CN110874454A - Method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density - Google Patents

Method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density Download PDF

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CN110874454A
CN110874454A CN201911138236.0A CN201911138236A CN110874454A CN 110874454 A CN110874454 A CN 110874454A CN 201911138236 A CN201911138236 A CN 201911138236A CN 110874454 A CN110874454 A CN 110874454A
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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 continuous checking data of the fixed sample plot of the moso bamboos to be tested in the target area; calculating the biological value of the single bamboo at each age of each diameter; calculating the actual measurement probability of the number of the moso bamboo plants in each fixed sample plot; estimating the probability of the number of the moso bamboo plants in each fixed sample plot; calculating the total number of the moso bamboo plants; estimating the combined probability density value of the diameter at breast height and age of the moso bamboos by using a mixed Copula density function to obtain the number of the moso bamboo plants of each age class of each diameter order; and calculating an accurate estimation value of the moso bamboo carbon reserves. The method can quantitatively describe the ecological function of the moso bamboos in the area, can complete measurement and calculation only by knowing the edge distribution value of the breast diameter and the age of the moso bamboos in the area and the area of the moso bamboo forest, and does not need the measured value of the breast diameter and age joint density of the moso bamboos, and has wide applicability.

Description

Method for accurately measuring and calculating regional scale moso bamboo carbon reserves 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
The forest carbon reserve is calculated by estimating greenhouse gas CO between a land ecosystem and the atmosphere2The key to the exchange capacity (DixonR K, 1994) and has been the subject of research in important scientific programs such as the international geobiosphere program (IGBP), the World Climate Research Program (WCRP) and the international human factors program for global environmental changes (IHDP). How to accurately measure and calculate the forest carbon reserves is a great issue (Brown, 2002) which is receiving great attention from the international scientific community.
The bamboo belongs to the subfamily of Bambusoideae of Gramineae, and has about 150 plants, 1225 plants, and bamboo forest area of 3100-ten thousand hm2And is called the second forest of the world. China is at the center of the distribution of bamboos in the world, bamboo resources are quite rich, the prior bamboo plants 34 belong to 534 species, account for about 40 percent of the bamboo species in the world, the area of the bamboo forest reaches 601 ten thousand hectares, and the area of the Phyllostachys pubescens (Phyllostachys pubescens) is 443 ten thousand hm2And accounts for about 70% of the area of the bamboo forest in China (Zhou national model, et al, 2017).
Moso bamboo, as a special plant, differs from other plants by: 1) the high growth of the moso bamboo is finished within 1 year, 2) for a single moso bamboo, when the high growth is finished, the bamboo height is not changed any more, but the carbon reserve is changed, the change of the carbon reserve is mainly caused by age, the breast diameter and the age of the moso bamboo are considered as main factors influencing the carbon reserve of the single moso bamboo, so that a binary biomass model (Zhou national model, 2006) of the single moso bamboo is constructed, the estimation of the regional carbon reserve of the moso bamboo by the breast diameter and the age is also considered in the research, and the study shows that the carbon fixing capacity of the moso bamboo forest is strong, and the annual carbon fixing capacity of the tree layer of the forest stand is 5.097 thm-2(Zhou national model, Jiang Peikun, 2004), 1.46 times of China fir in fast growing stage (Fangqing et al, 2002), 1.33 times of rain forest in tropical mountain region (Li Ityd et al, 1998), and 2.16 times of China fir forest in 27 years in Sunan (Ruan hong Hua et al, 1997), so that the carbon sink function of bamboo forest is recognized at home and abroad.
