An ocean meteorological data assimilation method based on adaptive scale decomposition

Abstract

The application relates to the technical field of marine meteorological data assimilation, in particular to a marine meteorological data assimilation method based on self-adaptive scale decomposition. An original data set is acquired and preprocessed to obtain a two-dimensional matrix. Based on an empirical orthogonal function analysis method EOF, dimension reduction is carried out on the initial matrix to obtain a spatial mode which does not change with time. A spatial self-adaptive scale reduction model is constructed by using the correlation of points on the spatial mode. Grid setting is carried out on the spatial self-adaptive scale reduction model to obtain an optimized multiple network. A target functional is determined and scale-by-scale assimilation is carried out to obtain an analysis field. An accuracy calculation formula and an accuracy threshold value are determined. Sample observation values and sample analysis values of a sample to be analyzed are acquired, and the accuracy is calculated. The two-dimensional matrix is extracted and processed by the EOF, the spatial self-adaptive scale reduction model is obtained, and scale-by-scale assimilation of adaptive matching of spatial characteristics is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of marine meteorological data assimilation, and particularly relates to a marine meteorological data assimilation method based on adaptive scale decomposition. BACKGROUND

[0002] The traditional multi-scale assimilation method realizes the purpose of spatial expansion of analysis increments on different scales through scale decomposition. Among them, the multi-grid method uses the target function of the coarse grid to analyze the error long wave, so that the long wave of the analysis field can quickly converge, and then uses the target function of the fine grid to analyze the error short wave, so as to eliminate the confusion between different scales. Compared with the schemes such as spectral space asynchronous decomposition and multi-step assimilation, the multi-grid method has a significant advantage in the optimization angle of the approximation reduction of the background error covariance matrix with huge dimension and the acceleration of convergence speed.

[0003] However, the multi-grid data assimilation method uses a uniform downscaling method for scale decomposition, the grid change rate is 0.5, each multi-grid after coarsening is a structured grid, and the setting of different resolutions between multi-grids is based on empirical estimation, which is not universal for element fields with obvious spatial characteristics, high-resolution initial fields and observation data. An adaptive downscaling scheme is needed to make up for the theoretical deficiency of the traditional multi-grid method in setting the decorrelation length scale. SUMMARY

[0004] The present application provides a marine meteorological data assimilation method based on adaptive scale decomposition, which can solve the problem of inability to adaptively match the spatial characteristics of the downscaling of the existing marine meteorological data assimilation method.

[0005] The technical scheme of the present application is a marine meteorological data assimilation method based on adaptive scale decomposition, comprising:

[0006] S1: obtaining an original data set of a target area including an observation field and a numerical model prediction field; preprocessing the original data set to obtain a two-dimensional matrix accordingly;

[0007] S2: decomposing and processing the two-dimensional matrix by EOF to obtain a plurality of spatial modes accordingly;

[0008] Based on the correlation of the spatial points in each spatial mode, feature extraction is performed on the plurality of spatial modes respectively, and a spatial adaptive downscaling model is constructed by the positive and negative of the correlation coefficient in each spatial mode;

[0009] Based on the adaptive downscaling model, the spatial points are screened to obtain a spatial point distribution accordingly.

[0010] S3: based on the screened spatial point distribution, correspondingly setting the assimilation grid of each scale to obtain a multi-assimilation network corresponding to several spatial modes, including several heavy different scale assimilation grids;

[0011] S4: based on the multi-assimilation grid, determining the target functional of different scale assimilation grid;

[0012] The target functional is subjected to scale assimilation, and the final result is superimposed to obtain the analysis field.

[0013] Optionally, the step S1 comprises:

[0014] S11: obtaining the observation field of the target area; by adding random noise, obtaining the simulation field of the target area;

[0015] Determine the original data set including the observation field and the simulation field;

[0016] S12: for the original data set, sequentially perform time-space matching processing and outlier and missing value processing, and correspondingly obtain a two-dimensional matrix X of time samples mx spatial point number n;

[0017] The structure of the two-dimensional matrix X is as follows:

[0018]

[0019] Optionally, the step S2 comprises:

[0020] S21: based on EOF, extracting the two-dimensional matrix, and correspondingly obtaining several spatial modes;

[0021] Based on the correlation of the spatial points in each spatial mode, the feature extraction is performed for each spatial mode, and the spatial adaptive downscaling model is constructed by the positive and negative of the correlation coefficient in each spatial mode;

[0022] S22: performing arbitrary point selection operation on the to-be-selected points of each spatial mode, and correspondingly obtaining the selected points.

