Parameterized simulation of cross-diffusive vertical mixing processes for ocean forecasting methods and apparatus

Abstract

This invention discloses a parametric simulation method for ocean forecasting based on cross-density vertical mixing processes, comprising: Step 1, acquiring a three-dimensional multivariate marine environmental field, water depth data, vortex trajectory dataset, vortex kinetic energy data, and atmospheric driving field. The environmental field includes sea surface height, ocean temperature, ocean salinity, and meridional and zonal current velocities; the atmospheric driving field includes wind speed, sea surface pressure, 2-meter temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity; Step 2, introducing vortex horizontal asymmetry, constructing a parametric ocean model based on cross-density vertical mixing processes, and calculating the vertical mixing coefficient; Step 3, constructing a regional ocean model based on the regional ocean numerical model ROMS, and verifying the vertical mixing coefficient; Step 4, performing ocean forecasting using the parametric ocean model based on cross-density vertical mixing processes. This invention links vertical mixing with the influence of vortex horizontal asymmetry, improving the accuracy of multi-element ocean simulation.

Description

Technical Field

[0001] This invention belongs to the fields of marine numerical simulation technology and physical oceanography, and specifically relates to a parameterized simulation method and equipment for marine forecasting of cross-density vertical mixing processes. Background Technology

[0002] Currently, vertical mixing in the ocean significantly affects the exchange of momentum and energy within the ocean, and is crucial for the transport of physical and biochemical elements such as heat, salinity, momentum, and nutrients. In numerical simulations, vertical mixing directly impacts the accuracy of thermohaline circulation, stratification evolution, ocean thermal dynamics, and ecosystem structure. Because vertical mixing involves small-scale turbulent processes, while model resolution is much larger than this scale, appropriate parameterization of these processes is necessary.

[0003] Mesoscale eddies, with horizontal scales ranging from 50 to 300 kilometers and temporal scales from weeks to months, are ubiquitous in the global oceans. They dominate the kinetic energy of ocean circulation and are an important component of multi-scale ocean processes. Studies have shown that the vertical mixing rate in mesoscale eddies can be 1 to 2 orders of magnitude higher than that in the background ocean, playing a crucial regulatory role in global ocean heat redistribution, carbon cycling, and ecosystem dynamics. Their influence is closely related to factors such as eddy asymmetry, eddy intensity, background stratification, and topographic interactions, making them an important process in the parameterization of ocean circulation and climate models.

[0004] In existing coarse-resolution climate models, the parameterization scheme of eddy diffusion rate is generally used to characterize the impact of eddy mixing. These schemes assume that all eddy kinetic energy is dissipated, leading to inter-density mixing. However, in reality, only a portion of eddy kinetic energy is dissipated through forward cascades; a significant portion enters large-scale systems through reverse cascades. The dissipation of eddy kinetic energy is closely related to the horizontal asymmetry of the eddy. The more irregular the eddy's horizontal orientation, the more favorable it is for eddy energy to propagate to the sub-mesoscale, thereby dissipating energy and causing inter-density mixing.

[0005] In summary, existing eddy-induced mixing parameterization schemes are insufficient to accurately characterize mesoscale eddy processes, thus failing to clearly define the true contribution of mesoscale eddies to ocean mixing and failing to accurately reflect the spatial structure and intensity of ocean mixing. Numerical simulation results are insufficient to provide usable forecasting support for marine environmental safety. Therefore, this patent draws upon the ideas of the most advanced tidal-driven mixing parameterization schemes used in general ocean circulation models and proposes an improved calculation method for parameterizing trans-density vertical mixing processes, considering the horizontal asymmetry of eddies. Summary of the Invention

[0006] This invention provides a parameterized simulation method and equipment for ocean forecasting of cross-density vertical mixing processes to solve the technical problems existing in the prior art.

[0007] The technical solution adopted by this invention to solve the technical problems existing in the prior art is as follows: A parameterized simulation method for ocean forecasting across density vertical mixing processes, comprising the following steps: Step 1: Obtain the three-dimensional multivariable environmental field, water depth data, eddy trajectory dataset, eddy kinetic energy data, and atmospheric driving field of the ocean. The environmental field includes sea surface height, ocean temperature, ocean salinity, and ocean meridional and zonal current velocities; the atmospheric driving field includes wind speed, sea surface pressure, 2-meter temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity. Step 2: Introduce eddy horizontal asymmetry, construct an ocean parameterized model based on the cross-density vertical mixing process, and fit the vertical mixing coefficient; Step 3: Construct a regional ocean model based on the regional ocean numerical model ROMS and verify the vertical mixing coefficient; Step 4: Ocean forecasting is performed using a parameterized ocean model based on the cross-density vertical mixing process.

