A method, device, system and storage medium for searching for an ocean transmission barrier

Abstract

The present application relates to the technical field of data processing, in particular to a method and system for finding a marine transmission barrier and a storage medium, the method comprising: obtaining a differential equation of displacement by deriving a geostrophic flow field in a target sea area, and time-integrating the differential equation to obtain Lagrangian trajectories of fluid elements at all grid points in the target sea area; constructing a Poisson equation based on the relationship between the velocity vector and the partial derivative of the stream function, and combining the geostrophic flow field to obtain the stream function distribution of the target sea area in a target time period; in the target time period, time-integrating the stream function values of each fluid element in the target area along its Lagrangian trajectory and then taking the average to obtain the Lagrangian average stream function distribution field; determining an LASF contour with a maximum along-line stream function standard deviation less than a standard deviation threshold in the target time period, and determining the transmission barrier based on a material line coinciding with the LASF contour; the present application improves the accuracy and reliability of identifying the transmission barrier in a complex marine environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, in particular to a method and system for finding a marine transport barrier and a storage medium. BACKGROUND

[0002] Transport barriers play a crucial role in the marine environment, effectively hindering or altering the migration and diffusion of matter, energy and organisms between different sea areas, which has significant implications for maintaining marine ecological balance, ensuring sustainable use of marine resources and addressing marine pollution. However, due to the complexity, dynamics and vastness of the marine system, traditional methods for finding marine transport barriers often face many challenges.

[0003] The transport barriers identified by related technologies either do not extend far enough or the areas enclosed by the barriers are not large enough, making it difficult to apply or the results are not comprehensive. For example, when applied to the division of marine water bodies, the related technology may only obtain discontinuous transport barriers, which cannot completely distinguish different water bodies in motion; or the area enclosed by the closed transport barrier is too small, only obtaining partially divided water bodies, which cannot find all different water bodies in motion. SUMMARY

[0004] The present application aims to provide a method and system for finding a marine transport barrier and a storage medium, which can comprehensively divide different water bodies in motion as much as possible, and the obtained transport barrier can extend continuously far enough.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0006] In a first aspect, the present application provides a method for finding a marine transport barrier, comprising the following steps:

[0007] Obtaining the geostrophic flow field in the target sea area, obtaining the differential equation of displacement by differentiating the geostrophic flow field, and obtaining the Lagrangian trajectory of all fluid elements in the target sea area by time integration of the differential equation; the geostrophic flow field is the velocity vector of the fluid element at the corresponding time and position; the Lagrangian trajectory represents the flow field mapping relationship of all fluid elements in the flow field from the initial position at the initial time to the corresponding position over time within the study period;

[0008] According to the partial derivative relationship between the velocity vector and the stream function, and combining the sea surface height, gravitational acceleration and Coriolis parameter satisfied by the geostrophic flow field, a Poisson equation is constructed, and the stream function distribution of the target sea area in the target time period is obtained by solving the Poisson equation; the boundary condition of the stream function is determined according to the geostrophic flow;

[0009] averaging the time-integrated stream function values of each fluid element in the target region along its Lagrangian trajectory in the target time period, to obtain a Lagrangian averaged stream function distribution field;

[0010] determining an LASF contour with a maximum along-line stream function standard deviation less than a standard deviation threshold in the target time period, and determining a transport barrier based on a material line coinciding with the LASF contour; the LASF contour represents a curve formed by fluid elements with equal average stream function values in the Lagrangian averaged stream function distribution field, and the along-line stream function standard deviation represents a standard deviation of stream function values of all fluid elements forming the material line coinciding with the LASF contour at each time in the target time period.

[0011] Optionally, the time integration of the differential equation to obtain the Lagrangian trajectory of all grid fluid elements in the target sea area comprises:

[0012] decomposing the differential equation of displacement into differential equations of zonal and meridional components in the horizontal plane, and performing time integration operation on the differential equations of zonal and meridional components by using the time step adaptive fourth / fifth order Runge-Kutta method with interpolation;

[0013] calculating the local error of the fourth order solution and the fifth order solution during the time integration, and adjusting the time step when the local error is greater than the allowed maximum error, until the local error is lower than the allowed maximum error, and performing time integration operation based on the adjusted time step to obtain the zonal and meridional components of the fluid element at different times;

[0014] determining the plane coordinates of the fluid element at each time step based on the zonal and meridional components, and sequentially connecting the plane coordinates in time sequence to form the Lagrangian trajectory of the fluid element.

[0015] Optionally, the boundary condition of the stream function is determined by:

[0016] dividing the product of the negative Coriolis parameter and the sea surface height by the acceleration of gravity to obtain the upper and lower boundary conditions of the stream function;

[0017] solving the distribution of the stream function on the boundary by performing line integration on the velocity components on the left and right boundaries, to obtain the boundary stream function solution with the stream function value at the starting point of the boundary as the initial value, as the left and right boundary conditions of the stream function.

