Filtering method in ocean climate research and application thereof

Abstract

The application discloses a filtering method in marine climate research and application thereof, and comprises the following steps: (1) Fourier transform is conducted on time or space data x to obtain results in a frequency domain or a wave number domain; (2) a function is used to conduct a truncation processing on the frequency domain or the wave number domain, and low-pass and high-pass filtering frequency domain results are obtained respectively; (3) energy of the low-pass and high-pass filtering results is calculated and analyzed; (4) inverse Fourier transform is conducted on the low-pass filtering frequency domain or wave number domain result, and a large-scale characteristic distribution in the time or space domain can be obtained; (5) when the filtering result meets a filtering quality index in the frequency or wave number domain obtained in the step (3) by 20%, the function parameter in the step (2) belongs to a range of function parameters suitable for scale division; and (6) the filtering result is brought into a marine climate system of the earth to improve accuracy. The application aims to provide a filtering method and application for judging and improving scale division accuracy in marine climate research.

Description

Technical Field

[0001] This invention relates to the field of marine and atmospheric data processing technology, and in particular to a filtering method and its application in marine climate research. Background Technology

[0002] Motion processes at various scales are prevalent in the ocean and atmosphere. Based on spatial scale, they can be categorized into planetary-scale, large-scale, mesoscale, small-scale, and microscale motions. They can also be distinguished by temporal scale. Generally, the larger the spatial scale of a motion process, the larger its corresponding time scale. Currently, widely used filtering methods in this field include the moving average method, coarse-grained method, and Gaussian function or window function method. Observation of the frequency or wavenumber domain obtained by Fourier transform reveals that the low-pass filtered result still retains energy distribution in the high-frequency or high-wavenumber regions. Subtracting the low-pass filtered result from the original data yields the high-pass filtered result. Similarly, observation of the frequency or wavenumber domain obtained by Fourier transform reveals that the high-pass filtered result also retains energy distribution in the low-frequency or low-wavenumber regions. In particular, the total energy of the high-pass filtered result is small; the energy levels of the high-pass filtered results obtained using these methods are comparable in magnitude to those of the regions corresponding to the smaller distinguishing scales. This introduces significant errors into subsequent calculations, thereby affecting the accuracy of analyses of the physical quantity's impact on the Earth's oceanic climate system. Therefore, there is an urgent need for a truncation method in the frequency or wavenumber domain for oceanic climate research at different temporal and spatial scales, as well as a filtering method and its application to improve the accuracy of scale differentiation by evaluating the truncation results. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and to provide a filtering method and application for marine climate research at different time and spatial scales, which introduces truncation processing in the frequency domain or wavenumber domain, and judges the truncation results to improve the accuracy of scale differentiation.

[0004] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0005] A filtering method for marine climate research includes the following steps:

[0006] (1) Obtain the result in the frequency domain or wavenumber domain by taking the Fourier transform of the original time or space data x.

[0007] (2) Using the error function erf, activation function tanh, or sigmoid to analyze the frequency domain or wavenumber domain. After truncation, the low-pass filter frequency domain results were obtained. High-pass filter frequency domain results

[0008] The expression for the error function erf is:

[0009] The expression for the activation function tanh is:

[0010] The expression for the activation function sigmoid is:

[0011] The error function ERF performs scale differentiation on the spatiotemporal data, i.e., truncation in the three-dimensional frequency-wavenumber domain. The expressions for the resulting low-pass and high-pass filter parts are as follows:

[0012]

[0013]

[0014] When the activation function tanh is truncated, the expressions for the low-pass and high-pass filtering parts in the three-dimensional case are as follows:

[0015]

[0016]

[0017] When the sigmoid activation function is truncated, the low-pass and high-pass filtering parts in the three-dimensional case are expressed as follows:

[0018]

[0019]

[0020] Where ω is the frequency, and k and l are the wavenumber components in the latitudinal and meridional directions, respectively. a is the reciprocal of the time or spatial scale, and b is the inclination of the truncation edge. p, q, and r are function parameters, each taking a value of 0 or 1. When p = q = r = 1, the truncation magnitudes of this function are equal in the three directions; when any one of p, q, and r is equal to 0, the above equation represents truncation in the two-dimensional case; if p = 0, the above equation represents truncation in the two-dimensional wavenumber domain; if q = 0 or r = 0, the above equation represents truncation in the two-dimensional frequency-wavenumber domain.

