A grid-adapting submesoscale mixing parameterization method and system

Abstract

The application discloses a grid self-adapting mesoscale mixing parameterization method and system, which calculates effective resolution and frontal scale according to the spatial resolution of a marine model, and then calibrates the horizontal buoyancy gradient, calculates the sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux according to the calibrated horizontal buoyancy gradient, and then calculates the expression of the convection mixing effect and the mesoscale mixing effect, and the eddy viscosity coefficient and the eddy diffusion coefficient of the mesoscale mixing effect. The application solves the problem that the existing parameterization scheme cannot be applied to the coarse resolution marine model, and realizes the introduction of the effect of mesoscale mixing in different resolution marine models.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ocean numerical model parameterization, in particular to a grid-adaptive mesoscale mixing parameterization method and system. BACKGROUND

[0002] The ocean surface mixed layer is an important channel for the exchange between the ocean and the atmosphere, and its simulation accuracy is one of the important bases for measuring the simulation ability of the ocean model, and directly affects our understanding and future prediction of global warming and climate change. The dynamic process of the ocean surface mixed layer is complex, and different dynamic processes can produce turbulent mixing. However, it is currently difficult to explain how these complex dynamic processes produce turbulent mixing, resulting in a large deviation in the simulation of the ocean surface mixed layer by the ocean model.

[0003] The mesoscale symmetric instability process is one of the important dynamic processes widely existing in the ocean surface mixed layer, which can promote the positive cascade of energy and ultimately cause strong mixing. Observations show that the mixing strength caused by it at the front can be 3 orders of magnitude higher than the background value! Limited by its small spatial scale, the spatial resolution of the current mainstream ocean model cannot directly distinguish the mesoscale process, which makes it one of the key reasons for the deviation of the current ocean model in simulating the dynamic process of the ocean surface layer. At the front, convection and mesoscale symmetric instability usually occur at the same time and interact with each other, ultimately leading to the existence of two levels at the front. The existing mesoscale parameterization scheme considering the effect of convection reproduces the mixing effect strength depending on the horizontal buoyancy gradient strength, but the horizontal buoyancy gradient strength simulated by the ocean model is obviously related to its spatial resolution. Existing research shows that the spatial scale of the ocean surface mixed layer front closely related to the horizontal buoyancy gradient is in the order of hundreds of meters to 1 kilometer. This means that the current mesoscale induced mixing parameterization scheme is only applicable to high-resolution ocean models that can distinguish the surface mixed layer front, but it cannot be applied to coarse-resolution models such as climate ocean models with a spatial resolution of 10 kilometers. SUMMARY

[0004] The purpose of the present application is to provide a grid-adaptive 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 the mesoscale mixing effect parameterization considering the effect of convection in the climate model.

[0005] The grid-adaptive mesoscale mixing parameterization method provided by the present application comprises the following steps:

[0006] calculating the block potential vorticity and the negative block potential vorticity depth of the model grid points of the ocean model according to the ocean model;

[0007] The effective resolution is calculated according to the spatial resolution of the ocean model, the frontal scale is calculated according to the negative potential vorticity depth, the friction velocity and the convection velocity;

[0008] The calibrated horizontal buoyancy gradient is obtained by calibrating the horizontally buoyancy gradient averaged over the upper boundary layer depth using the effective resolution and the frontal scale;

[0009] The troposphere depth and the submesoscale mixed layer depth are calculated according to the friction velocity, the convection velocity and the geostrophic velocity;

[0010] The sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux are calculated according to the calibrated horizontal buoyancy gradient;

[0011] The expressions of the convection mixing effect and the submesoscale mixing effect are calculated, and the eddy viscosity coefficient and the eddy diffusivity coefficient of the submesoscale mixing effect are calculated.

[0012] Further, the calibrated horizontal buoyancy gradient is obtained by calibrating the horizontally buoyancy gradient averaged over the upper boundary layer depth using the effective resolution and the frontal scale includes:

[0013] The calibrated horizontal buoyancy gradient , wherein is the effective resolution, is the frontal scale, is the horizontal buoyancy gradient calculated according to the ocean model.

[0014] Further, the horizontal buoyancy gradient calculated according to the ocean model , wherein is the seawater buoyancy, and is the longitudinal and latitudinal coordinates of the grid point of the ocean model.

