A method of determining the age of a natural forest stand

Abstract

The application discloses a method for determining the age of natural forest stand, comprising the following steps: selecting the reserved wood with multi-period measured diameter at breast height to calculate the average diameter at breast height of the forest stand, dividing the forest stand site class according to the annual growth rate of the diameter at breast height of the forest stand, constructing a statistical model between the average diameter at breast height of the forest stand and the corresponding investigation time interval based on a theoretical growth equation, introducing a density variable to reflect the characteristics of the forest stand, constructing a site class dummy variable to reflect the site influence, and adopting a starting point constraint to transform the model form; reversely calculating the age calculation formula of the natural forest stand from the diameter growth model, determining the site class of the sample site, and estimating the age of the natural forest stand according to the initial diameter at breast height and parameters. The application provides a simple method for estimating the age of the natural forest stand by combining the multi-period diameter data of the reserved wood with the density condition of the forest stand and the site difference, effectively improves the investigation efficiency and estimation accuracy, and meets the demand of the forestry production and scientific research on the age data of the natural forest stand.

Description

Technical Field

[0001] The present invention relates to the technical field of forestry, and in particular to a method for determining the age of a natural forest stand. Background Art

[0002] Stand age is the arithmetic mean or weighted average of the ages of all individual trees within a stand. However, compared to plantations, natural forests have more complex diameter structure, age structure, species composition, and relationships between trees. The age distribution gradient of individual trees within natural stands is large, and due to factors such as competition, pests and diseases, and natural aging and death, the number of surviving trees in a stand at different times is not completely consistent. Therefore, stand age data is difficult to obtain. However, natural stands have strong ecosystem stability, resistance to interference, and self-repair capabilities. Determining the age of natural forests provides basic data for classifying stands into age classes and age groups, studying stand succession dynamics, and evaluating site quality. It is of great significance for implementing the protection and restoration of my country's natural forest resources and formulating a forestry system for sustainable forest management.

[0003] The method that natural stand age is determined at present has visual method, drilling standard wood pith core to check annual ring, regression model estimation method and remote sensing estimation method etc., wherein visual method is highly subjective, standard wood method investigation workload is large and cost is high, remote sensing estimation method is applicable to inversion forest age in a large range. Existing large amounts of research have shown that there is a close growth relationship between forest tree diameter at breast height and forest tree age, in the regression model estimation method in the past, the model of single tree level needs a large amount of analytical wood data, easily produces single tree cumulative error when indirectly calculating forest age and the scope of application of the model is small, therefore, starting from the forest stand level, setting up the regression model between forest stand age and forest stand characteristic factor (such as forest stand average diameter at breast height) to estimate the age of natural stand is a kind of simple and feasible method. Continuous multi-phase diameter at breast height survey data are easy to obtain and measurement error is small, can also continue to reflect forest tree diameter at breast height growth and forest stand growth dynamics, therefore the present invention is based on the relationship between the multi-phase diameter at breast height data of retained wood and corresponding survey time interval to infer natural stand age. Summary of the Invention

[0004] The present invention aims at solving the defects of the prior art and provides a method for determining the age of a natural forest stand.

[0005] In order to achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

[0006] A method for determining the age of a natural forest stand comprises: selecting retained trees with multi-period measured diameters at breast height to calculate the average diameter at breast height of the stand; dividing the stand site grades based on the annual growth rate of the diameter at breast height of the stand; constructing a statistical model between the average diameter at breast height of the stand and the corresponding survey time interval based on a theoretical growth equation; and then determining the age of the natural forest stand by inverting the stand age calculation formula through the model.

[0007] Furthermore, the method for determining the age of a natural forest stand comprises the following steps:

[0008] Step 1: Fit the relationship between the average DBH of multi-period stands and the corresponding survey time intervals to determine the model parameters:

[0009] Based on the theoretical growth equation, a relationship model between the average DBH of the stand and the corresponding survey time interval was established. The three models to be selected are:

[0010] (1) Model 1: Based on the Mitscherlich growth equation, the site grade is reflected in the parameter A by constructing a dummy variable. The model form is as follows:

[0011]

[0012] (2) Model 2: Based on the Richards growth equation, the site grade is reflected in the parameter A by constructing a dummy variable. The model form is as follows:

[0013]

[0014] (3) Model 3: Based on the Richards growth equation, the site grade is reflected in both parameters A and C by constructing dummy variables. The model form is as follows:

[0015]

[0016] in,

[0017]

[0018]

[0019] In formulas (1) to (5): D gij is the average DBH of the stand in the jth period of the i-th plot, k is the number of survey periods, D gi1 is the average DBH of the stand in the first phase of the i-th plot, ad j is the time interval between the jth period and the initial stage of the survey, N is the number of site grades, S n is a dummy variable (i.e., when the site grade belongs to the nth grade, its value is 1, otherwise it is 0), d is the difference in parameter a between adjacent site grades, g is the difference in parameter c between adjacent site grades, BAL ij It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot and the j-th period, and r is a parameter related to density.

[0020] The model parameters are obtained by fitting the equation:

[0021] Step 1-1: Select k trees with k measured DBH data during the survey period. Each plot must have at least 5 trees. Calculate the average DBH of the stand of the trees in each plot at different periods.

