A boundary detection and location method for transboundary water pollution

Abstract

The present invention discloses a boundary detection and positioning method applicable to cross-border water pollution, which relates to the field of river water quality monitoring technology. According to the data obtained in the longitudinal and transverse directions of the river channel at each monitoring point in the selected basin, a two-dimensional hydrodynamic model of the selected basin is established, and then a diffusion model of the target pollutant is constructed in combination with the obtained target pollutant concentration. A set of areas to be located is identified and integrated in each time period. The spatial distribution position and concentration gradient value of the concentration steep change area are used to screen out the concentration steep change areas that are spatially adjacent and have the same concentration gradient change trend through cluster analysis, and the boundary contour of the pollutant is fitted and generated in combination with the flow velocity field direction information. The present invention integrates the concentration steep change areas identified in each time period, performs cluster analysis based on their spatial distribution and gradient change trend, optimizes the pollution boundary contour fitting in combination with the flow velocity field direction information, and adapts to the pollution boundary detection needs in complex water environments.

Description

Technical Field

[0001] The present invention relates to the technical field of river water quality monitoring, and in particular to a boundary detection and positioning method suitable for transboundary water pollution. Background Art

[0002] Transboundary environmental governance is both a key and a challenge for coordinated regional development. Boundary effects are a significant factor influencing cross-border regional development. Existing environmental governance policies suffer from varying degrees of "boundary failure" in practice. For example, the fluidity of water bodies, and the significant spatiotemporal dynamics of pollutant diffusion and concentration distribution, often lead to a long-term, repetitive governance dilemma, with the transition from "turbid and polluted water" to "clear and sweet water."

[0003] In actual river basins, pollution boundaries can undergo significant spatial movement due to factors such as water flow velocity, direction, and seasonal hydrological changes. For example, during the flood season, the pollution boundary within a river basin may expand to further downstream areas with the water flow; during the dry season, the reduced flow velocity causes pollutants to be retained in specific areas, and the boundary shrinks or localized accumulation occurs. The shape and range of pollutant boundaries change over time. These hydrological dynamics cause the diffusion path and distribution range of pollutants to exhibit nonlinear changes, making it difficult to reflect the true process of pollutant diffusion through simple monitoring data. This dynamic characteristic of the pollution boundary determines that the impact range of pollutants will continue to change shape over time and with the distribution of water flow.

[0004] Therefore, in order to fully understand the spatiotemporal variation characteristics of pollutant diffusion, it is necessary to pay attention to the dynamic boundary changes during the pollutant diffusion process, so as to improve the pertinence and effectiveness of transboundary river basin environmental governance. Summary of the Invention

[0005] 1) Technical issues solved

[0006] The present invention provides a boundary detection and positioning method suitable for transboundary water pollution, which can fit the pollution boundary area by calculating the spatial variation rate of pollutant concentration.

[0007] 2) Technical solution

[0008] To achieve the above objectives, the present invention provides the following technical solution: a boundary detection and positioning method applicable to transboundary water pollution, comprising:

[0009] Based on the topographic information and river cross-section data of the selected watershed, monitoring points are set up at the upstream and downstream boundary points of the selected watershed and at the entrances and exits of each tributary. The target pollutant concentration, water flow rate, and water flow rate are obtained at each monitoring point in the longitudinal and transverse directions of the river;

[0010] Using the topographic data of the selected watershed, the river section data and the water flow and water velocity obtained at each of the monitoring points, a two-dimensional hydrodynamic model of the selected watershed is established to describe the velocity field and flow distribution of the water body in the horizontal direction;

[0011] Based on the velocity field and flow rate distribution provided by the two-dimensional hydrodynamic model and the target pollutant concentrations obtained at various monitoring points, a diffusion model of the target pollutant is constructed to describe the diffusion path and concentration distribution of the target pollutant in the selected watershed;

[0012] Setting multiple time periods based on a time sequence, calculating the concentration gradient of the pollutant in the selected watershed according to the concentration distribution of the target pollutant described by the diffusion model simulation in each time period, and identifying the area with abrupt concentration changes;

[0013] In the concentration sudden change areas identified in each time period, the concentration sudden change areas with continuous spatial distribution characteristics in any adjacent time periods are screened out and integrated into a set of areas to be located;

[0014] The spatial distribution positions and concentration gradient values ​​of the concentration steep change areas in the set of areas to be located are used to screen out the concentration steep change areas that are spatially adjacent and have consistent concentration gradient change trends through cluster analysis, and the boundary contours of the pollutants are fitted and generated in combination with the flow velocity field direction information.

