An evaluation method for an ocean meteorological data assimilation scheme based on linear decomposition

Abstract

This application relates to the field of marine meteorological data assimilation technology, and particularly to an evaluation method for a marine meteorological data assimilation scheme based on linear decomposition. The method includes: determining a scale decomposition evaluation model; obtaining an original error signal, performing linear decomposition on the original error signal to determine an initial decomposition scheme, and evaluating it through the scale decomposition evaluation model; if the sum of the scale terms is positive, the decomposition is effective, and the initial decomposition scheme is output; if the sum of the scale terms is negative, the decomposition is ineffective; determining the scale terms that are negative, and based on the negative scale terms, re-determining the scale requirements of the error signal and performing re-decomposition to obtain an updated decomposition scheme; repeating the above steps and evaluating the updated decomposition scheme until the evaluation is effective. This application calculates parameters through an explicit evaluation formula, which can not only evaluate the effectiveness of the scale decomposition scheme in data assimilation, but also quantify the reasons for the decomposition failure, and guide the optimization scheme to further explore the linear correlation in the space.

Description

Technical Field

[0001] The present application relates to the technical field of marine meteorological data assimilation, and particularly relates to an evaluation method for a marine meteorological data assimilation scheme based on linear decomposition. Background Art

[0002] In the field of marine meteorology, the advantage of multi-scale data assimilation lies in its ability to smooth error components of different scales, integrate the decorrelation scale effects between scales, and theoretically weaken error components within all scale ranges layer by layer to obtain an optimal initial field. In fact, traditional data assimilation methods are all based on linear assumptions, while the real fields of the atmosphere and ocean are non-linear.

[0003] An ideal scale initial decomposition scheme can completely decompose a non-linear signal into a superposition of linear signals of different scales according to the natural laws of spatio-temporal changes, but there are difficulties in practical applications. Currently, the scale initial decomposition scheme for multi-scale assimilation selects empirical filtering parameter settings under the influence of factors such as computational resources and difficulties in implementing the cost function, and thus can only achieve a linear approximation, without discussing or explaining the treatment of the remaining non-linear part.

[0004] Therefore, how to objectively perform "optimal" scale decomposition of background errors, objectively evaluate the quality of scale decomposition, and perform feedback adjustment through evaluation results is the key problem faced by current multi-scale data assimilation. Summary of the Invention

[0005] The present application provides an evaluation method for a marine meteorological data assimilation scheme based on linear decomposition, which can solve the problems of how to objectively perform "optimal" scale decomposition of background errors, objectively evaluate the "quality" of scale decomposition, and perform feedback adjustment through evaluation results.

[0006] The technical solution of the present application is an evaluation method for a marine meteorological data assimilation scheme based on linear decomposition, including:

[0007] S1: Based on the scale requirements of the error signal, perform linear decomposition on the original error signal, and correspondingly obtain a number of error signals of different scales, and correspondingly determine a scale decomposition evaluation model for evaluating error signals of different scales from different original error signals through a number of scale terms;

[0008] S2: Obtain a number of original error signals regarding the target area;

[0009] Determine the scale requirements of the error signal regarding the target area, and based on the scale requirements of the error signal of the target area, perform linear decomposition on each original error signal of the target area, and correspondingly determine the initial decomposition scheme regarding the target area;

[0010] S3: Evaluate the initial decomposition scheme through the scale decomposition evaluation model based on the positive or negative of the scale terms and the positive or negative of the sum of several scale terms;

[0011] If the sum of several scale terms is positive, evaluate the decomposition as effective and output the initial decomposition scheme;

[0012] S4: If the sum of several scale terms is negative, evaluate the decomposition as ineffective;

[0013] Determine the scale terms that are negative. Based on the scale terms that are negative, re-determine the scale requirement of the error signal for the target area, and based on the re-determined scale requirement of the error signal for the target area, re-decompose each original error signal for the target area, and correspondingly obtain an updated decomposition scheme; repeat steps S3 - S4 to evaluate the updated decomposition scheme until the evaluation of the updated decomposition scheme is effective, and output the updated decomposition scheme.

