Natural resource asset big data analysis accounting method

Abstract

The present application relates to data analysis and processing technical field, and further relates to natural resource asset big data analysis and accounting method, the method comprises the following steps: step 1: obtaining the physical inventory of different resource types in each period, obtaining the loss amount of different resource loss types in each period;Step 2: the normalized matrix of each period is calculated according to the half-life weight resource side covariance matrix and loss side covariance matrix, and the resource side covariance matrix and loss side covariance matrix are respectively decomposed, and the orthogonal basis vector with the largest contribution to the overall variation is extracted;Step 3: according to the orthogonal basis vector and the smoothed singular spectrum, the resource contribution and liability cost are linearly combined to obtain the principal component difference after removing the stray noise.The present application can effectively suppress data jump, improve the continuity, accuracy and interpretability of the accounting result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of data analysis and processing, and particularly relates to a natural resource asset big data analysis and accounting method. BACKGROUND

[0002] In recent years, with the deepening of the ecological civilization construction and the green development concept, how to scientifically and comprehensively account for natural resource assets has become a common focus of decision-making departments and academia. Natural resource asset accounting aims to measure and reflect the physical stock of forests, farmland, grassland, wetland, groundwater and other resources and their corresponding ecological depletion in a unified value scale, providing a basis for macroeconomic decision-making, ecological compensation policy and natural capital management.

[0003] Some scholars have realized the annual monitoring of forest area, wetland area and groundwater dynamics based on the SEEA framework, combined with remote sensing and geographic information system technology, and completed the monetization by multiplying the unit price. However, these methods mostly remain in single-period static accounting, and lack of in-depth revelation of the mutual influence of each resource category and depletion type, and often treat each period of data independently, ignoring the dynamic evolution process of the resource-depletion coupling structure.

[0004] In terms of dynamic accounting, some studies have proposed the introduction of system dynamics and stock-flow models into resource accounting, such as dynamic estimation of groundwater recoverable reserves based on hydrological models, and forest carbon cycle models based on biogeochemical processes. This kind of method can simulate the continuous change of resource stock and depletion over time, but in the high-dimensional space of multiple resources and multiple depletions, it often needs to build a large number of professional models, resulting in complex model structure, numerous parameters and difficulty in calibration; in addition, the coupling boundary between models often relies on empirical setting, making it difficult to ensure the objectivity and consistency of cross-system interaction effects. Some scholars have introduced principal component analysis (PCA) into ecological environment monitoring for extracting dominant factors from multi-dimensional indicators to reduce dimensions and capture main variations. This PCA-based method can reveal the correlation and main fluctuation direction among indicators, but typical practices only decompose at a single period or a few time points, lack of constraints on the smooth evolution of covariance structure, leading to "jumping" phenomenon in time series, making it difficult to reflect the smooth transition between resources and depletions.

[0005] Further, in recent years, the development of environmental information fusion and big data technology provides technical support for the integration of multi-source heterogeneous data. The use of resource stock and depletion data obtained from multiple channels such as remote sensing, telemetry, and statistical yearbook can meet the demand for full-space, full-factor dynamic monitoring. However, existing researches directly use these data after preprocessing for single-period accounting or simple time series analysis, and do not fully utilize high-dimensional matrix decomposition technology to reveal the internal coupling rules in the time dimension. The specific manifestations are as follows: (1) In the unified matrix of multiple resources and multiple depletions, direct standardization by column or by row cannot simultaneously consider cross-category coordinated fluctuations; (2) Covariance estimation usually assumes equal weights of historical data, and fails to consider the importance of recent information and the balance of long-term memory; (3) Direct reconstruction of principal components after feature decomposition ignores the continuity of adjacent period feature spectrum and energy conservation, which easily causes truncation error and noise amplification; (4) Simple PCA or SVD method lacks the positive and negative sign distinction from the perspective of the ecological system, and is difficult to be directly used for asset-liability parallel accounting. SUMMARY

[0006] The main purpose of the present application is to provide a natural resource asset big data analysis and accounting method, which builds a unified resource-liability matrix, uses half-life weighted covariance estimation, orthogonal feature decomposition and singular spectrum smoothing recursion, extracts the main variation structure of natural resource assets and ecological depletion, and outputs the net value index in the form of principal component difference, realizing the dynamic coordinated accounting of resource gain and liability cost. Compared with the prior art, the present application can effectively suppress data jump, improve the continuity, accuracy and interpretability of the accounting results, and provide scientific and reliable technical support for natural resource balance sheet compilation, ecological compensation evaluation and green policy making.

[0007] To solve the above problems, the technical scheme of the present application is as follows:

[0008] The natural resource asset big data analysis and accounting method comprises the following steps:

[0009] Step 1: Obtain the physical stock of different resource types in each period, and obtain the depletion amount of different resource depletion types in each period; fill the left asset block of the matrix with the physical stock multiplied by the resource unit price, fill the right liability block of the matrix with the depletion amount multiplied by the repair cost, form a time point matrix, and normalize each element in the time point matrix to obtain a normalized matrix of each period;

[0010] Step 2: Calculate the resource-side covariance matrix and the loss-side covariance matrix by half-life weighting for each period of the normalized matrix, and perform eigen decomposition on the resource-side covariance matrix and the loss-side covariance matrix respectively to extract the orthogonal basis vectors that contribute most to the overall variance; place the singular spectrum of the normalized matrix of adjacent two periods into the discrete Lyapunov equation, recursively update under the premise of maintaining energy conservation, eliminate the jumping phenomenon caused by single dynamic resource liability matrix decomposition truncation, and make the coupling structure evolve smoothly over time to obtain the smoothed singular spectrum;

[0011] Step 3: According to the orthogonal basis vectors and the smoothed singular spectrum, linearly combine the resource contribution and liability cost to obtain the principal component difference after removing the stray noise.

[0012] Further, the resource types include: forest, arable land, grassland, wetland and groundwater; the physical stock includes: live standing timber volume , forest area , forest biomass carbon storage , effective arable land area , soil organic matter stock , available grassland area , above-ground available pasture amount , natural wetland area , average water storage of wetlands , static recoverable groundwater storage and annual recoverable groundwater volume ; the resource loss types include: carbon emissions, water overexploitation and soil degradation; the loss amount includes: fossil fuel CO2 emissions , industrial process CO2 emissions , agricultural methane / nitrous oxide emissions , groundwater overexploitation , surface water over-exploitation , new water and soil loss and increased sedimentation land area .

[0013] Further, the point matrix of the period is:

[0014] ;

[0015] wherein, is the physical stock vector of the period ; is the loss amount vector of the period ; is diagonal operation; is the unit price of the corresponding physical stock cost; The ecological restoration unit cost corresponding to the loss amount.

[0016] Further, each element in the time point matrix is normalized as follows:

[0017] ;

[0018] Wherein, represents the mean operation of all elements of the matrix; is the standard deviation operation of all elements of the matrix; L is a full 1 column vector of adaptive dimension; is the transpose operation.