[0023] Optionally, the step S3 comprises:

[0024] S31: judging whether the correlation coefficient between the screened spatial points and the remaining points in each spatial mode is greater than 0;

[0025] S32: if greater than 0, the selected points and the to-be-selected points with the correlation coefficient greater than 0 between the selected points are attributed to the set C;

[0026] If less than 0, the selected points are attributed to the set F and the points in the set F are removed;

[0027] S33: repeating the steps S31-S32, and correspondingly obtaining a multi-analysis network including a plurality of assimilation networks with different scales.

[0028] Optionally, the step S4 includes:

[0029] S41: determining a target functional of the optimized multi-network; and a formula of an incremental form of the target functional is as follows:

[0030]

[0031] wherein n represents an n-th layer assimilation network, and n=1, 2, …, N;

[0032] Y (n) represents an observation increment matched with a background field on an n-th scale;

[0033] B (n) and O (n) respectively represent a background field error and an observation error covariance matrix on a corresponding scale;

[0034] H (n) represents an observation operator on the scale;

[0035] S42: performing a grid coarsening process step by step for the optimized multi-network based on a multi-grid algorithm, until being smoothed to a coarsest network;

[0036] S43: sequentially performing a network interpolation process, and correspondingly obtaining an analysis field;

[0037] A formula of the analysis field is as follows:

[0038]

[0039] wherein X a represents a final analysis field after assimilation;

[0040] X b represents a model initial field;

[0041] ε (n) represents an analysis result on each grid.

[0042] Optionally, the method further includes:

[0043] S5: determining a precision calculation formula based on a sample observation value and a sample analysis value, and a precision threshold value;

[0044] obtaining a sample observation value of a sample to be analyzed in a target area, and determining a sample analysis value of the sample to be analyzed according to the analysis field, and calculating a calculation precision corresponding to the sample to be analyzed based on the precision calculation formula;

[0045] The precision calculation formula is as follows:

[0046]

[0047] In the formula, represents a sample observation value of a sample i to be analyzed; represents a sample analysis value of a sample i to be analyzed.

[0048] Beneficial effects:

[0049] The application obtains a two-dimensional matrix by preprocessing an original data set, and obtains a spatial self-adaptive scale reduction model by extracting and processing the two-dimensional matrix through EOF, so as to realize spatial non-uniform scale reduction. The application also constructs a scale-by-scale assimilation grid by performing correlation analysis on a spatial mode. The application also obtains an analysis field of data assimilation by performing scale-by-scale solving of a data assimilation target functional and superimposition, so as to obtain a data assimilation technology applicable to a structure and a non-structure mode grid, and objectively realize spatial uniform scale reduction instead of artificial setting of a correlation length scale.

[0050] In summary, the application can solve the problem of non-adaptive matching of spatial characteristics of elements in the existing ocean meteorological data assimilation method, and is applicable to element fields with obvious spatial characteristics, high-resolution initial fields of a mode and observation data. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, other drawings can also be obtained by those skilled in the art without any creative labor under the premise of these drawings.

[0052] Figure 1 FIG. 1 is a flowchart of an ocean meteorological data assimilation method based on self-adaptive scale decomposition in the embodiments of the application;

[0053] Figure 2 FIG. 2 is a flowchart of determining an optimized multi-network based on an initial multi-network in the embodiments of the application;

[0054] Figure 3 FIG. 3 is a flowchart of gradually performing grid coarsening processing on the optimized multi-network in the embodiments of the application. DETAILED DESCRIPTION

[0055] Embodiments will be described in detail below with reference to examples illustrated in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the following embodiments are not meant to represent all implementations consistent with the present disclosure. Rather, they are merely examples of systems and methods consistent with some aspects of the present disclosure as detailed in the claims.

[0056] The present application provides a marine meteorological data assimilation method based on adaptive scale decomposition, as shown in Figure 1 Figure 1 The present application provides a marine meteorological data assimilation method based on adaptive scale decomposition, as shown in

[0057] S1: Obtain the original data set of the target area including the observation field and the numerical model prediction field; preprocess the original data set to obtain a two-dimensional matrix accordingly.

[0058] Specifically, the Princeton Ocean Model (POM) is used to establish a regional ocean model in the embodiments of the present application. The model is set to cover the northern South China Sea, the southern East China Sea, the Luzon Strait, and part of the northwest Pacific Ocean, with a horizontal resolution of 1 / 12° (about 8.5-9.0 km) and a vertical layering of 35 layers using a sigma coordinate system. The POM applies an internal and external mode separation technique, with a barotropic (external mode) and baroclinic (internal mode) time step of 7.5s and 450s, respectively. The model uses the ETOPO5 topographic data set, and the initial field and open boundary conditions are obtained from the Global Ocean Data Assimilation and Reanalysis System (GLORYS2V4) of Mercator Ocean.

