A method, electronic device and storage medium for identifying a rossby wave in an idealized numerical model

Abstract

The present application relates to the technical field of numerical simulation and analysis of ocean dynamics and geofluid mechanics, and particularly relates to a method for identifying vortex Rossby wave in an ideal numerical model, an electronic device and a storage medium; specifically, a unified characteristic radius and characteristic variable extraction rule and modal decomposition process are adopted under a vortex reference frame, which can be applicable to various vortex structures in the ocean, can stably identify VRW under different idealized experimental settings, and can calculate parameters such as phase velocity, frequency and dominant direction wave number, so as to improve the repeatability and comparability of the results; in addition, the present application compares the diagnostic results obtained by the Holfmoller slope with the theoretical calculation of the frequency dispersion relationship, and determines the dominant wave number in combination with the modal energy contribution, which can effectively reduce the influence of numerical noise and modal aliasing on the identification conclusion and the extraction of characteristic parameters, and improve the stability and reliability of identification and calculation.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and analysis technology of ocean dynamics and geohydrodynamics, specifically to a method, electronic device and storage medium for identifying vortex Rossby waves in an ideal numerical model. Background Technology

[0002] Vortex Rossby waves (VRWs) are a common and important wave process in ocean mesoscale eddies. Their propagation characteristics are closely related to the potential vortex distribution, vortex morphology, and the interaction between the vortex and its environment. In idealized numerical model studies, constructing eddies with controllable background fields and boundary conditions and simulating their evolution is an important means of revealing the generation, development, and propagation of VRW modes. To quantitatively characterize the propagation direction, frequency, and phase velocity of VRWs, it is usually necessary to identify and parameterize the spatiotemporal signals in the model output.

[0003] Existing methods for identifying and analyzing VRWs often combine theoretical calculations of dispersion relations with mode output diagnostics. For example, theoretical frequencies or phase velocities are calculated based on given vortex background parameters, and the propagation speed and direction are estimated by using the slope of the spatial phase change over time, combined with a Hovmöller spatiotemporal distribution diagram. This type of method is applicable not only to axisymmetric vortices but also to elliptical vortices, tilted vortices, or other asymmetric vortex structures. However, in practical analysis, different vortex structures are highly sensitive to the selection of characteristic parameters and signal extraction methods. For example, differences in characteristic radius, characteristic orientation, and reference frame settings can lead to unstable phase velocity results obtained from Hovmöller diagram construction and slope fitting. Furthermore, the reliability of comparing theoretical calculations and diagnostic results is reduced if unified parameter extraction rules are lacking. In addition, numerical discretization errors and noise interference can easily cause mode aliasing, thus affecting the determination of the dominant wavenumber and the repeatability of characteristic parameter extraction.

[0004] In summary, although existing methods can identify VRWs under different vortex conditions, they lack a unified parameter extraction rule and identification process for different vortex structures. This makes it difficult to stably and repeatedly identify VRWs and calculate their characteristic parameters such as phase velocity, frequency, and dominant orientation mode under different vortex structures and different idealized experimental settings, thus affecting the comparability and consistency of interpretation between different experimental results. Summary of the Invention

[0005] The purpose of this invention is to propose a method for identifying vortex Rossby waves in ideal numerical models, addressing the lack of unified parameter extraction rules and identification processes for different vortex structures in existing technologies.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for identifying vortex Rossby waves in an ideal numerical model includes the following steps: Step S1: Obtain the ocean multivariable field and calculate the characteristic analysis variables based on the ocean multivariable field; Step S2: The feature analysis variables are time series data. The feature analysis variables, which exist in the Cartesian coordinate system, are interpolated to the vortex coordinate system. The vortex coordinate system is a polar coordinate system constructed based on the feature analysis variables. Step S3: Take the radius corresponding to the maximum value of the tangential velocity azimuth average in the vortex coordinate system as the characteristic radius, obtain the angular-time signal at the characteristic radius and average it with the azimuth at the initial time to obtain the disturbance signal; Step S4: Perform azimuth Fourier decomposition on the disturbance signal and calculate the modal contribution to determine the dominant azimuth wavenumber m; Step S5: Determine the disturbance signal corresponding to the dominant azimuth wave m as the dominant mode wave signal, construct the Hofmoller spatiotemporal distribution map based on the dominant mode wave signal, calculate the phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m, and calculate the theoretical phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m through the dispersion relation. Step S6: Perform consistency judgment on the theoretical phase velocity and the actual phase velocity; When the characteristics of a vortex Rossby wave are satisfied, the dominant mode wave signal corresponding to the dominant azimuth wave number m is output. If the characteristics of the vortex Rossby wave are not met, then step S5 is re-executed for the dominant mode wave signal with a dominant azimuth wavenumber of m+1.

