Method for building full-cycle crown breadth model of Chinese fir

Abstract

The invention provides a Chinese fir full-period crown breadth model research and construction method, belongs to the field of model construction, and constructs a single-tree full-growth-period crown breadth prediction model. The system analyzes the dynamic characteristics of crown breadth growth and the multi-scale influence mechanism thereof. The basic model taking the diameter at breast height and the tree height as core variables well reflects the tree growth law, the age dummy variable effectively captures the dynamic change characteristics of the crown breadth in different growth stages, and the introduction of the mixed effect model significantly improves the precision and applicability of the model (R2 = 0.717, RMSE = 0.502), so that the model has good application prospects. The macroscopic and microscopic influence of the block and sample plot effect on crown breadth growth is quantified. The comprehensive consideration of environmental heterogeneity and random effect is the key of whole growth cycle modeling, and an important scientific basis is provided for sustainable management of forest resources and dynamic monitoring of an ecological system. The method and the framework are suitable for other tree species or ecological systems, and a new thought is provided for optimizing crown breadth prediction, revealing the effect of environmental factors and improving the carbon sink evaluation precision.

Description

Technical Field

[0001] The invention relates to the field of model construction, and in particular to a method for developing a full-cycle crown width model of Chinese fir. Background Art

[0002] As a key parameter for measuring tree crown size, crown width plays a vital role in forestry management and single tree research. Crown width not only directly reflects the growth status of trees, but also is an important input variable in growth and yield models, such as aboveground biomass models and base area increment models. In addition, crown width is also used to assess the health and vitality of trees. By monitoring the changes and morphological characteristics of crown width, the physiological state of trees can be effectively reflected. The size and morphology of the crown are closely related to the photosynthetic efficiency of the forest, affecting the carbon fixation capacity and energy flow of the entire forest community, and thus affecting the climate regulation function. The different structures of the crown width promote the maintenance of forest species diversity, provide a variety of habitats for a variety of organisms, and enhance the stability and resilience of the ecosystem. In many disciplines such as forest ecology, forestry, and forest management, accurate measurement and prediction of crown width are essential for the formulation of scientific forest management plans, including management measures such as reasonable thinning, selection and breeding of excellent tree species, and optimization of forest structure. Detailed information about the crown helps to understand the management of ecosystem characteristics, such as forest productivity, biodiversity, and wildlife habitats. Through the full growth cycle monitoring and analysis of crown width data, the health status and service functions of forest ecosystems can be effectively evaluated, and the formulation of sustainable forest management and ecological protection strategies can be supported, which is of great significance for promoting the sustainable use of forest resources and the optimization of ecological functions. Therefore, as a multifunctional ecological indicator, the importance of crown width is not only reflected in the growth of trees at a single level, but runs through all aspects of forest ecosystems, becoming an indispensable key parameter in the precise measurement of forests. Although crown width is an important parameter reflecting the growth status of trees, measuring crown width (CW) of each tree in all plots is time-consuming, labor-intensive, and costly. Therefore, how to construct a high-precision crown width prediction model for the entire growth cycle has become the core and focus of current research.

[0003] Traditional crown width prediction model methods mainly rely on statistical methods to establish quantitative relationships between crown width and factors such as breast diameter, tree height, and stand density. With the deepening of research, researchers have gradually introduced multiple regression analysis and nonlinear models to more comprehensively describe the complex relationship between crown width and multiple variables. These models have evolved from simple least squares model regression, linear models to complex nonlinear models, and then to mixed effect models that consider random effects and fixed effects, gradually improving the accuracy and applicability of predictions. However, although these models have achieved remarkable results in the short term or a specific growth period, their prediction accuracy and applicability are often limited in the crown width model prediction for the entire growth cycle, because there are significant differences in the crown width growth rate of different age groups, and traditional models fail to consider the factors of the entire growth cycle in crown width prediction. The crown width prediction for the entire growth cycle needs to take into account the physiological and morphological changes of trees at different growth stages, as well as the long-term effects of environmental factors and human intervention measures. In order to achieve a more reliable prediction for the entire growth cycle, by introducing age groups into the model and introducing dummy variables to analyze the effects of different age structures on the crown width of Chinese fir, the model can better adapt to the growth characteristics of Chinese fir in different age groups. In addition, considering that the crown width model of the entire growth cycle can not only accurately reflect the dynamic process of tree growth, but also provide profound insights into the long-term health and stability of forest ecosystems, it makes up for the shortcomings of traditional models in long-term predictions and has important application value and research significance.

