A method of determining the age of individual trees in a natural stand

Abstract

The application discloses a method for determining the age of single trees in natural forest stands, comprising the following steps: selecting reserved trees with multi-period measured diameter at breast height (DBH) in the natural forest stand, classifying the trees according to the annual growth rate of DBH, constructing a dummy variable of the tree grade based on a theoretical growth equation and adopting a starting point constraint, establishing a statistical model of the multi-period DBH of the single tree and the corresponding investigation time interval, and inversely deducing the age of the single tree through the model. The application solves the problem of obtaining the age of the single tree in the natural forest stand without affecting the growth of the tree and reducing the investigation work by combining the multi-period DBH data of the reserved tree with the differentiation condition of the trees in the forest stand, provides the age data for establishing the growth model of the natural forest reserves, and is helpful for monitoring the dynamic change of the natural forest resources and evaluating the site quality of the forest stand.

Description

Technical Field

[0001] This invention relates to the field of forestry technology, and in particular to a method for determining the age of individual trees in a natural forest stand. Background Technology

[0002] Natural forests have complex stand structures, characterized by mixed planting, multi-layered vegetation, and heterogeneous age. The tree species composition within a stand is diverse, with trees of varying ages. The competitive relationships and growth patterns among trees change continuously with increasing age. Compared to planted forests of the same age, the spatial and temporal distribution of tree components in natural forests is more rational, exhibiting stronger resistance to disturbance and richer species diversity. Individual tree age in natural forest stands is a crucial foundation for studying tree growth patterns, stand regeneration and succession dynamics, and evaluating site quality. However, the age distribution gradient of trees within natural forest stands is significant. While various methods have been used to determine individual tree age, the destructive analytical disc method can provide relatively accurate results, but it involves a large workload in the field and causes damage to the trees. Instrumental methods, on the other hand, are costly and inefficient, hindering large-scale application. Therefore, constructing models to predict tree age is a feasible and simple method.

[0003] Numerous studies have demonstrated a close growth relationship between diameter at breast height (DBH) and tree age. Previous research employed a spatial-for-temporal approach, using trunk analysis to obtain diameter and age data to simulate DBH growth and create age lookup tables. However, due to the limited availability of modeling data, the models suffered from low accuracy and limited applicability. DBH data is a commonly used survey factor in tree growth models, offering advantages such as low measurement error and ease of acquisition. Continuous DBH data from multiple periods accurately reflects the dynamics of DBH growth in forest stands, laying the foundation for establishing relevant DBH growth models. Therefore, this invention, based on continuous survey data at fixed intervals, uses time-series data of individual tree DBH and corresponding survey time intervals to construct an individual tree DBH growth model, thereby inferring the age of individual trees in natural forest stands and providing a convenient method for obtaining tree age. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a method for determining the age of individual trees in a natural forest stand.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for determining the age of individual trees in a natural forest stand includes: selecting retained trees with measured diameter at breast height (DBH) over multiple periods in the natural forest stand, classifying the trees according to the annual growth rate of DBH, constructing dummy variables for tree grades based on theoretical growth equations and using starting point constraints, establishing a statistical model of DBH of individual trees over multiple periods and corresponding survey time intervals, and then inferring the age of individual trees from the model.

[0007] Furthermore, the method for determining the age of individual trees in a natural forest stand includes the following steps:

[0008] Step 1: Fit the relationship between the diameter at breast height (DBH) of individual trees across multiple periods and the corresponding survey time intervals to determine the model parameters:

[0009] Based on the theoretical growth equation, a relationship model between the diameter at breast height (DBH) of individual trees and the corresponding survey time intervals was established. There are two types of DBH growth models for individual trees, as follows:

[0010] Model 1: Based on the Mitscherlich growth equation, this model uses a starting point constraint and reflects forest grading in parameter A. The model form is as follows:

[0011]

[0012] Model 2: Based on the Richards growth equation, this model employs a starting point constraint and incorporates forest grading in parameters A and C. The model form is as follows:

[0013]

[0014] in,

[0015] A=a1·S1+(a1+d1)·S2+(a1+2d1)·S3 (3)

[0016] C=c1·S1+(c1+g1)·S2+(c1+2g1)·S3 (4)

[0017] In the formula: D ij D represents the measured diameter at breast height (DBH) of the i-th retained tree in the j-th period, where m is the survey period number. i1 ad is the measured diameter at breast height (DBH) of the i-th retained tree at the initial stage of the survey. j Let be the time interval between period j and the initial stage of the survey, a1, b, and c1 be model parameters, and S1, S2, and S3 be dummy variables for the final tree classification (when the retained tree is the dominant tree in the natural stand, S1 = 1, S2 = S3 = 0; when the retained tree is the average tree in the natural stand, S2 = 1, S1 = S3 = 0; when the retained tree is the suppressed tree in the natural stand, S3 = 1, S1 = S2 = 0), d1 be the difference of parameter a between adjacent tree grades, and g1 be the difference of parameter c between adjacent tree grades.

[0018] The model parameters were obtained by fitting a single tree diameter at breast height (DBH) growth model:

[0019] Step 1-1: Taking the dominant tree species in a natural forest plot as the research object, select the trees with measured diameter at breast height (DBH) in multiple periods and use their DBH data as modeling data. Each tree has a unique sample tree number.

[0020] Steps 1-2: Based on the theoretical growth equation, establish the relationship between the diameter at breast height (DBH) of individual trees in multiple periods and the corresponding survey time intervals;

[0021] Steps 1-3: Using the starting point-constrained basic diameter at breast height (DBH) growth model, convert the model form;

[0022] Steps 1-4: Calculate the annual growth rate of the diameter at breast height (DBH) of the retained trees based on the first and last DBH measurements, and use ordered sample clustering to perform initial forest tree classification for the retained trees in the sample plot;

[0023] Steps 1-5: Combining the initial forest tree classification results, the Richards growth equation is used as the classification equation to obtain the final forest tree classification.

[0024] Steps 1-6: Construct dummy variables based on the final tree classification, reparameterize the model parameters, and determine the final individual tree diameter at breast height growth model;

[0025] Steps 1-7: Use the least squares method to fit and obtain the model parameters.

