CN110874454B - Regional scale moso bamboo carbon reserve accurate measurement and calculation method based on mixed probability density - Google Patents

Regional scale moso bamboo carbon reserve accurate measurement and calculation method based on mixed probability density Download PDF

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CN110874454B
CN110874454B CN201911138236.0A CN201911138236A CN110874454B CN 110874454 B CN110874454 B CN 110874454B CN 201911138236 A CN201911138236 A CN 201911138236A CN 110874454 B CN110874454 B CN 110874454B
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刘恩斌
朱月清
周国模
施拥军
杜华强
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Zhejiang A&F University ZAFU
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Abstract

The invention discloses a method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density, which comprises the following steps: collecting Mao Zhugu fixed-sample area continuous checking data of the year to be tested of the target area; calculating the biomass value of the single moso bamboo at each age level of each diameter step; calculating actual measurement probability of the plant numbers of the moso bamboos in each fixed sample area; estimating the probability of the number of the mao bamboo plants in each fixed sample area; calculating Mao Zhuzong plants; estimating the breast diameter age joint probability density value of the phyllostachys pubescens by using a mixed Copula density function to obtain the phyllostachys pubescens plant number of each diameter step and each age step; and calculating an accurate estimation value of the moso bamboo carbon reserves. The method can quantitatively describe the ecological functions of the regional moso bamboos, can finish measurement and calculation only by knowing the edge distribution value of the breast diameters and ages of the regional moso bamboos and the area of the moso bamboos without the actual measurement value of the joint density of the breast diameters and ages of the moso bamboos, has wide applicability, and also realizes the interconversion between single moso bamboos, the moso bamboos and 3 regions of different-scale moso bamboos carbon reserves, and has high estimation precision.

Description

Regional scale moso bamboo carbon reserve accurate measurement and calculation method based on mixed probability density
Technical Field
The invention relates to a method for measuring and calculating regional moso bamboo carbon reserves, in particular to a method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density.
Background
Forest carbon reserve measurement and calculation is to estimate greenhouse gas CO between land ecosystem and atmosphere 2 The key to exchange capacity (Dixon R K, 1994) and is the subject of serious scientific programs such as International Global Biosphere Program (IGBP), world Climate Research Program (WCRP), and Global Environment change International humane factor program (IHDP). How to accurately calculate the carbon reserves of forests is a major issue of great concern to the international scientific community (Brown, 2002).
Bamboo belongs to the plant of the subfamily Phyllostachys of Gramineae, has about 150 genus and 1225 species worldwide, and has a bamboo forest area of 3100 tens of thousands of hm 2 Referred to as the "world second forest". The distribution center of the world bamboos in China is rich in bamboo resources, 34 species of the existing bamboo plants account for about 40% of the world bamboos, the area of the bamboo forest reaches 601 ten thousand hectares, and the area of the moso bamboos (Phyllostachys pubescens) is 443 ten thousand hm 2 Accounting for about 70% of the area of the national bamboo forest (Zhou Guomo, etc., 2017).
Moso bamboo is a special plant, and is different from other plants: 1) The high growth of moso bamboos is completed within 1 st year, 2) for single moso bamboos, when the high growth is completed, the bamboo height is not changed, but the carbon storage is changed, the change of the carbon storage is mainly caused by age, and research shows that the chest diameter and age of the moso bamboos are main factors influencing the carbon storage of single moso bamboos, thereby constructing a single moso bamboo binary biomass model (Zhou Guomo, 2006), the research also considers the chest diameter and age to estimate the regional moso bamboo carbon storage, and the research shows that the moso bamboo has strong carbon fixation capacity and the annual carbon fixation of tree layers of the forest stand is 5.097t hm -2 (Zhou Guomo, jiang Peikun, 2004) is 1.46 times that of fir in the fast-growing stage (Fang Xi et al, 2002), 1.33 times that of rain forest in tropical mountain areas (Li Yide et al, 1998), and 2.16 times that of fir forest in 27 years in southeast (Ruan Honghua et al, 1997), so that the bamboo forest carbon sink function is approved at home and abroad.
