Mesh-adaptive sub-mesoscale hybrid parameterization method and system

Abstract

The invention discloses a grid-adaptive sub-mesoscale hybrid parameterization method and system, and the method comprises the steps: calculating an effective resolution and a frontal scale according to the spatial resolution of an ocean model, carrying out the calibration of a horizontal buoyancy gradient, and calculating an air-sea interface buoyancy flux and a horizontal Akkerman buoyancy flux according to the calibrated horizontal buoyancy gradient; and calculating to obtain expressions of the convective mixing effect and the sub-mesoscale mixing effect, and a vortex viscosity coefficient and a vortex diffusion coefficient of the sub-mesoscale mixing effect. According to the method, the problem that an existing parameterization scheme cannot be applied to a coarse-resolution ocean model at present is solved, and the effect of introducing sub-mesoscale mixing into ocean models with different resolutions is achieved.

Description

Technical Field

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

[0002] The upper ocean mixing layer is a crucial channel for ocean-atmosphere exchange, and the accuracy of its simulations is a key indicator of the simulation capabilities of ocean models, directly impacting our understanding and predictions of global warming and climate change. The dynamic processes of the upper ocean mixing layer are complex, with various processes capable of generating turbulent mixing. However, it remains difficult to explain how these complex dynamic processes produce turbulent mixing, leading to significant biases in ocean models' simulations of the upper ocean mixing layer.

[0003] Submesoscale symmetric instability is a significant and widespread dynamic process in the upper ocean mixing layer, promoting positive energy cascades that ultimately lead to strong mixing. Observations show that the mixing intensity induced by this process at fronts can be three orders of magnitude higher than the background value! Limited by its small spatial scale, the spatial resolution of current mainstream ocean models cannot directly resolve submesoscale processes, making this a key reason for the bias in current ocean models' simulation of upper ocean dynamic processes. At fronts, convection processes and submesoscale symmetric instability usually occur simultaneously and interact, ultimately resulting in two layers at the front. Existing submesoscale parameterization schemes considering convection effects reproduce mixing intensity that depends on the horizontal buoyancy gradient intensity, but the horizontal buoyancy gradient intensity simulated by ocean models is clearly related to its spatial resolution. Existing research indicates that the spatial scale of the upper ocean mixing layer front, which is closely related to the horizontal buoyancy gradient, is on the order of hundreds of meters to 1 kilometer. This means that current submesoscale induced mixing parameterization schemes are only applicable to high-resolution ocean models that can resolve the upper mixing layer front, but not to coarse-resolution models such as climate-ocean models with spatial resolutions on the order of 10 kilometers. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a grid-adaptive sub-mesoscale mixing parameterization method and system, which can automatically calibrate the horizontal buoyancy gradient according to the spatial resolution of the ocean model, and realize the application of sub-mesoscale mixing effect parameterization considering convection effects in climate models.

[0005] Technical solution: The mesh-adaptive sub-mesoscale hybrid parameterization method of the present invention includes the following steps:

[0006] Calculate the block potential vorticity and negative block potential vorticity depth at the model grid points based on the ocean model;

[0007] The effective resolution is calculated based on the spatial resolution of the ocean model, and the frontal scale is calculated based on the negative block vortex depth, friction velocity, and convection velocity.

[0008] The horizontal buoyancy gradient of the upper boundary layer depth averaged is calibrated using the effective resolution and frontal scale to obtain the calibrated horizontal buoyancy gradient.

[0009] The depth of the troposphere and the depth of the sub-mesoscale mixing layer are calculated based on friction velocity, convection velocity, and geostrophic velocity.

[0010] Calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibrated horizontal buoyancy gradient.

[0011] Calculate the expressions for convective mixing effects and submesoscale mixing effects, and calculate the eddy viscosity coefficient and eddy diffusion coefficient of the submesoscale mixing effect.

[0012] Further, the calibration of the horizontal buoyancy gradient averaged at the upper boundary layer depth using the effective resolution and frontal scale to obtain the calibrated horizontal buoyancy gradient includes:

[0013] Calibrate horizontal buoyancy gradient ,in For effective resolution, For frontal scale, This represents the horizontal buoyancy gradient calculated based on the ocean model.