[0004] In addition, different blocks and plots also reflect different growth differences, which may be caused by the geographical environment (such as soil type, humidity, climatic conditions, etc.), and have a significant impact on the formation of crown width. The two-level mixed effect model can effectively separate the variation at the block and plot levels, provide more accurate parameter estimates, and capture the interactions between different levels, thereby improving the explanatory power and predictive ability of the model. Although the two-level mixed effect model has been widely used in dealing with multi-level data such as blocks and plots, the research on crown width prediction has mostly focused on a single growth stage or short-term prediction, and failed to comprehensively consider the multi-level environmental factors and age group changes in the entire growth cycle. Based on the crown width model of the full growth cycle, this study added blocks and plots as parameters to establish a two-level mixed effect model. By combining the dual mixed effects of blocks and plots, the interaction between environmental factors and age group changes is comprehensively processed, which is suitable for complex ecosystem analysis and significantly enhances the explanatory power and applicability of the model to deal with multiple factors. This multi-level model not only improves the accuracy of crown width prediction, accurately reflects the dynamic process of tree growth, and provides profound insights into the long-term health and stability of forest ecosystems, but also makes up for the shortcomings of traditional models in long-term predictions. It has important application value and research significance. Summary of the invention

[0005] The purpose of this patent is to solve the problems mentioned in the above background technology and provide a method for developing a full-cycle crown width model of Chinese fir.

[0006] The technical solution of the present invention provides: a method for developing a full-cycle crown width model of Chinese fir, comprising the following steps:

[0007] S101: Data collection and processing of ground survey of Chinese fir forest

[0008] The single tree field survey data excluded dead trees, dead branches, and litter of lower vegetation. The survey information included tree species, diameter at breast height, tree height, height under branches, crown width, growth status, site type, forest age, age group, etc. The tree species in the study area were all artificial Chinese fir forests. The data set was divided into a training set and a validation set in a ratio of 7:3; 70% of the data was used for modeling and 30% for validation.

[0009] S102: Variable selection

[0010] The following eight key variables were selected: DBH, H, HCB, CW, AG, SD, DH and CD. The growth parameter variables of Chinese fir were screened by Pearson, and the VIF<10 collinearity test was performed to avoid the interdependence between multiple predictor variables. Finally, two variables with the highest correlation with the CW were selected as the independent variables of the model to construct binary model, dummy variable model and two-level mixed effect model.

[0011] S103: Univariate and bivariate model building

[0012] aBasic model construction

[0013] Six crown width models with biological significance were selected as candidate basic models, namely, allometric model, power function model, exponential function model, logistic model, Richard function model, and linear model. The variables with the highest influence coefficient and correlation were used as independent variables to construct a binary model to fit the data.

[0014] Allometric model: CW i =β 0 +β 1 x 1 +β 2 x 2 +β 3 (x 1 × 2 )+ε i (1)

[0015] Power function model: CW i =β 0 x 1 β1 x 2 β 2 +ε i (2)

[0016] Exponential function model: CW i =β 0 exp(β 1 x 1 +β 2 x 2 )+ε i (3)

[0017] Logistic Model:

[0018] Richard function model:

[0019] Linear Model: CW i =β 0 +β 1 x 1 +β 2 x 2 +ε i (6)

[0020] Among them, x1 and x2 are the variables with the highest influence coefficient and correlation; β1, β2, β3 are the parameters to be estimated, and ε is the error term;

[0021] The study used the coefficient of determination R 2 The fitting and prediction performance of the six theoretical crown growth models were compared by using four indicators: root mean square error (RMSE), total relative error (TRE), and Akaike information criterion (AIC). The model with the best fitting effect was selected as the basic model for the subsequent construction of the crown hybrid model. The calculation is shown in formulas (7)-(10):

[0022]

[0023]

[0024]

[0025] AIC=2k-2ln(L)(10)

[0026] Where: is the observed value of the dependent variable; is the predicted value of the dependent variable by the model; is the average value of the observed values; N is the number of observed values; K is the number of parameters in the model; L is the maximum likelihood of the model;

[0027] b Construction of dummy variable model

[0028] When the model considers both the plot index effect and the influence of age group on crown width, the age group AG is first introduced into the model as a dummy variable, and a dummy variable model is established to evaluate the influence of different forest ages on crown width; AG includes five categories: young forest, middle-aged forest, near-mature forest, mature forest and over-mature forest; when constructing the model, a certain age group is selected as the reference group, and the variables of other age groups are transformed into quantitative variables and assigned values ​​of 0 or 1 in the regression analysis; when there are n categorical variables, it is usually necessary to set one category as the reference group, so the number of dummy variables is n-1; through this method, the dummy variable model can flexibly compare the differences between different forest age groups and the reference group;

[0029]

[0030] c Establishment of two-level mixed effects model

[0031] The validation process of the mixed effect model is mainly carried out by evaluating the goodness of fit of the model and the accuracy of the random effect estimation. In terms of the evaluation of the goodness of fit of the model, the residual analysis is first used to check whether the model has systematic deviations to ensure that the residuals meet the assumptions of normality and uniformity and have no significant heteroscedasticity. In addition, the cross-validation method is used to evaluate the generalization ability of the model, that is, the prediction performance of the model on unseen data is verified by dividing the data set into a training set and a validation set to test its robustness and prediction consistency. Regarding the estimation of random effects, the model uses maximum likelihood estimation (MLE) to optimize the parameters of fixed effects and random effects.

