A parameterization optimization method for ocean vertical mixing

Abstract

The application provides a marine vertical mixing parameterization optimization method, and belongs to the technical field of marine physics. In the method, the initial vertical eddy-induced mixing coefficient output by the KPP scheme is extracted under each operation time step of the ocean circulation model, the flow line curvature radius and the vortex asymmetry parameter are calculated in sequence, and the mixing coefficient is quantitatively corrected by using the parameter; the corrected coefficient is written into the KPP turbulent diffusion calculation module, the original core algorithm is unchanged, and then the global physical field adaptation processing is completed in combination with the transport equation. The scheme is based on the regulation and control mechanism of the vortex asymmetry deformation on the vertical mixing, effectively improves the simulation accuracy of the vortex active area and the west boundary flow area, and has good practicability and universality.

Description

Technical Field

[0001] This application relates to the field of marine physics technology, and in particular to a method for vertical hybrid parameterization optimization in the ocean. Background Technology

[0002] Vertical mixing is a core dynamic process regulating global ocean circulation, heat and salinity transport, ocean carbon cycle, and air-sea interaction. The simulation accuracy of vertical mixing parameterization schemes directly determines the operational reliability of various ocean numerical models and climate prediction models. Currently, the K-Profile Parameterization (KPP) scheme, with its high computational efficiency and clear physical framework, is widely used in mainstream ocean circulation models such as MITgcm, ROMS, HYCOM, NEMO, and POP. This scheme divides the water body into two parts: the ocean surface boundary layer and the ocean interior, and processes them separately. Strong mixing and nonlocal transport phenomena are simulated in the surface boundary layer, while weak mixing characteristics dominated by shear instability, internal wave breaking, and dual diffusion processes are characterized in the ocean interior. The boundary layer thickness is determined by the Richardson number, and the vertical diffusion coefficients of the boundary layer region and the ocean interior are solved separately. A nonlocal flux term is introduced to characterize the reverse gradient transport brought about by convective mixing. Finally, the diffusion coefficient and its derivative are made continuous in the boundary layer position through smoothing. The obtained vertical diffusion coefficients are substituted into the temperature, salinity, and momentum transport equations to complete the overall simulation of vertical turbulent mixing in the ocean.

[0003] Mesoscale eddies are widely distributed in the ocean, with most exhibiting significant asymmetric morphological characteristics. Traditional KPP parameterization schemes do not incorporate these asymmetric features, making them unsuitable for the actual mixing conditions in eddy-active ocean areas. In densely distributed eddy regions and areas where eddies interact with western boundary currents, the vertical mixing intensity simulated by this scheme shows significant deviations, leading to discrepancies between simulated results and actual data regarding circulation structure, eddy dissipation, and heat and mass transport. Currently, there is a lack of vertical mixing optimization methods with clearly defined physical mechanisms, simple computation, and easy integration into existing ocean circulation models. Existing improvement methods generally suffer from insufficient adaptability and high barriers to entry. Summary of the Invention

[0004] Based on this, this application provides a marine vertical hybrid parameterization optimization method to solve the problems of traditional KPP parameterization schemes not taking into account vortex asymmetry and having large deviations in simulation results in vortex activity areas. At the same time, it meets the requirements of easy scheme integration, no need for additional observation data, and low computational cost.

[0005] According to one aspect of this application, a method for parameterized optimization of marine vertical mixing is provided, comprising: Run the ocean circulation model. At each computation time step of the ocean circulation model, extract the eastward flow velocity, northward flow velocity, east-west grid length, and north-south grid length of each grid point, and read the initial vertical eddy mixing coefficient output by the KPP parameterization scheme in the ocean circulation model. Based on the eastward flow velocity, the northward flow velocity, and the partial derivative of the flow velocity, the radius of curvature of the instantaneous horizontal streamline at each grid point is determined. By combining the radius of curvature, the east-west length of the grid, and the north-south length of the grid, the dimensionless vortex asymmetry parameters are determined; Based on the vortex asymmetry parameter, the initial vertical vortex-induced mixing coefficient is corrected to obtain the corrected vertical vortex-induced mixing coefficient. The corrected vertical eddy mixing coefficient was written into the turbulent diffusion calculation module of the KPP parameterization scheme of the ocean circulation model to complete the configuration of the ocean vertical eddy mixing parameters. Based on the ocean circulation model with completed parameter configuration, the temperature, salinity, and momentum field of seawater in the sea area are adapted globally.