[0019] Further, the resource side covariance matrix is:

[0020] ;

[0021] Wherein, is the backtracking period offset index, when represents period, when represents period, and so on; is the maximum backtracking depth; is the half-life decay factor, satisfying ; is the normalized physical inventory vector of period; is the resource side weighted mean calculated according to the half-life decay factor, with as the sample;

[0022] The loss side covariance matrix is:

[0023] ;

[0024] Wherein, is the normalized loss amount vector of period; is the loss side weighted mean calculated according to the half-life decay factor, with as the sample.

[0025] Further, the orthogonal basis vector is obtained by solving the following formula:

[0026] ;

[0027] ;

[0028] Wherein, is the resource side basis vector; This is the basis vector for loss measurement; and Together they form orthogonal basis vectors; The resource-side diagonal feature spectrum; The diagonal characteristic spectrum was measured for loss.

[0029] Furthermore, the smoothed singular spectrum for:

[0030] ;

[0031] in, The original singular spectrum is calculated using the following formula:

[0032] ;

[0033] The solution variable that minimizes the Frobenius residual is the optimal smooth transformation matrix. Numerically, this is a minimal rotation or minimal pseudo-shear that aligns the energy of the smoothed singular spectrum with the original singular spectrum. The calculation formula is as follows:

[0034] ;

[0035] in, for The original spectrum of strange phenomena during that period;

[0036] Furthermore, Principal component difference during the period for:

[0037] ;

[0038] in, ,for The dimension; ,for The dimension; for A normalized vector of physical inventory during a given period; for The normalized loss vector for each period; For direct sum operations, ; Represents the real number field; , to select the matrix for the symbol.

[0039] The natural resource asset big data analysis and accounting method of the present invention has the following beneficial effects:

[0040] This invention establishes a dynamic resource liability matrix, uniformly representing different types of physical stock of natural resources and ecological losses within the same matrix framework. This achieves a symmetrical characterization of resource gains and losses, ensuring consistency of the accounting system in both physical and monetary terms. By introducing a half-life-weighted covariance estimation method, this invention effectively enhances the sensitivity of recent data to the accounting results while preserving the historical memory of cumulative effects during resource evolution, avoiding temporal information distortion caused by simple equal-weighted summation. Compared to traditional static accounting, this invention utilizes eigenvalue decomposition technology to extract the dominant variation directions of resource assets and ecological liabilities, and maintains the continuous evolution of the singular spectrum over time through an optimal smoothing transformation matrix. This significantly reduces the problem of result jumps caused by data fluctuations, improving the temporal stability and consistency of the indicators.

[0041] Furthermore, this invention establishes a sign separation mechanism for assets and liabilities during the principal component reconstruction process, enabling the simultaneous reflection of resource accumulation and loss diffusion effects in a single numerical indicator. This ensures that the accounting results for natural resource assets not only possess quantitative characteristics but also intuitively reveal the changing trends of natural capital gains and losses. The final output principal component difference indicator combines directionality and intensity, and can be directly used for compiling natural resource asset and liability statements, calculating ecological compensation amounts, and evaluating green development performance, significantly enhancing the policy application value and decision-making support capabilities of the accounting results. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the device structure of a slurry discharge pipeline blockage detection and automatic slurry discharge control device based on acoustic wave feedback recognition, provided in an embodiment of the present invention. Detailed Implementation

[0043] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0044] refer to Figure 1 A method for big data analysis and accounting of natural resource assets, the method comprising:

[0045] Step 1: Obtain the physical inventory of different resource types in each period, and obtain the loss amount of different resource loss types in each period; multiply the physical inventory by the resource unit price to fill the asset block on the left side of the matrix, and multiply the loss amount by the repair cost to fill the liability block on the right side of the matrix, forming a point-in-time matrix, and normalize each element in the point-in-time matrix to obtain the normalized matrix for each period.

[0046] In the big data analysis and accounting methods for natural resource assets, step one undertakes the fundamental task of converting multi-source, heterogeneous physical information on natural resources and ecological loss information into a unified measurement framework. The principle behind this can be understood as a combination of value mapping and structured coding. First, a complete data collection system needs to be established for resources such as forests, arable land, grasslands, wetlands, and groundwater, as well as loss categories such as carbon emissions, water over-extraction, and soil degradation. This system must simultaneously satisfy temporal continuity and spatial consistency to ensure that the decomposition process can capture real dynamic evolution signals.

[0047] In practice, physical quantities of resources can be obtained annually or quarterly through official or industry standard methods such as forestry surveys, remote sensing area interpretation, groundwater monitoring well water level inversion, and land surveys. Data on losses rely on energy statistics, sewage discharge permit reports, water intake monitoring, and soil erosion remote sensing inversion, and are combined with quality control processes to eliminate missing data and outliers.

[0048] Secondly, under a unified monetary valuation standard, a price benchmark reflecting the cost of regeneration or substitution is selected for the resource side, and a price benchmark reflecting the cost of ecological restoration or environmental governance is selected for the loss side. By multiplying each point-in-time physical record by its corresponding unit price, resource entries are filled into the asset block on the left side of the matrix, and loss entries are filled into the liability block on the right side of the matrix. This asset-liability parallel structure not only preserves the symmetrical relationship between resource gain and environmental load, but also provides a numerical set with consistent shape and clear dimensions for subsequent covariance estimation and singular spectrum extraction.

[0049] Subsequently, to eliminate the impact of price scale differences and resource category heterogeneity on the stability of the matrix structure, the constructed point-in-time matrix needs to be standardized. In implementation, all elements in the matrix are treated as the same random population. First, the overall mean is calculated, then the overall standard deviation is calculated, and finally, a linear transformation is performed on each element, removing the mean and dividing by the standard deviation. This not only suppresses dimensional expansion caused by sudden surges in individual resource prices or sudden spikes in losses, but also ensures that the asset and liability sides have the same zero center and unit variance in a statistical sense, thereby reducing the distortion of principal component directions by extreme values ​​in subsequent eigenvalue decomposition. Compared to column-based standardization, overall standardization strengthens the weight of cross-category cooperative relationships in the covariance matrix, laying the foundation for accurate capture of dynamic coupling structures. After standardization, the matrix for each period is stored in chronological order, which can be directly input into the half-life weighting process in step two, and is also convenient for quick retrieval in annual assessments, scenario analyses, or policy simulations.

[0050] Step 2: For the normalized matrix of each period, recalculate the resource-side covariance matrix and the loss-side covariance matrix according to the half-decay option. Perform eigenvalue decomposition on the resource-side covariance matrix and the loss-side covariance matrix respectively, and extract the orthogonal basis vectors that contribute the most to the overall variation. Put the singular spectrum of the normalized matrix of two adjacent periods into the discrete Lyapunov equation, and recursively update it while maintaining energy conservation. This eliminates the jump-step phenomenon caused by the truncation of the single dynamic resource-liability matrix decomposition, allowing the coupled structure to evolve smoothly over time, and obtains the smoothed singular spectrum.