[0022] Steps 1-2: Calculate the distance-independent competition index BAL based on all individual trees in the plot;

[0023] Steps 1-3: After determining the annual growth rate using the average DBH of the first and last two stands, the modeling plots were classified into site classes;

[0024] Steps 1-4: Incorporate the effects of density and site into the base model, apply starting point constraints, and transform the model form;

[0025] Steps 1-5: Establish the relationship between the average DBH of multi-period stands and the corresponding survey time intervals, and use the least squares method to fit and obtain the model parameters.

[0026] Step 2: Reverse the stand age calculation formula and estimate the stand age using the model parameters and the first-period DBH data:

[0027] Step 2-1: Determine the calculation formula of stand age from the DBH growth model;

[0028] Step 2-2, determine the site class of the sample plot;

[0029] Step 2-3: Define the parameters based on the site class of the sample plot, and then estimate the initial age of the sample plot based on the average DBH of the first stand;

[0030] Steps 2-4: Based on the time intervals of different survey periods, the ages of the sample plots in the remaining periods can be obtained.

[0031] Furthermore, in steps 1-1 and 1-2, the process of obtaining modeling data is as follows:

[0032] The stand age is the average age of each single tree in the stand. At the same time, in order to avoid the influence of the difference in the number of trees in the sample plot on the modeling effect, the average DBH of the stand is used to estimate the stand age. The basic data are continuous survey data at fixed intervals. The measured DBH of all single trees in the sample plot is recorded in each survey. The first survey period is used as the starting point and the last survey period is used as the end point, with a total of k survey periods. Since competition among trees in the stand can lead to the death of trees, the retained trees that survived k survey periods in the sample plot are screened to participate in the modeling, that is, there are k measured DBH data in k survey periods, and the number of retained trees is required to be no less than 5. The average DBH of the sample plot is calculated based on the DBH of the retained trees after screening in the sample plot. g, calculated using the formula (6). All individual trees in the plot reflect the density of the stand. Therefore, taking all individual trees as the main body, the sum of the basal area at breast height (BAL) of individual trees in the plot that are larger than the average DBH of the stand per unit area is calculated using the formula (7).

[0033] Average diameter at breast height (DBH) of the stand g , the calculation formula is as follows:

[0034]

[0035] Where: p is the number of trees retained in the plot, d i Reserve the tree diameter at breast height for the i-th tree.

[0036] The distance-independent competition index BAL is calculated as follows:

[0037]

[0038] Where: T is the number of trees with a breast diameter greater than the average breast diameter of the stand in the plot, d i is the DBH of the ith tree, and s is the area of ​​the sample plot.

[0039] Furthermore, in steps 1-3, the site classification of the sample plots includes the following steps:

[0040] Step 3: Classify the site level of the sample plot:

[0041] Step 3-1: The average DBH data of multiple stands in the same plot are all marked with plot numbers to distinguish different plots and ensure that the same plot is at the same site level at different times, and are arranged in ascending order by plot number;

[0042] Step 3-2: Calculate the annual growth rate v using the average DBH of the first and last two periods, arrange them in descending order, and perform initial classification using ordered sample clustering to obtain the number of classification levels N;

[0043]

[0044] Where: D gk is the average DBH of the stand in the kth phase (the last phase) of the plot, ad k is the time interval between the first and last survey periods.

[0045] Step 3-3, obtain the final site grade based on DBH classification: take the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, establish a statistical model of the two based on the Mitscherlich growth equation, construct a dummy variable based on the initial site grade, and re-parameterize the model parameter A. The classification equation is in the form of formula (1). After fitting, the final site grade of each plot can be obtained.

[0046] Furthermore, in steps 1-4, to enhance the applicability and stability of the basic model, it is necessary to introduce density variables and reflect site effects, and restrict the model to be constrained by the starting point. The conversion model form includes the following steps:

[0047] Step 4: Incorporate the effects of density and site into the base model and use starting point constraints:

[0048] Step 4-1: Using the stand average DBH as the dependent variable and the corresponding survey time interval as the independent variable, the Mitscherlich growth equation and the Richards growth equation were used to establish the relationship between the two. The model was constructed as follows:

[0049]

[0050]

[0051] Where: age1 i is the initial forest age of the i-th plot (unknown), a is a parameter reflecting the forest production potential, b is a parameter related to the growth rate of the tree species, and c is a parameter related to the assimilation power exponent w.