[0008] Furthermore, in step 1, the sources for obtaining the three-dimensional multivariable marine environmental field data include: the World Ocean Atlas WOA18 climatological data provided by the U.S. National Center for Environmental Information, with a spatial resolution of 1 / 4°; the Global Eddy-Resolved Physical Ocean Reanalysis Dataset (GLORYS) provided by the Mercator Marine Service of France, with a spatial resolution of 1 / 12° and a time period covering 1993 to the present; and the Global Monthly Mean Simple Ocean Data Assimilation System (SODA3.15.2) data developed by the University of Maryland, with a spatial resolution of 0.5° and a time period covering 1980 to 2024.

[0009] Furthermore, in step 1, the sources for obtaining water depth data include: Global Ocean Topography (GEBCO 2024) provided by the International Hydrographic Organization and the Intergovernmental Oceanographic Commission of UNESCO, with a horizontal resolution of 15 arcseconds.

[0010] Furthermore, in step 1, the sources for obtaining the vortex trajectory dataset include: Meta 3.2 provided by the French Ocean Satellite Data Archive, Validation and Interpretation Center, with a time range from 1993 to 2022; the eddy kinetic energy data is obtained by synthesizing and analyzing Argo data collected by remote sensing and the Global Ocean Real-Time Observation Network, and combining it with the surface modal projection method to obtain 2°×2° results for the entire ocean depth.

[0011] Furthermore, in step 1, the sources for obtaining atmospheric driving field data include the fifth-generation global atmospheric reanalysis dataset ERA5 provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has a spatial resolution of 1 / 4° and covers the period from 1950 to the present.

[0012] Furthermore, in step 2, the method for constructing a marine parametric model based on the cross-density vertical mixing process includes the following steps: Buoyancy frequency is calculated using temperature and salinity profile data from environmental field data. : ; In the formula: The frequency of buoyancy; It is the acceleration due to gravity. 9.81 ; For reference density, 1025 ; It is density; These are vertical coordinates; Bottom topographic roughness was calculated using water depth data: ; ; ; ; ; In the formula: For terrain roughness; For grid point numbers; For the first Weight of each grid point; For the first Water depth at each grid point; For the first Weight function for each grid point; This is a normalization constant; For from the first The radial distance from each grid point to the center of the circle; Standard deviation; The radius of the region where the grid point is located; For water depth; This is a weighted average of the water depths; It is a weighted average function; Introducing the structure function of the vortex dissipation vertical profile : ; In the formula: It is a high attenuation scale; For structure functions; Introducing a dimensionless vortex asymmetry metric to measure the strength of horizontal vortex asymmetry: ; ; In the formula: To measure the dimensionless quantity of vortex asymmetry; The horizontal asymmetric intensity of the vortex; The perimeter of the outermost boundary of the vortex; To and The circumference of a circle with an area equal to the area enclosed by the enclosed region; This is a function to find the maximum value. CA is used to characterize the degree to which the vortex shape deviates from an ideal circular structure; Based on the above variables, calculate the vertical mixing coefficient across density: ; In the formula: It is the vertical mixing coefficient across density; For mixing efficiency; The vortex energy dissipation rate; The buoyancy frequency is near the bottom layer; It is the vortex kinetic energy near the bottom layer.

[0013] Furthermore, in step 3, the method for constructing a regional ocean model based on the regional ocean numerical model ROMS includes the following steps: Using ROMS, a regional ocean model of a certain ocean region is constructed by adopting a three-dimensional, nonlinear, topographically-following coordinate-based baroclinic primitive equation regional ocean model. The grid is divided with a horizontal resolution of 0.25° and a vertical division of 25 layers. The surface layer tensile coefficient is... The tensile coefficient of the bottom layer The water depth data comes from GEBCO 2024, with the water depth range set to 10 ~ 5500m. In order to reduce the impact of large gradient terrain on the accuracy of model simulation, the water depth data is smoothed. The atmospheric driving field variables required for model operation are all derived from monthly average data of a specific month in the atmospheric reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF), with a horizontal resolution of 0.25°×0.25°. The atmospheric driving field variable data are provided in an unaligned grid format. The model initial field, open boundary mesothermal salinity, sea surface height, and three-dimensional velocity are derived from SODA 3.15.2 monthly average reanalysis data.

[0014] Furthermore, in step 3, in order to obtain the initial equilibrium field of the matching mode itself, it is first adjusted through the Spin-up process, which refers to the time period required to run from the initial state to near physical equilibrium.