[0014] Optionally, step S1 includes:

[0015] S11: Perform linear decomposition on the original error signal regarding ocean data based on the scale requirement of the error signal, and correspondingly obtain several error signals of different scales;

[0016] When decomposing to obtain error signals of two scales, the decomposition formula is as follows:

[0017]

[0018] In the formula, X a and Y a respectively represent different original error signals;

[0019] and both represent large-scale signals; and represent small-scale signals;

[0020] S12: According to the decomposition formula, correspondingly determine the scale decomposition evaluation model for evaluating different-scale error signals from different original error signals through several scale terms;

[0021] The scale decomposition evaluation model is as follows:

[0022]

[0023] In the formula, cov(X a , Y a ) represents the covariance of the original error signal between spatial points;

[0024] and is a scale term, representing the covariance of the large-scale error signal, representing the covariance of the small-scale error signal;

[0025] and are cross-correlation terms, both representing the cross-covariance between error signals of different scales.

[0026] Optionally, in step S2, linear decomposition is performed on each original error signal of the target area by EOF / FFT, and accordingly, an initial decomposition scheme for the target area is determined.

[0027] Optionally, step S2 includes:

[0028] S21: Obtain a number of original error signals regarding the target area;

[0029] S22: Determine the scale requirements of a number of error signals regarding the target area;

[0030] S23: Based on the scale requirements of a number of error signals of the target area, perform linear decomposition on each original error signal of the target area respectively, and accordingly determine a number of initial decomposition schemes regarding the target area and corresponding to different error signal scale requirements respectively;

[0031] Step S3 includes:

[0032] S31: Based on the positive or negative of the scale terms and the positive or negative of the sum of a number of scale terms, evaluate each initial decomposition scheme through a scale decomposition evaluation model, including whether the decomposition is effective and the decomposition effect;

[0033] S32: In each initial decomposition scheme, if the sum of a number of scale terms is positive, evaluate the decomposition as effective and output the initial decomposition scheme;

[0034] S33: In each initial decomposition scheme evaluated as having an effective decomposition, if the sum of the covariances of a number of scale term error signals is greater than the covariance of the original error signal, the greater the sum of the covariances of a number of scale term error signals, the stronger the linear correlation between spatial points is evaluated. If the cross-correlation term is negative, the greater the absolute value of the cross-correlation term, the better the decomposition effect is evaluated.

[0035] Optionally, step S4 includes:

[0036] S41: If the sum of a number of scale terms is positive and the cross-correlation term is negative, evaluate the decomposition effect as better;

[0037] S42: If the sum of several scale terms is negative, the evaluation is that the decomposition is invalid; for the scale terms determined to be negative, based on the negative scale terms, re-determine the scale requirement of the error signal for the target area, and based on the re-determined scale requirement of the error signal for the target area, re-decompose each original error signal for the target area, and accordingly obtain an updated decomposition scheme; repeat steps S3 - S4 above to evaluate the updated decomposition scheme until the evaluation of the updated decomposition scheme is effective, and output the updated decomposition scheme;

[0038] S43: For several initial decomposition schemes / updated decomposition schemes evaluated as effectively decomposed, select the best decomposition scheme according to the decomposition effect.

[0039] Advantageous effects:

[0040] The present application provides a scale decomposition evaluation model for multi-scale data assimilation, which uses an explicit evaluation formula for parameter calculation. It can not only evaluate the effectiveness of the scale decomposition scheme, but also further guide the improvement of the spatial linear correlation. The goal of scale decomposition is to improve the scale terms in the evaluation formula, so that the correlation coefficient of the spatial points after decomposition can obtain a higher value, which only needs to be higher than that before decomposition. It can also be adjusted according to the evaluation results. Therefore, the scale decomposition evaluation model improves the theoretical framework of the multi-scale data assimilation method and provides a new idea for its optimization;

[0041] Therefore, the present application can solve the problems of how to objectively perform "optimal" scale decomposition on background errors, objectively evaluate the "good or bad" of scale decomposition, and perform feedback adjustment based on the evaluation results. Description of the drawings

[0042] In order to more clearly illustrate the technical solutions of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0043] Figure 1 It is a schematic flowchart of an evaluation method for a marine meteorological data assimilation scheme based on linear decomposition in an embodiment of the present application;

