Forest stock annual update method based on data assimilation

Abstract

The application discloses a forest stock annual updating method based on data assimilation, relates to the technical field of forest stock monitoring, and aims at the problem that the existing monitoring method usually relies on long time series data, and the time series data is discontinuous and difficult to be directly applied in the case that only 1 / 5 sample plots are investigated every year, thereby leading to inaccurate forest stock monitoring. The application adopts a mixed estimation method to fuse annual limited sample plot data and a forest growth model, introduces a calibration mechanism based on a covariance structure, can compensate for data defects caused by annual sample scarcity and time series observation fault zones, can still output stable and reliable overall mean estimation under the condition that the number of single-year effective sample plots is insufficient and time series is discontinuous, effectively compresses estimation variance, and improves the accuracy of forest stock monitoring.

Description

Technical Field

[0001] This application relates to the field of forest stock volume monitoring technology, specifically a method for annual updating of forest stock volume based on data assimilation. Background Technology

[0002] "A five-year cycle, with one-fifth of the plots surveyed each year" is a method for forest resource inventory. All fixed monitoring plots in a province or region are divided into five groups, and only one group (i.e., 1 / 5 of the plots) is surveyed each year. After five years, all plots have been surveyed, forming a complete cycle.

[0003] Annual dynamic monitoring of forest resources is an important component of the unified natural resource survey and monitoring system. Its core task is to obtain information on the annual changes of key indicators such as forest stock volume, so as to provide data support for ecological protection, carbon sequestration and forest management.

[0004] Early studies employed methods such as Kalman filtering to use predicted data generated by stand growth models as supplementary information to update historical inventory data. For example, Kalman filtering was used to dynamically correct the previous inventory data; and growth model predictions were incorporated as observed values ​​for updating. Subsequent research further developed this into particle filtering (sequential Monte Carlo method) to handle nonlinear problems.

[0005] These methods typically rely on long-term series data, but when only 1 / 5 of the sample plots are surveyed each year, the time-series data is discontinuous and difficult to apply directly. This leads to inaccurate monitoring of forest stock volume. Summary of the Invention

[0006] The purpose of this invention is to address the problem that existing monitoring methods typically rely on long-term series data, which are discontinuous and difficult to apply directly when only 1 / 5 of the sample plots are surveyed each year. This leads to inaccurate forest stock volume monitoring, and the invention provides a method for annual updating of forest stock volume based on data assimilation.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] The annual update method for forest stock volume based on data assimilation includes the following steps:

[0009] Step 1: For each sample plot within the study area, obtain the stock volume of that plot. Divide the sample plots according to forest stand type based on the dominant tree species, and obtain the stock volume per unit area based on the area of ​​the sample plot. ;

[0010] Step 2: Construct growth equations for different forest stand types in the study area, select the optimal growth equation, and obtain the timber volume of different forest stand types within the sample plot based on the optimal growth equation. Then, based on the timber volume of all trees within the sample plot and the area of ​​the sample plot, obtain the volume per unit area. ;

[0011] Step 3: Construct a mixed estimation model for ME and incorporate the accumulation per unit area. and volume per unit area Inputting the ME mixture estimation model yields an annual estimate of the average total forest stock volume. , is represented as:

[0012] ,

[0013] ,

[0014] in, This represents the linearized value of the volume per unit area obtained from the sample plot survey for each year. The covariance matrix of observation errors in the sample plot survey. This is the annual difference matrix. For a progressive upper limit, This is the annual error matrix. For The estimated value;

[0015] Step 4: Acquire remote sensing data of the study area, and combine the remote sensing data of the study area with the volume per unit area. Annual estimates of the average total forest stock As basic data;

[0016] Step 5: Based on remote sensing data, extract vegetation index, original band reflectance, texture features and topographic factors, and use vegetation index, original band reflectance, texture features and topographic factors as auxiliary variables;

[0017] Step 6: Construct a SUR regression model and input the basic data and auxiliary variables into the SUR regression model to obtain the accumulation prediction results. ;

[0018] Step 7: Use BLUP to predict the accumulation volume. The calibration was performed to obtain the calibrated estimate of forest stock volume. ;

[0019] Step 8: Use the Bootstrap method to estimate the calibrated forest stock volume. Uncertainty analysis was conducted to obtain the Bootstrap estimate of the overall mean of forest stock volume, which is the annual monitoring result of forest stock volume.

[0020] Furthermore, the remote sensing data includes Landsat series remote sensing image data and digital elevation model data.

[0021] Furthermore, the optimal growth equation is obtained by linearizing the Logistic equation, and the linearized growth equation is expressed as:

[0022] ,

[0023] in, These are the model parameters.

[0024] Furthermore, the forest stand types include coniferous forests, pure broad-leaved forests, mixed coniferous and broad-leaved forests, and mixed broad-leaved forests.

[0025] Furthermore, the volume of the sample plot in step 1 is obtained through a single-dimensional or two-dimensional volume table of the study area.

[0026] Furthermore, the vegetation indices include NDVI, EVI, DVI, GRVI, SAVI, RVI, and ARVI;

[0027] The topographic factors include elevation, slope, and aspect.

[0028] Furthermore, the texture features are obtained based on the gray-level co-occurrence matrix, and the texture features include mean, variance, homogeneity, contrast, dissimilarity, entropy, and second moment of angle.

[0029] Furthermore, the SUR regression model is expressed as:

[0030] ,

[0031] in, For model parameter vectors, It is a block diagonal matrix. For the dependent variables of different sub-models, For the first The design matrix corresponding to each independent variable For the error vector, The number of sub-models, =1,2,..., , For the first There are one independent variable, and the system's error term. For a multivariate normal vector, satisfying , The variance-covariance matrix is ​​as follows, representing the mean of the accumulation:

[0032] ,

[0033] in, The model parameter vector is a positive definite symmetric matrix. Estimating in two steps using the feasible generalized least squares method:

[0034] First, the initial model is fitted using ordinary least squares to obtain the residuals. Then calculate using residuals A consistent estimator for each element in the matrix, and thus obtain The estimated Substituting into the following formula yields an estimate of the parameter vector β. :

[0035] ,

[0036] in, To design the transpose of the matrix, for An identity matrix of order 1.

[0037] Furthermore, the calibration in step 7 specifically involves:

[0038] use Calibration is performed, among other things. For the first SUR sub-model The obtained calibrated value vector, as well as for The elements in and For dimension and subvectors, For sub-model The predicted value vector.

[0039] Furthermore, the specific steps of step 8 are as follows:

[0040] For the seemingly unrelated model, the first The dependent variable corresponding to each sub-model has the true population mean. Represented as:

[0041] ,

[0042] population mean estimate Represented as:

[0043] ,

[0044] The Bootstrap residual procedure is used to construct a resampling model for a multiple linear regression model, and from... Random samples are drawn from the model and then added back to the multiple linear regression model to form resampled or bootstrap samples. For each resample, the main model parameters are re-estimated. ,variance and standard deviation , is represented as:

[0045] ,

[0046] ,

[0047] ,

[0048] in, For the first Each resampled Bootstrap estimate For the first The measured value of the accumulation. For sample size, The total capacity refers to all sample plots in the study area. This represents the total number of Bootstrap resampling attempts. This is the sequence number of a particular Bootstrap resampling. for The estimated value, It is a positive definite symmetric matrix.

