An unstructured grid adaptive submesoscale hybrid parameterization method and system

Abstract

The application discloses a kind of unstructured grid adaptive mesoscale mixing parameterization method and system, the method includes: in the ocean model of unstructured grid, the sea surface horizontal density gradient defined on the edge is calculated, after the sea surface horizontal density gradient is corrected according to effective resolution and frontal scale, the sea surface horizontal buoyancy gradient is calculated again;Then, the sea surface horizontal Ekman buoyancy flux is calculated according to the sea surface horizontal buoyancy gradient and the sea surface wind stress;If the sea surface horizontal Ekman buoyancy flux is positive, then the mixing coefficient in the boundary layer is further calculated.The application can effectively introduce the influence of symmetric instability process on boundary layer mixing in global unstructured grid ocean model, and significantly improve the simulation effect of mixed layer depth under coarse resolution.

Description

Technical Field

[0001] This invention relates to the field of ocean numerical model parameterization, and in particular to a sub-mesoscale hybrid parameterization method and system for unstructured grid adaptive parameterization. Background Technology

[0002] Numerical simulation is an important tool in physical oceanography research. Due to limitations in actual computational resources, the grid resolution of ocean models is finite. For subgrid physical processes with spatial scales smaller than the grid scale, the model itself cannot directly analyze them, and it is necessary to introduce their physical effects through parameterization methods to improve the accuracy of the model results. Submesoscale symmetric instability processes within the upper boundary layer of the ocean typically occur in regions with strong horizontal buoyancy gradients, causing strong vertical motion, promoting mixing within the upper boundary layer, and thus affecting changes in the mixing layer depth and the exchange of matter and energy between the sea surface and the atmosphere.

[0003] Current global ocean models cannot fully resolve to sub-mesoscale processes due to limitations in model resolution. Models with coarse resolution exhibit a systematic bias of an overestimation of the mixing layer depth. Developing corresponding sub-mesoscale parameterization schemes can improve the simulation effect within the boundary layer and enhance the model's simulation capabilities.

[0004] The parameterization of sub-mesoscale symmetric instability relies on the horizontal buoyancy gradient. Coarse-resolution models cannot accurately simulate this gradient, limiting the applicability of parameterization schemes, which are currently mainly used in high-resolution regional ocean models. On the other hand, unstructured grid ocean models have developed rapidly in recent years. Compared with regular latitude and longitude grids, unstructured grids can avoid the singularity problem at the poles, support smooth resolution refinement, and utilize computational resources more efficiently, thus improving computational efficiency. However, due to the fundamental differences between unstructured grids and regular latitude and longitude grids in terms of spatial discretization and gradient calculation, current parameterization schemes for sub-mesoscale symmetric instability developed based on conventional latitude and longitude grids cannot be directly ported to global models using unstructured grid frameworks. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to solve the technical problem that existing sub-mesoscale symmetric instability parameterization schemes are difficult to apply directly to relatively coarse unstructured grid global ocean models, and to provide an adaptive sub-mesoscale hybrid parameterization method and system for unstructured grids.

[0006] Technical solution: The unstructured mesh adaptive sub-mesoscale hybrid parameterization method of the present invention includes the following steps:

[0007] In an unstructured mesh ocean model, the sea surface horizontal density gradient is calculated based on the density field at the cell center; the sea surface horizontal density gradient is defined on the edge.

[0008] The effective resolution is calculated based on the spatial resolution of the ocean model; the sea surface horizontal density gradient is corrected based on the effective resolution and the frontal scale.

[0009] The horizontal buoyancy gradient of the sea surface is calculated based on the corrected horizontal density gradient of the sea surface.

[0010] The sea surface horizontal Ekman buoyancy flux is calculated based on the sea surface horizontal buoyancy gradient and sea surface wind stress.

[0011] If the sea surface horizontal Ekman buoyancy flux is positive, then the mixing coefficient within the boundary layer is calculated based on the sea surface horizontal buoyancy gradient.