[0044] Figure 2 It is a schematic logical diagram of linear decomposition for an original error signal in an embodiment of the present application;

[0045] Figure 3 It is a schematic logical diagram of evaluating an initial decomposition scheme through a scale decomposition evaluation model in an embodiment of the present application;

[0046] Figure 4It is the frequency distribution diagram of the spatial filtering scheme of the target algorithm for two scales in the embodiment of the present application;

[0047] Figure 5 It is the numerical distribution diagram of the cross - correlation term between the single - point and the spatial point for two scales in the embodiment of the present application;

[0048] Figure 6 It is the numerical distribution diagram of the cross - correlation term between the single - point and the spatial point for five scales in the embodiment of the present application. Detailed implementation manners

[0049] The embodiments will be described in detail below, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following embodiments do not represent all implementation manners consistent with the present application. They are only examples of systems and methods consistent with some aspects of the present application detailed in the claims.

[0050] The present application provides an evaluation method for an ocean meteorological data assimilation scheme based on linear decomposition, as Figure 1 shown, Figure 1 It is the flow schematic diagram of the evaluation method for the ocean meteorological data assimilation scheme based on linear decomposition in the embodiment of the present application, including:

[0051] S1: Based on the scale requirements of the error signal, perform linear decomposition on the original error signal, and accordingly obtain several error signals of different scales, and accordingly determine a scale decomposition evaluation model for evaluating the error signals of different scales from different original error signals through several scale terms.

[0052] Specifically, analyze the spatio - temporal characteristics of the background field error of the numerical model, and use the spatial filtering scheme of the target algorithm to divide different scales.

[0053] Among them, step S1 includes:

[0054] S11: Based on the scale requirements of the error signal, perform linear decomposition on the original error signal regarding ocean data, and accordingly obtain several error signals of different scales;

[0055] When decomposing to obtain error signals of two scales, the decomposition formula is as follows:

[0056]

[0057] In the formula, Xa and Ya respectively represent different original error signals;

[0058] and both represent large - scale signals; and represent small-scale signals.

[0059] S12: According to the decomposition formula, accordingly determine a scale decomposition evaluation model for evaluating error signals of different scales from different original error signals through a number of scale terms;

[0060] The scale decomposition evaluation model is as follows:

[0061]

[0062] where cov(X a , Y a ) represents the covariance of the original error signal between spatial points;

[0063] and are scale terms, represents the covariance of the large-scale error signal, represents the covariance of the small-scale error signal;

[0064] and are cross-correlation terms, both representing the cross-covariance between error signals of different scales.

[0065] Specifically, as Figure 2 shown, Figure 2 is a logical schematic diagram for linear decomposition of the original error signal in the embodiment of the present application. The above formula explicitly decomposes the original signal into two scale signals, large scale and small scale. The left side of the equation is the covariance of the original signal between spatial points, and the right side is the superposition of the covariance of different scale signals and the cross-covariance between different scales, which are called scale terms and cross-correlation terms.

[0066] S2: Obtain a number of original error signals regarding the target area;

[0067] Determine the error signal scale requirement regarding the target area, and based on the error signal scale requirement of the target area, perform linear decomposition on each original error signal of the target area, and accordingly determine an initial decomposition scheme regarding the target area.

[0068] Specifically, use the spatial filtering scheme of the target algorithm to decompose into different scales according to the spatio-temporal distribution law of the error, calculate the covariance cov(X a , Y a ), the scale terms of each scale and the cross-correlation terms between different scales.

[0069] Among them, step S2 includes:

[0070] S21: Obtain a number of original error signals regarding the target area;

[0071] S22: Determine a number of error signal scale requirements regarding the target area;

[0072] S23: Based on the number of error signal scale requirements of the target area, perform linear decomposition on each original error signal of the target area respectively, and accordingly determine a number of initial decomposition schemes regarding the target area and corresponding to different error signal scale requirements respectively.

[0073] Specifically, since the scale decomposition schemes of different multi-scale data assimilations can all be reduced to linear filtering decompositions, taking the two related scales of large scale and small scale as an example to discuss the rationality of reduction and approximation problems in scale decomposition.