[0051] First, to avoid treating outdated information from earlier observations the same as high-frequency fluctuations from recent observations, the algorithm introduces a half-decay weighting when calculating the covariance between the resource and loss sides. The most recent sample is placed at the peak of the weighting, which decays exponentially with each backtracking period. This enhances sensitivity to the latest disturbances while ensuring robustness over long periods. In implementation, the system maintains a sliding window in memory, using a recursive formula to periodically update the weighted mean and covariance. This allows for online output of the latest covariance estimate without repeatedly traversing all historical data, which is particularly important for scenarios with multiple indicator dimensions and a continuous flow of data.

[0052] Next, the algorithm performs eigenvalue decomposition on the weighted covariance matrices of the resource side and the loss side respectively, obtaining orthogonal vector groups sorted by variance contribution. To balance information integrity and dimensionality reduction efficiency, a cumulative contribution rate threshold is set. When the cumulative explanatory power reaches this threshold, truncation stops, thus forming two sets of low-dimensional orthogonal bases, which represent the dominant directions of asset enhancement signals and liability aggravation signals in the multivariable space, respectively. Since the asset side and the liability side are physically complementary, a joint framework needs to be constructed to ensure that they remain orthogonal and comparable in the overall space. The algorithm ensures numerical orthogonality by applying QR renormalization to the joint matrix after dimensional concatenation, while preserving the original variance sorting order. After completing the orthogonal expansion, directly using the feature spectrum of the current period often introduces sharp jumps caused by extreme events or sampling errors, resulting in non-smooth trajectories in subsequent principal component reconstruction.

[0053] To address this issue, the framework employs a discrete Lyapunov recursive approach: treating the singular spectra of two adjacent periods simultaneously as both state and target variables, and obtaining a set of minimum rotation mappings under energy conservation constraints. This ensures that the new spectrum closely matches the current period's samples while maintaining continuity with the previous period. The solution process can utilize gradient descent or approximate closed-form solutions; a typical implementation involves finding the orthogonal matrix with the minimum residual in the Frobenius norm sense. As time progresses, the system continuously outputs a smoothed spectral sequence and its corresponding rotation matrix. This continuous trajectory is equivalent to extracting a low-dimensional manifold from a high-dimensional resource-liability space, characterizing the intrinsic trend of net natural capital change. To ensure computational feasibility for long-term operation at large provincial or national scales, incremental feature updates and block-based random subspace iteration techniques are incorporated into the code. By iterating only on local subspaces to approximate the full set of features, the overall complexity of matrix multiplication and eigenvalue decomposition is significantly reduced. Simultaneously, Householder reflection is used at the end of each iteration to recalibrate orthogonality, preventing basis vector shifts caused by floating-point error accumulation. In terms of parameter settings, the half-life length, sliding window width, cumulative contribution rate threshold, and upper limit of rotation step size are all subjected to sensitivity tests through grid search combined with the Akaike information criterion to ensure that stable and physically interpretable smooth feature spectra can be output under data distributions in different regions and industries.

[0054] Step 3: Based on the orthogonal basis vectors and the smoothed singular spectrum, recombine the resource contribution and debt cost linearly to obtain the principal component difference after removing spurious noise.

[0055] First, the system utilizes a common coordinate system established by orthogonal basis vectors in the resource and liability dimensions to perform coordinate transformations on the normalized physical inventory vector and loss vector at the current time point. This compresses their coordinate representations into the principal subspace filtered by the cumulative contribution rate. This not only significantly reduces dimensionality and eliminates multicollinearity but also ensures that different categories of indicators can be directly added after projection without considering dimensional differences. Next, to ensure a strict numerical distinction between positive contributions and negative costs, the system embeds a sign selection matrix during basis vector concatenation. The resource-side projection is assigned a positive sign, and the liability-side projection a negative sign. The scale of each principal direction is adjusted according to the variance weights corresponding to the singular spectrum, ensuring that the influence of each component on the total difference after transformation remains consistent with its true variation contribution. The weights here are not simply variance proportions but rather energy distribution ratios determined by minimizing the residuals during singular spectrum smoothing, thus naturally including structural evolution information under time continuity constraints. After symbol weighting is completed, the system performs matrix inner product along each axis of the principal subspace to compress all components into a scalar sequence. At the end of the compression, a uniform mean backfill is performed to offset the baseline shift caused by the previous standardization steps.

[0056] This sequence is the principal component difference trajectory after removing stray noise and extreme values. Its positive or negative value directly characterizes the direction of net increase or decrease in natural capital in the current period, while its absolute value quantifies the tension between resource-side gains and liability-side costs. At the implementation level, to ensure real-time performance and scalability, the code adopts a hybrid architecture of vectorized batch processing and incremental updates: when new data arrives, only the latest basis vectors and singular spectra need to be projected and weighted onto a single time slice, without repeating historical samples; if a sudden change in resource structure or loss structure is detected, the basis vector and spectral weight reassessment module is triggered to ensure that the transformation matrix reflects the latest coupling pattern in a timely manner. To prevent misjudgments of the sign matrix due to data drift during long-term operation, the system has a built-in dynamic threshold discrimination mechanism that corrects the sign boundary in real time by monitoring the statistical distribution of resource and liability projections, ensuring that the net value direction judgment always remains consistent with economic-ecological reality. Furthermore, the principal component difference trajectory can be mapped back to a monetary scale or an ecosystem service value scale according to management needs, and can be further superimposed with scenario shock simulations to assess the lagged impact of policy adjustments, market fluctuations, or climate events on net natural capital.

[0057] Furthermore, the resource types include: forests, arable land, grasslands, wetlands, and groundwater; the physical stock includes: standing timber volume. Forest area Forest biomass carbon storage Effective arable land area Soil organic matter stock Usable grassland area The amount of harvestable pasture on the ground Natural wetland area Average water volume of wetlands Static recoverable groundwater reserves Annual exploitable groundwater volume The types of resource loss include: carbon emissions, water over-extraction, and soil degradation; the amount of loss includes: fossil fuel CO2 emissions. CO2 emissions from industrial processes Agricultural methane / nitrous oxide emissions Over-extraction of groundwater Surface water withdrawal exceeding quota New soil erosion and increase the area of ​​desertified land .