[0052] Step 4-2: To reflect the differences in average DBH growth under different stand densities and improve the accuracy of the model in estimating natural stand age, the distance-independent competition index BAL is introduced on the basis of equations (9) and (10). The model is constructed as follows:

[0053]

[0054]

[0055] Step 4-3: There is diversity in the sites between forest stands within a large area. Reflecting the impact of site differences on the average DBH of the forest stands in the model will improve model performance and enhance model applicability. After dividing the sample plots into site levels, the model parameters a or c are re-parameterized by constructing dummy variables. The model is constructed as follows:

[0056] Based on formula (11), parameter a is re-parameterized to reflect site differences:

[0057]

[0058] Based on formula (12), parameter a is re-parameterized to reflect site differences:

[0059]

[0060] Based on formula (12), parameters a and c are re-parameterized to reflect site differences:

[0061]

[0062] in,

[0063] Step 4-4: To improve the stability of the model parameters, the starting point is used to constrain the stand diameter growth model so that it passes through the restriction point (age1 i , D gi1 ), the model is constructed as follows:

[0064] Take formula (13) as an example:

[0065] When the model passes the starting point,

[0066]

[0067] Formula (16) combined with formula (13) eliminates the unknown age parameter age1 i After that, the DBH growth model constrained by the starting point can be obtained, namely Model 1:

[0068]

[0069] Similarly, when using the starting point constraints (14) and (15), Model 2 and Model 3 are obtained:

[0070]

[0071]

[0072] Furthermore, in step 2-1, the calculation formula for the initial age of the stand is derived as follows:

[0073] Take Model 1 as an example:

[0074] Because Model 1 eliminates age1 from equations (16) and (13) i After obtaining the initial forest age parameter, the calculation formula can be reversed through formula (13) containing the unknown initial forest age parameter:

[0075]

[0076] Where agej i is the age of the jth period in the ith plot.

[0077] Among them, when the average breast diameter of the first stand D gi1 When calculating, ad j =0, the calculation formula becomes as follows:

[0078]

[0079] Where, BAL i1 It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot in the first period.

[0080] Similarly, when using Model 2 and Model 3, the general formula for calculating forest age is as follows:

[0081]

[0082]

[0083] Furthermore, in step 2-2, since the site conditions of the sample plots are divided into N levels during the modeling process, if the age of a sample plot with an unknown site level is estimated, it is necessary to determine the site level in which it is located before determining the dummy variable value of the parameter reflecting the site level and estimating the stand age.

[0084] Step 5: Determine the site grade of the sample plot (taking Model 1 as an example)

[0085] Step 5-1: Assuming the site grade of the sample plot is m, the dummy variable value of parameter A can be obtained from formula (4): A = a + (m-1)·d;

[0086] Step 5-2: According to formula (17), the initial age of the plot at site class m can be estimated from the first DBH data: i ;

[0087]

[0088] Step 5-3: According to formula (17), the final age of the plot at site class m can be estimated from the final DBH data: i ;

[0089]

[0090] Where, BAL ik It is the sum of the basal areas at breast height of all individual trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot in the k-th period.

[0091] Step 5-4: Calculate the difference between the estimated forest age intervals at the first and last stages and the actual age interval when the plot is at site class m;

[0092] OSC=|agek i -age1 i -ad k | (23)

[0093] Step 5-5: There are N site classes in total. Repeat the above steps. The site class with the smallest OSC value is determined as the site class of the sample plot.

[0094] Compared with the prior art, the advantages of the present invention are:

[0095] The diameter at breast height data is a measured data that is easy to obtain continuously in field surveys and has a small measurement error. By taking the average diameter at breast height of the stand as the dependent variable and the corresponding survey time interval as the independent variable, the theoretical growth equation is used to establish the relationship between the two to achieve the estimation of unknown forest age. Compared with the visual inspection method, it has higher accuracy. Compared with the standard wood core counting method, it has the advantages of low cost, no damage to tree growth and easy application. Compared with the regression model estimation method constructed using analytical wood data, it has the advantages of simple data acquisition and low workload. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 Flow chart for the implementation of the method of the present invention;

[0097] Figure 2 The diameter at breast height growth model is established using Model 1 in Example 1 of the present invention, and the distribution map of the initial forest age of the sample plot is then inferred;

[0098] Figure 3 This is a comparison chart of estimating the initial age of a plot using three models in Example 1 of the present invention;

[0099] Figure 4 The diameter-at-breast-height growth model is established using Model 1 in Example 2 of the present invention, and the distribution map of the initial stand age of the sample plot is then inferred;

[0100] Figure 5 This is a comparison chart of estimating the initial age of a plot using three models in Example 2 of the present invention. DETAILED DESCRIPTION

[0101] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0102] It should be noted that the formula numbers in the Summary of the Invention, Example 1 and Example 2 are all independent systems and there is no shared number.

[0103] Example 1

[0104] The basic data are sample trees and plots from five phases of forest resource inventory in Guangdong Province from 1997 to 2017. The interval between adjacent survey periods is 5 years, and the fixed sample plot area is 0.0667 hm2. 2 The stand origin is natural forest, and the tree species is oak. A method for determining the age of a natural forest stand includes the following steps:

[0105] Step 1: Fit the relationship between the average DBH of the five-period stand and the corresponding survey time interval to determine the model parameters:

[0106] Step 1-1: Using the 1997 survey data as the initial data and the 2017 survey data as the final data, select k retained trees with k measured DBH data during the survey period. Each plot must contain at least 5 retained trees, for a total of 44 plots. Calculate the average DBH of the retained trees in each plot at different periods.

[0107] Average diameter at breast height (DBH) of the stand g , the calculation formula is as follows:

[0108]

[0109] Where: p is the number of trees retained in the plot, d i Reserve the tree diameter at breast height for the i-th tree.