[0015] Furthermore, the two-dimensional hydrodynamic model is constructed based on the shallow water equations, wherein the shallow water equations include the continuity equation and the momentum equation. Specifically:

[0016] Combining the topographic information and river section data of the selected watershed, discretizing the shallow water equations, and dividing the selected watershed into a plurality of calculation grids;

[0017] Based on the water flow and water velocity obtained in the longitudinal and transverse directions of the river channel at each monitoring point, positionally associating them with the corresponding grid according to the positional relationship, and initializing the two-dimensional hydrodynamic model;

[0018] The two-dimensional hydrodynamic model preliminarily simulates the horizontal velocity field of the water body in the target basin, the flow rate per unit time through each section of the river channel, and the turbulence intensity of the water flow. The simulation results are based on the physical parameters within the grid and the hydrodynamic interactions between adjacent grids.

[0019] The preliminary simulation results of the two-dimensional hydrodynamic model were compared with the monitored water flow and velocity data, and the model was calibrated using an error minimization method.

[0020] Furthermore, the diffusion model of the target pollutant is constructed using the convection-diffusion equation. The convection-diffusion equation is used to describe the diffusion and migration behavior of the target pollutant in the selected watershed. The equation form is:

[0021]

[0022] in, is the concentration of the target pollutant, also expressed as time and two-dimensional space function; For the horizontal The water flow rate, For the longitudinal direction of the river The water flow rate is: and All are derived from the simulation results of the two-dimensional hydrodynamic model; For the horizontal The diffusion coefficient, For the longitudinal direction of the river The diffusion coefficient of is the attenuation coefficient of the target pollutant; is the source term, which represents the degradation rate of the target pollutant.

[0023] Furthermore, the diffusion model of the target pollutant receives the water flow rate data of the constructed two-dimensional hydrodynamic model, and receives the target pollutant concentration obtained in the longitudinal and transverse directions of the river channel at each monitoring point, so as to simulate the diffusion path and concentration distribution of the target pollutant in the selected watershed.

[0024] Furthermore, the simulation results of the diffusion model of the target pollutant are compared with the target pollutant concentration data obtained at each monitoring point, so as to The diffusion coefficient and to update.

[0025] Furthermore, based on the diffusion path and concentration distribution of the target pollutant in the selected watershed described by the diffusion model, the concentration change gradient value of the pollutant in the selected watershed is calculated in each of the time periods, specifically:

[0026] Extracting the pollutant concentration value of each grid in the watershed in each time period through the simulated concentration distribution;

[0027] The pollutant concentration values ​​of any adjacent grids are compared, and grids with concentration gradient values ​​greater than a preset gradient value are screened out according to the gradient calculation formula and merged into one area, which is defined as the concentration sudden change area.

[0028] Furthermore, based on the concentration sudden change areas identified in each time period, the screened concentration sudden change areas are integrated into the set of areas to be located through spatial and temporal continuity screening. Specifically:

[0029] Obtaining the grid position distribution of the concentration sudden change area identified in any adjacent time period;

[0030] A region proximity condition is set, and for the concentration sudden change regions that meet the proximity condition, their continuity is marked according to the time series, and the concentration sudden change regions that appear continuously in multiple time periods are screened out and integrated into the set of regions to be located.

[0031] Furthermore, the spatial position and corresponding concentration gradient value of each concentration steep change area are extracted from the set of areas to be located, the concentration gradient change direction of each concentration steep change area is calculated, and a cluster analysis is performed on the extracted concentration steep change area data, that is, the directionality and change amplitude of the concentration gradient between areas are compared, and the concentration steep change areas with consistent gradient direction and change amplitude within the set range are screened.

[0032] Furthermore, for each area of ​​steep concentration change screened after clustering, the extension path of the boundary is preferentially fitted along the direction of the water flow according to the direction of the velocity field to ensure that the boundary contour is consistent with the water flow distribution trend. Then, the outer contour of the concentration gradient distribution is constructed by curve fitting to generate the boundary of the target pollutant.