[0032] On the basis of the full-cycle growth model, the study used block and plot as two levels of random effects to construct a two-level nonlinear mixed effect model to predict crown width; the fixed effect of the model was used to explain the overall influence of the variables with the highest correlation with crown width on crown width, while the random effect part of block and plot allowed the introduction of variability between different blocks and plots; the optimal two-level mixed effect model was selected to explain and predict the changes in tree crown width; its formula is:

[0033]

[0034] y ij represents the crown amplitude of the jth plot in the ith block; f(φi, vij) represents a nonlinear function that depends on the linear predictor φi and other covariates v ij ; ε ij represents the error term, which is usually assumed to follow a normal distribution N(0,σ 2 ), which is used to capture random errors that cannot be explained by the model; It means there are M blocks in total, each block contains Ma plots, and the total number of plots is j = 1, ..., ni means there are plots in each block; Ai is the design matrix, containing the predictor variables of fixed effects; β is the fixed effect coefficient vector; The design matrix contains random effect variables associated with block-plot interactions; The random effects at the block level are assumed to have a mean of 0 and a variance of N(0,Ψ (Block) )’s multivariate normal distribution; The design matrix contains random effect variables associated with block-plot interactions; The random effects at the block and plot interaction level are assumed to have a mean of 0 and a variance of N(0,Ψ (Block×Plot) ) is normally distributed; the random effect assumption and the error term assumption are independent of each other and both obey the normal distribution.

[0035] As a preferred embodiment, in step S103, when the basic model is constructed, R 2 The larger it is, the higher the model fitting accuracy is; the smaller the RMSE is, the higher the model prediction accuracy is; the smaller the TRE is, the better the prediction performance is; the smaller the AIC is, the better the model fitting effect is.

[0036] Preferably, in step S103, when establishing a two-level mixed effects model, a two-level nonlinear mixed effects model is constructed on the basis of the full-cycle growth model to predict the crown width; in the first level, the block group is used as a random effect to reflect the impact of environmental differences and management measures between different block groups on tree growth; in the second level, the sample plot is used as a random effect to further capture the variability between different sample plots in the same block group; by using this nested two-level nonlinear mixed effects model, it is possible to more accurately describe complex data structures and explain the interaction of factors at different levels on tree growth.

[0037] Beneficial effects of the present invention:

[0038] As an important economic tree species widely planted in southern China, Chinese fir is not only the main source of timber for the forestry industry, but also an important tree species for maintaining regional ecological balance, increasing carbon sinks, regulating water sources and reducing soil erosion. Its growth and development are affected by many factors, especially the change of crown width. In order to construct an effective crown width prediction model for Chinese fir throughout the growth cycle, this study took Chinese fir as the research object, used 133 plots with a total of 16,101 Chinese fir trees, and established a crown width inversion model for the full growth cycle of pure artificial forests, taking into account the growth differences of crown width at different growth stages. The purpose of this study is to 1) develop a crown width model for Chinese fir throughout the growth cycle and improve the accuracy of the crown width model. 2) Develop a secondary nonlinear mixed effect model covering the entire growth cycle, using block groups and plots as random effects, to provide an accurate reference for forest management activities under different environmental conditions. By establishing a crown width model for the entire growth cycle, it is intended to provide technical support for forest resource surveys and accurate improvement of forest quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the present disclosure, the following briefly introduces the drawings required to be used in some embodiments of the present disclosure. Obviously, the drawings described below are only drawings of some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can also be obtained based on these drawings. In addition, the drawings described below can be regarded as schematic diagrams, and are not limitations on the actual size of the products involved in the embodiments of the present disclosure, the actual process of the method, the actual timing of the signal, etc.

[0040] Figure 1 Correlation coefficient between crown width and each variable and collinearity test ((a) correlation coefficient between CW and other variables (b) collinearity between CW and each variable. The y-axis is VIF value).

[0041] Figure 2 Comparison of residual plots of three models. DETAILED DESCRIPTION

[0042] In order to enable those skilled in the art to better understand the technical solutions in this application, the following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this application.

[0043] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of this application.

[0044] The present invention is described in further detail below by way of examples.

[0045] Example 1

[0046] The data of this embodiment are collected from 133 sample plots in Lechang City, Yingde City, Heping County, Lianshan County, Longshan County, Yunnan County and Shixing County, Guangdong Province, China. The geographical coordinates of Guangdong Province are 109°45′ to 117°20′ east longitude and 20°09′ to 25°31′ north latitude. As of 2023, the province's forest area is about 10.85 million hectares, accounting for 57.1% of the total land area, and the forest coverage rate is about 9.6 million hectares, with a forest coverage rate of 53.9%. This makes it one of the important ecological protection areas in southern China. The terrain of the province is dominated by mountains, hills, plains, and water bodies, with an overall trend of high north and low south. Guangdong has a subtropical monsoon climate with obvious changes in the four seasons, warm and humid spring, hot and rainy summer, mild and less rainy autumn, and cool and dry winter. There is also significant regional climate diversity in the province. The precipitation in the region has obvious monsoon characteristics. Affected by the southeast monsoon, the rainfall is abundant in summer, and in winter, it is affected by the cold and dry northwest wind, with little precipitation and dryness.

