Wind field data fusion method based on principal component analysis method

Abstract

The invention discloses a wind field data fusion method based on a principal component analysis method, and the method comprises the following steps: (1), carrying out the PCA decomposition of a data matrix of mode prediction and a new data matrix of replaced observation data in a preset fusion region; (2) respectively selecting first s modals and time coefficients corresponding to the first s modals, reconstructing and generating main items of two groups of data, calculating residual information of an original data matrix after the main items are removed, and replacing the main items of the original data matrix with main items of new data (3) in combination with the residual information of the original data matrix, obtaining fresh air field data fused with observation data; according to the method, the credibility of the mode forecast data is improved, and the diversity of the data is fully embodied.

Description

Technical Field

[0001] The invention relates to the field of atmospheric science and technology, and in particular to a wind field data fusion method based on principal component analysis. Background Art

[0002] In meteorology and related fields, there is an increasing demand for single-variable high-resolution forecasts, which requires forecast systems to accurately capture and predict subtle changes in the atmosphere. However, a series of challenges have been encountered when applying traditional data assimilation techniques to ultra-high-resolution numerical forecast models, especially in areas or periods where observational data are scarce.

[0003] Traditional data assimilation methods, such as the three-dimensional variational method, not only rely on large computer resources, but also consume huge resources when maintaining a continuously operating assimilation system. It usually goes through multiple links such as global model forecast, regional model forecast, data release and download, data processing and application, and each link takes a certain amount of time. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a wind field data fusion method based on principal component analysis, which adaptively extracts spatial modes and time coefficients through principal component analysis (PCA), and uses the basis function adjustment function of PCA to solve the problem of fusing the current situation where only sparse observation data is available with high-resolution model forecast results.

[0005] Technical solution: The wind field data fusion method based on principal component analysis described in the present invention comprises the following steps:

[0006] (1) In the pre-set fusion area, PCA decomposition is performed on the model forecast data matrix and the new data matrix of the replaced observation data respectively;

[0007] (2) Select the first s modes and their corresponding time coefficients respectively, reconstruct the main items of the two sets of data, calculate the remaining information after removing the main items from the original data matrix, and replace the main items of the original data matrix with the main items of the new data;

[0008] (3) Combine the remaining information of the original data matrix to obtain new wind field data after integrating the observed data.

[0009] Furthermore, in step (1), the PCA decomposition formulas for the model forecast data matrix and the replaced new data matrix are as follows:

[0010] X=VZ

[0011] Among them, X represents the data matrix; V represents the spatial mode; and Z represents the time coefficient.

[0012] Performing PCA decomposition on the data matrix yields:

[0013] X m×n =V m×n Z n×n

[0014] Among them, X m×n Represents the original data matrix; V m×n Represents the spatial mode; Z n×n Represents the time coefficient; where m represents

[0015] The time dimension, n represents the space dimension; X m×n It is expressed as:

[0016]

[0017] Among them, i represents the i-th moment, and j represents the j-th grid point.

[0018] The observed data x i ′ ,j Substitute into the original data matrix to form a new data matrix X ′ m×n , where X ′ m×n It is expressed as:

[0019]

[0020] Furthermore, step (2) is specifically as follows:

[0021]

[0022] in, Using the following formula:

[0023]

[0024] Among them, X m×n Decomposed into two parts, X 1-s Indicates the modality of the first s items, i.e. the main item; X res Represents the residual mode, that is, the remainder, where v i represents the spatial mode of the i-th mode; z i represents the time coefficient of the i-th mode;

[0025] Using the following formula:

[0026]

[0027] Furthermore, step (3) is specifically as follows:

[0028]

[0029] Among them, X new Indicates the new wind field data obtained.

[0030] The wind field data fusion system based on principal component analysis method described in the present invention comprises:

[0031] Decomposition module: used to perform PCA decomposition on the model forecast data matrix and the new data matrix of replaced observation data in the pre-set fusion area;

[0032] Replacement module: used to select the first s modes and their corresponding time coefficients respectively, reconstruct the main items of the two sets of data, calculate the remaining information after removing the main items from the original data matrix, and replace the main items of the original data matrix with the main items of the new data;

[0033] Fusion module: used to combine the remaining information of the original data matrix to obtain new wind field data after fusing the observed data.

[0034] Furthermore, in the decomposition module, the PCA decomposition formulas for the model forecast data matrix and the replaced new data matrix are as follows:

[0035] X=VZ

[0036] Among them, X represents the data matrix; V represents the spatial mode; and Z represents the time coefficient.