[0018] Optionally, the method further comprises:

[0019] spatially interpolating the stream function distribution of the target sea area in the target time period by the Lagrangian trajectory of the fluid element, to obtain the stream function value of the fluid element at the corresponding time position.

[0020] Optionally, the determining the transport barrier based on the material line coinciding with the LASF contour line comprises:

[0021] For the material line corresponding to the closed contour line, when the standard deviation of the stream function along the line is always less than the standard deviation threshold, the material line is taken as the transport barrier.

[0022] For the material line corresponding to the non-closed contour line, the line segment of the material line, along which the standard deviation of the stream function is continuously less than the standard deviation threshold, is taken as the transport barrier.

[0023] In a second aspect, an embodiment of the present application provides a device for searching a marine transport barrier, the device comprising:

[0024] A first module is configured to obtain a geostrophic flow field in a target sea area, derive a differential equation of displacement from the geostrophic flow field, and perform time integration on the differential equation to obtain Lagrangian trajectories of fluid elements at all grid points in the target sea area; the geostrophic flow field is a velocity vector of a fluid element at a corresponding time and position; and the Lagrangian trajectory represents a flow field mapping relationship in which all fluid elements in the flow area move from an initial position to a corresponding position over time within a study time period.

[0025] A second module is configured to construct a Poisson equation based on a partial derivative relationship between the velocity vector and the stream function, in combination with a sea surface height, a gravitational acceleration and a Coriolis parameter satisfied by the geostrophic flow field, and solve the Poisson equation to obtain a stream function distribution of the target sea area in a target time period; and a boundary condition of the stream function is determined according to the geostrophic flow.

[0026] A third module is configured to perform time integration on stream function values of each fluid element in the target area along its Lagrangian trajectory in the target time period, and then take an average value to obtain a Lagrangian average stream function distribution field.

[0027] A fourth module is configured to determine an LASF contour line with a maximum standard deviation of the stream function along the line being less than a standard deviation threshold in the target time period, and determine a transport barrier based on a material line coinciding with the LASF contour line; the LASF contour line represents a curve formed by fluid elements with equal average stream function values in the Lagrangian average stream function distribution field; and the standard deviation of the stream function along the line represents a standard deviation of stream function values of all fluid elements forming the material line coinciding with the LASF contour line at each time in the target time period.

[0028] In a third aspect, an embodiment of the present application provides a system for searching a marine transport barrier, the system comprising:

[0029] at least one processor;

[0030] at least one memory configured to store at least one program;

[0031] When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of the above.

[0032] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, wherein a processor executable program is stored, and the processor executable program is used for executing the method described above when executed by a processor.

[0033] The present application has the following beneficial effects: the present application introduces the key physical quantity of Lagrangian average stream function (LASF), combines the motion trajectory of fluid elements with the overall transport characteristics of the flow field, and effectively overcomes the limitations of the traditional Euler frame under instantaneous characteristic analysis. Specifically, the present method first constructs a displacement differential equation through the geostrophic flow field, accurately solves the Lagrangian trajectory of the fluid element by using the adaptive Runge-Kutta method, and ensures the accuracy and stability of the trajectory calculation in the complex flow field; secondly, the Poisson equation is constructed based on the geostrophic equilibrium relationship to solve the stream function distribution, and the boundary conditions are reasonably set in combination with the geostrophic flow characteristics, so that the stream function can truly reflect the large-scale circulation structure; further, the LASF distribution field is obtained by time integration and averaging along the trajectory, which can smooth the short-term flow field disturbance and highlight the transport rule under the long-time scale; finally, the stable LASF contour lines with material isolation capacity are accurately identified by defining the standard deviation of the stream function along the line, whether it is a closed contour line as a whole or a continuous stable line segment of a non-closed contour line, which can be effectively captured. This method based on the Lagrangian average framework not only reduces the dependence on high spatiotemporal resolution data, improves the robustness in the case of data noise or missing, but also generates continuous and wider range of transport barriers, which provides more reliable scientific basis for the prediction of marine pollutant diffusion, the division of marine ecological protection areas, and the planning of marine resource development, etc. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the related art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0035] Figure 1 The flow chart of the method for finding the marine transport barrier in the embodiments of the present application;

[0036] Figure 2 The position distribution diagram of the closed transport barrier under the advection effect and the Lagrangian particle in the SSH contour line at the initial time and after 60 days in the embodiments of the present application;

[0037] Figure 3 Figure 1 is a structural diagram of a searching device for a marine transport barrier in an embodiment of the present application;

[0038] Figure 4 Figure 2 is a structural diagram of a searching system for a marine transport barrier in an embodiment of the present application. DETAILED DESCRIPTION

[0039] The concept, specific structure and generated technical effects of the present application will be described clearly and completely in combination with embodiments and drawings to fully understand the purpose, scheme and effects of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0040] The technical terms involved in the present application will be introduced first as follows:

[0041] Transport barrier: invisible barrier of water body movement in the ocean, water body on one side of the barrier is difficult to move to the other side across the barrier, and water bodies on both sides of the barrier have different movement characteristics.