[0047] The method for developing a full-cycle crown width model for Chinese fir includes the following steps: data collection and preprocessing

[0048] S101: Ground survey data of Chinese fir forest

[0049] The single tree field survey data was collected in March 2024. A ground data survey was conducted on 133 plots of 30m×30m. The data excluded dead fallen trees, dead branches, litter of lower vegetation, etc., which were non-human damage caused by natural factors (such as wind, insect pests, etc.), as well as missed, wrong and repeated data. By removing these irrelevant data, it is ensured that only healthy and research-suitable tree samples are included in the model analysis. A total of 16,101 Chinese fir trees were collected. The survey information includes tree species, diameter at breast height, tree height, height under branches, crown width, growth status, site type, forest age, age group and other data. The tree species in the study area are all artificial Chinese fir forests (Table 1). The collection and processing of data strictly follow the standard field survey process to ensure the accuracy and reliability of the data. In this embodiment, the data set is divided into a training set and a validation set in a ratio of 7:3. 70% of the data is used for modeling and 30% for validation.

[0050] Table 1 Summary statistics of model fitting and validation data

[0051]

[0052] S102: Variable selection

[0053] In addition to being related to DBH, crown width is also affected by other forest stand variables such as tree size and forest stand vitality factor, site condition factor, and forest stand competition factor. Based on existing research results, this example selected the following eight key variables: DBH, tree height (H), crown base height (HCB), crown width (CW), forest age (AG), forest stand density (SD), dominant tree height (DH), and canopy density (CD).

[0054] The growth parameter variables of Chinese fir were screened by Pearson, and the collinearity test of inflation coefficient VIF (VIF<10) was performed to avoid the interdependence between multiple predictor variables. Finally, two variables with the highest correlation with crown width were selected as independent variables of the model to construct binary model, dummy variable model and two-level mixed effect model.

[0055] S103: Univariate and bivariate model building

[0056] aBasic model construction

[0057] This example is based on the complete growth cycle data of a single fir tree in Guangdong Province to develop a crown growth model for fir. Six crown models with biological significance were selected as candidate basic models, namely, allometric model (model 1), power function model (model 2), exponential function model (model 3), logistic model (model 4), Richard function model (model 5), and linear model (model 6). The variables with the highest influence coefficient and correlation were used as independent variables to construct a binary model to fit the data.

[0058] CW i =β 0 +β 1 x 1 +β 2 x 2 +β 3 (x 1 × 2 )+ε i (1)

[0059] CW i =β 0 x 1 β 1 x 2 β 2 +ε i (2)

[0060] CW i =β 0 exp(β 1 x 1 +β 2 x 2 )+ε i (3)

[0061]

[0062]

[0063] CW i =β 0 +β 1 x 1 +β 2 x 2 +ε i (6)

[0064] Among them, x1 and x2 are variables with the highest influence coefficient and correlation; β1, β2, β3 are parameters to be estimated, and ε is the error term.

[0065] The study used the coefficient of determination (R 2 ), root mean square error (RMSE), total relative error (TRE), and Akaike information criterion (AIC) were used to compare the fitting and prediction performance of the six theoretical crown growth models. 2 The larger the value, the higher the model fitting accuracy; the smaller the RMSE, the higher the model prediction accuracy; the smaller the TRE, the better the prediction performance; the smaller the AIC, the better the model fitting effect. Finally, a model with the best fitting effect is selected as the basic model for the subsequent construction of the crown-width mixed model. The calculation is shown in formulas (7)-(10):

[0066]

[0067]

[0068]

[0069] AIC=2k-2ln(L) (10)

[0070] Where: is the observed value of the dependent variable; is the predicted value of the dependent variable by the model; is the average of the observed values; N is the number of observations; K is the number of parameters in the model; and L is the maximum likelihood of the model.

[0071] b Construction of dummy variable model

[0072] Dummy variables are an important tool for processing categorical variables. They convert categorical variables into binary variables so that they can be included in regression models for analysis. When the model considers both the plot index effect and the effect of age group on crown width, the age group (AG) is first introduced into the model as a dummy variable to establish a dummy variable model to evaluate the effect of different stand ages on crown width. The division of age groups can distinguish the growth differences of trees at different age stages. By introducing dummy variables, the effects of different stand ages can be quantified as categorical variables, thereby better understanding the effects of each developmental stage on the biomass of Chinese fir and analyzing the contribution of different age groups to the total biomass.

[0073] Among them, AG includes five categories: young forest, middle-aged forest, near-mature forest, mature forest and over-mature forest. When constructing the model, a certain age group was selected as the reference group, and the variables of other age groups were transformed into quantitative variables and assigned values ​​of 0 or 1 in the regression analysis. When there are n categorical variables, it is usually necessary to set one category as the reference group, so the number of dummy variables is n-1. In this way, the dummy variable model can flexibly compare the differences between different forest age groups and the reference group. This method not only simplifies the processing of age group variables, but also enhances the model's ability to interpret multi-category data, enabling an in-depth understanding of the staged impact of forest age on crown growth.