[0037] Performing PCA decomposition on the data matrix yields:

[0038] X m×n =V m×n Z n×n

[0039] Among them, X m×n Represents the original data matrix; V m×n Represents the spatial mode; Z n×n Represents the time coefficient; where m represents

[0040] The time dimension, n represents the space dimension; X m×n It is expressed as:

[0041]

[0042] Among them, i represents the i-th moment, and j represents the j-th grid point.

[0043] The observed data x i ′ ,j Substitute into the original data matrix to form a new data matrix X ′ m×n , where X ′m×n It is expressed as:

[0044]

[0045] Further, in the replacement module, the details are as follows:

[0046]

[0047] in, Using the following formula:

[0048]

[0049] Among them, X m×n Decomposed into two parts, X 1-s Indicates the modality of the first s items, i.e. the main item; X res Represents the residual mode, that is, the remainder, where v i represents the spatial mode of the i-th mode; z i represents the time coefficient of the i-th mode;

[0050] Using the following formula:

[0051]

[0052] Furthermore, in the fusion module, the details are as follows:

[0053]

[0054] Among them, X new Indicates the new wind field data obtained.

[0055] An electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, it implements any one of the wind field data fusion methods based on principal component analysis.

[0056] A storage medium described in the present invention stores a computer program, and when the computer program is executed by a processor, it implements any one of the wind field data fusion methods based on principal component analysis.

[0057] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention can be well applied to the fusion requirements of sparse observation data and high-resolution model forecast results, and can quickly fuse sparse observation data into high spatial resolution model forecast results, and can adaptively fuse sparse observation information with high-resolution model results according to different weather characteristics, which not only improves the credibility of model forecast data, but also makes the diversity of data fully reflected. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 a is the wind field u before fusion at 18:00 on September 5, 2021, Figure 1 b is the ERA5u wind field at 18:00 on September 5, 2021, Figure 1 c is the wind field of ERA5 minus u before fusion at 18:00 on September 5, 2021 (unit: m / s);

[0059] Figure 2 a is the wind field u after the main items of the original data are reconstructed by replacing the main items of the new data with the main items of the first 6 modes of the new data of the present invention, Figure 2 b is the data after ERA5 minus fusion (unit: m / s);

[0060] Figure 3 a is the v wind field before fusion at 18:00 on September 5, 2021 in this embodiment 2, Figure 3 b is the ERA5v wind farm at 18:00 on September 5, 2021, Figure 3 c is the wind field of ERA5 minus v before fusion at 18:00 on September 5, 2021 (unit: m / s);

[0061] Figure 4 a is the wind field v after the new data of the present invention replaces the original data main item with the first 6 modal main items, Figure 4 b is the data after ERA5 minus fusion (unit: m / s);

[0062] Figure 5 a is the uv wind field before fusion at 18:00 on September 5, 2021, Figure 5 b is the ERA5uv wind field at 18:00 on September 5, 2021, Figure 5 c is the uv wind field (unit: m / s) after the main items of the original data are reconstructed by replacing the main items of the first 6 modes of the new data. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0064] Example 1

[0065] This embodiment selects ERA5 reanalysis data and FNLu wind field reanalysis data in the 132-133°E, 15-16°N area from September 1 to 5, 2021, where the time resolution is 6 hours and the spatial resolution is 0.25°×0.25°, and uses ERA5 reanalysis data as observation data to introduce the present invention.

[0066] S1, in the pre-set fusion area 132-133°E, 15-16°N, select the ERA5 data of any point to replace the FNL data at the same location. Here, the grid point 132.5°E, 15.5°N at 18:00 on September 5, 2021 is selected. Figure 1 a is the u wind field before fusion at 18:00 on September 5, 2021, Figure 1 b is the ERA5u wind field at 18:00 on September 5, 2021, Figure 1 c is the wind field u before ERA5 minus fusion at 18:00 on September 5, 2021. The data matrix of the model forecast and the new data matrix that replaced the observed data were decomposed by PCA to obtain the time coefficient and spatial mode.

[0067] S2, respectively selects the first 6 modes and their corresponding time coefficients, reconstructs the main terms of the two sets of data, calculates the remaining information after removing the main terms from the original data matrix, and further replaces the main terms of the original data matrix with the main terms of the new data.

[0068] S3, combined with the remaining information of the original data matrix, obtains the new wind field data after fusion of the observed data. Figure 2 a is the wind field u after the main items of the original data are reconstructed by replacing the main items of the original data with the main items of the first 6 modes of the new data. Figure 2 b is the data after ERA5 minus the fusion data. It can be seen that the difference between the fusion data and the ERA5 data is smaller.