[0021] (3) The energy of the low-pass and high-pass filtering results is calculated and analyzed. To quantify the filtering quality, 'a' is used as the target to distinguish frequencies or wavenumbers. The energy of the ideal low-pass filtering result is then calculated as follows: The energy of the ideal high-pass filter result is The effective portion is defined as the energy component within the desired distinguishing scale range in the frequency domain after filtering, and the error portion is defined as the energy component outside the desired distinguishing scale range in the frequency domain after filtering. The following four proportions can be obtained:

[0022] ①The effective proportion of the low-pass filter is:

[0023] ②The low-pass filter error ratio is:

[0024] ③ The effective proportion of the high-pass filter is:

[0025] ④ The high-pass filter error ratio is:

[0026] Among them, the closer the effective filtering ratio is to 1, the better the filtering effect; the closer the filtering error ratio is to 0, the better the filtering effect. To obtain a parameter characterizing the overall filtering quality, the filtering quality index is defined as:

[0027] Q = |1-valid L |+|1-valid H |+|error L |+|error H | (1-7)

[0028] Q is the filter quality index;

[0029] (4) Results of low-pass filtering in the frequency domain or wavenumber domain Performing an inverse Fourier transform yields a large-scale feature distribution x in the time or spatial domain. L x L This is the result of low-pass filtering, obtained by subtracting the low-pass filtered result x from the original data x. L Obtain the small-scale feature distribution x H x H This is the result of high-pass filtering;

[0030] (5) When the filtering result satisfies that the filtering quality index Q in the frequency or wavenumber domain obtained in step (3) is less than 20%, i.e. 0.2, and satisfies that the low-pass filtering result feature distribution in the time or spatial domain after inverse transformation in step (4) does not have any outliers exceeding the size of the original data, then the function parameter in step (2) belongs to the range of function parameters suitable for scale differentiation. If the above two judgment criteria cannot be met at the same time, then the function parameter in step (2) does not belong to the range of function parameters suitable for scale differentiation, and it is necessary to return to step (2) to change the size of the function parameter and recalculate.

[0031] (6) Through steps (2) to (5), the smaller Q is, the more suitable the function parameters for scale differentiation are. Substitute the obtained function parameters into the function in step (2) to obtain the filtering result.

[0032] (7) Introduce the filtering results into the Earth's ocean climate system to improve the accuracy of the results on the Earth's ocean climate system.

[0033] It also includes the application of a filtering method, based on a filtering method in marine climate research, applied to scale analysis, energy cascade, interaction of motion processes at different scales, vortex characteristics research, weather forecasting, filtering out the influence of internal waves, and revealing the structure of ocean stripes.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The filtering method in this invention utilizes truncation functions in the frequency or wavenumber domains, including the error function erf, the activation function tanh, or the sigmoid function. The truncation expression is simple and intuitive. Furthermore, this method overcomes the problem of incomplete filtering in existing scale differentiation methods by using evaluation criteria in both the frequency or wavenumber domain and the time and spatial domains, resulting in more accurate scale differentiation results. Attached Figure Description

[0036] Figure 1 This is a flowchart of the filtering method of the present invention;

[0037] Figure 2 This is a schematic diagram of the frequency domain low-pass filter and high-pass filter obtained in the embodiment;

[0038] Figure 3 This is a schematic diagram showing how the effective low-pass ratio, effective high-pass ratio, low-pass error ratio, and high-pass error ratio change with the filter parameters obtained in the embodiment.