[0007] The above technical solution produces the following technical effects: The technical solution of this application adopts a unified feature radius and feature variable extraction rule and mode decomposition process under the vortex reference frame, which can be applied to various vortex structures in the ocean. It can stably identify VRW and calculate parameters such as phase velocity, frequency and dominant azimuth wavenumber under different idealized experimental settings, thereby improving the repeatability and comparability of the results. In addition, this application compares the diagnostic results obtained by Hofmüller slope with the theoretical calculation of dispersion relation, and determines the dominant wavenumber by combining the modal energy contribution, which can effectively reduce the impact of numerical noise and mode mixing on the identification conclusion and feature parameter extraction, and improve the stability and reliability of identification and calculation.

[0008] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical model of this application, in step S1, the ocean multivariable field includes three-dimensional flow field data. Temperature data Salinity data and density data At least one of them; Characteristic analysis variables include relative vorticity or normalized relative vorticity ; Relative vorticity satisfies: ; Normalized relative vorticity satisfies: ; in, For Coriolis parameters.

[0009] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical model according to this application, the process of constructing the vortex coordinate system in step S2 includes the following steps: Step S21: Using the normalized relative vorticity or relative vorticity at each time step as the feature analysis variable, search for the maximum or minimum value of the normalized relative vorticity as the vortex center point at the current time. Step S22: Establish a vortex coordinate system with the vortex center as the farthest point; Step S23: Map the characteristic analysis variables in the Cartesian coordinate system to the vortex coordinate system using interpolation.

[0010] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical pattern according to this application, the calculation process of the disturbance signal in step S3 includes the following steps: Step S31: Obtain the flow field data in the vortex coordinate system constructed in step S2. The flow field data is the tangential velocity in the vortex coordinate system. ; Step S32: Calculate the tangential velocity in the vortex coordinate system. azimuth average of tangential flow velocity The formula for calculating the azimuth average of the tangential flow velocity is: ; in, The coordinates are radial, representing the distance from the center of the vortex outwards; Use time coordinates; These are the azimuth coordinates; Step S33: Determine the feature radius The characteristic radius is the radius corresponding to the point where the tangential velocity reaches its maximum value in the azimuth direction. The expression is: ; Step S34, at the feature radius The characteristic analysis variables that reflect the characteristics of the vortex Rossby wave are obtained, and the characteristic analysis variables are analyzed along the azimuth angle. Uniform sampling and interpolation are used to obtain the azimuth-time signal; satisfy The range of equally spaced sampling values; Step S35: Subtract the tangential velocity azimuth average output disturbance signal at the initial moment from the characteristic analysis variables in the angular-time signal.

[0011] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical pattern according to this application, in step S33, the characteristic radius is... A stable characteristic radius is obtained by a moving average of 3-5 time steps on the time axis. .

