Ocean mode temperature and salinity prediction method based on variable limit integral method, program, equipment and storage medium

Abstract

The invention belongs to the technical field of ocean numerical modes, and particularly relates to an ocean mode temperature and salinity prediction method based on a variable limit integral method, a program, equipment and a storage medium. The method comprises the following steps: constructing an ocean mode three-dimensional computational domain, determining fluid motion parameters in the computational domain, predicting total time length and predicting step length, and constructing an ocean mode temperature equation and a salinity equation; in each iteration, a horizontal advection term and a horizontal diffusion term in the ocean mode temperature equation and the salinity equation are solved by adopting a variable-limit integral method, the temperature and the salinity are predicted by utilizing an implicit variable-limit integral numerical format of a vertical diffusion term, and a calculation mode brought by a time splitting algorithm is filtered by utilizing a weak filter; and ocean mode temperature and salinity prediction is realized. According to the method, the variable limit integral is introduced into the solution of the ocean mode thermohaline equation, so that the simulated thermohaline is more accurate, the stability of the ocean mode is greatly improved, and the simulation effect of the ocean mode is particularly better at a large terrain.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean numerical models, and in particular relates to an ocean model temperature and salinity prediction method, program, device and storage medium based on a variable limit integration method. Background Art

[0002] The ocean numerical model is a numerical model that quantitatively describes the physical phenomena and changing patterns of the ocean. It is an important means of large-scale, all-round and continuous research on the ocean, and a core tool for ocean and climate research and prediction. The ocean numerical model simulates physical quantities such as the temperature and salinity flow field and density of seawater by numerically solving the governing equations of ocean motion. The governing equations of ocean motion reflect extremely complex physical processes such as ocean dynamics and thermodynamics, and their establishment follows the laws of conservation of momentum, temperature and salinity, and conservation of mass. The governing equations of ocean motion are nonlinear partial differential equations, and their analytical solutions cannot be accurately given. It is necessary to design a numerical solution method, combined with the initial conditions of the temperature and salinity flow and boundary conditions such as the sea-air interface and the water body boundary, to achieve simulation and prediction of the ocean.

[0003] Existing ocean numerical models mostly employ the finite difference method and the finite volume method. Examples of ocean numerical models using the finite difference method include the POM model, the HYCOM hybrid coordinate ocean circulation model, the ROMS regional ocean numerical model, and the MASNUM three-dimensional ocean circulation model. Among numerical models implemented using the difference method, the central difference scheme and the upwind scheme are often used for spatial discretization, while the Euler scheme and the leapfrog scheme are often used for temporal discretization. For temporal discretization, difference schemes can be further divided into two categories: explicit and implicit. Explicit methods are computationally simple and easy to implement, but they impose strict restrictions on step size, making convergence and stability of the iterative scheme difficult to guarantee. Implicit methods offer good computational stability and can appropriately relax step size restrictions, but they also have high algorithmic complexity. Currently, the accuracy of most mainstream ocean numerical models implemented using the finite difference method is theoretically first-order on non-uniform grids and second-order on uniform grids. Manual intervention is often required to ensure model stability.

[0004] Some ocean numerical models are based on the finite volume method, such as the MITgcm model for atmospheric and oceanic circulation simulations, the FVCOM model, which incorporates both ocean circulation and ecological modules, and three-dimensional models such as Casulli that employ unstructured meshes. Triangular or unstructured meshes are often used in these models, and some also consider the establishment of conservative numerical schemes. However, the higher-precision finite volume methods are often complex, require additional techniques to mitigate numerical dispersion, and are computationally expensive.