[0069] Example 2

[0070] This embodiment selects the v wind field of the area selected in Embodiment 1, and fuses the wind field data using the same method as Embodiment 1.

[0071] Depend on Figure 3 c and Figure 4 From the comparison of b, it can be seen that the difference between the fused v wind field and ERA5 is much smaller.

[0072] In addition, the u wind field and the v wind field are synthesized by Figure 5 The analysis shows that the fused wind field is closer to the ERA5 wind field.

Claims

1. A wind field data fusion method based on principal component analysis, characterized in that: The following steps are involved: (1) In the pre-set fusion area, PCA decomposition is performed on the model forecast data matrix and the new data matrix of the replaced observation data respectively; (2) Select the first s modes and their corresponding time coefficients respectively, reconstruct the main items of the two sets of data, calculate the remaining information after removing the main items from the original data matrix, and replace the main items of the original data matrix with the main items of the new data; (3) Combine the remaining information of the original data matrix to obtain new wind field data after integrating the observed data.

2. The wind field data fusion method based on principal component analysis according to claim 1 is characterized in that: In step (1), the PCA decomposition formulas for the model forecast data matrix and the replaced new data matrix are as follows: X=VZ Among them, X represents the data matrix; V represents the spatial mode; and Z represents the time coefficient. Performing PCA decomposition on the data matrix yields: X mm×nn =V mm×nn Z nn×nn Among them, X m×n Represents the original data matrix; V m×n Represents the spatial mode; Z n×n represents the time coefficient; m represents the time dimension, n represents the space dimension; X m×n It is expressed as: Among them, i represents the i-th moment, and j represents the j-th grid point. The observed data x i ′ ,j Substitute into the original data matrix to form a new data matrix X ′ m×n , where X ′ m×n It is expressed as:

3. A wind field data fusion method based on principal component analysis according to claim 2, characterized in that: Step (2) is as follows: in, Using the following formula: Among them, X mm×nn Decomposed into two parts, X 1-ss Indicates the modality of the first s items, i.e. the main item; X rrrrss Represents the residual mode, that is, the remainder, where v ii represents the spatial mode of the i-th mode; z ii represents the time coefficient of the i-th mode; Using the following formula:

4. A wind field data fusion method based on principal component analysis according to claim 3, characterized in that: Step (3) is as follows: Among them, X nnrrnn Indicates the new wind field data obtained.

5. A wind field data fusion system based on principal component analysis, characterized in that: include: Decomposition module: used to perform PCA decomposition on the model forecast data matrix and the new data matrix of replaced observation data in the pre-set fusion area; Replacement module: used to select the first s modes and their corresponding time coefficients respectively, reconstruct the main items of the two sets of data, calculate the remaining information after removing the main items from the original data matrix, and replace the main items of the original data matrix with the main items of the new data; Fusion module: used to combine the remaining information of the original data matrix to obtain new wind field data after fusing the observed data.

6. A wind field data fusion system based on principal component analysis method according to claim 5, characterized in that: In the decomposition module, the PCA decomposition formulas for the model forecast data matrix and the replaced new data matrix are as follows: X=VZ Among them, X represents the data matrix; V represents the spatial mode; and Z represents the time coefficient. Performing PCA decomposition on the data matrix yields: X mm×nn =V mm×nn Z nn×nn Among them, X m×n Represents the original data matrix; V m×n Represents the spatial mode; Z n×n represents the time coefficient; m represents the time dimension, n represents the space dimension; X m×n It is expressed as: Among them, i represents the i-th moment, and j represents the j-th grid point. The observed data x i ′ ,j Substitute into the original data matrix to form a new data matrix X ′ m×n , where X ′ m×n It is expressed as:

7. A wind field data fusion system based on principal component analysis method according to claim 6, characterized in that: In the replacement module, the details are as follows: in, Using the following formula: Among them, X mm×nn Decomposed into two parts, X 1-ss Indicates the modality of the first s items, i.e. the main item; X rrrrss Represents the residual mode, that is, the remainder, where v ii represents the spatial mode of the i-th mode; z ii represents the time coefficient of the i-th mode; Using the following formula:

8. A wind field data fusion system based on principal component analysis method according to claim 7, characterized in that: In the fusion module, the details are as follows: Among them, X nnrrnn Indicates the new wind field data obtained.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into a processor, a wind field data fusion method based on principal component analysis according to any one of claims 1 to 4 is implemented.

10. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a wind field data fusion method based on principal component analysis according to any one of claims 1 to 4 is implemented.

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