[0033] 3) Beneficial effects:

[0034] Compared with the prior art, this invention has the following beneficial effects:

[0035] The present invention introduces a two-dimensional hydrodynamic model and a pollutant diffusion model, and combines the terrain data and cross-sectional characteristics of the selected watershed to obtain the flow velocity field, flow distribution and target pollutant concentration distribution information within the watershed. Based on the time series, multiple time periods are set, and the concentration gradient of the pollutant diffusion process in each time period is calculated to identify areas with sudden concentration changes. It can reflect the dynamic characteristics of the pollutant concentration range changing with time and water flow.

[0036] By clustering the spatial distribution and gradient change trends of areas with steep concentration changes, and combining the velocity field direction information to optimize the pollution boundary contour fitting, the deviation caused by local anomalies is reduced while improving the accuracy of boundary positioning, adapting to the needs of pollution boundary detection in complex water environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flow chart of a method for detecting and locating boundaries of transboundary water pollution provided by an embodiment of the present invention;

[0038] Figure 2 A flow chart of establishing a two-dimensional hydrodynamic model in a boundary detection and location method for transboundary water pollution provided by an embodiment of the present invention;

[0039] Figure 3 A schematic diagram of identifying areas with abrupt concentration changes in a boundary detection and location method for transboundary water pollution provided by an embodiment of the present invention;

[0040] Figure 4 A schematic diagram of a model simulation boundary in a boundary detection and positioning method for transboundary water pollution provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0042] In the description of the present invention, it should be understood that the terms "longitudinal", "transverse", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0043] In addition, the terms "first", "second", etc., if used, are merely used to distinguish and describe, and should not be understood as indicating or implying relative importance.

[0044] It should be noted that, in the absence of conflict, the features in the embodiments of the present invention may be combined with each other.

[0045] Water pollution monitoring and tracking are crucial issues in modern environmental protection, particularly in transboundary water pollution, where pollutants can migrate from one river basin or region to another, involving complex hydraulic conditions and pollution diffusion patterns. However, existing monitoring and tracking technologies have significant shortcomings in addressing transboundary water pollution, primarily in the following areas.

[0046] In the management of transboundary water pollution, extensive research has been conducted on the existence and impact of boundary pollution, but the spatial and temporal evolution characteristics and mechanisms of boundary pollution remain insufficient. This is because boundary pollution is closely related not only to the emission intensity of pollution sources, land use changes, and basin topography, but also to hydrological flow information within the basin. Ignoring this dynamic nature makes it difficult to accurately assess the true impact of pollutants on the transboundary regional environment. Alternatively, without a spatial and temporal continuous description of the dynamic changes of pollutants across the entire basin, it is difficult to fully reflect the diffusion characteristics and evolution of pollutants at the boundary.

[0047] To solve the above problems, combined Figures 1 to 4 As shown, embodiments of the present invention propose a method for detecting and locating the boundaries of transboundary water pollution. This method leverages hydrodynamics, pollutant migration and diffusion theory, and statistical optimization techniques, taking into account both the mechanistic analysis of pollutant diffusion and the complexity of actual river environments. Its efficiency, accuracy, and dynamic nature make it an important technical means for addressing the boundary detection and source tracing of transboundary water pollution, providing a scientific basis and practical support for water pollution control and regional collaboration.

[0048] Specifically, first, S10 is performed: based on the topographic information and river section data of the selected basin, monitoring points are set at the upstream and downstream boundary points of the selected basin and the entrances and exits of each tributary, and the target pollutant concentration, water flow and water flow rate are obtained at the longitudinal and transverse directions of the river at each monitoring point. The selection of monitoring points within the basin is the key to this step, and reference is made to the Figure 3 , monitoring points include:

[0049] The upstream and downstream boundary points are located at the upstream and downstream junction of the basin and are used to monitor the input and output of pollutants to ensure that the monitoring covers the impact range of the entire basin.

[0050] The tributary entrance points are selected at the entrances of tributaries with higher pollution risks, such as industrial wastewater discharge points or concentrated domestic sewage discharge areas, to monitor the impact of tributaries on the water quality of the main river.

[0051] Monitoring points are set up at key sections of the river according to the changes in flow velocity and flow in the river basin, such as river bends or areas where flow changes dramatically.

[0052] Taking a certain transboundary river basin as an example, a forest reserve in the upper reaches of the basin can be selected as a reference point for clean water sources, tributary monitoring points can be set up near the centralized sewage outlets of towns in the middle reaches, and boundary monitoring points can be set up at the cross-border provincial boundaries in the lower reaches to form a monitoring network that covers the entire upstream and downstream areas.