[0005] In recent years, we have proposed and developed a new method for numerically solving partial differential equations—the variable limit integration method. This method demonstrates significant advantages in designing conservative, high-precision numerical schemes. The variable limit integration method, an improvement on the finite volume method, was first applied to the calculation of wood moisture content problems. Its characteristics are that variable limit integration is performed near grid nodes (with variable integration limits to be determined) and that approximation functions (such as high-precision approximation functions) can be flexibly selected near the integration grid points to calculate the integral. Compared with the difference method, the variable limit integration method utilizes the "weighted" information of all points near the grid point, rather than just the information at the grid point, to construct the scheme. Furthermore, through the design and selection of special integration limit parameters and approximation functions, the variable limit integration can be reduced to finite differences. Summary of the Invention

[0006] The present invention aims to address the problems of low precision and difficulty maintaining a constant value in current mainstream numerical solution methods for ocean models by providing a method, program, device, and storage medium for ocean model temperature and salinity prediction based on the variable limit integration method. This invention introduces a variable limit integration numerical method that is both conservative and easily achieves high precision into the temperature and salinity solution of ocean numerical models. This method not only ensures the physical rationality and long-term stability of the ocean model, but also improves the computational accuracy and efficiency of existing numerical models to a certain extent.

[0007] The ocean model temperature and salinity prediction method based on the variable limit integration method includes the following steps:

[0008] Construct a three-dimensional ocean model calculation domain, determine the fluid motion parameters, total prediction time and prediction step in the calculation domain, and construct the ocean model temperature equation and salinity equation; in each iteration, use the variable limit integration method to solve the horizontal advection term and horizontal diffusion term in the ocean model temperature equation and salinity equation, use the implicit variable limit integration numerical format of the vertical diffusion term to predict temperature and salinity, and use a weak filter to filter out the calculation mode brought by the time splitting algorithm to realize the ocean model temperature and salinity prediction.

[0009] Furthermore, the fluid motion parameters in the calculation domain are determined, including the water surface height D(t,x,y), water depth H(t,x,y), flow velocity U(t,x) in the x direction, flow velocity V(t,y) in the y direction, flow velocity ω(t,σ) in the σ direction, and thermal diffusivity A in the horizontal direction. H (t,x,y), thermal diffusivity K in the vertical direction H (t,σ), solar radiation intensity R(t,σ);

[0010] Determine the total prediction time t max With the prediction step length Δt, the total number of predictions is B=t max / Δt; For each measuring point in the three-dimensional calculation domain of the ocean model, in the horizontal direction, the distance from the measuring point to the origin is sequentially numbered as i = 1, 2, ..., N; in the vertical direction, the vertical coordinate of the measuring point is sequentially numbered as k = 1, 2, ..., N; N is the total number of measuring points in the calculation domain;

[0011] The initial temperature T(0,x,y), one-step predicted temperature T(1,x,y), initial salinity S(0,x,y), and one-step predicted temperature S(1,x,y) of the computational domain are all known.

[0012] Furthermore, the horizontal advection term of the ocean model temperature equation is solved by the variable limit integration method, specifically:

[0013] The horizontal advection term Adv(S(t,x,y)) of the ocean model temperature equation is:

[0014]

[0015] The three terms in the horizontal advection term Adv(S(t,x,y)) are solved using the variable limit integration method;

[0016] make Let u ai =U(t,x i ), e ai =D(t,x i ,y i )·T(t,x i ,y i );

[0017] Transformed into the following system of equations:

[0018]

[0019] Solve the system of equations, u ai With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving ai value, fitted to the function p a (t,x,y);

[0020] make Let u bi =V(t,x i ), e ai =D(t,x i ,y i )·T(t,x i ,y i ), which is transformed into the following system of equations:

[0021]

[0022] Solve the system of equations, u bi With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving bi value, fitted to the function p b (t,x,y);

[0023] make Let u ci =ω(t,σ i ), e ci =T(t,x i ,y i ), which is transformed into the following system of equations:

[0024]

[0025]

[0026] Solve the system of equations, u ci With e ci All are known items, and the p of all measuring points in the computational domain is obtained by solving ci value, fitted to the function p c (t,σ);

[0027] Horizontal advection term Adv(T(t,x,y))=p a (t,x,y)+p b (t,x,y)+p c (t,σ);

[0028] The variable limit integration method is used to solve the horizontal advection term in the ocean model salinity equation. The solution process is the same as the horizontal advection term of the ocean model temperature equation mentioned above. It is only necessary to replace the temperatures T(t,x,y) and T(t-1,x,y) in the solution process with the salinities S(t,x,y) and S(t-1,x,y).

