Method and system for three-dimensional variational assimilation dimension reduction calculation

Abstract

The invention belongs to the technical field of data three-dimensional variation assimilation analysis, discloses a novel method for three-dimensional variation assimilation dimension reduction calculation, and provides possible improvement in form for a three-dimensional variation assimilation calculation scheme according to a corresponding matrix derivation rule so as to provide corresponding reference for data assimilation. The invention provides a new method for three-dimensional variation assimilation dimension reduction calculation, which is beneficial for remarkably improving the calculation efficiency, is beneficial for shortening the evaluation period and reducing the construction cost in the aspect of new energy development, is beneficial for improving the timeliness of forecasting in the aspect of weather and ocean forecasting, and better provides efficient guarantee for economic construction and livelihood construction.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of three-dimensional variational assimilation analysis technology, and particularly relates to a new method and system for three-dimensional variational assimilation dimensionality reduction calculation. Background Technology

[0002] In many fields related to economic development and people's livelihood, such as new energy assessment, global climate change research, air-sea interaction research, and meteorological and marine forecasting, big data calculation and analysis are involved. Therefore, a scientific and efficient calculation method is particularly important.

[0003] Based on Bayes' principle, in 1986, Acrorenc laid the mathematical foundation for the three-dimensional variational assimilation principle [1]. Subsequently, the cost function was:

[0004] J(x)=(xx b ) T B -1 (xx b )+(yH[x]) T R -1 (yH[x]) (1)

[0005] The meanings of the terms in the formula are well-known and will not be elaborated here. Here, H[x] is considered to be in linear form. It is worth noting that the principle of extrema is generally used to approximate x in order to find the extrema of the substitution function. The gradient of this function with respect to x is:

[0006]

[0007] Solve for x such that To satisfy the condition that J is minimized, both classic and commonly used algorithms require converting the feature field into a vector before calculating the covariance matrix. Because the feature field is written as a vector, for an (m×n) feature field distribution, the dimensions of the relevant background covariance matrix (B, H, R) will be (mn×mn), increasing the required memory by a factor of mn. This represents a terrifyingly large computational load for both numerical computation and assimilation analysis.

[0008] Based on matrix analysis and error distribution theory, since the error distributions among the elements in an element field are relatively independent, and the actual expression of the cost function is the trace of the covariance matrix, the matrix form can be approximately preserved to obtain the cost function based on this independence. If a matrix form is used, for an (m×n) element field distribution, the dimensions of the relevant background covariance matrices (B, H, R) will still be close to mn, thus simplifying the calculation.

[0009] In a current technology that assimilates lightning data into a three-dimensional variational system, lightning data is converted into a "proxy radar echo" format by establishing a statistical mapping relationship between lightning frequency and the maximum proxy radar echo of a vertical column. This data is then directly assimilated into the 3D-Var system for severe convective weather forecasting. This method improves the accuracy of precipitation forecasts, especially by fitting statistical relationships in plains and mountainous areas, and constructing a lightning-echo conversion model using a nonlinear S-curve function ([Patent Image][1]).

[0010] While this technology improves the accuracy of precipitation forecasting in severe convective weather, it focuses on innovative methods of transforming observational data and does not address the assimilation system itself, particularly the dimensionality reduction and matrix simplification issues in the calculation of the background error covariance matrix or cost function. Therefore, in large-scale three-dimensional assimilation applications, it still faces challenges such as large assimilation computation scale, low computational efficiency, and difficulty in meeting rapid operational needs, lacking methods for dimensionality reduction or reconstruction optimization of the covariance matrix's characteristic structure. Summary of the Invention

[0011] To address the problems existing in the prior art, this invention provides a novel method for three-dimensional variational assimilation and dimensionality reduction computation.

[0012] This invention is implemented as follows: a novel method for three-dimensional variational assimilation and dimensionality reduction computation, the method comprising:

[0013] Based on the corresponding matrix differentiation rules, a possible formal improvement to the three-dimensional variational assimilation calculation scheme is proposed, in order to provide a reference for data assimilation.