[0015] Further, the sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux calculated according to the calibrated horizontal buoyancy gradient includes:

[0016] The sea-air interface buoyancy flux , the horizontal Ekman buoyancy flux ;

[0017] wherein, is the gravitational acceleration, is the thermal expansion coefficient, is the net heat flux, is the seawater density constant, is the specific heat of seawater, is the salt shrinkage coefficient, is the net freshwater flux, is the sea surface salinity, is the sea surface wind stress vector, is the vertical unit vector, is the Coriolis parameter.

[0018] Further, the calculation of the tropospheric depth and the submesoscale mixed layer depth according to the friction velocity, the convection velocity and the geostrophic velocity includes:

[0019] The tropospheric depth is calculated according to the following formula and the submesoscale mixed layer depth is calculated according to the following formula ,

[0020] ;

[0021] wherein, is the friction velocity, is the convection velocity, is the negative block potential vorticity depth, is a constant, is the angle between the wind direction and the geostrophic flow direction, is the geostrophic velocity magnitude.

[0022] Further, the expression of the convection mixing effect is as follows:

[0023] ;

[0024] wherein, is the vertical flux of the tracer particle, is the sea surface flux of the tracer particle, is the seawater depth.

[0025] Further, the expression of the submesoscale mixing effect is as follows:

[0026] ;

[0027] wherein, , is the seawater depth.

[0028] Further, the eddy viscosity coefficient corresponding to the submesoscale mixing effect is:

[0029] ;

[0030] The eddy diffusion coefficient corresponding to the submesoscale mixing effect is:

[0031] ;

[0032] wherein, is the balanced Richardson number.

[0033] Further, the diffusion coefficient of the tracer particle corresponding to the submesoscale mixing effect is:

[0034] ;

[0035] wherein, is the balanced Richardson number.

[0036] The grid-adaptive mesoscale mixing parameterization system comprises:

[0037] A negative potential vorticity depth calculation unit is configured to calculate the potential vorticity and the negative potential vorticity depth of the model grid point of the ocean model according to the ocean model;

[0038] An effective resolution and frontal scale calculation unit is configured to calculate the effective resolution according to the spatial resolution of the ocean model, and calculate the frontal scale according to the negative potential vorticity depth, the friction velocity and the convection velocity;

[0039] A horizontal buoyancy gradient calibration unit is configured to calibrate the horizontal buoyancy gradient averaged over the upper boundary layer depth by using the effective resolution and the frontal scale to obtain a calibrated horizontal buoyancy gradient;

[0040] A troposphere and mesoscale mixing layer depth calculation unit is configured to calculate the troposphere depth and the mesoscale mixing layer depth according to the friction velocity, the convection velocity and the geostrophic flow velocity;

[0041] A buoyancy flux calculation unit is configured to calculate the air-sea interface buoyancy flux and the horizontal Ekman buoyancy flux according to the calibrated horizontal buoyancy gradient;

[0042] A convection mixing effect and mesoscale mixing effect calculation unit is configured to calculate the expression of the convection mixing effect and the mesoscale mixing effect, and calculate the eddy viscosity coefficient and the eddy diffusivity coefficient of the mesoscale mixing effect.

[0043] Advantages: compared with the prior art, the advantages of the present application are that: (1) the present application establishes a submesoscale mixing parameterization method and system which can be adapted and adjusted according to the resolution of the ocean model and coupled with the convection effect, solves the problem that the existing parameterization scheme cannot be applied to the coarse resolution ocean model, and realizes the introduction of the effect of submesoscale mixing in different resolution ocean models. The present application can significantly improve the simulation effect of the ocean model on the upper ocean mixed layer, help to improve the prediction ability of the ocean model, and thus provide more reliable scientific basis for coping with climate change and extreme marine disasters, and has great application prospect in regional and climate ocean model simulation. (2) The present application considers the scale characteristics of the frontal surface in the upper ocean mixed layer based on the spectral slope characteristics of the horizontal buoyancy gradient, and corrects the horizontal buoyancy gradient in the coarse resolution ocean model. The corrected horizontal buoyancy gradient can depict the dynamics characteristics of the frontal surface in the upper ocean mixed layer, and thus be applied to the submesoscale mixing effect parameterization scheme. (3) The present application considers the grid resolution difference of the ocean model, and can adaptively obtain the mixing strength according to the grid, which can be used for climate ocean model simulation and improve the simulation accuracy of the climate model. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The flow chart of the submesoscale mixing parameterization method of the embodiment of the present application.