China is in the center of bamboo distribution in the world, and the bamboo forest is provided with a plurality of widely distributed provinces, wherein the area and the yield of the bamboo forest in Zhejiang province are located at the front of the whole country, so that accurate estimation of the carbon storage of the bamboo forest in Zhejiang province has very important significance for accurately estimating the influence of the bamboo forest on the global climate change. At present, the estimation of regional scale forest carbon reserves mainly adopts a scale conversion method (Zhang Min, 2004; Zhang X Q., 2002; Fang, J.Y, 2001), but due to the complexity of forest ecosystems and the defects of the conventional scale conversion method (Brown S, 1984; Isaev A, 1995; Johnson WC, 1983; Zhou GS, 2002), the estimation results of forest vegetation biomass on the same scale by different scholars are greatly different (DixonR.K, 1994; Zhouyu, 2000; Square-Yun, 1996). Based on this, the national model proposes a moso bamboo biomass scale conversion method (national model, 2011) based on a minimum scale, and the method needs to know the total number of moso bamboo plants in an area to be estimated, and the total number of the moso bamboo plants is counted according to measured data, so that the method has certain hysteresis quality and cannot be used for predicting the future moso bamboo biomass in the area scale. The mixed probability density model is a very flexible and powerful statistical modeling tool, and a large number of practical problems are a mixed model with clear physical significance, so that the mixed model becomes an important tool (xu Xiao Ling, 2011) for analyzing complex phenomena, and the moso bamboo area is the most easily obtained in all quantitative indexes of the moso bamboo forest, therefore, how to combine the mixed probability density model with the moso bamboo area, and the new regional scale moso bamboo carbon reserve estimation method is a topic which is very worthy of research.
Disclosure of Invention
The invention aims to provide a method for accurately measuring and calculating regional scale moso bamboo carbon reserves based on mixed probability density. The method can quantitatively describe the ecological function of the moso bamboos in the area, can complete measurement and calculation only by knowing the edge distribution value of the breast diameter and the age of the moso bamboos in the area and the area of the moso bamboo forest, and does not need the measured value of the breast diameter and age joint density of the moso bamboos, and has wide applicability.
The technical scheme of the invention is as follows: the method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density comprises the following steps:
collecting continuous checking data of N moso bamboo fixed sample plots of a year to be measured in a target area, and summarizing the continuous checking data of the N moso bamboo sample plots into two-dimensional statistics data of the diameter of breast height and age of a moso bamboo forest according to the number of plants;
step two, calculating the biological value of the single bamboo of each diameter and each age of the target area according to a formula (1), wherein the formula (1) is as follows:
Figure BDA0002280135470000031
wherein i is 5,2, …, m, j is 1,2, …, n, H (D)i,aj) Is the biomass of the single bamboo plant of the ith diameter and the jth age class ajThe age of the individual Phyllostachys pubescens, herein denoted the j-th age, DiThe diameter of the single bamboo is the diameter of the breast height, and the ith diameter is represented;
setting the area of each moso bamboo fixed sample plot as a unit area;
step four, obtaining the total area A of the moso bamboo forest of the object area of the year to be measured by looking up the statistical data of the forest area of the object area;
step five, selecting the minimum value and the maximum value of the number of the moso bamboo plants in unit area as s1 and s2 respectively;
step six, calculating the actual measurement probability of the number of moso bamboo plants of each fixed sample plot of the year to be measured in the target area by using a nuclear density method;
step seven, estimating the probability of the number of moso bamboo plants in each fixed sample plot in the year to be measured in the target area by using a mixed Weibull density function f (x), and fitting parameters of the mixed Weibull density function f (x) by using a maximum likelihood method to obtain g (x);
step eight, calculating the total number of the moso bamboo plants of the year to be measured in the object area according to a formula (2), wherein the formula (2) is as follows:
Figure BDA0002280135470000032
wherein K is the total number of moso bamboo plants of the year to be measured in 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 the moso bamboo forest of the year to be measured in the target area;
step nine, estimating the combined probability density value of the diameter of the moso bamboo breast diameter and the age of the target area to be measured by using a mixed Copula density function according to the two-dimensional statistical data of the diameter of the moso bamboo breast diameter and the age of the moso bamboo forest gathered in the step one, and combining the total number of the moso bamboo plants in the area calculated in the step eight to obtain the number of the plants of each diameter grade and each age grade of the moso bamboo in the target area to be measured;
step ten, calculating an accurate estimation value of the carbon storage of the moso bamboos of the year to be measured in the target area by using the single moso bamboo biomass value of each size grade obtained in the step two and the number of the moso bamboos of each size grade obtained in the step nine according to a formula (3), wherein the formula (3) is as follows:
Figure BDA0002280135470000041
in the formula h (D)i,aj) The biomass of the single bamboo plant of the ith diameter and the jth age class MTotalThe total carbon reserves of the moso bamboos of the years to be measured in the target area, m is the maximum diameter step value of the moso bamboos (the minimum diameter step value of the moso bamboos is 5), N is the maximum age step value of the moso bamboos, and N is the average value of the maximum diameter step values of the moso bamboosijThe number of the moso bamboo plants of the ith diameter order and the jth age order is shown, and w is the conversion coefficient of the moso bamboo biomass and the carbon reserve.