[0074] There are many methods for the spatial filtering scheme of the target algorithm. If the Fourier (FFT) decomposition algorithm is used, that is, the error signal is artificially decomposed into high frequency and low frequency. Similar to the decomposition schemes of most multi-scale data assimilations, this decomposition method is empirical and not objective. If the empirical orthogonal function (EOF) decomposition algorithm is used, natural scale decomposition can be achieved.

[0075] Using the spatial filtering scheme of the target algorithm, it is decomposed into different scales according to the spatio-temporal distribution law of the error, and the covariance cov(X a , Y a ) of the original signal, the scale terms of each scale and the cross-correlation terms between different scales are calculated.

[0076] In the FFT decomposition, the cross-correlation terms are usually negative, so the evaluation result of the decomposition scheme can be obtained only through the magnitude of the cross-correlation terms. Since it is calculated that the numerical value of the cross-correlation terms in the EOF decomposition is zero, it is necessary to discuss the decomposition effect of calculating the scale terms, and the calculation amount is relatively large.

[0077] In actual operation, the historical ocean reanalysis data is sourced from the CORA reanalysis data provided by the National Marine Information Center. The data format is in NetCDF format, and the NetCDF is read and stored using the MATLAB program. The specific program steps are as follows:

[0078] (1) Determine the time range and spatial range of the required data, which is determined by setting the date and longitude and latitude;

[0079] (2) Judge whether the year is a leap year. If it is a leap year, the 29th day of February of that year is excluded;

[0080] (3) Read the required longitude, latitude and sea surface temperature. Here, 99°E - 150°E and 10°S - 52°N are selected;

[0081] (4) Since the CORA dataset is variable-grid data, a specific grid of 1 / 2 grid is selected in this experiment;

[0082] (5) Repeat steps (3) and (4) until the required longitude, latitude, year, month, and day data are selected.

[0083] In this embodiment, in order to remove the annual cycle signal, the data is detrended, and the long-term relatively stable or slowly varying components of the original sequence are removed.

[0084] The data sequence f(x, y, z, t) can be detrended as follows:

[0085]

[0086] Among them, Take the annual average sea surface temperature from 1960 to 2016.

[0087] The error signal statistically analyzed from the reanalysis data is decomposed by FFT into different scales. Taking two scales as an example, calculate the covariance cov(X a , Y a ) of the original signal, the scale terms of each scale and the cross-correlation terms between different scales.

[0088] In the embodiment of this application, each original error signal can be decomposed into two scales and five scales respectively, and then the decomposition scheme and decomposition effect are discussed. The decomposition scheme of two scales divides it into two correlated scales of large scale and small scale, which is the simplest scale decomposition method.

[0089] S3: Based on the positive and negative of the scale terms and the positive and negative of the sum of several scale terms, evaluate the initial decomposition scheme through the scale decomposition evaluation model;

[0090] If the sum of several scale terms is positive, it is evaluated that the decomposition is effective, and the initial decomposition scheme is output.

[0091] Among them, step S3 includes:

[0092] S31: Based on the positive and negative of the scale terms and the positive and negative of the sum of several scale terms, evaluate each initial decomposition scheme through the scale decomposition evaluation model for including whether the decomposition is effective and the decomposition effect;

[0093] S32: In each initial decomposition scheme, if the sum of several scale terms is positive, it is evaluated that the decomposition is effective, and the initial decomposition scheme is output;

[0094] S33: In each initially decomposed solution evaluated as effectively decomposed, if the sum of the covariances of several scale - term error signals is greater than the covariance of the original error signal, the greater the sum of the covariances of the several scale - term error signals, the stronger the evaluated linear correlation between spatial points. If the cross - correlation term is negative, the greater the absolute value of the cross - correlation term, the better the evaluated decomposition effect.

[0095] Specifically, as Figure 3 shown, Figure 3 is a logical schematic diagram for evaluating the initially decomposed solution through the scale - decomposition evaluation model in the embodiment of the present application. First, calculate the values of the scale terms and the cross - correlation terms. When all scale terms are positive, the scale - decomposition solution is effective, and the covariance after the superposition of the scale terms is greater than that of the original signal, that is, the linear correlation between spatial points is stronger. At the same time, the greater the negative value of the cross - correlation term, the greater the absolute value means the better the decomposition effect.