[0045] Figure 2 The verification result schematic diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0046] The technical solutions of the present application will be further described below in combination with the drawings.

[0047] As shown in the figure, the grid-adaptive submesoscale mixing parameterization method comprises the following steps. Figure 1

[0048] Step 1: calculating the block potential and negative block potential vortex depth of the ocean grid point according to the ocean model.

[0049] Specifically, the ocean model such as the nearshore regional ocean model ROMS, CROCO, MIT ocean circulation model MITgcm, etc. is to solve the Reynolds-averaged Navier-Stokes equation, and the basic quantities such as seawater temperature, salinity and flow rate are output. The seawater buoyancy is calculated according to the temperature and salinity, and the zonal and meridional flow rates are calculated according to the flow rate. The following formula is used to calculate the block potential vortex :

[0050] ;

[0051] wherein, is the Coriolis parameter, is the seawater buoyancy, ,​ respectively the zonal and meridional flow velocity, zonal and meridional coordinates, is the vertical relative vorticity, is the difference of a variable between a given depth and the surface value, and the angle bracket is the depth average.

[0052] If it is negative, i.e. the negative potential vorticity depth is calculated, otherwise the submesoscale mixing parameterization is not performed.

[0053] The negative potential vorticity depth H can be determined according to the following criterion: from the surface, the is calculated for each depth in turn, when the calculated negative potential vorticity becomes positive at a certain depth, i.e. , at this time the corresponding depth is H.

[0054] Step 2, according to the spatial resolution of the ocean model, the effective resolution is calculated, and the frontal scale is calculated according to the negative potential vorticity depth, the friction velocity and the convection velocity.

[0055] Specifically, due to the numerical dissipation problem of the ocean model, for the effective resolution , in general, its size is about 7 times the model grid resolution s, therefore it can be calculated according to the following expression:

[0056] ;

[0057] For the frontal scale , according to the parameters reflecting the strength of the sea-air interface flux calculated in the ocean model, the following formula is used for calculation,

[0058] ;

[0059] wherein, is a constant, and are the mechanical and potential energy conversion rates, and are the friction velocity and the convection velocity, and H is the negative potential vorticity depth. reflects the strength of the sea-air interface flux.

[0060] Step 3, the effective resolution and the frontal scale are used to calibrate the horizontally averaged buoyancy gradient of the upper boundary layer depth, to obtain the calibrated horizontally averaged buoyancy gradient.

[0061] Specifically, the formula of the calibrated horizontally averaged buoyancy gradient is:

[0062] ​;

[0063] where, is the pre-calibrated horizontal buoyancy gradient, which can be calculated by the buoyancy of seawater is calculated directly by the model grid size:

[0064] .

[0065] Step 4, calculate the depth of the troposphere and the depth of the submesoscale mixed layer according to the friction velocity, the convection velocity and the geostrophic velocity.

[0066] Specifically, the depth of the troposphere and the depth of the submesoscale mixed layer are calculated by the following expression:

[0067] ;

[0068] where, is a constant, is the thickness of the troposphere, is the thickness of the submesoscale mixed layer, is the magnitude of the geostrophic velocity, is the angle between the wind direction and the geostrophic flow direction.

[0069] Step 5, calculate the sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux according to the calibrated horizontal buoyancy gradient.

[0070] Specifically, the sea-air interface buoyancy flux includes two parts caused by the heat flux and the salt flux , and the expression is:

[0071] ;

[0072] The expression of the horizontal Ekman buoyancy flux is:

[0073] ;

[0074] where, is the acceleration of gravity, is the thermal expansion coefficient, is the net heat flux, is the seawater density constant, is the specific heat of seawater, is the salt shrinkage coefficient, is the net fresh water flux, is the sea surface salinity, is the sea surface wind stress vector, is the unit vector in the vertical direction, is the Coriolis parameter.