[0014] Furthermore, the horizontal buoyancy gradient calculated based on the ocean model... ,in For seawater buoyancy, and These are the meridional and latitudinal coordinates of the grid points in the ocean model.

[0015] Further, the calculation of the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibrated horizontal buoyancy gradient includes:

[0016] Air-sea interface buoyancy flux Horizontal Ekman buoyancy flux ;

[0017] in, It is the acceleration due to gravity. The coefficient of thermal expansion is Net heat flux, The density constant of seawater For the specific heat of seawater, The coefficient of salt shrinkage. For net freshwater flux, The salinity of the sea surface. The sea surface wind stress vector. It is a unit vector in the vertical direction. These are Coriolis parameters.

[0018] Furthermore, the calculation of the tropospheric depth and the sub-mesoscale mixing layer depth based on friction velocity, convection velocity, and geostrophic velocity includes:

[0019] The depth of the troposphere can be calculated using the following formula. and sub-mesoscale mixing layer depth ,

[0020] ;

[0021] in, For friction speed, For convection velocity, The depth of the negative block vortex. It is a constant. The angle between the wind direction and the geostrophic flow direction. The magnitude of the earth's rotation speed.

[0022] Furthermore, the expression for the convective mixing effect is as follows:

[0023] ;

[0024] in, The vertical flux of the tracer particles. The sea surface flux of tracer particles. This refers to the depth of the seawater.

[0025] Furthermore, the expression for the sub-mesoscale mixing effect is as follows:

[0026] ;

[0027] in, , This refers to the depth of the seawater.

[0028] Furthermore, the eddy viscosity coefficient corresponding to the sub-mesoscale mixing effect is:

[0029] ;

[0030] The eddy diffusion coefficient corresponding to the sub-mesoscale mixing effect is:

[0031] ;

[0032] in, To balance the Richardson number.

[0033] Furthermore, the diffusion coefficient of the tracer particles corresponding to the sub-mesoscale mixing effect is:

[0034] ;

[0035] in, To balance the Richardson number.

[0036] The mesh-adaptive sub-mesoscale hybrid parameterization system of the present invention includes:

[0037] The negative block potential vortex depth calculation unit is used to calculate the block potential vortex and negative block potential vortex depth of the model grid points based on the ocean model.

[0038] The effective resolution and frontal scale calculation unit is used to calculate the effective resolution based on the spatial resolution of the ocean model, and to calculate the frontal scale based on the negative block vortex depth, friction velocity, and convection velocity.

[0039] A horizontal buoyancy gradient calibration unit is used to calibrate the depth-averaged horizontal buoyancy gradient of the upper boundary layer using the effective resolution and frontal scale, so as to obtain a calibrated horizontal buoyancy gradient.

[0040] The tropospheric and sub-mesoscale mixed layer depth calculation unit is used to calculate the tropospheric depth and sub-mesoscale mixed layer depth based on friction velocity, convection velocity, and geostrophic velocity.

[0041] The buoyancy flux calculation unit is used to calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibration horizontal buoyancy gradient.

[0042] The calculation unit for convective mixing effect and sub-mesoscale mixing effect is used to calculate the expressions for convective mixing effect and sub-mesoscale mixing effect, and to calculate the eddy viscosity coefficient and eddy diffusion coefficient of sub-mesoscale mixing effect.

[0043] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: (1) The present invention establishes a sub-mesoscale mixing parameterization method and system that can be adaptively adjusted according to the resolution of the ocean model and coupled with the convection effect, which solves the problem that the existing parameterization schemes cannot be applied to coarse resolution ocean models, and realizes the introduction of sub-mesoscale mixing effects in ocean models of different resolutions. The present invention can significantly improve the simulation effect of ocean models on the mixing layer above the ocean, which helps to improve the prediction capability of ocean models, thereby providing a more reliable scientific basis for responding to climate change and extreme ocean disasters, and has great application prospects in regional and climate ocean model simulation. (2) Based on the spectral slope characteristics of the horizontal buoyancy gradient, the present invention considers the scale characteristics of the front in the mixing layer above the ocean and corrects the horizontal buoyancy gradient in the coarse resolution ocean model; the corrected horizontal buoyancy gradient can characterize the dynamic characteristics of the front in the mixing layer above the ocean, and thus can be applied to the sub-mesoscale mixing effect parameterization scheme. (3) The present invention considers the difference in ocean model grid resolution, and can adaptively obtain the mixing intensity according to the grid, which can be used for climate ocean model simulation and improve the accuracy of climate model simulation. Attached Figure Description

[0044] Figure 1 This is a flowchart of the sub-mesoscale hybrid parameterization method according to an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram illustrating the verification results of an embodiment of the present invention. Detailed Implementation

[0046] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0047] like Figure 1 As shown, the mesh-adaptive sub-mesoscale hybrid parameterization method includes the following steps.