[0029] Furthermore, the horizontal diffusion term of the ocean model temperature equation is solved by the variable limit integration method, specifically:

[0030] The horizontal diffusion term Dif(T(t-1,x,y)) of the ocean model temperature equation is:

[0031]

[0032] The two terms in the horizontal diffusion term are solved separately using the variable limit integration method;

[0033] make Transformed into the following system of equations:

[0034]

[0035] edi As the known term, solve the equations to obtain the p of all measuring points in the computational domain. di value, fitted to the function p d (t-1,x,y);

[0036] make Transformed into the following system of equations:

[0037]

[0038] e ei As the known term, solve the equations to obtain the p of all measuring points in the computational domain. ei value, fitted to the function p e (t-1,x,y);

[0039] Horizontal diffusion term Dif(T(t-1,x,y))=p d (t-1,x,y)+p e (t-1,x,y);

[0040] The variable limit integration method is used to solve the horizontal diffusion term in the ocean model salinity equation. The solution process is the same as that of solving the horizontal diffusion term in the ocean model temperature equation. It is only necessary to replace the temperatures T(t,x,y) and T(t-1,x,y) in the solution process with the salinities S(t,x,y) and S(t-1,x,y).

[0041] Furthermore, the temperature is predicted using the implicit variable limit integral numerical format of the vertical diffusion term, specifically:

[0042] Calculate the intermediate variable of temperature

[0043]

[0044] The numerical format of the implicit variable limit integration using the vertical diffusion term is:

[0045]

[0046] make

[0047]

[0048] Among them, d z represents the vertical grid step size, k1 and k2 are constants;

[0049]

[0050]

[0051] Solve the equations to obtain T(t+1,x i ,y i ) value, and fitting it to the function T(t+1,x,y) to get the temperature prediction at the next moment;

[0052]

[0053] Furthermore, the salinity is predicted using the implicit variable limit integral numerical format of the vertical diffusion term, specifically:

[0054] Calculate intermediate variables for salinity

[0055]

[0056] The numerical format of the implicit variable limit integration using the vertical diffusion term is:

[0057]

[0058] make

[0059]

[0060] Among them, d z represents the vertical grid step size, k1 and k2 are constants;

[0061]

[0062] Solve the equations to obtain S(t+1,x i ,y i ) value, and fitting it to the function S(t+1,x,y) to obtain the salinity prediction at the next moment;

[0063]

[0064] Furthermore, the use of a weak filter to filter out the computational mode brought about by the time splitting algorithm is specifically as follows:

[0065]

[0066] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned ocean model temperature and salinity prediction method based on the variable limit integration method.

[0067] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned ocean model temperature and salinity prediction method based on the variable limit integration method.

[0068] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned ocean model temperature and salinity prediction method based on the variable limit integration method.

[0069] The beneficial effects of the present invention are:

[0070] The present invention introduces variable limit integral into the solution of the ocean model temperature-salinity equation, which can make the simulated temperature-salinity more accurate and greatly improve the stability of the ocean model. The simulation effect of the ocean model shows better calculation results, especially in large terrain (terrain with drastic changes). BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 Schematic diagram of the C grid of variables u and e in the present invention.

[0072] Figure 2 This is a comparison chart of the temperature, salinity, and flow velocity at the center of the strait in an embodiment of the present invention.

[0073] Figure 3 Graphs showing the temperature (left) and salinity (right) time history of I-POM and O-POM under different steep terrain parameters A under the zero Coriolis force test at the sea threshold in an embodiment of the present invention.

[0074] Figure 4 Schematic diagram of the temperature cross-section of I-POM (left), O-POM (middle), and the difference between the two (right) under the threshold test in an embodiment of the present invention.

[0075] Figure 5 1 is a time history diagram of seawater flow rate under the sea threshold test with and without Coriolis force in an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings.