[0015] Further, in step 3, January climatological data from SODA 3.15.2 is used as the initial field, driven by the ERA5 forcing field of the monthly mean climatological data and the SODA 3.15.2 boundary field, with a simulation period of 50 years; thus, stable climatological simulation results are obtained. In the simulation, the boundary conditions for the free sea surface, barotropic flow field, and three-dimensional temperature-salinity flow field are Chapman_explicit boundary conditions, Shchepetkin boundary conditions, and Rad-Nudging mixed boundary conditions, respectively; the horizontal and vertical momentum and temperature-salinity advection adopt third-order windward and fourth-order central advection schemes, respectively; the vertical mixing scheme is KPP; and the horizontal diffusion and viscosity coefficient are 50 m. 2 s -1 In addition, a sponge layer with a width of approximately 250 km and a viscosity coefficient of 500 m at the boundary was also constructed. 2 s -1 The simulation time step is 360 s.

[0016] The present invention also provides an apparatus for a parameterized simulation ocean forecasting method for a cross-density vertical mixing process, comprising a memory and a processor, wherein the memory is used to store a computer program; and the processor is used to execute the computer program and, when executing the computer program, implement the steps of the parameterized simulation ocean forecasting method for a cross-density vertical mixing process as described above.

[0017] The advantages and positive effects of this invention are as follows:

[0018] (1) The physical mechanism is more reasonable This invention provides an improved calculation method for parameterizing vertical mixing processes across densities. Compared with traditional vertical parameterization schemes, this method directly correlates the mixing coefficient with the geometric properties of mesoscale eddies, making the parameterization scheme closer to the physical essence and reducing the errors of traditional vertical parameterization schemes under complex terrain and flow fields. It can be widely applied in fields such as fisheries, shipping, and disaster early warning, providing a scientific basis for related decision-making.

[0019] (2) Enhance the forecast accuracy of multiple marine elements This invention introduces the asymmetry of mesoscale eddies to optimize the vertical mixing process, thereby improving the simulation performance of regional ocean models for multiple sea surface elements. Compared to the K-Profile Parameterization (KPP) scheme, this method can better simulate the mixing process and improve the simulation results of ocean stratification. This lays a technical foundation for improving the level of medium- and long-term marine environmental safety assurance.

[0020] This method links vertical mixing with the influence of eddy horizontal asymmetry, effectively improving the accuracy of multi-element ocean simulation. Based on the parameterized calculation method for cross-density vertical mixing processes provided in this patent, the constructed regional ocean model significantly improves the accuracy of multi-element sea surface simulation compared to the KPP scheme, while ensuring computational efficiency and simulation accuracy. This lays a technical foundation for effectively improving the level of medium- and long-term marine environmental safety forecasting and protection, thus possessing significant scientific and application value. Attached Figure Description

[0021] Figure 1 This is a flowchart of a parameterized simulation ocean forecasting method for a cross-density vertical mixing process according to the present invention.

[0022] Figure 2 This is a diagram of a parametric ocean model based on a transdensity vertical mixing process, which introduces horizontal asymmetry of eddies.

[0023] Figure 3 This is a comparison chart of the Spin-up results and SODA 3.15.2.

[0024] Figure 4 This is a comparison chart of sea surface temperature, salinity, current field, and sea surface height for several different models.

[0025] Figure 5 This is a comparison chart of the mixed layer depth for different months in several models.

[0026] ROMS: ROMS model (Regional Ocean Modeling System), a three-dimensional regional ocean numerical model.

[0027] GLORYS: Global Eddy-Resolved Physical Ocean Reanalysis Model.

[0028] The post-model reporting experiment was divided into two groups, EXP0 and EXP1, with a time range of 2011 to 2015. The initial field was the result of January of the 50th year of the Spin-up, and the forcing field and boundary field were the actual ERA5 and SODA 3.15.2 monthly average data.

[0029] The vertical hybrid model of EXP0 adopts the KPP scheme.

[0030] EXP1 is a marine parametric model based on the cross-density vertical mixing process of the present invention.

[0031] The cross-density mixing scheme only considers the variation of the mixing coefficient with space. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0033] The following are the Chinese definitions of English words, phrases, and abbreviations: K-Profile Parameterization (KPP): K-Profile parameterization; Kolmogorov: The smallest scale of Kolmogorov turbulence; Mellor-Yamada: Ocean boundary layer model; HYCOM is a data assimilation hybrid coordinate ocean model funded by the U.S. National Ocean Partnership Program and others. Thorpe: An empirical method for estimating atmospheric optical turbulence profiles; The Smagorinsky model is a subgrid-scale stress model widely used in Large Eddy Simulation (LES) to simulate the influence of small-scale eddies that are not analyzed by meshes on large-scale flows in turbulence. GM: The GM model (Grey Model) is a core modeling method in grey system theory proposed by Chinese scholar Deng Julong in 1982. It is mainly used to deal with prediction and analysis problems of small sample, information-poor, and uncertain systems. PP: In the fields of environmental science or water resource management, PP refers to the Projection Pursuit model, which is a statistical analysis method. Spin-up: refers to the process by which a model adjusts itself to reach equilibrium under conditions of non-equilibrium initial conditions or disturbances. ROMS: The ROMS model (Regional Ocean Modeling System) is an open-source three-dimensional regional ocean numerical model that is widely used to simulate a variety of ocean phenomena, from global-scale circulation to small-scale water movement in estuaries and nearshore areas. EKE: Eddy energy data; WOA 18: Atlas of the World Oceans; GLORYS: Global Eddy-Resolved Physical Ocean Reanalysis Dataset; SODA 3.15.2: Global monthly mean simple ocean data assimilation system data; GEBCO 2024: Global Ocean Topography; Meta 3.2: Provided by the French Center for Marine Satellite Data Archiving, Verification and Interpretation; Argo: The Argo program, short for Geostrophic Oceanography Real-Time Observation Array, is an important component of the Global Ocean Observing System (GOOS). ECMWF: European Centre for Medium-Range Weather Forecasts; ERA5: The fifth-generation global atmospheric reanalysis dataset; ECCO: An Earth system model developed by NASA to estimate global ocean circulation and climate conditions.