[0042] Lagrangian coherent structures (LCSs): marine transport barriers identified under the Lagrangian framework, which are divided into three categories: parabolic, elliptic, and hyperbolic.

[0043] Material line: virtual curve composed of fluid microelements, the shape of the curve changes with the movement of the fluid microelements thereon.

[0044] The identification of transport barriers is mainly divided into Euler method and Lagrangian method. Past researches believe that the boundary of a nonlinear vortex has the function of transport barrier, which can limit the movement of the internal water body and carry the internal water body to propagate for a long distance (Chelton et al., 2011). Based on this cognition, various vortex identification methods emerge, the most widely used of which are the method of identifying vortex based on sea surface height (SSH) contour and the method of identifying vortex based on geometric characteristics of vortex flow field. At the same time, based on the potential vorticity conservation theorem, Zhang et al. (2014) believe that the closed potential vorticity (PV) contour on the isopycnal surface has the function of limiting the outflow of the internal water body of the vortex, which is similar to a transport barrier, and this is used as the basis for identifying the boundary of the vortex. However, more and more researches based on the Lagrangian perspective find that the boundary of the vortex under the Euler perspective cannot completely limit the movement of the internal water body, and through the tracking of Lagrangian particles in the vortex, it is found that the water body inside the vortex boundary identified by the identification method under the Euler framework leaks very seriously (Abernathey & Haller, 2018; Beron-Vera et al., 2013, 2019; Liu et al., 2019; Wang et al., 2016; Xia et al., 2022).

[0045] Unlike the Eulerian framework, which focuses only on instantaneous states, the Lagrangian framework, which focuses on particle motion, is more suitable for research on water transport and for identifying transport barriers. Transport barriers identified under the Lagrangian framework are also known as Lagrangian coherent structures (LCSs). LCSs, as matter surfaces (three-dimensional) or matter lines (two-dimensional), possess the highest local velocities relative to other nearby matter surfaces to efficiently attract or repel particles (Farazmand & Haller, 2012; Haller, 2015; Prants, 2023), and can be divided into three main categories: Elliptic and parabolic LCSs are closely related to features such as vortices and jets, and belong to invariant manifolds (Haller, 2015; Oettinger et al., 2016); Hyperbolic LCSs are stable and unstable manifolds associated with a hyperbolic point, which can cleverly distinguish regions in the fluid with different long-term dynamic characteristics (Haller, 2023). Currently, methods for identifying transport barriers based on the Lagrange framework can be divided into two main categories: the first category is diagnostic methods, which identify transport barriers through fluid characteristics, including methods such as FTLE, FSLE, Mesochronic Analysis, Trajectory Length, Trajectory Complexity, and Shape Coherence; the second category is analytical methods, which identify transport barriers through complete mathematical theoretical derivation, including methods such as Transfer Operator Method, Dynamic Laplace Operator Method, Hierarchical Coherent Pairs, Fuzzy Cluster Analysis, Spectral Clustering, Geodesic Theory of LCS, and LAVD.

[0046] Among the numerous Lagrangian methods, the Finite-Time Lyapunov Exponent (FTLE) method is the most widely used one, which seeks transport barriers by measuring the maximum finite-time growth exponent experienced under infinitesimal perturbations of initial conditions (Abraham et al., 2000; Prants, 2023; Waugh et al., 2006). Although the FTLE method is relatively simple to apply, it cannot give material lines that explicitly correspond to transport barriers, and it cannot be used to detect elliptical LCSs associated with vortices (Hadjighasem et al., 2017; Haller, 2015), which cannot construct accurate closed transport barriers to calculate the transport of trapped water bodies. Another important Lagrangian method is the LCSs identification method based on the Cauchy-Green strain tensor proposed by Haller & Beron-Vera, (2013), which detects elliptical LCSs with strong coherence, and its vortex boundary has the same mathematical solution as a black hole in the universe, which can well isolate the water inside and outside the vortex, so it is also called a black hole vortex. However, such a vortex boundary is relatively rare in the real ocean. Subsequently, Haller et al., (2016) proposed a LCSs identification method based on the Lagrangian Average Vorticity Deviation (LAVD), and the identified LCSs are called Rotating Coherent Lagrangian Vortices (RCLVs). Beron-Vera et al., (2019) found through further research that even in a complex ocean environment with multiple scales of motion, this method can still identify coherent vortices with relatively compact and ordered structures. The boundary of the vortex can well limit the outflow of the internal water body, acting as a transport barrier.

[0047] Referring to Figure 1 The present application provides a method for finding an ocean transport barrier, the method comprising the following steps:

[0048] S100, obtaining a geostrophic flow field in a target sea area, deriving a differential equation of displacement from the geostrophic flow field, and performing time integration on the differential equation to obtain Lagrangian trajectories of all grid fluid elements in the target sea area; the geostrophic flow field is the velocity vector of the fluid element at the corresponding time and position; the Lagrangian trajectory represents the flow field mapping relationship of all fluid elements in the flow field from the initial time position to the corresponding position over time within the study period;

[0049] Specifically, the geostrophic flow field in the target sea area is obtained, and the differential equation of displacement is derived Time integration can obtain the Lagrangian trajectories of all grid fluid elements in the target sea area, wherein represents the derivative of displacement with respect to time, is the velocity vector of the fluid microelement at time . It is noted that by grid division of the target sea area, a plurality of grid points are obtained, each of which represents a position of a fluid microelement.