[0059]

[0060] The meteorological forcing field is interpolated from the ERA-5 reanalysis data set of the European Centre for Medium-Range Weather Forecasts (ECMWF), including surface wind speed, total cloud cover, and 10m air temperature data, with a horizontal resolution of 1 / 4° and a time resolution of 1h.

[0061] The output results of the long-term operation of the ocean numerical model Spin-up from 1993 to 2010 are used as the observation field; random noise is added to the initial field module to re-spin the numerical model to a stable prediction as the simulation field.

[0062] S1 includes:

[0063] S11: Obtain the observation field of the target area; obtain the simulation field of the target area by adding random noise;

[0064] ​​Determine a raw data set including an observation field and a simulation field.

[0065] S12: For the raw data set, sequentially perform a spatio-temporal matching process and an outlier and missing value processing, and accordingly obtain a two-dimensional matrix X of time samples mxspatial point numbers n.

[0066] The structure of the two-dimensional matrix X is as follows:

[0067]

[0068] Specifically, for the raw data set, perform spatio-temporal matching, outlier and missing value processing, construct an initial error frequency signal of the element field, and obtain a two-dimensional matrix X of time samples mxspatial point numbers n.

[0069]

[0070] S2: Perform decomposition processing on the two-dimensional matrix by EOF, and accordingly obtain a plurality of spatial modes;

[0071] Based on the correlation of the spatial points in each spatial mode, feature extraction is performed on the plurality of spatial modes respectively, and a spatial adaptive downscaling model is constructed by the positive and negative of the correlation coefficients in each spatial mode;

[0072] Based on the adaptive downscaling model, the spatial points are screened, and accordingly the spatial point distribution is obtained.

[0073] Specifically, the EOF decomposition adaptively decomposes the spatial frequency signal into a stationary part and a non-stationary part, and simultaneously decomposes the data matrix into a spatial field that does not change with time and a group of time series, which maximizes the decomposition of the original element field into a plurality of main modes.

[0074] As shown in the following formula: Figure 2 Figure 2 is a flowchart of determining an optimized multi-network based on an initial multi-grid in the embodiment of the application, and step S2 includes:

[0075] S21: Based on EOF, perform extraction processing on the two-dimensional matrix, and accordingly obtain a plurality of spatial modes;

[0076] Based on the correlation of the spatial points in each spatial mode, feature extraction is performed on the plurality of spatial modes respectively, and a spatial adaptive downscaling model is constructed by the positive and negative of the correlation coefficients in each spatial mode.

[0077] Specifically, the cross product of X and its transpose matrix X T is calculated by using the two-dimensional matrix, and a square matrix is obtained:

[0078] ​

[0079] If X is already treated as anomaly, then C is called covariance matrix; if X is already standardized (i.e. mean of each row of data in C is 0, and standard deviation is 1), then C is called correlation coefficient matrix.

[0080] The eigenvalues λ and eigenvectors V of square matrix C are calculated, which satisfy the following relationship:

[0081] C m×m ×V m×m =V m×m ×Λ m×m

[0082] where Λ is a diagonal matrix of m x m, i.e.

[0083]

[0084] Each non-zero λ corresponds to a column of eigenvectors, which is called EOF. For example, the eigenvector corresponding to λ1 is called the first EOF mode. Projecting the EOF onto the original data matrix X, we get the time coefficients (i.e. principal components) corresponding to all spatial eigenvectors;

[0085]

[0086] The formula of spatially adaptive downscaling model is shown as follows:

[0087] X=EOF×PC

[0088] which is equivalent to the following form:

[0089]

[0090] where i = 1, 2, …, m; j = 1, 2, …, n;

[0091] t hi denotes the time function corresponding to the hth mode when m = i;

[0092] l hj denotes the spatial function corresponding to the hth mode when n = j.

[0093] The empirical orthogonal function analysis method (EOF) is used to analyze the structural characteristics in matrix data, and the spatial eigenvectors of SST are extracted. The ith eigenvector is called the ith mode: EOF_{i}. The spatial mode reflects the spatial distribution characteristics of SST.

[0094] The principal component (PC) corresponds to the time variation, also known as the time coefficient, which reflects the weight variation of the corresponding spatial mode with time. The EOF decomposes the original temperature field into the sum of the product of the time coefficient and the spatial mode.