[0039] Figure 4 This is a schematic diagram showing the variation of the filter quality index Q with the filter parameters obtained in the example and comparing it with the results of the existing methods mentioned in the background art;

[0040] Figure 5 This is a schematic diagram showing the low-pass filter error ratio and high-pass filter error ratio obtained in the embodiment under the optimal filter quality index Q, and comparing them with the results of existing methods mentioned in the background art.

[0041] Figure 6 This is a schematic diagram showing the time-domain low-pass filtering time series in the embodiment and its results compared with those of existing methods mentioned in the background art. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] like Figure 1 As shown, a filtering method in marine climate research includes the following steps:

[0044] (1) Obtain the result in the frequency domain or wavenumber domain by taking the Fourier transform of the original time or space data x.

[0045] (2) Using the error function erf, activation function tanh, or sigmoid to analyze the frequency domain or wavenumber domain. After truncation, the low-pass filter frequency domain results were obtained. High-pass filter frequency domain results

[0046] The expression for the error function erf is:

[0047] The expression for the activation function tanh is:

[0048] The expression for the activation function sigmoid is:

[0049] The error function ERF performs scale differentiation on the spatiotemporal data, i.e., truncation in the three-dimensional frequency-wavenumber domain. The expressions for the resulting low-pass and high-pass filter parts are as follows:

[0050]

[0051]

[0052] When the activation function tanh is truncated, the expressions for the low-pass and high-pass filtering parts in the three-dimensional case are as follows:

[0053]

[0054]

[0055] When the sigmoid activation function is truncated, the low-pass and high-pass filtering parts in the three-dimensional case are expressed as follows:

[0056]

[0057]

[0058] Where ω is the frequency, and k and l are the wavenumber components in the latitudinal and meridional directions, respectively. a is the reciprocal of the time or spatial scale, and b is the inclination of the truncation edge. p, q, and r are function parameters, each taking a value of 0 or 1. When p = q = r = 1, the truncation magnitudes of this function are equal in the three directions; when any one of p, q, and r is equal to 0, the above equation represents truncation in the two-dimensional case; if p = 0, the above equation represents truncation in the two-dimensional wavenumber domain; if q = 0 or r = 0, the above equation represents truncation in the two-dimensional frequency-wavenumber domain.

[0059] (3) The energy of the low-pass and high-pass filtering results is calculated and analyzed. To quantify the filtering quality, 'a' is used as the target to distinguish frequencies or wavenumbers. The energy of the ideal low-pass filtering result is then calculated as follows: The energy of the ideal high-pass filter result is The effective portion is defined as the energy component within the desired distinguishing scale range in the frequency domain after filtering, and the error portion is defined as the energy component outside the desired distinguishing scale range in the frequency domain after filtering. The following four proportions can be obtained:

[0060] ①The effective proportion of the low-pass filter is:

[0061] ②The low-pass filter error ratio is:

[0062] ③ The effective proportion of the high-pass filter is:

[0063] ④ The high-pass filter error ratio is:

[0064] Among them, the closer the effective filtering ratio is to 1, the better the filtering effect; the closer the filtering error ratio is to 0, the better the filtering effect. To obtain a parameter characterizing the overall filtering quality, the filtering quality index is defined as:

[0065] Q = |1-valid L |+|1-valid H |+|error L |+|error H | (1-7)

[0066] Q is the filter quality index;

[0067] (4) Results of low-pass filtering in the frequency domain or wavenumber domain Performing an inverse Fourier transform yields a large-scale feature distribution x in the time or spatial domain. L x L This is the result of low-pass filtering, obtained by subtracting the low-pass filtered result x from the original data x. L Obtain the small-scale feature distribution x H xH This is the result of high-pass filtering;

[0068] (5) When the filtering result satisfies that the filtering quality index Q in the frequency or wavenumber domain obtained in step (3) is less than 20%, i.e. 0.2, and satisfies that the low-pass filtering result feature distribution in the time or spatial domain after inverse transformation in step (4) does not have any outliers exceeding the size of the original data, then the function parameter in step (2) belongs to the range of function parameters suitable for scale differentiation. If the above two judgment criteria cannot be met at the same time, then the function parameter in step (2) does not belong to the range of function parameters suitable for scale differentiation, and it is necessary to return to step (2) to change the size of the function parameter and recalculate.