[0077] This paper introduces the variable limit integration method into the temperature and salinity solution of an ocean model. Within the C network, a variable limit integration scheme is designed for the horizontal transport and horizontal diffusion terms in the temperature and salinity equation. A variable limit integration scheme is also designed for the vertical diffusion term in the equation and, combined with the difference method, ultimately forms an implicit fully discrete scheme. The stability of the variable limit integration scheme is analyzed and embedded in the ocean model, verifying its effectiveness and effectiveness in improving temperature and salinity simulations.

[0078] First, a variable-limit integration scheme was designed and constructed for the thermohaline equation, one of the governing equations for ocean motion, using the Arakawa-C grid. Based on the different characteristics of the horizontal advection, horizontal diffusion, and vertical diffusion terms in the thermohaline equation, corresponding variable-limit integration schemes were designed for the Arakawa-C grid and embedded into the POM ocean model.

[0079] The POM ocean model embeds a 2.5-order turbulence closure model to resolve vertical turbulent viscosity and diffusivity. Horizontal turbulent viscosity and diffusivity are based on the Smagorinsk parameterization scheme, avoiding errors caused by artificially selected mixing coefficients. An orthogonal curvilinear grid is used in the horizontal direction, and the variable space configuration uses an Arakawa-C grid to better match coastal boundaries. σ coordinates are used in the vertical direction to facilitate handling of rugged terrain. Horizontal time differences are explicit, while the vertical time difference is implicit. The latter eliminates the time constraint of the vertical coordinates and allows for fine vertical resolution in the surface and bottom boundary layers. The model employs a free surface and mode separation scheme. The outer mode is two-dimensional, using a short time step to calculate water level and vertical mean velocity. The inner mode is three-dimensional, using a long time step to calculate three-dimensional velocity, temperature, salinity, and turbulence parameters. Based on the hydrostatic approximation and the Boussinesq assumption, it incorporates complete thermodynamic processes and is a fully baroclinic model. The POM employs a leapfrog differencing scheme and a splitting operator technique, with explicit horizontal and temporal differencing schemes and implicit vertical differencing schemes. To eliminate computational modes generated by the leapfrog scheme, a temporal filter is applied at each time integration level.

[0080] Arakawa-C grids offer horizontal grids that can be divided into orthogonal curvilinear grids and unstructured grids. Orthogonal curvilinear grids can be flexibly adjusted to specific simulation requirements and terrain characteristics, better adapting to complex terrain and flow conditions. C grids are particularly effective in simulating barotropic pressure fluctuations and also allow for accurate differentiation of pressure gradient forces and velocity divergence.

[0081] The vertical σ coordinate maintains a uniform grid number across the entire vertical direction, can be arbitrarily layered, and automatically adapts to depth contours, ensuring high vertical resolution even in shallow waters. By introducing a coordinate transformation, σ = 0 at the ocean surface and -1 at the seafloor. Since σ increases monotonically from the seafloor to the surface, this mapping ensures a one-to-one correspondence between z and σ.

[0082] The potential temperature equation in the Reynolds average conservation form under the σ coordinate is as follows:

[0083]

[0084] The advection term Adv(T) and the horizontal diffusion term Dif(T) are:

[0085]

[0086] T represents temperature, D represents water surface height, H represents water depth, U, V, and ω represent flow velocities in three directions respectively, and A H With K H denote the thermal diffusivities in the horizontal and vertical directions, respectively.

[0087] Similarly, the salinity equation in the Reynolds average conservation form under the σ coordinate is:

[0088]

[0089] The advection term Adv(S) and the horizontal diffusion term Dif(S) are consistent with those in the potential temperature equation.

[0090] Get the predicted total time t max With the prediction step length Δt, the total number of predictions is B=t max / Δt;

[0091] For each measuring point in the computational domain, in the horizontal direction, they are numbered in ascending order of distance from the measuring point to the origin as i = 1, 2, ..., N; in the vertical direction, they are numbered in ascending order of vertical coordinates as k = 1, 2, ..., N; N is the total number of measuring points in the computational domain.