[0048] Step 1: Calculate the block position and negative block position vortex depth of the ocean grid points based on the ocean model.

[0049] Specifically, ocean models such as the nearshore ocean models ROMS and CROCO, and the MIT ocean circulation model MITgcm, all solve the Reynolds-averaged Navier-Stokes equations, using seawater temperature, salinity, and current velocity as the basic output quantities. Seawater buoyancy is calculated from temperature and salinity, and meridional and zonal current velocities are calculated from current velocity. The following formula calculates the potential vorticity of the block. :

[0050] ;

[0051] in, Coriolis parameters, For seawater buoyancy, , These represent the meridional and zonal flow velocities, respectively. and Meridian and latitudinal coordinates This refers to the vertical relative vorticity. The value represents the difference between a variable at a given depth and its surface value; the angle brackets represent the average depth.

[0052] If it is a negative value, that is If the negative block vortex depth is calculated, then sub-mesoscale mixing parameterization is not performed.

[0053] The depth H of the negative vortex layer can be determined according to the following criteria: calculate the depth of each layer sequentially starting from the surface. When the calculated negative potential vortex becomes positive at a certain depth, that is... At this point, the corresponding depth is H.

[0054] Step 2: Calculate the effective resolution based on the spatial resolution of the ocean model, and calculate the frontal scale based on the negative block vortex depth, friction velocity, and convection velocity.

[0055] Specifically, due to the numerical dissipation problem in ocean models, for effective resolution... Generally speaking, its size is equal to the model mesh resolution. It is approximately 7 times s, therefore it can be calculated using the following expression:

[0056] ;

[0057] For the scale of the front The intensity of atmospheric-sea interface fluxes can be calculated using the parameters obtained from ocean models, and the following formula can be used for calculation.

[0058] ;

[0059] in, It is a constant. and The conversion rate between mechanical energy and potential energy. and denoted as friction velocity and convection velocity, and H as the depth of the negative vortex layer. It reflects the strength of the flux at the air-sea interface.

[0060] Step 3: Use the effective resolution and frontal scale to calibrate the horizontal buoyancy gradient of the upper boundary layer depth average to obtain the calibrated horizontal buoyancy gradient.

[0061] Specifically, calibrating the horizontal buoyancy gradient The formula is:

[0062] ;

[0063] in, It is the horizontal buoyancy gradient before calibration, which can be obtained through seawater buoyancy. The following can be calculated directly using the model mesh size:

[0064] .

[0065] Step 4: Calculate the tropospheric depth and sub-mesoscale mixed layer depth based on friction velocity, convection velocity, and geostrophic velocity.

[0066] Specifically, the hydrosphere depth and the sub-mesoscale mixing layer depth are calculated using the following expressions:

[0067] ;

[0068] in, It is a constant. For tropospheric thickness, The thickness of the sub-mesoscale hybrid layer. The magnitude of the earth rotation velocity, It is the angle between the wind direction and the geostrophic flow direction.

[0069] Step 5: Calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibrated horizontal buoyancy gradient.

[0070] Specifically, air-sea interface buoyancy flux Including those caused by heat flux Caused by salt flux Two parts, the expression of which is:

[0071] ;

[0072] Horizontal Ekman buoyancy flux The expression is:

[0073] ;

[0074] in, It is the acceleration due to gravity. The coefficient of thermal expansion is Net heat flux, The density constant of seawater For the specific heat of seawater, The coefficient of salt shrinkage. For net freshwater flux, The salinity of the sea surface. The sea surface wind stress vector. It is a unit vector in the vertical direction. These are Coriolis parameters.