[0053] The key water quality parameters monitored include basic water quality parameters, target pollutant concentrations and hydrological parameters, which are specifically listed below.

[0054] Target pollutant concentration: Based on the actual pollution situation, select the concentration of specific pollutants (such as heavy metals, ammonia nitrogen, and petroleum) to monitor at each monitoring point and obtain pollutant concentration data.

[0055] Hydrological parameters: Water flow and water velocity are obtained in the longitudinal and transverse directions of the river at each monitoring point.

[0056] Among them, longitudinal monitoring of river channels can reflect the path and rate of pollutant diffusion along the mainstream direction. Long-distance pollution diffusion is often dominated by longitudinal flow velocity and flow. Mastering longitudinal data helps to simulate the macroscopic laws of the pollutant diffusion process and is an important basis for identifying and locating pollution sources.

[0057] Cross-channel monitoring of river channels can reveal the spatial distribution of pollutant concentrations within a watershed, particularly in areas of low flow velocity, such as riverbanks or backflow zones, which can form pollutant accumulation or diffusion blind spots. Cross-flow, such as lateral backflow or tributary injection, significantly influences the diffusion shape and boundary profile of pollutants. Obtaining cross-channel data can help improve the accuracy of pollutant boundary fitting.

[0058] At the entrance of the tributary near the industrial park, the concentration of heavy metals (such as lead and cadmium) is monitored, and parameters such as DO, COD and flow are monitored at upstream and downstream points to analyze the spread of pollution.

[0059] It is understandable that by obtaining the spatiotemporal distribution information of water quality at key locations within the basin, basic data can be provided for subsequent model construction. Combined with the actual spatiotemporal monitoring point layout and parameter collection methods, it is possible to ensure the precise positioning and full coverage of water quality problems in transboundary basins, laying a data foundation for pollution boundary identification and source analysis.

[0060] After acquiring data at the monitoring points, S20 proceeds to establish a two-dimensional hydrodynamic model of the selected basin using the topographic data of the selected basin, river cross-section data, and the water flow and velocity data acquired at each monitoring point. This model describes the horizontal velocity field and flow distribution of the water body. This step aims to establish a two-dimensional hydrodynamic model based on the basin's topography, river cross-section data, and velocity and flow data. This model simulates the flow characteristics of the water body, such as velocity field, flow rate, and turbulence intensity, providing a physical basis for analyzing pollutant migration and diffusion patterns and identifying pollution boundaries.

[0061] Two-dimensional hydrodynamic models are based on shallow water equations and are suitable for simulating flow characteristics in shallow bodies of water, such as rivers and lakes. Their mathematical form consists of two core equations: the conservation of mass equation (the continuity equation) and the conservation of momentum equation (the two-dimensional momentum equation).

[0062] Specifically, the mass conservation equation describes the mass conservation relationship of the water body and represents the change in water level per unit time. Its formula is:

[0063]

[0064] in, For water depth units: m ), that is, the water level; For water to flow Flow velocity component in the direction (unit: m / s ), For water flow Flow velocity component in the direction (unit: m / s ).

[0065] The momentum conservation equation describes the change in momentum of a fluid on a horizontal plane. It is affected by factors such as fluid inertia, gravity, and bottom friction. Its formula is:

[0066]

[0067]

[0068] in, and For external forces x and Directional component; and The driving force is caused by the water level gradient.

[0069] By solving the above two equations, the flow characteristics of water at any time on a plane can be simulated.

[0070] Specifically, a digital elevation model is used to describe the topography of the basin, and surveying and mapping data is used to obtain cross-sectional information of the river channel, including width, depth, and slope shape. Dynamic parameters such as flow velocity, flow rate, and water depth in the basin are collected as initial and boundary conditions. The study area is divided into a two-dimensional grid, with each grid node storing the water depth. The shallow water equations are discretized using the finite difference method, finite volume method, or finite element method, and the partial differential equations are converted into algebraic equations for easy computer solution. Physical quantities such as flow velocity. The grid can be a regular rectangular grid or an unstructured triangular grid based on the actual terrain.

[0071] Regarding the setting of boundary conditions, in some embodiments, specifically:

[0072] At the upstream boundary, set the inflowing water volume or flow rate;

[0073] At the downstream boundary, set the water level or free outflow condition;

[0074] At the boundary nodes, no-slip conditions are set to simulate the influence of river banks on flow velocity.