[0050] The obtained Lagrangian trajectory can be reflected by flow field mapping, and the formula is:

[0051] ;

[0052] wherein, represents flow field mapping of all fluid microelements in the flow field from time to time , represents the initial position of the fluid microelement at time , is the position of the fluid microelement at time . It is noted that, time to time

[0053] is the target time period, and the movement path and position change of the fluid microelement in the entire research period can be clearly presented by the Lagrangian trajectory, thereby providing basic data support for subsequent calculation of stream function distribution. S200, according to the relationship between the velocity vector and the partial derivative of the stream function, a Poisson equation is constructed in combination with the sea surface height, gravitational acceleration and Coriolis parameter satisfied by the geostrophic flow field, and the stream function distribution of the target sea area in the target time period is obtained by solving the Poisson equation; the boundary condition of the stream function is determined according to the geostrophic flow;

[0054] Specifically, the stream function distribution of the target sea area in the target time period is calculated every day in this step .

[0055] For an incompressible and sourceless flow field, the stream function satisfies the equation:

[0056] ;

[0057] wherein, , and , are the zonal and latitudinal components of the velocity and position vectors respectively.

[0058] According to the above formula, it can be deduced that the stream function satisfies the Poisson equation:

[0059] ;

[0060] ​wherein, is the Laplacian operator, is the stream function.

[0061] Considering that the geostrophic current satisfies the characteristics of passive incompressibility, the embodiment determines the boundary condition of the stream function according to the geostrophic current. The geostrophic current field satisfies the equation:

[0062] ;

[0063] wherein, is the sea surface height, is the gravitational acceleration, is the Coriolis parameter, , is the earth rotation angular velocity, is the latitude, in the northern hemisphere , in the southern hemisphere .

[0064] S300, in the target time period, the stream function value of each fluid microelement in the target region along its Lagrangian trajectory is time-integrated and then averaged to obtain a Lagrangian average stream function distribution field;

[0065] Specifically, the Lagrangian average stream function (LASF) distribution in the target time period is calculated according to the Lagrangian trajectory and the stream function distribution of each day:

[0066] ;

[0067] wherein, is the position of the fluid microelement at the moment moves to the position at the moment , which also reflects the Lagrangian trajectory of the fluid microelement, is the stream function value at the position at the moment obtained by spatially interpolating the stream function distribution of the target sea area in the target time period through the Lagrangian trajectory of the fluid microelement; is the time scale defined by the user according to the research requirement, the effective time range of the transmission barrier is from to , in this time range, the stream function value possessed by each fluid microelement in the research area at each moment is time-integrated, and finally divided by the time scale , that is, the Lagrangian average stream function (LASF) distribution field in the research area can be obtained.

[0068] ​S400, determine an LASF contour line with a maximum along-line stream function standard deviation less than a standard deviation threshold in a target time period, and determine the transport barrier based on a material line coinciding with the LASF contour line; the LASF contour line represents a curve formed by fluid elements with equal average stream function values in the Lagrangian average stream function distribution field, and the along-line stream function standard deviation represents a standard deviation of stream function values of all fluid elements forming the material line coinciding with the LASF contour line at each time in the target time period.

[0069] The LASF contour line can intuitively reflect the trend and structural characteristics of fluid motion in the flow field. In the specific implementation process, first, the standard deviation of the Lagrangian average stream function distribution field needs to be calculated, which is used to measure the dispersion degree of the stream function value in the spatial distribution. The smaller the standard deviation, the more concentrated the distribution of the stream function value in the region, the more stable the motion state of the fluid element, and the lower the dispersion of the trajectory, which has the potential condition to form a transport barrier. By setting a reasonable standard deviation threshold, the LASF contour line with an along-line stream function standard deviation less than the threshold is screened out. The material line corresponding to these LASF contour lines can effectively limit the exchange between the internal water body and the external water body, and thus is determined as the marine transport barrier. This method realizes the accurate identification of the transport barrier in the complex marine environment by combining the tracking of the Lagrangian trajectory and the spatiotemporal variation characteristics of the stream function, and provides important technical support for the fields of ocean circulation research, pollutant diffusion prediction, and marine ecological protection.

[0070] Specifically, the LASF contour line that meets a certain condition is found, and the material line coinciding with the LASF contour line is the transport barrier. The LASF contour line is divided into closed and non-closed contour lines. For the material line coinciding with each LASF contour line, the total flow across the line that causes the deformation of the material line is proportional to the along-line stream function standard deviation .The definition of the along-line stream function standard deviation is as follows:

[0071] ;

[0072] wherein, is the stream function value of the i-th fluid element constituting the material line at a certain time, is the total number of all fluid elements constituting the material line, is the average stream function value of all fluid elements at the time.