[0058] Within the dynamic resource-liability matrix decomposition framework, to ensure that asset and liability blocks accurately reflect the true physical basis of natural capital increases and decreases, it is necessary to establish quantifiable and traceable observation links for five main resource categories—forests, arable land, grasslands, wetlands, and groundwater—and their corresponding losses. The forest component first calculates the standing timber volume. This parameter is based on national or provincial continuous survey data of diameter at breast height (DBH) and height, and incorporates tree species-site factor correction coefficients. After conversion using the biomass equation, it is summarized by forest stand. Forest area... Forest land masks were extracted using Sentinel-2 and Landsat-8 multispectral imagery through random forest classification, and then geometrically corrected using stereo image pairs from the National Geodetic Surveying and Mapping System-1 to ensure that the area error was controlled within one percent; forest biomass carbon storage in accordance with Calculated by multiplying by the forest type-specific timber density and then by a carbon content factor of 0.47, derived from the IPCC Terrestrial Carbon Pool Guidelines. For arable land and grassland, the amount of harvestable forage is... Primary productivity was estimated by inverted U-shaped fitting of the MODISNDVI-EVI time series curve, and then multiplied by the measured hay-to-green weight conversion rate of the transect cut; if artificial grazing exists in the region, a correction factor was extracted from the silage and hay yield entries in the crop statistical yearbook.

[0059] wetland area The water-land boundary was determined by combining GF-62m multispectral radar with spaceborne synthetic aperture radar and watershed segmentation. The average water volume of the wetland was obtained. The water depth for each pixel is then summed by area integration using the ICESat-2 optical-laser trace inversion results. If the laser penetration is insufficient, underwater DEM extrapolation is used as a supplement. Static recoverable reserves of groundwater are also considered. Annual recoverable volume All of these are derived from regional groundwater resource assessment reports, among which Calculated by integral from the core sample water content curve. This was obtained based on a long-term reinjection-extraction balance model and driven by a 30-year precipitation series. Moving to the liability side, fossil fuels... Emissions The final consumption figures for coal, oil, and gas are directly taken from the energy balance sheet and multiplied by the carbon emission factors of each fuel; industrial processes Emissions Calculated by multiplying the output of industries such as cement, lime, and electrolytic aluminum by the chemical decomposition coefficient; Agriculture Emissions Calculated based on livestock head count, fertilizer application rate, and IPCCTier2 emission coefficient. Groundwater over-extraction. The excess surface water intake is obtained by subtracting the replenishment volume of the same diameter from the monthly monitored flow rate of each well. The newly added soil erosion volume is obtained by comparing the readings of automatic flow monitoring piles on the water resources allocation platform with the approved water withdrawal limit. The interannual slope roughness difference index constructed using Sentinel-1 / 2 and the USLE model , , Factor coupling inversion, increasing the area of ​​desertified land The sandy land spectral index from the Landsat time series and the random forest change detection algorithm are used for identification. After all parameters are acquired, they are mapped to the asset and liability blocks of the matrix using a unified monetary scale or an ecological restoration cost scale, respectively. After overall standardization, they enter the subsequent half-life weighting and singular spectrum smoothing process to achieve dynamic accounting of natural capital across scales, sectors, and media.

[0060] Furthermore, Time point matrix of the period for:

[0061] ;

[0062] in, for The physical stock vector of a given period; for The loss vector over time; This is a diagonal operation; This refers to the unit cost price corresponding to the physical inventory. The unit cost of ecological restoration corresponding to the amount of loss.

[0063] This matrix expression maps resource asset values ​​and ecological liability costs to a strictly consistent monetary dimension by constructing two symmetric diagonal submatrices within the same square matrix. This ensures that subsequent singular spectral decomposition can compare their strengths within the same metric space. The upper left submatrix is... Composition, in which Bundle Physical inventory during the period Place them sequentially along the diagonal to achieve orthogonal separation between resource categories; then right-multiply by the column vector. This is equivalent to applying a regeneration or substitution cost coefficient to each diagonal element, directly converting each resource quantity into monetary value. Because the diagonal structure ensures no overlap between different resources, the monetary valuations of each asset-side item will not interfere with each other due to linear mixing, providing a clear numerical source for determining the principal direction of the covariance matrix. The lower right submatrix uses... Complete the same mapping, only here. This represents a loss vector, with each component quantified by the unit price of ecological restoration. This translates into the governance costs that need to be invested; the symbols and resources remain positively consistent, but in the subsequent principal component difference calculation stage, the symbol matrix will be used to calculate the difference. Achieve separation of positive and negative assets.

[0064] Filling the remaining positions of the matrix with zeros signifies that assets and liabilities are accounted for independently in an accounting sense, while being encapsulated within the same matrix. This ensures that their combined contribution to the total energy during singular value decomposition can be uniformly captured. This construction... Essentially, it's a weighted resource-liability value lattice: diagonal elements carry the monetary dimension of resources or losses, while off-diagonal elements are zero, ensuring the variance distribution is entirely determined by each diagonal element. This mathematically reduces covariance estimation to variance aggregation of a weighted scalar sequence. Inputting this structure into subsequent standardization processes, with the overall mean and standard deviation uniformly processed for all elements, further suppresses scale imbalances caused by orders of magnitude differences in unit prices across different resource categories. Finally, after half-life weighting, eigenvalue decomposition, and singular spectrum smoothing, and The projection in the low-dimensional principal subspace can accurately correspond to the dominant fluctuation direction of resource gains and debt costs, which is the principal component difference. The linear combination of these vectors provides the basis vectors with the largest variation, accelerating the convergence of principal components and improving explanatory power. Therefore, this matrix not only numerically achieves monetary homogenization of assets and liabilities, but also lays a sparse and orthogonal initial condition for subsequent dynamic decomposition in terms of its algebraic structure.

[0065] Furthermore, the normalization process is performed on each element in the time-point matrix as follows:

[0066] ;

[0067] in, This represents the operation of averaging all elements of a matrix. This is the standard deviation operation for all elements of the matrix; L is a column vector of all 1s in the fit dimension; This is for the transpose operation.

[0068] Normalization transforms the absolute monetary quantities in the resource-liability value lattice into dimensionless standard fractions, bringing asset and liability blocks to the same statistical scale and eliminating dimensional interference for half-life covariance estimation and subsequent singular spectrum extraction. Specifically, the time-point matrix is ​​first normalized. Perform the calculation of the mean of all elements, denoted as Then, using column vectors Rather than transpose outer product generation and Mean matrices of the same order will The difference between this matrix and the matrix is ​​used to eliminate the overall translation error. This step ensures that each element of the resulting matrix is ​​symmetrically distributed around zero. Then, calculations are performed... Standard deviation of all elements Dividing the aforementioned zero-mean matrix by this scalar normalizes the variance, resulting in the standardized matrix. Since both the mean and standard deviation are calculated at the full matrix level, the resource side and the liability side share a unified center and divergence. Therefore, their contributions to the covariance matrix are entirely driven by relative volatility, without being affected by differences in unit price magnitudes. This overall normalization strategy differs from column-by-column or row-by-row normalization; its advantage lies in preserving the absolute magnitude of cross-category coordinated volatility, making the half-life-weighted calculation... and It accurately reflects the coupling strength between asset gains and ecological costs. In online implementation, it only needs to be updated immediately after the new matrix is ​​written. and Standardization is then achieved by performing a division on the difference results. The computational complexity is linearly related to the number of elements, facilitating long-term operation at the provincial or national level. When this standardized product is input into the eigenvalue decomposition stage, its zero-center and unit variance properties ensure that the extraction of the principal direction is not distorted by extreme values, and also ensure that the energy conservation constraints in singular spectrum smoothing are measured on a uniform scale. Ultimately, Together with the orthogonal basis and smoothed singular spectrum of the subsequent output, it defines the low-dimensional manifold of resource assets and ecological liabilities in the time dimension, which is the principal component difference. It provides a stable and comparable numerical basis.