The center of world bamboo distribution in China is provided with a plurality of provinces with widely distributed phyllostachys pubescens, wherein the area and the yield of phyllostachys pubescens in Zhejiang province are all in the forefront of China, so that accurate estimation of phyllostachys pubescens carbon reserves in Zhejiang province has very important significance for accurately evaluating the influence of phyllostachys pubescens on global climate change. The current estimation of regional scale forest carbon reserves mainly adopts a scale conversion method (Zhao Min, 2004; zhang X Q.,2002; fang, j.y., 2001), but the complexity of a forest ecosystem and the defects of a common scale conversion method (Brown S,1984;Isaev A,1995;Johnson WC,1983;Zhou GS,2002) lead to large difference of estimation results of forest vegetation biomass of the same scale by different scholars (Dixon R.K,1994; zhou Yurong, 2000; square cloud, 1996). Based on this, zhou Guomo proposes a method (Zhou Guomo, 2011) for scaling the moso bamboo biomass based on the minimum scale, which requires knowing the Mao Zhuzong plant number of the region to be estimated, and the Mao Zhuzong plant number is counted according to the measured data, so that there is a certain hysteresis, and therefore it cannot be used to predict the moso bamboo biomass in the future of the region scale. The mixed probability density model is a very flexible and powerful statistical modeling tool, and a large number of problems are actually mixed models with definite physical significance, so that the mixed models become important tools (Xu Xiaoling, 2011) for analyzing complex phenomena, and the areas of moso bamboos are the easiest to obtain in all quantization indexes of the moso bamboos, so that how to combine the mixed probability density model with the areas of the moso bamboos provides a new area-scale moso bamboos carbon reserve estimation method to be studied.
Disclosure of Invention
The invention aims to provide an accurate measurement and calculation method for regional scale moso bamboo carbon reserves based on mixed probability density. The method can quantitatively describe the ecological functions of the regional moso bamboos, can finish measurement and calculation only by knowing the edge distribution value of the breast diameters and ages of the regional moso bamboos and the area of the moso bamboos without the actual measurement value of the joint density of the breast diameters and ages of the moso bamboos, has wide applicability, and also realizes the interconversion between single moso bamboos, the moso bamboos and 3 regions of different-scale moso bamboos carbon reserves, and has high estimation precision.
The technical scheme of the invention is as follows: the regional scale moso bamboo carbon reserve accurate measurement and calculation method based on the mixed probability density comprises the following steps:
collecting continuous checking data of N moso bamboo fixed sample areas of the object area to be tested, and collecting the continuous checking data of the N moso bamboo sample areas into two-dimensional statistical data of the chest diameter and age of the moso bamboo forest according to the number of strains;
step two, calculating the biomass value of the single plant of each age class of each radial order in the target area according to a formula (1), wherein the formula (1) is as follows:
Figure GDA0004137760470000031
wherein i=5, 6,7, …, m, j=1, 2, …, n, H (D) i ,a j ) Is the biomass of the single plant of the moso bamboo of the ith diameter order and the jth age order, a j Age of individual moso bamboo, here, represents the j-th age group, D i The breast diameter of the single phyllostachys pubescens is represented as an ith diameter step;
step three, setting the area of each moso bamboo fixed sample area as a unit area;
step four, obtaining the total area A of the phyllostachys pubescens in the object area of the year to be detected by consulting the forest area statistical data of the object area;
step five, selecting the minimum value and the maximum value of the plant numbers of all the moso bamboos in unit area as s1 and s2 respectively;
step six, calculating actual measurement probability of the plant numbers of the moso bamboos in each fixed sample land in the year to be measured in the target area by using a nuclear density method;
estimating the probability of the number of the moso bamboo plants in each fixed sample plot of the year to be measured in the object area by using a mixed Weibull density function f (x), and fitting the parameters of the mixed Weibull density function f (x) by using a maximum likelihood method to obtain g (x);
step eight, calculating Mao Zhuzong plants of the year to be measured of the target area according to a formula (2), wherein the formula (2) is as follows:
Figure GDA0004137760470000032
k is Mao Zhuzong plants of the year to be measured of the target area, x is the number of moso bamboo plants in unit area, the upper limit is s2, the lower limit is s1, g (x) is a probability density function of the number of moso bamboo plants in unit area, and A is the total area of moso bamboo forests of the year to be measured of the target area;
step nine, estimating the joint probability density value of the breast diameter and age of the moso bamboos in the year to be measured in the object area by using a mixed Copula density function according to the summarized two-dimensional statistical data of the breast diameter and age of the moso bamboos in the step one, and combining the total plant number of the moso bamboos in the area calculated in the step eight to obtain the plant number of each diameter step and each age level of the moso bamboos in the year to be measured in the object area;
step ten, calculating an accurate estimation value of the carbon reserve of the moso bamboos in the year to be measured in the target area by using a formula (3) from the biomass value of the single moso bamboos in each diameter step and each age step obtained in step nine, wherein the formula (3) is as follows:
Figure GDA0004137760470000041
h (D) i ,a j ) Is the biomass of the single plant of the moso bamboo of the ith diameter order and the jth age order, M Total The total carbon reserve of the moso bamboo of the year to be measured in the target area is m is the maximum diameter step value of the moso bamboo, the minimum diameter step value of the moso bamboo is 5, N is the maximum age step value of the moso bamboo, and N ij The plant number of the phyllostachys pubescens is the i-th diameter order and the j-th age level, and w is the conversion coefficient of the phyllostachys pubescens biomass and the carbon reserve.