In the method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density, the formula (4) for calculating the actual measurement probability of the number of moso bamboo plants of each fixed sample plot in the year to be measured in the target region by using the kernel density method is as follows:
Figure BDA0002280135470000042
where n is a fixed number of samples, f (X) is the probability value at a certain point X, X1,X2,…,XnIs a sample taken from the population with density function f, k () called the kernel function; h is more than 0 and is the bandwidth; X-XiTo estimate point to sample XiThe distance of (c).
In the 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 a function expression (5) of the mixed Weibull density function is as follows:
Figure BDA0002280135470000051
formula (III) β1,β2The shape parameter for the mixed Weibull density function, x is an independent variable, here representing the number of bamboo plants per unit area, η1，η,2To scale parameters of the hybrid Weibull density function,
Figure BDA0002280135470000052
is a weight coefficient, and
Figure BDA0002280135470000053
in the method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density, the determination of the mixed Copula density function comprises the following steps:
a. estimating the joint density value of the diameter of breast and the age of moso bamboo by respectively adopting a normal Copula density function, a t-Copula density function, a Gumbel Copula density function, a Clayton Copula density function and a Frank Copula density function, and selecting an optimal Copula density function from the joint density values;
b. constructing 3 mixed Copula density functions by taking the optimal Copula density function as a necessary selected composition function according to the property of each Copula density function and the estimation result of the breast diameter and age joint density value of the moso bamboo to be measured in the target area;
c. compiling a maximum likelihood method program by matlab software, respectively fitting parameters of 3 mixed Copula density functions, and further obtaining an estimated value of each mixed Copula density function to the joint probability density of each diameter order and each age level of moso bamboos;
d. and comparing the actually measured probability of the moso bamboo breast diameter and age joint density with the estimated value of the mixed Copula density function to the moso bamboo breast diameter and age joint probability density, and selecting the mixed Copula density function with the highest accuracy.
Compared with the prior art, the method utilizes the continuous checking data of the moso bamboo fixed sample plot of the year to be measured in the object area to calculate the biological value of the single moso bamboo and the total number of the moso bamboo in each age class of each radius step of the area scale, further, the probability density of the number of the moso bamboo in the sample plot is estimated by using the mixed Weibull probability density function, the combined density of the breast diameter and the age of the moso bamboo in the area is respectively estimated by using 5 binary Copula density functions which have wider application range and lower requirement than the commonly used tree-measuring factor binary probability density function, the maximum likelihood function value of each Copula density function is obtained according to the density value of each Copula density function obtained by estimation, further, the binary optimal Copula density function of the breast diameter and the optimal Copula density function is selected as the selected composition function of the mixed Copula density function, and then a plurality of mixed Copula density functions are constructed according to the characteristics of other Copula density functions, the method comprises the steps of respectively estimating the breast diameter and age joint density of the moso bamboos in the area, selecting a mixed Copula density function with the highest accuracy, obtaining the number of the moso bamboo plants of each grade of the diameter by combining the total number of the moso bamboo plants in the area, finally calculating the accurate estimation value of the carbon storage of the moso bamboos in the area by the biological quantity value of the single moso bamboo of each grade of the diameter and the number of the moso bamboo plants of each grade of the diameter and each grade of the diameter, only needing the edge distribution value of the breast diameter and the age of the moso bamboos in the area and the area of the moso bamboos, and not needing the measured value of the breast diameter and age joint density of the moso bamboos, so that the method has wide applicability.
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 combined distribution, and the type of the variable edge distribution is not limited, so that the application range of the Copula function is very wide, the variety of the Copula function is more, each function has unique functions, a certain Copula function is used independently to have certain defects, the mixed Copula function can integrate the advantages of the plurality of Copula functions, and the binary combined density estimation precision for describing the phyllostachys pubescens breast diameter age in Zhejiang province by using the mixed Copula density function is very high.