[0075] Step 6, the expressions of the convective mixing effect and the mesoscale mixing effect are calculated, and the eddy viscosity coefficient and the eddy diffusivity coefficient of the mesoscale mixing effect are calculated.

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

[0077] ;

[0078] wherein, is the vertical flux of temperature, salinity or any tracer particle, is the sea surface flux of the tracer particle, is the depth of seawater.

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

[0080] ;

[0081] wherein, .

[0082] The corresponding eddy viscosity coefficient is:

[0083] ;

[0084] The corresponding eddy diffusivity coefficient is:

[0085] ;

[0086] wherein, is the equilibrium Richardson number.

[0087] In addition, the mesoscale process can cause the diffusion coefficient of the tracer particle along the density surface, and the size of the flux can be calculated according to the following expression:

[0088] .

[0089] The method described in the present application is verified by specific experiments.

[0090] Step 1: Model preparation.

[0091] (1.1) Computer preparation: prepare a computer with Linux operating system or supercomputing server, and 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) Model preparation: upload the CROCO code written for the parameterization of the mesoscale mixing effect to the server and decompress it.

[0093] Step 2: Data acquisition.

[0094] (2.1) Obtain topographic data: Obtain global spatial resolution 2' seafloor topographic data from the ETOPO Global Relief Model website to prepare for subsequent grid making.

[0095] (2.2) Obtain ECMWF atmospheric forcing data: Obtain monthly mean data of the Kuroshio Extension region from 2010 to 2019 with a spatial resolution of 0.25 degrees from the ECMWF website. The variables include: 10 meter wind speed, 2 meter dew point temperature, 2 meter air temperature, evaporation, precipitation, sensible heat flux, latent heat flux, net shortwave radiation, net longwave radiation, etc. Used to make model atmospheric forcing field files.

[0096] (2.3) Obtain GLORYS ocean reanalysis data: Obtain monthly mean ocean reanalysis data of the Kuroshio Extension region from 2010 to 2019 with a spatial resolution of 1 / 12 degrees from the GLORYS website. The variables include: temperature, salinity, horizontal flow velocity and sea surface height. Used to make initial field and boundary field files.

[0097] (2.4) Obtain ARGO observation data: Download 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 mixed layer depth comparison.

[0098] Step three: model configuration.

[0099] (3.1) Select the simulation area and make the grid: Use the MATLAB program provided by CROCO to make the grid file. The selected area for this experiment is from 15 degrees north to 45 degrees north and from 130 degrees east to 180 degrees. In order to embody the self-adaptation problem of grid resolution change of the present application, three sets of different resolution grids are made, namely 60 kilometers, 25 kilometers and 10 kilometers.

[0100] (3.2) Make initial field, boundary field and forcing field according to the simulation area: According to the three sets of different resolution grids, use the MATLAB program provided by CROCO to make the corresponding atmospheric forcing field files from 2010 to 2019 using ECMWF data, and make the initial field and boundary field files from 2010 to 2019 using GLORYS ocean reanalysis data.

[0101] (3.3) Upload the grid, forcing field, initial field and boundary field files made to the server.

[0102] Step four: model run.

[0103] (4.1) Compile the model; modify the CROCO code path in the jobcomp file according to the location of the CROCO model code; modify the grid number, vertical layer number and computing core number in the param.h file according to the model grid number, computing resource requirement (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 path in the croco.in file according to the grid, forcing field, initial field and boundary field file path; modify the simulation time step (60km model: dt = 900s; 25km model: dt = 600s; 25km model: dt = 300s), output time step (1 day) and simulation time length (10 years) according to different grid files. After modification, run jobcomp to compile the model.

[0104] (4.2) Submit the task: after compilation, submit the task to carry out simulation. After simulation, carry out subsequent processing and analysis on the daily average data output by the model.

[0105] Step five: result verification.

[0106] (5.1) Calculate the mixed layer thickness output by the model: according to the density field output by the simulation, the upper ocean mixed layer depth in the three simulation experiments is calculated respectively. Here, the mixed layer is defined as the difference between the density and the density at a depth of 10 meters reaches 0.03kg / m 3 . For the calculated mixed layer depth, monthly average is carried out to obtain monthly average data. Considering the time required for model spinup and the fact that mesoscale is only active in winter, only the winter of the last three years, i.e. January-March of 2017-2019, is taken for comparison.