In the above method for accurately measuring and calculating the storage amount of regional-scale moso bamboo carbon based on the mixed probability density, the formula (4) for calculating the actual measurement probability of the number of moso bamboo plants in each fixed sample land in the year to be measured in the target region by using the nuclear density method is as follows:
Figure GDA0004137760470000042
wherein n is a fixed pattern number, f (X) is a probability value at a point X, X 1 ,X 2 ,…,X n Is a sample extracted from the population with a density function f, k () being called a kernel function; h > 0 is bandwidth; X-X i To estimate the point to sample X i Distance at (c).
In the above method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density, the mixed Weibull density function is a mixture of two Weibull probability density functions, and the function expression (5) is:
Figure GDA0004137760470000051
beta in 1 ,β 2 The shape parameter of the mixed Weibull density function is that x is an independent variable, and the number of the phyllostachys pubescens plants per unit area is expressed in the specification 1 ，η ,2 To mix the scale parameters of the Weibull density function,
Figure GDA0004137760470000052
is a weight coefficient, and->
Figure GDA0004137760470000053
In the above method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density, the determining of the mixed Copula density function includes the following steps:
a. estimating the joint density value of the breast diameter age of the phyllostachys pubescens by adopting a normal density function, a t-Copula density function, a Gumbel Copula density function, a Clayton Copula density function and a Frank Copula density function respectively, and selecting an optimal Copula density function from the joint density values;
b. according to the property of each Copula density function and the estimation result of the joint density value of the breast diameter and the age of the phyllostachys pubescens in the year to be measured in the object region, constructing 3 mixed Copula density functions by taking the optimal Copula density function as a necessary composition function;
c. programming a maximum likelihood method program by matlab software, and respectively fitting parameters of 3 mixed Copula density functions to obtain estimated values of cascade probability density of each diameter step and each age step of the moso bamboo by each mixed Copula density function;
d. and comparing the actually measured probability of the breast diameter age joint density of the phyllostachys pubescens with the estimated value of the mixed Copula density function on the breast diameter age joint probability density of the phyllostachys pubescens, and selecting the mixed Copula density function with the highest accuracy from the estimated value.
Compared with the prior art, the invention utilizes Mao Zhugu fixed sample plot continuous checking data of the year to be tested of the object region to calculate the biological value of single plant moso bamboos of each diameter step of each age step of the region scale and the number of the region scale Mao Zhuzong plants, further, estimates the probability density of the number of moso bamboos in the sample region by using a mixed Weibull probability density function, respectively estimates the regional moso bamboo diameter age joint density by using 5 binary Copula density functions which have wider application range and lower requirements than the conventional tree measurement factor binary probability density function, obtains the maximum likelihood function value of each Copula density function according to the density value of each Copula density function obtained by estimation, further selects the binary optimal Copula density function of each Copula diameter age, uses the optimal Copula density function as the necessary composition function of the mixed Copula density function, and further obtains the characteristics of other Copula density functions, constructing a plurality of mixed Copula density functions, respectively estimating the regional phyllostachys pubescens breast diameter age joint density, selecting the mixed Copula density function with highest accuracy, combining the regional scale Mao Zhuzong plant number to obtain the phyllostachys pubescens plant number of each diameter step and each age level, finally calculating the accurate estimation value of regional scale phyllostachys pubescens carbon reserves according to the individual phyllostachys pubescens biomass value of each diameter step and each age level phyllostachys pubescens plant number of each diameter step, only needing the regional phyllostachys pubescens breast diameter and age edge distribution value and phyllostachys pubescens forest area, and not needing the actual measurement value of phyllostachys pubescens breast diameter age joint density, therefore, the applicability is very wide, because the obtained regional phyllostachys pubescens carbon reserves are accumulated by the individual phyllostachys carbon reserves, the estimation method considers the smallest scale unit (individual phyllostachys pubescens), realizes the mutual conversion between the individual phyllostachys and regional 3 different scale phyllostachys carbon reserves, the estimation accuracy is high.
