A volume annual yield method based on numerical differentiation

Abstract

The application provides a volume annual increment method based on numerical differentiation, combines a diameter at breast height-height model and a binary volume model, deduces a simple formula for calculating height and volume annual increment by using a numerical differentiation idea, divides data into multiple time stages in view of time distribution characteristics of every five years of a class of data, calculates diameter at breast height annual growth rates of each stage under the premise that diameter at breast height growth rates in the same stage are equal, generates a recursive formula of volume quantity year by year, compares true value data and prediction data, calculates relative errors and average relative errors of each sample, evaluates prediction accuracy of the annual increment method, and realizes year-by-year interpolation of volume in the class of data.

Description

I. Technical Field

[0001] This invention relates to a method for calculating annual volume based on numerical differentiation. II. Technical Background

[0002] The collection and survey cycle for forest resource data is too long, with some surveys typically requiring five years. This extended survey cycle leads to data lag, thus limiting a comprehensive understanding and monitoring of forest ecosystems. Obtaining annual forest resource data is a challenging task. Due to the long survey cycle, continuous data cannot be obtained, necessitating an addressing of missing data for intermediate years. By establishing appropriate annual data extraction methods, missing years in the data sequence can be filled, resulting in continuous annual forest resource data.

[0003] Accurate timber volume information is crucial for ecosystem assessment and monitoring. By calculating annual timber volume, we can understand changes in carbon storage within forest ecosystems, predict timber supply, help policymakers develop rational logging plans, and support the planning and management of the timber industry. The traditional approach involves collecting timber volume data and using interpolation methods to estimate missing years, thus obtaining annual timber volume data. The advantage of this method is that the interpolation function passes through every data point, ensuring data continuity and smoothness, resulting in a relatively coherent timber volume sequence. However, this method only considers the mathematical expression of timber volume data and does not fully consider the underlying ecological context and tree growth patterns, failing to accurately reflect the true state and dynamic changes of the ecosystem. III. Summary of the Invention

[0004] This invention provides a novel method for annual volume estimation based on numerical differentiation. Compared to traditional mathematical interpolation methods, this invention combines tree growth information and its ecological background to propose a novel annual volume estimation method. First, it combines the diameter-at-breast height (DBH) model and the binary volume model, using the idea of ​​numerical differentiation to derive concise formulas for calculating the annual growth of tree height and volume. By multiplying the annual DBH growth rate by the corresponding tree height, the annual growth of tree height can be estimated; by multiplying the annual DBH growth rate by the corresponding volume, the annual growth of volume can be estimated. Then, considering the time distribution characteristics of a type of data that is estimated every five years, the data is divided into multiple time periods, each with a five-year cycle. Assuming that the DBH growth rate is equal within the same period, the annual DBH growth rate for each period is calculated. Then, the annual volume growth is calculated using the previously derived formulas, and a recursive formula for annual volume estimation is generated to achieve annual volume estimation. Finally, the accuracy of the annual data is evaluated by comparing it with the true value and calculating the average relative error, in order to verify the reliability and accuracy of the method.

[0005] Main invention content:

[0006] 1. Establish a simple calculation method to directly derive tree height growth and volume growth from diameter at breast height (DBH) growth rate;

[0007] 2. Establish a method for calculating annual volume figures applicable to a specific type of data;

[0008] This invention has the following advantages compared to existing methods:

[0009] (1) Compared with traditional methods that require complex measurements and observations, this method uses numerical differentiation to directly derive the annual growth of tree height and volume from the annual growth rate of tree diameter at breast height, thus improving the efficiency of data acquisition.

[0010] (2) Traditional volume interpolation methods only consider the mathematical expression of volume data and ignore the ecological meaning. However, this method couples the structure of diameter at breast height (DBH) growth rate, binary volume, and DBH-tree height model to realize the annual volume output, which can better reflect the growth pattern and ecological characteristics of trees, making the prediction results more accurate and reliable.

[0011] (3) Traditional survey methods usually require field investigations, which are labor-intensive. However, this method can predict timber volume year by year by applying the annual data generation method, thereby reducing the workload of forestry surveys. IV. Detailed Implementation

[0012] 1. Derive a concise formula for calculating the annual growth of tree height and volume.

[0013] According to the diameter at breast height (DBH) - tree height model, H = aD b Perform total differential operation on this expression The annual growth ΔH of tree height is derived as follows:

[0014]

[0015] Where ΔH is the tree height growth, H is the tree height, ΔD is the diameter at breast height (DBH) growth, D is the DBH, p = ΔD / D is the annual DBH growth rate, and a and b are parameters. The annual tree height growth can be obtained by multiplying the annual DBH growth rate by the corresponding tree height.

[0016] According to the binary volume model V=cD d H e Perform total differential operation on this expression The annual volume growth ΔV is derived as follows:

[0017]

[0018] Where ΔV is the volumetric growth, V is the volume, and c, d, and e are parameters. The annual volumetric growth can be obtained by multiplying the annual diameter at breast height (DBH) growth rate by the corresponding volume.

[0019] 2. Generate a recursive formula for annual timber volume, using a single tree as the smallest calculation unit, to estimate the annual timber volume of a single tree.

[0020] Using data from four phases, the diameter at breast height (DBH) of a single log at four time points (D0, D5, D...) can be obtained. 10 D 15 and volume V0, V5, V 10 V 15 These four periods of data are divided into three time periods, each lasting five years: the first period is from year 0 to 5, the second period is from year 5 to 10, and the third period is from year 10 to 15.