[0069] (6) Through steps (2) to (5), the smaller Q is, the more suitable the function parameters for scale differentiation are. Substitute the obtained function parameters into the function in step (2) to obtain the filtering result.

[0070] (7) Introduce the filtering results into the Earth's ocean climate system to improve the accuracy of the results on the Earth's ocean climate system.

[0071] This embodiment processes AVISO satellite data over a period of 26 years. The data has a temporal resolution of 1 day and a spatial resolution of 1 / 4°. It analyzes the changes in ocean surface height at selected locations, taking one year as the time scale as an example, and performs low-pass and high-pass filtering.

[0072] (1) The Fourier transform of the daily ocean surface height data η at a certain location point in the satellite data over approximately 26 years yields the result in the frequency domain.

[0073] (2) The goal is to use a year, or 365 days, as the time scale to perform low-pass and high-pass filtering on the original data. This is achieved using the expression for the error function erf:

[0074]

[0075]

[0076] Taking the parameters q and r to 0 in equations (1-1) and (1-2), for the frequency domain The truncation process is performed, where parameter a in formulas (1-1) and (1-2) is set to 1 / 365, and the actual value is 5×10. 4 Substituting the parameter b, which controls the tilt of the truncation edge, into the calculations, the low-pass filter frequency domain results are obtained. High-pass filter frequency domain results The expressions for the low-pass filter and the high-pass filter are respectively:

[0077]

[0078]

[0079] in This is considered to be a low-pass filter that removes the impact of annual fluctuations with a time scale of less than 365 days. It is a high-pass filtered portion that retains only the effects of annual fluctuations with a time scale of less than 365 days, resulting in the original frequency domain data. Low-pass filter section and high-pass filter section See attached Figure 2 .

[0080] (3) The energy of the low-pass and high-pass filtering results is calculated and analyzed. To quantify the filtering quality, 1 / 365 ( / day) is taken as the ideal distinguishing frequency. The energy of the ideal low-pass filtering result is then calculated as follows: The energy of the ideal high-pass filter result is The low-pass filter frequency domain results obtained in step 2 are also available. High-pass filter frequency domain results The effective portion is defined as the energy component within the desired distinguishing scale range in the frequency domain after filtering, and the error portion is defined as the energy component outside the desired distinguishing scale range in the frequency domain after filtering. The following four proportions can be obtained:

[0081] ①The effective proportion of the low-pass filter is:

[0082] ②The low-pass filter error ratio is:

[0083] ③ The effective proportion of the high-pass filter is:

[0084] ④ The high-pass filter error ratio is:

[0085] In this method, the closer the effective filtering ratio is to 1, the better the filtering effect; the closer the filtering error ratio is to 0, the better the filtering effect. Under this ratio analysis method, the filtering parameter is defined as L', and its corresponding frequency domain parameter is a' = 1 / L'. Substituting the changing a' into formulas (1-8) and (1-9), we can obtain the results of the four ratios varying with the filtering parameter L' when the desired discrimination scale is 365 days. The results of the four ratios varying with the filtering parameter L' obtained by this method are shown in the appendix. Figure 3 As shown. It can be obtained from the attached... Figure 3It can be seen that the effective proportion and error proportion of the low-pass filter change relatively little with changes in the filter parameters, while the effective proportion and error proportion of the high-pass filter change significantly with changes in the filter parameters. Similarly, the results for the four proportions of the commonly used moving average method and Hanning window method mentioned in the background section, as well as the filter parameter L', can be obtained; these results are not included in the attached figures here. To obtain a parameter characterizing the overall filtering quality of the low-pass and high-pass filters, the filter quality index Q is defined as:

[0086] Q = |1-valid L |+|1-valid H |+|error L |+|error H | (1-7)

[0087] The smaller the Q value, the better the filtering effect.