[0034] Please see Figures 1 to 5 A parameterized simulation method for ocean forecasting across density vertical mixing processes, comprising the following steps: Step 1: Obtain the three-dimensional multivariable environmental field, water depth data, eddy trajectory dataset, eddy kinetic energy data, and atmospheric driving field of the ocean. The environmental field includes sea surface height, ocean temperature, ocean salinity, and ocean meridional and zonal current velocities; the atmospheric driving field includes wind speed, sea surface pressure, 2-meter temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity. Step 2: Introduce eddy horizontal asymmetry, construct an ocean parameterized model based on the cross-density vertical mixing process, and fit the vertical mixing coefficient; Step 3: Construct a regional ocean model based on the regional ocean numerical model ROMS and verify the vertical mixing coefficient; Step 4: Ocean forecasting is performed using a parameterized ocean model based on the cross-density vertical mixing process.

[0035] Step 3 may also include the following steps: A comparative experiment was conducted between an ocean parameterization model based on cross-density vertical mixing processes and a regional ocean model constructed based on the regional ocean numerical model ROMS to evaluate the forecast accuracy of the ocean parameterization model based on cross-density vertical mixing processes.

[0036] Preferably, in step 1, the sources for obtaining the three-dimensional multivariable marine environmental field data include: the World Ocean Atlas WOA18 climatological data provided by the U.S. National Center for Environmental Information, with a spatial resolution of 1 / 4°; the Global Eddy-Resolved Physical Ocean Reanalysis Dataset (GLORYS) provided by the Mercator Marine Service of France, with a spatial resolution of 1 / 12° and a time period covering 1993 to the present; and the Global Monthly Mean Simple Ocean Data Assimilation System (SODA) 3.15.2 developed by the University of Maryland, with a spatial resolution of 0.5° and a time period covering 1980 to 2024.

[0037] Preferably, in step 1, the source of the water depth data may include: Global Ocean Topography (GEBCO 2024) provided by the International Hydrographic Organization and the Intergovernmental Oceanographic Commission of UNESCO, with a horizontal resolution of 15 arcseconds.

[0038] Preferably, in step 1, the source of the vortex trajectory dataset may include: Meta 3.2 provided by the French Ocean Satellite Data Archive, Verification and Interpretation Center, with a time range from 1993 to 2022; the eddy kinetic energy data is obtained by synthesizing and analyzing Argo data collected by remote sensing and the Global Ocean Real-Time Observation Network, and combining it with the surface modal projection method to obtain the 2°×2° result of the entire ocean depth.

[0039] Preferably, in step 1, the source of atmospheric driving field data may include the fifth-generation global atmospheric reanalysis dataset ERA5 provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has a spatial resolution of 1 / 4° and covers the period from 1950 to the present.

[0040] Preferably, in step 2, the method for constructing a marine parametric model based on the cross-density vertical mixing process may include the following steps: Buoyancy frequency is calculated using temperature and salinity profile data from environmental field data. : ; In the formula: The frequency of buoyancy; It is the acceleration due to gravity. 9.81 ; For reference density, 1025 ; It is density; These are vertical coordinates; Bottom topographic roughness was calculated using water depth data: ; ; ; ; ; In the formula: For terrain roughness; For grid point numbers; For the first Weight of each grid point; For the first Water depth at each grid point; For the first Weight function for each grid point; This is a normalization constant; For from the first The radial distance from each grid point to the center of the circle; Standard deviation; The radius of the region where the grid point is located; For water depth; This is a weighted average of the water depths; It is a weighted average function; Introducing the structure function of the vortex dissipation vertical profile : ; In the formula: It is a high attenuation scale; For structure functions; Introducing a dimensionless vortex asymmetry metric to measure the strength of horizontal vortex asymmetry: ; ; In the formula: To measure the dimensionless quantity of vortex asymmetry; The horizontal asymmetric intensity of the vortex; The perimeter of the outermost boundary of the vortex; To and The circumference of a circle with an area equal to the area enclosed by the enclosed region; This is a function to find the maximum value. CA is used to characterize the degree to which the vortex shape deviates from an ideal circular structure; Based on the above variables, calculate the vertical mixing coefficient across density: ; In the formula: It is the vertical mixing coefficient across density; For mixing efficiency; The vortex energy dissipation rate; The buoyancy frequency is near the bottom layer; It is the vortex kinetic energy near the bottom layer.