[0006] In one implementation, the radius of curvature of the instantaneous horizontal streamline is calculated according to the following formula: In the formula, and The eastward and northward flow velocities correspond to the grid points. , Eastward flow velocity exist Partial derivatives in the direction, , Northward flow velocity exist Partial derivatives in direction.

[0007] In one implementation, the partial derivatives of each velocity are solved using the central difference method. In this method, the difference formula is constructed using the velocity data of the target grid point and adjacent grid points, and the partial derivatives of the global velocity are calculated grid by grid and time step by time.

[0008] In one implementation, the vortex asymmetry parameter is calculated according to the following formula: In the formula, East-west grid length, The north-south grid length; the vortex asymmetry parameter A dimensionless parameter with a value greater than or equal to 1.

[0009] In one implementation, the modified vertical vortex-induced mixing coefficient is calculated according to the following formula: In the formula, The initial vertical vortex-induced mixing coefficient is... This is the corrected vertical vortex-induced mixing coefficient.

[0010] In one implementation, the initial vertical vortex-induced mixing coefficient is determined according to the KPP parameterization scheme. The calculated vertical diffusion coefficient; where The boundary layer thickness is defined as the depth at which the Richardson number reaches a critical value; The turbulent velocity scale; For a function of type , its cubic polynomial form is... Four coefficients Obtained through the upper and lower boundary conditions of the boundary layer; For standardized vertical coordinates.

[0011] In one implementation, the ocean circulation pattern is any one of MITgcm, ROMS, HYCOM, NEMO, and POP.

[0012] In one implementation, the original initial vertical vortex-induced mixing coefficient in the traditional KPP parameterization scheme is replaced with a modified vertical vortex-induced mixing coefficient, while keeping the original boundary layer determination, nonlocal flux calculation, and smoothing operation logic of the KPP parameterization scheme unchanged.

[0013] In one implementation, after completing the global adaptation process, the method further includes: building a model test scenario based on the β-plane approximation conditions, setting up a control group and an experimental group respectively, conducting multiple sets of ideal numerical experiments, and extracting simulated data for a specified duration for comparative analysis.

[0014] In one implementation, the ideal numerical experiment sets up two types of terrain conditions: flat terrain and Gaussian terrain, and configures two types of wind field conditions: cosine structure wind field and Jet wind field. The simulation duration of the complete mode is set to the first duration, and the simulation data of the most recent second duration is extracted for comparative analysis, wherein the first duration is longer than the second duration.

[0015] This application provides a parameterized optimization method for ocean vertical mixing, which integrates eddy asymmetry parameters into the KPP vertical mixing parameterization process, constructs corresponding coefficient correction relationships, and compensates for the shortcomings of traditional schemes that do not consider eddy morphology characteristics, effectively improving the simulation accuracy of eddy active regions. The entire calculation relies solely on the model's own output data, making the computation simple and efficient. Furthermore, it can directly interface with existing KPP frameworks and mainstream ocean circulation models, resulting in low integration difficulty, strong versatility, and no additional burden on model operation. Attached Figure Description

[0016] Figure 1 This is a flowchart of a marine vertical hybrid parameterization optimization method in one embodiment; Figure 2 This is a logical schematic diagram of a marine vertical hybrid parameterization optimization method in one embodiment; Figure 3 This is a schematic diagram of the initial vertical temperature distribution, two types of wind fields, and Gaussian terrain in a CA parameterization scheme in one embodiment; Figure 4 This is a schematic diagram illustrating the differences in sea surface height field between different test groups under two working conditions in one embodiment. Figure 5 This is a schematic diagram of the multi-year average eddy advection component, flow velocity, and numerical differences between test groups in one embodiment. Figure 6 This is a schematic diagram illustrating the variation characteristics of eddy advection and difference values ​​in each group of experiments in one embodiment. Figure 7 This is a schematic diagram showing the circulation comparison results under the Jet wind field condition in one embodiment and the abnormal circulation distribution caused by the wind field difference. Detailed Implementation

[0017] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0018] The terms used in this application are explained below.