[0095] The different modes after decomposition represent the original element field achieving adaptive downscaling in space. Specifically, based on the temporal and spatial correspondence (taking high-frequency signals leads to lower spatial correlation; taking low-frequency signals leads to higher spatial correlation), in the grid setting of multi-grid data assimilation, each scale is mapped to each spatial mode of EOF decomposition, allowing for a more reasonable setting of assimilation grids at different scales and avoiding the computationally expensive background error covariance matrix.

[0096] S22: Perform arbitrary point selection operation on the points to be selected for each spatial mode, and obtain the selected points accordingly.

[0097] S3: Based on the filtered spatial point distribution, assimilation grids of various scales are set one by one to obtain a multi-assimilation network corresponding to several spatial modes, which includes assimilation grids of several different scales.

[0098] Step S3 includes:

[0099] S31: Determine whether the correlation coefficient between the filtered spatial points and the remaining points in the current spatial mode is greater than 0;

[0100] S32: If the value is greater than 0, the selected point and the unselected points with a correlation coefficient greater than 0 with the selected point will be assigned to set C;

[0101] If the value is less than 0, the selected point is assigned to set F and points in set F are removed.

[0102] S33: Repeat steps S31 to S32 to obtain a multiple assimilation network that includes assimilation networks of several different scales.

[0103] Specifically, the spatially adaptive downscaling model transforms information from spatial modes into the meshes required for assimilation at each layer. Figure 3 As can be seen, for the correlation analysis of the nth mode, firstly, we randomly select a point and determine whether the correlation coefficient between the point and each point in space is greater than 0. If it is greater than 0, the point and all points with a correlation coefficient greater than 0 belong to set C and are retained at a smaller scale. Otherwise, it belongs to set F and is removed from the current grid points, thus obtaining the nth grid.

[0104] S4: Determine the target functional of assimilation grids at different scales based on multiple assimilation grids;

[0105] The objective functional is subjected to scale-wise assimilation, and the final results are superimposed to obtain the analysis field.

[0106] Among them, such as Figure 3 As shown, Figure 3 This is a schematic diagram of the process for progressively coarsening the mesh in an embodiment of the present application. Step S4 includes:

[0107] S41: Determine the objective function of the optimized multi-network; the incremental form of the objective function is as follows:

[0108]

[0109] In the formula, n represents the assimilation network of the nth layer, n = 1, 2, …, N;

[0110] Y (n) represents the observation increment matched with the background field on the nth scale;

[0111] B (n) and O (n) respectively represent the background field error and observation error covariance matrix on the corresponding scale;

[0112] H (n) represents the observation operator on the scale.

[0113] S42: Based on the multi-grid algorithm, gradually perform grid coarsening processing on the optimized multi-network until it is smoothed to the coarsest network.

[0114] Specifically, the multi-grid method is used to solve the variational assimilation equation, that is, the assimilation equation is approximated by step-by-step smoothing, and the assimilation result is corrected step by step, achieving the effect of multi-scale information correction.

[0115] S43: Perform network interpolation processing in turn, and correspondingly obtain the analysis field;

[0116] The formula of the analysis field is as follows:

[0117]

[0118] In the formula, X a represents the final analysis field after assimilation;

[0119] X b represents the model initial field;

[0120] ε (n) represents the analysis result on each heavy grid.

[0121] Specifically, the multi-grid algorithm solves the objective function of the variational method, starting from the model grid of the assimilation grid, and gradually coarsens the grid to the coarsest grid.

[0122] The first calculation is performed from the coarsest grid, and the obtained analysis field is gradually interpolated to finer grids. The final analysis result is represented as the superposition of the analysis results on each heavy grid, realizing the scale-by-scale optimization of the objective function. The final analysis field is as follows:

[0123]

[0124] S5: determining a precision calculation formula based on the sample observation value and the sample analysis value, and a precision threshold value;

[0125] obtaining the sample observation value of the sample to be analyzed in the target area and determining the sample analysis value of the sample to be analyzed according to the analysis field, and calculating the calculation precision corresponding to the sample to be analyzed based on the precision calculation formula;

[0126] The precision calculation formula is as follows:

[0127]

[0128] In the formula, represents the sample observation value of the sample to be analyzed i; represents the sample analysis value of the sample to be analyzed i;

[0129] obtaining the sample observation value of the sample to be analyzed in the target area and determining the sample analysis value of the sample to be analyzed according to the analysis field, and calculating the calculation precision corresponding to the sample to be analyzed based on the precision calculation formula.