The Weibull distribution is strong in adaptability and simple in integral form, the Weibull distribution is widely applied to the research of unitary probability distribution of tree measuring factors, the mixed Weibull density model has wider applicability than a single Weibull density model, the number of the moso bamboo plants in unit area is a factor which must be considered for estimating the carbon reserve of the moso bamboo in regional scale, and the probability density of the moso bamboo plants in unit area is described by adopting the combined Weibull density model so as to cope with the complexity of the distribution of the moso bamboo plants in unit area.
Based on the method, the ecological function of the regional moso bamboos is quantitatively described by taking the regional moso bamboos as objects, combining the special biological characteristics of the moso bamboos and the area of the regional moso bamboo forest and applying a mixed probability density model to directly and accurately estimate the total carbon reserve of the regional moso bamboos, the technical support is provided for the international negotiation of the moso bamboo carbon transaction, and the foundation is laid for the new regional scale forest carbon reserve method.
In conclusion, the ecological function of the regional moso bamboos can be quantitatively described, the calculation can be completed only by knowing the edge distribution value of the breast diameter and the age of the regional moso bamboos and the area of the moso bamboo forest, and the measured value of the joint density of the breast diameter and the age of the moso bamboos is not needed, so that the applicability is wide, the interconversion of the carbon reserves of 3 moso bamboos with different scales in a single plant, the forest stand of the moso bamboos and the region is realized, and the estimation precision is high.
Drawings
FIG. 1 is a graph showing probability density of the number of bamboo plants per unit area.
Detailed Description
The invention is further illustrated by the following figures and examples, which are not to be construed as limiting the invention.
Example (b): the method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density accurately measures and calculates the total carbon reserves of the moso bamboo in the whole province of Zhejiang province in 2009 in the embodiment, and comprises the following steps:
step one, collecting continuous checking data of N moso bamboo fixed sample plots in 2009 of Zhejiang province, wherein in the embodiment, a continuous checking system of data sources and forest resources is established in 1979 of Zhejiang province, and 5 years is taken as a re-checking period. 4250 fixed sample plots were arranged, the grid of sample points was 4km × 6km, the sample plots were square in shape, with a side length of 28.28m and an area of 800m 2. 177 continuous checking sample plots of moso bamboos in 2009 are used for research, and the basic conditions of the moso bamboo sample plots are as follows: the number of the moso bamboo plants in each sample plot is 22-897, the diameter of the moso bamboo in each sample plot is 5-15 cm, and the age is more than 1-4 degrees (the current-year-old bamboo is 1 degree bamboo; the 2-3-year-old bamboo is 2 degree bamboo, and so on). The survey factors of the sample plot include soil thickness, slope direction (1: north, 2: north-east, 3: east, 4: south-east, 5: south, 6: south-west, 7: west, 8: north-west, 9: mountain top without slope), slope position (1: ridge, 2: upper, 3: middle, 4: lower, 5: valley, 6: flat), slope, elevation (10m-1200m), average breast diameter of the sample plot, number of sample plots, breast diameter and age of each moso bamboo in the sample plot, and the like.
Step two, calculating the biological value of the single bamboo of each diameter and each age of the target area according to a formula (1), wherein the formula (1) is as follows:
Figure BDA0002280135470000081
wherein i is 5,2, …, m, j is 1,2, …, n, H (D)i,aj) The biomass (Kg) of the single bamboo plant of the ith diameter and the jth age class ajThe age of the individual Phyllostachys pubescens is herein referred to as the j-th age (degree), DiThe diameter of the single-plant moso bamboo breast height is represented as the ith diameter (cm);
the model is established according to the growth rule of the common biomass model and the moso bamboo and by combining the biomass survey data of the moso bamboo in Zhejiang province, and the correlation coefficient R of the model20.937, the estimation precision under the confidence level of 0.05 is 96.43 percent, the total system error is-0.021 percent, and the biomass estimation precision requirement is met (Zhou national model, 2006);
the biomass value (Kg) of the single bamboo of each grade of diameter and each age according to the formula (1) is shown in Table 1:
TABLE 1 biological values of individual Phyllostachys Pubescens of various diameter classes
Figure BDA0002280135470000082
Setting the area of each moso bamboo fixed sample plot as a unit area;
step four, obtaining the total area A of the moso bamboo forest of the object area of the year to be measured by looking up the statistical data of the forest area of the object area;
step five, selecting the minimum value and the maximum value of the number of the moso bamboo plants in unit area as s1 and s2 respectively;
step six, calculating the actual measurement probability of the number of moso bamboo plants of each fixed sample plot of the year to be measured in the target area by using a nuclear density method;