[0019] Vortex asymmetry parameters ( ): A dimensionless parameter used to quantify the degree of irregularity in the horizontal morphology of mesoscale vortices. The larger the value, the more intense the vortex deformation, and the stronger the ability of the edge to induce sub-mesoscale processes through strain.

[0020] KPP parameterization is a widely used vertical mixing parameterization scheme in global ocean circulation models. It simulates the mixing process in the upper ocean by constructing boundary layer depth and turbulent diffusion coefficient profiles.

[0021] Submesoscale processes: Ocean dynamic processes with a spatial scale of 1-10 km and a temporal scale of 1-10 days, mainly induced by mesoscale eddy deformation and frontal instability, which can significantly promote cross-density surface mixing and positive energy cascading.

[0022] Relative vorticity advection: The transport process of relative vorticity of fluid micro-particles with advection motion is one of the core dynamic terms regulating the evolution of ocean circulation structure.

[0023] Planar approximation: A commonly used approximation method in ocean numerical simulation, which approximates the Coriolis parameters. Represented as latitude linear functions ( This is used to simulate the effect of Earth's rotation on circulation as latitude changes.

[0024] Cross-density surface mixing: The mixing process of seawater across isodense surfaces is an important pathway for the vertical transport of heat, salinity and substances in the ocean.

[0025] The complete process of the KPP scheme can be summarized as follows: First, the key surface forcing fields, such as friction velocity and buoyancy flux, are calculated based on sea surface wind stress, heat flux, and freshwater flux. Then, the shallowest depth equal to the critical value is found by calculating the Richardson number at various depths from the sea surface as the ocean surface boundary layer thickness. Subsequently, the local turbulent diffusion coefficients dominated by shear instability, internal wave breaking, and double diffusion processes in the ocean interior are calculated, as well as the turbulent diffusion coefficients in the boundary layer based on surface forcing intensity, boundary layer thickness, and type function. Next, a nonlocal flux term is introduced to simulate the reverse gradient transport phenomenon caused by convective mixing. Finally, a smoothing function is used to ensure the continuity of the diffusion coefficients and their derivatives between the boundary layer and the ocean interior at the boundary layer, thereby obtaining the vertical turbulent diffusion coefficient profile of the entire water column. Substituting these values ​​into the transport equations for temperature, salinity, and momentum completes the parameterized calculation of the turbulent mixing process.

[0026] The core of the KPP scheme is to transform arbitrary physical quantities The vertical turbulent flux can be decomposed into two parts: local gradient flux and nonlocal flux. ...Equation 1 in, For the vertical velocity disturbance component, The perturbation component of the physical quantity being decomposed. For vertical turbulent flux, The vertical diffusion coefficient is... For vertical coordinates, This is a non-local item.

[0027] Vertical diffusion coefficient The expression is: ...Equation 2 in, The boundary layer thickness is defined as the depth at which the Richardson number reaches a critical value; The turbulent velocity scale; It is a function of type , usually in cubic polynomial form. Its four coefficients can be obtained through the upper and lower boundary conditions of the boundary layer; For standardized vertical coordinates.

[0028] With the development of high-resolution ocean observation and numerical simulation technologies, studies have confirmed that ocean mesoscale eddies generally exhibit irregular horizontal morphology and asymmetric spatial distribution. When eddies deform, they generate strong strain fields in their edge regions, inducing sub-mesoscale processes with spatial scales ranging from 1 to 10 kilometers and temporal scales ranging from 1 to 10 days. These sub-mesoscale processes can drive energy transfer and dissipation at various levels, while significantly enhancing seawater mixing across density surfaces, with mixing intensity significantly higher than that of traditional boundary layer turbulent mixing. However, traditional KPP parameterization schemes only design for large-scale ocean dynamic processes and boundary layer turbulence, without considering the asymmetric deformation characteristics of mesoscale eddies, and cannot quantify the enhancing effect of sub-mesoscale processes induced by eddy edge strain on cross-density surface mixing. In areas with dense eddy distribution, especially in sea areas where eddies interact with western boundary currents, traditional KPP schemes significantly underestimate local vertical mixing intensity, resulting in significant deviations between model simulations of ocean circulation structure, eddy dissipation processes, heat and mass transport results and actual ocean conditions. At the same time, the industry currently lacks vertical mixing correction methods that can accurately combine the asymmetric characteristics of eddies, have clear physical mechanisms, and have low computational overhead. Most existing improvement methods are complex in structure, require additional observation data, and are difficult to integrate directly into mainstream ocean circulation models that are already in large-scale use, resulting in significant deficiencies in applicability and scalability.