[0014] Furthermore, the proposed three-dimensional variational assimilation calculation scheme includes possible formal improvements, specifically:

[0015] The objective function is rewritten in the following form:

[0016] J(X)=J1(X)+J2(X)(3)

[0017] in,

[0018]

[0019] and

[0020]

[0021] In the formula, Trace is the trace operator of the matrix, where AXD is the matrix representation of the corresponding observation form H[x]. According to the matrix calculation principle and the field regression principle, there exist A, D, R1, B1, R2, B2 that satisfy J(X)=J1(X)+J2(X) and H[X]=AXD.

[0022] Furthermore, the proposed improvements to the three-dimensional variational assimilation calculation scheme also include:

[0023] Taking J1(X) as an example, a variational assimilation solution strategy is adopted:

[0024]

[0025] Take the derivative of J1(X) with respect to X:

[0026]

[0027] In the formula, G = Y - AX b D; According to the principle of extrema, deriving J1(X), we get:

[0028]

[0029] In the formula, according to the matrix decomposition theorem, DD T It can be decomposed into U T λ D U, where, λ D For DD T The eigenvalue diagonal matrix, U is an identity orthogonal matrix, U T U=UU T =I, where I is the identity matrix;

[0030] Multiply both sides of the above equation by U T It can be transformed into:

[0031]

[0032] Here, when the above equation is directly reduced to zero, it represents the solution proposed in the introduction. In this case, the above equation can be reduced to the expression for XU. T Solving for (XU), the above equation is equivalent to:

[0033]

[0034] For simplicity, the part containing XU is rewritten as follows:

[0035]

[0036] In the above formula, the matrix subscript S means that the matrix is ​​a symmetric matrix, corresponding to F1.

[0037] F1 = B 1S X b U T +A T R 1GS D T U T +A T R1S AX b U T Λ D

[0038] In the formula,

[0039] Similarly, for J2(X), we have:

[0040]

[0041] in, A T A = V T λ A V, XV = VX, F2 = VA T R 2GS D T +Λ A VX b DR 2S D T +VX b B 2S ;

[0042] Solve the two analytical equations simultaneously:

[0043]

[0044] Using the extremum condition, the above equation can be transformed into an equation:

[0045] B 1S (XX b )+(XX b B 2S +A T R 1S A(XX b )DD T +A T A(XX b )DR 2S D T

[0046] =A T (R 1GS +R 2GS )D T (13)

[0047] The analytical field that is solved is the case where the equation holds.

[0048] Furthermore, the proposed improvements to the three-dimensional variational assimilation calculation scheme also include:

[0049] For the case where the observations are in the form of an identity matrix (excluding terms that do not contain X):

[0050]

[0051] Where G = YX b , but, for:

[0052]

[0053] Based on the extreme value condition, then:

[0054]

[0055] This equation is the Sylvester equation, which can be solved directly using lyap in MATLAB. The solvability condition of the equation is: and If there are no common eigenvalues, then the solution to the above equation is XX. b =Δ, then the analytical field is: X a =Δ+X b The equation also has an iterative solution scheme; however, it will not be discussed further here.

[0056] In this case, the vector form of the extremum condition based on equation (2) (where g = yH[x]) b ]):

[0057] (B -1 +H T R -1 H)Δ-H T R -1 g = 0 (16)

[0058] In the formula, g is the column vector of G expanded in the order of X, and the rest is the same as the cost function in the introduction; according to matrix theory and field regression practice, these two equations are equivalent.

[0059] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0060] First, this invention proposes a novel method for three-dimensional variational assimilation and dimensionality reduction computation. Unlike other existing schemes, this method starts from the original cost function and simplifies the computation process based on matrix algebra theory, thereby significantly improving computational efficiency and reducing storage space. In the development of new energy sources, it helps to shorten the evaluation cycle and reduce construction costs. In meteorological and marine forecasting, it helps to improve the timeliness of forecasts, thus providing more efficient support for economic and social development.