[0088] (4) Results of low-pass filtering in the frequency domain Performing an inverse Fourier transform yields the low-pass filter result η in the time domain. L The characteristic distribution of η. The result η obtained by subtracting the low-pass filtered value from the original data η. L The high-pass filtering result η in the time domain is obtained. H The characteristic distribution. For example... Figure 6 As shown, the time series η is obtained by time-domain low-pass filtering. L And a comparison with the low-pass filtering results of the commonly used moving average method and Hanning window method mentioned in the background art, since the high-pass filtered time series η H The results cannot be easily judged visually in the graph, therefore η is not considered separately. H The results are shown in the attached figures.

[0089] (5) The determination method must simultaneously satisfy the following conditions: the filter quality index Q in the frequency domain in step (3) is less than 20%, i.e., 0.2, and the low-pass filter result η in the time domain after inverse transformation in step (4) is... L If the feature distribution does not contain outliers exceeding the size of the original data, then the function parameters in step (2) belong to the range of function parameters suitable for scale differentiation.

[0090] The variation of the filter quality index Q with the filter parameter L' in this embodiment, and its comparison with the results of the commonly used moving average method and Hanning window method mentioned in the background art, are shown in the appendix. Figure 4As shown, the filter quality index Q of the moving average method and the Hanning window method is greater than 0.2 across all filter parameters L'. However, in this embodiment, the filter quality index Q is less than 0.1 within the range of filter parameter L' from 340.9 to 444.8, meaning that the filter quality index Q within this range is within the acceptable range of 20%. Furthermore, the filter quality index Q reaches its minimum value when the filter parameter L' is 381.3, which represents the optimal case in the frequency domain for this method. The low-pass filter error ratio and high-pass filter error ratio under the optimal filter quality index Q, and their comparison with the filtering results of the commonly used moving average method and Hanning window method mentioned in the background art, are shown in the appendix. Figure 5 In this embodiment, the low-pass and high-pass filtering error ratios are both smaller than the other two methods, especially the high-pass filtering error ratio, which is an order of magnitude smaller than the other two methods and remains within an acceptable range, meeting the frequency domain evaluation criteria. The time-domain low-pass filtering result η is observed. L Feature distribution map (i.e., attached) Figure 6 The time series in the dataset has no outliers in its characteristic distribution that exceed the size of the original data, i.e., the η obtained in this embodiment... L The change is smooth and consistent with the change trend of the other two methods, which can meet the time domain evaluation criteria.

[0091] If both of the above criteria are met, then the actual value of the function parameter of the truncated function in step 2 falls within the range of function parameters suitable for scale differentiation. If both criteria are not met, then the actual value of the function parameter of the truncated function in step 2 does not fall within the range of function parameters suitable for scale differentiation, and it is necessary to return to step 2, change the value of the function parameter, and recalculate until it passes the above criteria. Figure 5 and Figure 6 If the actual values ​​of the selected function parameters simultaneously meet the above two criteria, then they can be determined to be function parameters suitable for scale differentiation.

[0092] (6) Through steps (2) to (5), the value of the function parameter suitable for low-pass and high-pass filtering with a time scale of one year, i.e., with 365 days as the distinguishing scale, can be obtained. Substituting the function parameter into formulas (1-8) and (1-9) in step (2), a better scale distinguishing result, i.e., the filtering result, can be obtained. The better low-pass filtering result obtained in this embodiment is shown in the appendix. Figure 6 The time series η L .