[0075] Step 6: Calculate the expressions for the convective mixing effect and the sub-mesoscale mixing effect, and calculate the eddy viscosity coefficient and eddy diffusion coefficient of the sub-mesoscale mixing effect.

[0076] Specifically, the mixing effect caused by the convection process is parameterized by the following expression:

[0077] ;

[0078] in, This represents the vertical flux of temperature, salinity, or any tracer particle. To trace the flux of particles to the sea surface. This refers to the depth of the seawater.

[0079] Specifically, the sub-mesoscale mixing effect can be calculated using the following piecewise function:

[0080] ;

[0081] in, .

[0082] The corresponding eddy viscosity coefficient is:

[0083] ;

[0084] The corresponding eddy diffusion coefficient is:

[0085] ;

[0086] in, To balance the Richardson number.

[0087] Furthermore, submesoscale processes can induce the diffusion coefficient of tracer particles along the density surface, the magnitude of which can be calculated using the following expression:

[0088] .

[0089] The method described in this invention will be verified through specific experiments below.

[0090] Step 1: Pattern preparation.

[0091] (1.1) Computer preparation: Prepare a computer with a Linux operating system or a supercomputing server. The specific hardware requirements depend on the size of the simulation area. In this embodiment, a supercomputing server is used, and remote operation is performed through an SSH client tool.

[0092] (1.2) Mode preparation: Upload the CROCO code that writes sub-mesoscale mixing parameters to the server and decompress it.

[0093] Step 2: Data Acquisition.

[0094] (2.1) Obtaining topographic data: Obtain seabed topographic data with a global spatial resolution of 2' from the ETOPO Global Relief Model website to prepare for subsequent mesh production.

[0095] (2.2) Obtaining ECMWF atmospheric forcing data: Monthly mean data of the air-sea interface in the Kuroshio Extension region from 2010 to 2019 with a spatial resolution of 0.25 degrees were obtained from the ECMWF website. Variables included: 10-meter wind speed, 2-meter dew point temperature, 2-meter air temperature, evaporation, precipitation, sensible heat flux, latent heat flux, net shortwave radiation, and net longwave radiation. These were used to create the atmospheric forcing field file for the model.

[0096] (2.3) Obtaining GLORYS ocean reanalysis data: Monthly mean ocean reanalysis data for the Kuroshio Extension region from 2010 to 2019 with a spatial resolution of 1 / 12 degree were obtained from the GLORYS website. Variables included: temperature, salinity, horizontal current velocity, and sea surface height. These were used to create initial and boundary field files.

[0097] (2.4) Obtain ARGO observation data: Download the monthly mean ocean temperature and salinity data of the Kuroshio extension region from 2010 to 2019 with a spatial resolution of 0.5 degrees from the Roemmich-Gilson Argo Climatology website for the purpose of mixing layer depth comparison.

[0098] Step 3: Model configuration.

[0099] (3.1) Selecting the simulation area and creating the mesh: The mesh file was created using the MATLAB program provided by CROCO. The area selected for this experiment was 15°N to 45°N latitude and 130°E to 180°E longitude. To demonstrate the adaptive problem of the present invention to changes in mesh resolution, three sets of meshes with different resolutions were created, namely 60 km, 25 km and 10 km.

[0100] (3.2) Create initial field, boundary field and forcing field based on simulation area: Based on three sets of grids with different resolutions, use the MATLAB program provided by CROCO to create corresponding atmospheric forcing field files for 2010-2019 using ECMWF data, and create initial field and boundary field files for 2010-2019 using GLORYS ocean reanalysis data.

[0101] (3.3) Upload the completed mesh, forced field, initial field and boundary field files to the server.

[0102] Step 4: Mode Operation.

[0103] (4.1) Compile the model; modify the CROCO code path in the jobcomp file according to the location of the CROCO mode code; modify the number of grids, vertical layers, and computational cores in the param.h file according to the number of model grids and computational resource requirements (60km model: LLm0=98, MMm0=70, N=60, NP_XI=11, NP_ETA=8; 25km model: LLm0=198, MMm0=141, N=60, NP_XI=11, NP_ETA=8; 10km model: LLm0=598, MMm0=423, N=60, NP_XI=11, NP_ETA=8); modify the corresponding paths in the croco.in file according to the paths of the grid, forced field, initial field, and boundary field files; modify the simulation time step according to different grid files (60km model: dt = 900s; 25km model: dt = For the 600s; 25km model: dt = 300s), output time step (1 day) and simulation time length (10 years). After modification, run jobcomp to compile the model.