[0026] Step 2: Reverse the formula for calculating the age of a single tree, and estimate the age of a single tree using model parameters and initial diameter at breast height (DBH) data:

[0027] Step 2-1: Derive the age calculation formula from the single tree diameter at breast height growth model;

[0028] Step 2-2: Determine the tree class of a single tree within the natural forest stand and the corresponding dummy variable parameter values;

[0029] Steps 2-3: Calculate the initial age of a single tree based on the initial diameter at breast height (DBH) data;

[0030] Steps 2-4: Based on the time intervals of the corresponding survey periods, the age of individual trees in the remaining periods can be obtained.

[0031] Furthermore, the requirements for selecting modeling data are as follows:

[0032] This study uses the dominant tree species within a natural forest plot as the research object. The basic data consists of continuous survey data at fixed intervals, with the diameter at breast height (DBH) of all individual trees in the plot measured within each survey period. The first survey period is used as the starting point, and the last survey period as the ending point, for a total of m survey periods. Individual trees participating in the modeling must have continuous time-series data, meaning there are m measured DBH data points across the m survey periods. Because competition among trees can lead to tree death and the existence of trees that have reached the required DBH, the time-series data for some trees within the plot may be incomplete across the m survey periods. Therefore, trees that survived all m survey periods are selected for modeling, meaning each surviving tree has m measured DBH data points.

[0033] Furthermore, in steps 1-2 and 1-3, establishing a basic diameter at breast height (DBH) growth model and employing starting point constraints includes the following steps:

[0034] Step 3: Use the starting point-constrained basic diameter at breast height (DBH) growth model:

[0035] Step 3-1: Using the multi-period diameter at breast height (DBH) of the retained trees as the dependent variable and the corresponding survey time interval as the independent variable, the relationship between the Mitscherlich growth equation and the Richards growth equation is established to obtain the basic single-tree DBH growth model. The model is constructed as follows:

[0036]

[0037]

[0038] In the formula: age1 i Let be the initial age (unknown) of the i-th retained tree, 'a' be a parameter reflecting the tree's growth potential, 'b' be a parameter related to the tree species' growth rate, and 'c' be a parameter related to the assimilation power exponent w.

[0039]

[0040] Step 3-2: To enhance model stability, based on equations (5) and (6), constrain the model to pass through the starting point (age1). i D i1 The model is constructed as follows:

[0041] Using the starting point constraint formula (5):

[0042] When the model passes the starting point

[0043]

[0044] Combining equations (5) and (7) eliminates the unknown age parameter age1. i Then, a single-tree diameter at breast height growth model constrained by the starting point is obtained, and the model form is as follows:

[0045]

[0046] Similarly, when equation (6) is constrained by the starting point, the model transformation is as follows:

[0047]

[0048] Furthermore, in steps 1-4 and 1-5, within natural forest stands, competition for resources leads to differences in the degree of forest differentiation. To reveal this phenomenon, the annual growth rate of diameter at breast height (DBH) is used for forest classification, replacing the three types of forest trees (dominant trees, average trees, and suppressed trees) with three grades. The final forest classification results include the following steps:

[0049] Step 4: Determine the final forest tree classification results:

[0050] Step 4-1: Each retained tree is labeled with a unique sample tree number, and the trees are arranged in ascending order according to the sample tree number;

[0051] Step 4-2: Calculate the annual growth rate v of the diameter at breast height (DBH) for each retained tree using the DBH at both the first and last two periods.

[0052]

[0053] In the formula: v i To preserve the annual growth rate of the diameter at breast height (DBH) of the i-th tree, D im ad is the measured diameter at breast height (DBH) of the i-th retained tree in the m-th (last) stage. m The time interval between the first and last survey periods.

[0054] Step 4-3: Sort the annual growth rate v of the diameter at breast height of all the retained trees in the sample plot in descending order, and use ordered sample clustering to perform initial forest tree classification, dividing the retained trees in the sample plot into 3 levels;

[0055] The ordered sample clustering algorithm uses the optimal segmentation method for classification. Its minimum error function recursive formula is shown in equation (11). Then, the samples are classified according to the minimum error function value.

[0056] θ(p0(l,n))=min l≤X≤n {θ(p0(l-1,X-1))+D(X,n)} (11)

[0057] In the formula: θ represents the loss function for classification, p0 represents the classification scheme, l is the number of categories, X represents the number of samples of a certain class, n represents the number of trees retained in the sample plot, and D represents the sum of squared deviations of a certain class of samples.

[0058] Step 4-4: Based on Richards' growth equation, the initial three tree grades are re-parameterized using dummy variables constructed at equal intervals to establish the relationship between the diameter at breast height (DBH) of the retained trees and the corresponding survey time intervals. After fitting, the final tree grading results for each retained tree in the sample plot are obtained, and the grading equation is shown in Equation (12). In the final tree grading results, Grade 1 represents the retained tree as the dominant tree in the sample plot, Grade 2 represents the retained tree as the average tree in the sample plot, and Grade 3 represents the retained tree as the suppressed tree in the sample plot.

[0059]

[0060] Where A2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, C2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, F1, F2, F3 are dummy variables of the initial tree classification (when classifying the initial tree classification, if the retained tree is grade 1, then F1=1, F2=F3=0; if the retained tree is grade 2, then F2=1, F1=F3=0; if the retained tree is grade 3, then F3=1, F1=F2=0), d2 is the difference of parameter a between adjacent tree grades, and g2 is the difference of parameter c between adjacent tree grades.

[0061] Furthermore, in steps 1-6, to improve the applicability of the single-tree diameter at breast height (DBH) growth model and reflect the influence of forest differentiation degree on single-tree DBH growth, the final forest classification results are introduced into equations (8) and (9) using the dummy variable method to obtain the final single-tree DBH growth model. The model is constructed as follows:

[0062] Based on equation (8), the final forest grading results are re-parameterized by constructing dummy variables at equal intervals to obtain Model 1:

[0063]

[0064] Based on equation (9), the final forest grading results are constructed using dummy variables at equal intervals, and parameters a and c are further parameterized to obtain Model 2:

[0065]

[0066] Among them, A=a1·S1+(a1+d1)·S2+(a1+2d1)·S3, C=c1·S1+(c1+g1)·S2+(c1+2g1)·S3.