The Copula function is used as a powerful tool for multivariate modeling, the edge distribution of a plurality of random variables can be connected together to form joint distribution, the types of the variable edge distribution are not limited, therefore, the application range of the Copula function is very wide, the Copula function is more in variety, each function has a unique function, a certain Copula function is singly used, certain defects are caused, the advantages of a plurality of Copula functions can be integrated into a whole, and the binary joint density estimation precision of the Zhejiang mao bamboo chest diameter age is described by using the mixed Copula density function.
The Weibull distribution has strong adaptability and simple integral form, is widely applied to researches on unitary probability distribution of tree measurement factors, and the mixed Weibull density model has wider applicability than a single Weibull density model, and the plant number of the phyllostachys pubescens in unit area is a factor which must be considered in estimating the regional scale phyllostachys pubescens carbon reserves.
Based on the method, the ecological function of the regional moso bamboo is quantitatively described by taking the regional moso bamboo as an object, combining the special biological characteristics of the regional moso bamboo with the area of the regional moso bamboo forest and applying the mixed probability density model to directly and accurately estimate the total carbon reserve of the regional moso bamboo, so that technical support is provided for international negotiations of the moso bamboo carbon transaction, and a foundation is laid for the proposal of a new regional scale forest carbon reserve method.
In conclusion, the ecological functions of the regional moso bamboo can be quantitatively described, the measurement and calculation can be completed only by knowing the edge distribution value of the breast diameter and age of the regional moso bamboo and the area of the moso bamboo forest without the actual measurement value of the joint density of the breast diameter and age of the moso bamboo, the applicability is wide, the mutual conversion among 3 different-scale moso bamboo carbon reserves of a single plant of moso bamboo, the moso bamboo forest and the regional moso bamboo is realized, and the estimation precision is high.
Drawings
FIG. 1 is a graph of probability density of the number of moso bamboo strains per unit area.
Detailed Description
The invention is further illustrated by the following figures and examples, which are not intended to be limiting.
Examples: the method for accurately measuring and calculating the regional-scale moso bamboo carbon reserves based on the mixed probability density in the embodiment accurately measures and calculates the total carbon reserves of the moso bamboo in Zhejiang province in 2009, and comprises the following steps:
step one, collecting N pieces of continuous checking data of fixed-pattern areas of moso bamboos in 2009 in Zhejiang province, wherein the continuous checking system of the data sources and the forest resources is established in 1979 in Zhejiang province, and taking 5 years as a rechecking period. The number of fixed sample sites is 4 to 250, the sample point grid is 4km multiplied by 6km, the shape of the sample site is square, the side length is 28.28m, and the area is 800m2. The basic conditions of the phyllostachys pubescens sample plot are as follows: the number of moso bamboo plants in each sample plot is 22-897, the chest diameter of moso bamboo in each sample plot is 5-15 cm, the age is 1-4 DEG or more (1 DEG bamboo is recorded as current annual bamboo; 2-3 annual bamboo is recorded as 2 DEG bamboo, and so on). The investigation factors of the sample plot comprise soil layer thickness, slope direction (1: north, 2: northeast, 3: east, 4: southeast, 5: south, 6: southwest, 7: west, 8: northwest, 9: no slope direction, i.e. mountain top), slope position (1: ridge, 2: upper part, 3: middle part, 4: lower part, 5: valley, 6: flat land), slope, elevation (10 m-1200 m), average breast diameter of the sample plot, plant number of the sample plot, breast diameter and age of each plant of moso bamboo in the sample plot, and the like.