[0075] Through iterative algorithms, such as the explicit Euler method and the implicit finite difference method, the water depth and flow velocity of each grid point are gradually updated to simulate the dynamic evolution of the water body.

[0076] For example, in a certain interprovincial river basin (such as the middle and lower reaches of a section of the Yangtze River), a two-dimensional hydrodynamic model is established using the following data:

[0077] The topographic data are 30m resolution DEM data of the basin obtained from remote sensing data;

[0078] The river cross section is obtained by hydrographic survey equipment to obtain the river width, depth and slope;

[0079] The hydrological data are velocity and flow time series data obtained through buoy current meters, with a time step of 5 minutes to simulate flow changes within 1 hour.

[0080] In summary, the construction and solution of a two-dimensional hydrodynamic model lays the foundation for accurate simulation of water flow characteristics. The model fully considers the basin's topography, river cross-sections, and dynamic hydrological characteristics, providing high-resolution dynamic data support for subsequent pollutant dispersion models, thereby improving the accuracy and scientific nature of pollution source tracing and boundary identification.

[0081] Then, S30 is performed: Based on the velocity field and flow distribution provided by the two-dimensional hydrodynamic model, combined with the target pollutant concentrations obtained at each monitoring point, a diffusion model of the target pollutant is constructed to describe the diffusion path and concentration distribution of the target pollutant in the selected watershed. By combining the physical and chemical properties of the target pollutant and dynamically correcting the model based on monitoring data, the accuracy of the pollutant diffusion simulation is improved, thereby providing support for tracing the pollution source and identifying the pollution boundary.

[0082] Specifically, the convection-diffusion equation is a fundamental equation that describes the migration and diffusion of pollutants in water. It primarily considers two main forces: convection and diffusion. Convection refers to the migration of pollutants with the movement of water, and the speed of the water flow directly affects the propagation rate of pollutants. Diffusion refers to the gradual spread of pollutants from areas of high concentration to areas of low concentration due to the random motion of pollutants molecules. The diffusion coefficient reflects the diffusion capacity of pollutants.

[0083] In general, the convection-diffusion equation can be written as

[0084]

[0085] in, is the target pollutant concentration, indicating the time and space Function (unit: mg / L ).

[0086] For water flowing Flow velocity in direction (unit: m / s ), For water flow Flow velocity in direction (unit: m / s ), are derived from the output of the two-dimensional hydrodynamic model.

[0087] For The diffusion coefficient in the direction, For The diffusion coefficient in the direction reflects the diffusion degree of pollutants in the water body (unit: m² / s ), which can usually be divided into two parts: molecular diffusion and turbulent diffusion.

[0088] is the attenuation coefficient of the target pollutant; It is a source term (such as the impact of emission sources, rainfall, etc.), which represents the generation or consumption of pollutants per unit volume.

[0089] Because each pollutant has unique migration and diffusion characteristics, specific physicochemical properties such as solubility, diffusion coefficient, and reaction rate are analyzed. For example, the diffusion coefficients of pollutants such as dissolved oxygen, ammonia nitrogen, and phosphorus in water can usually be obtained from experimental data or literature. The diffusivity and convection properties of target pollutants (such as heavy metals and organic matter) can be adjusted based on their molecular weight and water temperature.

[0090] For different pollutants, different empirical formulas can be used to estimate their diffusion coefficients. Common formulas are as follows:

[0091] Molecular diffusion coefficient :

[0092]

[0093] in, is the temperature, is the viscosity of water, It is a constant and usually depends on different pollutants.

[0094] Turbulent diffusion coefficient , the turbulent diffusion coefficient usually depends on the flow velocity and turbulence intensity of the fluid and can be estimated through numerical simulation or empirical formula.

[0095] By comparing continuously collected water quality monitoring data (such as concentration data) with the model's predictions, model parameters (such as diffusion coefficients and source terms) can be dynamically adjusted. In some embodiments, Kalman wave filtering or least squares methods are used. Kalman wave filtering dynamically adjusts parameters such as diffusion coefficients and flow rates based on the difference between the estimated error and the model's predictions, making the model more consistent with the actual data.

[0096] The convection-diffusion equation is discretized using numerical methods such as the difference method, finite element method, and finite difference method, and solved through computer programs to simulate the migration and diffusion process of pollutants.