[0093] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A filtering method for marine climate research, characterized in that: Includes the following steps: (1) Obtain the result in the frequency domain or wavenumber domain by taking the Fourier transform of the original time or space data x. (2) Using the error function erf, activation function tanh, or sigmoid to analyze the frequency domain or wavenumber domain. After truncation, the low-pass filter frequency domain results were obtained. High-pass filter frequency domain results The expression for the error function erf is: The expression for the activation function tanh is: The expression for the activation function sigmoid is: The error function ERF performs scale differentiation on the spatiotemporal data, i.e., truncation in the three-dimensional frequency-wavenumber domain. The expressions for the resulting low-pass and high-pass filter parts are as follows: When the activation function tanh is truncated, the expressions for the low-pass and high-pass filtering parts in the three-dimensional case are as follows: When the sigmoid activation function is truncated, the low-pass and high-pass filtering parts in the three-dimensional case are expressed as follows: Where ω is the frequency, k and l are the wavenumber components in the latitudinal and meridional directions, respectively; a is the reciprocal of the time or spatial scale, b is the inclination of the truncation edge; p, q and r are function parameters, each taking a value of 0 or 1. When p = q = r = 1, the truncation magnitudes of this function are equal in the three directions; when any one of p, q and r is equal to 0, the above formula indicates truncation in the two-dimensional case; if p = 0, the above formula indicates truncation in the two-dimensional wavenumber domain; if q = 0 or r = 0, the above formula indicates truncation in the two-dimensional frequency-wavenumber domain. (3) The energy of the low-pass and high-pass filtering results is calculated and analyzed. To quantify the filtering quality, 'a' is used as the target to distinguish frequencies or wavenumbers. The energy of the ideal low-pass filtering result is then calculated as follows: The energy of the ideal high-pass filter result is The effective portion is defined as the energy component within the desired distinguishing scale range in the frequency domain after filtering, and the error portion is defined as the energy component outside the desired distinguishing scale range in the frequency domain after filtering. The following four proportions can be obtained: ①The effective proportion of the low-pass filter is: ②The low-pass filter error ratio is: ③ The effective proportion of the high-pass filter is: ④ The high-pass filter error ratio is: Among them, the closer the effective filtering ratio is to 1, the better the filtering effect; the closer the filtering error ratio is to 0, the better the filtering effect. To obtain a parameter characterizing the overall filtering quality, the filtering quality index is defined as: Q=1-valid L +1-valid H +error L +error H (1-7) Q is the filter quality index; (4) Results of low-pass filtering in the frequency domain or wavenumber domain Performing an inverse Fourier transform yields a large-scale feature distribution x in the time or spatial domain. L x L This is the result of low-pass filtering, obtained by subtracting the low-pass filtered result x from the original data x. L Obtain the small-scale feature distribution x H x H This is the result of high-pass filtering; (5) When the filtering result satisfies that the filtering quality index Q in the frequency or wavenumber domain obtained in step (3) is less than 20%, i.e. 0.2, and satisfies that the low-pass filtering result feature distribution in the time or spatial domain after inverse transformation in step (4) does not have any outliers exceeding the size of the original data, then the function parameter in step (2) belongs to the range of function parameters suitable for scale differentiation. If the above two judgment criteria cannot be met at the same time, then the function parameter in step (2) does not belong to the range of function parameters suitable for scale differentiation, and it is necessary to return to step (2) to change the size of the function parameter and recalculate. (6) Through steps (2) to (5), the smaller Q is, the more suitable the function parameters for scale differentiation are. Substitute the obtained function parameters into the function in step (2) to obtain the filtering result. (7) Introduce the filtering results into the Earth's ocean climate system to improve the accuracy of the results on the Earth's ocean climate system.

2. An application of a filtering method, based on a filtering method in marine climate research, characterized by: It is applied to scale analysis, energy cascade, interaction of motion processes at different scales, vortex characteristic research, weather forecasting, filtering out the influence of internal waves, and revealing the structure of ocean stripes.

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