[0067] Furthermore, in step 2-1, the derivation process of the age calculation formula derived from the single-tree diameter at breast height growth model is as follows:

[0068] Taking Model 1 as an example:

[0069] Eliminating age1 by equations (5) and (7) i Then, by constructing dummy variables for forest grade, we can obtain Model 1. Then, we can use Equation (5) containing unknown initial age parameters to back-calculate the formula:

[0070]

[0071] In the formula, agej i Let j be the age of the i-th retained tree at stage j.

[0072] Since the method of using dummy variables is adopted to reparameterize parameter a, replacing a with A, the final calculation formula for the age of a single tree can be obtained:

[0073]

[0074] When推算时,ad i1 is calculated from the initial diameter at breast height D j = 0, that is, the calculation formula becomes as follows:

[0075]

[0076] Similarly, when using Model 2 for modeling, the calculation formula for the age of a single tree is as follows:

[0077]

[0078] Furthermore, in step 2-2, determining the parameter values of the tree class dummy variables includes the following steps:

[0079] When estimating the initial stand age of the retained trees participating in the modeling, since the tree classification has been carried out before modeling, it is only necessary to clarify which class of trees the retained trees belong to according to the final tree classification result to determine the value of parameter A. For example: if the retained tree is a dominant tree in the plot, then A = a1; if the retained tree is an average tree in the plot, then A = a1 + d1; if the retained tree is a suppressed tree in the plot, then A = a1 + 2d1.

[0080] For the remaining sample trees that are of the same dominant species in the plot but do not meet the requirement of having complete time series data within m investigation periods, that is, this sample tree has only k measured diameters at breast height data (1 < k < m) within m investigation periods. If the parameter value of the tree class dummy variable of this sample tree is to be determined, at least two periods of diameter at breast height data are required to determine which class of trees this sample tree belongs to in the plot.

[0081] Step Five: Determine the tree class where the sample tree is located in the plot (taking Model 1 as an example):

[0082] Step 5-1: Assume that this sample tree is a dominant tree in the plot, then parameter A = a1;

[0083] Step 5-2: According to Equation (14), calculate the initial age age 首 of the sample tree when it is a dominant tree from the initial diameter at breast height D1;

[0084]

[0085] Step 5-3: According to Equation (14), calculate the final age age k of the sample tree when it is a dominant tree from the final diameter at breast height D 末 ; It should be noted that the part "当由首期胸径D 推算时,ad " in the original text seems to be incomplete or unclear in expression. The translation is based on the best understanding, but there may be some inaccuracies in this part.

[0086]

[0087] Step 5-4: When the sample tree is the dominant tree, calculate the difference between the estimated age interval between the first and last periods and the actual age interval.

[0088] OSC = |age 末 -age 首 -ad k | (19)

[0089] Among them, ad k The time interval between the first and last survey periods is defined as the time interval between the first and last survey periods for sample trees with only k measured diameters at breast height (DBH) within m survey periods.

[0090] Step 5-5: Assume the sample tree is an average tree and a suppressed tree in the sample plot respectively. Repeat the above steps. The tree with the smallest OSC value is the forest grade of the sample tree in the sample plot.

[0091] Compared with the prior art, the advantages of the present invention are as follows:

[0092] Compared to the analytical wood disc method, it does not require felling trees and has a low workload; compared to instrumental methods (such as core sampling with a growth cone, micro-destructive testing with a tree needle, and X-ray method using cross-sectional annual ring images), it has advantages such as low cost, high efficiency, and easy promotion and application; compared to model estimation methods that use tree height, cross-sectional area, and other tree measurement factors, it has advantages such as easy data acquisition and small factor measurement errors. Attached Figure Description

[0093] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0094] Figure 2 The distribution diagram of the initial age of a single tree with the first diameter at breast height (DBH) is derived from the two single-tree DBH growth models constructed in Embodiment 1 of the present invention.

[0095] Figure 3 This is a comparison diagram of the initial age estimation of three types of trees using different individual tree diameter at breast height (DBH) growth models in Embodiment 1 of the present invention.

[0096] Figure 4 The distribution diagram of the initial age of a single tree with the first diameter at breast height (DBH) is derived from the two single-tree DBH growth models constructed in Embodiment 2 of the present invention.

[0097] Figure 5 This is a comparison diagram of the initial age estimation of three types of trees using different individual tree diameter at breast height (DBH) growth models in Embodiment 2 of the present invention. Detailed Implementation

[0098] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0099] It should be noted that the formula numbers in the invention content, Embodiment 1 and Embodiment 2 are all self-contained systems and there is no shared numbering.

[0100] Example 1

[0101] The basic data consisted of five forest resource surveys conducted in Guangdong Province from 1997 to 2017, with a five-year interval between adjacent survey periods and a fixed sample plot area of ​​0.0667 hm². 2 The stand originated from a natural forest, with plot number 146. The dominant tree species in the plot are oaks. A method for determining the age of individual trees in a natural forest stand is presented, with the following specific steps:

[0102] Step 1: Fit the relationship between the diameter at breast height (DBH) of the five retained trees and the corresponding survey time intervals to determine the model parameters:

[0103] Step 1-1: Using oak, the dominant tree species in the natural forest sample plot, as the research object, the survey data in 1997 was used as the initial data and the survey data in 2017 was used as the final data. 42 trees with measured diameter at breast height (DBH) in 5 survey periods from 1997 to 2017 were selected for modeling. Their DBH data were used as the modeling data, and each tree was distinguished by a unique sample tree number.

[0104] Steps 1-2: Based on the theoretical growth equation, establish the relationship between the diameter at breast height (DBH) of individual trees in multiple periods and the corresponding survey time intervals;

[0105] Using the multi-period diameter at breast height (DBH) of preserved trees as the dependent variable and the corresponding survey time interval as the independent variable, the relationship between the Mitscherlich growth equation and the Richards growth equation is established respectively, resulting in a basic single-tree DBH growth model. The model is constructed as follows:

[0106]

[0107]

[0108] In the formula: D ij ad is the measured diameter at breast height (DBH) of the i-th retained tree in the j-th period. j Let j be the time interval between period j and the beginning of the survey, age1 i Let be the initial age (unknown) of the i-th retained tree, 'a' be a parameter reflecting the tree's growth potential, 'b' be a parameter related to the tree species' growth rate, and 'c' be a parameter related to the assimilation power exponent w.