[0049] The beneficial effects of this invention are:

[0050] This application employs a hybrid estimation method that integrates annual limited sample plot data with forest growth models and introduces a calibration mechanism based on covariance structure. This can compensate for data deficiencies caused by the scarcity of annual samples and time-series observation gaps. Even under conditions of insufficient number of effective sample plots in a single year and discontinuous time series, it can still output a stable and reliable overall mean estimate, effectively compressing the estimation variance and improving the accuracy of forest stock volume monitoring. Attached Figure Description

[0051] Figure 1 Schematic diagram of growth equations for different forest stand types Figure 1 ; Figure 2 Schematic diagram of growth equations for different forest stand types Figure 2 ; Figure 3 Schematic diagram of growth equations for different forest stand types Figure 3 ; Figure 4 Schematic diagram of growth equations for different forest stand types Figure 4 ; Figure 5 Illustration of dynamic estimation results of forest stock volume with different sample sizes Figure 1 ; Figure 6 Illustration of dynamic estimation results of forest stock volume with different sample sizes Figure 2 ; Figure 7 Comparison before and after BLUP correction Figure 1 ; Figure 8 Comparison before and after BLUP correction Figure 2 ; Figure 9 Comparison before and after BLUP correction Figure 3 ; Figure 10 Comparison before and after BLUP correction Figure 4 ; Figure 11 Comparison before and after BLUP correction Figure 5 ; Figure 12 A distribution chart of estimated annual statistics; Figure 13 A map showing the distribution of sample plots in the Genhe City experimental zone; Figure 14 A schematic diagram illustrating the dynamic estimation results of forest stock volume with different sample sizes; Figure 15 A schematic diagram showing the general situation of the Genhe City Experimental Zone; Figure 16 Illustration of BLUP correction results and accuracy Figure 1 ; Figure 17 Illustration of BLUP correction results and accuracy Figure 2 ; Figure 18 Illustration of BLUP correction results and accuracy Figure 3 ; Figure 19 Illustration of BLUP correction results and accuracy Figure 4 ; Figure 20 Illustration of BLUP correction results and accuracy Figure 5 . Detailed Implementation

[0052] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0053] Specific Implementation Method 1: The annual update method for forest stock volume based on data assimilation described in this implementation method includes:

[0054] The overall system architecture includes three processing stages: time-series data assimilation stage, multi-source data collaborative modeling stage, and spatial calibration and scale inference stage.

[0055] Phase 1: Time-series data assimilation and annual monitoring

[0056] Data preparation and preprocessing

[0057] (1) Data source: Forest resources continuous inventory data (5-year cycle, 1 / 5 of the sample plots are surveyed each year), the sample plot area is 0.06 hm2; the data content includes: tree species, diameter at breast height (DBH), forest stand type.

[0058] (2) Calculation of stock volume of sample plots: Using existing volume tables or volume models, the stock volume of each sample plot is calculated, and thus the stock volume per unit area is obtained:

[0059] Single tree volume → plot volume, plot volume → volume per unit area (m³ / ha).

[0060] (3) Forest stand classification: According to the dominant tree species of the sample plot, the sample plot is divided into forest stand types: coniferous forest, broad-leaved pure forest, coniferous and broad-leaved mixed forest, and broad-leaved mixed forest.

[0061] Growth model construction and linearization

[0062] (1) Selection of growth model

[0063] This study compares different growth equations and selects the one with the best fit. The growth equation with the best fit selected in this application is then calculated. RMSE as an evaluation indicator , Select the optimal model parameters. The growth equation that best fits the data in this application is the Logistic equation: .Note: The coefficient of determination; For sample size; For the first The observation value (the first) (volume of the trees) For the first 1 observation; RMSE is the mean squared error; The dependent variable is the average stand volume. The independent variable is the average age of the sample plot (age), which usually represents time. Asymptotic upper limit (saturation capacity); For position parameters, the control curve is in The initial value when =0; The intrinsic growth rate determines the steepness of the curve's ascent; is the base of the natural logarithm.

[0064] Get all within a unit area This leads to the accumulation per unit area output by the growth equation.

[0065] Linearization of the growth equation

[0066] Transform the nonlinear growth model (Logistic equation) to make it conform to the linear model form: This transforms nonlinear relationships into linear ones and model parameters into random effects. The goal is to reduce computational complexity, facilitate multi-time-series modeling, and improve stability.

[0067] Based on sample plot data, a Logistic growth equation for the average age and stock volume of each forest stand type was constructed, and the equation was converted into a linear form using linearization techniques to facilitate subsequent calculations.

[0068] In summary, the ME mixture estimation model is expressed as:

[0069] ,

[0070] First, the transformation values ​​corresponding to the predicted values ​​of the growth equation are:

[0071]

[0072] Logistic transformation was performed on the measured volume per unit area of ​​the sample plot:

[0073]

[0074] Establish an observation model:

[0075]

[0076] in: This is the fixed effects part. This is the random error component.

[0077] in, Let be the random measurement error at the t-th observation. For a progressive upper limit, This provides accurate data on the stock volume of the sample plots. It is the product of the population growth potential index and the average age of the stand. The accumulation amount predicted by the growth model;

[0078]

[0079] Then perform the inverse transformation:

[0080]

[0081] in, This represents the linearized value of the volume per unit area obtained from the sample plot survey for each year. The covariance matrix of observation errors in the sample plot survey. This is an annual difference matrix, used to describe the changes between adjacent years. Annual error matrix;

[0082] Table 1. Basic Model Logistic Growth Equation

[0083]

[0084] Construction of hybrid estimation models

[0085] (1) Data fusion method

[0086] The following two types of information are integrated: sample plot observation data (real data) (real volume per unit area); growth model prediction data (trend information).

[0087] Obtain real data and input it into the fitted Logistic equation to obtain predicted data.

[0088] The formula for the ME mixture estimation model is: .Note: For the first The measured value including error observed in the second observation; For the first The corresponding real but unobservable latent variables; For the first Random measurement errors during each observation are typically assumed. and Independent and following a mean of 0 and a variance of . It follows a normal distribution.

[0089] The growth equation is linearized as follows: Further rewriting as follows:

[0090] , This represents the ME mixture estimation model. ; Indicates the first To ensure consistency, the true value of the annual average accumulation was also linearized. ,

[0091] Note: It represents ; This represents the sample plot observation data (real data).

[0092] (2) Time constraint mechanism

[0093] Constructing time series constraints: smoothing changes between adjacent years; controlling abnormal fluctuations by limiting them through transformation equations. Changes over time , ,in, Independent of It is another one with a mean of 0 and a variance of . A random variable. (Range 0.01~1) represents the unknown scaling factor to be estimated, which determines the random effect. Smoothness over time.