[0012] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical model according to this application, the determination of the dominant azimuth wave in step S4 includes the following steps: Step S41: Perform Discrete Fourier Decomposition on the disturbance signal in azimuth coordinates to obtain the mode coefficients with azimuth wavenumber m. The modal coefficients are calculated as follows: ; in, This is a disturbance signal; For the first Each sampling point corresponds to an azimuth angle value; t represents the time data, and M represents the highest order of the azimuth wavenumber. This represents the total number of azimuth angle samples. Step S42: Calculate the modal intensity index of azimuth wavenumber m. The formula for calculating the modal strength index is: ; in, The range of values ​​for a specified time period; Step S43: Calculate the energy proportion K of the modal intensity index corresponding to the wavenumber m in each direction. The expression for the energy proportion K is: K= in, It is the sum of all modal intensity indices; Step S44: Determine the azimuth wavenumber m with the largest energy percentage K as the dominant azimuth wavenumber.

[0013] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical model of this application, in step S5, the characteristic analysis variables in the Hofmüller spatiotemporal distribution map are... The slope is obtained by performing linear regression on the trajectory on the plane. The phase velocity of the corresponding dominant mode oscillation signal is obtained by calculating the slope. .

[0014] As a further improvement to the method for identifying vortex Rossby waves in an ideal numerical mode according to this application, in step S6, the dominant azimuth wavenumber m corresponds to the theoretical phase velocity of the dominant mode wave signal. The calculation formula is: ; Where n is the vertical wavenumber of the dominant mode wave signal; k is the radial wavenumber of the dominant mode wave signal; The feature radius; This represents the average angular velocity corresponding to the characteristic radius in the vortex coordinate system; The formula for calculating the average inertial parameter is as follows: ; This is the mean potential vortex, and the formula for calculating the mean potential vortex is: ,in Let be the partial derivative of the tangential velocity with respect to the vertical coordinate z. ; This represents the value of the radial gradient of the average potential vortex at the characteristic radius; It is the mean absolute vorticity, the mean absolute vorticity The expression is: Absolute vorticity The expression is: , This application also describes an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a method for identifying vortex Rossby waves in an ideal numerical pattern as described above.

[0015] In addition, this application also designs a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause the computer to perform a method for identifying vortex Rossby waves in an ideal numerical pattern as described above. Attached Figure Description

[0016] Figure 1 This is a simplified flowchart of identifying vortex Rossby waves in an ideal numerical model in this invention. Figure 2 Hovmöller plots of normalized relative vorticity for three idealized vortices in the embodiments. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To facilitate an accurate understanding of the solutions provided in the following embodiments of the present invention, the terms involved in the present invention will be explained as follows before describing the technical solutions provided by the present invention: Vortex Rossby waves (VRWs) are important wave processes that are prevalent within mesoscale eddies in the ocean. Their propagation characteristics are closely related to the potential vortex distribution, morphological structure, and interaction between the eddy and the environment. Essentially, they are waves supported by potential vortex gradients within the eddy background flow field, and their frequency, phase velocity, and other characteristics can be identified through modal decomposition, spatiotemporal diagram analysis, and other methods.

[0019] Idealized numerical models are numerical simulation tools that simplify complex disturbance factors in real ocean / atmosphere environments by setting controllable background fields and boundary conditions. They are specifically used to construct vortices and simulate their evolution process and are an important research method for revealing the generation and development mechanism of vortex Rossby waves.

[0020] Relative vorticity: A physical quantity describing the intensity of local rotational motion of a fluid relative to the Earth's surface; its vertical component is calculated using the following formula: (u and v are the latitudinal and longitudinal components of the horizontal velocity field, respectively).

[0021] Absolute vorticity: It is the rotational intensity of a fluid in an absolute coordinate system (fixed in outer space). It is composed of planetary vorticity (vorticity caused by the Earth's rotation, corresponding to the Coriolis parameter) and relative vorticity vector. The vertical component is the sum of the Coriolis parameter and the relative vorticity.

[0022] Cartesian coordinate system: also known as rectangular coordinate system, it describes spatial position through mutually orthogonal x (east-west), y (north-south), and z (vertical) axes. It is a commonly used coordinate system for numerical model output and is suitable for numerical calculation and analysis in regular regions.

[0023] Polar coordinate system: A coordinate system with the center point of the vortex as the origin and describing the spatial position through radial distance (radius) and azimuth angle. It can effectively simplify the analysis of vortex-like rotating structures and facilitate the extraction of the radial and azimuth features of the vortex.