Step two, calculating the biomass value of the single plant of each age class of each radial order in the target area according to a formula (1), wherein the formula (1) is as follows:
Figure GDA0004137760470000081
wherein i=5, 6,7, …, m, j=1, 2, …, n, H (D) i ,a j ) Is the biomass (Kg) of the individual plant of the moso bamboo of the ith diameter order and the jth age order, a j Age of individual moso bamboo, here, represents the j-th age (degree), D i The breast diameter of a single phyllostachys pubescens is represented as an i-th diameter step (cm);
the model is established according to a common biomass model and the growth rule of moso bamboos and by combining with the biomass survey data of the moso bamboos in Zhejiang province, and the correlation coefficient R of the model 2 =0.937, the estimated accuracy at 0.05 confidence level is 96.43%, the total systematic error is-0.021%, and the accuracy requirements for biomass estimation are met (Zhou Guomo, 2006);
the biomass value (Kg) of the single plant moso bamboo of each age class of each diameter step is obtained according to the formula (1) and is shown in the table 1:
TABLE 1 biological values of individual moso bamboos at each diameter and each age level
Figure GDA0004137760470000082
Step three, setting the area of each moso bamboo fixed sample area as a unit area;
step four, obtaining the total area A of the phyllostachys pubescens in the object area of the year to be detected by consulting the forest area statistical data of the object area;
step five, selecting the minimum value and the maximum value of the plant numbers of all the moso bamboos in unit area as s1 and s2 respectively;
step six, calculating actual measurement probability of the plant numbers of the moso bamboos in each fixed sample land in the year to be measured in the target area by using a nuclear density method;
the kernel density estimation method (Wang Yuanfei, 2007) mainly estimates the density of a dot or line pattern by means of a moving cell (corresponding to a window). General definitionThe method comprises the following steps: set X 1 ,X 2 ,…,X n Is a sample taken from a population with a distribution density function f, estimates the probability value at a point x, typically using estimation equation (4):
Figure GDA0004137760470000091
wherein n is a fixed pattern number, f (X) is a probability value at a point X, X 1 ,X 2 ,…,X n Is a sample extracted from the population with a density function f, k () being called a kernel function; h > 0 is bandwidth; X-X i To estimate the point to sample X i Distance at;
the nuclear density method for calculating the actual measurement probability of the plant number of the phyllostachys pubescens in unit area has the advantages that: 1) estimating the population without introducing prior assumption on data distribution, only acquiring data characteristics from the sample itself, so that the method can be used for estimating sample distribution information of any shape, 2) reducing human subjective factors without calculating group distances and group numbers, and 3) obtaining probability of plant numbers of moso bamboos in unit area without losing sample information. Therefore, the probability of obtaining the plant number of the moso bamboo in unit area by estimation of the nuclear density method is very real, and the probability is taken as the actual measurement probability of the plant number of the moso bamboo in unit area in the embodiment;
estimating the probability of the number of the moso bamboo plants in each fixed sample plot of the year to be measured in the object area by using a mixed Weibull density function f (x), and fitting the parameters of the mixed Weibull density function f (x) by using a maximum likelihood method to obtain g (x);
the mixed Weibull density function is a mixture of two Weibull probability density functions, and the function expression (5) is as follows:
Figure GDA0004137760470000092
beta in 1 ,β 2 The shape parameter of the mixed Weibull density function is that x is an independent variable, and the number of the phyllostachys pubescens plants per unit area is expressed in the specification 1 ，η ,2 To mix the scale parameters of the Weibull density function,
Figure GDA0004137760470000102
is a weight coefficient, and->
Figure GDA0004137760470000103
Describing the plant number probability density of the 2009 phyllostachys pubescens continuous check sample plot by using a mixed Weibull density function, and fitting function parameters by using a maximum likelihood method, wherein the fitting result of the parameters is as follows:
Figure GDA0004137760470000104
determining the coefficient R 2 The probability density chart of the plant numbers of the plot is shown in fig. 1 by using matlab software, and as can be seen from fig. 1, the mixed Weibull distribution can describe the probability density of the plant numbers of the moso bamboo in unit area very accurately, wherein the weight of two Weibull density functions in the mixed density functions is 0.9846 and 0.0154 respectively;
step eight, calculating Mao Zhuzong plants of the year to be measured of the target area according to a formula (2), wherein the formula (2) is as follows:
Figure GDA0004137760470000101
k is Mao Zhuzong plants of the year to be measured of the target area, x is the number of moso bamboo plants in unit area, the upper limit is s2, the lower limit is s1, g (x) is a probability density function of the number of moso bamboo plants in unit area, and A is the total area of moso bamboo forests of the year to be measured of the target area;