[0094] Matrix construction and parameter solving in mixed estimation models

[0095] After completing the aforementioned linearization and time series constraint construction, in order to achieve a unified estimate of the annual average forest stock volume, this step represents the relevant variables in a matrix format and constructs the corresponding covariance structure, as follows:

[0096] Step 1: Variable Matrix Construction: Represent the sample plot observation data (volume per unit area) and model (linearized model) prediction data for each year as vector forms: , ,in, This represents the mean vector of stock volume obtained from sample plot observations; This represents the mean vector of accumulation predicted based on the growth model. Indicates the length of the time series (number of years).

[0097] Step 2, Error Structure Definition: Introduce two random error vectors: Indicates observation error; This represents the error due to time variation; both are random vectors with a mean of 0.

[0098] Step 3: Constructing the constraint matrix. It is used to describe the relationship between adjacent years, and its characteristics are as follows: the matrix dimension is ( -1)× Each row contains non-zero values ​​only in adjacent year positions; the non-zero elements are arranged in the range [-1, 1]; the elements in the remaining positions are 0. This matrix is ​​used to constrain the smooth change of forest stock volume over time.

[0099] Step 4, Covariance Matrix Construction: Establish the error covariance structure: The observation error covariance matrix is ​​represented as: ,

[0100] The time transition error covariance matrix is ​​expressed as: ,

[0101] in: Depend on The submatrix is ​​constructed from... One Submatrix multiplied Composition, that is Introducing a scaling factor Scaling; This design is used to control the smoothness of changes in time series. It enables the modeling of uncertainties in dynamic changes over time.

[0102] Step 5, Parameter Estimation Process: Here, the unknown scaling factor... This is used to balance the magnitudes of observation error and transfer error, and is solved by maximizing likelihood estimation. Assume the error term... and It originates from a multivariate normal distribution. Through analysis of... Performing a grid search from 0.01 to 1 (in increments of 0.01) minimizes the joint log-likelihood function L, thus obtaining... , and scaling factor The best estimate is expressed as:

[0103] ,

[0104] ,

[0105] Joint log-likelihood function :

[0106] ,

[0107] The updated variance is:

[0108] ,

[0109] Updated for:

[0110] ,

[0111] When the covariance matrix With the unknown scaling factor estimated, the mixed estimation can be written as:

[0112] ,

[0113] The estimated variance is: ,

[0114] For the sake of consistency, remember: as well as .

[0115] Step Six, Result Definition: For ease of consistent expression, the calculation result is defined as follows: and These represent the annual estimate and variance estimate of the updated average total forest stock, respectively.

[0116] The output results are: the annual mean forest stock volume; variance estimate; and standard error. The annual estimate of the average forest stock volume obtained in the above steps is then subjected to nonlinear processing to obtain an updated unbiased estimate of the overall mean forest stock volume. This step completes the calculation of the ME mixture estimation model.

[0117] Table 2 Annual Estimated Statistics for Simple Random Sampling and Mixed Estimation Models under a 1 / 5 Sample Sampling

[0118]

[0119] (5) Evaluation indicators

[0120] The selected evaluation indicators include the estimated population mean, the standard deviation of the estimated population mean, the standard error of the estimated population mean, and the confidence interval of the estimated population mean. Note: Because this application could not obtain fixed sample plot data with a five-year cycle and one-fifth of the sample plots surveyed each year, data from five phases of forest resource inventory were used. A sampling method without replacement was employed, selecting one-fifth of the sample plots each year to simulate the sampling design of the national Class I inventory. The study concludes that the population estimate obtained based on five phases of data, selecting one-fifth of the sample plots each year, and using data assimilation methods, has better variance accuracy than traditional sampling methods and is also suitable for the national survey method of selecting one-fifth of the sample plots each year for population estimate.

[0121] Phase Two: Collaborative Modeling of Multi-Source Data

[0122] In this phase, multi-source data for spatial modeling are acquired, including: annual average forest stock volume data obtained based on the first phase of mixed estimation; continuous forest resource inventory plot data (5-year cycle, 1 / 5 plot per year); Landsat series remote sensing image data (corresponding to the 5-year growth period); and digital elevation model (DEM) data (spatial resolution of 30m).

[0123] The above data are uniformly spatially registered and temporally matched to build a unified data foundation.

[0124] Based on remote sensing image data, auxiliary variables related to forest stock volume are extracted, including: vegetation indices (such as NDVI, EVI, DVI, GRVI, SAVI, RVI, ARVI); original band reflectance; texture features, which are calculated based on the gray-level co-occurrence matrix (GLCM) and include mean, variance, homogeneity, contrast, dissimilarity, entropy, and second moment; and topographic factors (elevation, slope, etc.). The above variables are then standardized to eliminate dimensional differences and improve model stability.

[0125] To achieve multi-source collaborative estimation of forest stock volume, a regression model system SUR (seemingly uncorrelated regression model) composed of multiple sub-models is constructed. For such a system, the dependencies between equation variables can be captured by constructing a residual model for each equation. This model uses the variance-covariance matrix of the error to describe these dependencies. Its basic form is as follows: The SUR model takes the following form:

[0126] ,

[0127] Or simply as in Indicates the number of sub-models. =1,2,..., , Represents the number of observations;

[0128] , It is the model parameter vector; It is a block diagonal matrix. It is the first Design matrix corresponding to each dependent variable; It is an error vector, and all elements correspond to the first... One dependent variable. The system's error term. It is a multivariate normal vector that satisfies .

[0129] The model system comprises: a main accumulation model (constraining overall mean consistency); a remote sensing prediction model (describing spatial distribution); and auxiliary sub-models (characterizing residual correlation structure). Each sub-model corresponds to a dependent variable; correlation is allowed between error terms in the sub-models; and the model system achieves multivariate collaborative estimation through unified modeling. By constructing a multi-model system, the system unifies the modeling of temporal scale information (first-stage results) and spatial scale information (remote sensing data), achieving spatiotemporal collaborative constraints.

[0130] Parameter estimation methods:

[0131] The variance-covariance matrix is ​​as follows: ,

[0132] in, It is a positive definite symmetric matrix, composed of the error variance specific to each sub-model and the error covariance between sub-models. Simulated Linear dependence between the errors of each sub-model. Parameter vector The estimation is performed in two steps using the feasible generalized least squares method. First, the initial model is fitted using ordinary least squares to obtain the residuals. Then, the residuals are calculated. Consistent estimator of each element The estimated Substituting into the following formula yields the parameter vector. The estimated value : ,

[0133] The variance-covariance matrix is ​​obtained through this step. and parameter vector estimates .

[0134] The covariance matrix is ​​used to characterize the statistical dependencies between different data sources and is the core input for subsequent BLUP calibration.

[0135] The following examples are from 2005 and 2010 (the first two formulas are the master model and supporting sub-models for 2005; the latter two formulas are the master model and supporting sub-models for 2010):

[0136] ,

[0137] ,

[0138] ,

[0139] ,

[0140] Phase 3: BLUP Calibration and Scale Inference

[0141] After completing the SUR model construction, the following data were obtained for calibration: prediction results of each sub-model; remote sensing observation data; covariance matrix and estimated model parameters.