[0069] Furthermore, the resource-side covariance matrix for:

[0070] ;

[0071] in, For the backtracking offset index, when Time indicates During that period, when Time indicates The same applies to different periods; Maximum backtracking depth; The half-life decay factor satisfies ; for A normalized vector of physical inventory during a given period; For The resource-side weighted average is calculated based on the half-life decay factor, using the sample as an example.

[0072] Loss-side covariance matrix for:

[0073] ;

[0074] in, for The normalized loss vector for each period; For The weighted average of the loss side is calculated based on the half-life decay factor, using the sample as an example.

[0075] In dynamic resource liability matrix decomposition methods, a statistical characterization that can both preserve historical information and highlight the latest signals is needed to capture the true intensity of the coordinated fluctuations between various resources such as forests, arable land, and wetlands, and various losses such as carbon emissions and water over-extraction. To this end, the mathematical concept of half-life weighted covariance is introduced. Its core is to treat time as the continuous input axis of an exponentially decaying filter: the latest normalized resource vector... Assign weights The previous issue gave In the previous issue, it was given And so on, until the backtracking depth. Similarly, for the loss vector The same weight sequence is also applied. (Exponential kernel) The physical meaning lies in simulating the rate at which resource and environmental systems "forget" historical shocks—when near The system retains long memory, and early samples still contribute significantly to the covariance; when much smaller The system quickly discards outdated information and focuses only on the most recent coupling structure. Using this weight as coefficient, a linear combination of historical samples is performed to first obtain a weighted mean vector. This vector ensures that the covariance center recursively approaches the latest observation over time; then, for each period... Subtracting the mean, performing an outer product, multiplying by the corresponding weights, and summing them up, yields the resource-side weighted covariance matrix. The outer product makes the matrix... The Meta is strictly equal to resource category and Between in the past The expected covariance, adjusted for index weights during the period, provides a full structural description of the multivariate dependencies within the resource. Similarly, the covariance on the loss side... use and By replacing the inputs, the coupling strength between loss variables such as carbon emissions, water consumption, and soil erosion can be modeled on the same scale. Since all input vectors have been standardized as a whole, the magnitude of the covariance spectrum simply represents the relative fluctuation energy and is no longer affected by differences in unit or price magnitudes. This ensures that the feature vectors extracted by subsequent singular value decomposition are numerically fair in taking into account both resource and loss aspects.

[0076] Further analysis of the statistical properties of this formula reveals that the matrix and It must be symmetric and positive definite, because for any non-zero vector All This positive definiteness ensures that subsequent eigenvalue decomposition can stably obtain a set of orthogonal bases, and makes the square root spectrum usable for singular value energy measurement. In terms of algorithm implementation, the half-life framework naturally supports recursion: as long as the weighted mean and covariance of the previous period are stored, when the new period's data... Arrival, can be achieved through By directly updating the mean and then incrementally correcting the covariance using the Sherman-Morrison formula, the computational complexity is kept within a certain range. Instead ;here This incremental strategy is particularly important for multi-year rolling monitoring at a national scale, as it ensures that the server completes backend covariance refresh while simultaneously streaming data in real time. Regarding parameter selection, and Together they determine the "effective memory length". During the model training phase, a set of optimal values ​​is determined by minimizing intertemporal prediction errors or the AIC criterion, ensuring that the covariance neither excessively smooths out new trends nor overly amplifies noise. Ultimately, these two sets of half-life covariance matrices, as a dynamic second-order characterization of the resource-liability system, generate eigenvectors and eigenvalues ​​after singular spectral decomposition, reflecting the latest coupling principal direction and energy distribution of asset gains and liability pressures. This provides compliant input for subsequent smoothing spectrum recursion and ensures that the net asset value indicator has sufficient real-time responsiveness to policy interventions and natural disturbances during the principal component difference reconstruction phase.

[0077] Furthermore, the orthogonal basis vectors are obtained by solving the following formula:

[0078] ;

[0079] ;

[0080] Among them, For resource-side basis vectors; This is the basis vector for loss measurement; and Together they form orthogonal basis vectors; The resource-side diagonal feature spectrum; The diagonal characteristic spectrum was measured for loss.

[0081] In the dynamic resource-liability matrix decomposition framework, in order to transform the multivariate fluctuation structure implied by the half-life weighted covariance matrix into a set of linearly independent coordinate axes arranged in descending order of variance contribution, it is necessary to modify the resource-side matrix. and loss side matrix Perform eigenvalue decomposition separately. This decomposition is equivalent to solving the eigenvalue problem with respect to a symmetric positive definite matrix: on the resource side, find the column vector group. Make each column satisfy ;all Collect into a diagonal matrix .because A vector is symmetric and positive definite; it must possess a set of mutually orthogonal eigenvectors with a norm of one over the real number field, and all eigenvalues ​​must be positive. Orthogonality guarantees that the set of vectors... A complete basis is formed, and any normalized resource vector can be uniquely represented as a linear combination of this basis; the magnitude of the eigenvalue measures the variance strength in the direction of the corresponding eigenvector, thus providing an objective basis for ranking.

[0082] Completely isomorphic to the loss end: The intrinsic decomposition produces a set of eigenvectors. and diagonal characteristic spectrum In computer implementations, specialized algorithms for symmetric matrices, such as block QR or Jacobi rotation, are commonly used to ensure numerical stability and reduce time complexity. Within, of which These are the resource dimension and the loss dimension, respectively. After completing the decomposition on both sides, we can... and The base is formed by piecing together the diagonal pieces. The matrix in the entire Maintaining column orthogonality in 3D space, due to the quadratic form This holds true consistently, thus avoiding the introduction of quantity distortion. The geometric meaning of this joint basis is to project resource assets and ecological liabilities onto mutually independent principal directions, allowing their synergies and conflicts to be most clearly expressed in a low-dimensional space. If further dimensionality reduction is needed, the first few columns can be truncated according to the eigenvalue proportion threshold, which significantly reduces the computational load of subsequent singular spectrum smoothing and principal component reconstruction without losing the main variation information. When the time index increases to... At this time, due to the slight change in half-life covariance, the angle between the new eigenvector set and the old vector set is usually small. Therefore, subspace iteration or a warm start from the previous result can be used to accelerate feature updates. Ultimately, and The square root will occupy a diagonal position in the singular spectrum matrix, used to quantify the variance energy of asset gains and debt costs, while and This provides orthogonal directions for the principal component difference projection. The above eigenvalue decomposition steps enable multi-source heterogeneous indices to be reduced to an orthogonal framework with clear physical meaning, minimized noise, and continuous time tracking through a rigorous linear algebra process. This lays the algebraic foundation and statistical reliability for subsequent energy conservation smoothing recursion and net difference index reconstruction.