[0110] Steps 1-2: Calculate the distance-independent competition index BAL based on all individual trees in the plot;

[0111] BAL is the sum of the basal areas at breast height of all trees in a stand that are larger than the average breast diameter of the stand within a unit area. The calculation formula is as follows:

[0112]

[0113] Where: T is the number of trees with a breast diameter greater than the average breast diameter of the stand in the plot, d i is the DBH of the ith tree, and s is the area of ​​the sample plot.

[0114] Steps 1-3: After determining the annual growth rate using the average DBH of the first and last two stands, the modeling plots were classified into site classes;

[0115] Step 1-3-①, the average DBH data of multiple stands in the same plot are all marked with plot numbers to distinguish different plots and ensure that the same plot is at the same site level at different times, and are arranged in ascending order by plot number;

[0116] Step 1-3-②: Calculate the annual growth rate v using the average DBH of the first and last two stands, arrange them in descending order, and perform initial classification using ordered sample clustering to divide the site grades into five categories;

[0117]

[0118] Where: D gk is the average DBH of the stand in the kth period (2017), D g1 is the average DBH of the stands in the first phase (1997), ad k is the time interval between the first and last survey periods (in Example 1, ad k =20).

[0119] Step 1-3-③, obtain the final site grade based on the DBH classification: take the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, establish a statistical model of the two based on the Mitscherlich growth equation, construct a dummy variable based on the initial classification of site grade, and re-parameterize the model parameter A. After fitting, the final site grade of each plot can be obtained.

[0120] The classification equation is as follows:

[0121]

[0122]

[0123] Where: D gij is the average DBH of the stand in the i-th plot in the j-th period, ad j is the time interval between the jth period and the initial stage of the survey, N is the number of site grades (in Example 1, N = 5), S n is a dummy variable (i.e., when the site grade belongs to the nth grade, its value is 1, otherwise it is 0), d is the difference in parameter a between adjacent site grades, BAL ij It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot and the j-th period, and r is a parameter related to density.

[0124] Steps 1-4: Incorporate the effects of density and site into the base model, apply starting point constraints, and transform the model form;

[0125] Step 1-4-①, using the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, respectively use the Mitscherlich growth equation and the Richards growth equation to establish the relationship between the two. The model is constructed as follows:

[0126]

[0127]

[0128] Where: age1 i is the initial forest age of the i-th plot (unknown), a is a parameter reflecting the forest production potential, b is a parameter related to the growth rate of the tree species, and c is a parameter related to the assimilation power exponent w.

[0129] Step 1-4-②: To reflect the differences in average DBH growth under different stand densities and improve the accuracy of the model in estimating natural stand age, the distance-independent competition index BAL is introduced on the basis of equations (6) and (7). The model is constructed as follows:

[0130]

[0131]

[0132] Step 1-4-③: Reflect the impact of site differences on the average DBH of the stand in the model to improve the applicability of the model. After dividing the site grades, re-parameterize the model parameters a or c by constructing dummy variables. The model is constructed as follows:

[0133] Based on formula (8), parameter a is re-parameterized to reflect site differences:

[0134]

[0135] Based on formula (9), parameter a is re-parameterized to reflect site differences:

[0136]

[0137] Based on formula (9), parameters a and c are re-parameterized to reflect site differences:

[0138]

[0139]

[0140] in, g is the difference in parameter c between adjacent site grades.

[0141] Step 1-4-④, in order to improve the stability of the model parameters, the starting point is used to constrain the stand diameter growth model so that it passes through the restriction point (age1 i , D gi1 ), the model is constructed as follows:

[0142] Take formula (10) as an example:

[0143] When the model passes the starting point,

[0144]

[0145] Formula (14) combined with formula (10) eliminates the unknown age parameter age1 i After that, the DBH growth model constrained by the starting point can be obtained, namely Model 1:

[0146]

[0147] Similarly, when using the starting point constraints (11) and (12), Model 2 and Model 3 can be obtained:

[0148]

[0149]

[0150] Steps 1-5: Use Model 1, Model 2, and Model 3 to establish the relationship between the average DBH of the five stands and the corresponding survey time intervals, and use the least squares method to fit and obtain the model parameters.

[0151] Step 2: Reverse the stand age calculation formula and estimate the stand age using the model parameters and the first-period DBH data:

[0152] Step 2-1: Determine the calculation formula of stand age from the DBH growth model;

[0153] Take Model 1 as an example:

[0154] Because Model 1 eliminates age1 from equations (10) and (14) i After obtaining the initial forest age parameter, the calculation formula can be reversed through formula (10) containing the unknown initial forest age parameter:

[0155]

[0156] Where agej i is the age of the jth period in the ith plot.

[0157] Among them, when the average breast diameter of the first stand D gi1 When calculating, ad j =0, the calculation formula becomes as follows:

[0158]

[0159] Where, BAL i1 It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot in the first period.

[0160] Similarly, when using Model 2 and Model 3, the general formula for calculating forest age is as follows:

[0161]

[0162]

[0163] Step 2-2, determine the site class of the sample plot (since the estimated site class is known, only one-to-one correspondence is required);

[0164] Step 2-3: Determine the parameters based on the site class of the sample plot, and then substitute the average DBH of the first-stage stand into the formula to estimate the initial age of the sample plot;

[0165] Determination of parameter description: Assuming that the site grade of the sample plot is m, the dummy variable value of parameter A can be obtained from formula (5), A = a + (m-1)·d, and the dummy variable value of parameter C can be obtained from formula (13), C = c + (m-1)·g.