[0142] Construct a data assimilation mechanism based on Optimal Linear Unbiased Prediction (BLUP):

[0143] The variables in the multi-model system are divided into: variables to be calibrated (target variables) and observed variables (auxiliary variables). The prediction results are corrected by using the covariance relationship between the variables.

[0144] Essentially, it transforms the marginal distribution of variables into a conditional distribution, thereby achieving optimal adjustment of the predicted values.

[0145] Suppose there exists a dimensional random vector And divide it into two parts ,in and They are respectively the dimensions of and The subvectors that satisfy . The variable to be calibrated; These are observed variables.

[0146] Calculate the calibration value based on the BLUP method:

[0147] Its first and second moments are known:

[0148] ,

[0149] ,

[0150] These relationships can be collectively represented as: .

[0151] if If observed, then The optimal linear predictor is:

[0152] ,

[0153] ,

[0154] when When it follows a multivariate normal distribution or marginal distribution and given hour The conditional distributions of all values ​​are also normally distributed. This favorable property makes BLUP the best predictor. , If we replace them with their estimates , and The resulting formula is called the (empirical) best linear unbiased prediction (BLUP).

[0155] Calibration steps: Extract submatrices from the covariance matrix; calculate calibration terms (consisting of the differences between observed values ​​and model expectations); correct the original predicted values.

[0156] Output: Calibrated estimate of forest stock volume

[0157] Uncertainty assessment

[0158] To evaluate the model's stability and prediction accuracy, the Bootstrap method was used to perform uncertainty analysis on the BLUP-processed SUR:

[0159] Resampling data construction

[0160] After model calibration is completed, resampled data is constructed based on the residuals of the multi-model system:

[0161] Randomly resample the residual vector ε of the regression model; assume the residuals follow a mean of 0 and a covariance of Σ. k × k The model follows a multivariate normal distribution; residual samples are randomly drawn from this distribution and superimposed onto the original model predictions; this generates a new resampled dataset (Bootstrap sample).

[0162] (2) Resampling process

[0163] Set the number of resampling times to B (preferably 3000), and perform the following operations for each Bootstrap sample: input the resampled data into the original regression model; re-estimate the model parameters; calculate the corresponding population mean estimate, which will yield a set of resampled estimates.

[0164] (3) Calculation of statistics

[0165] For each resampling, the main model parameters are re-estimated. , variance and standard deviation.

[0166] ;

[0167] ;

[0168] ;

[0169] in, It is the first Each resampled Bootstrap estimate =1, ..., ,and =3000.

[0170] (4) Result output

[0171] Through the above calculations, we obtain: the Bootstrap estimate of the overall mean of forest stock volume; the variance estimate; the standard error; and the confidence interval.

[0172] Technical Effect Description

[0173] The Bootstrap resampling method can effectively assess the uncertainty of model estimation results, improve the stability of confidence interval estimation, and support the simultaneous estimation and calibration of multiple model parameters under limited sample conditions.

[0174] Phase 4: Model-based population mean inference

[0175] 1. Inference of the overall mean of annual regional forest stock volume from ME mixed estimates

[0176] In the key technologies for annual regional forest stock volume estimation based on ME mixture estimation, this study compares the performance differences in population mean inference between the one-fifth sample obtained by simple random sampling without replacement and the estimation results of the ME mixture estimation model. The evaluation indicators selected include the population mean estimate, the standard deviation of the population mean estimate, the standard error of the population mean estimate, and the confidence interval of the population mean estimate. The specific formulas are as follows:

[0177] Population mean estimate: ,

[0178] Standard deviation of the population mean estimate: , ,

[0179] Standard error of population mean estimate (SE): ,

[0180] Confidence interval for population mean estimate: ,in, Representing the Secondary sampling.

[0181] 2. Spatiotemporal consistency estimation of forest stock volume, corrected for population mean inference

[0182] This study uses the coefficient of determination (R²), root mean square error (RMSE), and relative root mean square error (rRMSE%) to evaluate the accuracy of the population mean inference results after correction for the spatiotemporal consistency estimation of forest stock volume. The formulas for these indicators are as follows:

[0183] ,

[0184] ,

[0185] ,

[0186] in, It's the sample size. It is the first The predicted value of the accumulation. For the first The measured value of the accumulation. This represents the average of the measured values ​​of the accumulated volume.

[0187] In forest surveys, model predictions are presented as confidence intervals for population parameters. Therefore, it is necessary to demonstrate the impact of the proposed correction procedure on the estimation of population parameter confidence intervals. In this study, we primarily focus on the population mean estimate. The confidence interval for the seemingly unrelated model. The dependent variable corresponding to each sub-model, the real It can be calculated as follows: ,

[0188] The model's estimators are expressed as: ,

[0189] Its confidence interval can be obtained through the Bootstrap procedure. The Bootstrap method is based on the concept of resampling. Under pre-calibration, it applies the Bootstrap residual procedure to construct a resampled version of the multiple linear regression model, focusing on the residuals. Perform resampling, and from Random samples are drawn from the model and then added back to the multiple linear regression model to form resampled or bootstrap samples. For each resample, the main model parameters are re-estimated. , variance and standard deviation.

[0190] Steps for implementing the extended parameter self-help method:

[0191] Bootstrap method before calibration (SUR model prediction): Parameterized residual bootstrap

[0192] 1. Resample each Bootstrap =1,..., ( =3000): Generate a new residual vector from the estimated residual distribution of the SUR model. Add the new residuals to the original SUR predictions to form the Bootstrap sample. Refit the SUR model with this Bootstrap sample to obtain new parameter estimates. Calculate the mean estimate of this Bootstrap sample. .

[0193] 2. Calculate the mean of all Bootstrap estimates: .

[0194] 3. Calculation Bootstrap variance:

[0195] Bootstrap method after calibration (after BLUP data assimilation): Extended parameter Bootstrap:

[0196] The goal is to address the underestimation of BLUP variance that may occur with standard Bootstrap. This involves simulating the uncertainties in the BLUP prediction process within Bootstrap.

[0197] Initialization: using raw data Fit the SUR model to obtain parameter estimates. and .

[0198] Generate Bootstrap Samples: Generate "observational" level errors and construct auxiliary sample data. Calculate intermediate BLUP predictions Generate BLUP error Construct Bootstrap data for "non-sample" regions .combination and Form a complete Bootstrap sample .

[0199] Re-estimation in Bootstrap:

[0200] Using Bootstrap samples Re-estimate the parameters of the SUR model and obtain and And thus obtain .

[0201] Calculate the BootstrapBLUP mean:

[0202] Two BLUPs were computed using Bootstrap samples and different parameter estimates: Use the initial In Bootstrap, in fixed The result obtained ; Re-estimated using Bootstrap and BLUP results Convert to population mean estimate and .

[0203] Calculate variance

[0204] Use based on and The difference is used to calculate the final Bootstrap variance estimate:

[0205] ,

[0206] Repeat the above steps, =3000 times, and check whether the estimated value is stable.