[0029] Based on this, this application provides an optimization method for KPP parameterization. This method establishes a quantitative relationship between vortex asymmetry and vertical vortex-induced mixing intensity, clarifies the physical mechanism of sub-mesoscale mixing induced by vortex asymmetry deformation, and to some extent compensates for the mechanistic deficiencies of existing technologies. Simultaneously, without requiring additional observational data, it achieves a computationally efficient parameterization method that is easy to integrate into existing mainstream ocean circulation models, improving the universality and practicality of the scheme.

[0030] See Figure 1 The present application provides a marine vertical hybrid parameterization optimization method, which includes the following steps S101-S106.

[0031] S101: Run the ocean circulation model. At each time step of the ocean circulation model, extract the eastward flow velocity, northward flow velocity, east-west grid length, and north-south grid length of each grid point, and read the initial vertical eddy mixing coefficient output by the KPP parameterization scheme in the ocean circulation model. S102: Determine the radius of curvature of the instantaneous horizontal streamline at each grid point based on the eastward flow velocity, the northward flow velocity, and the partial derivative of the flow velocity. S103: Combine the radius of curvature, the east-west length of the grid, and the north-south length of the grid to determine the dimensionless vortex asymmetry parameters; S104: Based on the vortex asymmetry parameter, the initial vertical vortex-induced mixing coefficient is corrected to obtain the corrected vertical vortex-induced mixing coefficient. S105: Write the corrected vertical eddy mixing coefficient into the turbulent diffusion calculation module of the KPP parameterization scheme of the ocean circulation model to complete the configuration of the ocean vertical eddy mixing parameters; S106: Based on the ocean circulation model with completed parameter configuration, perform global adaptation processing on seawater temperature, salinity, and momentum field within the sea area.

[0032] Running the ocean circulation model and completing the corresponding data extraction and reading is the starting point of the entire parameterized optimization method. The ocean circulation model will continuously iterate according to preset rules. Within each fixed computation time step, the program traverses all grid cells in the computational domain, collecting the basic flow field data of eastward and northward velocities for each grid point. At the same time, it reads the inherent east-west and north-south length parameters of the grid. The above data are inherent parameters generated in real time during the operation of the ocean circulation model, without the need for supplementary data from external observation equipment. Based on this, the initial vertical eddy mixing coefficient output by the KPP scheme calculation within the model is retrieved simultaneously. This coefficient is the core parameter for vertical mixing simulation in traditional schemes. Step S101 ensures the uniformity and real-time nature of the data source by uniformly collecting the native data of the model, and also allows subsequent parameter calculations to be carried out based on the existing operating system, simplifying the overall data preparation process.

[0033] This application can run on various ocean circulation numerical models, including MITgcm, ROMS, HYCOM, NEMO, and POP. MITgcm is highly versatile and adaptable to ocean dynamic process simulations at different spatiotemporal scales. ROMS is a regional ocean model focusing on nearshore and shelf dynamic processes, offering flexible resolution and suitability for nearshore circulation and small-to-medium scale eddies. HYCOM, designed for mixed coordinate systems, balances large-scale ocean circulation with detailed upper ocean processes and is commonly used for global ocean environmental simulation and forecasting. NEMO is widely used for global and regional ocean climate simulations and is a crucial ocean module in climate system models, frequently applied in long-term ocean evolution analysis. POP primarily focuses on global ocean circulation simulation and has long been used in research related to ocean circulation and air-sea interactions. The optimization method in this application is compatible with any of the above models, requiring no changes to the core logic for different models. It can be directly embedded into existing operating systems, demonstrating strong platform adaptability.