[0109] Steps 1-3: Using the starting point-constrained basic diameter at breast height (DBH) growth model, convert the model form;

[0110] To enhance model stability, based on equations (1) and (2), the model is constrained to pass through the starting point (age1). i D i1 The model is constructed as follows:

[0111] Taking equation (1) as an example:

[0112] When the model passes the starting point

[0113]

[0114] Combining equations (1) and (3) eliminates the unknown age parameter age1. i Then, a single-tree diameter at breast height growth model constrained by the starting point can be obtained, and the model form is as follows:

[0115]

[0116] Similarly, when equation (2) is constrained by the starting point, the model transformation is as follows:

[0117]

[0118] In the formula: D i1 The measured diameter at breast height (DBH) of the i-th retained tree is given at the beginning of the survey.

[0119] Steps 1-4: Calculate the annual growth rate of the diameter at breast height (DBH) of the retained trees based on the first and last DBH measurements, and use ordered sample clustering to perform initial forest tree classification for the retained trees in the sample plot;

[0120] Step 1-4-① Each retained tree is labeled with a unique sample tree number, and the trees are arranged in ascending order according to the sample tree number;

[0121] Step 1-4-②: Calculate the annual growth rate v of diameter at breast height (DBH) for each retained tree using the first and last DBH periods;

[0122]

[0123] In the formula: v i To preserve the annual growth rate of the diameter at breast height (DBH) of the i-th tree, D i5 denoted as , where is the measured diameter at breast height (DBH) of the i-th retained tree at the end of the period, and ad5 is the time interval between the first and last survey periods (ad5 = 20 in this embodiment).

[0124] Step 1-4-③: Arrange the annual growth rate v of the diameter at breast height of all the retained trees in the sample plot in descending order, and use ordered sample clustering to perform initial forest tree classification, dividing the retained trees in the sample plot into 3 levels;

[0125] The ordered sample clustering algorithm uses the optimal segmentation method for classification. Its minimum error function recursive formula is shown in equation (7). Then, the samples are classified according to the minimum error function value.

[0126] θ(p0(l,n))=min l≤X≤n {θ(p0(l-1,X-1))+D(X,n)} (7)

[0127] In the formula: θ represents the loss function for classification, p0 represents the classification scheme, l is the number of categories, X represents the number of samples of a certain class, n represents the number of trees retained in the sample plot, and D represents the sum of squared deviations of a certain class of samples.

[0128] Steps 1-5: Combining the initial forest tree classification results, the Richards growth equation is used as the classification equation to obtain the final forest tree classification.

[0129] Based on Richards' growth equation, the initial three tree grades were re-parameterized by constructing dummy variables at equal intervals to establish the relationship between the diameter at breast height (DBH) of the retained trees and the corresponding survey time intervals. After fitting, the final tree grading results for each retained tree in the sample plot were obtained, and the grading equation is shown in Equation (8). In the final tree grading results, Grade 1 represents the retained tree as the dominant tree in the sample plot, Grade 2 represents the retained tree as the average tree in the sample plot, and Grade 3 represents the retained tree as the suppressed tree in the sample plot.

[0130]

[0131] Where A2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, C2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, F1, F2, F3 are dummy variables of the initial tree classification (when classifying the initial tree classification, if the retained tree is grade 1, then F1=1, F2=F3=0; if the retained tree is grade 2, then F2=1, F1=F3=0; if the retained tree is grade 3, then F3=1, F1=F2=0), d2 is the difference of parameter a between adjacent tree grades, and g2 is the difference of parameter c between adjacent tree grades.

[0132] Steps 1-6: Construct dummy variables based on the final tree classification, reparameterize the model parameters, and determine the final individual tree diameter at breast height growth model;

[0133] To improve the applicability of the model and reflect the influence of tree differentiation degree on the diameter at breast height (DBH) of individual trees, the final tree classification results were introduced into equations (4) and (5) using the dummy variable method to obtain the final DBH growth model for individual trees. The model is constructed as follows:

[0134] Based on equation (4), the parameter a is re-parameterized by constructing dummy variables at equal intervals from the final forest grading results, thus obtaining Model 1:

[0135]

[0136] Based on equation (5), the final forest grading results are constructed using dummy variables at equal intervals, and parameters a and c are further parameterized to obtain Model 2:

[0137]

[0138] in,

[0139] A=a1·S1+(a1+d1)·S2+(a1+2d1)·S3 (11)

[0140] C=c1·S1+(c1+g1)·S2+(c1+2g1)·S3 (12)

[0141] In the formula, a1 and c1 are model parameters, and S1, S2, and S3 are dummy variables for the final tree classification (when the retained tree is the dominant tree in the natural stand, S1 = 1, S2 = S3 = 0; when the retained tree is the average tree in the natural stand, S2 = 1, S1 = S3 = 0; when the retained tree is the suppressed tree in the natural stand, S3 = 1, ...

[0142] S1=S2=0), d1 is the difference of parameter a between adjacent tree grades, and g1 is the difference of parameter c between adjacent tree grades.

[0143] Steps 1-7: Use the least squares method to fit and obtain the model parameters.

[0144] Model 1:

[0145]

[0146] Model 2:

[0147]

[0148] Step 2: Reverse the formula for calculating the age of a single tree, and estimate the age of a single tree using model parameters and initial diameter at breast height (DBH) data:

[0149] Step 2-1: Derive the age calculation formula from the single tree diameter at breast height growth model;

[0150] Taking Model 1 as an example:

[0151] Eliminating age1 by equations (1) and (3) i Then, by constructing dummy variables for forest grade, we can obtain Model 1. The calculation formula can then be derived by back-calculating equation (1) containing unknown initial age parameters:

[0152]

[0153] In the formula, agej i Let j be the age of the i-th retained tree at stage j.

[0154] Since the parameter 'a' is re-parameterized using the dummy variable method, replacing 'a' with 'A' yields the final formula for calculating the age of a single tree:

[0155]

[0156] When the initial thoracic diameter D i1 When calculating, ad j =0, meaning the calculation formula becomes as follows:

[0157]

[0158] Similarly, when using Model 2 for modeling, the formula for calculating the age of a single tree is as follows:

[0159]

[0160] Step 2-2: Determine the tree class of a single tree within the natural forest stand and the corresponding dummy variable parameter values;

[0161] When estimating the initial stand age of the retained trees participating in the modeling, since the trees have already been classified before modeling, the value of parameter A can be determined simply by clarifying which category the retained tree belongs to based on the final tree classification results. For example: if the retained tree is the dominant tree in the sample plot, then A = a1; if the retained tree is the average tree in the sample plot, then A = a1 + d1; if the retained tree is the suppressed tree in the sample plot, then A = a1 + 2d1.