[0061] From the perspective of actual computational results, this scheme achieves data assimilation while significantly reducing the computational load of related solutions. The example demonstrates that this scheme greatly simplifies the calculation and storage of the covariance matrix: for an (m×n) feature field distribution (100×100 in the example), the dimensions of the relevant background covariance matrices (B, H, R) are reduced from (mn×mn) to m×m and n×n (i.e., from 10000×10000 to 100×100), and the corresponding solution equation for the cost function is ultimately simplified to the Sylvius equation, further simplifying the computation. For three-dimensional fields (or three-dimensional feature fields in four-dimensional variational assimilation), they can also be transformed into matrix form for calculation, thereby reducing the computational and storage load.

[0062] In the example, a homogeneous error distribution was constructed, and a square computational domain was used. From a practical calculation perspective, the estimation of the covariance matrix is ​​crucial to the accuracy of the analysis field; this can be estimated using historical data. For non-homogeneous error distributions and non-square computational domains, the construction of the covariance matrix requires further exploration.

[0063] Second, the expected benefits and commercial value of the technical solution of the present invention after transformation are as follows: the method can conveniently realize data assimilation. Due to the reduction of the corresponding computational load, the assimilation scheme can be more easily ported and accelerated. At the same time, since it starts from the cost function itself, the calculation is closer to the original theory.

[0064] The technical solution of this invention overcomes technical bias: Currently, mainstream variational assimilation schemes, when dealing with the error covariance matrix, often employ empirical methods to decompose the matrix due to its large magnitude in order to solve for the corresponding cost function, rarely constructing a solution based on the cost function itself. This solution can provide a reference for solving this type of equation. Attached Figure Description

[0065] Figure 1 This is a flowchart of a three-dimensional variational assimilation and dimensionality reduction calculation method provided in an embodiment of the present invention.

[0066] Figure 2 This is an assimilation result diagram of a single wave process provided in an embodiment of the present invention.

[0067] Figure 3 The following are simple ideal experiments provided by embodiments of the present invention: (a) ideal field; (b) background field; (c) observation field; (d) assimilation field based on the scheme in this paper.

[0068] Figure 4 This is an ideal experiment provided by the embodiments of the present invention, and the ideal field is the same as... Figure 3(a): (ab) are the observation data processed to grid points. (a) is the mean error distribution estimate based on the Monte Carlo experiment, where the contour interval is 0.2, >0.2 is a solid line, <-0.2 is a dashed line, and =±0.2 is the corresponding bold line; (b) is the observation error variance estimate based on the Monte Carlo experiment; (c) background field; (d) observation field; (e) assimilation field based on the scheme in this paper; (f) assimilation field calculated based on vector form. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0070] In existing numerical weather prediction and ocean simulation systems, three-dimensional variational assimilation methods are widely used to combine observational information with model background fields to obtain an analysis field that more closely approximates the real-world situation. However, traditional methods require processing extremely high-dimensional state vectors in large-scale grid scenarios, resulting in massive matrix operations when calculating the cost function, making optimization difficult to complete within a limited timeframe. This problem directly restricts the real-time performance and accuracy of assimilation systems in practical applications, thus urgently requiring a dimensionality-reducing and efficient computational method to address the computational bottleneck faced by existing technologies in industrial applications.

[0071] This invention introduces trace operator reconstruction technology in the cost function construction stage, decomposing the observation error term and the background error term into two independent parts. This allows the cost function to be formally transformed into a more easily solvable block structure. By ensuring the operator mapping relationship H\[X]=AXD, the mathematical simplification of the cost function can be achieved while maintaining the consistency between observation and background. This design not only ensures the physical rationality of the cost function expression but also provides a regular algebraic structure for subsequent variational derivation, avoiding the computational difficulties caused by excessively large matrix sizes in traditional methods.

[0072] In solving for the extremum conditions, this method first performs variational differentiation on the cost function J1(X) related to the observation error to obtain the gradient conditions with respect to the state variable X. This process is equivalent to constructing the Euler-Lagrange equations. By differentiating the cost function and setting it to zero, the necessary conditions satisfied by the optimal solution can be obtained. This step is a core component in numerical assimilation theory, ensuring that the solution of the analysis field is statistically closest to the real atmospheric or oceanic state.