[0012] Furthermore, the sea surface horizontal density gradient The calculation method is as follows:

[0013] ;

[0014] in, The distance between the centers of the two units on the side of the edge. The set of cells adjacent to the edge. For unit Relative to the edge The direction coefficient of the unit normal vector, For unit The sea surface density value at the center.

[0015] Furthermore, correcting the sea surface horizontal density gradient based on the effective resolution and frontal scale includes: the corrected sea surface horizontal density gradient. The calculation method is as follows:

[0016] ;

[0017] in, For effective resolution, This refers to the frontal scale.

[0018] Further, the corrected sea surface horizontal density gradient is interpolated to the cell center to calculate the sea surface horizontal buoyancy gradient; the sea surface horizontal buoyancy gradient The calculation method is as follows:

[0019] ;

[0020] in, It is the acceleration due to gravity. For reference density.

[0021] Furthermore, the method for calculating the sea surface horizontal Ekman buoyancy flux (EBF) is as follows:

[0022] ;

[0023] in, The sea surface wind stress vector. Coriolis constant, It is a unit vector in the vertical direction.

[0024] Furthermore, the mixing coefficient includes the vertical turbulent viscosity coefficient. :

[0025] ;

[0026] in, For the geospatial shear production item, its expression is:

[0027] ;

[0028] Where H is the depth of the sea surface boundary layer.

[0029] Furthermore, the mixing coefficient includes the vertical turbulent mixing coefficient. :

[0030] ;

[0031] in, The Prandtl number for turbulence is calculated using the following formula:

[0032] ;

[0033] in, For the overall Richardson number.

[0034] The unstructured mesh adaptive sub-mesoscale hybrid parameterization system of the present invention includes:

[0035] The sea surface horizontal density gradient calculation cell is used to calculate the sea surface horizontal density gradient based on the density field at the cell center in an unstructured mesh ocean model; the sea surface horizontal density gradient is defined on the edge.

[0036] The sea surface horizontal density gradient correction unit is used to calculate the effective resolution based on the spatial resolution of the ocean model; and to correct the sea surface horizontal density gradient based on the effective resolution and the frontal scale.

[0037] The sea surface horizontal buoyancy gradient calculation unit is used to calculate the sea surface horizontal buoyancy gradient based on the corrected sea surface horizontal density gradient.

[0038] The sea surface horizontal Ekman buoyancy flux calculation unit is used to calculate the sea surface horizontal Ekman buoyancy flux based on the sea surface horizontal buoyancy gradient and sea surface wind stress.

[0039] The mixing coefficient calculation unit calculates the mixing coefficient within the boundary layer based on the sea surface horizontal Ekman buoyancy flux if the sea surface horizontal buoyancy gradient is positive.

[0040] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the unstructured mesh adaptive sub-mesoscale hybrid parameterization method.

[0041] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the aforementioned sub-mesoscale hybrid parameterization method for unstructured meshes.

[0042] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:

[0043] (1) Through the adaptive adjustment mechanism based on grid resolution of the present invention, the horizontal buoyancy gradient on the unstructured grid can be accurately calculated without relying on the high-resolution regular grid, effectively characterizing the vertical mixing caused by the sub-mesoscale symmetric instability process in the upper boundary layer of the ocean, thereby improving the systematic bias of the mixing layer depth being too deep in the coarse resolution model, and significantly improving the simulation effect of the mixing layer depth under coarse resolution, especially in the Southern Ocean and the western boundary current, where sub-mesoscale symmetric instability is prevalent.

[0044] (2) This invention can enhance the simulation capability of unstructured grid global ocean models for mixing within the boundary layer, expand the applicability of existing sub-mesoscale symmetric instability parameterization schemes under different grid types and resolutions, provide more accurate simulation results of the upper ocean structure and mixing processes for global climate simulation, and improve the reliability of air-sea interaction and heat and material flux estimation. It has important scientific research and practical application value. Attached Figure Description

[0045] Figure 1 This is a flowchart of the hybrid parameterization method of the present invention.

[0046] Figure 2 This is a comparison chart of different hybrid parameterization methods and observation results in embodiments of the present invention. Detailed Implementation

[0047] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0048] like Figure 1 As shown, the sub-mesoscale hybrid parameterization method for unstructured mesh adaptive parameters includes the following steps.