[0041] Preferably, in step 3, the method for constructing a regional ocean model based on the regional ocean numerical model ROMS may include the following steps: ROMS can be used to construct a regional ocean model for a certain ocean region using a three-dimensional, nonlinear, topography-following coordinate-based baroclinic primitive equation regional ocean model. The grid is divided with a horizontal resolution of 0.25° and a vertical division of 25 layers. The surface layer tensile coefficient is... The tensile coefficient of the bottom layer The water depth data comes from GEBCO 2024, with the water depth range set to 10~5500m. In order to reduce the impact of large gradient terrain on the model simulation accuracy, the water depth data is smoothed.

[0042] The atmospheric driving field variables required for model operation are all derived from monthly average data of a specific month in the atmospheric reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF), with a horizontal resolution of 0.25°×0.25°. The atmospheric driving field variable data are provided in an unaligned grid format. The model initial field, open boundary mesothermal salinity, sea surface height, and three-dimensional velocity are derived from SODA 3.15.2 monthly average reanalysis data.

[0043] Preferably, in step 3, in order to obtain the initial equilibrium field of the matching mode itself, it can be adjusted first through the Spin-up start-up process. The Spin-up start-up process refers to the time period required to run from the initial state to close to physical equilibrium.

[0044] Preferably, in step 3, January climatological data from SODA 3.15.2 can be used as the initial field, driven by the ERA5 forcing field of the monthly mean climatological data and the SODA 3.15.2 boundary field, with a simulation period of 50 years; thus, stable climatological simulation results are obtained. In the simulation, the boundary conditions for the free sea surface, barotropic flow field, and three-dimensional temperature-salinity flow field are Chapman_explicit boundary conditions, Shchepetkin boundary conditions, and Rad-Nudging mixed boundary conditions, respectively; the horizontal and vertical momentum and temperature-salinity advection adopt third-order windward and fourth-order central advection schemes, respectively; the vertical mixing scheme is KPP; and the horizontal diffusion and viscosity coefficient are 50 m. 2 s -1 In addition, a sponge layer with a width of approximately 250 km and a viscosity coefficient of 500 m at the boundary was also constructed. 2 s -1 The simulation time step is 360 s.

[0045] The present invention also provides an apparatus for a parameterized simulation ocean forecasting method for a cross-density vertical mixing process, comprising a memory and a processor, wherein the memory is used to store a computer program; and the processor is used to execute the computer program and, when executing the computer program, implement the steps of the parameterized simulation ocean forecasting method for a cross-density vertical mixing process as described above.

[0046] The workflow and working principle of the present invention are further described below with reference to preferred embodiments: 1. Obtain the data required for calculating the mixing coefficients and building the model: This project aims to acquire three-dimensional, multivariable marine environmental fields, water depth data, eddy trajectory datasets, eddy kinetic energy data, and atmospheric driving fields. The marine environmental fields include sea surface height, ocean temperature, ocean salinity, and meridional and zonal current velocities. The marine environmental field data collected in this project include: climatological data from the World Ocean Atlas (WOA 18) provided by the U.S. National Center for Environmental Information, with a spatial resolution of 1 / 4°; the Global Eddy-Resolved Physical Ocean Reanalysis Dataset (GLORYS) provided by the Mercator Marine Service of France, with a spatial resolution of 1 / 12° and a time span from 1993 to the present; and data from the Global Monthly Mean Simple Ocean Data Assimilation System (SODA 3.15.2) developed by the University of Maryland, with a spatial resolution of 0.5° and a time span from 1980 to 2024. The water depth data is provided by the Global Ocean Topography (GEBCO 2024) from the International Hydrographic Organization and the Intergovernmental Oceanographic Commission of UNESCO, with a horizontal resolution of 15 arcseconds. The eddy trajectory dataset is Meta 3.2 provided by the French Ocean Satellite Data Archive, Validation and Interpretation Centre, covering the period from 1993 to 2022. The EKE data is a 2°×2° result of the entire ocean depth obtained by synthesizing remote sensing and Argo data and combining them with the "surface modal" projection method. The atmospheric driving field, including 10m wind speed, sea surface pressure, 2m temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity, is provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) Fifth Generation Global Atmospheric Reanalysis Dataset (ERA5), with a spatial resolution of 1 / 4° and a time period covering 1950 to the present.