[0107] (5.2) Calculate the observed mixed layer thickness: according to the temperature and salinity data observed by ARGO, the density of seawater at different depths is calculated, and the upper ocean mixed layer depth in the corresponding region and winter is calculated.

[0108] (5.3) Verify the effect of the application: compare the upper mixed layer depth obtained by the model with the observation, and evaluate the effect of the parameterization scheme.

[0109] Table 1 Comparison of the application method with the simulation of the mixed layer without considering parameterization and without calibrating parameterization

[0110]

[0111] The comparison results of the mixed layer depth of the method of the application and the simulation without considering parameterization and the uncalibrated parameterization are shown in Table 1. The mixed layer depth is defined as the depth at which the sea water density changes by 0.03 kg / m 3 The uncalibrated parameterization refers to the simulation result considering the existing submesoscale mixing parameterization. Figure 2 The verification result is shown in the schematic diagram. Figure 2 a, b and c are respectively the simulation results in the 60 km, 25 km and 10 km models, the black curve is the observed mixed layer thickness distribution with latitude, the blue curve is the simulation result without considering the submesoscale mixing parameterization, the yellow curve is the simulation result considering the uncalibrated parameterization, and the red curve is the simulation result considering the method of the application.

[0112] It can be found from the comparison that the result of the uncalibrated parameterization is obviously deeper than the observation, and the uncalibrated parameterization improves the deviation to a certain extent, and the mixed layer thickness obtained by the method of the application is obviously less deviated, which indicates that the effect of the method of the application is obviously improved compared with the existing method.

[0113] The grid-adaptive submesoscale mixing parameterization system comprises:

[0114] A negative block potential vorticity depth calculation unit is configured to calculate the block potential vorticity and the negative block potential vorticity depth of the ocean grid point according to the ocean model;

[0115] An effective resolution and frontal scale calculation unit is configured to calculate the effective resolution according to the spatial resolution of the ocean model, and calculate the frontal scale according to the negative block potential vorticity depth, the friction velocity and the convection velocity;

[0116] A horizontal buoyancy gradient calibration unit is configured to calibrate the horizontal buoyancy gradient averaged on the upper boundary layer depth by using the effective resolution and the frontal scale to obtain a calibrated horizontal buoyancy gradient;

[0117] A troposphere and submesoscale mixed layer depth calculation unit is configured to calculate the troposphere depth and the submesoscale mixed layer depth according to the friction velocity, the convection velocity and the geostrophic flow velocity;

[0118] A buoyancy flux calculation unit is configured to calculate the sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux according to the calibrated horizontal buoyancy gradient;

[0119] A convection mixing effect and submesoscale mixing effect calculation unit is configured to calculate the expression of the convection mixing effect and the submesoscale mixing effect, and calculate the eddy viscosity coefficient and the eddy diffusivity coefficient of the submesoscale mixing effect.

Claims

1. A grid-adapting submesoscale mixing parameterization method, characterized in that, The method comprises the following steps: calculating the baroclinic potential vorticity and the depth of the negative baroclinic potential vorticity at the grid points of the model mesh according to the ocean model; the baroclinic potential vorticity is calculated by the following formula: baroclinic potential vorticity , is the Coriolis parameter, is the buoyancy of seawater, , are the zonal and meridional flow velocities respectively, and are the zonal and meridional coordinates respectively, is the vertical relative vorticity, is the difference between a variable at a given depth and the surface value, and the angle bracket is the corresponding depth average; When the negative block vortex depth H is calculated, which is calculated as follows: the depth of each layer is calculated in sequence from the surface layer , and when the calculated negative block vortex becomes positive at a certain depth, that is , the corresponding depth is H. The effective resolution is calculated according to the spatial resolution of the ocean model, and the frontal scale is calculated according to the negative block potential vorticity depth, friction velocity and convection velocity; frontal scale , is constant, and is the mechanical and potential energy conversion rate, and is the friction velocity and the convection velocity, H is the negative block potential vorticity depth; The calibrated horizontal buoyancy gradient is obtained by calibrating the horizontally averaged buoyancy gradient in the upper boundary layer depth using the effective resolution and the frontal scale; The troposphere depth and the submesoscale mixed layer depth are calculated according to the friction velocity, the convection velocity and the geostrophic current velocity; The tropospheric depth is calculated according to the following formula and the sub-mesoscale mixed layer depth : ； wherein, is a constant, is the angle between the wind direction and the geostrophic flow direction, is the geostrophic flow speed magnitude; The sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux are calculated according to the calibrated horizontal buoyancy gradient; The expressions of the convection mixing effect and the submesoscale mixing effect are calculated, and the eddy viscosity coefficient and the eddy diffusion coefficient of the submesoscale mixing effect are calculated; the expression of the submesoscale mixing effect is as follows: ； where, , is the sea water depth, is the sea-air interface buoyancy flux, is the horizontal Ekman buoyancy flux.