[0207] Results Display:

[0208] Table 3 Annual Estimated Statistics Before and After BLUP Correction

[0209]

[0210] Compared with existing annual forest resource monitoring technologies, this application constructs a multi-stage processing method based on data assimilation to achieve high-precision estimation and multi-scale consistent updates of forest stock volume under low sampling intensity conditions, which has the following advantages:

[0211] (1) Improve estimation accuracy and achieve spatiotemporal consistency

[0212] Because this application uses a hybrid estimation method to integrate plot data with a growth model, and introduces a calibration mechanism based on covariance structure, it can still obtain stable overall mean estimation results even with a small sample size. Therefore, it can effectively reduce the estimation variance and achieve consistent expression of forest stock volume at the provincial, municipal, county and small plot scales.

[0213] (2) Achieve unbiased calibration of prediction results

[0214] Because this invention introduces a prediction correction method based on statistical dependence in a multi-model system, it can dynamically adjust the model output using newly added observation data, thereby avoiding the systematic bias problem caused by the accumulation of model errors in traditional methods and achieving unbiased forest stock estimation results.

[0215] (3) Enhance the ability to fuse multi-source data

[0216] Because this invention constructs a multi-model collaborative modeling framework and explicitly establishes the error correlation between different data sources, remote sensing data, sample plot data, and topographic data can be collaboratively estimated in a unified model, thus improving the effectiveness of multi-source data fusion and the overall stability of the model.

[0217] (4) Enhance the reliability of uncertainty assessment

[0218] Because this invention employs a resampling-based statistical evaluation method, it repeatedly samples the model residuals and reconstructs the parameter estimation process, thereby obtaining stable variance estimation results under limited sample conditions. This avoids the problem of low uncertainty estimation in traditional methods and improves the reliability of statistical inference results.

[0219] (5) Meet the needs of business applications

[0220] Because this invention constructs a complete processing flow from data acquisition, model building, prediction calibration to multi-scale output, it enables the automatic updating and spatial representation of forest stock volume data, thus meeting the practical application needs of dynamic monitoring and refined management of forest resources.

[0221] (1) Alternatives to time series data assimilation methods

[0222] In the time series data assimilation stage, in addition to using a hybrid estimation model, a state-space model-based data assimilation method, such as the Kalman filter or particle filter method, can be used to dynamically estimate and update the time series of forest stock volume.

[0223] Among them, when the time series data is long and has obvious state transition characteristics, Kalman filtering or particle filtering methods can be preferred.

[0224] When the time series data is short or the sampling intensity is low, the hybrid estimation method described in this invention is preferred.

[0225] (2) Alternatives to multi-source data collaborative modeling methods

[0226] In the multi-source data modeling stage, in addition to multi-model collaborative regression, other multivariate joint modeling methods can be used, such as structural equation modeling, joint mixed effects modeling, and multi-task regression modeling. All of these methods can achieve joint modeling of multiple variables and characterization of error relationships, thereby realizing the collaborative fusion of multi-source data.

[0227] (3) Alternatives to model calibration methods

[0228] In the model prediction calibration stage, in addition to using methods based on optimal linear unbiased prediction, parameter update methods based on probabilistic statistical inference can also be used, such as Bayesian hierarchical models and parameter estimation methods based on prior and posterior distribution updates. These methods can also achieve dynamic calibration and error correction of the model prediction results.

[0229] (4) Alternatives to the growth model

[0230] In constructing forest growth models, in addition to the Logistic growth model, other functional models describing forest growth processes can be used, such as the Richards growth model, the Gompertz growth model, and other nonlinear growth models. All of these models can describe the growth characteristics of different forest stand types through parameter adjustments.

[0231] (5) Alternatives to sampling methods

[0232] In the data acquisition phase of sample plots, in addition to simple random sampling, other sampling methods can be used, such as stratified sampling, systematic sampling, and phased sampling. All of these sampling methods can improve sample representativeness under different conditions and can be used for forest stock volume estimation.

[0233] (6) Alternative solutions for remote sensing data and feature construction

[0234] In the process of extracting remote sensing variables, in addition to spectral and texture features, other types of remote sensing features can also be used, such as: multi-temporal remote sensing features; radar data features (such as SAR); and lidar data features (such as LiDAR point cloud indices). All of these features can be used to enhance the input information of forest volume estimation models.

[0235] Example:

[0236] This application uses Genhe City in the Greater Khingan Mountains Key State-owned Forest Area of ​​Inner Mongolia as the experimental area. This region is located in the central part of the western slope of the Greater Khingan Mountains, at an altitude of 700-1300m. It has a cold-temperate humid forest climate with an annual precipitation of 400-500mm, mainly concentrated in July and August. The mountain ranges mostly run north-south, with a topography characterized by high elevations in the northeast and low elevations in the southwest. The region is rich in forest resources, with a forest coverage rate as high as 88.04%. It is a typical cold-temperate bright coniferous forest (taiga) ecosystem, dominated by Dahurian larch (Larix gmelinii) (accounting for 80% of the forest area), interspersed with broad-leaved species such as birch (Betula platyphylla) and aspen (Populus davidiana). Its vast forest area and abundant standing timber volume together constitute an ideal experimental area for verifying new forest resource monitoring methods. Location as follows: Figure 13 As shown:

[0237] Study area data

[0238] A total of 62 fixed sample plots were established for the Class I survey in the study area, arranged at 8km × 8km intervals according to the systematic sampling principle. Each sample plot was rectangular, with an area of ​​0.06 hm2 (10m × 60m). The data resources used in the inventory work were one-fifth of the Class I inventory data for each year from 2019 to 2023 provided by the Genhe Forestry Bureau. The relevant survey factors of the sample plots were determined according to the "Technical Regulations for Continuous Inventory of National Forest Resources" (hereinafter referred to as the "Technical Regulations"), and consisted of topography, altitude, slope aspect, slope position, slope gradient, soil type, soil thickness, humus layer thickness, origin, average age, average diameter at breast height, average height, standing volume, and stand density. The descriptive statistics of the sample plots are shown in Table 4.

[0239] Table 4. Descriptive statistics of the sample plots

[0240]

[0241] Simple random sampling

[0242] Simple random sampling (SRS) is a basic and widely used sampling method, suitable for situations where the population distribution is relatively uniform. Unbiased estimates of population parameters can be made using sample statistics. However, this method suffers from large variance in small samples or when the population exhibits high spatial heterogeneity, affecting the accuracy of the estimation. This study uses forest resource inventory data as a basis and employs simple random sampling to obtain estimates of the population parameters for the initial year's municipal forest stock volume.

[0243] , ,in, For sample size; For the first Observations of each sample unit; This is an estimate of the sample mean; This represents the sample variance.

[0244] Data assimilation based on hybrid estimation

[0245] (1) Linear mixed model

[0246] The mixture estimation model (ME) is used to dynamically update forest stock volume obtained from simple random sampling. This model can be viewed as a linear mixture model without fixed effects, and its general form is: ,

[0247] in, For the observation vector, For fixed effects parameters, and These are the random effects and the error term, respectively.