[0130] The numerical value of the calculation precision is compared with the precision threshold value;

[0131] If the calculation precision is greater than or equal to the precision threshold value, the analysis field is iteratively updated for the simulation field, and steps S1-S5 are repeated until the calculation precision is less than the precision threshold value, and the corresponding sample analysis value is output.

[0132] The embodiments of the present application are described in detail above, but the content is only the preferred embodiments of the present application, and cannot be considered as limiting the scope of the present application. Any equivalent changes and improvements made within the scope of the present application should still belong to the patent coverage of the present application.

Claims

1. A marine meteorological data assimilation method based on adaptive scaling decomposition, characterized in that, include: S1: Obtain the raw dataset of the target region, including the observation field and the numerical model forecast field; among them, the output of the long-term spin-up of the ocean numerical model is used as the observation field; random noise is added to the initial field module to make the numerical model spin-up to a stable forecast as the simulation field; The original dataset is preprocessed to obtain a two-dimensional matrix. S2: The two-dimensional matrix is ​​decomposed using EOF, resulting in several spatial modes. Based on the correlation of spatial points in each spatial mode, feature extraction is performed for several spatial modes respectively, and a spatial adaptive downscaling model is constructed by using the positive and negative signs of the correlation coefficient in each spatial mode. Based on the adaptive downscaling model, spatial points are filtered to obtain the corresponding spatial point distribution; S3: Based on the filtered spatial point distribution, assimilation grids of various scales are set one by one to obtain a multi-assimilation network corresponding to several spatial modes, including several assimilation grids of different scales. S4: Determine the target functional of assimilation grids at different scales based on multiple assimilation grids; The objective functional is subjected to multi-scale assimilation, and the final results are superimposed to obtain the analysis field. Step S4 includes: S41: Determine the objective functional for optimizing the multi-network; the incremental form of the objective functional is shown below: ； In the formula, Indicates the first Layered assimilation network, ; Indicates the relationship with the first Observational increments for background field matching at scale; and These represent the background field error and observation error covariance matrices at the corresponding scales, respectively. This represents the observation operator at that scale; S42: Based on the multi-grid algorithm, the multi-grid optimization is gradually coarsened until it is smoothed to the coarsest grid. S43: Perform network interpolation processing sequentially to obtain the analysis field accordingly; The formula for the analytical field is shown below: ; In the formula, This represents the final analytical field after assimilation; Indicates the initial field of the mode; This represents the analysis results on each grid.

2. The marine meteorological data assimilation method based on adaptive scaling decomposition according to claim 1, characterized in that, Step S1 includes: S11: Obtain the observation field of the target area; obtain the simulated field of the target area by adding random noise; S12: Determine the original dataset including the observation field and the simulation field; S13: For the original dataset, perform spatiotemporal matching processing and outlier and missing value processing in sequence to obtain a two-dimensional matrix X of time sample m × number of spatial points n; The structure of the two-dimensional matrix X is shown below: .

3. The marine meteorological data assimilation method based on adaptive scaling decomposition according to claim 1, characterized in that, Step S2 includes: S21: Based on EOF, extraction processing is performed on a two-dimensional matrix to obtain several spatial modes accordingly; Based on the correlation of spatial points in each spatial mode, feature extraction is performed for several spatial modes respectively, and a spatial adaptive downscaling model is constructed by using the positive and negative signs of the correlation coefficient in each spatial mode. S22: Perform arbitrary point selection operation on the points to be selected for each spatial mode, and obtain the selected points accordingly.

4. The marine meteorological data assimilation method based on adaptive scaling decomposition according to claim 1, characterized in that, Step S3 includes: S31: Determine whether the correlation coefficient between the filtered spatial points and the remaining points in the current spatial mode is greater than 0; S32: If the value is greater than 0, the selected point and the unselected points with a correlation coefficient greater than 0 with the selected point will be assigned to set C; If the value is less than 0, the selected point is assigned to set F and the points in set F are removed. S33: Repeat steps S31 to S32 to obtain a multiple assimilation network that includes assimilation networks of several different scales.

5. The marine meteorological data assimilation method based on adaptive scaling decomposition according to claim 1, characterized in that, Also includes: S5: Determine the accuracy calculation formula based on sample observations and sample analysis values, as well as the accuracy threshold; The system acquires the sample observation values ​​of the sample to be analyzed in the target area and determines the sample analysis values ​​of the sample to be analyzed based on the analysis field, and calculates the calculation accuracy corresponding to the sample to be analyzed based on the accuracy calculation formula. The accuracy calculation formula is as follows: ; In the formula, Indicates the sample to be analyzed The sample observations; Indicates the sample to be analyzed The sample analysis values.

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