the nuclear density estimation method (wangsiefei, 2007) is mainly to estimate the density of a point or line pattern by means of a moving cell (corresponding to a window). Generally defined as: let X1,X2,…,XnIs a sample taken from the population with a distribution density function f, and estimates the probability value at a certain point x, usually by using the estimation formula (4):
Figure BDA0002280135470000091
where n is a fixed number of samples, f (X) is the probability value at a certain point X, X1,X2,…,XnIs a sample taken from the population with density function f, k () called the kernel function; h is more than 0 and is the bandwidth; X-XiTo estimate point to sample XiThe distance of (d);
the method for calculating the actually measured probability of the moso bamboo plant number in unit area by the nuclear density method has the advantages that: 1) the estimation of the total does not need to introduce prior hypothesis of data distribution, and only obtains data characteristics from the sample, so that the estimation can be used for estimating sample distribution information of any shape, 2) the calculation of group distance and group number is not needed, so that the artificial subjective factors are reduced, and 3) the sample information is not lost while the probability of the number of moso bamboo plants in unit area is obtained. Therefore, the probability of the number of moso bamboo plants in unit area estimated by the kernel density method is very real, and in the embodiment, the probability is taken as the actual measurement probability of the number of moso bamboo plants in unit area;
step seven, estimating the probability of the number of moso bamboo plants in each fixed sample plot in the year to be measured in the target area by using a mixed Weibull density function f (x), and fitting 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 BDA0002280135470000092
formula (III) β1,β2The shape parameter for the mixed Weibull density function, x is an independent variable, here representing the number of bamboo plants per unit area, η1，η,2To scale parameters of the hybrid Weibull density function,
Figure BDA0002280135470000102
is a weight coefficient, and
Figure BDA0002280135470000103
describing the plant number probability density of the continuous checking sample plot of the phyllostachys pubescens in 2009 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 BDA0002280135470000104
determining the coefficient R20.9960, drawing probability density graphs of the number of the same strains by matlab software as shown in fig. 1, and as can be seen from fig. 1, the mixed Weibull distribution can very accurately describe the probability density of the number of the moso bamboo strains per unit area, wherein the weights of the two Weibull density functions in the mixed density function are 0.9846 and 0.0154 respectively;
step eight, calculating the total number of the moso bamboo plants of the year to be measured in the object area according to a formula (2), wherein the formula (2) is as follows:
Figure BDA0002280135470000101
wherein K is the total number of moso bamboo plants of the year to be measured in 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 the moso bamboo forest of the year to be measured in the target area;
the area of the phyllostachys pubescens forest in 2009 from Zhejiang forest resource annual gazette is 69.55 ten thousand hectares, and the area of each phyllostachys pubescens sample checked continuously is 800m2Therefore, the total province is 86.9375X 105The same sample is continuously checked by moso bamboos, and the formula (2) can obtain 1.6921 multiplied by 10 in 2009 of the whole province9Planting moso bamboo;
step nine, estimating the combined probability density value of the diameter of the moso bamboo breast diameter and the age of the target area to be measured by using a mixed Copula density function according to the two-dimensional statistical data of the diameter of the moso bamboo breast diameter and the age of the moso bamboo forest gathered in the step one, and combining the total number of the moso bamboo plants in the area calculated in the step eight to obtain the number of the plants of each diameter grade and each age grade of the moso bamboo in the target area to be measured;
common Copula density functions include a normal Copula density function, a t-Copula density function and an archimedes Copula density function, wherein the Gumbel Copula density function, the Clayton Copula density function and the Frank Copula density function are the most common 3 archimedes Copula density functions, so that the 5 two-dimensional Copula density functions are adopted in the embodiment to estimate the joint density of the phyllostachys pubescens breast diameter age;
in the following tables, Gu, Fr, Cl, t, Gau represent two-dimensional Gumbel Copula density functions, frank Copula density functions, Clayton Copula density functions, t-Copula density functions, normal Copula density functions, respectively;
writing a maximum likelihood method program by matlab software, and fitting various Copula density function parameters to obtain parameters of a Gumbel Copula density function, a Frank Copula density function, a Clayton Copula density function, a t-Copula density function and a normal Copula density function as follows: 1.0550, 1.1755, 0.3475 and 0.1626, the degree of freedom is 12.6439 and 0.0000, and the density function density value of Copula of each diameter order of each age class of moso bamboo is shown in table 2;
according to each Copula density function value, solving a likelihood function corresponding to the Copula density function, wherein the Copula density function with the maximum likelihood function value is the optimal Copula density function;
TABLE 2 Copula Density function density values of various diameters of various ages of Moso bamboo