[0073] To further reduce computational complexity, this invention performs eigenvalue decomposition on the error covariance matrix DDT, representing it as UTλDU. Leveraging the properties of the orthogonal matrix U, the original high-dimensional state space can be mapped to a low-dimensional subspace spanned by eigenvectors. Within this subspace, the scale of matrix operations is significantly reduced, and the complex covariance propagation problem is simplified to a finite-dimensional eigenvalue weighted operation, thereby greatly improving numerical computation efficiency. This dimensionality reduction strategy is particularly suitable for the demands of rapid iteration and large-scale parallelism in industrial applications.

[0074] In the final solution stage of the analysis field, this method combines the analytical expression of J2(X) with the aforementioned extremum conditions to form an optimization equation that considers both observation constraints and background information. Through this process, the obtained analysis field not only ensures a good fit to the observation data but also maintains consistency and dynamic equilibrium with the model background. This method avoids numerical instability while maintaining physical consistency, enabling the analysis results to maintain high stability and reliability in subsequent model integrations.

[0075] The proposed three-dimensional variational assimilation and dimensionality reduction method constructs a complete low-complexity assimilation process through a series of steps, including cost function decomposition, trace operator reconstruction, eigenvalue decomposition for dimensionality reduction, and extreme value condition solving. Its working principle ensures mathematical rigor while also considering efficiency and scalability in industrial applications. It can significantly improve the computational bottleneck of existing three-dimensional variational assimilation systems in large-scale grid and high-frequency operational scenarios, providing a new technical approach for operational applications in meteorology, oceanography, and environmental monitoring.

[0076] like Figure 1 As shown in the figure, the three-dimensional variational assimilation and dimensionality reduction calculation method provided by the present invention is characterized by comprising:

[0077] S101, construct the cost function J(X) and rewrite it as J(X)=J1(X)+J2(X);

[0078] Among them, J1(X) and J2(X) are established based on the observation error term and the background error term, respectively, and are reconstructed using the matrix trace operator to ensure that H[X] = AXD;

[0079] S102, by taking the variational derivative of J1(X), we obtain the extremum condition for X;

[0080] S103, for DD T Perform eigenvalue decomposition to obtain U T λ D U, using an orthogonal matrix U to perform dimensionality reduction operations, simplifies computational complexity;

[0081] S104, combined with the analytical expression of J2(X), can be solved simultaneously to obtain the analytical field that satisfies the extremum condition.

[0082] The embodiments of the present invention provide for DD T The decomposition satisfies U T U=UU T =I,λ D The matrix is ​​a diagonal matrix, and the decomposition result is used to transform the original problem into a matrix solution in a low-dimensional space.

[0083] The three-dimensional variational assimilation and dimensionality reduction calculation method provided in this embodiment of the invention includes:

[0084] When the observation operator is an identity matrix, the cost function is simplified to J(X) = J1(X) + J2(X), and the extreme value condition is obtained;

[0085] The matrix X is obtained by using the Sylvester equation in the form AX + XB = C and then employing numerical methods.

[0086] The solution condition is that when A and B have no common eigenvalues, the solution to the equation is unique, and the obtained solution is the analysis field.

[0087] The Sylvester equations provided in this embodiment of the invention are calculated using a numerical linear algebra library, and the matrix sparsity is preserved during the solution process to improve computational efficiency.

[0088] An embodiment of the present invention provides a three-dimensional variational assimilation and dimensionality reduction computational device comprising:

[0089] The cost function building module is used to build and rewrite the cost function J(X)=J1(X)+J2(X);

[0090] The matrix factorization module is used to decompose DD. T Perform eigenvalue decomposition and output orthogonal and diagonal matrices;

[0091] The extremum solution module is used to obtain the analysis field based on the derivative conditions of J1(X) and J2(X);

[0092] The results output module is used to transmit the solved analysis field to subsequent numerical models or forecasting systems.

[0093] The matrix factorization module provided in this embodiment of the invention is configured to execute U using a parallel computing unit. T λ D U-decomposition is used to achieve efficient computation of ultra-large-scale data.

[0094] An embodiment of the present invention provides a three-dimensional variational assimilation application system comprising:

[0095] Atmospheric observation data interface, used to acquire multi-source observation data;

[0096] The background field input module is used to provide the background field output by the numerical weather prediction model.