[0074]

[0075] c Establishment of two-level mixed effects model

[0076] The mixed effects model was predicted by using the 'predict' function of the R language and the 'anova' function for stepwise model comparison, and the appropriate combination of fixed and random effects was selected. The model structure was optimized by comparing the AIC and other indicators of different models. The validation process of the mixed effects model was mainly carried out by evaluating the goodness of fit of the model and the accuracy of the random effect estimation. In terms of the evaluation of the goodness of fit of the model, the residual analysis was first used to check whether the model had systematic deviations, ensuring that the residuals met the normality and uniformity assumptions and had no significant heteroscedasticity. In addition, the cross-validation method was applied to evaluate the generalization ability of the model, that is, the prediction performance of the model on unseen data was verified by dividing the data set into a training set and a validation set to test its robustness and prediction consistency. Regarding the estimation of random effects, the model used maximum likelihood estimation (MLE) to optimize the parameters of fixed and random effects. These methods accurately estimated the variance and effect size of the random effects by maximizing the likelihood function, thereby quantifying the variability between different levels.

[0077] Based on the full-cycle growth model, a two-level non-linear mixed effects model was constructed to predict crown width by studying the simultaneous use of blocks and plots as two levels of random effects. At the first level, the block is used as a random effect to reflect the environmental differences between different blocks and the impact of management measures on tree growth; at the second level, the plot is used as a random effect to further capture the variability between different plots within the same block. By using this nested two-level non-linear mixed effects model, the complex data structure can be more accurately described, and the interaction effects of factors at different levels on tree growth can be explained.

[0078] The fixed effects of the model are used to explain the overall impact of the variables most correlated with crown width on crown width, while the random effect parts of the blocks and plots allow for the introduction of variability between different blocks and plots. This can not only improve the prediction accuracy of the model but also reveal the growth patterns of trees under different environmental conditions and at different growth stages. Finally, the best two-level mixed effects model was selected to explain and predict the changes in tree crown width. The formula is as follows:

[0079]

[0080] y ij represents the crown width value (response variable) of the j-th plot in the i-th block; f(φi, vij) represents a non-linear function that depends on the linear predictor φi and other covariates v ij ; ε ij represents the error term, which is usually assumed to follow a normal distribution N(0, σ 2 ), and is used to capture the random errors that the model cannot explain. represents that there are a total of M blocks, each block contains Ma plots, and the total number of plots is j = 1,..., ni represents the number of plots in each block; Ai is the design matrix containing the predictor variables of the fixed effects; β is the vector of fixed effect coefficients; is the design matrix containing the random effect variables related to the interaction between blocks and plots; is the random effect at the block level, which is assumed to follow a multivariate normal distribution with a mean of 0 and a variance of N(0, Ψ (Block) ); is the design matrix containing the random effect variables related to the interaction between blocks and plots; is the random effect at the interaction level between blocks and plots, which is assumed to follow a normal distribution with a mean of 0 and a variance of N(0, Ψ (Block×Plot) ); The random effect assumption and the error term assumption are independent of each other and both follow a normal distribution.

[0081] Result Analysis

[0082] Parameter Optimization

[0083] Pearson correlation test showed that the correlation between eight growth parameters including DBH, tree height (H), crown base height (HCB), crown width (CW), stand age (A), stand density (SD), dominant tree height (DH) and canopy density (CD) and crown width (CW) was high. Then the inflation coefficient VIF (VIF < 10) was used as a collinearity test method. Figure 1 From a. in the figure, we can see that the effect of breast diameter on crown width is the most significant (correlation coefficient is 0.69), followed by a significant positive correlation between tree height and crown width (correlation coefficient is 0.59), and the VIF values ​​of breast diameter and tree height with crown width are all less than 10 ( Figure 1 Therefore, DBH and tree height were selected as the independent variables of the model, and a binary model with DBH and tree height as independent variables was constructed.

[0084] Binary Model

[0085] After determining that DBH and tree height (H) are the most critical variables affecting crown width (CW), DBH and tree height were used as independent variables in 6 basic models for modeling, and the goodness of fit of different models was evaluated by different parameters. Table 2 shows the evaluation indicators of the 6 models. Overall, in the modeling data and test data, all model indicators are close, and the R2 of the 6 models is above 0.47.

[0086] As shown in Table 2, the prediction effect of the allometric model is better than that of other models, and its fitting accuracy is the highest (R 2 =0.4898). At the same time, the Akaike information criterion (AIC), the coefficient of determination (R 2 ), root mean square error (RMSE) and total relative error (TRE) evaluation indicators, the allometric model showed the best prediction effect. Therefore, this model was determined to be the optimal model and used as the basic model for the subsequent construction of the full-cycle crown width model and the two-level mixed effect model.