Figure BDA0002280135470000111
Figure BDA0002280135470000121
TABLE 2
Figure BDA0002280135470000122
TABLE 2
Figure BDA0002280135470000123
Figure BDA0002280135470000131
As can be seen from table 2, the Gumbel Copula density function has asymmetry and tailgating correlation, i.e., the Copula density values of large radius and high age are relatively large, the t-Copula density function also has tailgating correlation, and the Clayton Copula density function, the Frank Copula density function and the normal Copula density function do not have tailgating correlation;
as shown in table 2, the likelihood function values of the Gumbel 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 Gumbel Copula density function is the optimal Copula density function, each of the following mixed Copula density functions includes a Gumbel Copula density function, and since the density function values of the normal Copula are all 1, the normal Copula density function is not considered when constructing the mixed Copula density function of the mao bamboo breast diameter age;
the estimated values of the other 4 Copula density functions except the normal Copula density function on the probability density of each diameter order of moso bamboos at each age level are shown in table 3:
TABLE 3 estimated and measured values of the Copula density function for probability density of different diameter orders of moso bamboo in different age classes
Figure BDA0002280135470000132
Figure BDA0002280135470000141
TABLE 3
Figure BDA0002280135470000142
TABLE 3
Figure BDA0002280135470000143
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 small diameter step moso bamboos of the low age level shown in the table 3 is larger, and because the Gumbel Copula density function and the t-Copula density function on the estimated values of the probability densities of the large diameter step moso bamboos and the high age level moso bamboos are larger, the t-Copula density function is not used as the composition function of the mixed Copula density function, so the Gumbel Copula density function, the Clayton Copula density function and the Frank Copula density function are selected as the composition functions of the mixed Copula density function;
and writing a maximum likelihood method program by matlab software, fitting parameters of each mixed Copula density function to obtain that the parameters of the GuFrCl function are (rho, theta, β, lambda) ═ (0.3902, 60.5809, 0.1737, 3.7994), and the parameters of the GuFr function are (b)1β, λ) ═ 0.8968, 1.0640, -1.6079, and the parameters of the GuCl function are (b)2θ, λ) — (0.7937, 1.0689, 0.0885), and the estimated value of each mixed Copula density function to the probability density of each diameter step of moso bamboo is shown in table 4:
TABLE 4 estimation of combined probability density of mixed Copula density function for diameter of breast height and age of moso bamboo
Figure BDA0002280135470000151
TABLE 4
Figure BDA0002280135470000152
TABLE 4
Figure BDA0002280135470000161
From the estimated values of the joint probability density of the measured probability and the mixed Copula density functions for the breast diameter and the age of the moso bamboo shown in table 4, the determination coefficients of the Gumbel Copula density function, the GuFrCl density function, the GuFr density function and the GuCl density function are 0.9841, 0.7028, 0.9914 and 0.9801, respectively. Therefore, the estimation precision of the GuFr density function on the combined density of the diameter at breast height and the age of the moso bamboo is the highest;
according to the estimation value of the GuFr density function on the breast diameter and age combined density of the phyllostachys pubescens in the whole province, the number of the phyllostachys pubescens in each grade of the diameter in the whole province in 2009 is obtained by combining the total number of the phyllostachys pubescens in the whole province in 2009 as shown in the following Table 5:
TABLE 52009 number of Phyllostachys pubescens of different ages of different diameter and rank in the whole province
Figure BDA0002280135470000162
Step ten, calculating an accurate estimation value of the carbon storage of the moso bamboos of the year to be measured in the target area by using the single moso bamboo biomass value of each size grade obtained in the step two and the number of the moso bamboos of each size grade obtained in the step nine according to a formula (3), wherein the formula (3) is as follows:
Figure BDA0002280135470000171
in the formula h (D)i,aj) The biomass of the single bamboo plant of the ith diameter and the jth age class MTotalIs to be measured for the object regionThe total carbon reserve of the moso bamboos in the year, m is the maximum diameter grade value of the moso bamboos (the minimum diameter grade value of the moso bamboos is 5), N is the maximum age grade value of the moso bamboos, and N is the total carbon reserve of the moso bamboos in the yearijThe number of moso bamboo plants of the ith diameter order and the jth age order is shown, and w is the conversion coefficient of the moso bamboo biomass and the carbon reserve;
the total biomass of the 2009 Moso bamboo of Zhejiang province of 2009 in each diameter order of the plant can be obtained from tables 1 and 5, and the total biomass of the 2009 Moso bamboo of the whole province obtained from formula (3) is 1.9879 × 1010(kilogram) and the biomass is multiplied by a conversion coefficient 0.5042 (Zhou national model, Jiang Peikun, 2004) of the moso bamboo biomass and the carbon reserve, so that the total carbon reserve of the moso bamboo in the whole province in 2009 is 1.0023 multiplied by 1010(kg).