[0097] The core module for assimilation computation is used to perform dimensionality reduction calculations and output the analysis field;

[0098] The results publishing module is used to apply the analysis field to numerical weather prediction or environmental simulation.

[0099] In existing three-dimensional variational assimilation methods, computational complexity and dimensionality constraints remain key issues limiting practical applications. Especially in numerical weather prediction and atmospheric circulation simulation, the objective function typically involves high-dimensional matrix operations and the embedding of large amounts of observational data, leading to excessively high costs for finding the extrema of traditional cost functions in engineering implementation. This invention formally reconstructs the three-dimensional variational assimilation cost function, decomposing the original complex cost function into two independently processable sub-terms, J1(X) and J2(X). By combining the matrix trace operator and field regression principles, high-dimensional computation can be converted into low-rank matrix operations. This reconstruction not only provides a dimensionality reduction basis for numerical computation but also establishes theoretical support for the widespread application of the assimilation framework in industry and scientific research.

[0100] In terms of working principle, the method uses the matrix decomposition theorem as its core tool. Through DD... T The spectral decomposition transforms the matrix equations, which are originally difficult to solve directly, into a combined representation of an identity orthogonal matrix and an eigenvalue diagonal matrix. The advantage of this decomposition method is that it preserves the basic structure of the cost function while simplifying gradient calculations. The process of deriving J1(X) embodies this idea: under extreme conditions, the first derivative of the cost function, after matrix orthogonal transformation, can be directly reduced to zero to obtain an equivalent expression for the analysis variables, thus avoiding the complex iterative convergence problem in traditional methods.

[0101] On the other hand, the processing of J2(X) introduces a similar matrix approach. In constructing A... T In the decomposition of A, singular value decomposition is used to rewrite some terms of the objective function as V and λ. A The combined structure ensures that the two sub-terms of the cost function maintain a high degree of formal symmetry and provides a simplified path for subsequent joint solutions. By simultaneously solving the analytical equations J1 and J2 and simplifying them to the Sylvester equation under extreme conditions, the method achieves a direct solution to the global analytical field. Since mature solvers and convergence criteria already exist in numerical linear algebra, engineering implementation can be directly accomplished using tools such as MATLAB, significantly improving practical operability.

[0102] For the special case where the observation matrix simplifies to an identity matrix, this method can further reduce it to a vectorized extremum condition. In this case, the cost function exhibits strict equivalence between matrix and vector forms, allowing the computation to be implemented alternately within both matrix theory and numerical algebra frameworks. This dual-track formulation provides greater flexibility for high-performance computing environments, reducing storage and transmission overhead under HPC or GPU parallelization conditions and enhancing the method's engineering adaptability.

[0103] At the industrial application level, this method directly addresses the problems of the curse of dimensionality and computational complexity in existing technologies. Traditional three-dimensional variational assimilation is often limited in practical operational systems due to its excessively high matrix dimensionality. For example, in the coupled assimilation of global and regional models, the matrix order and observation scale often reach millions. By introducing matrix decomposition and trace operators, this method can reduce the dimensionality of the problem to a controllable range and achieve near real-time operation in the assimilation system. The resulting application value is not only reflected in the improved accuracy of numerical weather prediction, but can also be extended to multidisciplinary scenarios such as ocean dynamics, air pollution forecasting, and energy and climate simulation.

[0104] Ultimately, the technological advancements of this method are reflected in three aspects: First, a new framework combining cost function reconstruction and matrix factorization is proposed, reducing computational complexity; second, a fast and solvable numerical form is established through the Sylvester equation and vectorization conditions, enabling seamless integration of theoretical methods into engineering implementation; and third, equivalence is maintained between simplified observation operators and complex matrix forms, providing a unified theoretical foundation for cross-scenario and multi-model extended applications. These improvements demonstrate a substantial breakthrough of this method within the existing three-dimensional variational assimilation framework, effectively addressing the technical bottlenecks of insufficient computational resource consumption and assimilation efficiency in industrial applications.