[0024] Mode decomposition refers to the process of decomposing a complex spatiotemporal signal into modal components with specific characteristics. This application decomposes the disturbance signal into modes with different azimuth wavenumbers through azimuth Fourier decomposition, and can calculate the amplitude and phase of each mode, thereby determining the dominant wavenumber.

[0025] Hovmöller diagram: A graph that shows the spatiotemporal evolution of physical quantities. It is usually plotted with time on the vertical axis and spatial coordinates (such as azimuth and radius) on the horizontal axis. By analyzing the slope of the signal in the graph, the propagation direction and phase velocity of the wave can be estimated.

[0026] Consistency criterion: a standard used to determine whether the diagnostic results are consistent with the theoretical model. In this application, the theoretical phase velocity of the vortex Rossby wave is compared with the diagnostic phase velocity. When the relative error between the two is within a controllable range, the signal is determined to satisfy the characteristics of the vortex Rossby wave.

[0027] Coriolis parameters: the vertical component of planetary vorticity, calculated using the following formula. ; ( This is the Earth's rotational angular velocity, approximately 7.292 × 10⁻⁶. -5 ; (latitude of the observation point) describes the deflection effect of the Earth's rotation on fluid motion, and its value varies with latitude.

[0028] The following describes the optimal implementation of a method for identifying vortex Rossby waves in an ideal numerical model, based on the technical solution of this invention. This implementation can identify VRWs and calculate their dominant azimuth wavenumber, frequency, phase velocity, and other characteristic parameters under a unified process.

[0029] Specifically, the method for identifying vortex Rossby waves in an ideal numerical model, as described in this application, includes the following steps: Step S1: Obtain the ocean multivariable field and calculate characteristic analysis variables based on the ocean multivariable field. The ocean multivariable field is an idealized numerical model output obtained from an external data system, covering core ocean dynamic elements such as sea surface height anomalies, zonal current velocities, and meridional current velocities. Preferably, the ocean multivariable field includes three-dimensional flow field data. Temperature data Salinity data and density data The data includes three-dimensional flow field data, containing horizontal velocity (u, v) and vertical velocity (w) components. This data forms the basis for calculating core parameters such as relative vorticity and tangential velocity, directly determining the accuracy of vortex Rossby wave identification. Temperature, salinity, and density are used to calculate potential vorticity and stratification parameters, and are key environmental variables for subsequent verification of vortex Rossby wave dispersion relationships. Density can be derived from temperature and salinity using the seawater state equation.

[0030] The characteristic analysis variables are diagnostic data output at each time step based on the aforementioned ocean multivariate field data. The characteristic analysis variables include relative vorticity. or normalized relative vorticity ; Relative vorticity satisfies: ; Normalized relative vorticity satisfies: ; in, For Coriolis parameters.

[0031] In step S1, the diagnostic quantities (normalized relative vorticity, relative vorticity) at each time step are time-aligned to ensure that the time steps are uniform and consistent, providing a standardized data foundation for subsequent spatiotemporal analysis (such as the construction of Hofmeyer diagrams).

[0032] Step S2: The feature analysis variables are time-series data. The feature analysis variables, which exist in a Cartesian coordinate system, are interpolated to a vortex coordinate system. The vortex coordinate system is a polar coordinate system constructed based on the feature analysis variables. The construction process of the vortex coordinate system includes the following steps: Step S21: In the specific implementation process, it is preferable to use the normalized relative vorticity at each time step as the feature analysis variable, and search for the maximum or minimum value of the normalized relative vorticity as the vortex center point at the current time, so as to ensure that the vortex center can still be tracked when the vortex is tilted or when the vortex shifts with time, thereby reducing the phase misalignment caused by the shift.

[0033] Step S22: Establish a vortex coordinate system with the vortex center as the far point; wherein, with the vortex center as the origin, generate a polar coordinate grid, the radial grid interval is consistent with the Cartesian grid resolution of the original mode (if the original grid is 1km, then the radial interval is set to 1km), and the azimuth direction is evenly divided into 360 parts (i.e., 1° interval) to ensure that the angular resolution meets the requirements of subsequent Fourier decomposition.