[0049] Step 1: In the unstructured mesh ocean model, calculate the sea surface horizontal density gradient based on the density field at the cell center; the sea surface horizontal density gradient is defined on the edge.

[0050] Specifically, the ocean model of the unstructured mesh in this embodiment is MPAS-Ocean. The unstructured mesh uses irregular elements (such as triangles, quadrilaterals or hexagons) to divide the ocean region. This type of mesh is usually established by Voronoi meshing, Delaunay triangulation or other finite element / finite volume mesh generation algorithms.

[0051] Specifically, the horizontal density gradient of the sea surface defined on the edge is calculated based on the density field defined at the center of the cell. The horizontal density gradient of the sea surface defined on the edge is:

[0052] ;

[0053] This represents the horizontal density gradient of the sea surface defined on the edge. This represents the distance between the centers of the units on both sides of the edge. Represents the set of cells adjacent to an edge. Representation unit Relative to the edge The direction coefficient of the unit normal vector, This represents the sea surface density value at the center of the cell.

[0054] Step 2: Calculate the effective resolution based on the spatial resolution of the ocean model; correct the sea surface horizontal density gradient based on the effective resolution and the frontal scale.

[0055] Specifically, effective resolution Approximately five times the model's grid resolution, this embodiment uses the length of the edge containing the sea surface density gradient to characterize the model's resolution.

[0056] Frontal Scale Conventional latitude-related approximation methods can be used for calculation:

[0057] ;

[0058] in Latitude.

[0059] The correction formula for the sea surface horizontal density gradient is:

[0060] ;

[0061] in The sea surface horizontal density gradient before correction. This is the corrected sea surface horizontal density gradient.

[0062] Step 3: Calculate the horizontal buoyancy gradient of the sea surface based on the corrected horizontal density gradient of the sea surface.

[0063] Specifically, the corrected sea surface horizontal density gradient field defined on the edge is interpolated to the cell center. In this embodiment, this is based on the radial basis function interpolation method, which can be achieved by calling the subroutine mpas_reconstruct in the mode. The sea surface horizontal buoyancy gradient is calculated using the following formula:

[0064] ;

[0065] in The horizontal buoyancy gradient at the sea surface. It is the acceleration due to gravity. This is the corrected sea surface horizontal density gradient. For reference density.

[0066] Step 4: Calculate the sea surface horizontal Ekman buoyancy flux based on the sea surface horizontal buoyancy gradient and sea surface wind stress.

[0067] Specifically, the formula for calculating the sea surface horizontal Ekman buoyancy flux (EBF) is as follows:

[0068] ;

[0069] in Represents the sea surface wind stress vector. This represents the horizontal buoyancy gradient at the sea surface. For reference density, Represents the Coriolis constant. It is a unit vector in the vertical direction.

[0070] Step 5: If the sea surface horizontal Ekman buoyancy flux is positive, calculate the mixing coefficient within the boundary layer based on the sea surface horizontal buoyancy gradient.

[0071] Specifically, first determine the sign of EBF. If EBF is greater than 0, it indicates that there is a symmetrical unstable process in the water layer, and the relevant mixing coefficient is expressed as:

[0072] ;

[0073] in The vertical turbulent viscosity coefficient related to momentum. Represents the Coriolis constant. This represents the horizontal buoyancy gradient at the sea surface. The expression for the geo-transfer shear production item is:

[0074] ;

[0075] Where H represents the depth of the sea surface boundary layer.

[0076] The vertical turbulent mixing coefficients related to temperature and salinity are:

[0077] ;

[0078] in The Prandtl number for turbulence is calculated using the following formula:

[0079] ;

[0080] in For the overall Richardson number.

[0081] If EBF is less than 0, the relevant mixing coefficients are not calculated.

[0082] The method described in this invention will be verified through specific experiments below.

[0083] Step 1: Prepare the hardware and software environment.

[0084] 1.1 Hardware Platform: A computer or high-performance computing server capable of running a Linux operating system. The specific hardware configuration should be selected based on the scope and resolution requirements of the numerical simulation area. This embodiment uses a high-performance computing cluster as the operating environment, and remote login and operation are performed through an SSH client tool to meet the computational needs of large-scale numerical simulations.