2. The grid-adapted submesoscale mixing parameterization method of claim 1, wherein, The calibrated horizontal buoyancy gradient is obtained by calibrating the horizontally averaged buoyancy gradient in the upper boundary layer depth using the effective resolution and the frontal scale comprises: Calibrating the horizontal buoyancy gradient wherein is the effective resolution, is the frontal scale, is the horizontal buoyancy gradient calculated from the ocean model.

3. The grid-adapted submesoscale mixing parameterization method of claim 2, wherein, said horizontal buoyancy gradient calculated from the ocean model wherein is the sea water buoyancy, and are the longitudinal and latitudinal coordinates of the ocean model grid point.

4. The grid-adapted submesoscale mixing parameterization method of claim 2, wherein, The sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux are calculated according to the calibrated horizontal buoyancy gradient comprises: Air-sea interface buoyancy flux , horizontal Ekman buoyancy flux ; where, g is the acceleration of gravity, α is the thermal expansion coefficient, Q is the net heat flux, ρ is the seawater density constant, c is the seawater specific heat, β is the salt contraction coefficient, Qw is the net freshwater flux, S is the sea surface salinity, τ is the sea surface wind stress vector, k is the vertical unit vector, K is the Coriolis parameter.

5. The grid-adapted submesoscale mixing parameterization method of claim 1, wherein, The expression of the convection mixing effect is as follows: ； wherein, is the vertical flux of tracer particles, is the sea surface flux of tracer particles, is the depth of the sea water.

6. The grid-adapted submesoscale mixing parameterization method of claim 5, wherein, The eddy viscosity coefficient corresponding to the submesoscale mixing effect is as follows: ； The eddy diffusion coefficient corresponding to the submesoscale mixing effect is as follows: ； wherein Richardson number for balance.

7. The grid-adapted submesoscale mixing parameterization method of claim 5, wherein, The diffusion coefficient of the tracer particle corresponding to the submesoscale mixing effect is as follows: ； wherein Richardson number for balance.

8. A grid adaptive submesoscale hybrid parameterization system based on the method of claim 1, characterized in that, It comprises: The negative block potential vorticity depth calculation unit is configured to calculate the block potential vorticity and the negative block potential vorticity depth of the model grid point according to the ocean model; The effective resolution and the frontal scale calculation unit is configured to calculate the effective resolution according to the spatial resolution of the ocean model, and calculate the frontal scale according to the negative block potential vorticity depth, the friction velocity and the convection velocity; The horizontal buoyancy gradient calibration unit is configured to calibrate the horizontally averaged buoyancy gradient in the upper boundary layer depth using the effective resolution and the frontal scale, and obtain the calibrated horizontal buoyancy gradient; The troposphere and submesoscale mixed layer depth calculation unit is configured to calculate the troposphere depth and the submesoscale mixed layer depth according to the friction velocity, the convection velocity and the geostrophic current velocity; The buoyancy flux calculation unit is configured to calculate the sea-air interface buoyancy flux and the horizontal Ekman buoyancy flux according to the calibrated horizontal buoyancy gradient; The convection mixing effect and the submesoscale mixing effect calculation unit is configured to calculate the expressions of the convection mixing effect and the submesoscale mixing effect, and calculate the eddy viscosity coefficient and the eddy diffusion coefficient of the submesoscale mixing effect.

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