[0162] Steps 2-3: Calculate the initial age of a single tree based on the initial diameter at breast height (DBH) data;

[0163] Steps 2-4: Based on the time intervals of the corresponding survey periods, the age of individual trees in the remaining periods can be obtained.

[0164] As shown in Table 1, when two theoretical growth equations are used to establish a single tree diameter at breast height (DBH) growth model, the fitting evaluation indices of each model are all excellent, with a coefficient of determination R0. 2 All values ​​were above 0.940, the standard deviation of the estimated value (SEE) was less than 1.2 cm, the mean prediction error (MPE) was less than 1.5%, the total relative error (TRE) was within ±1.2%, and the mean percentage standard error (MPSE) was less than 7.0%, indicating that the fitting effect of each model was good. However, compared with the model using the Richards growth equation, the model for single tree diameter at breast height (DBH) established using the Mitscherlich growth equation had a higher goodness of fit.

[0165] Table 1 shows the fitting results of establishing a single-tree diameter at breast height (DBH) growth model using two theoretical growth equations (oaks).

[0166]

[0167]

[0168] Figure 2 Two individual tree diameter-at-breast-diameter (DBH) growth models were used to calculate the distribution of initial tree age with initial DBH. The figures show that, when tree grades are the same, the larger the initial DBH of the retained trees, the older the estimated initial age. When the initial DBH of the retained trees is the same, the estimated age is highest for trees that are suppressed within the sample plot, followed by average trees, and lowest for dominant trees. These conclusions indicate that the degree of tree differentiation affects the growth rate of individual tree DBH. Dominant trees within a stand face less competition from other trees, allowing them to acquire more growth resources and thus reach the same DBH in a shorter time. Figure 3 The figure shows a comparison of the initial age estimates of three types of trees using two individual tree diameter-at-breast growth models. As can be seen from the figure, when the retained trees are average trees in the sample plot, the initial ages estimated by the two individual tree diameter-at-breast growth models are not significantly different. However, for dominant trees, the age estimated by the model constructed using the Richards growth equation is greater than that estimated by the model constructed using the Mitscherlich growth equation. For suppressed trees, the opposite is true, and the difference between the two is the largest among the three tree classes.

[0169] Example 2

[0170] The basic data consisted of five forest resource surveys conducted in Guangdong Province from 1997 to 2017, with a five-year interval between adjacent survey periods and a fixed sample plot area of ​​0.0667 hm². 2 The stand originated from a natural forest, with plot number 57. The dominant tree species in the plot is Phoebe zhennan. A method for determining the age of individual trees in a natural forest stand is described below:

[0171] Step 1: Fit the relationship between the diameter at breast height (DBH) of the five retained trees and the corresponding survey time intervals to determine the model parameters:

[0172] Step 1-1: Using Phoebe zhennan, the dominant tree species in the natural forest sample plot, as the research object, the survey data from 1997 as the initial data and the survey data from 2017 as the final data, 36 trees were selected as retainers with measured diameter at breast height (DBH) in 5 survey periods from 1997 to 2017 to participate in the modeling. Their DBH data were used as the modeling data, and each retainer was distinguished by a unique sample tree number.

[0173] Steps 1-2: Based on the theoretical growth equation, establish the relationship between the diameter at breast height (DBH) of individual trees in multiple periods and the corresponding survey time intervals;

[0174] Using the multi-period diameter at breast height (DBH) of preserved trees as the dependent variable and the corresponding survey time interval as the independent variable, the relationship between the Mitscherlich growth equation and the Richards growth equation is established respectively, resulting in a basic single-tree DBH growth model. The model is constructed as follows:

[0175]

[0176]

[0177] In the formula: D ij ad is the measured diameter at breast height (DBH) of the i-th retained tree in the j-th period. j Let j be the time interval between period j and the beginning of the survey, age1 i Let be the initial age (unknown) of the i-th retained tree, 'a' be a parameter reflecting the tree's growth potential, 'b' be a parameter related to the tree species' growth rate, and 'c' be a parameter related to the assimilation power exponent w.

[0178]

[0179] Steps 1-3: Using the starting point-constrained basic diameter at breast height (DBH) growth model, convert the model form;

[0180] To enhance model stability, based on equations (1) and (2), the model is constrained to pass through the starting point (age1). i D i1 The model is constructed as follows:

[0181] Taking equation (1) as an example:

[0182] When the model passes the starting point

[0183]

[0184] Combining equations (1) and (3) eliminates the unknown age parameter age1. i Then, a single-tree diameter at breast height growth model constrained by the starting point can be obtained, and the model form is as follows:

[0185]

[0186] Similarly, when equation (2) is constrained by the starting point, the model transformation is as follows:

[0187]

[0188] In the formula: D i1 The measured diameter at breast height (DBH) of the i-th retained tree is given at the beginning of the survey.

[0189] Steps 1-4: Calculate the annual growth rate of the diameter at breast height (DBH) of the retained trees based on the first and last DBH measurements, and use ordered sample clustering to perform initial forest tree classification for the retained trees in the sample plot;

[0190] Step 1-4-① Each retained tree is labeled with a unique sample tree number, and the trees are arranged in ascending order according to the sample tree number;

[0191] Step 1-4-②: Calculate the annual growth rate v of diameter at breast height (DBH) for each retained tree using the first and last DBH periods;

[0192]

[0193] In the formula: v i To preserve the annual growth rate of the diameter at breast height (DBH) of the i-th tree, D i5 denoted as , where is the measured diameter at breast height (DBH) of the i-th retained tree at the end of the period, and ad5 is the time interval between the first and last survey periods (ad5 = 20 in this embodiment).

[0194] Step 1-4-③: Arrange the annual growth rate v of the diameter at breast height of all the retained trees in the sample plot in descending order, and use ordered sample clustering to perform initial forest tree classification, dividing the retained trees in the sample plot into 3 levels;

[0195] The ordered sample clustering algorithm uses the optimal segmentation method for classification. Its minimum error function recursive formula is shown in equation (7). Then, the samples are classified according to the minimum error function value.

