through the coefficient of determination R². Then, the measured validation sample data for each main tree types are substituted into the obtained optimal DBH—tree height and age—DBH models. Through validation and calculation, the predicted values of tree height (DBH) for each tree types are obtained. By comparing the measured values of tree height (DBH) in the validation sample data, and calculating validation accuracy indicators such as the coefficient of determination and root mean square error for model validation, the evaluation criteria are established. The calculation formulas are as follows (Lu et al., 2015):

Relative: (1)${\displaystyle \begin{array}{c}\hfill {\mathrm{R}}^2=1-\frac{\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}{\sum _{i=1}^n{\left(y_i-{\bar{y}}_i\right)}^2}.\hfill \end{array}}$

Root Mean Squared Error: (2)${\displaystyle \begin{array}{c}\hfill RMSE=\sqrt{\frac{\sum _{i=1}^n{\left(\hat{y}i-yi\right)}^2}{n-p}}.\hfill \end{array}}$

Mean Relative Error: (3)${\displaystyle \begin{array}{c}\hfill MRE=\frac{\sum _{i=1}^n\frac{\widehat{y_i}-y_i}{y_i}}{n}\hfill \end{array}.}$

Mean Error: (4)${\displaystyle \begin{array}{c}\hfill \mathrm{ME}=\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\widehat{y_i}-y_i}{\mathrm{n}}\hfill \end{array}.}$

In the formula: $\hat{y}$ represents the predicted value of tree height (or DBH). y_i represents the measured value of tree height (or DBH). $\bar{y}$ presents the average value of tree height (or DBH). n represents the number of trees in the validation sample. And p represents the number of independent variables in the model.

Simulation results of the basic model for diameter at breast height tree height

Both the regression models for Spruce and Poplar reached a goodness-of-fit also being achieved the best performance. Spruce exhibited the highest correlation coefficient of 0.670 (p < 0.01), following an S-curve model, while Poplar had an optimal fitting coefficient of 0.794, with the best-fit model being the S-model. A Mixed wood composed of Ulmus, Salix, Fraxinus, and Robinia had a maximum correlation coefficient of 0.138, with the optimal model being the logarithmic model. The correlation between the average DBH and average tree height in the Mixed wood was not strong, attributed to the diversity of tree types. Due to the extremely small sample size, Sand jujube had a maximum correlation coefficient of only 0.208. Populus euphratica maintained a stable significance level, with the highest correlation coefficient reaching 0.622, and the optimal model was the S-curve model. The optimal fitting equations for each tree types are as follows in Table 6: the detailed calculation results are presented in Table 7. The optimal fitted curve is shown in Fig. 2.

Simulation results of the basic model for tree age-diameter at breast height (DBH)

All stand age-DBH models reached a significant level (P < 0.001). The growth model yielded the highest coefficient of determination (R² = 0.675) and thus best performed among all models tested. For Poplar, the stand age-average DBH models also reached the best-fit model being the S-curve model, which had an R² = 0.812 (P < 0.001). This indicated that as forest age increased, the average DBH of Poplar also increased, demonstrating a good correlation between the two. The growth models fitted for mixed wood all reached the highest coefficient of determination reaching R² = 0.397 (P < 0.001), and the optimal growth model belonged to the linear model. Overall, due to the heterogeneity of tree types in Mixed wood and the relatively small number of modeling samples, the coefficients of determination were not high overall. The forest age-average DBH growth models for Sand jujube all with good overall fit and the highest model coefficient reaching R² = 0.810. The optimal growth model belonged to the Logistic model. The stand age-average DBH growth models for Populus euphratica reached a significant level with P < 0.005. Compared with other tree types, the fitting coefficients for Populus euphratica were lower, with the highest coefficient of determination being R² = 0.442, and the optimal model was the S-model. This may be attributed to the smaller number of modeling samples for Populus euphratica. The optimal models for the relationship between stand age and average DBH for each tree types are Respectively,as shown in Table 8: the detailed calculation results are presented in Table 9. The optimal fitted curve is shown in Fig. 3.

Evaluation of the basic model’s accuracy

The optimal DBH—tree height models and stand age-DBH models for each dominant tree types in the Manas River Basin of Xinjiang were calculated. The precision of the models fitted to the validation data is shown in Table 10 below: for the single-types models, Populus euphratica exhibited the smallest values across all three indicators, indicating a relatively higher prediction accuracy and the best fitting effect. The Mixed wood models showed larger values for mean error, mean relative error, and root mean square error, indicating a relatively lower prediction accuracy and the worst fitting effect. Considering both the DBH-tree height and stand age-DBH models, although Sand jujube had smaller mean error and mean relative error, Populus euphratica maintained a low level of root mean square error and, compared to other types models, demonstrated more stable overall error performance. Therefore, comprehensive analysis suggests that Populus euphratica had the best prediction accuracy among these types. This may be due to its growth characteristics or environmental factors that make its growth data more consistent with the prediction models. The Mixed wood had the worst prediction accuracy, which is related to the diversity of tree types it contains and the heterogeneity of the data.