the area of the Mao bamboo forest in 2009 from annual gazette of forest resources in Zhejiang province is 69.55 ten thousand hectares, and the area of each continuous checking sample of the Mao bamboo is 800m 2 Therefore, 86.9375 ×10 is shared in the entire province 5 The continuous checking pattern of the moso bamboos can be obtained by the formula (2) and is 1.6921 multiplied by 10 in 2009 of the whole province 9 Plant Phyllostachys pubescens;
step nine, estimating the joint probability density value of the breast diameter and age of the moso bamboos in the year to be measured in the object area by using a mixed Copula density function according to the summarized two-dimensional statistical data of the breast diameter and age of the moso bamboos in the step one, and combining the total plant number of the moso bamboos in the area calculated in the step eight to obtain the plant number of each diameter step and each age level of the moso bamboos in the year to be measured in the object area;
the common Copula density functions include a normal Copula density function, a t-Copula density function and an archimedes Copula density function, wherein Gumbel Copula density function, a Clayton Copula density function and a Frank Copula density function are the most common 3 archimedes Copula density functions, so that the embodiment adopts the 5 two-dimensional Copula density functions to estimate the joint density of the breast diameter age of the phyllostachys pubescens;
in the tables below, gu, fr, cl, t, gau represent a two-dimensional Gumbel Copula density function, a Frank Copula density function, a Clayton Copula density function, a t-Copula density function, a normal Copula density function, respectively;
programming a maximum likelihood method program by matlab software, and then fitting the parameters of each Copula density function to obtain parameters of Gumbel Copula density function, frank Copula density function, clayton Copula density function, t-Copula density function and normal Copula density function, wherein the parameters are respectively as follows: 1.0550, 1.1755, 0.3475 and 0.1626, and degrees of freedom of 12.6439 and 0.0000, and further obtaining Copula density function density values of each diameter step of each age level of moso bamboo as shown in table 2;
according to the Copula density function values, likelihood functions of the corresponding Copula density functions are obtained, and the Copula density function with the maximum likelihood function value is the optimal Copula density function;
TABLE 2 Copula Density function Density values for diameter steps of Phyllostachys Pubescens at each age
Figure GDA0004137760470000111
Figure GDA0004137760470000121
Continuous table 2
Figure GDA0004137760470000122
Continuous table 2
Figure GDA0004137760470000123
Figure GDA0004137760470000131
As can be seen from Table 2, the Gumbel Copula density function has asymmetry, the upper tail is relevant, namely, the Copula density value of the large-diameter order and the advanced grade is larger, the t-Copula density function also has upper tail relevance, and the Clayton Copula density function, the Frank Copula density function and the normal Copula density function do not have upper tail relevance;
as shown in table 2, the likelihood function values of the gummel Copula density function, the Frank Copula density function, the Clayton Copula density function, the t-Copula density function and the normal Copula density function are 11.3454, 2.2044, 1.6129, 9.5339 and 0 respectively, so that the two-dimensional gummel Copula density function is the optimal Copula density function, and each of the following mixed Copula density functions contains gummel Copula density functions, and the normal Copula density function is 1, so that the normal Copula density function is not considered when the mixed Copula density function of the breast diameter age of the phyllostachys pubescens is constructed;
the estimated values of probability densities of the rest 4 Copula density functions except the normal Copula density function on each diameter step and each age step of the moso bamboo are shown in table 3:
TABLE 3 estimated and measured values of Copula Density function for probability Density of each diameter step for each age class of Phyllostachys Pubescens
Figure GDA0004137760470000132
Figure GDA0004137760470000141
Table 3 shows the sequence
Figure GDA0004137760470000142
Table 3 shows the sequence
Figure GDA0004137760470000143
Because the t-Copula density function also has lower tail correlation, the estimated value of the t-Copula density function on the probability density of the low-age grade small-diameter phyllostachys pubescens shown in the table 3 is larger, and the estimated value of the gummel Copula density function and the estimated value of the t-Copula density function on the probability density of the large-diameter grade and high-age grade phyllostachys pubescens are larger, so the t-Copula density function is not used as the component function of the mixed Copula density function, and therefore the gummel Copula density function, the Clayton Copula density function and the Frank Copula density function are selected as the component functions of the mixed Copula density function;