[0196] θ(p0(l,n))=min l≤X≤n {θ(p0(l-1,X-1))+D(X,n)} (7)

[0197] In the formula: θ represents the loss function for classification, p0 represents the classification scheme, l is the number of categories, X represents the number of samples of a certain class, n represents the number of trees retained in the sample plot, and D represents the sum of squared deviations of a certain class of samples.

[0198] Steps 1-5: Combining the initial forest tree classification results, the Richards growth equation is used as the classification equation to obtain the final forest tree classification.

[0199] Based on Richards' growth equation, the initial three tree grades were re-parameterized by constructing dummy variables at equal intervals to establish the relationship between the diameter at breast height (DBH) of the retained trees and the corresponding survey time intervals. After fitting, the final tree grading results for each retained tree in the sample plot were obtained, and the grading equation is shown in Equation (8). In the final tree grading results, Grade 1 represents the retained tree as the dominant tree in the sample plot, Grade 2 represents the retained tree as the average tree in the sample plot, and Grade 3 represents the retained tree as the suppressed tree in the sample plot.

[0200]

[0201] Where A2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, C2=a2·F1+(a2+d2)·F2+(a2+2d2)·F3, F1, F2, F3 are dummy variables of the initial tree classification (when classifying the initial tree classification, if the retained tree is grade 1, then F1=1, F2=F3=0; if the retained tree is grade 2, then F2=1, F1=F3=0; if the retained tree is grade 3, then F3=1, F1=F2=0), d2 is the difference of parameter a between adjacent tree grades, and g2 is the difference of parameter c between adjacent tree grades.

[0202] Steps 1-6: Construct dummy variables based on the final tree classification, reparameterize the model parameters, and determine the final individual tree diameter at breast height growth model;

[0203] To improve the applicability of the model and reflect the influence of tree differentiation degree on the diameter at breast height (DBH) of individual trees, the final tree classification results were introduced into equations (4) and (5) using the dummy variable method to obtain the final DBH growth model for individual trees. The model is constructed as follows:

[0204] Based on equation (4), the parameter a is re-parameterized by constructing dummy variables at equal intervals from the final forest grading results, thus obtaining Model 1:

[0205]

[0206] Based on equation (5), the final forest grading results are constructed using dummy variables at equal intervals, and parameters a and c are further parameterized to obtain Model 2:

[0207]

[0208] in,

[0209] A=a1·S1+(a1+d1)·S2+(a1+2d1)·S3 (11)

[0210] C=c1·S1+(c1+g1)·S2+(c1+2g1)·S3 (12)

[0211] In the formula, a1 and c1 are model parameters, S1, S2, and S3 are dummy variables for the final tree classification (when the retained tree is the dominant tree in the natural stand, S1 = 1, S2 = S3 = 0; when the retained tree is the average tree in the natural stand, S2 = 1, S1 = S3 = 0; when the retained tree is the suppressed tree in the natural stand, S3 = 1, S1 = S2 = 0), d1 is the difference of parameter a between adjacent tree grades, and g1 is the difference of parameter c between adjacent tree grades.

[0212] Steps 1-7: Use the least squares method to fit and obtain the model parameters.

[0213] Model 1:

[0214]

[0215] Model 2:

[0216]

[0217] Step 2: Reverse the formula for calculating the age of a single tree, and estimate the age of a single tree using model parameters and initial diameter at breast height (DBH) data:

[0218] Step 2-1: Derive the age calculation formula from the single tree diameter at breast height growth model;

[0219] Taking Model 1 as an example:

[0220] Eliminating age1 by equations (1) and (3) i Then, by constructing dummy variables for forest grade, we can obtain Model 1. The calculation formula can then be derived by back-calculating equation (1) containing unknown initial age parameters:

[0221]

[0222] In the formula, agej i Let j be the age of the i-th retained tree at stage j.

[0223] Since the parameter 'a' is re-parameterized using the dummy variable method, replacing 'a' with 'A' yields the final formula for calculating the age of a single tree:

[0224]

[0225] When the initial thoracic diameter D i1 When calculating, ad j =0, meaning the calculation formula becomes as follows:

[0226]

[0227] Similarly, when using Model 2 for modeling, the formula for calculating the age of a single tree is as follows:

[0228]

[0229] Step 2-2: Determine the tree class of a single tree within the natural forest stand and the corresponding dummy variable parameter values;

[0230] When estimating the initial stand age of the retained trees participating in the modeling, since the trees have already been classified before modeling, the value of parameter A can be determined simply by clarifying which category the retained tree belongs to based on the final tree classification results. For example: if the retained tree is the dominant tree in the sample plot, then A = a1; if the retained tree is the suppressed tree in the sample plot, then A = a1 + d1; if the retained tree is the average tree in the sample plot, then A = a1 + 2d1.

[0231] Steps 2-3: Calculate the initial age of a single tree based on the initial diameter at breast height (DBH) data;

[0232] Steps 2-4: Based on the time intervals of the corresponding survey periods, the age of individual trees in the remaining periods can be obtained.

[0233] As shown in Table 2, when two theoretical growth equations are used to establish a single tree diameter at breast height (DBH) growth model, the fitting evaluation indices of each model are all excellent, with a coefficient of determination R0. 2 All values ​​were above 0.950, the standard deviation of the estimated value (SEE) was less than 1.5 cm, the mean prediction error (MPE) was less than 1.3%, the total relative error (TRE) was within ±1.0%, and the mean percentage standard error (MPSE) was less than 5.5%, indicating that the fitting effect of each model was good. However, compared with the model using the Richards growth equation, the model for single-tree diameter at breast height (DBH) growth using the Mitscherlich growth equation had a higher goodness of fit.

[0234] Table 2 shows the fitting results of establishing a single-tree diameter at breast height (DBH) growth model using two theoretical growth equations (Phoebe zhennan).

[0235]

[0236] Figure 4 Two individual tree diameter-at-breast-diameter (DBH) growth models were used to calculate the distribution of initial tree age with initial DBH. The figures show that, when tree grades are the same, the larger the initial DBH of the retained trees, the older the estimated initial age. When the initial DBH of the retained trees is the same, the estimated age is highest for trees that are suppressed within the sample plot, followed by average trees, and lowest for dominant trees. These conclusions indicate that the degree of tree differentiation affects the growth rate of individual tree DBH. Dominant trees within a stand face less competition from other trees, allowing them to acquire more growth resources and thus reach the same DBH in a shorter time. Figure 5 This is a comparison chart of two individual tree diameter at breast height (DBH) growth models for estimating the initial age of three types of trees. As shown in the chart, when the retained trees are suppressed trees and average trees in the sample plot, the age estimated by the model constructed using the Richards growth equation is smaller than the age estimated by the model constructed using the Mitscherlich growth equation. However, for dominant trees, the opposite is true. Among the three tree grades, the difference in the estimated age of suppressed trees between the two models is the largest.