[0034] After acquiring complete flow field data, in S102, the radius of curvature of the instantaneous horizontal streamlines at each grid point is calculated based on the eastward and northward flow velocities and their corresponding spatial partial derivatives. The horizontal flow trajectory of ocean water can be abstracted as a continuous streamline shape. The radius of curvature of the streamlines can intuitively reflect the degree of curvature of the local flow field and is also a fundamental physical quantity characterizing the vortex morphology. In actual implementation, the flow velocity can be discretized using the central difference method to obtain the partial derivatives of the flow velocity in different directions. Then, combined with a preset calculation formula, the radius of curvature is calculated globally. This calculation process is entirely based on the flow field data output by the model. The calculation logic is simple and can be deeply adapted to the grid computing system of the ocean circulation model, ensuring the consistency of parameter solutions across the entire grid.

[0035] After obtaining the instantaneous horizontal streamline curvature radius at each grid point, in S103, this parameter, along with the east-west and north-south grid lengths, is used to further calculate the dimensionless vortex asymmetry parameters. These vortex asymmetry parameters are used to quantify the morphological deviation characteristics of ocean mesoscale vortices. The parameter values ​​are determined by both the degree of streamline curvature and the grid spatial scale. The calculation process uses a unified mathematical model, assigning parameters grid by grid. This transforms the geometric morphological characteristics of vortices into quantitative parameters that can participate in model calculations, establishing a bridge between vortex morphology and vertical mixing processes.

[0036] In S104, the initial vertical eddy mixing coefficient output by the KPP scheme is corrected using the solved eddy asymmetry parameters, ultimately yielding a corrected vertical eddy mixing coefficient that adapts to the eddy asymmetry characteristics. In this application's optimization method, a clear quantitative correction relationship is established between the two types of parameters. For eddy regions with different shapes and degrees of deformation, the value of the vertical mixing coefficient is adjusted accordingly, thereby reflecting the influence of the eddy asymmetry structure on the vertical mixing of seawater. Compared to the traditional fixed-value method, this correction method can better fit the actual ocean conditions in eddy-active areas, compensating for the shortcomings of traditional schemes that do not consider eddy characteristics at the core parameter level.

[0037] After correcting the mixing coefficient, in step S105, the new vertical eddy mixing coefficient is written into the turbulence diffusion calculation module of the KPP scheme within the ocean circulation model, thus completing the overall configuration of ocean vertical eddy mixing-related parameters. This step fully preserves the original core algorithms, boundary layer determination logic, nonlocal flux calculation, and data smoothing rules of the traditional KPP parameterization scheme, only replacing the mixing coefficient values ​​within the module, without requiring modifications to the original program architecture and computational logic. This integration method offers strong compatibility and can be directly applied to various mainstream ocean circulation models, significantly reducing the difficulty of scheme deployment and facilitating rapid adoption in existing simulation systems.

[0038] After completing all parameter configurations, in S106, global processing is performed based on the updated ocean circulation model. The configured KPP parameterization scheme is integrated into the temperature, salinity, and momentum transport equations, and global turbulent mixing adaptation is carried out for the seawater temperature, salinity, and momentum fields within the target sea area. The updated parameter system can accurately reflect the changes in mixing intensity caused by vortex asymmetry, making the model's simulation results for various ocean dynamic elements closer to the real ocean environment. This effectively improves the simulation accuracy in vortex-dense regions and the interaction region between vortices and western boundary currents, achieving the goal of ocean vertical mixing parameterization optimization based on vortex asymmetry.

[0039] As can be seen, this application introduces vortex asymmetry parameters ( )Quantify the irregularity of the horizontal vortex shape and further establish The proportional relationship with the vertical eddy mixing coefficient is used to correct the vertical mixing coefficient of the traditional KPP parameterization scheme, thereby effectively aiding in understanding the impact of eddy mixing on the vortex-western boundary flow system.

[0040] The marine vertical mixing parameterization optimization method provided in this application will be illustrated below with reference to a specific embodiment.

[0041] refer to Figure 2 The diagram illustrates the implementation logic of a parameterized optimization method for marine vertical mixing in this embodiment. The entire process includes data acquisition, radius of curvature calculation, asymmetric parameter calculation, vertical mixing coefficient correction, parameterized scheme integration, and numerical experimental verification.

[0042] In the data acquisition phase, the eastward current velocity at each time step and each grid point is extracted from the output of ocean circulation models (such as MITgcm). Northward flow velocity And the east-west grid length of the grid. North-South grid length Simultaneously, the vertical vortex-induced mixing coefficient, which does not consider vortex asymmetry, calculated using the traditional KPP parameterization scheme is obtained. (The "vertical vortex-induced mixing coefficient that does not consider vortex asymmetry") ", that is, the vertical diffusion coefficient calculated by Equation 2 described above. ).