[0085] 1.2 Software Environment: The software includes a Fortran compiler, parallel MPI library, NetCDF library, and PIO library required for model compilation and execution. It also includes the MPAS-Ocean (Model for Prediction Across Scales-Ocean) model with a sub-mesoscale hybrid parameterization scheme, as well as the MPAS-Ocean model without a parameterization scheme; the JIGSAW program for generating and processing unstructured meshes; the geometric_features program; the MPAS-Tools toolkit; the SOSIE program for initial field creation; and the NCL (NCARCommand Language) program for creating forced fields, visualizing simulation outputs, and performing post-processing analysis.

[0086] Step 2: Data preparation.

[0087] 2.1 Obtaining Topographic Data: Download global topographic field data with a resolution of 0.1 degrees from the publicly available database of the model.

[0088] 2.2 Obtaining Vertical Grid Data: Download the vertical grid data, which consists of 80 layers of surface encryption, from the publicly available database.

[0089] 2.3 Obtaining Atmospheric Forcing Data: Download monthly mean data of the global air-sea interface with a spatial resolution of 0.25 degrees for the period 2019–2021 from the ERA5 reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). Variables include: 10-meter wind speed, sea surface atmospheric pressure, sea ice coverage, average total precipitation rate, average runoff rate, average evaporation rate, average sea surface latent heat flux, average sea surface sensible heat flux, average sea surface net longwave radiation flux, average sea surface downward longwave radiation flux, and average sea surface downward shortwave radiation flux. Download monthly mean sea surface wind stress data with a spatial resolution of 0.25 degrees from the Global Ocean Monthly Mean Sea Surface Wind and Stress from Scatterometer and Model dataset provided on the Copernicus Marine Environment Monitoring Service (CMEMS) website.

[0090] 2.4 Obtaining Initial Field Data: Temperature, salinity, current velocity, and sea surface height data for January 1, 2019, were downloaded from the Global Ocean Renanlysis and Simulations (GLORYS) dataset provided by CMEMS to create the initial field.

[0091] 2.5 Acquiring Argo Observational Data: Download temperature and salinity data with a spatial resolution of 1 degree from the website of the Hangzhou Global Ocean Argo System Field Scientific Observation and Research Station for the period from 2019 to 2021 for mixed layer depth comparison. The selected data product is the Global Ocean Argo Grid Dataset (GDCSM_Argo).

[0092] Step 3: Model configuration.

[0093] 3.1 Compile the MPAS-Ocean mode according to the actual hardware platform and software environment.

[0094] 3.2 First, use the JIGSAW program to generate an unstructured triangular mesh, then use MPAS-Tools to convert it into a quasi-hexagonal mesh required by the model, and use the geometric_features program to mask the land area, finally obtaining the unstructured horizontal mesh required for model operation.

[0095] 3.3 Based on the existing terrain data, vertical grid data, and GLORYS data, configure the namelist.ocean.init and streams.ocean.init files in the pattern to generate the initial field data required by the pattern.

[0096] 3.4. Use NCL to interpolate the ERA5 forced field data on the regular latitude and longitude grid onto the unstructured horizontal grid to obtain the forced field required for model operation.

[0097] Step 4: Mode Operation.

[0098] Mode 1: The original oceanographic model without the method of this invention, which uses the KPP scheme (K-Profile Parameterization).

[0099] Mode 2: The marine mode that incorporates the method of this invention uses the vertical hybrid parameterization scheme of the KPP scheme and the parameterization method proposed in this invention.

[0100] 4.1 Modify the namelist.ocean file, set the simulation time step to 5 minutes, the total simulation time to 3 years, enable the vertical hybrid parameterization option, and select the KPP scheme for the vertical hybrid parameterization scheme; use the default settings for the remaining settings.