[0237] The single-tree diameter at breast height (DBH) growth models constructed in Embodiments 1 and 2 of this invention are only applicable to the age estimation of retained trees and sample trees of the same species with more than two DBH data in the sample plots involved in the modeling. However, the modeling method and process provided by this invention can provide reference and guidance for the age estimation of single trees in natural forest stands of other regions or other tree species.

[0238] The methods described above according to the invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be stored as software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the processing methods described herein. Furthermore, when a general-purpose computer accesses the code used to implement the processing shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the processing shown herein.

[0239] As described above, the embodiments and descriptions of this invention are merely preferred embodiments to illustrate the basic principles and main features of the invention. However, the scope of protection of this invention is not limited to the above embodiments. Without departing from the definitions of the appended claims, this invention can have various modifications. For example, the number of survey periods and the constraint points used in the basic model may differ. The dependent variable is not limited to diameter at breast height (DBH) data; this invention is also applicable to growth models of volume, biomass, and carbon storage to infer the age of individual trees. The theoretical growth equations used for modeling are not limited to the Mitscherlich and Richards growth equations, which are the basic growth models with good implementation results in this invention. Other theoretical growth equations can also be used as basic models. In short, all obvious modifications derived therefrom are within the scope of protection of this invention.

[0240] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A method for determining the age of individual trees in a natural forest stand, characterized in that, include: Select trees with measured diameter at breast height (DBH) in multiple periods from natural forest stands, classify the trees according to their annual DBH growth rate, construct dummy variables for tree grades based on theoretical growth equations and adopt starting point constraints, establish a statistical model of DBH of individual trees in multiple periods and corresponding survey time intervals, and then infer the age of individual trees through the model. The method for determining the age of individual trees in a natural forest stand includes the following steps: Step 1: Fit the relationship between the diameter at breast height (DBH) of individual trees across multiple periods and the corresponding survey time intervals to determine the model parameters: Based on the theoretical growth equation, a relationship model between the diameter at breast height (DBH) of individual trees and the corresponding survey time intervals was established. There are two types of DBH growth models for individual trees, as follows: Model 1: Based on the Mitscherlich growth equation, this model uses a starting point constraint and reflects forest grading in parameter A. The model form is as follows: ）， Model 2: Based on the Richards growth equation, this model employs a starting point constraint and incorporates forest grading in parameters A and C. The model form is as follows: ）， in, ， ， In the formula: Here, m represents the measured diameter at breast height (DBH) of the i-th retained tree in the j-th period, where m is the survey period number. The measured diameter at breast height (DBH) of the i-th retained tree at the initial stage of the survey. The time interval between period j and the initial stage of the survey. b For model parameters, , , For the final tree classification, when the retained trees are the dominant trees in the natural stand, , When the retained trees are the average number of trees in a natural stand, , When the retained timber is suppressed timber in a natural forest stand, , , This represents the difference in parameter 'a' between adjacent tree grades. This represents the difference in parameter c between adjacent tree grades; The model parameters were obtained by fitting a single tree diameter at breast height (DBH) growth model: Step 1-1: Taking the dominant tree species in a natural forest plot as the research object, select the trees with measured diameter at breast height (DBH) in multiple periods and use their DBH data as modeling data. Each tree has a unique sample tree number. Steps 1-2: Based on the theoretical growth equation, establish the relationship between the diameter at breast height (DBH) of individual trees in multiple periods and the corresponding survey time intervals; Steps 1-3: Using the starting point-constrained basic diameter at breast height (DBH) growth model, convert the model form; Steps 1-4: Calculate the annual growth rate of the diameter at breast height (DBH) of the retained trees based on the first and last DBH measurements, and use ordered sample clustering to perform initial forest tree classification for the retained trees in the sample plot; Steps 1-5: Combining the initial forest tree classification results, the Richards growth equation is used as the classification equation to obtain the final forest tree classification. Steps 1-6: Construct dummy variables based on the final tree classification, reparameterize the model parameters, and determine the final individual tree diameter at breast height growth model; Steps 1-7: Use the least squares method to fit the model and obtain the model parameters; Step 2: Reverse the formula for calculating the age of a single tree, and estimate the age of a single tree using model parameters and initial diameter at breast height (DBH) data: Step 2-1: Derive the age calculation formula from the single tree diameter at breast height growth model; Step 2-2: Determine the tree class of a single tree within the natural forest stand and the corresponding dummy variable parameter values; Steps 2-3: Calculate the initial age of a single tree based on the initial diameter at breast height (DBH) data; Steps 2-4: Based on the time intervals of the corresponding survey periods, the age of individual trees in the remaining periods can be obtained.

2. The method for determining the age of individual trees in a natural forest stand according to claim 1, characterized in that: The requirements for selecting modeling data in step 1-1 are as follows: The dominant tree species in a natural forest plot are used as the research object. The basic data are continuous survey data at fixed intervals. The diameter at breast height (DBH) of all individual trees in the plot needs to be measured in each survey period. The first survey period is used as the starting point and the last survey period is used as the ending point, for a total of m survey periods. The individual trees participating in the modeling need to have continuous time series data, that is, there are m measured DBH data in m survey periods. Since tree competition will lead to tree death and the existence of advanced trees that have reached the starting DBH, the time series data of some trees in the plot will not be complete in m survey periods. Therefore, the trees that survived in all m survey periods in the plot are selected to participate in the modeling, that is, each tree has m measured DBH data.