[0096] As Figure 4 、 Figure 5 and Figure 6 shown, Figure 4 is the frequency distribution diagram of the spatial filtering scheme of the target algorithm for two scales in the embodiment of the present application, Figure 5 is the numerical distribution diagram of the cross - correlation terms between a single point and spatial points for two scales in the embodiment of the present application, Figure 6 is the numerical distribution diagram of the cross - correlation terms between a single point and spatial points for five scales in the embodiment of the present application.

[0097] S4: If the sum of several scale terms is negative, it is evaluated as ineffective decomposition;

[0098] Determine the scale terms that are negative. Based on the negative scale terms, re - determine the scale requirements of the error signal for the target region, and based on the re - determined scale requirements of the error signal for the target region, re - decompose each original error signal for the target region, and correspondingly obtain an updated decomposition solution; repeat steps S3 - S4 to evaluate the updated decomposition solution until the evaluation of the updated decomposition solution is effective, and output the updated decomposition solution.

[0099] Step S4 includes:

[0100] S41: If the sum of several scale terms is positive and the cross - correlation term is negative, it is evaluated that the decomposition effect is better;

[0101] S42: If the sum of several scale terms is negative, it is evaluated that the decomposition is invalid; for the scale terms determined to be negative, based on the negative scale terms, re-determine the scale requirement of the error signal for the target area, and based on the re-determined scale requirement of the error signal for the target area, re-decompose each original error signal for the target area, and accordingly obtain an updated decomposition scheme; repeat steps S3 - S4, evaluate the updated decomposition scheme until the evaluation of the updated decomposition scheme is valid, and output the updated decomposition scheme;

[0102] S43: For several initial decomposition schemes / updated decomposition schemes evaluated as having valid decompositions, select the best decomposition scheme according to the decomposition effect.

[0103] Specifically, when the scale terms have different signs, count the positive and negative values of the sum of the scale terms. When the value is positive after all the scale terms are superimposed, the cross-correlation term is negative at this time, which means the scale decomposition scheme is valid; otherwise, the scale decomposition scheme is invalid. The scale terms with negative values can be further optimized to improve the decomposition effect.

[0104] In the embodiment of the present application, the sum of the scale terms of the spatial points of the two-layer decomposition scheme is positive and the sum of the cross-correlation terms is negative, but its absolute value is small. When the cross-correlation term is negative, the superposition of the single-scale correlations after scale decomposition

[0105] is higher than the correlation between the two points before decomposition, which means that the scale decomposition has a positive effect. Therefore, it can be judged that the decomposition scheme of the two scales is valid.

[0106] If the scale decomposition scheme increases the number of layers of scale decomposition to 5 scales, as Figure 6 shown, the sum of the scale terms of the spatial points is positive and the sum of the cross-correlation terms is negative. Substituting into the evaluation formula, it can be judged that the decomposition scheme of the five scales is valid.

[0107] By comparing the two decomposition schemes, it can be found that the absolute value of the cross-correlation term obtained by the decomposition scheme of the five scales is significantly increased compared with the cross-correlation term of the two scales. Substituting into the evaluation formula, it can be obtained that the superposition value of the scale terms obtained by the decomposition scheme of the five scales is greater than the superposition of the scale terms of the two scales. Thus, it can be judged that the decomposition scheme of the five scales is more "optimal".

[0108] The above has described the embodiments of the present application in detail, but the content is only the preferred embodiments of the present application and cannot be considered as limiting the scope of implementation of the present application. All equivalent changes and improvements made according to the scope of the present application should still fall within the scope covered by the patent of the present application.