[0043] The radius of curvature calculation step is a new addition to the optimization method in this application. Its purpose is to provide the radius of curvature for the calculation of asymmetric parameters. Specifically, the radius of curvature of the instantaneous horizontal streamline at each grid point can be calculated based on the velocity field data. Its physical meaning is to quantify the local curvature of streamlines, reflecting the deformation intensity of the vortex. The specific formula is as follows: ...Equation 3 in, and The magnitudes of the eastward and northward flow velocities corresponding to the grid points, , Eastward flow velocity exist Partial derivatives in the direction, , Northward flow velocity exist Specifically, the partial derivatives of the direction can be calculated using the central difference method. This involves constructing a difference formula using the velocity data of the target grid point and adjacent grid points, and then calculating the partial derivatives of the global velocity grid by grid and time step by time.

[0044] In the asymmetric parameter calculation stage, based on the radius of curvature ( The vortex asymmetry parameter CA at each grid point is calculated using the equivalent length of the grid and the vortex itself. The calculation formula is: ...Formula 4 in, This is a dimensionless parameter with a value greater than or equal to 1. When hour, This indicates that the streamlines are approximately straight lines and the vortex shape is regular; when When decreasing, An increase in the value indicates an increase in the curvature of the streamlines and an enhancement of vortex asymmetry.

[0045] In the vertical mixing coefficient correction stage, based on the physical mechanism of vortex asymmetry promoting cross-density surface mixing, a vortex asymmetry parameter is established. The mixing coefficient of the traditional KPP scheme is corrected based on its proportional relationship with the vertical vortex-induced mixing coefficient. The corrected vertical vortex-induced mixing coefficient ( The calculation formula is: ...Formula 5 This formula shows that the stronger the vortex asymmetry, the larger the vertical mixing coefficient, which accurately reflects the enhanced effect of vertical mixing induced by vortex deformation.

[0046] In the parameterization scheme integration stage, the corrected vertical vortex-induced mixing coefficient ( Substitute the turbulent diffusion calculation module of the KPP parameterization scheme into the original vertical eddy mixing coefficient ( This completes the vertical mixing parameterization process that considers the influence of vortex asymmetry; that is, the Kv calculated by the KPP scheme for each grid point is multiplied by CA. This integration process does not require modification of the core framework of the KPP scheme, but only requires adding a CA correction step in the mixing coefficient calculation stage.

[0047] The numerical experimental verification process is described below.

[0048] To verify the effectiveness of the proposed CA parameterization optimization scheme in improving the vertical mixing process of the vortex-western boundary flow system, this application conducted six sets of ideal numerical experiments based on the MITgcm model. The experiments employed a β-plane approximation and a linearized equation of state configuration, neglecting the influence of salinity, and setting the Coriolis gradient parameter f0 = 5 × 10⁻⁶. -5 β = 2.15 × 10 -11 The model has a horizontal resolution of 5 km and a vertical resolution ranging from 10 m to 600 m. The total simulation duration is 120 years (first duration), and the mean field data from the last 20 years (second duration) are used as the basis for analysis. The experiment is divided into three control experiments and three optimization experiments. Ctrl, BathyCtrl, and JetCtrl are control groups without CA parameterization, corresponding to the flat terrain cosine wind field, Gaussian terrain cosine wind field, and flat terrain Jet wind field conditions, respectively. CtrlCA, BathyCA, and JetCA are optimization groups that incorporate the CA parameterization of this application. Except for whether CA parameterization is loaded, the model configurations of each group are completely identical. Detailed design can be seen in Table 1.

[0049] Table 1 Parameterization scheme - ideal numerical experiment Figure 3 The diagram shows the initial vertical temperature distribution, two types of wind fields, and Gaussian topography for this experiment. Specifically, it illustrates the initial vertical temperature distribution, zonal wind field (cos / jet wind fields are represented by black / red lines), and Gaussian topography for the CA parameterization scheme-ideal numerical experiment.