[0248] (2) Mixed estimation model

[0249] This study uses a hybrid estimation algorithm, combined with a linearized form of the Logistic growth equation, to achieve annual updates of forest stock volume. The basic form of the hybrid estimation model is as follows:

[0250] , ,

[0251] in, For the first Annual linearized observed accumulation, The volume is the linearized growth equation for different forest stand types. For observation error, For process error, The scaling factor controls the smoothness over time. The model is further expressed as: ,

[0252] in, This is the constraint matrix, reflecting the time dynamics. Model parameter estimation is based on simple random sampling results: These are sample estimates. The covariance matrix represents the predicted values ​​from the growth model. This is a diagonal matrix whose elements are the sampling variances. Scale factor The result is obtained by maximizing the log-likelihood function in the interval [0.01, 1] through grid search. Since the sampling estimate is unbiased, the mixture estimate is also unbiased.

[0253] (3) Calculation of random effects parameters

[0254] Considering that forest stock volume is a fixed effect, this study introduces model linearization to improve the stability and interpretability of the estimation. Based on sample plot data, forest stands are divided into four stand types according to dominant tree species, and a growth relationship model between stand age and stock volume is established. The Logistic equation is used: ,

[0255] After linearization, it becomes: ,in, , , These are the model parameters. Linearization helps improve the efficiency of parameter estimation and provides a structural basis for hybrid estimation.

[0256] (4) Inference of the overall mean of annual regional forest stock volume from ME mixed estimation

[0257] In the key technologies for annual regional forest stock volume estimation based on ME mixture estimation, this study compares the performance differences in population mean inference between the one-fifth sample obtained by simple random sampling without replacement and the estimation results of the ME mixture estimation model. The evaluation indicators selected include the population mean estimate, the standard deviation of the population mean estimate, the standard error of the population mean estimate, and the confidence interval of the population mean estimate. The specific formulas are as follows:

[0258] ①Estimated population mean: ,

[0259] ② Variance and standard deviation of the population mean estimate: , ,

[0260] ③ Standard error of population mean estimate (SE): ,

[0261] ④ Confidence interval for the population mean estimate ,in, It's the sample size. It is the number of sample draws to estimate the population mean by drawing one-fifth of the sample. For the first The population mean estimated by the second sampling. For the first The measured value of the accumulation.

[0262] Test Results and Analysis

[0263] This application addresses the problems of high cost, poor timeliness, and insufficient accuracy due to small sample sizes in traditional forest resource monitoring methods. Using Genhe City in the Greater Khingan Mountains region of Inner Mongolia as a pilot area, and based on data from one-fifth of the Class I forest resource inventory plots each year from 2019 to 2023, a ME-based mixture estimation model was constructed. This model was compared with traditional simple random sampling methods to systematically evaluate its accuracy and performance in annual forest stock volume updates. The results and analysis mainly focus on the fitting of the stand growth equation, the effect of annual stock volume updates, and dynamic trends.

[0264] Growth equations for different forest stand types

[0265] This application reveals the dynamic pattern of forest stock volume change with age by analyzing the growth equations of four forest stand types. Figures 1-4The growth curves of all stand types exhibit a typical Logistic growth trend, but with significant differences: pure broadleaf forests show rapid early growth, with stock volume increasing rapidly between 20 and 40 years, followed by a significant slowdown in growth rate after maturity; pure coniferous forests show a slow and sustained growth process, maintaining growth potential even in older stages; mixed coniferous and broadleaf forests show good growth in the middle stage, possibly due to the complementary effect between tree species; the growth trajectory of mixed broadleaf forests is similar to that of pure broadleaf forests, but shows better maintenance capacity at maturity. Fluctuations in model parameters across different years reflect the influence of environmental factors on the growth process. These stand-specific growth patterns provide a theoretical basis for annual forest stock volume regeneration based on mechanistic models and a scientific basis for developing differentiated forest management strategies.

[0266] Annual update results of accumulation

[0267] From 2019 to 2023, the mixed estimation model (ME) demonstrated a significant advantage over simple random sampling (SRS) in annual forest stock volume updates (Table 5). Specifically, with the same sample size, the mixed estimation model greatly reduced the estimation uncertainty, with its standard deviation (12.00–14.13 m³ / ha) decreasing by approximately 44% compared to simple random sampling (13.22–21.35 m³ / ha), and the corresponding standard error decreasing from approximately 4.00 m³ / ha to approximately 2.87 m³ / ha. In estimating the overall mean, the results from the mixed estimation model were also closer to the true value. In conclusion, by effectively utilizing auxiliary information and maintaining a similar sample size, the mixed estimation model achieved more accurate and stable estimation results, demonstrating its higher application value and reliability in forestry resource surveys.

[0268] Table 5 Estimators for Simple Random Sampling and Mixed Estimation Models

[0269]

[0270] Dynamic change trend

[0271] From a dynamic trend perspective, the estimated values ​​(93.89-104.65 m³ / ha) of the mixed estimation model consistently approximate the trajectory of the actual value (94.49-103.54 m³ / ha). Figure 14 The shaded area in the chart visually demonstrates that the 95% confidence interval bandwidth of the mixed estimation model is much narrower than that of simple random sampling, further proving that it can provide more accurate and reliable interval estimates while capturing the true dynamic changes in accumulation.

[0272] In summary, the hybrid estimation model, by integrating growth mechanisms and historical information, has successfully achieved annual updates with high accuracy and low variance even with small sampling, providing strong technical support for dynamic monitoring and management decisions of forest resources.

[0273] This application addresses the problems of small sample size and high variance in annual forest resource monitoring methods by proposing a technique for annual forest stock volume generation based on a mixture estimation (ME) model. This technique constructs a spatiotemporal dynamic update framework by coupling historical sampling data with stand growth equations.

[0274] In an empirical application in Genhe City, Inner Mongolia, this technology demonstrated certain performance characteristics: under the sampling condition of surveying 1 / 5 of the sample plots annually, the mixed estimation model significantly reduced the uncertainty of the estimation. Its standard deviation (12.00-14.13 (m³ / ha)) decreased by approximately 44% compared to simple random sampling (13.22-21.35 (m³ / ha)), and the corresponding standard error also decreased from approximately 4.00 m³ / ha to approximately 2.87 m³ / ha. Regarding the estimation of the overall mean, the results of the mixed estimation model were also closer to the true value. This technology effectively solves the problem of unstable estimation with small samples, providing a reliable technical path for achieving low-cost, high-timeliness, and verifiable annual data collection and dynamic management of municipal forest resources.

[0275] Experimental area and data

[0276] Overview of the study area

[0277] The experimental area for this study is located in Genhe City, a key state-owned forest area in the Greater Khingan Mountains of Inner Mongolia. (See...) Figure 15 As shown, this region is located in a cold-temperate humid forest climate zone, with predominantly mountainous terrain and a forest coverage rate as high as 88.04%. It is a typical cold-temperate bright coniferous forest ecosystem with Dahurian larch as the dominant tree species. Its complete forest types and rich resource base provide an ideal experimental environment for verifying remote sensing-assisted statistical inference techniques.