[0021] Taking the first stage as an example, we will estimate the annual volume. First, based on D0 and D5, we will calculate the annual growth rate of diameter at breast height (DBH) for the first stage. Assuming the annual growth rate of diameter at breast height is constant in the first stage, i.e., p 年度0 =p 年度1 =p 年度2 =p 年度3 =p 年度4 =p 0,5 Then, based on the previously derived annual volume growth ΔV 年度(i,i+1) =V 年度i ·p 年度i The formula (e+f·b) is used to calculate the annual volume growth ΔV. 年度(i,i+1) For example: using V0,p 年度0 Substitute ΔV 年度(i,i+1) =V 年度i ·p 年度i (e+f·b) can be used to calculate ΔV 年度(0,1) Finally, the recurrence relation V is generated. 年度i+1 =V 年度i +ΔV 年度(i,i+1) The annual volumetric volume V1, V2, V3, V4, V5 from year 0 to 5 is calculated as follows:

[0022] V 年度0 =V0

[0023] V 年度1 =V 年度0 +ΔV 年度(0,1) =V0+V0·p 年度0 (d+e·b)

[0024] V 年度2 =V 年度1 +ΔV 年度(1,2)=V 年度1 +V 年度1 ·p 年度1 (d+e·b)

[0025] V 年度3 =V 年度2 +ΔV 年度(2,3) =V 年度2 +V 年度2 ·p 年度2 (d+e·b)

[0026] V 年度4 =V 年度3 +ΔV 年度(3,4) =V 年度3 +V 年度3 ·p 年度3 (d+e·b)

[0027] V 年度5 =V 年度4 +ΔV 年度(4,5) =V 年度4 +V 年度4 ·p 年度4 (d+e·b)

[0028] Similarly, calculate the annual growth rate of diameter at breast height in the second stage. p 年度5 =p 年度6 =p 年度7 =p 年度8 =p 年度9 =p 5,10 In order to obtain the annual volume V 年度6 V 年度7 V 年度8 V 年度9 V 年度10 Calculate the annual growth rate of diameter at breast height in the third stage. p 年度10 =p 年度11 =p 年度12 =p 年度13 =p 年度14 =p 10,15 In order to obtain the annual volume V 年度11 V 年度12 V 年度13 V 年度14 V 年度15 .

[0029] 3. Compare the true data and the predicted data, calculate the relative error for each sample and the average relative error, and evaluate the prediction accuracy of the annual output method. Volume V0, V5, V at each time point. 10 V 15 This is true data. Because V exists... 年度0=V0, so we only need to compare the actual volume V5 and V of each sample. 10 V 15 With the predicted volume V 年度5 V 年度10 V 年度15 First, calculate the relative error for each sample. Then calculate the average relative error of all samples. A smaller mean relative error value indicates that the predicted result is closer to the true data, suggesting higher prediction accuracy.

Claims

1. A method for calculating annual volume based on numerical differentiation. Its key features are as follows: First, it combines the diameter-at-breast height (DBH) model with the binary volume model, using numerical differentiation to derive concise formulas for calculating the annual growth of tree height and volume. Second, considering the time distribution characteristics of a class of data collected every five years, the data is divided into multiple time periods. Assuming that the DBH growth rate is equal within the same period, the annual DBH growth rate for each period is calculated, along with the annual volume growth, generating a recursive formula for year-by-year volume estimation. Finally, by comparing with the true values, the average relative error is calculated to evaluate the accuracy of the year-by-year data, thus verifying the reliability and accuracy of the method. The specific steps are as follows: 1) Derive a concise formula for calculating the annual growth of tree height and volume; Based on the diameter at breast height-tree height model Perform total differential operation on this expression Derive the annual growth of tree height ,as follows: in For tree height growth, For the height of the tree, This is the growth in diameter at breast height. Diameter at breast height, The annual growth rate of diameter at breast height. The parameter is used to calculate the annual growth rate of the diameter at breast height (DBH) by multiplying it by the corresponding tree height. According to the binary volume model Perform total differential operation on this expression Derivation of annual volume growth ,as follows: in Volumetric growth For volume, The parameter is used to calculate the annual growth rate of the diameter at breast height (DBH) by multiplying it by the corresponding volume. 2) Generate a recursive formula for the annual volume of timber, using a single tree as the smallest calculation unit, to estimate the annual volume of a single tree; By using data from four phases of the first type, the diameter at breast height of a single log at four different time points can be obtained. and volume The data from these four periods are divided into three time periods, each lasting five years: the first period is from year 0 to 5, the second period is from year 5 to 10, and the third period is from year 10 to 15. Taking the first stage as an example, we will estimate the annual volume of timber; firstly, based on Calculate the annual growth rate of diameter at breast height in the first stage. Assuming the annual growth rate of diameter at breast height is equal in the first stage, that is Based on the previously derived annual volume growth... This formula calculates the annual growth of timber volume. ;use Substitute It can be calculated Finally, the recurrence formula is generated. Calculate the annual volume of timber from year 0 to 5. ,as follows: Similarly, calculate the annual growth rate of diameter at breast height in the second stage. , In order to obtain the annual volume ; Calculate the annual growth rate of sternal diameter in the third stage. , In order to obtain the annual volume ; 3) Compare the true data and the predicted data, calculate the relative error for each sample and the average relative error, and evaluate the prediction accuracy of the annual output method; volume at each time point. This is true data; due to the existence of Therefore, it is only necessary to compare the actual volume of each sample. With the predicted volume ; First calculate the relative error for each sample. Then calculate the average relative error of all samples. .

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