[0166] Steps 2-4: Based on the time intervals of different survey periods, the ages of the sample plots in the remaining four periods can be obtained.

[0167] Table 1 lists the fitting evaluation indices for the three models used to establish DBH growth models, and Table 2 lists the parameter values ​​of each model after fitting. As shown in Table 1, when Model 1, Model 2, and Model 3 were used to fit the relationship between the average DBH of 44 plots of natural oak forests in Guangdong Province during the five periods and the corresponding survey time intervals, the fitting effect of each model was good, and the coefficient of determination R 2 All are above 0.9760, the standard deviation (SE E) of the estimates is less than 0.8 cm, the mean predicted error (MPE) and total relative error (TRE) approach 0, and the mean percentage standard error (MPSE) is less than 3.5%. As shown in Table 2, the parameter values ​​of the models do not differ much, indicating that the fitting results are stable.

[0168] Table 1 Fitting results of different models for establishing DBH growth models (Guangdong Province)

[0169]

[0170] Table 2 Parameters of different model forms for fitting DBH growth models (Guangdong Province)

[0171]

[0172] Figure 2 This is a scatter plot of the initial age of the 44 plots estimated by Model 1 and the average DBH of the first stand. The higher the level, the worse the site condition. That is, the site condition of level 1 is the best and the site condition of level 5 is the worst. Figure 2 It can be seen that when the average DBH of the stands in the same site class is larger, the estimated stand age is older; when the average DBH of the stands is not different, the higher the site class, the older the estimated stand age. These conclusions indicate that site conditions affect the growth rate of DBH; better site conditions mean that the stands will reach the same DBH in a shorter time. Figure 3 This is a comparison chart of three different model forms used to build models and infer the initial age of the sample plot. From the median and mean of the box plot, combined with the distribution of the scatter plot, it can be seen that the estimation effects of the three models are not much different, indicating that the estimation effects are stable.

[0173] Example 2

[0174] The basic data are sample trees and plots from five phases of forest resource inventory in Jilin Province from 1997 to 2017. The interval between adjacent survey periods is 5 years, and the fixed sample plot area is 0.06 hm2. 2 The stand origin is natural forest, and the tree species is oak. A method for determining the age of a natural forest stand includes the following steps:

[0175] Step 1: Fit the relationship between the average DBH of the five-period stand and the corresponding survey time interval to determine the model parameters:

[0176] Step 1-1: Using the 1997 survey data as the initial data and the 2017 survey data as the final data, select k retained trees with k measured DBH data during the survey period. Each plot must contain at least 5 retained trees, for a total of 554 plots. Calculate the average DBH of the retained trees in each plot at different periods.

[0177] Average diameter at breast height (DBH) of the stand g , the calculation formula is as follows:

[0178]

[0179] Where: p is the number of trees retained in the plot, d i Reserve the tree diameter at breast height for the i-th tree.

[0180] Steps 1-2: Calculate the distance-independent competition index BAL based on all individual trees in the plot;

[0181] BAL is the sum of the basal areas at breast height of all trees in a stand that are larger than the average breast diameter of the stand within a unit area. The calculation formula is as follows:

[0182]

[0183] Where: T is the number of trees with a breast diameter greater than the average breast diameter of the stand in the plot, d i is the DBH of the ith tree, and s is the area of ​​the sample plot.

[0184] Steps 1-3: After determining the annual growth rate using the average DBH of the first and last two stands, the modeling plots were classified into site classes;

[0185] Step 1-3-①, the average DBH data of multiple stands in the same plot are all marked with plot numbers to distinguish different plots and ensure that the same plot is at the same site level at different times, and are arranged in ascending order by plot number;

[0186] Step 1-3-②: Calculate the annual growth rate v using the average DBH of the first and last two stands, arrange them in descending order, and perform initial classification using ordered sample clustering to divide the site grades into 9 categories;

[0187]

[0188] Where: D gk is the average DBH of the stand in the kth period (2017), D g1 is the average DBH of the stands in the first phase (1997), ad k is the time interval between the first and last survey periods (in Example 2, ad k =20).

[0189] Step 1-3-③, obtain the final site grade based on the DBH classification: take the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, establish a statistical model of the two based on the Mitscherlich growth equation, construct a dummy variable based on the initial classification of site grade, and re-parameterize the model parameter A. After fitting, the final site grade of each plot can be obtained.

[0190] The classification equation is as follows:

[0191]

[0192]

[0193] Where: D gij is the average DBH of the stand in the i-th plot in the j-th period, ad j is the time interval between the jth period and the initial stage of the survey, N is the number of site grades (in Example 2, N = 9), S n is a dummy variable (i.e., when the site grade belongs to the nth grade, its value is 1, otherwise it is 0), d is the difference in parameter a between adjacent site grades, BAL ij It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot and the j-th period, and r is a parameter related to density.