[0050] Experimental results show that after introducing CA parameterization to correct the vertical eddy mixing coefficient, the differences in the sea surface height field are mainly concentrated on the south side of the circulation and the northwest side of the western boundary current terminus, while the response on the northeast side of the circulation is weak. This spatial distribution characteristic is stable under both flat-bottomed and Gaussian topographic conditions. Figure 4 The differences in sea surface height field between different test groups under two different operating conditions are shown respectively. Figure 4 (a) Characteristics of the difference in sea surface height (SSH) between CtrlCA and Ctrl experiment (average of years 101–120), with the black line representing the average SSH of the Ctrl experiment; Figure 4 (b) Same Figure 4 (a), but this represents the difference between the BathyCA and BathyCtrl experiments. Analysis based on the simplified relative vorticity control equations reveals significant spatial differences in the vorticity advection characteristics on the north and south sides and east and west sides of the circulation under traditional experimental conditions, which jointly regulate the development and weakening of the western boundary flow. Figure 5The data presents the multi-year average eddy advection component, flow velocity, and numerical differences between experimental groups. Figure 5 (a) Zonal vorticity advection component (blue line), zonal velocity (black line), and zonal vorticity advection difference between CtrlCA and Ctrl experiments (red line); Figure 5 (b) Same Figure 5 (a), but with meridional distribution characteristics. It can be seen that after introducing CA parameterization, the eddy advection anomaly and the background eddy advection show a significant negative correlation, with correlation coefficients reaching -0.47 and -0.52, proving that the CA optimization scheme mainly improves the mixing simulation bias of the traditional KPP scheme by enhancing vertical mixing and promoting the dissipation of the marine eddy process.

[0051] The response characteristics of different regions of the circulation to CA parameterization are significantly different. Figure 6 This diagram illustrates the variation characteristics of eddy advection and its difference in each experimental group. The eddy advection anomaly in the northeast corner of the circulation is weak and can be balanced by the background circulation; the optimized scheme has minimal impact on the circulation structure in this region. The circulation anomaly in the southeast corner propagates westward with the β effect, gradually accumulating to form a significant circulation change. The southwest side is affected by insufficient local mixing and the westward propagation disturbance from the east, resulting in more significant changes in sea surface height. Although the eddy advection anomaly is stronger in the northwest side, the enhanced vertical mixing effectively constrains the range of circulation changes. The control experiment after changing to the Jet wind field conditions further validated the universality of this scheme. Figure 7 This presents the circulation comparison results under Jet wind field conditions and the abnormal circulation distribution caused by wind field differences. Figure 7 (a) Same Figure 3 However, this is a comparison of the results from the JetCA and JetCtrl experiments; Figure 7 (b) Anomalous circulation distribution caused by differences in wind fields between the JetCA and BathyCA experiments. Figure 7 It can be seen that the changes in the circulation background caused by wind field adjustment will not change the core role of CA parameterization, and the response effect of anticyclonic circulation to parameterization optimization is more prominent, which fully proves that the optimization scheme of this application can stably and effectively improve the accuracy of ocean vertical mixing simulation in the coupled region of vortex and western boundary current.

[0052] In summary, this application introduces vortex asymmetry parameters into the KPP vertical mixing parameterization scheme, establishes corresponding quantitative correction relationships, determines the control mechanism of vortex asymmetry deformation on vertical mixing, and presents the physical process of sub-mesoscale mixing induced by vortex asymmetry. It can distinguish the mixing differences brought about by different vortex morphologies, and has a more solid physical foundation compared to traditional schemes. This application solves for relevant parameters using instantaneous horizontal streamline curvature radius and grid resolution. The entire calculation process only uses the velocity field data output by the ocean circulation model itself, without supplementing external observation data or setting empirical parameters. The calculation process is simple and efficient, adaptable to different sea areas and various circulation systems, and has a wider range of applications. This scheme can be directly integrated into the traditional KPP parameterization framework, using the original core algorithm without modifying the existing program architecture. It can be quickly applied to mainstream ocean circulation models such as MITgcm and ROMS, with a low overall computational burden and no significant increase in model operating costs, making it very convenient for practical application. Multiple sets of ideal numerical experiments have confirmed that this application can accurately reflect the effect of vortex asymmetry on the structure of ocean circulation, effectively improving the simulation accuracy. In areas with severe vortex deformation, such as the western boundary current terminus and the southern side of the circulation, the simulation results are more consistent with the real ocean dynamic state.