[0087] Table 2. Fitting accuracy of binary model

[0088]

[0089] Dummy variable model

[0090] Dummy variables are used to represent different age groups. Based on the analysis of each test, the model with the dummy variable applied to parameter a shows the best fit result. As shown in Table 3, after adding the qualitative factor of age group, the model R 2The value of the R2 of the binary allometric model was 0.507, which was 3.35% higher than that of the binary allometric model, and the AIC was reduced by 1.77%. The RMSE and TRE were reduced by 1.92% and 4.48%, respectively. Compared with the binary allometric model, the fitting error of the model was significantly reduced after adding the age group, and it had a better fitting effect. This shows that the change of crown width is not only closely related to the age of the trees, but also affected by the growth differences between different age groups.

[0091] Table 3

[0092]

[0093] Note: It is expressed as five age groups, namely AGE 1 Young forest, AGE 2 Middle-aged forest, AGE 3 Nearly mature forest, AGE 4 Mature forest, AGE 5 Overmature forest.

[0094] Construction of two-level nonlinear mixed effects model

[0095] Based on Model 13, a two-level random effect model with region and plot was established (Model 14). Various forms of models were tried, and the influence of random effects on parameters was studied. Finally, when the region Block was applied to b+c and the plot effect was applied to parameter b, all indicators of the model were optimal. The evaluation indicators of the model are shown in the following table.

[0096]

[0097] Where: CW ijk represents the canopy width of the kth tree in the jth plot in the ith region, AGE i Dummy variables representing the five growth stages, i = 1, 2, 3, 4, 5, u ik represents the random effect of the kth tree in the ith block, v ijk represents the random effect of the kth tree in the jth plot of the ith block, DBH ijk H represents the diameter at breast height of the kth tree in the jth plot in the ith region, and H represents the height of the kth tree in the jth plot in the ith region.

[0098] As shown in Table 4, the prediction effect of the nested two-level mixed effect model is significantly improved compared with the basic binary model and dummy variable model. 2 reached 0.717. In the modeling results, the fitting accuracy of the two-level mixed effect model R 2It was 31.66% higher than the basic binary model and 29.99% higher than the dummy variable model. The RMSE value and AIC value were 25.74% and 27.39% lower than the basic binary model, and 24.19% and 26.08% lower than the dummy variable model. This shows that the model covering the entire growth cycle has a stronger explanatory power in explaining the variability of crown width in this model. The random effect model further revealed the impact of regional environmental differences and plot heterogeneity on the dynamic evolution of crown width, indicating that the growth process of crown width is a complex dynamic system affected by the interaction of multiple factors.

[0099] Table 4

[0100]

[0101] from Figure 2 From the residual plot, the residuals of the three models are distributed around the zero value, but the residuals of the binary allometric model and the dummy variable model show certain heteroscedastic characteristics, and the residuals show a larger fluctuation range when the fitting value is large. In contrast, the residual distribution of the two-level NLME model is more uniform and the heteroscedastic phenomenon is less, indicating that it can better capture the random effects in the data and eliminate heteroscedasticity. In addition, from the perspective of fitting accuracy, the residual distribution range of the two-level NLME model is the smallest, and the fitting accuracy is better than other models, further demonstrating its advantages in dealing with complex data structures.

[0102] discuss

[0103] This embodiment constructs a crown width prediction model for the entire growth cycle of southern Chinese fir. First, a model that better describes the relationship between crown width and diameter at breast height is determined from common models as the basic model, which is also consistent with Fu's approach. This embodiment selects the allometric model as the optimal basic model. In the model variable screening process, the diameter at breast height (DBH) is selected as the core independent variable, and the tree height is selected as the second independent variable of the binary model. The changes in the diameter at breast height and the tree height are two important aspects of tree growth. There is a close correlation between the two growth relationships, reflecting the trade-off between horizontal growth and vertical growth of trees. The diameter at breast height is the core factor of the crown width model, which is consistent with the results of previous studies. The allometric relationship between the diameter at breast height and the crown width has been verified in the research of many tree species, especially in the prediction of the growth dynamics of trees. The diameter at breast height has been proven to be one of the most reliable indicators for predicting the size of the crown width, the overall growth status of trees and the amount of wood stock due to its easy measurement and high correlation. Adding tree height as the second explanatory factor in variable screening further improves the framework of the crown width model, and its importance is consistent with some research results. As an important factor affecting the variability of crown width, tree height can not only reflect the overall growth status of trees, but also supplement the crown width variation information that cannot be captured by the diameter at breast height. For example, in trees of different age groups, the contribution of tree height is particularly significant. The combination of the two laid the foundation for the establishment of a full growth cycle crown width model in the later stage of the article.