[0278] Study area data

[0279] Remote sensing and auxiliary data: From 2019 to 2023, Landsat 8 satellite imagery data acquired through Google Earth during the growing season (June-September) and 30m resolution DEM data were used. These data were used to extract spectral, texture features, and topographic factors such as slope and aspect, which were then used as remote sensing auxiliary variables in the modeling.

[0280] Plot data: This study is based on the Class I forest resource inventory data provided by the Genhe City Forestry Bureau from 2019 to 2023. A total of 62 fixed plots were established in the study area, with 1 / 5 of the Class I forest resource inventory fixed plots surveyed each year, totaling 62 plots. The plots were systematically laid out in an 8km × 8km pattern. Survey factors included average age and average diameter at breast height (DBH). When processing the plot data, the volume of each tree was calculated by tree species based on the one-yuan standing timber volume table for the Greater Khingan Mountains region. The total volume of each plot was then calculated, and the volume per hectare was further converted from the plot area.

[0281] This application presents a complete "point (sample plot) - area (administrative divisions at all levels)" multi-scale annual forest stock volume renewal technology system, which specifically includes the following three core stages:

[0282] Time series data assimilation and annual output stage

[0283] Based on data from one-fifth of the sample plots each year, a ME mixture estimation model coupled with a Logistic stand growth equation was used to assimilate and update forest stock volume at the city-level scale over time. This stage aims to address the issue of large initial estimation variance caused by small annual sample sizes, providing a high-quality time-series data foundation for subsequent spatial expansion.

[0284] Multi-source data collaborative modeling

[0285] Forest stock volume and its associated support variables constitute a complete variable system requiring multiple models. The dependent variables of this system may not necessarily be independent. Interactions may exist between the random residuals of individual models. For such complex model systems, the interrelationships and dependencies between multivariate residuals can be captured by constructing an error variance-covariance matrix. The off-diagonal covariance elements of the matrix provide additional information about the process, which is helpful for calibration procedures using BLUP (Best Linear Unbiased Predictions).

[0286] The final SUR model determined by the study consists of four sub-models, capable of simultaneously predicting four dependent variables. The first sub-model is a model built based on the results of the mixture estimation, used to ensure that the mean of the spatial distribution of annual updated forest stock is consistent with the annual mean assimilated by the mixture estimation. The second sub-model is a forest stock estimation model built based on remote sensing data, used to assist in the statistical inference of forest stock using remote sensing data. The remaining two models are classified as support sub-models, which are intercept models derived from the expected values ​​of the variables in the remote sensing variable pool that have the highest correlation with the residuals of the first two sub-models.

[0287] It seems that, besides simultaneously estimating forest resource parameters, another important motivation for uncorrelated regression models is to obtain the estimated variance-covariance matrix. A data assimilation procedure for the optimal linear unbiased estimator, used to calibrate the estimates of one or more sub-models using new observations from one or more sub-models.

[0288] The seemingly unrelated regression model construction: A SUR system containing four sub-models is established:

[0289] Sub-model 1 (main model): A linear model is constructed using the time-assimilated stock volume as the independent variable and the true value of the stock volume in the sample plot.

[0290] Sub-model 2 (main model): Using selected remote sensing variables such as texture features, band features and topographic factors (DEM) extracted from remote sensing images (such as the Landsat series) as independent variables, a linear model is constructed with the measured volume.

[0291] Sub-models 3 and 4 (supportive sub-models): The variables selected from the remote sensing variable pool that have the highest correlation with the residuals of the first two main models are used as dependent variables. Their design matrix is ​​the intercept term, which is used to capture systematic residual patterns.

[0292] Parameter and covariance matrix estimation: The parameter vector and error variance-covariance matrix of the SUR system are estimated in two steps using the feasible generalized least squares method. This matrix quantifies the interrelationships and uncertainties among the residuals of all sub-models and is a key input for the subsequent BLUP calibration procedure.

[0293] Space calibration and multi-scale inference stage

[0294] In a model system composed of multiple sub-models, the residuals of these sub-models may be correlated. This study uses residual correlation to calibrate the estimates or residuals of all sub-models based on the optimal linear unbiased estimator. It is assumed that there exists a... dimensional random vector And divide it into two parts ,in and They are respectively the dimensions of and The subvectors that satisfy Given its first and second moments:

[0295] ,

[0296] in addition These relationships can be collectively represented as:

[0297] ,

[0298] if If observed, then The optimal linear unbiased predictor (BLUP) is:

[0299] ,in:

[0300] ,

[0301] when When it follows a multivariate normal distribution or marginal distribution and given hour The conditional distributions of all variables are normally distributed. This favorable property makes BLUP the best predictor. , If we replace them with their estimates , and The resulting formula is called the (Empirical) Best Linear Unbiased Prediction (EBLUP). Note that the second term of the two parameters in the conditional multivariate normal distribution is... and The calibration items. These calibration items are essentially... The marginal distribution parameters are adjusted to their given values. of The conditional distribution parameters of the random variable form the basis of the correction procedure in this application. The correction procedure can be viewed as adjusting the marginal distribution parameters of the random variable to the conditional distribution parameters of the given observed joint distribution variable.

[0302] By setting , , as well as yes The elements in, and yes A subset, using Calibration is performed, where BLUP ( ) refers to the first one under discussion SUR sub-model The obtained calibrated value vector; where, It is the SUR sub-model that participated in the calibration. The (new) dependent variable observations. For sub-model The predicted value vector (i.e., the corresponding (The product of the design matrix and the parameter estimates).

[0303] In forest surveys, model predictions are presented as confidence intervals for population parameters. Therefore, it is necessary to demonstrate the impact of the proposed correction procedure on the estimation of population parameter confidence intervals. In this study, we primarily focus on the population mean estimate. The confidence interval for the seemingly unrelated model. The dependent variable corresponding to each sub-model, the real It can be calculated as follows: The model's estimator is expressed as: ;

[0304] Its confidence interval can be obtained through the Bootstrap procedure. The Bootstrap method is based on the concept of resampling. Under pre-calibration, it applies the Bootstrap residual procedure to construct a resampled version of the multiple linear regression model, focusing on the residuals. Perform resampling, and from Random samples are drawn from the model and then added back to the multiple linear regression model to form resampled or bootstrap samples. For each resample, the main model parameters are re-estimated. , variance and standard deviation.

[0305] Using the proposed SUR model and BLUP calibration procedure, it is possible to simultaneously estimate and calibrate multiple model parameters.

[0306] BLUP correction significantly improves estimation accuracy

[0307] Analysis of results from 2019 to 2023 over five consecutive years shows that the calibration model developed in this study demonstrates outstanding performance in improving the accuracy and stability of forest stock volume prediction: the BLUP correction technique significantly reduced the RMSE in each year. This calibration method not only significantly reduced prediction errors but also maintained... The high level of 0.91–0.94 demonstrates that the model has high fitting stability and reliability in each year, providing solid technical support for dynamic monitoring and high-precision annual updates of forest resources.