[0104] (4.2) Submit the task: After compilation, submit the task to start the simulation. After the simulation is completed, perform further processing and analysis on the daily average data output by the model.

[0105] Step 5: Result Verification.

[0106] (5.1) Calculation of the mixing layer thickness output by the model: Based on the density field output by the simulation, the depth of the mixing layer in the ocean was calculated in the three simulation experiments. Here, the mixing layer is defined as the density difference between the density at a depth of 10 meters and the density at a depth of 0.03 kg / m. 3 The calculated mixing layer depths were averaged monthly to obtain monthly average data. Considering the time required for model spin-up and the fact that sub-mesoscale activity is only relatively high in winter, only the winter months of the last three years (January to March 2017-2019) are compared here.

[0107] (5.2) Calculate the thickness of the observed mixing layer: Based on the temperature and salinity data observed by ARGO, calculate the seawater density at different depths and calculate the depth of the mixing layer in the ocean during winter in the corresponding region and year.

[0108] (5.3) Verify the effect of the present invention: Compare the upper mixing layer depth obtained by the model with the observation to evaluate the effect of the parameterization scheme.

[0109] Table 1. Comparison of the method of the present invention with simulated hybrid layers without considering parameterization and without calibrating parameterization.

[0110]

[0111] Table 1 shows the comparison results of the mixing layer depth using the method of the present invention with that of simulations without parameterization or calibration. The mixing layer depth is defined as the change in seawater density relative to a depth of 10 meters reaching 0.03 kg / m³. 3 The depth. Among them, "not considering parameterization" refers to simulation results that do not consider sub-mesoscale mixed parameterization, and "not calibrated parameterization" refers to simulation results that consider existing sub-mesoscale mixed parameterization. Figure 2 The image shown is a schematic diagram of the verification results. Figure 2 In the figure, a, b, and c represent the simulation results in the 60km, 25km, and 10km models, respectively. The black curve represents the observed distribution of the mixing layer thickness with latitude. The blue curve represents the simulation results without considering sub-mesoscale mixing parameterization. The yellow curve represents the simulation results considering uncalibrated parameterization. The red curve represents the simulation results considering the method of this invention.

[0112] The comparison reveals that the result without parameterization is significantly deeper than the observation, while the lack of parameterization improves this bias to some extent. The mixed layer thickness obtained by the method of this invention has a significantly smaller bias, indicating that the method of this invention is significantly better than the existing methods.

[0113] The mesh-adaptive sub-mesoscale hybrid parameterization system of the present invention includes:

[0114] The negative block potential vortex depth calculation unit is used to calculate the block potential vortex and negative block potential vortex depth of ocean grid points based on the ocean model.

[0115] The effective resolution and frontal scale calculation unit is used to calculate the effective resolution based on the spatial resolution of the ocean model, and to calculate the frontal scale based on the negative block vortex depth, friction velocity, and convection velocity.

[0116] A horizontal buoyancy gradient calibration unit is used to calibrate the depth-averaged horizontal buoyancy gradient of the upper boundary layer using the effective resolution and frontal scale, so as to obtain a calibrated horizontal buoyancy gradient.

[0117] The tropospheric and sub-mesoscale mixed layer depth calculation unit is used to calculate the tropospheric depth and sub-mesoscale mixed layer depth based on friction velocity, convection velocity, and geostrophic velocity.

[0118] The buoyancy flux calculation unit is used to calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibration horizontal buoyancy gradient.

[0119] The calculation unit for convective mixing effect and sub-mesoscale mixing effect is used to calculate the expressions for convective mixing effect and sub-mesoscale mixing effect, and to calculate the eddy viscosity coefficient and eddy diffusion coefficient of sub-mesoscale mixing effect.