[0104] In order to establish a crown width model for the entire growth cycle, this embodiment introduces dummy variables into the crown width prediction model to capture the dynamic characteristics of crown width growth at different stages, quantify the staged effects of different age groups on the crown width growth of Chinese fir, and effectively solve the problem that categorical variables cannot be directly included in the regression model. Previous studies have mainly focused on the crown width characteristics in a specific growth period or under static conditions, and few studies have established models for the dynamic change process of the entire growth cycle. Therefore, this embodiment believes that it is of great significance to establish a crown width model for the entire growth cycle. On the one hand, the division of age groups enables the capture of the growth characteristics of trees at different development stages, and its impact on the crown width reflects the dynamic changes of Chinese fir in young forests, middle-aged forests, near-mature forests, mature forests and over-mature forests, which improves the applicability of the model in long-term predictions, provides a scientific basis for forest management and management, and improves the accuracy and ecological explanatory power of predictions. On the other hand, the crown width model for the entire growth cycle helps to optimize the sustainable use of forest resources. In the study of climate change, ecological protection and forest carbon sinks, high-precision crown width prediction can support more scientific decision-making. In addition, the applicability of the model is not limited to specific tree species or regions, but can also provide theoretical and methodological support for other forest ecosystems and for forest dynamics monitoring on a global scale.

[0105] When constructing a crown width prediction model for the entire growth cycle, it was found that only by introducing dummy variables to quantify the impact of different age groups on crown width growth, although the stage-by-stage dynamic changes in crown width were captured to a certain extent, the accuracy improvement of the model was relatively limited. Studies have shown that regional environmental differences and plot heterogeneity play an important role in the growth process of trees. Ignoring these factors may lead to inaccurate descriptions of the model's crown width growth dynamics. When studying the relationship between crown width and environmental factors, it was found that the introduction of random effects can effectively improve the fitting accuracy and prediction performance of the model. Therefore, this embodiment further adopts a two-level mixed effects model, and incorporates block and plot effects as random effects into the model to cope with crown width changes caused by environmental heterogeneity. The introduction of the mixed effects model not only significantly improved the model's fitting accuracy and prediction performance (R 2 The results show that the improvement in the proposed method and the decrease in RMSE are both significant), and the effects of different environmental factors on crown growth are quantified from a statistical perspective. Specifically, the block effect captures the long-term impact of regional environmental differences (such as climate conditions, soil types, etc.) on tree crowns, while the plot effect reflects the competition relationship and resource allocation pattern between individual trees at the micro scale. By distinguishing these two types of environmental factors, this example reveals the multi-scale dynamic mechanism of crown growth, which provides an important reference for the construction of future full-growth cycle crown models.

[0106] This example reveals the dynamic characteristics of crown width growth and its multi-scale mechanism of Chinese fir by constructing a crown width prediction model for the entire growth cycle. The results show that the model with diameter at breast height as the core variable and tree height as an auxiliary factor can better describe the relationship between crown width and tree growth. The allometric relationship between diameter at breast height and crown width has been widely verified in a variety of tree species, and the introduction of tree height further improves the sensitivity and stability of the model, especially in the dynamic changes of crown width at different age groups. In order to capture the stage characteristics of crown width growth, this paper introduces dummy variables to quantify the age group effect, but the dummy variable model has limited explanatory power for environmental heterogeneity. To this end, the study adopted a mixed effects model, incorporating block and plot effects as random effects, which significantly improved the model accuracy (R 2 The results show that comprehensive consideration of environmental heterogeneity and random effects is the key to modeling the entire growth cycle, providing important theoretical support for forest resource management and ecosystem research.

[0107] in conclusion

[0108] This example systematically reveals the dynamic characteristics of crown width growth and its multi-scale influencing mechanism by constructing a crown width prediction model for the entire growth cycle of Chinese fir, and comprehensively using the allometric model, dummy variable model and mixed effect model. The results show that the model with DBH and tree height as the core explanatory variables can effectively reflect the main characteristics of crown width and tree growth, and the introduction of age group dummy variables further captures the dynamic change characteristics of crown width at different growth stages. In contrast, the mixed effect model significantly improves the accuracy and applicability of the model (R2=0.717, RMSE=0.502) by quantifying the macro and micro effects of environmental factors such as block groups and plots on crown width growth. The study fully proves the necessity of comprehensively considering environmental heterogeneity and random effects in crown width prediction, and provides a scientific basis for a comprehensive understanding of the ecological mechanism of Chinese fir crown width growth. This example not only provides theoretical support for crown width modeling of Chinese fir throughout its growth cycle, but also provides important practical guidance for the sustainable management of forest resources, carbon sink assessment and dynamic monitoring of ecosystems.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

[0110] The above describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claim involved.