[0308] Table 6. Accuracy Test Results of BLUP Data Assimilation Technology

[0309]

[0310] Empirical analysis based on five consecutive years from 2019 to 2023 shows that the "Annual Renewal Technology System for Forest Stock Volume Based on Remote Sensing-Assisted Statistical Inference" constructed in this study has achieved significant results in improving the accuracy and stability of estimation: reaching 91.4% and the 90BLUP correction technology improving the RMSE percentage by more than 77% in each year (with the highest percentages in 2019 and 2021 being 0.0%). Figures 16-20Scatter plot analysis further shows that the corrected predicted values ​​closely follow the distribution of the true values, with a significant reduction in outliers. This effectively enhances the estimation consistency in the "point-to-area" scale transformation, alleviates the spatial heterogeneity problem caused by insufficient sample size, and significantly corrects the model's problems of overestimating low values ​​and underestimating high values. This technology, through a three-stage processing of "time-series data assimilation - multi-source data collaborative modeling - BLUP spatial calibration," combined with Bootstrap uncertainty assessment, achieves multi-scale, high-precision, and unbiased annual updates of forest stock volume with limited samples, providing reliable technical support for dynamic monitoring and "mapped" management of forest resources.

[0311] Based on the spatial distribution map of forest stock volume in Genhe City from 2019 to 2023, the spatial pattern of stock volume after BLUP correction remained stable in most years. However, abnormally high values ​​appeared in some areas in 2021 and 2023 (reaching maximum values ​​of 331.175 and 758.175 respectively), significantly deviating from the levels of other years. This suggests that there may be special interference factors in these years, or that the model needs further optimization when handling extreme values. Overall, this technical system has achieved multi-year continuous spatial explicit stock volume mapping, providing an important basis for dynamic monitoring of forest resources.

[0312] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A method for annual updating of forest stock volume based on data assimilation, characterized in that... Includes the following steps: Step 1: For each sample plot within the study area, obtain the stock volume of that plot. Divide the sample plots according to forest stand type based on the dominant tree species, and obtain the stock volume per unit area based on the area of ​​the sample plot. ; Step 2: Construct growth equations for different forest stand types in the study area, select the optimal growth equation, and obtain the timber volume of different forest stand types within the sample plot based on the optimal growth equation. Then, based on the timber volume of all trees within the sample plot and the area of ​​the sample plot, obtain the volume per unit area. ; Step 3: Construct a mixed estimation model for ME and incorporate the accumulation per unit area. and volume per unit area Inputting the ME mixture estimation model yields an annual estimate of the average total forest stock volume. , represented as: ， ， in, This represents the linearized value of the volume per unit area obtained from the sample plot survey for each year. The covariance matrix of observation errors in the sample plot survey. This is the annual difference matrix. For a progressive upper limit, This is the annual error matrix. for The estimated value; Step 4: Acquire remote sensing data of the study area, and combine the remote sensing data of the study area with the volume per unit area. Annual estimates of the average total forest stock As basic data; Step 5: Extract vegetation index, original band reflectance, texture features and topographic factors based on remote sensing data, and use the extracted vegetation index, original band reflectance, texture features and topographic factors as auxiliary variables; Step 6: Construct a SUR regression model and input the basic data and auxiliary variables into the SUR regression model to obtain the accumulation prediction results. ; Step 7: Use BLUP to predict the accumulation volume. The calibration was performed to obtain the calibrated estimate of forest stock volume. ; Step 8: Use the Bootstrap method to estimate the calibrated forest stock volume. Uncertainty analysis was conducted to obtain the Bootstrap estimate of the overall mean of forest stock volume, which is the annual monitoring result of forest stock volume.

2. The annual update method for forest stock volume based on data assimilation according to claim 1, characterized in that... The remote sensing data includes Landsat series remote sensing image data and digital elevation model data.

3. The annual update method for forest stock volume based on data assimilation according to claim 2, characterized in that... The optimal growth equation is obtained by linearizing the Logistic equation. The linearized growth equation is expressed as follows: ， in, These are the model parameters.

4. The annual update method for forest stock volume based on data assimilation according to claim 3, characterized in that... The forest stand types include coniferous forests, pure broad-leaved forests, mixed coniferous and broad-leaved forests, and mixed broad-leaved forests.

5. The annual update method for forest stock volume based on data assimilation according to claim 4, characterized in that... The volume of the sample plot in step 1 is obtained through a single-dimensional or two-dimensional volume table of the study area.

6. The annual update method for forest stock volume based on data assimilation according to claim 5, characterized in that... The vegetation indices include NDVI, EVI, DVI, GRVI, SAVI, RVI, and ARVI; the topographic factors include elevation, slope, and aspect.

7. The annual update method for forest stock volume based on data assimilation according to claim 6, characterized in that... The texture features are obtained based on the gray-level co-occurrence matrix, and the texture features include mean, variance, homogeneity, contrast, dissimilarity, entropy, and second moment of angle.

8. The method for annual updating of forest stock volume based on data assimilation according to claim 7, characterized in that... The SUR regression model is expressed as follows: ， in, For model parameter vectors, It is a block diagonal matrix. For the dependent variables of different sub-models, For the first The design matrix corresponding to each independent variable For the error vector, The number of sub-models, =1,2,..., , For the first There are one independent variable, and the system's error term. For a multivariate normal vector, satisfying , The variance-covariance matrix is ​​as follows, representing the mean of the accumulation: ， in, The model parameter vector is a positive definite symmetric matrix. Estimating in two steps using the feasible generalized least squares method: First, the initial model is fitted using ordinary least squares to obtain the residuals. Then calculate using residuals A consistent estimator for each element in the matrix, and thus obtain ,Will Substituting into the following formula yields an estimate of the parameter vector β. : ， in, To design the transpose of the matrix, for An identity matrix of order 1.

9. The annual update method for forest stock volume based on data assimilation according to claim 8, characterized in that... The calibration in step 7 specifically involves: use Calibration is performed, among other things. For the first SUR sub-model The obtained calibrated value vector, as well as for The elements in and For dimension and subvectors, For sub-model The predicted value vector.

10. The method for annual updating of forest stock volume based on data assimilation according to claim 9, characterized in that... The specific steps of step 8 are as follows: For the seemingly unrelated model, the first The dependent variable corresponding to each sub-model has the true population mean. Represented as: ， population mean estimate Represented as: ， The Bootstrap residual procedure is used to construct a resampling model for a multiple linear regression model, and from... Random samples are drawn from the model and then added back to the multiple linear regression model to form resampled or bootstrap samples. For each resample, the main model parameters are re-estimated. ,variance and standard deviation , represented as: ， ， ， in, For the first Each resampled Bootstrap estimate For the first The measured value of the accumulation. For sample size, The total capacity refers to all sample plots in the study area. This represents the total number of Bootstrap resampling attempts. This is the sequence number of a particular Bootstrap resampling iteration. for The estimated value, It is a positive definite symmetric matrix.

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