[0194] Steps 1-4: Incorporate the effects of density and site into the base model, apply starting point constraints, and transform the model form;

[0195] Step 1-4-①, using the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, respectively use the Mitscherlich growth equation and the Richards growth equation to establish the relationship between the two. The model is constructed as follows:

[0196]

[0197]

[0198] Where: age1 iis the initial forest age of the i-th plot (unknown), a is a parameter reflecting the forest production potential, b is a parameter related to the growth rate of the tree species, and c is a parameter related to the assimilation power exponent w.

[0199] Step 1-4-②: To reflect the differences in average DBH growth under different stand densities and improve the accuracy of the model in estimating natural stand age, the distance-independent competition index BAL is introduced on the basis of equations (6) and (7). The model is constructed as follows:

[0200]

[0201]

[0202] Step 1-4-③: Reflect the impact of site differences on the average DBH of the stand in the model to improve the applicability of the model. After dividing the site grades, re-parameterize the model parameters a or c by constructing dummy variables. The model is constructed as follows:

[0203] Based on formula (8), parameter a is re-parameterized to reflect site differences:

[0204]

[0205] Based on formula (9), parameter a is re-parameterized to reflect site differences:

[0206]

[0207] Based on formula (9), parameters a and c are re-parameterized to reflect site differences:

[0208]

[0209]

[0210] in, g is the difference in parameter c between adjacent site grades.

[0211] Step 1-4-④, in order to improve the stability of the model parameters, the starting point is used to constrain the stand diameter growth model so that it passes through the restriction point (age1 i , D gi1 ), the model is constructed as follows:

[0212] Take formula (10) as an example:

[0213] When the model passes the starting point,

[0214]

[0215] Formula (14) combined with formula (10) eliminates the unknown age parameter age1 i After that, the DBH growth model constrained by the starting point can be obtained, namely Model 1:

[0216]

[0217] Similarly, when using the starting point constraints (11) and (12), Model 2 and Model 3 can be obtained:

[0218]

[0219]

[0220] Steps 1-5: Use Model 1, Model 2, and Model 3 to establish the relationship between the average DBH of the five stands and the corresponding survey time intervals, and use the least squares method to fit and obtain the model parameters.

[0221] Step 2: Reverse the stand age calculation formula and estimate the stand age using the model parameters and the first-period DBH data:

[0222] Step 2-1: Determine the calculation formula of stand age from the DBH growth model;

[0223] Take Model 1 as an example:

[0224] Because Model 1 eliminates age1 from equations (10) and (14) i After obtaining the initial forest age parameter, the calculation formula can be reversed through formula (10) containing the unknown initial forest age parameter:

[0225]

[0226] Where agej i is the age of the jth period in the ith plot.

[0227] Among them, when the average breast diameter of the first stand D gi1 When calculating, ad j =0, the calculation formula becomes as follows:

[0228]

[0229] Where, BAL i1 It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average breast diameter of the stand within the unit area of ​​the i-th plot in the first period.

[0230] Similarly, when using Model 2 and Model 3, the general formula for calculating forest age is as follows:

[0231]

[0232]

[0233] Step 2-2, determine the site class of the sample plot (since the estimated site class is known, only one-to-one correspondence is required);

[0234] Step 2-3: Determine the parameters based on the site class of the sample plot, and then substitute the average DBH of the first-stage stand into the formula to estimate the initial age of the sample plot;

[0235] Determination of parameter description: Assuming that the site grade of the sample plot is m, the dummy variable value of parameter A can be obtained from formula (5), A = a + (m-1)·d, and the dummy variable value of parameter C can be obtained from formula (13), C = c + (m-1)·g.

[0236] Steps 2-4: Based on the time intervals of different survey periods, the ages of the sample plots in the remaining four periods can be obtained.

[0237] Table 3 lists the fitting evaluation indices of the three models used to establish DBH growth models, and Table 4 lists the parameter values ​​of each model after fitting. As shown in Table 3, when Model 1, Model 2, and Model 3 were used to fit the relationship between the average DBH of 554 plots of natural oak forests in Jilin Province and the corresponding survey time intervals, the fitting effect of each model was good, and the coefficient of determination R 2 All are above 0.9960, the standard deviation SEE of the estimated values ​​is less than 0.4 cm, the average predicted error MPE and total relative error TRE tend to 0, and the average percentage standard error MPSE is less than 1.5%.

[0238] Table 3 Fitting results of different models for establishing DBH growth models (Jilin Province)

[0239]

[0240]

[0241] Table 4 Parameters of different model forms for fitting DBH growth models (Jilin Province)

[0242]

[0243] Figure 4 This is a scatter plot of the initial age of 554 plots estimated by Model 1 and the average DBH of the first stand. The higher the level, the worse the site condition. That is, the site condition of level 1 is the best and the site condition of level 9 is the worst. Figure 4It can be seen that when the average DBH of the stands in the same site class is larger, the estimated stand age is older; when the average DBH of the stands is not different, the higher the site class, the older the estimated stand age. These conclusions indicate that site conditions affect the growth rate of DBH; better site conditions mean that the stands will reach the same DBH in a shorter time. Figure 5 This is a comparison chart of three different model forms used to build models and infer the initial age of the sample plot. At the same level, the comparison of the scatter distribution and average value of the three model estimates shows that the estimation effects of the three models are not much different, indicating that the estimation effects are stable.