programming a maximum likelihood method program by matlab software, and fitting the parameters of each mixed Copula density function to obtain the parameters of the GuFrCl function as (rho, theta, beta, lambda) = (0.3902, 60.5809,0.1737,3.7994), wherein the parameters of the GuFr function are as follows: (b) 1 β, λ) = (0.8968,1.0640, -1.6079), the parameters of the GuCl function are: (b) 2 θ, λ) = (0.7937,1.0689,0.0885), and further the estimated values of probability density of each diameter step and each age step of moso bamboo by each mixed Copula density function are shown in table 4:
TABLE 4 estimation of the joint probability Density of the chest diameter age of Phyllostachys Pula by the Mixed Copula Density function
Figure GDA0004137760470000151
Continuous table 4
Figure GDA0004137760470000152
Continuous table 4
Figure GDA0004137760470000161
According to the actual measurement probability shown in table 4 and the estimated value of the joint probability density of each mixed Copula density function to the breast diameter age of the phyllostachys pubescens, the determination coefficients of Gumbel Copula density function, guFrCl density function, guFr density function and GuCl density function are 0.9841, 0.7028, 0.9914 and 0.9801 respectively. Therefore, the estimation accuracy of the GuFr density function on the breast diameter and age joint density of the phyllostachys pubescens is highest;
according to the estimated value of GuFr density function on the breast diameter and age combined density of Mao bamboo in full province, combining the number of the Mio bamboo in full province Mao Zhuzong in 2009 to obtain the number of the Mao bamboo in each diameter and stage and each age stage in full province in 2009, see the following table 5:
table 5 Phyllostachys Pubescens plant numbers of various diameter steps and age groups in 2009
Figure GDA0004137760470000162
Step ten, calculating an accurate estimation value of the carbon reserve of the moso bamboos in the year to be measured in the target area by using a formula (3) from the biomass value of the single moso bamboos in each diameter step and each age step obtained in step nine, wherein the formula (3) is as follows:
Figure GDA0004137760470000171
h (D) i ,a j ) Is the biomass of the single plant of the moso bamboo of the ith diameter order and the jth age order, M Total The total carbon reserve of the moso bamboo of the year to be measured in the target area is m is the maximum diameter order value of the moso bamboo (the minimum diameter order value of the moso bamboo is 5), N is the maximum age order value of the moso bamboo, and N ij The plant number of the phyllostachys pubescens is the i-th diameter order and the j-th age level, and w is the conversion coefficient of the phyllostachys pubescens biomass and the carbon reserve;
from tables 1 and 5, the total biomass of the respective diameter steps and the respective ages of the Phyllostachys Pubescens in 2009 in Zhejiang province was obtained, and the total biomass of the Phyllostachys Pubescens in Zhejiang province was 1.9879 ×10 from the formula (3) 10 (kg), the biomass multiplied by the conversion factor 0.5042 of the moso bamboo biomass and the carbon reserves (Zhou Guomo, gingerPegging, 2004) to obtain a total carbon storage of 1.0023 ×10 in 2009 10 (kg).
Copula probability density function used in this example:
the distribution function (6) of Gumbel Copula is:
Figure GDA0004137760470000172
in the formula (6), u is a phyllostachys pubescens breast diameter edge distribution function, v is a phyllostachys pubescens age edge distribution function, and lambda is a parameter;
the density function (7) of Gumbel Copula is:
Figure GDA0004137760470000173
the meanings of variables and parameters in the formula (7) are the same as those in the formula (6);
the Clayton Copula distribution function (8) is:
Figure GDA0004137760470000181
in the formula (8), u is a phyllostachys pubescens breast diameter edge distribution function, v is a phyllostachys pubescens age edge distribution function, and θ is a parameter;
the Clayton Copula density function (9) is:
Figure GDA0004137760470000182
the meanings of variables and parameters in the formula (9) are the same as those in the formula (8);
the Frank Copula distribution function (10) is:
Figure GDA0004137760470000183
in the formula (10), u is a phyllostachys pubescens breast diameter edge distribution function, v is a phyllostachys pubescens age edge distribution function, and beta is a parameter;
the Frank Copula density function (11) is:
Figure GDA0004137760470000184
the variables and parameters in formula (11) have the same meaning as formula (10);
the study expressed GuFrCl as a mixture of Gumbel Copula density function, frank Copula density function and Clayton Copula density function, guFr as a mixture of Gumbel Copula density function and Frank Copula density function, guCl as a mixture of Gumbel Copula density function and Clayton Copula density function, thus resulting in a mixed Copula density function (Nelsen R B,2006; hu L, 2006):
Figure GDA0004137760470000185
(10) Wherein ρ is a proportional parameter, and the meanings of the rest variables and parameters are the same as those of the above formulas;
GuFr(u,v；b 1 ,β,λ)＝b 1 c G (u,v；λ)+(1-b 1 )c F (u,v；β)
(11) In b 1 The weight is used, and the meanings of the rest variables and parameters are the same as the above formula;
GuCl((u,v；b 2 ,θ,λ)＝b 2 c G (u,v；λ)+(1-b 2 )c c (u,v；θ)
(12) In b 2 The weight is the rest variables and parameters have the same meaning as the above formula.