[0034] Step S23: Map the characteristic analysis variables from the Cartesian coordinate system to the vortex coordinate system using interpolation. Specifically, use bilinear interpolation or cubic spline interpolation to map all variables (normalized relative vorticity, velocity, temperature, etc.) from the Cartesian coordinate system onto a polar coordinate grid. Note: Preserve the spatiotemporal continuity of the variables during interpolation to avoid introducing additional noise that could affect subsequent modal analysis. For polar coordinate regions exceeding the original Cartesian grid range, use neighborhood mean imputation or extrapolation to ensure the integrity of the data in the vortex reference system.

[0035] Step S3: The radius corresponding to the maximum value of the tangential velocity azimuth average in the vortex coordinate system is taken as the characteristic radius. The angular-time signal at the characteristic radius is obtained and averaged with the initial time azimuth to obtain the disturbance signal. The calculation process of the disturbance signal includes the following steps: Step S31: Obtain the flow field data in the vortex coordinate system constructed in step S2. The flow field data is the tangential velocity in the vortex coordinate system. That is, the polar coordinate flow field data of the vortex reference frame after the transformation in step S2, namely the tangential flow velocity at each radial layer, each azimuth angle, and each moment.

[0036] Step S32: Calculate the tangential velocity in the vortex coordinate system. azimuth average of tangential flow velocity The formula for calculating the azimuth average of the corresponding tangential velocity is: ; in, The coordinates are radial, representing the distance from the center of the vortex outwards; Use time coordinates; These are the azimuth coordinates; Step S33: Determine the feature radius The characteristic radius is the radius corresponding to the point where the tangential velocity reaches its maximum value in the azimuth direction. The expression is: ; Specifically, in the above steps, by analyzing each moment... The maximum value is searched radially, and the corresponding radial coordinate is the initial characteristic radius. To reduce the influence of numerical noise and short-term vortex fluctuations, the value is calculated for 3-5 consecutive time steps. By performing a moving average, a stable characteristic radius can be obtained. ,Right now:

[0037] Where n is the size of the sliding window (3-5). This is the model time step. If the searched extreme point is located near the vortex boundary, it needs to be re-evaluated in conjunction with the vortex potential distribution or sea surface height anomaly to avoid mistakenly identifying the boundary region as the core.

[0038] Step S34, at the feature radius The characteristic analysis variables that reflect the characteristics of the vortex Rossby wave are obtained, and the characteristic analysis variables are analyzed along the azimuth angle. Uniform sampling and interpolation are used to obtain the azimuth angle of the angular-time signal. satisfy The range of equally spaced sampling values; specifically, when the feature analysis variable is normalized relative vorticity. At that time, select characteristic analysis variables that clearly reflect VRW at the characteristic radius. and along the azimuth angle Uniform sampling, followed by interpolation to obtain the angular-time signal ; Among them, the above angular-time signals satisfy: ; Step S35: Subtract the initial tangential velocity azimuth average output disturbance signal from the characteristic analysis variables in the angular-time signal. Specifically, when the characteristic analysis variables are... At that time, by constructing perturbation components The normalized relative vorticity was subtracted from the azimuth average at the initial moment. ,get .

[0039] Step S4: Perform azimuth Fourier decomposition on the disturbance signal and calculate the modal contribution to determine the dominant azimuth wavenumber m; wherein, the determination of the dominant azimuth wavenumber includes the following steps: Step S41: Perform Discrete Fourier Decomposition on the disturbance signal in azimuth coordinates to obtain the mode coefficients with azimuth wavenumber m. The modal coefficients are calculated as follows: ; in, This is a disturbance signal; For the first Each sampling point corresponds to an azimuth angle value; t represents the time data, and M represents the highest order of the azimuth wavenumber. This represents the total number of azimuth angle samples. Specifically, when the feature analysis variable selected in step S3 is When the above modal coefficients are used, the calculation method is as follows:

[0040] in, To analyze variables by feature The modal coefficients of the disturbance signal are calculated from the constructed angular-time signal. The above formula for calculating the modal coefficients is a discrete Fourier series (or a variant of the discrete Fourier transform), used to transform the signal in the spatial domain (angular domain). Decomposed into different angular frequency components m, the frequency domain component corresponding to each angular frequency is obtained. Each azimuth wavenumber m corresponds to a specific vortex wave structure. For example, m=1 corresponds to an eccentric wave with a single peak, and m=2 corresponds to an elliptical wave with two peaks. The modal coefficients directly reflect the intensity and propagation state of the structure at the current moment.

[0041] Step S42: Calculate the modal intensity index of azimuth wavenumber m. The formula for calculating the modal strength index is: ; in, The range of values ​​for a specified time period; Step S43: Calculate the energy proportion K of the modal intensity index corresponding to the wavenumber m in each direction. The expression for the energy proportion K is: K= in, It is the sum of all modal intensity indices; Step S44: Determine the azimuth wavenumber m with the largest energy proportion K as the dominant azimuth wavenumber. .

[0042] Step S5: The disturbance signal corresponding to the dominant azimuth wave m is identified as the dominant mode wave signal. A Hofmoller spatiotemporal distribution map is constructed based on the dominant mode wave signal. The phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m is calculated, and the theoretical phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m is calculated through the dispersion relation. Specifically, the characteristic analysis variables in the Hofmoller spatiotemporal distribution map are... The slope is obtained by performing linear regression on the trajectory on the plane. The phase velocity of the corresponding dominant mode oscillation signal is obtained by calculating the slope. Wherein, the dominant azimuth wavenumber m corresponds to the theoretical phase velocity of the dominant mode wave signal. The calculation formula is: ; Where n is the vertical wavenumber of the dominant mode wave signal; k is the radial wavenumber of the dominant mode wave signal; The feature radius; This represents the average angular velocity corresponding to the characteristic radius in the vortex coordinate system; The formula for calculating the average inertial parameter is as follows: ; This is the mean potential vortex, and the formula for calculating the mean potential vortex is: ,in Let be the partial derivative of the tangential velocity with respect to the vertical coordinate z. It is worth noting that the tangential velocity... This refers to the tangential flow velocity in Cartesian coordinates; in the specific calculation process... The calculation satisfies: ; The radial gradient of the average potential vortex is represented at the characteristic radius. It is the mean absolute vorticity, the mean absolute vorticity The expression is: Absolute vorticity The expression is: , This indicates stratification. Stratification refers to the static stratification stability of the atmosphere or ocean, N.2 The square of the buoyancy frequency reflects the stability of the fluid stratification. Its magnitude directly affects the vertical structure and propagation characteristics of vortex Rossby waves, and it is an indispensable key parameter in deriving the dynamic relationship of vortex waves and identifying vortex Rossby waves.

[0043] Step S6: Perform a consistency judgment between the theoretical phase velocity and the actual phase velocity. In practice, this application uses a method where the relative error is very small, specifically less than a certain set error threshold, for judgment. If the relative error is very small, the signal can be determined to satisfy the characteristics of VRW. Based on the obtained theoretical frequency... The azimuth phase velocity can be calculated. radial phase velocity And the theoretical value was compared with the observed phase velocity. If the relative error obtained is very small, it can be determined that the signal meets the characteristics of VRW.

[0044] Specifically, when the characteristics of a vortex Rossby wave are satisfied, the dominant mode wave signal corresponding to the dominant azimuth wave number m is output. If the characteristics of a vortex Rossby wave are not met, step S5 is re-executed for the dominant mode wave signal with a dominant azimuth wavenumber of m+1. It is worth noting that the dominant mode wave signal output in this application, in addition to including the disturbance signal of the mode corresponding to the dominant azimuth wavenumber described above, can also simultaneously output key characteristic parameters of the VRW, including the dominant azimuth wavenumber, azimuth phase velocity, radial phase velocity, and modal energy percentage, thus fully quantifying the propagation and structural characteristics of the VRW.