[0244] The parameter values ​​listed in Examples 1 and 2 of the present invention are only applicable to the distribution range of the modeling samples used, but the modeling method and process provided by the present invention can provide reference and reference for model construction in other regions.

[0245] The method according to the present invention described above 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 that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a special-purpose processor or programmable or special-purpose hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, a processor or hardware, the processing method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the processing shown here, the execution of the code converts the general-purpose computer into a special-purpose computer for executing the processing shown here.

[0246] As described above, the embodiments and descriptions of the present invention are only preferred specific implementation methods of the present invention, which are used to describe the basic principles and specific implementation steps of the present invention, but the protection scope of the present invention is not limited to the above embodiments. There are also many variations of the present invention. For example, the survey period can be flexibly changed, the dependent variable is not limited to the average breast diameter of the stand, but is also applicable to the average volume of the stand, biomass and carbon storage, etc. The theoretical growth equation used for modeling is not limited to the Mitscherlich growth equation and the Richards growth equation. In short, obvious variations derived from this are all within the protection scope of the present invention.

Claims

1. A method for determining the age of a natural forest stand, characterized in that: include: The average DBH of the stand was calculated by selecting retained trees with multiple measured DBH. The stand sites were divided into different grades based on the annual DBH growth rate. A statistical model between the average DBH of the stand and the corresponding survey time interval was constructed based on the theoretical growth equation. The age of the natural stand was then determined by inverting the stand age calculation formula using the model. The method for determining the age of a natural forest stand includes the following steps: Step 1: Fit the relationship between the average DBH of multi-period stands and the corresponding survey time intervals to determine the model parameters: Based on the theoretical growth equation, a relationship model between the average DBH of the stand and the corresponding survey time interval was established. The three models to be selected are: (1) Model 1: Based on the Mitscherlich growth equation, the site grade is reflected in the parameter A by constructing a dummy variable. The model form is as follows: (2) Model 2: Based on the Richards growth equation, the site grade is reflected in the parameter A by constructing a dummy variable. The model form is as follows: (3) Model 3: Based on the Richards growth equation, the site grade is reflected in both parameters A and C by constructing dummy variables. The model form is as follows: in, In formulas (1) to (5): D gij is the average DBH of the stand in the jth period of the i-th plot, k is the number of survey periods, D gi1 is the average DBH of the stand in the first phase of the i-th plot, ad j is the time interval between the jth period and the initial stage of the survey, N is the number of site grades, S n is a dummy variable, d is the difference between the parameter a of adjacent site grades, g is the difference between the parameter c of adjacent site grades, BAL ij is the sum of the basal areas at breast height of all trees in the stand that are larger than the average DBH of the stand within the unit area of ​​the i-th plot in the j-th period, and r is a parameter related to density; The model parameters are obtained by fitting the equation: Step 1-1: Select k trees with k measured DBH data during the survey period. Each plot must have at least 5 trees. Calculate the average DBH of the stand of the trees in each plot at different periods. Steps 1-2: Calculate the distance-independent competition index BAL based on all individual trees in the plot; The calculation formula of the competition index BAL is as follows: Where: T is the number of trees with a breast diameter greater than the average breast diameter of the stand in the plot, d i is the DBH of the i-th tree, s is the area of ​​the plot; Steps 1-3: After determining the annual growth rate using the average DBH of the first and last two stands, the modeling plots were classified into site classes; Steps 1-4: Incorporate the effects of density and site into the base model, apply starting point constraints, and transform the model form; Steps 1-5: Establish the relationship between the average DBH of multi-period stands and the corresponding survey time intervals, and use the least squares method to fit and obtain the model parameters; Step 2: Reverse the stand age calculation formula and estimate the stand age using the model parameters and the first-period DBH data: Step 2-1: Determine the calculation formula of stand age from the DBH growth model; Step 2-2, determine the site class of the sample plot; Step 2-3: Define the parameters based on the site class of the sample plot, and then estimate the initial age of the sample plot based on the average DBH of the first stand; Steps 2-4: Based on the time intervals of different survey periods, the ages of the sample plots in the remaining periods can be obtained.

2. The method for determining the age of a natural forest stand according to claim 1, wherein: In steps 1-1 and 1-2, the process of obtaining modeling data is as follows: Stand age is the average age of each individual tree in the stand. In order to avoid the influence of the number of trees in the sample plot on the modeling effect, the average DBH of the stand is used to estimate the stand age. The basic data are continuous survey data at fixed intervals. The measured DBH of all individual trees in the sample plot is recorded in each survey period. The first survey period is used as the starting point and the last survey period is used as the end point, with a total of k survey periods. Since competition among trees in the stand can lead to tree death, the retained trees that survived in k survey periods in the sample plot are selected for modeling, that is, there are k measured DBH data in k survey periods, and the number of retained trees is required to be no less than 5. The average DBH of the sample plot is calculated based on the DBH of the retained trees after screening. g , the calculation formula is as follows: (6); all the individual trees in the plot reflect the density of the stand, so all the individual trees are taken as the main body, and the sum of the breast height basal area of ​​the individual trees in the plot that are larger than the average breast height diameter of the stand per unit area, BAL, is calculated. The calculation formula is as follows: (7); Average diameter at breast height (DBH) of the stand g , the calculation formula is as follows: Where: p is the number of trees retained in the plot, d i Reserve the tree diameter at breast height for the i-th tree.