[0073] In the embodiments provided by the application, firstly, the geostrophic flow field in the target sea area is obtained, the differential equation of displacement is obtained by derivation of the geostrophic flow field, and the Lagrangian trajectory of all grid fluid elements in the target sea area is obtained by time integration of the differential equation, thereby laying a foundation for subsequent calculation of the stream function distribution and the Lagrangian mean stream function distribution field. Then, the Poisson equation is constructed according to the sea surface height, the gravity acceleration and the Coriolis parameter satisfied by the geostrophic flow field, and the stream function distribution of the research time period is solved by combining the partial derivative relationship between the zonal component and the meridional component of the velocity vector and the stream function, thereby providing a key parameter for subsequent analysis of the motion state of the fluid element. Then, the stream function value of each fluid element along the Lagrangian trajectory of the fluid element is time-integrated in the target time period, and the average value is taken, to obtain the Lagrangian mean stream function distribution field, which can reflect the average motion characteristics of the fluid element on a long time scale, and is helpful for identifying the stable structure in the flow field. Finally, the LASF contour line with a maximum along-line stream function standard deviation less than a standard deviation threshold in the target time period is determined, and the material line coinciding with the contour line is determined as a transport barrier, and this process fully utilizes the characteristics of the stream function standard deviation for measuring the discrete degree of the stream function value, thereby ensuring that the identified transport barrier has good stability and isolation, and can effectively limit the exchange between the internal water body and the external water body. The entire method process closely surrounds the motion characteristics of the fluid under the Lagrangian framework, from flow field acquisition to trajectory calculation, and then to stream function analysis and barrier identification, thereby effectively overcoming the limitations of the traditional Eulerian perspective method in the identification of the transport barrier, the transport barrier obtained by the application can divide the water bodies with different motion states as comprehensively as possible, and the obtained transport barrier can continuously extend far enough, thereby improving the accuracy and reliability of the identification of the transport barrier in the complex marine environment.

[0074] In some embodiments, the time integration of the differential equation obtains the Lagrangian trajectory of all grid fluid elements in the target sea area, including:

[0075] The differential equation of displacement is decomposed into differential equations of the zonal component and the meridional component on the horizontal plane, and the differential equations of the zonal component and the meridional component are respectively time-integrated by using the time step adaptive fourth / fifth order Runge-Kutta method with interpolation;

[0076] In the time integration process, the local error of the fourth order solution and the fifth order solution is calculated, and the time step is adjusted when the local error is greater than the allowed maximum error, until the local error is lower than the allowed maximum error, and the time integration operation is performed based on the adjusted time step, to obtain the zonal component and the meridional component of the fluid element at different time;

[0077] The plane coordinates of the fluid element at each time step are determined based on the zonal component and the meridional component, and the plane coordinates are sequentially connected in time order to form the Lagrangian trajectory of the fluid element.

[0078] Specifically, the differential equation of displacement is decomposed into differential equations of longitudinal component and latitudinal component in the horizontal plane, and the time integral operation is carried out on the two component equations respectively by using the step-adaptive four / five order Runge-Kutta method with interpolation, wherein, in the time integral process, the local error of the four order solution and the five order solution is calculated and compared with the allowed maximum error, if the local error is greater than the allowed maximum error, the time step is re-adjusted, the integral calculation is repeated until the local error is lower than the allowed maximum error, thereby obtaining the position component of the fluid microelement at different time.

[0079] The complete plane coordinates of the fluid microelement at each integral time are determined through the integral results of the longitudinal component and the latitudinal component, and these coordinates are sequentially connected in time sequence to form a continuous trajectory curve, which is the Lagrange trajectory of the fluid microelement from the initial time to the target time.

[0080] In the embodiment, the equation The component form in the horizontal plane can be written as and The time integral operation of the two equations adopts the step-adaptive four / five order Runge-Kutta method with interpolation, and the specific formula is as follows: Taking the solution of the longitudinal component as an example, the specific formula is as follows:

[0081] ;

[0082] ;

[0083] Wherein, represents the time step, is the slope at different stages, and are the four order weight coefficient and the five order weight coefficient respectively; is the position component at the current time, and are the four order solution and the five order solution, i.e. the position component at the next time obtained by the solution.

[0084] If the local error is greater than the allowed maximum error, the time step is re-adjusted, and the above calculation process is repeated until the local error is lower than the allowed maximum error.

[0085] By this method, the position component of the fluid microelement at different time and can be obtained. Thus, the Lagrange trajectory of the fluid microelement is obtained.

[0086] In some embodiments, the boundary conditions of the stream function are determined in the following manner:

[0087] The upper and lower boundary conditions of the stream function are obtained by dividing the product of the negative Coriolis parameter and the sea surface height by the gravitational acceleration.

[0088] By performing line integration on the velocity components on the left and right boundaries, the distribution of the stream function on the boundaries is solved, and the boundary stream function solution with the stream function value at the boundary starting point as the initial value is obtained, which serves as the left and right boundary conditions of the stream function.