[0105] This invention provides a novel method for three-dimensional variational assimilation and dimensionality reduction computation, the method comprising:

[0106] Based on the corresponding matrix differentiation rules, a possible formal improvement to the three-dimensional variational assimilation calculation scheme is proposed, in order to provide a reference for data assimilation.

[0107] Furthermore, the proposed three-dimensional variational assimilation calculation scheme includes possible formal improvements, specifically:

[0108] The objective function is rewritten in the following form:

[0109] J(X)=J1(X)+J2(X)(3)

[0110] in,

[0111]

[0112] and

[0113]

[0114] In the formula, Trace is the trace operator of the matrix, where AXD is the matrix representation of the corresponding observation form H[x]. According to the matrix calculation principle and the field regression principle, there exist A, D, R1, B1, R2, B2 that satisfy J(X)=J1(X)+J2(X) and H[X]=AXD.

[0115] Furthermore, the proposed improvements to the three-dimensional variational assimilation calculation scheme also include:

[0116] Taking J1(X) as an example, a variational assimilation solution strategy is adopted:

[0117]

[0118] Take the derivative of J1(X) with respect to X:

[0119]

[0120] In the formula, G = Y - AX b D; According to the principle of extrema, deriving J1(X), we get:

[0121]

[0122] In the formula, according to the matrix decomposition theorem, DD T It can be decomposed into U T λ D U, where, λ D For DD T The eigenvalue diagonal matrix, U is an identity orthogonal matrix, U T U=UU T =I, where I is the identity matrix;

[0123] Multiply both sides of the above equation by U T It can be transformed into:

[0124]

[0125] Here, when the above equation is directly reduced to zero, it represents the solution proposed in the introduction. In this case, the above equation can be reduced to the expression for XU. T Solving for (XU), the above equation is equivalent to:

[0126]

[0127] For simplicity, the part containing XU is rewritten as follows:

[0128]

[0129] In the above formula, the matrix subscript S means that the matrix is ​​a symmetric matrix, corresponding to F1.

[0130] F1 = B 1S X b U T +A T R 1GS D T U T +A T R 1S AX b U T Λ D

[0131] In the formula,

[0132] Similarly, for J2(X), we have:

[0133]

[0134] in, A T A = V T λ A V, XV = VX, F2 = VA T R 2GS D T +Λ A VX b DR 2S D T +VX b B 2S ;

[0135] Solve the two analytical equations simultaneously:

[0136]

[0137] Using the extremum condition, the above equation can be transformed into an equation:

[0138] B 1S (XX b )+(XX b B 2S +A T R 1S A(XX b )DD T +A T A(XX b )DR 2S D T

[0139] =A T (R 1GS +R 2GS )D T(13)

[0140] The analytical field that is solved is the case where the equation holds.

[0141] Furthermore, the proposed improvements to the three-dimensional variational assimilation calculation scheme also include:

[0142] For the case where the observations are in the form of an identity matrix (excluding terms that do not contain X):

[0143]

[0144] Where G = YX b , but, for:

[0145]

[0146] Based on the extreme value condition, then:

[0147]

[0148] This equation is the Sylvester equation, which can be solved directly using lyap in MATLAB. The solvability condition of the equation is: and If there are no common eigenvalues, then the solution to the above equation is XX. b =Δ, then the analytical field is: X a =Δ+X b The equation also has an iterative solution scheme; however, it will not be discussed further here.

[0149] In this case, the extremum condition in vector form is:

[0150] (B -1 +H T R -1 H)Δ-H T R -1 In the equation g = 0, g is the column vector of G expanded in the order of X, and the rest is the same as the cost function in the introduction; according to matrix theory and field regression practice, these two equations are equivalent.

[0151] I. Specific application areas or related products of this invention.

[0152] The program design of this scheme is relatively simple and the method is easy to construct, and it can be used for the assimilation of marine and atmospheric data. Figure 2 This is a comparison of the assimilation results for a single wave process based on this method (corresponding to an observation trajectory of a satellite altimeter), where "o" represents the background field, "*" represents the observation field, and "—" represents the assimilation field. It can be seen that the assimilation results based on this method reproduce the background field information quite well.