3. The method for determining the age of a natural forest stand according to claim 2, wherein: In steps 1-3, the site classification of the sample plot includes the following steps: Step 3: Classify the site level of the sample plot: Step 3-1: The average DBH data of multiple stands in the same plot are all marked with plot numbers to distinguish different plots and ensure that the same plot is at the same site level at different times, and are arranged in ascending order by plot number; Step 3-2: Calculate the annual growth rate v using the average DBH of the first and last two periods, arrange them in descending order, and perform initial classification using ordered sample clustering to obtain the number of classification levels N; Where: D gk is the average DBH of the stand in the kth phase of the plot, ad k is the time interval between the first and last survey periods; Step 3-3, obtain the final site grade based on DBH classification: take the average DBH of the stand as the dependent variable and the corresponding survey time interval as the independent variable, establish a statistical model of the two based on the Mitscherlich growth equation, construct a dummy variable based on the initial site grade, and re-parameterize the model parameter A. The classification equation is in the form of formula (1). After fitting, the final site grade of each plot can be obtained.

4. The method for determining the age of a natural forest stand according to claim 3, wherein: In steps 1-4, to enhance the applicability and stability of the basic model, it is necessary to introduce density variables and reflect site effects, and restrict the model to constrained by the starting point. The conversion model form includes the following steps: Step 4: Incorporate the effects of density and site into the base model and use starting point constraints: Step 4-1: Using the stand average DBH as the dependent variable and the corresponding survey time interval as the independent variable, the Mitscherlich growth equation and the Richards growth equation were used to establish the relationship between the two. The model was constructed as follows: Where: age1 i is the initial forest age of the i-th plot, a is a parameter reflecting the forest production potential, b is a parameter related to the growth rate of the tree species, and c is a parameter related to the assimilation power index w. Step 4-2: To reflect the differences in average DBH growth under different stand densities and improve the accuracy of the model in estimating natural stand age, the distance-independent competition index BAL is introduced on the basis of equations (9) and (10). The model is constructed as follows: Step 4-3: There is diversity in the sites between forest stands within a large area. Reflecting the impact of site differences on the average DBH of the forest stands in the model will improve model performance and enhance model applicability. After dividing the sample plots into site levels, the model parameters a or c are re-parameterized by constructing dummy variables. The model is constructed as follows: Based on formula (11), parameter a is re-parameterized to reflect site differences: Based on formula (12), parameter a is re-parameterized to reflect site differences: Based on formula (12), parameters a and c are re-parameterized to reflect site differences: in, Step 4-4: To improve the stability of the model parameters, the starting point is used to constrain the stand diameter growth model so that it passes through the restriction point (age1 i , D gi1 ), the model is constructed as follows: Using the starting point constraint formula (13): When the model passes the starting point, Formula (16) combined with formula (13) eliminates the unknown age parameter age1 i After that, the DBH growth model constrained by the starting point can be obtained, namely Model 1: Similarly, when using the starting point constraints (14) and (15), Model 2 and Model 3 are obtained:

5. The method for determining the age of a natural forest stand according to claim 4, wherein: In step 2-1, the calculation formula for the initial stand age is derived as follows: Because Model 1 eliminates age1 from equations (16) and (13) i After obtaining the initial forest age parameter, the calculation formula can be reversed through formula (13) containing the unknown initial forest age parameter: Where agej i is the age of the jth period of the i-th plot; Among them, when the average breast diameter of the first stand D gi1 When calculating, ad j =0, the calculation formula becomes as follows: Where, BAL i1 It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average DBH of the stand within the unit area of ​​the i-th plot in the first period; When using Model 2 and Model 3, the general formula for calculating forest age is as follows:

6. The method for determining the age of a natural forest stand according to claim 5, wherein: In step 2-2, since the site conditions of the sample plots are divided into N levels during the modeling process, if the age of a sample plot with an unknown site level is to be estimated, the site level must be determined before the dummy variable value of the parameter reflecting the site level can be determined, and then the stand age can be estimated; Step 5: Determine the site grade of the sample plot; Step 5-1: Assuming the site grade of the sample plot is m, the dummy variable value of parameter A can be obtained from formula (4): A = a + (m-1)·d; Step 5-2: According to formula (17), the initial age of the plot at site class m can be estimated from the first DBH data: i ; Step 5-3: According to formula (17), the final age of the plot at site class m can be estimated from the final DBH data: i ; Where, BAL ik It is the sum of the basal areas at breast height of all trees in the stand that are larger than the average DBH of the stand within the unit area of ​​the i-th plot in the k-th period; Step 5-4: Calculate the difference between the estimated forest age intervals at the first and last stages and the actual age interval when the plot is at site class m; OSC=|more i -age1 i -ad k | (23) Step 5-5: There are N site classes in total. Repeat the above steps. The site class with the smallest OSC value is determined as the site class of the sample plot.

Images