[0089] It should be noted that solving the stream function requires finding the solution to the Poisson equation under specific boundary conditions. An adaptive fourth / fifth-order Runge-Kutta method with interpolation is employed. This method calculates the stream function solutions for the left and right boundaries by integrating the meridional and zonal components of the velocity vector along the boundary path, combined with the initial stream function value.

[0090] Specifically, by comparing the stream function equation with the geostrophic flow field equation, and considering that the Coriolis parameter can be used at the upper and lower boundaries... approximate, The value is approximately independent over a small latitudinal span (e.g., within 5°). Since the value changes, the Coriolis parameter can be approximated as a constant value that does not change with latitude over a small latitudinal span, using the formula... To set the upper and lower boundary conditions. The left and right boundaries are defined using the following formula: Integrate to obtain the solutions for the left and right boundaries. The stream function value at the boundary initiation point. and These are the start and end coordinates of the left and right boundaries, respectively. The integration operation still uses the adaptive fourth / fifth-order Runge-Kutta method with interpolation described above.

[0091] In some embodiments, the method further includes:

[0092] Spatial interpolation of the stream function distribution of the target sea area during the target time period is performed using the Lagrange trajectory of the fluid element to obtain the stream function value of the fluid element at the corresponding time position.

[0093] It should be noted that when calculating the Lagrange mean stream function distribution, the stream function value of the fluid element at a certain moment is obtained by spatial interpolation of the original stream function distribution field (the stream function distribution of the study time period) through its Lagrange trajectory. That is, based on the position of the fluid element at that moment, the corresponding stream function value is obtained by interpolation from the stream function distribution field of that day, and then time integration and averaging are performed.

[0094] In some embodiments, determining the transport barrier based on the material line coinciding with the LASF contour line includes:

[0095] For the material line corresponding to the closed isoline, the material line is regarded as a transport barrier when the standard deviation of stream function along the line is less than the standard deviation threshold all the time;

[0096] For the material line corresponding to the non-closed isoline, the segment of the material line where the standard deviation of stream function along the line is less than the standard deviation threshold continuously is regarded as a transport barrier.

[0097] Specifically, for the material line coinciding with the closed LASF isoline, when the standard deviation of stream function along the line increases with time, the material line is more likely to break, and the internal water body is more likely to leak; on the contrary, when the standard deviation of stream function along the line does not change or decreases with time, the material line is more stable, and the internal water body is less likely to leak, and the material line can act as a transport barrier. Therefore, a smaller standard deviation threshold can be set, and when the standard deviation of stream function along the material line coinciding with the closed LASF isoline is less than the standard deviation threshold all the time, the material line is regarded as a transport barrier. For the material line coinciding with the non-closed LASF isoline, since it generally extends for a long time and crosses various complex flow fields, it is not easy to meet the condition that the standard deviation of stream function along the entire line is less than the standard deviation threshold. To solve this problem, a segment of the material line can be found, where the standard deviation of stream function along the segment is less than the standard deviation threshold. The non-closed material line segment meets the condition that the standard deviation of stream function along the segment remains small all the time, and thus can also act as a transport barrier. The standard deviation threshold can be adjusted according to the specific marine environmental characteristics of the target sea area and the requirements of the research on the stability of the transport barrier.

[0098] Figure 2 The position distribution diagrams of Lagrangian particles in the closed transport barrier (subgraphs (a) to (b)) and the SSH isoline (subgraphs (c) to (d)) under the advection effect at the initial time and after 60 days. The color of the particles enclosed in each closed material line in the diagram depends on the maximum standard deviation of stream function along the material line within 60 days. The transport barrier related to the vortex and the SSH isoline boundary are black. The right subgraphs ((a)-1 to (d)-1) show the local close-up of the transport barrier and the SSH isoline vortex in the red square area in the left subgraphs ((a) to (d)), and the gray curve is the stream function isograde. As a comparison, the magenta particles show the distribution of the particles inside the transport barrier extracted by the existing relatively most perfect Lagrangian transport barrier searching method at the initial time and after 60 days.

[0099] Figure 2 ​Figures (a) to (b) of the drawings show the closed transport barrier in the South Atlantic Ocean extracted by the present application and the position distribution of fluid elements inside the barrier before and after 60 days. As a comparison, the magenta particles in the figures show the distribution of fluid elements inside the transport barrier extracted by the prior art. Meanwhile, (c) to (d) show the position distribution of fluid elements inside the SSH contour considered as the transport barrier by the prior art before and after 60 days. It can be seen that the water body inside the closed SSH contour considered as the transport barrier by the prior art leaks very seriously after 60 days, the contour boundary is no longer closed, and a lot of water elements inside escape to develop into filamentous structures. Although the transport barrier extracted by the prior art can limit the leakage of water elements inside, it can effectively distinguish the water elements inside which keep compact and orderly motion from the surrounding water elements which diffuse seriously and move irregularly, but its coverage area is extremely limited. The closed transport barrier extracted based on the present application is much larger than the transport barrier extracted by the prior art in terms of coverage area, and can also effectively limit the motion of water elements inside. In addition, the prior art cannot realize the search of continuous ocean basin scale non-closed transport barriers, and the non-closed transport barriers identified based on the prior art are always discontinuous and cannot be connected to extend to the ocean basin scale, while the present application can also identify continuous non-closed transport barriers which can extend to the ocean basin scale.