[0047] 2. Calculate the mixing coefficient across isodense surfaces: To calculate the mixing coefficient across isodense surfaces, a series of variables need to be calculated first, as follows.

[0048] Buoyancy frequency is calculated using temperature and salinity profile data from environmental field data. : ; In the formula: The frequency of buoyancy; It is the acceleration due to gravity. 9.81 ; For reference density, 1025 ; It is density; These are vertical coordinates; Bottom topographic roughness was calculated using water depth data: ; ; ; ; ; In the formula: For terrain roughness; For grid point numbers; Let i be the weight function for the i-th grid point; Let be the water depth at the i-th grid point; For weighting functions; This is a normalization constant; Let be the radial distance from the i-th grid point to the center of the circle; Standard deviation; The radius of the region where the grid point is located; For water depth; This is a weighted average of the water depths; It is a weighted average function; Introducing the structure function of the vortex dissipation vertical profile : ; In the formula: It is a high attenuation scale; For structure functions; Introducing a dimensionless vortex asymmetry metric to measure the strength of horizontal vortex asymmetry: ; ; In the formula: To measure the dimensionless quantity of vortex asymmetry; The horizontal asymmetric intensity of the vortex; The perimeter of the outermost boundary of the vortex; To and The circumference of a circle with an area equal to the area enclosed by the enclosed region; This is a function to find the maximum value. CA is used to characterize the degree to which the vortex shape deviates from an ideal circular structure; Based on the above variables, calculate the vertical mixing coefficient across density: ; In the formula: It is the vertical mixing coefficient across density; For mixing efficiency; The vortex energy dissipation rate; The buoyancy frequency is near the bottom layer; It is the vortex kinetic energy near the bottom layer.

[0049] Figure 2 Transdensity mixing coefficients at water depths of 250m, 1000m, and 3000m are given. It is evident that transdensity mixing is basally intensified, with the intensity at 3000m significantly greater than at 1000m. Furthermore, these coefficients are significantly increased in areas with strong western boundary currents, the Antarctic Circumpolar Current region, and areas with high topographic roughness, reaching a maximum of 10. -3 That's all. In reality, there are many seamounts in the global ocean. Near seamounts, due to the interaction of eddies and currents and topography, mesoscale movements are more active, and transdensity mixing is significantly enhanced.

[0050] 3. Construct a regional ocean model: To verify the effectiveness of the improved cross-isodensity surface parameterization scheme, we further utilized ROMS to construct a regional ocean model using the South China Sea as the study area. ROMS is a three-dimensional, nonlinear, topographically-following coordinate-based baroclinic primitive equation regional ocean model jointly developed by Rutgers University's Institute for Marine and Coastal Sciences and the University of California, Los Angeles, among other institutions. In recent years, the ROMS model has been widely applied by researchers to simulate ocean motions at various scales, covering a broad range of research areas such as air-sea coupling, ecology, geology, and data assimilation.

[0051] Here, the simulation region is 99.00°~133.75°E, 1.50°~29.17°N, with all boundaries being open except for the western boundary, which is set as a closed boundary. The grid has a horizontal resolution of 0.25° and is divided into 25 vertical layers, with a surface stretching factor of... The tensile coefficient of the bottom layer The water depth data comes from GEBCO 2024, with a range of 10 to 5500 m. To reduce the impact of large gradient terrain on the accuracy of the model simulation, we smoothed the water depth data appropriately.

[0052] The forced field variables required for model operation, such as wind speed, sea surface pressure, 2-meter temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity, are all derived from ERA May average data with a horizontal resolution of 0.25°×0.25° and a non-aligned grid. The model initial field, open boundary mesothermal salinity, sea surface height, and three-dimensional velocity are derived from SODA 3.15.2 May average reanalysis data.

[0053] To obtain an initial equilibrium field that matches the model's own equilibrium, the model is first adjusted through a spin-up process. Specifically, January climatological data from SODA 3.15.2 is used as the initial field, driven by the ERA5 forcing field of the monthly mean climatological data and the SODA 3.15.2 boundary field, with a simulation period of 50 years. This yields stable climatological simulation results. In the simulation, the boundary conditions for the free sea surface, barotropic flow field, and three-dimensional thermo-salinity flow field are Chapman_explicit, Shchepetkin, and Rad-Nudging mixed boundary conditions, respectively; the horizontal and vertical momentum and thermo-salinity advection schemes are third-order upwind and fourth-order central advection schemes, respectively; the vertical mixing scheme is KPP; and the horizontal diffusion and viscosity coefficient are 50 m. 2 s -1 In addition, a sponge layer approximately 250 km wide was constructed, with a viscosity coefficient of 500 m at its boundaries. 2 s -1 The simulation time step is 360 s.