[0101] 4.2 Modify the streams.ocean file of the model, configuring the input interfaces for the actual forced field and the initial field in sequence, setting the output file path, and setting the output step size to one day. The vertical mixing coefficients in the model (such as the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient) affect the vertical mixing intensity between the upper and lower water layers, thereby changing the evolution of the temperature and density profiles, and indirectly determining the thickness of the mixing layer. Therefore, the mixing layer depth is selected as the output variable to measure the effect of the parameterization scheme.

[0102] 4.3 Run the original ocean mode without introducing parameterization schemes according to the actual operating platform configuration.

[0103] 4.4. The initial field and forced field that have already been processed are used. Since the parameterization method proposed in this invention is used together with the KPP scheme, and since all vertical hybrid parameterization modules in the mode are concentrated together, they can be run directly on the basis of the original mode configuration without modifying the running configuration. Therefore, the parameterization scheme of this invention is introduced.

[0104] Step 5: Result Evaluation.

[0105] 5.1 Organize the mixed layer depth data (resolution of one day, duration of three years) obtained from the simulation of Mode 1 and Mode 2 in step four, and use NCL to interpolate it to the latitude and longitude grid where the previously downloaded Argo observation data is located, for subsequent comparative analysis.

[0106] 5.2 Calculating the Argo Mixed Layer Depth (ArgoMLD) of Argo observation data products: First, determine the criterion for the mixed layer depth. Select a reference depth of a reference surface layer (usually ten meters) and search downwards. When the density of a certain layer differs from the density of the reference depth by 0.03 kg / m³, the search continues. 3 The depth of this layer is defined as the depth of the bottom of the mixing layer. In MATLAB, the geopotential density is calculated using temperature and salinity data from the data product, and the mixing layer depth is calculated based on the criteria, ultimately obtaining the seasonally averaged mixing layer depth data.

[0107] 5.3 The mixing layer depths obtained from model simulations before and after incorporating the method of this invention are compared with observational data to evaluate the effectiveness of the parameterization scheme. The mixing layer depth before incorporating the method of this invention is denoted as KPP MLD, and the mixing layer depth after incorporating the method of this invention is denoted as SI MLD. Considering that symmetric instability has significant spatiotemporal distribution characteristics globally and tends to occur in the western boundary current region of the ocean and the Southern Ocean during winter, the average mixing layer depths in the Northern Hemisphere, Southern Hemisphere, and the Kuroshio Extension region during winter were selected for comparison. Table 1 shows the comparison results of the three. It can be found that the coarse resolution model has a systematic overestimation of the mixing layer depth due to its inability to fully resolve the physical processes within the boundary layer. However, after incorporating the parameterization method of this invention, this systematic bias is reduced, effectively improving the model's simulation performance. This performance improvement is even more significant in regions where symmetric instability is prevalent.

[0108] 5.4, Figure 2 The figure shows a comparison between model simulation results and observational results for the latitudinal average mixing layer depth in the Kuroshio Extension region before and after incorporating the method of this invention. The horizontal axis represents latitude, and the vertical axis represents the mixing layer depth. The figure shows that after incorporating the parameterization method of this invention, the difference between the model simulation results and the observational results is significantly reduced, indicating that this method effectively improves the model's simulation performance.

[0109] Table 1. Comparison of simulated and observed mixed layer depths before and after the introduction of the method of this invention.

[0110]

[0111] The unstructured mesh adaptive sub-mesoscale hybrid parameterization system of the present invention includes:

[0112] The sea surface horizontal density gradient calculation cell is used to calculate the sea surface horizontal density gradient based on the density field at the cell center in an unstructured mesh ocean model; the sea surface horizontal density gradient is defined on the edge.

[0113] The sea surface horizontal density gradient correction unit is used to calculate the effective resolution based on the spatial resolution of the ocean model; and to correct the sea surface horizontal density gradient based on the effective resolution and the frontal scale.

[0114] The sea surface horizontal buoyancy gradient calculation unit is used to calculate the sea surface horizontal buoyancy gradient based on the corrected sea surface horizontal density gradient.

[0115] The sea surface horizontal Ekman buoyancy flux calculation unit is used to calculate the sea surface horizontal Ekman buoyancy flux based on the sea surface horizontal buoyancy gradient and sea surface wind stress.