Parameter selection for multivariate nonlinear forest growth models

By calculating the correlation coefficient R between DBH and various random factors, the specific results are shown in Table 11: the correlation coefficient R between elevation data (Km) and DBH is 0.520, which is the largest absolute value of positive correlation coefficients among the Environmental Covariates, indicating the strongest correlation between elevation data and DBH. Next, annual precipitation (P) and minimum of maximum daily temperature (TXn) have relatively strong correlations with tree DBH, with correlation coefficients R both being 0.410. The correlation coefficient R between vapor pressure deficit (KPa) and DBH is—0.060, which is the smallest absolute value of the correlation coefficients listed, suggesting the weakest correlation between vapor pressure deficit and DBH. Based on the comparison of correlation coefficients, the three Environmental Covariates with the strongest correlations with DBH—elevation data (DEM), annual precipitation (P), and minimum of maximum daily temperature (TXn)—are introduced into the basic model for the construction of a multivariate nonlinear forest growth model. Prior to constructing the multivariate nonlinear growth models, we performed multicollinearity diagnostics for all candidate independent variables. The variance inflation factor (VIF) method was used to assess the degree of collinearity among the variables. The results indicated that the VIF values for all variables were below the threshold of 5 (specific values: DEM = 2.3, Annual Precipitation = 2.134, TXn = 1.676), demonstrating the absence of severe multicollinearity issues. Therefore, these variables were deemed suitable for simultaneous inclusion in the model for analysis.

Simulation results of the multivariate nonlinear forest growth model

Based on the basic model, the three environmental covariates with the strongest correlations with DBH—elevation data (DEM), annual precipitation (P), and minimum of maximum daily temperature (TXn)—are introduced to construct a multivariate nonlinear forest growth model. Ultimately, the multivariate nonlinear forest growth models for each dominant tree types are determined. The specific results are shown in Table 12 below:

The calculation results indicate that the inclusion of Environmental Covariates has improved the model accuracy for dominant tree types overall, but a decreasing trend in model accuracy is observed for individual types. The specific results are shown in Table 13: The root mean square errors (RMSE) for DBH-tree height have decreased to some extent. For example, the RMSE for Spruce has decreased from 12.819 to 2.390, that for Poplar has decreased to 1.710, the RMSE for Mixed wood has reduced from 8.367 to 2.010, the RMSE for Sand jujube has decreased from 3.036 to 1.740, while the RMSE for Populus euphratica has increased by 0.572. For the age-DBH models of dominant tree types, the accuracy of the age-DBH model for Spruce and Mixed wood has improved, decreasing from 3.330 to 3.100 and from 11.860 to 5.410, respectively. However, for Poplar, Sand jujube, and Populus euphratica, the RMSEs have increased slightly. In terms of the model evaluation metric R², the R² for the DBH-tree height model of Poplar has increased to 0.800, and the R² for the DBH-tree height of Mixed wood has improved to 0.473. Additionally, the accuracy of the age-DBH model for Mixed wood has increased from 0.397 to 0.571, and the accuracy of the age-DBH model for Sand jujube has risen from 0.810 to 0.890. Overall, the incorporation of random effects has improved the accuracy of the models, but there are certain limitations.

Evaluation of the accuracy of multivariate nonlinear models

The calculations were performed on a 30% validation sample to obtain the accuracy test values for the multivariate nonlinear DBH-tree height models and multivariate nonlinear age-DBH models for each dominant tree types. The specific results are shown in Table 14 below. In the DBH-tree height models, Mixed wood exhibited larger values for the accuracy assessment coefficients, indicating poorer fitting accuracy. For Sand jujube, the mean error, mean relative error, and root mean square error were all relatively small, indicating the best fitting accuracy. Among the age-DBH model group, Sand jujube had the smallest mean error of 3.420 and the lowest mean relative error of 0.230, demonstrating the best fitting accuracy. Mixed wood had the lowest RMSE of 0.110, indicating good fitting accuracy as well. Overall, Sand jujube showed the best fitting accuracy, while Mixed wood had an average fitting performance.