[0083] Furthermore, the smoothed singular spectrum for:

[0084] ;

[0085] in, The original singular spectrum is calculated using the following formula:

[0086] ;

[0087] The solution variable that minimizes the Frobenius residual is the optimal smooth transformation matrix. Numerically, this is a minimal rotation or minimal pseudo-shear that aligns the energy of the smoothed singular spectrum with the original singular spectrum. The calculation formula is as follows:

[0088] ;

[0089] in, for The original strange spectrum of the period.

[0090] When the dynamic resource-liability matrix decomposition framework enters the spectral smoothing stage, it is necessary to connect the energy distribution sequences obtained from the previous period and the current period after eigenvalue decomposition into a continuous trajectory, thereby avoiding spectral jumps caused by limited cross-sectional samples or extreme shocks. To this end, the diagonal spectral features of the resource side and the loss side are square-rooted and then concatenated into a block diagonal matrix. Each diagonal element of this matrix is ​​the square root of the variance in the corresponding principal direction after normalization, which can be directly interpreted as the discrete distribution of the "overall fluctuation energy of resources-liabilities" in the current period. If we simply consider... and Using it in stages will result in energy gaps during principal component difference reconstruction; therefore, a smoothing transformation matrix is ​​introduced. Its solution is strictly limited to a constrained minimization problem: finding the minimum value among all candidate matrices that satisfy the column orthogonality constraint. In the middle, find a set that makes The solution whose Frobenius norm is globally minimized is... The objective function actually measures the performance of the previous period's spectral analysis. The energy residual when aligned with the principal axis of the current period spectrum after transformation; the smaller the sum of squares of the residuals, the smoother the energy distribution between the two periods and the fewer jumps.

[0091] because and Given that both matrices are positive definite block diagonal matrices, it can be proven that the optimal solution to this optimization problem is... It definitely exists and can be represented by the superposition of orthogonal rotations and upper and lower triangular pseudo-shearings; numerical solutions often employ symmetric bilateral Jacobi iteration or Bartels–Stewart structured Lyapunov iteration, with convergence always occurring within ten iterations. The results are... Then, through construction The smoothed singular spectrum was obtained, in which This indicates that the conjugate transpose is used to preserve spectral energy conservation. It can be proven that... The condition holds true consistently, meaning the total energy sum is completely consistent with the original singular spectrum, but individual eigenvalues ​​are fine-tuned to minimize the distance to the previous spectrum in the Frobenius norm sense. Geometrically, this is equivalent to applying a minimum rotation or minimum pseudo-shear to the current energy ellipsoid in the Euclidean space spanned by eigenvectors, gently shifting its principal half-axis direction to be as collinear as possible with the previous principal half-axis; therefore, the spectral sequence forms a smooth curve on the time axis without steep inflection points. In implementation, due to... Dimensions are only The algorithm's complexity mainly stems from several matrix multiplications and QR decompositions, resulting in an overall complexity of [missing information]. However, by using the results from the previous period as initial values, the calculation can be reduced to [a smaller value] within the incremental framework. After smoothing is complete, The diagonal elements are reconstructed as principal component differences to construct energy weights, ensuring the continuous variation of the projection intensity of resource contribution and loss cost in the low-dimensional space; while The orthogonality of the basis vectors ensures that they remain homogeneous after rotation, without introducing inter-basis correlation. Through this smoothing singular spectrum mechanism, the dynamic resource liability matrix decomposition not only achieves intertemporal energy conservation algebraically, but also constructs a strong constraint on the smooth evolution of the principal direction in a statistical sense, providing a stable, coherent, and high-resolution time series basis for the final output net difference index.

[0092] Furthermore, Principal component difference during the period for:

[0093] ;

[0094] in, ,for The dimension; ,for The dimension; for A normalized vector of physical inventory during a given period; for The normalized loss vector for each period; For direct sum operations, ; Represents the real number field; , to select the matrix for the symbol.

[0095] In the final stage of the dynamic resource-liability matrix decomposition method, it is necessary to decompose the remaining components. The high-dimensional projection in the joint space is compressed into a single metric to allow direct observation of the direction and magnitude of net changes in natural capital at the macroscopic level. Principal component differences are constructed for this purpose. Composed of a series of linear mappings and symbolic constraints, it inherits the main statistical structure extracted from the previous eigenvalue decomposition and singular spectral smoothing, while ensuring that the results are interpretable in an economic sense. First, the current normalized resource vector... With normalized loss vector Collate the rows to form the length. column vectors This column vector is still in the original index coordinate system. Although its components have been standardized as a whole, they still exhibit correlation; therefore, it needs to be right-multiplied by a block diagonal matrix. First, project the resource end and the loss end onto their respective orthogonal principal directions. Because... and All vectors originate from the eigenvalue decomposition of a symmetric positive definite covariance matrix. Their column vectors are pairwise orthogonal and have a norm of one. The product operation actually performs a rotational and scale-preserving orthogonal transformation, ensuring that the projection result does not introduce numerical amplification or reduction, and minimizing the correlation between resources and losses, allowing each component to independently express the main variance information. After this step, the intermediate vector is in the "principal direction" coordinate system, but it does not yet reflect the true importance of each principal direction—in high-dimensional statistics, directions with larger variances often explain greater overall fluctuations. Therefore, a diagonal weight matrix is ​​introduced. Each diagonal element is the square root of the corresponding eigenvalue. The square root is chosen instead of the original eigenvalues ​​because the eigenvalues ​​of the covariance measure variance; after square rooting, they become the standard deviation, which aligns with the scale of the normalized vector, thus aligning the weight transformation in terms of dimensions. After left multiplication of the diagonal weights, the coordinates of each principal direction are magnified or reduced to a level directly proportional to their explanatory power, ensuring that subsequent summation does not allow low-energy directions to mask the contributions of high-energy directions.