[0100] Referring to Figure 3 The present application provides a device for searching ocean transport barriers, comprising:

[0101] The first module is configured to obtain the geostrophic flow field in the target sea area, derive the differential equation of displacement from the geostrophic flow field, and obtain the Lagrangian trajectory of all fluid elements in the target sea area by time integration of the differential equation; the geostrophic flow field is the velocity vector of the fluid element at the corresponding time and position; the Lagrangian trajectory represents the flow field mapping relationship of all fluid elements in the flow area from the initial position at the initial time to the corresponding position over the study period;

[0102] The second module is configured to construct the Poisson equation according to the partial derivative relationship between the velocity vector and the stream function, in combination with the sea surface height, gravitational acceleration and Coriolis parameter satisfied by the geostrophic flow field, and solve the Poisson equation to obtain the stream function distribution of the target sea area in the target time period; the boundary condition of the stream function is determined according to the geostrophic flow;

[0103] The third module is configured to obtain the Lagrangian mean stream function distribution field by time integration of the stream function value of each fluid element in the target region along its Lagrangian trajectory and then taking the average value in the target time period;

[0104] A fourth module is configured to determine an LASF contour line with a maximum along-stream standard deviation of stream function in a target time period being less than a standard deviation threshold, and determine the transport barrier based on a material line coinciding with the LASF contour line; the LASF contour line represents a curve formed by fluid elements with equal average stream function values in a Lagrangian average stream function distribution field, and the along-stream standard deviation of stream function represents a standard deviation of stream function values of all fluid elements forming the material line coinciding with the LASF contour line at each time in the target time period.

[0105] It can be seen that the contents in the above method embodiments are all applicable to the present device embodiments, the present device embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0106] Corresponding to the method of Figure 1 , with reference to Figure 4 , the present embodiment provides a system for searching a marine transport barrier, comprising:

[0107] at least one processor;

[0108] at least one memory configured to store at least one program;

[0109] When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0110] It can be seen that the contents in the above method embodiments are all applicable to the present system embodiments, the present system embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0111] In addition, the present embodiment also discloses a computer program product or a computer program, which is stored in a computer readable storage medium. The processor of the computer device can read the computer program from the computer readable storage medium, and the processor executes the computer program, so that the computer device executes the above method. Similarly, the contents in the above method embodiments are all applicable to the present storage medium embodiments, the present storage medium embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0112] As will be appreciated by one of ordinary skill in the art, all or a portion of the methods disclosed herein can be embodied in software, firmware, hardware, or any suitable combination thereof. Any of the physical components or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or as hardware, or as an integrated circuit, such as an application- specific integrated circuit. Such software can be distributed on computer readable media, which can comprise computer storage media (or non-transitory media) and communication media (or transitory media). As is well known to those of ordinary skill in the art, the term computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer. Further, as is well known to those of ordinary skill in the art, communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave or other transport mechanism, and includes any information delivery media.

[0113] The above description is that of the preferred embodiments of the present disclosure. However, the present disclosure is not limited to the embodiments described above. It will be appreciated by those skilled in the art that any equivalent or modification of the present disclosure is possible without departing from the spirit of the present disclosure, and such equivalents or modifications are included in the scope of the present disclosure as defined by the appended claims.

Claims

1. A method for locating ocean transport barriers, characterized in that, The method includes the following steps: The geostrophic flow field within the target sea area is obtained. The differential equation of displacement is obtained by differentiating the geostrophic flow field. The Lagrange trajectory of all lattice fluid elements within the target sea area is obtained by time integration of the differential equation. The geostrophic flow field is the velocity vector of the fluid element at the corresponding time and position. The Lagrange trajectory represents the flow field mapping relationship of all fluid elements in the watershed moving from their initial position to their corresponding position over time during the study period. Based on the relationship between the velocity vector and the partial derivative of the stream function, and combined with the sea surface height, gravitational acceleration, and Coriolis parameters satisfied by the geostrophic flow field, the Poisson equation is constructed. Solving the Poisson equation yields the stream function distribution of the target sea area in the target time period. The boundary conditions of the stream function are determined based on the geostrophic flow field. Within the target time period, the average value of the stream function along the Lagrange trajectory of each fluid element in the target region is obtained by time integration. The formula for the Lagrange average stream function distribution field is: ； in, for Location at any time Fluid micro-elements in The position reached at any given time This also reflects the Lagrange trajectory of the fluid element. To determine the stream function distribution of the target sea area within the target time period using its Lagrange trajectory. Spatial interpolation is performed at time... Location The stream function value at that location; The effective time range of the transmission barrier is from [time scale customized by user according to research needs] to [time scale]. Start to Within this time range, the stream function of each fluid element in the target region at each time step. Integrate the value over time and then divide by the time scale. Thus, the Lagrange mean stream function distribution field within the target region can be obtained; The LASF contour lines with the maximum standard deviation of the stream function along the line being less than a standard deviation threshold are identified within the target time period. The transport barriers are determined based on the material lines that coincide with these LASF contour lines. The LASF contour lines represent the curves formed by fluid elements with equal average stream function values ​​in the Lagrange mean stream function distribution field. The standard deviation of the stream function along the line represents the standard deviation of the stream function values ​​of all fluid elements that make up the material lines that coincide with the LASF contour lines at each moment within the target time period.