[0153] II. Evidence related to the technical effects obtained by the embodiments of the present invention.

[0154] The ideal element field distribution used in the three-dimensional variational assimilation of this invention is as follows: Figure 3 (a), Figure 3 The mid-field feature field was generated and processed using MATLAB's `peaks` function, and its dimension is 100×100; background field distribution... Figure 4 The elements are ideal fields superimposed with random error fields, with the maximum absolute error being 1.4815, the root mean square error being 0.4572, the mean absolute error being 0.9396, and the mean error being -0.9396. Figure 4 The elements are ideal fields superimposed with random error fields, where the maximum absolute error is 1.6000, the root mean square error is 0.4944, the mean absolute error is 1.0132, and the mean error is -1.0132; the analysis field is as follows: Figure 3 (d), where the maximum absolute error is 1.5548, the root mean square error is 0.4200, the mean absolute error is 0.3406, and the mean error is -0.0527. Figure 4 For the ideal experiment using the same ideal field but with an unstructured grid distribution, the results show that the assimilation results using this scheme still reproduce the original distribution of the element field very well.

[0155] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0156] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A three-dimensional variational assimilation dimension reduction calculation method, characterized in that, Comprising: Step 1, constructing a cost function J(X) and rewriting it as J(X) = J1(X) + J2(X); Wherein, J1(X) and J2(X) are respectively based on observation error terms and background error terms, reconstructed using matrix trace operators to ensure H[X] = AXD; Step 2, variational derivation of J1(X) to obtain the extreme condition about X; Step 3, feature decomposition on DD T to obtain U T λ D U, using the orthogonal matrix U to realize dimension reduction operation, and simplify the calculation complexity; Step 4, combined with the analytical expression of J2(X), the simultaneous solution is obtained to satisfy the extreme condition of the analysis field.

2. The method of claim 1, wherein, The decomposition of the pair DD T satisfies U T U = UU T = I, λ D is a diagonal matrix, and the decomposition is used to convert the original problem into a matrix solution in a low-dimensional space.

3. A three-dimensional variational assimilation dimension reduction calculation method, characterized in that, Comprising: In the case of the observation operator being a unit matrix, the cost function is simplified as J(X) = J1(X) + J2(X), and the extreme condition is obtained; Expressed in the form of Sylvester equation AX + XB = C, the matrix X is obtained by calling the numerical solution method; The solution condition is that A and B have no common eigenvalue, and the equation has a unique solution, which is the analysis field.

4. The method of claim 3, wherein, The Sylvester equation is calculated by a numerical linear algebra library, and the matrix sparsity is preserved during the calculation to improve the calculation efficiency.

5. A three-dimensional variational assimilation dimension reduction computing device, comprising: Comprising: A cost function construction module for establishing and rewriting the cost function J(X) = J1(X) + J2(X); a matrix decomposition module configured to decompose the DD T perform eigenvalue decomposition and output an orthogonal matrix and a diagonal matrix; An extreme solution module for solving the analysis field according to the derivative conditions of J1(X) and J2(X); A result output module for transmitting the solved analysis field to subsequent numerical models or prediction systems.

6. The apparatus of claim 5, wherein, The matrix decomposition module is configured to perform U T λ D decomposition using parallel computing units to achieve efficient computation on super large scale data.

7. A computer program, characterised in that, When the program is executed by the processor, the steps of the three-dimensional variational assimilation dimension reduction calculation method of any one of claims 1-4 are implemented.

8. The computer program of claim 7, wherein, The program calls matrix trace operators and Sylvester equation solvers during execution to realize dimension reduction and fast solution of the cost function.

9. A computer-readable storage medium having stored thereon program instructions, wherein, The program instructions are executed by the processor to implement the method steps of any one of claims 1-4.

10. A three-dimensional variational assimilation application system based on the method of any one of claims 1 to 4, characterized in that, The system comprises: An atmospheric observation data interface for obtaining multi-source observation data; A background field input module for providing a background field output by a numerical prediction model; An assimilation calculation core module for performing dimension reduction calculation and outputting an analysis field; A result publishing module for applying the analysis field to numerical weather prediction or environmental simulation.

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