Claims

1. A mesh-adaptive sub-mesoscale hybrid parameterization method, characterized in that, Includes the following steps: Calculate the block potential vorticity and negative block potential vorticity depth at the model grid points based on the ocean model; The effective resolution is calculated based on the spatial resolution of the ocean model, and the frontal scale is calculated based on the negative block vortex depth, friction velocity, and convection velocity. The horizontal buoyancy gradient of the upper boundary layer depth averaged is calibrated using the effective resolution and frontal scale to obtain the calibrated horizontal buoyancy gradient. The depth of the troposphere and the depth of the sub-mesoscale mixing layer are calculated based on friction velocity, convection velocity, and geostrophic velocity. Calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibrated horizontal buoyancy gradient. Calculate the expressions for convective mixing effects and submesoscale mixing effects, and calculate the eddy viscosity coefficient and eddy diffusion coefficient of the submesoscale mixing effect.

2. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 1, characterized in that, The calibration of the horizontal buoyancy gradient, which is the average depth of the upper boundary layer, using the effective resolution and frontal scale, includes: Calibrate horizontal buoyancy gradient ,in For effective resolution, For frontal scale, This represents the horizontal buoyancy gradient calculated based on the ocean model.

3. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 2, characterized in that, The horizontal buoyancy gradient calculated based on the ocean model ,in For seawater buoyancy, and These are the meridional and latitudinal coordinates of the grid points in the ocean model.

4. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 2, characterized in that, The calculation of the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibrated horizontal buoyancy gradient includes: Air-sea interface buoyancy flux Horizontal Ekman buoyancy flux ; in, It is the acceleration due to gravity. The coefficient of thermal expansion is... Net heat flux, The density constant of seawater For the specific heat of seawater, The coefficient of salt shrinkage. For net freshwater flux, The salinity of the sea surface. The sea surface wind stress vector. It is a unit vector in the vertical direction. These are Coriolis parameters.

5. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 4, characterized in that, The calculation of tropospheric depth and sub-mesoscale mixed layer depth based on friction velocity, convection velocity, and geostrophic velocity includes: The depth of the troposphere can be calculated using the following formula. and sub-mesoscale mixing layer depth , ； in, For friction speed, For convection velocity, The depth of the negative block vortex. It is a constant. The angle between the wind direction and the geostrophic flow direction. The magnitude of the earth's rotation speed.

6. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 5, characterized in that, The expression for the convective mixing effect is as follows: ； in, The vertical flux of the tracer particles. The sea surface flux of tracer particles. This refers to the depth of the seawater.

7. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 5, characterized in that, The expression for the sub-mesoscale mixing effect is as follows: ； in, , This refers to the depth of the seawater.

8. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 7, characterized in that, The eddy viscosity coefficient corresponding to the sub-mesoscale mixing effect is: ； The eddy diffusion coefficient corresponding to the sub-mesoscale mixing effect is: ； in, To balance the Richardson number.

9. The mesh-adaptive sub-mesoscale hybrid parameterization method according to claim 7, characterized in that, The diffusion coefficient of the tracer particles corresponding to the sub-mesoscale mixing effect is: ； in, To balance the Richardson number.

10. A mesh-adaptive sub-mesoscale hybrid parameterization system, characterized in that, include: The negative block potential vortex depth calculation unit is used to calculate the block potential vortex and negative block potential vortex depth of the model grid points based on the ocean model. The effective resolution and frontal scale calculation unit is used to calculate the effective resolution based on the spatial resolution of the ocean model, and to calculate the frontal scale based on the negative block vortex depth, friction velocity, and convection velocity. A horizontal buoyancy gradient calibration unit is used to calibrate the depth-averaged horizontal buoyancy gradient of the upper boundary layer using the effective resolution and frontal scale, so as to obtain a calibrated horizontal buoyancy gradient. The tropospheric and sub-mesoscale mixed layer depth calculation unit is used to calculate the tropospheric depth and sub-mesoscale mixed layer depth based on friction velocity, convection velocity, and geostrophic velocity. The buoyancy flux calculation unit is used to calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux based on the calibration horizontal buoyancy gradient. The calculation unit for convective mixing effect and sub-mesoscale mixing effect is used to calculate the expressions for convective mixing effect and sub-mesoscale mixing effect, and to calculate the eddy viscosity coefficient and eddy diffusion coefficient of sub-mesoscale mixing effect.

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