Claims (4)

1. The method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density is characterized by comprising the following steps of:
collecting continuous checking data of N moso bamboo fixed sample areas of the object area to be tested, and collecting the continuous checking data of the N moso bamboo sample areas into two-dimensional statistical data of the chest diameter and age of the moso bamboo forest according to the number of strains;
step two, calculating the biomass value of the single plant of each age class of each radial order in the target area according to a formula (1), wherein the formula (1) is as follows:
Figure FDA0004137760460000011
wherein i=5, 6,7, …, m, j=1, 2, …, n, H (D) i ,a j ) Is the biomass of the single plant of the moso bamboo of the ith diameter order and the jth age order, a j Age of individual moso bamboo, here, represents the j-th age group, D i The breast diameter of the single phyllostachys pubescens is represented as an ith diameter step;
step three, setting the area of each moso bamboo fixed sample area as a unit area;
step four, obtaining the total area A of the phyllostachys pubescens in the object area of the year to be detected by consulting the forest area statistical data of the object area;
step five, selecting the minimum value and the maximum value of the plant numbers of all the moso bamboos in unit area as s1 and s2 respectively;
step six, calculating actual measurement probability of the plant numbers of the moso bamboos in each fixed sample land in the year to be measured in the target area by using a nuclear density method;
estimating the probability of the number of the moso bamboo plants in each fixed sample plot of the year to be measured in the object area by using a mixed Weibull density function f (x), and fitting the parameters of the mixed Weibull density function f (x) by using a maximum likelihood method to obtain g (x);
step eight, calculating Mao Zhuzong plants of the year to be measured of the target area according to a formula (2), wherein the formula (2) is as follows:
Figure FDA0004137760460000021
k is Mao Zhuzong plants of the year to be measured of the target area, x is the number of moso bamboo plants in unit area, the upper limit is s2, the lower limit is s1, g (x) is a probability density function of the number of moso bamboo plants in unit area, and A is the total area of moso bamboo forests of the year to be measured of the target area;
step nine, estimating the joint probability density value of the breast diameter and age of the moso bamboos in the year to be measured in the object area by using a mixed Copula density function according to the summarized two-dimensional statistical data of the breast diameter and age of the moso bamboos in the step one, and combining the total plant number of the moso bamboos in the area calculated in the step eight to obtain the plant number of each diameter step and each age level of the moso bamboos in the year to be measured in the object area;
step ten, calculating an accurate estimation value of the carbon reserve of the moso bamboos in the year to be measured in the target area by using a formula (3) from the biomass value of the single moso bamboos in each diameter step and each age step obtained in step nine, wherein the formula (3) is as follows:
Figure FDA0004137760460000022
h (D) i ,a j ) Is the biomass of the single plant of the moso bamboo of the ith diameter order and the jth age order, M Total The total carbon reserve of the moso bamboo of the year to be measured in the target area is m is the maximum diameter step value of the moso bamboo, the minimum diameter step value of the moso bamboo is 5, N is the maximum age step value of the moso bamboo, and N ij The plant number of the phyllostachys pubescens is the i-th diameter order and the j-th age level, and w is the conversion coefficient of the phyllostachys pubescens biomass and the carbon reserve.
2. The method for accurately measuring and calculating the regional scale moso bamboo charcoal reserves based on the mixed probability density according to claim 1, wherein the method comprises the following steps of: the actual measurement probability of the phyllostachys pubescens plants in each fixed sample area of the object area to be measured is calculated by using a nuclear density method as follows:
Figure FDA0004137760460000023
wherein n is a fixed pattern number, f (X) is a probability value at a point X, X 1 ,X 2 ,…,X n Is a sample extracted from the population with a density function f, k () being called a kernel function; h > 0 is bandwidth; X-X i To estimate the point to sample X i Distance at (c).
3. The method for accurately measuring and calculating the regional scale moso bamboo charcoal reserves based on the mixed probability density according to claim 1, wherein the method comprises the following steps of: the mixed Weibull density function is a mixture of two Weibull probability density functions, and the function expression (5) is as follows:
Figure FDA0004137760460000031
beta in 1 ,β 2 The shape parameter of the mixed Weibull density function is that x is an independent variable, and the number of the phyllostachys pubescens plants per unit area is expressed in the specification 1 ，η ,2 To mix the scale parameters of the Weibull density function,
Figure FDA0004137760460000032
is a weight coefficient, and->
Figure FDA0004137760460000033
4. The method for accurately measuring and calculating the regional scale moso bamboo charcoal reserves based on the mixed probability density according to claim 1, wherein the method comprises the following steps of: the determination of the hybrid Copula density function comprises the following steps:
a. estimating the joint density value of the breast diameter age of the phyllostachys pubescens by adopting a normal density function, a t-Copula density function, a Gumbel Copula density function, a Clayton Copula density function and a Frank Copula density function respectively, and selecting an optimal Copula density function from the joint density values;
b. according to the property of each Copula density function and the estimation result of the joint density value of the breast diameter and the age of the phyllostachys pubescens in the year to be measured in the object region, constructing 3 mixed Copula density functions by taking the optimal Copula density function as a necessary composition function;
c. programming a maximum likelihood method program by matlab software, and respectively fitting parameters of 3 mixed Copula density functions to obtain estimated values of cascade probability density of each diameter step and each age step of the moso bamboo by each mixed Copula density function;
d. and comparing the actually measured probability of the breast diameter age joint density of the phyllostachys pubescens with the estimated value of the mixed Copula density function on the breast diameter age joint probability density of the phyllostachys pubescens, and selecting the mixed Copula density function with the highest accuracy from the estimated value.
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