[0096] However, weighting based solely on single-period feature spectra can still lead to sharp jumps between adjacent periods, because the main direction ranking is affected by outliers when the sample size is limited. To mitigate this phenomenon, the optimal smoothing transformation matrix was constructed in the previous stage. It minimizes The Frobenius residual seeks a set of minimum rotations or pseudo-shears that align the current spectrum as closely as possible with the previous spectrum in terms of energy distribution. Multiplying the weight matrix by the left or right is equivalent to fine-tuning the order and weights of the principal directions without changing the overall energy sum, thus ensuring the continuity of the spectral curves between the two periods. Therefore, in the definition of principal component differences, the weight matrix is ​​first multiplied by... Rotate, then participate in subsequent calculations. In this way, when making intertemporal comparisons, if the natural resource system does not undergo substantial structural changes, The trajectory will then appear as a smooth curve, not a jagged one. After this triple mapping, the vectors still have no distinction between positive and negative signs; the components on the resource side and the loss side are only numerical in magnitude, but in the same direction. To strictly distinguish between asset contribution and liability cost numerically, a sign selection matrix is ​​introduced. Multiplying the matrix by the middle vector on the left will keep the resource-side coordinates positive and the loss-side coordinates negative, thus providing an intuitive economic expression of "positive resource gain and negative ecological loss." Simultaneously... Only the sign is changed, the amplitude remains the same, so the statistical energy is not affected. Next, the row vector is multiplied on the left. This involves linearly summing all signed components at once. The reason for using an all-1 row vector instead of a weighted row vector is that each component has already been summed by the square root of its eigenvalues. The relative importance of each component has already been demonstrated in the first two steps through comprehensive weighting; adding further weighting would only create redundancy. Thus, the scalar is obtained. It can be written as

[0097] ;

[0098] in and Representing the resource side and loss side after orthogonal projection and smooth rotation, respectively. The coordinates of the principal direction. This formula demonstrates... The clear economic meaning is as follows: the first term is the sum of resource gains amplified by the standard deviation of each principal direction, and the second term is the sum of ecological losses amplified by the standard deviation of each principal direction. The difference between the two is the net value of natural capital in the current period. If This indicates that the rate of resource accumulation exceeds the rate of environmental degradation in the statistical master subspace, resulting in a net increase in natural capital; if This means that the investment in ecological restoration cannot keep up with the consumption, resulting in a net loss of natural assets; if Approaching zero indicates that resources and liabilities are almost balanced. Since all steps are linear mappings, The gradient with respect to the input vector can be directly calculated and used for sensitivity analysis. ,in It is a set of unit basis vectors on the resource side, which can be used in policy simulation to assess the marginal impact of fluctuations in individual resource indicators on the overall net value.

[0099] From the perspective of intertemporal continuity, It also satisfies the energy conservation condition. Because Obtained by Frobenius minimum residual, guaranteeing that... and The weighted spectral differences between them are minimal, and since the resource and loss dimensions are fixed, if the external shock is mild, It will show slight fluctuations; only when certain resources suffer severe damage or there is a sudden surge in emissions at the point of consumption, Only then will the curve show a significant drop, which is precisely the anomaly that regulators need to pay the most attention to. At the algorithm implementation level, to avoid issues related to matrix dimensions... The increased size creates a computational bottleneck, which can be addressed by merging and simplifying the process: because Only It can be pre-loaded in memory Transpose and weight by column to generate a single-row matrix. When updating the period, simply use... We can obtain the result by performing a dot product with the new input vector. The time complexity is reduced to This design makes the method suitable for rolling accounting of large regions and long sequences. Finally, Multiplying by the base-period weighted coefficients of resource unit price and restoration unit price, it can be directly converted into a monetary net value series, providing quantitative support for ecological compensation, natural resource liability statement compilation, or carbon neutrality assessment. As can be seen from the above derivation, the principal component difference formula, through four levels of transformation—orthogonal projection, energy weighting, sign constraint, and linear aggregation—condenses rich, chaotic, and multi-scale resource-liability data into a statistically optimal single indicator with clear economic meaning. This conforms to the principles of linear algebra and meets the decision-making needs of macro-governance scenarios.

[0100] Principal component difference In the entire dynamic resource-liability matrix decomposition method, it plays the final aggregation role "from multiple dimensions to units." It converges normalized information scattered across eighteen dimensions, including forest stock, wetland water storage, groundwater over-extraction, and carbon emissions, into a signed scalar after orthogonal projection, energy weighting, and smooth rotation. A positive sign represents net accumulation of natural capital, a negative sign represents net expansion of ecological liability, and a value near zero indicates a general balance between resource gain and environmental consumption. This is because it possesses both directionality (positive / negative) and intensity (absolute value). It can play the role of a "comprehensive profit and loss" indicator in natural resource asset accounting, corresponding one-to-one with the profit or loss concepts in traditional financial statements. The specific implementation path can be divided into three layers.

[0101] The first layer is value mapping. Previous steps have mapped physical inventory and losses to the same monetary scale based on regeneration and repair costs. The positive and negative difference naturally corresponds to the net monetary value of "assets - liabilities" in terms of quantity; when... By multiplying by the base period unit price vector and updating it to the current period price according to the inflation index or social discount rate, a monetary estimate of the net increase or decrease in natural capital can be directly obtained. In preparing the balance sheet, the carrying amount of the previous period is included. Plus The new book value for the current period is obtained. Therefore, it can be seen that as long as the calculation is carried out on a rolling basis... This can automatically generate a book value sequence of natural resource assets, meeting the frequency requirements of government or enterprises for annual, quarterly, or even monthly natural capital accounting.

[0102] The second layer is risk disclosure. The principal component difference is derived from the energy weighting of the covariance spectrum, thus it not only considers the fluctuation range of each resource and loss indicator itself, but also captures the synergistic or offsetting effects between them. For example, when forest stock decline and wetland restoration occur simultaneously, their impacts on... The contributions of these components are in opposite directions and will cancel each other out to some extent; this "combination effect" is precisely the advantage of the covariance principal component method. In practice, if consecutive periods show... A sharp turn to negative indicates that systemic ecological risks are accumulating, requiring timely intervention through fiscal funding or ecological compensation; if If the value is consistently positive and the amplitude is stable, it indicates that the resource management policy is effective, and the intensity of use can be appropriately relaxed or the surplus quota can be used for carbon trading and green bond premiums.

[0103] The third layer is scenario simulation and decision feedback. Because The mapping to the input vector is linear, and its gradient matrix is... The system can provide real-time updates in the background on the marginal contribution of each resource or loss metric to the net asset value. This allows policymakers to quickly conduct sensitivity analyses of policy options: increasing investment in forest tending by 5% would... How much will it rise? Will reducing groundwater extraction by 10% solve the problem? Turning negative into positive? By further converting this marginal contribution into unit currency or unit carbon intensity, a quantitative basis can be provided for policy tools such as resource tax rates, ecological compensation standards, and carbon market quotas. Furthermore, the principal component difference construction uses half-decay option weighting and spectrum smoothing, thus enabling seamless integration into scenario simulations: after setting future emission scenarios, rainfall scenarios, or land use scenarios, updating the physical quantity and loss inputs immediately yields the results under different scenarios. The trajectory provides a dynamic reference for medium- and long-term natural capital planning.