2. The method according to claim 1, characterized in that, The process of integrating the differential equation over time to obtain the Lagrange trajectories of all lattice fluid elements within the target sea area includes: The differential equation of displacement is decomposed into differential equations of meridional and zonal components on the horizontal plane. The differential equations of meridional and zonal components are then integrated using the adaptive fourth / fifth-order Runge-Kutta method with interpolation time step. During the time integration process, the local errors of the fourth-order and fifth-order solutions are calculated, and the time step is adjusted when the local error is greater than the maximum allowable error until the local error is lower than the maximum allowable error. Based on the adjusted time step, the time integration operation is performed to obtain the meridional and zonal components of the fluid element at different times. The planar coordinates of the fluid element at each time step are determined based on the meridional and zonal components. The planar coordinates are then connected sequentially in chronological order to form the Lagrange trajectory of the fluid element.

3. The method according to claim 2, characterized in that, The boundary conditions of the stream function are determined in the following way: The upper and lower boundary conditions of the stream function are obtained by dividing the product of the negative Coriolis parameter and the sea surface height by the gravitational acceleration. By performing line integration on the velocity components on the left and right boundaries, the distribution of the stream function on the boundaries is solved, and the boundary stream function solution with the stream function value at the boundary starting point as the initial value is obtained, which serves as the left and right boundary conditions of the stream function.

4. The method according to claim 3, characterized in that, The method further includes: Spatial interpolation of the stream function distribution of the target sea area during the target time period is performed using the Lagrange trajectory of the fluid element to obtain the stream function value of the fluid element at the corresponding time position.

5. The method according to claim 1, characterized in that, The determination of the transport barrier based on the material line coinciding with the LASF contour line includes: For a material line corresponding to a closed contour line, if the standard deviation of the stream function along the line is always less than the standard deviation threshold, the material line is regarded as a transport barrier. For a material line corresponding to a non-closed contour line, the line segment along the material line whose stream function standard deviation is continuously less than the standard deviation threshold is regarded as a transmission barrier.

6. A device for locating marine transport barriers, characterized in that, The device includes: The first module is used to obtain the geostrophic flow field within the target sea area, differentiate the geostrophic flow field to obtain the differential equation of displacement, and perform time integration on the differential equation to obtain the Lagrange trajectory of all grid-point fluid micro-elements within the target sea area; the geostrophic flow field is the velocity vector of the fluid micro-elements at the corresponding time and position; the Lagrange trajectory represents the flow field mapping relationship of all fluid micro-elements in the watershed starting from their initial position and moving to their corresponding positions over time during the study period; The second module is used to construct the Poisson equation based on the relationship between the velocity vector and the partial derivative of the stream function, combined with the sea surface height, gravitational acceleration and Coriolis parameters satisfied by the geostrophic flow field, and to solve the Poisson equation to obtain the stream function distribution of the target sea area in the target time period; the boundary conditions of the stream function are determined based on the geostrophic flow field. The third module is used to calculate the average value of the stream function along the Lagrange trajectory of each fluid element in the target region within the target time period, and then obtain the Lagrange average stream function distribution field. The formula for the Lagrange average stream function distribution field is: ； in, for Location at any time Fluid micro-elements in The position reached at any given time This also reflects the Lagrange trajectory of the fluid element. To determine the stream function distribution of the target sea area within the target time period using its Lagrange trajectory. Spatial interpolation is performed at time... Location The stream function value at that location; The effective time range of the transmission barrier is from [time scale customized by user according to research needs] to [time scale]. Start to Within this time range, the stream function of each fluid element in the target region at each time step. Integrate the value over time and then divide by the time scale. Thus, the Lagrange mean stream function distribution field within the target region can be obtained; The fourth module is used to determine the LASF contour lines where the maximum standard deviation of the stream function along the line is less than the standard deviation threshold within the target time period, and to determine the transport barrier based on the material line coinciding with the LASF contour line. The LASF contour line represents the curve formed by fluid elements with equal average stream function values ​​in the Lagrange mean stream function distribution field, and the standard deviation of the stream function along the line represents the standard deviation of the stream function values ​​of all fluid elements that make up the material line coinciding with the LASF contour line at each moment within the target time period.

7. A system for locating marine transport barriers, characterized in that, The system includes: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 5.

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