Copula probability density function used in this example:
the distribution function (6) of Gumbel Copula is:
Figure BDA0002280135470000172
in the formula (6), u is a moso bamboo breast diameter edge distribution function, v is a moso bamboo age edge distribution function, and lambda is a parameter;
the density function (7) of Gumbel Copula is:
Figure BDA0002280135470000173
the variables and parameters in formula (7) have the same meanings as in formula (6);
the Clayton Copula distribution function (8) is:
Figure BDA0002280135470000181
in the formula (8), u is a moso bamboo breast diameter edge distribution function, v is a moso bamboo age edge distribution function, and theta is a parameter;
the Clayton Copula density function (9) is:
Figure BDA0002280135470000182
the variables and parameters in formula (9) have the same meanings as in formula (8);
the Frank Copula distribution function (10) is:
Figure BDA0002280135470000183
in the formula (10), u is a moso bamboo breast diameter edge distribution function, v is a moso bamboo age edge distribution function, and β is a parameter;
the Frank Copula density function (11) is:
Figure BDA0002280135470000184
the variables and parameters in formula (11) have the same meanings as in formula (10);
GuFr represents the mixture of Gumbel Copula density function, Frank Copula density function and Clayton Copula density function, GuFr represents the mixture of Gumbel Copula density function and Frank Copula density function, GuCl represents the mixture of Gumbel Copula density function and Clayton Copula density function, thus obtaining the following mixed Copula density function (Nelsen R B, 2006; Hu L, 2006):
Figure BDA0002280135470000185
(10) wherein rho is a proportional parameter, and the meanings of the rest variables and the parameters are the same as the above formulas;
GuFr(u,v；b1,β,λ)＝b1cG(u,v；λ)+(1-b1)cF(u,v；β)
(11) in the formula b1The rest variables and parameters have the same meanings as the above formulas for weight;
GuCl(u,v；b2,θ,λ)＝b2cG(u,v；λ)+(1-b2)cc(u,v；θ)
(12) in the formula b2For weight, the remaining variables and parameters have the same meaning as above.