[0092] Obtain the water surface height D(t,x,y), water depth H(t,x,y), flow velocity U(t,x) in the x direction, flow velocity V(t,y) in the y direction, flow velocity ω(t,σ) in the σ direction, and thermal diffusivity A in the horizontal direction in the calculation domain H (t,x,y), thermal diffusivity K in the vertical direction H (t,σ), solar radiation intensity R(t,σ);

[0093] Solving the temperature equation involves the following steps:

[0094] Step 1: Get the initial temperature T(0,x,y) of the computational domain and the one-step predicted temperature T(1,x,y); initialize t=1;

[0095] Step 2: Calculate the intermediate variable of temperature

[0096]

[0097] Among them, D(t+1,x,y), D(t-1,x,y), T(t-1,x,y), and Δt are all known;

[0098]

[0099] The three terms in the horizontal advection term Adv(T(t,x,y)) are solved using the variable limit integration method;

[0100] make Let u ai =U(t,x i ), e ai =D(t,x i ,y i )·T(t,x i ,y i ), which is transformed into the following system of equations:

[0101]

[0102] Solve the system of equations, u ai With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving ai value, fitted to the function p a (t,x,y);

[0103] make Let u bi =V(t,x i ), e ai =D(t,x i ,y i )·T(t,x i ,y i ), which is transformed into the following system of equations:

[0104]

[0105] Solve the system of equations, u bi With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving bi value, fitted to the function p b (t,x,y);

[0106] make , let u ci =ω(t,σ i ), e ci =T(t,x i ,y i ), which is transformed into the following system of equations:

[0107]

[0108] Solve the system of equations, u ci With e ci All are known items, and the p of all measuring points in the computational domain is obtained by solving ci value, fitted to the function p c (t,σ);

[0109] Horizontal advection term Adv(T(t,x,y))=p a (t,x,y)+p b (t,x,y)+p c (t,σ);

[0110]

[0111] The two terms in the horizontal diffusion term are solved separately using the variable limit integration method;

[0112] make Transformed into the following system of equations:

[0113]

[0114] e di As the known term, solve the equations to obtain the p of all measuring points in the computational domain. di value, fitted to the function p d (t-1,x,y);

[0115] make Transformed into the following system of equations:

[0116]

[0117] e ei As the known term, solve the equations to obtain the p of all measuring points in the computational domain. ei value, fitted to the function p e (t-1,x,y); horizontal diffusion term Dif(T(t-1,x,y))=p d (t-1,x,y)+p e (t-1,x,y);

[0118] Step 3: Calculate the temperature prediction T(t+1,x,y) at the next moment using the implicit variable limit integral numerical format of the vertical diffusion term;

[0119]

[0120] Among them, D(t+1,x,y), Δt, All are known;

[0121] make

[0122]

[0123] Among them, d z represents the vertical grid step size, k1 and k2 are constants;

[0124]

[0125] Solve the system of equations:

[0126]

[0127] Step 4: Use a weak filter to filter out the computational modes brought by the time splitting algorithm;

[0128] make

[0129] Step 5: If t < B, set t = t + 1 and return to step 2; otherwise, output T(t + 1, x, y) to complete the temperature prediction in the computational domain.

[0130] The horizontal advection term and horizontal diffusion term in the ocean model salinity equation are solved by the variable limit integration method. The solution process is the same as that of solving the horizontal advection term in the ocean model temperature equation. Only the temperature T(t,x,y) and T(t-1,x,y) in the solution process need to be replaced by the salinity S(t,x,y) and S(t-1,x,y). When solving the vertical diffusion term in the ocean model salinity equation, delete

[0131] The solution of the ocean model salinity equation specifically includes the following steps:

[0132] Step (1): Obtain the initial salinity S(0,x,y) and one-step predicted temperature S(1,x,y) of the computational domain; initialize t = 1;

[0133] Step (2): Calculate the intermediate variable of salinity

[0134]

[0135] Among them, D(t+1,x,y), D(t-1,x,y), S(t-1,x,y), and Δt are all known;

[0136]