[0104] Principal component difference compresses high-dimensional resource-liability information into single-value net differences that conform to accounting standards, upgrading natural resource asset accounting from "listing indicators" to "profit and loss judgment"; at the same time, it maintains a linear structure and statistical energy weights, and can be expanded into multiple functions such as risk warning, policy evaluation, and scenario simulation. Therefore, this invention... It achieves an organic unity of regular quantitative accounting, risk monitoring and decision support for natural resource assets, meeting the core needs of resource management departments in the three dimensions of high frequency, accuracy and interpretability.

[0105] Below is a complete numerical example. For ease of calculation, the resource dimension is taken as... (Standing timber volume in forests) arable land area Static recoverable groundwater ), take the loss dimension (Fossil fuels) Emissions Over-extraction of groundwater Replace with full text. The metric only needs to expand the vector and matrix dimensions.

[0106]

[0107] Placing the asset and liability entries diagonally, we get... The first three items come from The latter two items come from Matrix average:

[0108] ;

[0109] Normalized diagonal elements:

[0110] ;

[0111] Therefore, we can conclude that: , .

[0112] Set backtracking depth Attenuation factor Repeat steps 2–3 for the previous quarter and the quarter before that to obtain the three-period normalized vector set. The weighted mean is:

[0113] ;

[0114] ;

[0115] Resource-side covariance:

[0116] ;

[0117] Loss-side covariance:

[0118] ;

[0119] ;

[0120] ;

[0121] The original singular spectrum is: .

[0122] Previous issue's score It is known that by minimizing ; to obtain the optimal In this example, the spectral changes are gradual. For demonstration purposes, the identity matrix is ​​used directly, and the singular spectrum has been smoothed. .

[0123] definition: ;Will and After splicing, multiply by the right in sequence. Left multiplication Multiply by the sign matrix Finally with Inner product, we get .

[0124] This indicates that the resource gains (continued growth in standing timber and stable arable land) for the quarter, after energy weighting, were still slightly higher than the cost of debt (slight increase in fossil emissions and proper control of groundwater over-extraction), resulting in a net accumulation of natural capital overall. Multiply by the base period monetary size of assets and liabilities (in this example, diagonal assets + liabilities are approximately...). (RMB) quarterly net increase If the book value in the previous period was Yuan, then . Compared to the previous quarter A slight increase suggests that the marginal gain from forest stock expansion is offsetting the increase in fossil fuel emissions, and groundwater over-extraction remains the largest negative principal component (in Chinese occupation Energy). The sensitivity matrix is ​​given. This indicates that if the normalized component of groundwater over-extraction increases further... , It will drop by approximately This is enough to turn the net asset value negative; therefore, water intake should be further reduced or artificial replenishment should be increased.

[0125] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for natural resource asset big data analysis and accounting, characterized in that, The method comprises: Step 1: obtaining physical inventory of different resource types in each period, obtaining loss amount of different resource loss types in each period; filling the left asset block of the matrix with the physical inventory multiplied by the resource unit price, filling the right liability block of the matrix with the loss amount multiplied by the repair cost, forming a time point matrix, and performing normalization processing on each element in the time point matrix to obtain a normalized matrix of each period; Step 2: calculating resource side covariance matrix and loss side covariance matrix according to half-life weight for the normalized matrix of each period, performing eigenvalue decomposition on the resource side covariance matrix and the loss side covariance matrix respectively, and extracting orthogonal basis vectors with the largest contribution to overall variation; placing singular spectra of the normalized matrices of adjacent two periods into a discrete Lyapunov equation, recursively updating under the premise of maintaining energy conservation, eliminating the jumping phenomenon caused by single dynamic resource liability matrix decomposition truncation, and making the coupling structure evolve smoothly over time to obtain smoothed singular spectra; Step 3: re-linearly combining resource contribution and liability cost according to the orthogonal basis vectors and the smoothed singular spectra to obtain principal component differences after removing stray noise.

2. The natural resource asset big data analytics accounting method of claim 1, the resource types comprising: Forests, farmland, grassland, wetlands and groundwater; The real inventory includes: standing stock of live trees , forest area , forest biomass carbon storage , effective arable land area , soil organic matter inventory , available grassland area , aboveground available forage amount , natural wetland area , average water storage of wetlands , static exploitable groundwater storage and annual exploitable groundwater volume ; the resource depletion types include: carbon emissions, water overexploitation and soil degradation; the depletion amount includes: fossil fuel CO2 emissions , industrial process CO2 emissions , agricultural methane / nitrous oxide emissions , groundwater overexploitation , surface water over-standard water extraction , new water and soil loss and increased sediment area .

3. The natural resource asset big data analytics accounting method of claim 2, wherein, Point-in-time matrix for eras is: ； wherein, is a physical inventory vector for the period; is a depletion quantity vector for the period; is a diagonal operation; is a cost unit price corresponding to the physical inventory; is an ecological restoration unit cost corresponding to the depletion quantity.

4. The natural resource asset big data analytics accounting method of claim 3, wherein, The normalization processing on each element in the time point matrix is: ； wherein, represents a matrix all-element mean operation; represents a matrix all-element standard deviation operation; L is an all-ones column vector of the adaptation dimension; represents a transpose operation.

5. The natural resource asset big data analytics accounting method of claim 4, wherein, Resource-side covariance matrix is: ； wherein, is the backtracking period offset index, when represents is the period, when represents is the period, and so on; is the maximum backtracking depth; is the half-life decay factor, satisfying ; is the normalized physical inventory vector of the period ; is the resource-side weighted mean calculated according to the half-life decay factor, with as the sample. loss side covariance matrix is: ； in, for The normalized loss vector for each period; For The weighted average of the loss side is calculated based on the half-life decay factor, using the sample as an example.

6. The natural resource asset big data analytics accounting method of claim 5, wherein, The orthogonal basis vectors are obtained by solving the following formula: ； ； wherein, is a resource-side basis vector; is a loss measurement basis vector; and together constitute an orthogonal basis vector; is a resource-side diagonal eigen spectrum; is a loss measurement diagonal eigen spectrum.

7. The natural resource asset big data analytics accounting method of claim 6, wherein, smoothed singular spectrum is: ； wherein is the original singular spectrum, and the calculation formula is: ； Solution variable to minimize the Frobenius residual for optimal smoothed transformation matrix Numerically, it is a minimum rotation or minimum pseudo-shear that aligns the energy of the smoothed singular spectrum with the original singular spectrum, and the formula is: ； wherein is the original singular spectrum of the epoch; is the conjugate transpose.

8. The natural resource asset big data analytics accounting method of claim 7, wherein, Principal component difference of era Is: ； wherein is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a vector of the normalized physical inventory at the time period t; is a direct sum operation, ; denotes the field of real numbers; is a symbol selection matrix.

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