[0045] Example 1 To further demonstrate the technical effects of the technical solution of this application, this embodiment presents an experimental analysis of the above-mentioned technical solution. See [link to detailed experimental analysis] for more information. Figure 2 The Hovmöller plots of the normalized relative vorticity of the vortices for the three idealized structures are shown.

[0046] The first row contains three images (in order as follows): Figure 2 In the diagram, a, b, and c represent the Hovmöller plot of t–θ at a fixed radius. The three plots in the second row (in order) are... Figure 2 In the diagram, d, e, and f represent the Hovmöller plot of t–r at a fixed azimuth angle. For details, see [link to Hovmöller plot]. Figure 2 Circular vortex structure (see) Figure 2 In Figure 2 a, Figure 2 d; where the dominant azimuth wavenumber m=4), elliptical vortex (see Figure 2 In Figure 2 b, see Figure 2 In Figure 2e; where the dominant azimuth wavenumber m=2), tilted vortex (see Figure 2 In Figure 2 c, see Figure 2 In Figure 2 f; dominant azimuth wavenumber m=1). Solid lines represent positive values, and dashed lines represent negative values.

[0047] As described above, the Hovmöller plots of the three vortices with different initial structures all exhibit an alternating distribution of tilted positive and negative stripes along the time direction. This is a typical characteristic of the outward propagation of vortex Rossby waves, perfectly matching the wave signal characteristics identified by the method in this application. It can be seen that this method can accurately capture the existence of vortex Rossby waves for vortices with different dominant azimuth wave numbers and different initial morphologies, unaffected by differences in the initial structure of the vortex. Compared to traditional identification methods that are prone to identification errors due to changes in vortex morphology, this method provides clearer and more accurate results, exhibits stronger robustness, and can adapt to vortex Rossby wave identification under various idealized vortex scenarios, fully verifying the effectiveness and reliability of the technical solution in this application.

[0048] It is noteworthy that those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0049] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0050] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0051] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

[0053] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0054] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for identifying vortex Rossby waves in an ideal numerical model, characterized in that, Includes the following steps: Step S1: Obtain the ocean multivariable field and calculate the characteristic analysis variables based on the ocean multivariable field; Step S2: The feature analysis variables are time-series data. The feature analysis variables, which exist in Cartesian coordinates, are interpolated to a vortex coordinate system, which is a polar coordinate system constructed based on the feature analysis variables. Step S3: Take the radius corresponding to the maximum value of the tangential velocity azimuth average in the vortex coordinate system as the characteristic radius, obtain the angular-time signal at the characteristic radius, and average it with the azimuth at the initial time to obtain the disturbance signal. Step S4: Perform azimuth Fourier decomposition on the disturbance signal and calculate the modal contribution to determine the dominant azimuth wavenumber m. Step S5: Determine the disturbance signal corresponding to the dominant azimuth wave m as the dominant mode wave signal, construct the Hofmoller spatiotemporal distribution map based on the dominant mode wave signal, calculate the phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m, and calculate the theoretical phase velocity of the dominant mode wave signal corresponding to the dominant azimuth wave number m through the dispersion relation. Step S6: Determine the consistency between the theoretical phase velocity and the actual phase velocity. When the characteristics of a vortex Rossby wave are met, the dominant mode wave signal corresponding to the dominant azimuth wave number m is output. When the vortex Rossby wave characteristics are not met, step S5 is re-executed for the dominant mode wave signal with a dominant azimuth wavenumber of m+1.

2. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 1, characterized in that, In step S1, the ocean multivariable field includes three-dimensional flow field data. Temperature data Salinity data and density data At least one of them; The characteristic analysis variables include relative vorticity. or normalized relative vorticity ; The relative vorticity satisfies: ； The normalized relative vorticity satisfies: ； in, For Coriolis parameters.

3. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 2, characterized in that, In step S2, the process of constructing the vortex coordinate system includes the following steps: Step S21: Using the normalized relative vorticity or the relative vorticity at each time step as the feature analysis variable, search for the maximum or minimum value of the normalized relative vorticity as the vortex center point at the current time. Step S22: Establish the vortex coordinate system with the center of the vortex as the origin. Step S23: Map the feature analysis variables in the Cartesian coordinate system to the vortex coordinate system using interpolation.

4. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 2, characterized in that, In step S3, the calculation process of the disturbance signal includes the following steps: Step S31: Obtain the flow field data in the vortex coordinate system constructed in step S2, wherein the flow field data is the tangential velocity in the vortex coordinate system. ; Step S32: Calculate the tangential velocity in the vortex coordinate system. azimuth average of tangential flow velocity The formula for calculating the azimuth average of the tangential flow velocity is: ; in, The coordinates are radial, representing the distance from the center of the vortex outwards; Use time coordinates; These are the azimuth coordinates; Step S33: Determine the feature radius The characteristic radius is the radius corresponding to the point where the tangential flow velocity reaches its maximum value in the azimuth direction. The expression is: ; Step S34, at the feature radius The feature analysis variables that reflect the characteristics of the vortex Rossby wave are obtained, and the feature analysis variables are analyzed along the azimuth angle. Uniform sampling and interpolation are used to obtain the azimuth-time signal; satisfy The range of equally spaced sampling values; Step S35: Subtract the tangential velocity azimuth average at the initial moment from the characteristic analysis variables in the angular-time signal and output the disturbance signal.

5. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 4, characterized in that, In step S33, the feature radius is... A stable characteristic radius is obtained by performing a moving average over 3-5 time steps on the time axis. .

6. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 1, characterized in that, In step S4, the determination of the dominant azimuth wave includes the following steps: Step S41: Perform Discrete Fourier Decomposition on the disturbance signal in azimuth coordinates to obtain the mode coefficients with azimuth wavenumber m. The modal coefficients are calculated as follows: ; in, The disturbance signal; For the first Each sampling point corresponds to an azimuth angle value; t is the time data, and M is the highest order of the azimuth wavenumber; This represents the total number of azimuth angle samples. Step S42: Calculate the modal intensity index of the azimuth wavenumber m. The formula for calculating the modal strength index is as follows: ; in, The range of values ​​for a specified time period; Step S43: Calculate the energy proportion K of the modal intensity index corresponding to each azimuth wavenumber m. The expression for the energy proportion K is: K= in, It is the sum of all the modal strength indices; Step S44: Determine the azimuth wavenumber m with the largest energy percentage K as the dominant azimuth wavenumber.

7. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 1, characterized in that, In step S5, the characteristic analysis variables described in the Hofmüller spatiotemporal distribution map are... The slope is obtained by performing linear regression on the trajectory on the plane. The phase velocity corresponding to the dominant mode fluctuation signal is obtained by calculating based on the slope. .

8. The method for identifying vortex Rossby waves in an ideal numerical model according to claim 4, characterized in that, In step S6, the dominant azimuth wavenumber m corresponds to the theoretical phase velocity of the dominant mode wave signal. The calculation formula is: ; Where n is the vertical wavenumber of the dominant mode wave signal; k is the radial wavenumber of the dominant mode wave signal; The feature radius; This represents the average angular velocity corresponding to the characteristic radius in the vortex coordinate system; The formula for calculating the average inertial parameter is as follows: ; It is the average potential vortex, and the formula for calculating the average potential vortex is: ,in Let be the partial derivative of the tangential velocity with respect to the vertical coordinate z. ; The radial gradient of the average potential vortex is represented at the characteristic radius. It is the mean absolute vorticity, the mean absolute vorticity The expression is: , Indicates a layered structure.

9. An electronic device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a method for identifying vortex Rossby waves in an ideal numerical pattern according to any one of claims 1 to 8.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, in, The computer instructions are used to cause the computer to perform a method for identifying vortex Rossby waves in an ideal numerical pattern according to any one of claims 1 to 8.

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