[0137] The three terms in the horizontal advection term Adv(S(t,x,y)) are solved using the variable limit integration method;

[0138] make Let u ai =U(t,x i ), e ai =D(t,x i ,y i )·S(t,x i ,y i ), which is transformed into the following system of equations:

[0139]

[0140]

[0141] Solve the system of equations, u ai With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving ai value, fitted to the function p a (t,x,y);

[0142] make Let u bi =V(t,x i ), e ai =D(t,x i ,y i )·S(t,x i ,y i ), which is transformed into the following system of equations:

[0143]

[0144] Solve the system of equations, u bi With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving bi value, fitted to the function p b (t,x,y);

[0145] make Let u ci =ω(t,σ i ), e ci =S(t,x i ,y i ), which is transformed into the following system of equations:

[0146]

[0147] Solve the system of equations, u ci With e ci All are known items, and the p of all measuring points in the computational domain is obtained by solving ci value, fitted to the function p c (t,σ);

[0148] Horizontal advection term Adv(S(t,x,y))=p a (t,x,y)+p b (t,x,y)+p c (t,σ);

[0149]

[0150] The two terms in the horizontal diffusion term are solved separately using the variable limit integration method;

[0151] make Transformed into the following system of equations:

[0152]

[0153] e di As the known term, solve the equations to obtain the p of all measuring points in the computational domain. di value, fitted to the function p d (t-1,x,y);

[0154] make Transformed into the following system of equations:

[0155]

[0156] e ei As the known term, solve the equations to obtain the p of all measuring points in the computational domain. ei value, fitted to the function p e (t-1,x,y);

[0157] Horizontal diffusion term Dif(S(t-1,x,y))=p d (t-1,x,y)+p e (t-1,x,y);

[0158] Step (3): Calculate the salinity prediction S(t+1,x,y) at the next moment using the implicit variable limit integral numerical format of the vertical diffusion term;

[0159]

[0160] Among them, D(t+1,x,y), Δt is known;

[0161] make

[0162]

[0163]

[0164] Among them, d z represents the vertical grid step size, k1 and k2 are constants;

[0165]

[0166] Solve the system of equations:

[0167]

[0168] Step (4): Use a weak filter to filter out the computational modes brought by the time splitting algorithm;

[0169] make

[0170] Step (5): If t < B, set t = t + 1 and return to step (2); otherwise, output S (t + 1, x, y) to complete the salinity prediction in the computational domain.

[0171] Example 1:

[0172] To address the different characteristics of the horizontal advection, horizontal diffusion, and vertical diffusion terms in the thermohaline equation, corresponding variable limit integration schemes were designed for the C grid. The I-POM results mentioned in the following numerical experiments refer to replacing the computational portion of the thermohaline equation in the O-POM model (the original POM model) with the designed variable limit integration scheme, while the remaining components continue to use the POM model.

[0173] 1. Strait Zero Start Calculation Example

[0174] This part of the calculation uses the strait terrain, the temperature is set to a constant 20℃, the salinity is set to a constant 35psu, there is no seawater flowing in or out of the boundary, and the seawater in the entire strait remains static. Starting the model, theoretically, the temperature and salinity remain constant at any time, and the flow rate is always zero. The temperature and salinity currents calculated by the model are all numerical errors. Figure 2 It can be seen that the maximum temperature deviations of I-POM and O-POM on the 60th day are 1.91×10 -3 and 3.24×10 -4 , I-POM decreased by 82.95%; the maximum salinity deviations of I-POM and O-POM on the 60th day were 1.47×10 -3 and 6.18×10 -4 , I-POM reduced it by 57.96%. Therefore, the variable limit integration format of the temperature-salinity equation significantly reduced the temperature and salinity simulation bias of the ocean model.