3. The method for determining the age of individual trees in a natural forest stand according to claim 1, characterized in that: In steps 1-2 and 1-3, establishing a basic diameter at breast height (DBH) growth model and using starting point constraints includes the following steps: Step 3: Use the starting point-constrained basic diameter at breast height (DBH) growth model: Step 3-1: Using the multi-period diameter at breast height (DBH) of the retained trees as the dependent variable and the corresponding survey time interval as the independent variable, the relationship between the Mitscherlich growth equation and the Richards growth equation is established to obtain the basic single-tree DBH growth model. The model is constructed as follows: ）， ）， In the formula: Let be the initial age of the i-th retained tree, 'a' be a parameter reflecting the tree's growth potential, 'b' be a parameter related to the tree species' growth rate, and 'c' be a parameter related to the assimilation power exponent w. ; Step 3-2: To enhance model stability, based on equations (5) and (6), constrain the model through the starting point ( , The model is constructed as follows: Using the starting point constraint formula (5): When the model passes the starting point ）， Combining equations (5) and (7) eliminates the unknown age parameter. Then, a single-tree diameter at breast height growth model constrained by the starting point is obtained, and the model form is as follows: ）， Similarly, when equation (6) is constrained by the starting point, the model transformation is as follows: 。 4. The method for determining the age of a single tree in a natural forest stand according to claim 3, characterized in that: In steps 1-4 and 1-5, within natural forest stands, competition for resources leads to differences in the degree of forest differentiation. To reveal this phenomenon, the annual growth rate of diameter at breast height (DBH) is used for forest classification, with three grades replacing three types of forest trees: dominant trees, average trees, and suppressed trees. The final forest classification results include the following steps: Step 4: Determine the final forest tree classification results: Step 4-1: Each retained tree is labeled with a unique sample tree number, and the trees are arranged in ascending order according to the sample tree number; Step 4-2: Calculate the annual growth rate v of the diameter at breast height (DBH) for each retained tree using the DBH at both the first and last two periods. ， In the formula: To preserve the annual growth rate of the diameter at breast height (DBH) of the i-th tree, The measured diameter at breast height (DBH) of the i-th retained tree at stage m is given. The time interval between the first and last survey periods is denoted as m, where period m is the last period. Step 4-3: Sort the annual growth rate v of the diameter at breast height of all the retained trees in the sample plot in descending order, and use ordered sample clustering to perform initial forest tree classification, dividing the retained trees in the sample plot into 3 levels; The ordered sample clustering algorithm uses the optimal segmentation method for classification. Its minimum error function recursive formula is shown in equation (11). Then, the samples are classified according to the minimum error function value. （11） In the formula: The loss function representing classification. Indicate the classification scheme, For the number of categories, Represents the number of samples in a certain class. This indicates the number of trees retained within the sample plot. Represents the sum of squares of deviations for a certain type of sample; Step 4-4: Based on Richards' growth equation, the three initial tree grades are re-parameterized by constructing dummy variables at equal intervals to establish the relationship between the diameter at breast height (DBH) of the retained trees and the corresponding survey time intervals. After fitting, the final tree grading results of each retained tree in the sample plot can be obtained. The grading equation is shown in equation (12). In the final tree grading results, grade 1 represents the retained tree as the dominant tree in the sample plot, grade 2 represents the retained tree as the average tree in the sample plot, and grade 3 represents the retained tree as the suppressed tree in the sample plot. ）， in, , , , , Let be the dummy variable for the initial tree classification. When classifying the initial tree classification, if we retain trees as level 1, then... , If wood is retained as level 2, then , If the wood is retained as level 3, then , , This represents the difference in parameter 'a' between adjacent tree grades. This represents the difference in parameter c between adjacent tree grades.

5. The method for determining the age of individual trees in a natural forest stand according to claim 4, characterized in that: In Steps 1-6, to improve the applicability of the individual tree diameter at breast height (DBH) growth model and reflect the influence of the degree of forest tree differentiation on the individual tree DBH growth, the final forest tree classification results are introduced into Equations (8) and (9) by means of dummy variables to obtain the final individual tree DBH growth model, and the model structure is as follows: Based on Equation (8), the final forest tree classification results are used to reparameterize parameter a by constructing dummy variables at equal intervals to obtain Model 1: ， Based on Equation (9), the final forest tree classification results are used to reparameterize both parameter a and parameter c by constructing dummy variables at equal intervals to obtain Model 2: ， in, , .

6. The method for determining the age of a single tree in a natural forest stand according to claim 5, characterized in that: In Step 2-1, the derivation process of the age calculation formula deduced from the individual tree DBH growth model is as follows: Based on Model 1: Eliminate by equations (5) and (7) Then, by constructing dummy variables for forest grade, we can obtain Model 1. Then, we can use Equation (5) containing unknown initial age parameters to inversely calculate the formula: ， In the formula, The age of the i-th retained tree at stage j; Since the method of dummy variables is used to reparameterize parameter a, A is used to replace a, and the final individual tree age calculation formula can be obtained: ， When the initial chest diameter During the calculation, The calculation formula then becomes as follows: ， Based on Model 2: The calculation formula for the individual tree age is as follows:

7. The method for determining the age of a single tree in a natural forest stand according to claim 6, characterized in that: In Step 2-2, determining the parameter values of the forest tree class dummy variables includes the following steps: When estimating the initial stand age of the retained trees participating in the modeling, since tree classification has already been performed before modeling, the value of parameter A can be determined simply by clarifying the category of the retained trees based on the final tree classification results; if the retained trees are dominant trees in the sample plot, then... ; If the retained timber is the average timber within the sample plot, then ; If the retained timber is compressed timber within the sample plot, then ; For the remaining sample trees that are the dominant tree species in the same plot but do not meet the requirement of having complete time series data within m investigation periods, that is, this sample tree has only k measured DBH data within m investigation periods, where 1 < k < m; if the parameter values of the forest tree class dummy variables of this sample tree need to be determined, at least two periods of DBH data are required to determine which type of forest tree this sample tree belongs to in the plot; Step Five: Determine the forest tree class where the sample tree is located in the plot: Step 5-1: Assuming the sample tree is the dominant tree in the sample plot, then the parameters... ; Step 5-2: According to formula (14), the initial chest diameter is... Early age at which the sample tree is the dominant tree ; ， Step 5-3: According to formula (14), from the final chest diameter Estimating the final age when the sample tree is the dominant tree ; ， Step 5-4: Calculate the difference between the deduced age interval of the first and last two periods and the actual age interval when the sample tree is a dominant tree; ， in, The time interval between the first and last survey periods for sample trees with only k measured diameters at breast height within m survey periods; Step 5-5: Assume that the sample tree is an average tree and a suppressed tree in the plot respectively, repeat the above steps, and the one with the smallest OSC value is the forest tree class of this sample tree in the plot.

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