[0054] After a long period of adjustment, the kinetic and thermodynamic processes of this result have been adapted to the model. Figure 2 Comparing the 10-year results after the spin-up with the multi-year average results from SODA 3.15.2, we can see that SST generally increases with decreasing latitude; SSS shows a decreasing distribution from the vicinity of the Luzon Strait in the northeast to the southwest, with the SSS in the Northwest Pacific being significantly higher than that in the South China Sea. The higher simulated salinity in the Gulf of Thailand may be related to the model not considering runoff; in addition, the western boundary currents in the South China Sea and the North Pacific are also clearly visible. The model simulation results can basically reflect the temperature, salinity, and flow field results in the South China Sea, and the simulation results are in good agreement with SODA 3.15.2, which can be used as the initial field for the next model report.

[0055] 4. Post-report comparison experiment based on regional ocean model: To verify the effectiveness of the new cross-density surface mixing scheme, a post-report comparison experiment was designed and related analyses were performed. The model post-report experiment consisted of two groups, EXP0 and EXP1, covering the period from 2011 to 2015. The initial field was the result from January of the 50th year of the Spin-up, and the forcing and boundary fields were actual ERA5 and SODA 3.15.2 monthly average data. The difference was that EXP0 used the KPP vertical mixing scheme, while EXP1 used an improved cross-density mixing scheme. The cross-density mixing scheme only considered the spatial variation of the mixing coefficient.

[0056] Figure 4 The results of two sets of experiments from 2015 were compared with GLORYS products, mainly focusing on key physical quantities such as sea surface temperature (SST), sea surface salinity (SSS), sea surface velocity, and sea surface height (SSH). The results show that the cross-density mixing scheme significantly improves upper-layer temperature compared to the KPP parameterization scheme, with the SST structure of EXP1 being closer to GLORYS. For salinity, the cross-density mixing scheme improves upper-layer salinity in the central South China Sea, with little overall difference between EXP0 and EXP1, and minimal difference compared to GLORYS in the Northwest Pacific. Compared to KPP, the cross-density mixing scheme results in lower sea surface velocities in more areas, moving closer to GLORYS, and also improves the flow field simulation to some extent. For sea surface height, the cross-density mixing scheme generally results in higher sea surface velocities compared to KPP, with little improvement, which may be related to the monthly average forced field used. Figure 5 Furthermore, the mixing layer depths for different months in the two sets of experiments were calculated. It can be seen that the mixing layer depth of EXP0 is lower than that of GLORYS, which is related to its higher SST simulation results. However, due to the improvement in temperature simulation results brought about by the cross-density mixing scheme, the mixing layer depth results of EXP1 are also improved compared to EXP0.

[0057] The embodiments described above are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, any equivalent changes or modifications made in accordance with the spirit disclosed in the present invention still fall within the patent scope of the present invention.

Claims

1. A parameterized simulation method for ocean forecasting of vertical mixing processes across density, characterized in that, This method includes the following steps: Step 1: Obtain the three-dimensional multivariable environmental field, water depth data, eddy trajectory dataset, eddy kinetic energy data, and atmospheric driving field of the ocean. The environmental field includes sea surface height, ocean temperature, ocean salinity, and ocean meridional and zonal current velocities; the atmospheric driving field includes wind speed, sea surface pressure, 2-meter temperature, sea surface temperature, shortwave radiation, cloud component, precipitation, and relative humidity. Step 2: Introduce eddy horizontal asymmetry, construct an ocean parameterized model based on the cross-density vertical mixing process, and fit the vertical mixing coefficient; Step 3: Construct a regional ocean model based on the regional ocean numerical model ROMS and verify the vertical mixing coefficient; Step 4: Ocean forecasting is performed using a parameterized ocean model based on the cross-density vertical mixing process.

2. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, In step 1, the sources for obtaining three-dimensional multivariate marine environmental field data include: the World Ocean Atlas WOA18 climatological data provided by the U.S. National Center for Environmental Information, with a spatial resolution of 1 / 4°; the Global Eddy-Resolved Physical Ocean Reanalysis Dataset (GLORYS) provided by the Mercator Marine Service of France, with a spatial resolution of 1 / 12° and a time period covering 1993 to the present; and the Global Monthly Mean Simple Ocean Data Assimilation System (SODA) 3.15.2 developed by the University of Maryland, with a spatial resolution of 0.5° and a time period covering 1980 to 2024.

3. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, In step 1, the sources of water depth data include: Global Ocean Topography GEBCO2024 provided by the International Hydrographic Organization and the Intergovernmental Oceanographic Commission of UNESCO, with a horizontal resolution of 15 arcseconds.

4. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, In step 1, the sources for obtaining the vortex trajectory dataset include: Meta3.2 provided by the French Ocean Satellite Data Archive, Validation and Interpretation Center, with a time range from 1993 to 2022; the eddy kinetic energy data is obtained by synthesizing and analyzing Argo data collected by remote sensing and the Global Ocean Real-Time Observation Network, and combining it with the surface modal projection method to obtain 2°×2° results for the entire ocean depth.

5. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, In step 1, the sources of atmospheric driving field data include the fifth-generation global atmospheric reanalysis dataset ERA5 provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has a spatial resolution of 1 / 4° and covers the period from 1950 to the present.

6. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, Step 2, the method for constructing a marine parametric model based on the cross-density vertical mixing process includes the following steps: Buoyancy frequency is calculated using temperature and salinity profile data from environmental field data. : ； In the formula: The frequency of buoyancy; It is the acceleration due to gravity. 9.81 ; For reference density, 1025 ; It is density; These are vertical coordinates; Bottom topographic roughness was calculated using water depth data: ； ； ； ； ； In the formula: For terrain roughness; For grid point numbers; For the first Weight of each grid point; For the first Water depth at each grid point; For the first Weight function for each grid point; This is a normalization constant; For from the first The radial distance from each grid point to the center of the circle; Standard deviation; The radius of the region where the grid point is located; For water depth; This is a weighted average of the water depths; It is a weighted average function; Introducing the structure function of the vortex dissipation vertical profile : ； In the formula: It is a high attenuation scale; For structure functions; Introducing a dimensionless vortex asymmetry metric to measure the strength of horizontal vortex asymmetry: ； ； In the formula: To measure the dimensionless quantity of vortex asymmetry; The horizontal asymmetric intensity of the vortex; The perimeter of the outermost boundary of the vortex; To and The circumference of a circle with an area equal to the area enclosed by the enclosed region; This is a function to find the maximum value. CA is used to characterize the degree to which the vortex shape deviates from an ideal circular structure; Based on the above variables, calculate the vertical mixing coefficient across density: ； In the formula: It is the vertical mixing coefficient across density; For mixing efficiency; The vortex energy dissipation rate; The buoyancy frequency is near the bottom layer; It is the vortex kinetic energy near the bottom layer.

7. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 1, characterized in that, Step 3, the method for constructing a regional ocean model based on the regional ocean numerical model ROMS includes the following steps: Using ROMS, a regional ocean model of a certain ocean region is constructed by adopting a three-dimensional, nonlinear, topographically-following coordinate-based baroclinic primitive equation regional ocean model. The grid is divided with a horizontal resolution of 0.25° and a vertical division of 25 layers. The surface layer tensile coefficient is... The tensile coefficient of the bottom layer The water depth data comes from GEBCO 2024, with the water depth range set to 10 ~ 5500m. In order to reduce the impact of large gradient terrain on the accuracy of model simulation, the water depth data is smoothed. The atmospheric driving field variables required for model operation are all derived from monthly average data of a specific month in the atmospheric reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF), with a horizontal resolution of 0.25°×0.25°. The atmospheric driving field variable data are provided in an unaligned grid format. The model initial field, open boundary mesothermal salinity, sea surface height, and three-dimensional velocity are derived from SODA 3.15.2 monthly average reanalysis data.

8. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 7, characterized in that, In step 3, in order to obtain the initial equilibrium field of the matching mode itself, it is first adjusted through the Spin-up process. The Spin-up process refers to the time period required to run from the initial state to close to physical equilibrium.

9. The parameterized simulation ocean forecasting method for cross-density vertical mixing processes according to claim 8, characterized in that, In step 3, January climatological data from SODA 3.15.2 is used as the initial field, driven by the ERA5 forcing field of the monthly mean climatological data and the SODA 3.15.2 boundary field, with a simulation period of 50 years; thus, stable climatological simulation results are obtained. In the simulation, the boundary conditions for the free sea surface, barotropic flow field, and three-dimensional temperature-salinity flow field are Chapman_explicit boundary conditions, Shchepetkin boundary conditions, and Rad-Nudging mixed boundary conditions, respectively; the horizontal and vertical momentum and temperature-salinity advection adopt third-order windward and fourth-order central advection schemes, respectively; the vertical mixing scheme is KPP; and the horizontal diffusion and viscosity coefficient are 50 m. 2 s -1 In addition, a sponge layer with a width of approximately 250 km and a viscosity coefficient of 500 m at the boundary was also constructed. 2 s -1 The simulation time step is 360 s.

10. An apparatus for a parameterized simulation method of ocean forecasting across density vertical mixing processes, comprising a memory and a processor, characterized in that, The memory is used to store a computer program; the processor is used to execute the computer program and, when executing the computer program, implement the steps of the parameterized simulation ocean forecasting method for the cross-density vertical mixing process as described in any one of claims 1 to 9.

Images