[0175] 2. Analysis of calculation results under sea sill terrain

[0176] Ignoring the Coriolis force, the sea threshold topography A is set to 0.2, 0.4, 0.6, and 0.8, with thermohaline stratification and water flowing into the west boundary at a rate of 0.2 m / s. Theoretically, the north-south (y-direction) thermohaline flow should be symmetrical. Figure 3 It can be seen that both the O-POM model (the original POM model) and the I-POM model (the POM model with the temperature-salinity component replaced with a variable limit integration format) can simulate the temperature-salinity flow under this still water setting. However, the O-POM model exhibits numerical instability after 6 to 8 days and stops calculating; the I-POM model remains stable throughout.

[0177] Depend on Figure 4Analysis shows that the running days from top to bottom are 5 days, 30 days and 60 days respectively. Figure 4 It can be seen that the results of O-POM and I-POM are not much different overall, but as the simulation time increases, the differences between the two begin to appear: in the 30-day and 60-day sections, the bottom of the sea sill, especially the downstream part, is significantly different. Figure 4 The I-POM simulations of salinity profiles at days 30 and 60 show multiple isothermal curves intersecting and converging along the contour just downstream of the sill crest. The isohalinity curve at the crest exhibits erratic fluctuations, demonstrating that I-POM can simulate the overflow mixing of seawater at this location, more closely matching actual seawater movement. In the 60-day I-POM temperature profile, overflow mixing even affects the surface water, while O-POM does not simulate a similar result. Therefore, the variable limit integral can capture the "overflow" phenomenon at the sill crest, significantly improving simulation results under large terrain conditions.

[0178] At the same time, the σ coordinate will have an adverse effect on the calculation of large terrain, but the introduction of variable limit integral can greatly alleviate these effects. The Coriolis force causes the sea water to deflect, slowing down the slope, so that the sea water does not flow vertically over the sea sill (head-on collision), but presents an acute angle. Figure 5 The figures are on days 4, 6, and 6.5, respectively. The first example shows a sill experiment without the Coriolis force. The horizontal flow velocity on day 6 shows a very obvious backflow phenomenon. This phenomenon becomes even more pronounced on day 6.5, with a higher backflow velocity. The velocity increases until the model collapses. The second example shows the presence of the Coriolis force, where the seawater velocity forms an acute angle with the sill, and the slope of the seawater over the sill is reduced. The Coriolis force deflects the seawater, slowing the slope of the seawater over the sill and alleviating the adverse effects of the σ coordinate on large terrain calculations. Therefore, the introduction of variable limit integrals can significantly mitigate the adverse effects of the σ coordinate on large terrain calculations.

[0179] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. Ocean model temperature and salinity prediction method based on variable limit integration method, characterized by: Construct a three-dimensional ocean model calculation domain, determine the fluid motion parameters, total prediction time and prediction step in the calculation domain, and construct the ocean model temperature equation and salinity equation; in each iteration, use the variable limit integration method to solve the horizontal advection term and horizontal diffusion term in the ocean model temperature equation and salinity equation, use the implicit variable limit integration numerical format of the vertical diffusion term to predict temperature and salinity, and use a weak filter to filter out the calculation mode brought by the time splitting algorithm to realize the ocean model temperature and salinity prediction.

2. The ocean model temperature and salinity prediction method based on the variable limit integral method according to claim 1 is characterized by: The fluid motion parameters determined in the calculation domain include the water surface height D(t,x,y), water depth H(t,x,y), flow velocity U(t,x) in the x direction, flow velocity V(t,y) in the y direction, flow velocity ω(t,σ) in the σ direction, and thermal diffusivity A in the horizontal direction. H (t,x,y), thermal diffusivity K in the vertical direction H (t,σ), solar radiation intensity R(t,σ); Determine the total prediction time t max With the prediction step length Δt, the total number of predictions is B=t max / Δt; For each measuring point in the three-dimensional calculation domain of the ocean model, in the horizontal direction, the distance from the measuring point to the origin is sequentially numbered as i = 1, 2, ..., N; in the vertical direction, the vertical coordinate of the measuring point is sequentially numbered as k = 1, 2, ..., N; N is the total number of measuring points in the calculation domain; The initial temperature T(0,x,y), one-step predicted temperature T(1,x,y), initial salinity S(0,x,y), and one-step predicted temperature S(1,x,y) of the computational domain are all known.