[0116] The mixing coefficient calculation unit calculates the mixing coefficient within the boundary layer based on the sea surface horizontal Ekman buoyancy flux if the sea surface horizontal buoyancy gradient is positive.

[0117] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the unstructured mesh adaptive sub-mesoscale hybrid parameterization method.

[0118] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the aforementioned sub-mesoscale hybrid parameterization method for unstructured meshes.

[0119] The computer-readable storage medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage devices, magnetic disk storage devices or other magnetic storage devices, flash memory or any other medium that can be used to store program code in the form of instructions or data structures and is accessible by a computer.

[0120] The processor is used to execute a computer program stored in memory to implement the various steps in the methods described in the above embodiments.

Claims

1. A sub-mesoscale hybrid parameterization method for unstructured meshes, characterized in that, Includes the following steps: In an unstructured mesh ocean model, the sea surface horizontal density gradient is calculated based on the density field at the cell center; the sea surface horizontal density gradient is defined on the edge. The effective resolution is calculated based on the spatial resolution of the ocean model; the sea surface horizontal density gradient is corrected based on the effective resolution and the frontal scale. The horizontal buoyancy gradient of the sea surface is calculated based on the corrected horizontal density gradient of the sea surface. The sea surface horizontal Ekman buoyancy flux is calculated based on the sea surface horizontal buoyancy gradient and sea surface wind stress. If the sea surface horizontal Ekman buoyancy flux is positive, then the mixing coefficient within the boundary layer is calculated based on the sea surface horizontal buoyancy gradient. The sea surface horizontal density gradient The calculation method is as follows: ； in, The distance between the centers of the two units on the side of the edge. The set of cells adjacent to the edge. For unit Relative to the edge The direction coefficient of the unit normal vector, For unit Sea surface density value at the center; Correcting the sea surface horizontal density gradient based on the effective resolution and frontal scale includes: the corrected sea surface horizontal density gradient. The calculation method is as follows: ； in, For effective resolution, For frontal scale; The corrected sea surface horizontal density gradient is interpolated to the cell center to calculate the sea surface horizontal buoyancy gradient; the sea surface horizontal buoyancy gradient... The calculation method is as follows: ； in, It is the acceleration due to gravity. For reference density; The method for calculating the sea surface horizontal Ekman buoyancy flux (EBF) is as follows: ； in, The sea surface wind stress vector. Coriolis constant, It is a unit vector in the vertical direction; The mixing coefficient includes the vertical turbulent viscosity coefficient. : ； in, For the geospatial shear production item, its expression is: ； Where H is the depth of the sea surface boundary layer; The mixing coefficient includes the vertical turbulent mixing coefficient. : ； in, The Prandtl number for turbulence is calculated using the following formula: ； in, For the overall Richardson number.

2. A sub-mesoscale hybrid parameterization system adaptive to unstructured meshes, characterized in that, The sub-mesoscale hybrid parameterization method for implementing unstructured mesh adaptation as described in claim 1 includes: The sea surface horizontal density gradient calculation cell is used to calculate the sea surface horizontal density gradient based on the density field at the cell center in an unstructured mesh ocean model; the sea surface horizontal density gradient is defined on the edge. The sea surface horizontal density gradient correction unit is used to calculate the effective resolution based on the spatial resolution of the ocean model; and to correct the sea surface horizontal density gradient based on the effective resolution and the frontal scale. The sea surface horizontal buoyancy gradient calculation unit is used to calculate the sea surface horizontal buoyancy gradient based on the corrected sea surface horizontal density gradient. The sea surface horizontal Ekman buoyancy flux calculation unit is used to calculate the sea surface horizontal Ekman buoyancy flux based on the sea surface horizontal buoyancy gradient and sea surface wind stress. The mixing coefficient calculation unit calculates the mixing coefficient within the boundary layer based on the sea surface horizontal Ekman buoyancy flux if the sea surface horizontal buoyancy gradient is positive.

3. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the sub-mesoscale hybrid parameterization method for unstructured meshes according to claim 1.

4. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the sub-mesoscale hybrid parameterization method for unstructured meshes according to claim 1.

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