Claims

1. An evaluation method for an ocean meteorological data assimilation scheme based on linear decomposition, characterized in that, Including: S1: Based on the scale requirement of the error signal, perform linear decomposition on the original error signal, and correspondingly obtain several error signals of different scales, and correspondingly determine a scale decomposition evaluation model for evaluating the error signals of different scales from different original error signals through several scale terms; S2: Obtain several original error signals regarding the target area; Determine the scale requirement of the error signal regarding the target area, and based on the scale requirement of the error signal of the target area, perform linear decomposition on each original error signal of the target area, and correspondingly determine the initial decomposition scheme regarding the target area; S3: Based on the positive or negative of the scale terms and the positive or negative of the sum of several scale terms, evaluate the initial decomposition scheme through the scale decomposition evaluation model; If the sum of several scale terms is positive, evaluate the decomposition as effective and output the initial decomposition scheme; S4: If the sum of several scale terms is negative, evaluate the decomposition as ineffective; Determine the negative scale terms, based on the negative scale terms, re-determine the scale requirement of the error signal regarding the target area, and based on the re-determined scale requirement of the error signal of the target area, perform re-decomposition on each original error signal of the target area, and correspondingly obtain an updated decomposition scheme; Repeat steps S3 - S4 above to evaluate the updated decomposition scheme until the evaluation of the updated decomposition scheme is effective, and output the updated decomposition scheme; The step S1 includes: S11: Based on the scale requirement of the error signal, perform linear decomposition on the original error signal regarding ocean data, and correspondingly obtain several error signals of different scales; When two scales of error signals are obtained by decomposition, the decomposition formula is as follows: where X a and Y a represent different original error signals respectively; and both represent large-scale signals; and represent small-scale signals; S12: According to the decomposition formula, correspondingly determine a scale decomposition evaluation model for evaluating the error signals of different scales from different original error signals through several scale terms; The scale decomposition evaluation model is as follows: where cov(X a ,Y a ) represents the covariance of the original error signal between spatial points; and are scale terms, representing the covariance of the large-scale error signal, representing the covariance of the small-scale error signal; and are related terms, both representing the cross-covariance between error signals of different scales.

2. The evaluation method for the ocean meteorological data assimilation scheme based on linear decomposition according to claim 1, characterized in that In step S2, perform linear decomposition on each original error signal of the target area through EOF / FFT, and correspondingly determine the initial decomposition scheme regarding the target area.

3. The evaluation method for the ocean meteorological data assimilation scheme based on linear decomposition according to claim 1, characterized in that, The step S2 includes: S21: Obtain several original error signals regarding the target area; S22: Determine several scale requirements of the error signal regarding the target area; S23: Based on several scale requirements of the error signal of the target area, perform linear decomposition on each original error signal of the target area respectively, and correspondingly determine several initial decomposition schemes regarding the target area and corresponding to different error signal scale requirements respectively; The step S3 includes: S31: Based on the positive or negative of the scale terms and the positive or negative of the sum of several scale terms, evaluate each initial decomposition scheme through the scale decomposition evaluation model, including whether the decomposition is effective and the decomposition effect; S32: In each initial decomposition scheme, if the sum of several scale terms is positive, evaluate the decomposition as effective and output the initial decomposition scheme; S33: In each initially decomposed solution evaluated as effectively decomposed, if the sum of the covariances of several scale term error signals is greater than the covariance of the original error signal, the greater the sum of the covariances of the several scale term error signals, the stronger the linear correlation between the evaluated spatial points. If the cross-correlation term is negative, the greater the absolute value of the cross-correlation term, the better the decomposition effect is evaluated.

4. The evaluation method for the marine meteorological data assimilation scheme based on linear decomposition according to claim 1, characterized in that, The said step S4 includes: S41: If the sum of several scale terms is positive and the cross-correlation term is negative, the decomposition effect is evaluated as better; S42: If the sum of several scale terms is negative, the decomposition is evaluated as invalid; determine the scale terms that are negative, based on the negative scale terms, re-determine the error signal scale requirements for the target area, and based on the re-determined error signal scale requirements for the target area, re-decompose each original error signal for the target area, and correspondingly obtain an updated decomposition solution; repeat the said steps S3 - S4, evaluate the updated decomposition solution until the evaluation of the updated decomposition solution is effective, and output the updated decomposition solution; S43: For several initially decomposed solutions / updated decomposition solutions evaluated as effectively decomposed, select the best decomposition solution according to the decomposition effect.

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