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 plots of a year to be measured in a target area, and summarizing the continuous checking data of the N moso bamboo sample plots into two-dimensional statistics data of the diameter of breast height and age of a moso bamboo forest according to the number of plants;
step two, calculating the biological value of the single bamboo of each diameter and each age of the target area according to a formula (1), wherein the formula (1) is as follows:
Figure FDA0002280135460000011
wherein i is 5,2, …, m, j is 1,2, …, n, H (D)i,aj) Is the biomass of the single bamboo plant of the ith diameter and the jth age class ajThe age of the individual Phyllostachys pubescens, herein denoted the j-th age, DiThe diameter of the single bamboo is the diameter of the breast height, and the ith diameter is represented;
setting the area of each moso bamboo fixed sample plot as a unit area;
step four, obtaining the total area A of the moso bamboo forest of the object area of the year to be measured by looking up the statistical data of the forest area of the object area;
step five, selecting the minimum value and the maximum value of the number of the moso bamboo plants in unit area as s1 and s2 respectively;
step six, calculating the actual measurement probability of the number of moso bamboo plants of each fixed sample plot of the year to be measured in the target area by using a nuclear density method;
step seven, estimating the probability of the number of moso bamboo plants in each fixed sample plot in the year to be measured in the target area by using a mixed Weibull density function f (x), and fitting parameters of the mixed Weibull density function f (x) by using a maximum likelihood method to obtain g (x);
step eight, calculating the total number of the moso bamboo plants of the year to be measured in the object area according to a formula (2), wherein the formula (2) is as follows:
Figure FDA0002280135460000021
wherein K is the total number of moso bamboo plants of the year to be measured in 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 the moso bamboo forest of the year to be measured in the target area;
step nine, estimating the combined probability density value of the diameter of the moso bamboo breast diameter and the age of the target area to be measured by using a mixed Copula density function according to the two-dimensional statistical data of the diameter of the moso bamboo breast diameter and the age of the moso bamboo forest gathered in the step one, and combining the total number of the moso bamboo plants in the area calculated in the step eight to obtain the number of the plants of each diameter grade and each age grade of the moso bamboo in the target area to be measured;
step ten, calculating an accurate estimation value of the carbon storage of the moso bamboos of the year to be measured in the target area by using the single moso bamboo biomass value of each size grade obtained in the step two and the number of the moso bamboos of each size grade obtained in the step nine according to a formula (3), wherein the formula (3) is as follows:
Figure FDA0002280135460000022
in the formula h (D)i,aj) The biomass of the single bamboo plant of the ith diameter and the jth age class MTotalThe total carbon reserves of the moso bamboos of the years to be measured in the target area, m is the maximum diameter step value of the moso bamboos (the minimum diameter step value of the moso bamboos is 5), N is the maximum age step value of the moso bamboos, and N is the average value of the maximum diameter step values of the moso bamboosijThe number of the moso bamboo plants of the ith diameter order and the jth age order is shown, and w is the conversion coefficient of the moso bamboo biomass and the carbon reserve.
2. The method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density as claimed in claim 1, wherein the method comprises the following steps: the formula (4) for calculating the actual measurement probability of the number of moso bamboo plants in each fixed sample plot of the year to be measured in the target area by using the nuclear density method is as follows:
Figure FDA0002280135460000023
where n is a fixed number of samples, f (X) is the probability value at a certain point X, X1,X2,…,XnIs a sample taken from the population of density functions f, k () is called the kernel functionCounting; h is more than 0 and is the bandwidth; X-XiTo estimate point to sample XiThe distance of (c).
3. The method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density as claimed in claim 1, wherein the method comprises the following steps: the mixed Weibull density function is a mixture of two Weibull probability density functions, and the function expression (5) is as follows:
Figure FDA0002280135460000031
formula (III) β1,β2The shape parameter for the mixed Weibull density function, x is an independent variable, here representing the number of bamboo plants per unit area, η1，η,2To scale parameters of the hybrid Weibull density function,
Figure FDA0002280135460000032
is a weight coefficient, and
Figure FDA0002280135460000033
4. the method for accurately measuring and calculating the regional scale moso bamboo carbon reserves based on the mixed probability density as claimed in claim 1, wherein the method comprises the following steps: the determination of the mixed Copula density function comprises the following steps:
a. estimating the joint density value of the diameter of breast and the age of moso bamboo by respectively adopting a normal Copula density function, a t-Copula density function, a Gumbel Copula density function, a Clayton Copula density function and a Frank Copula density function, and selecting an optimal Copula density function from the joint density values;
b. constructing 3 mixed Copula density functions by taking the optimal Copula density function as a necessary selected composition function according to the property of each Copula density function and the estimation result of the breast diameter and age joint density value of the moso bamboo to be measured in the target area;
c. compiling a maximum likelihood method program by matlab software, respectively fitting parameters of 3 mixed Copula density functions, and further obtaining an estimated value of each mixed Copula density function to the joint probability density of each diameter order and each age level of moso bamboos;
d. and comparing the actually measured probability of the moso bamboo breast diameter and age joint density with the estimated value of the mixed Copula density function to the moso bamboo breast diameter and age joint probability density, and selecting the mixed Copula density function with the highest accuracy.
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