[0053] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0054] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for vertical hybrid parameter optimization in the ocean, characterized in that, include: Run the ocean circulation model. At each computation time step of the ocean circulation model, extract the eastward flow velocity, northward flow velocity, east-west grid length, and north-south grid length of each grid point, and read the initial vertical eddy mixing coefficient output by the KPP parameterization scheme in the ocean circulation model. Based on the eastward flow velocity, the northward flow velocity, and the partial derivative of the flow velocity, the radius of curvature of the instantaneous horizontal streamline at each grid point is determined. By combining the radius of curvature, the east-west length of the grid, and the north-south length of the grid, the dimensionless vortex asymmetry parameters are determined; Based on the vortex asymmetry parameter, the initial vertical vortex-induced mixing coefficient is corrected to obtain the corrected vertical vortex-induced mixing coefficient. The corrected vertical eddy mixing coefficient was written into the turbulent diffusion calculation module of the KPP parameterization scheme of the ocean circulation model to complete the configuration of the ocean vertical eddy mixing parameters. Based on the ocean circulation model with completed parameter configuration, the temperature, salinity, and momentum field of seawater in the sea area are adapted globally.

2. The marine vertical hybrid parameterization optimization method according to claim 1, characterized in that, The radius of curvature of the instantaneous horizontal streamline is calculated according to the following formula: In the formula, and The eastward and northward flow velocities correspond to the grid points. , Eastward flow velocity exist Partial derivatives in the direction, , Northward flow velocity exist Partial derivatives in direction.

3. The marine vertical hybrid parameterization optimization method according to claim 2, characterized in that, The partial derivatives of each velocity are solved using the central difference method. The difference formula is constructed using the velocity data of the target grid point and adjacent grid points, and the partial derivatives of the global velocity are calculated grid by grid and time step by time.

4. The marine vertical hybrid parameterization optimization method according to claim 2, characterized in that, The vortex asymmetry parameter is calculated according to the following formula: In the formula, East-west grid length, The north-south grid length; the vortex asymmetry parameter A dimensionless parameter with a value greater than or equal to 1.

5. The marine vertical hybrid parameterization optimization method according to claim 4, characterized in that, The corrected vertical vortex-induced mixing coefficient is calculated according to the following formula: In the formula, The initial vertical vortex-induced mixing coefficient is... This is the corrected vertical vortex-induced mixing coefficient.

6. The marine vertical hybrid parameterization optimization method according to claim 5, characterized in that, The initial vertical vortex-induced mixing coefficient is calculated according to the KPP parameterization scheme. The calculated vertical diffusion coefficient; where The boundary layer thickness is defined as the depth at which the Richardson number reaches a critical value; The turbulent velocity scale; For a function of type , its cubic polynomial form is... Four coefficients Obtained through the upper and lower boundary conditions of the boundary layer; For standardized vertical coordinates.

7. The marine vertical hybrid parameterization optimization method according to claim 1, characterized in that, The ocean circulation model is any one of MITgcm, ROMS, HYCOM, NEMO, and POP.

8. The marine vertical hybrid parameterization optimization method according to claim 1, characterized in that, The original initial vertical vortex mixing coefficient in the traditional KPP parameterization scheme is replaced with the modified vertical vortex mixing coefficient, while keeping the original boundary layer determination, nonlocal flux calculation, and smoothing operation logic of the KPP parameterization scheme unchanged.

9. The marine vertical hybrid parameterization optimization method according to any one of claims 1-8, characterized in that, After completing the full-domain adaptation process, the method further includes: building a model test scenario based on the β-plane approximation conditions, setting up a control group and an experimental group respectively, conducting multiple sets of ideal numerical experiments, and extracting simulated data for a specified duration for comparative analysis.

10. The marine vertical hybrid parameterization optimization method according to claim 9, characterized in that, The ideal numerical experiment sets up two types of terrain conditions: flat terrain and Gaussian terrain, and two types of wind field conditions: cosine structure wind field and Jet wind field. The simulation duration of the complete mode is set to the first duration, and the simulation data of the most recent second duration is extracted for comparative analysis. The first duration is longer than the second duration.

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