3. The ocean model temperature and salinity prediction method based on the variable limit integral method according to claim 2, characterized in that: The variable limit integration method is used to solve the horizontal advection term of the ocean model temperature equation, specifically: The horizontal advection term Adv(S(t,x,y)) of the ocean model temperature equation is: The three terms in the horizontal advection term Adv(S(t,x,y)) are solved using the variable limit integration method; Let let u ai = U(t, x i ), e ai = D(t, x i , y i )·T(t, x i , y i ); Transformed into the following system of equations: Solve the system of equations, u ai With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving ai value, fitted to the function p a (t,x,y); make Let u bi =V(t,x i ), e ai =D(t,x i ,y i )·T(t,x i ,y i ), which is transformed into the following system of equations: Solve the system of equations, u bi With e ai All are known items, and the p of all measuring points in the computational domain is obtained by solving bi value, fitted to the function p b (t,x,y); make Let u ci =ω(t,σ i ), e ci =T(t,x i ,y i ), which is transformed into the following system of equations: Solve the system of equations, u ci With e ci All are known items, and the p of all measuring points in the computational domain is obtained by solving ci value, fitted to the function p c (t,σ); Horizontal advection term Adv(T(t,x,y))=p a (t,x,y)+p b (t,x,y)+p c (t,σ); The variable limit integration method is used to solve the horizontal advection term in the ocean model salinity equation. The solution process is the same as the horizontal advection term of the ocean model temperature equation mentioned above. It is only necessary to replace the temperatures T(t,x,y) and T(t-1,x,y) in the solution process with the salinities S(t,x,y) and S(t-1,x,y).

4. The ocean model temperature and salinity prediction method based on the variable limit integral method according to claim 3 is characterized by: The variable limit integration method is used to solve the horizontal diffusion term of the ocean model temperature equation, specifically: The horizontal diffusion term Dif(T(t-1,x,y)) of the ocean model temperature equation is: The two terms in the horizontal diffusion term are solved separately using the variable limit integration method; make Transformed into the following system of equations: e di As the known term, solve the equations to obtain the p of all measuring points in the computational domain. di value, fitted to the function p d (t-1,x,y); make Transformed into the following system of equations: e ei As the known term, solve the equations to obtain the p of all measuring points in the computational domain. ei value, fitted to the function p e (t-1,x,y); Horizontal diffusion term Dif(T(t-1,x,y))=p d (t-1,x,y)+p e (t-1,x,y); The variable limit integration method is used to solve the horizontal diffusion term in the ocean model salinity equation. The solution process is the same as that of solving the horizontal diffusion term in the ocean model temperature equation. It is only necessary to replace the temperatures T(t,x,y) and T(t-1,x,y) in the solution process with the salinities S(t,x,y) and S(t-1,x,y).

5. The ocean model temperature and salinity prediction method based on the variable limit integral method according to claim 4 is characterized by: The temperature is predicted using the implicit variable limit integral numerical format of the vertical diffusion term, specifically: Calculate the intermediate variable of temperature The numerical format of the implicit variable limit integration using the vertical diffusion term is: make Among them, d z represents the vertical grid step size, k1 and k2 are constants; Solve the equations to obtain T(t+1,x i ,y i ) value, and fitting it to the function T(t+1,x,y) to get the temperature prediction at the next moment; 6. The ocean model temperature and salinity prediction method based on the variable limit integration method according to claim 4, characterized in that: The salinity is predicted using the implicit variable limit integral numerical format of the vertical diffusion term, specifically: Calculate intermediate variables for salinity The numerical format of the implicit variable limit integration using the vertical diffusion term is: make Among them, d z represents the vertical grid step size, k1 and k2 are constants; Solve the equations to obtain S(t+1,x i ,y i ) value, and fitting it to the function S(t+1,x,y) to obtain the salinity prediction at the next moment; 7. The ocean model temperature and salinity prediction method based on the variable limit integration method according to claim 6, characterized in that: The method of using a weak filter to filter out the computational modes brought by the time splitting algorithm is as follows:

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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