[0111] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for developing a full-cycle crown width model for Chinese fir, characterized by: The following steps are involved: S101: Data collection and processing of ground survey of Chinese fir forest The single tree field survey data excluded dead trees, dead branches, and litter of lower vegetation. The survey information included tree species, diameter at breast height, tree height, height under branches, crown width, growth status, site type, forest age, age group, etc. The tree species in the study area were all artificial Chinese fir forests. The data set was divided into a training set and a validation set in a ratio of 7:3; 70% of the data was used for modeling and 30% for validation. S102: Variable selection The following eight key variables were selected: DBH, H, HCB, CW, AG, SD, DH and CD. The growth parameter variables of Chinese fir were screened by Pearson, and the VIF<10 collinearity test was performed to avoid the interdependence between multiple predictor variables. Finally, two variables with the highest correlation with the CW were selected as the independent variables of the model to construct binary model, dummy variable model and two-level mixed effect model. S103: Univariate and bivariate model building aBasic model construction Six crown width models with biological significance were selected as candidate basic models, namely, allometric model, power function model, exponential function model, logistic model, Richard function model, and linear model. The variables with the highest influence coefficient and correlation were used as independent variables to construct a binary model to fit the data. The study used the coefficient of determination R 2 The fitting and prediction performance of the six theoretical crown growth models were compared by using four indicators: root mean square error (RMSE), total relative error (TRE), and Akaike information criterion (AIC). The model with the best fitting effect was selected as the basic model for the subsequent construction of the crown hybrid model. The calculation is shown in formulas (7)-(10): AIC=2k-2ln(L)(10) Where: y i is the observed value of the dependent variable; is the model's predicted value for the dependent variable; is the mean of the observed values; N is the number of observed values; K is the number of parameters in the model; L is the maximum likelihood of the model; b Construction of dummy variable model When the model considers both the plot index effect and the influence of age group on crown width, the age group AG is first introduced into the model as a dummy variable, and a dummy variable model is established to evaluate the influence of different forest ages on crown width; AG includes five categories: young forest, middle-aged forest, near-mature forest, mature forest and over-mature forest; when constructing the model, a certain age group is selected as the reference group, and the variables of other age groups are transformed into quantitative variables and assigned values ​​of 0 or 1 in the regression analysis; when there are n categorical variables, it is usually necessary to set one category as the reference group, so the number of dummy variables is n-1; through this method, the dummy variable model can flexibly compare the differences between different forest age groups and the reference group; c Establishment of two-level mixed effects model The validation process of the mixed effect model is mainly carried out by evaluating the goodness of fit of the model and the accuracy of the random effect estimation. In terms of the evaluation of the goodness of fit of the model, the residual analysis is first used to check whether the model has systematic deviations to ensure that the residuals meet the assumptions of normality and uniformity and have no significant heteroscedasticity. In addition, the cross-validation method is used to evaluate the generalization ability of the model, that is, the prediction performance of the model on unseen data is verified by dividing the data set into a training set and a validation set to test its robustness and prediction consistency. Regarding the estimation of random effects, the model uses maximum likelihood estimation (MLE) to optimize the parameters of fixed effects and random effects. Based on the full-cycle growth model, the study used block and plot as two levels of random effects to construct a two-level nonlinear mixed effect model to predict crown width. The fixed effect of the model was used to explain the overall influence of the variables with the highest correlation with crown width on crown width, while the random effect of block and plot allowed the introduction of variability between different blocks and plots. The best two-level mixed effect model was selected to explain and predict the changes in tree crown width. The formula is: y ij represents the crown amplitude of the jth plot in the ith block; f(φi, vij) represents a nonlinear function that depends on the linear predictor φi and other covariates v ij ; ε ij represents the error term, which is usually assumed to follow a normal distribution N(0,σ 2 ), which is used to capture random errors that cannot be explained by the model; It means there are M blocks in total, each block contains Ma plots, and the total number of plots is Indicates that there are plots in each block; Ai is the design matrix, containing the predictor variables of fixed effects; β is the fixed effect coefficient vector; The design matrix contains random effect variables associated with block-plot interactions; The random effects at the block level are assumed to have a mean of 0 and a variance of N(0,Ψ (Block) )’s multivariate normal distribution; The design matrix contains random effect variables associated with block-plot interactions; The random effects at the block and plot interaction level are assumed to have a mean of 0 and a variance of N(0,Ψ (Block×Plot) ) is normally distributed; the random effect assumption and the error term assumption are independent of each other and both obey the normal distribution.

2. The method according to claim 1, characterized in that: In step S103, when the basic model is constructed, the formulas of the six basic models are: Allometric model: CW i =β0+β1x1+β2x2+β3(x1×x2)+ε i (1) Power function model: CW i =β0x1β1x2β2+ε i (2) Exponential function model: CW i =β0exp(β1x1+β2x2)+ε i (3) Logistic Model: Richard function model: Linear Model: CW i =β0+β1x1+β2x2+ε i (6) Among them, x1 and x2 are variables with the highest influence coefficient and correlation; β1, β2, β3 are parameters to be estimated, and ε is the error term.

3. The method according to claim 1, characterized in that: In step S103, when the basic model is constructed, R 2 The larger it is, the higher the model fitting accuracy is; the smaller the RMSE is, the higher the model prediction accuracy is; The smaller the TRE, the better the prediction performance; the smaller the AIC, the better the model fitting effect.

4. The method according to claim 1, characterized in that: In step S103, when establishing the two-level mixed effect model, a two-level nonlinear mixed effect model is constructed on the basis of the full-cycle growth model to predict the crown width; in the first level, the block group is used as a random effect to reflect the impact of environmental differences and management measures between different block groups on tree growth; in the second level, the sample plot is used as a random effect to further capture the variability between different sample plots in the same block group; by using this nested two-level nonlinear mixed effect model, it is possible to more accurately describe complex data structures and explain the interaction of factors at different levels on tree growth.

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