[0097] Taking the above-mentioned river pollution monitoring project as an example, the target pollutant is ammonia nitrogen. According to historical data, the diffusion coefficient of ammonia nitrogen is approximately D / s , the water flow velocity is u=0.3m / s At a certain moment, the ammonia nitrogen concentration at the midpoint of the river is =5mg / L By solving the spread of the pollutant in the river using numerical methods, we can predict:

[0098] In a given time period, the distribution of pollutant concentrations at different locations is obtained by numerically solving the convection-diffusion equation.

[0099] Based on actual water quality data collected regularly (e.g., data from continuous monitoring stations), the least squares method is used for dynamic correction to adjust the diffusion coefficient and correct the model bias.

[0100] In summary, by establishing the convection-diffusion equation and dynamically correcting monitoring data, this step can accurately simulate the migration and diffusion of pollutants in water bodies. Model parameters can be adjusted based on actual monitoring data, thereby improving the model's predictive capabilities. Ultimately, this can provide a scientific basis for locating pollution sources, identifying pollution boundaries, and managing water quality.

[0101] Then proceed to S40: set multiple time periods based on the time sequence, simulate the concentration distribution of the target pollutants described by the diffusion model in each time period, calculate the concentration change gradient value of the pollutants in the selected watershed, and identify the concentration sudden change area. And S50: in the concentration sudden change areas identified in each time period, screen out the concentration sudden change areas with continuous spatial distribution characteristics in any adjacent time periods, and integrate them into a set of areas to be located. The diffusion of pollutants in water bodies is not uniform, and rapid concentration changes often occur in certain areas. These areas are usually the locations of the pollutant boundaries. Through this method, the precise pollution boundary can be preliminarily determined, which further provides a basis for pollution source tracking and pollution control.

[0102] First, pollutant concentration data must be collected at multiple monitoring sections. The rate of change of pollutant concentration at each section must be calculated, and the concentration differences across sections must be compared. Next, by calculating the gradient of pollutant concentration across different sections, areas of most dramatic concentration change can be identified. These areas represent the potential boundaries of the pollutants. By focusing on these areas of abrupt change, the pollutant's spread can be determined, providing a scientific basis for subsequent pollution source tracing, monitoring, and control.

[0103] More specifically, the concentration gradient refers to the rate of change of pollutant concentration in space. The concentration gradient can be calculated by simple difference or differential methods.

[0104] For the concentration data on a monitoring section, its concentration gradient It can be calculated as follows:

[0105]

[0106] in, represents the concentration gradient inside the cross section; is the rate of change of the concentration of the target pollutant in the horizontal direction, is the rate of change of the concentration of the target pollutant in the vertical direction.

[0107] In a continuous water model, the concentration gradient can be expressed more accurately by differentiation as:

[0108]

[0109] In numerical models of some embodiments, finite difference methods or other numerical methods are often used to estimate such gradients.

[0110] In order to accurately identify areas with rapid concentration changes, it is first necessary to calculate the concentration gradient at multiple sections (such as cross sections of different watersheds or multiple monitoring points).

[0111] Calculate the rate of change of concentration between adjacent sections to identify areas of abrupt changes along the watershed:

[0112]

[0113] in, is the concentration change rate between sections, and are the average concentrations of adjacent sections, is the section spacing.

[0114] At each section, the rate of change of concentration with position is calculated. If the rate of change exceeds a threshold, the area is considered to have a sudden concentration change. This threshold can be set empirically or statistically. For example, the threshold can be set as the area where the concentration change rate is greater than a certain multiple of the standard deviation, or the threshold can be set based on the quantile of the dataset.

[0115] By analyzing the rate of change of concentration across multiple sections, all areas with large concentration gradients can be identified. These areas are where pollutant concentrations change most rapidly and typically represent the pollutant's diffusion boundaries. By combining information such as the flow characteristics of the river and the diffusion pattern of pollutants, the location of the farthest boundary of pollutant diffusion can be determined. For example, pollutants may spread downstream with the movement of the water flow. This allows identifying areas with abrupt changes downstream and predicting the further spread of pollutants. Furthermore, in some cases, clustering algorithms (such as K-means and DBSCAN) can be used to perform spatial clustering analysis on areas with abrupt concentration changes, thereby more clearly defining the scope and boundaries of the pollution source.

[0116] It can be understood that the spatial location and corresponding concentration gradient value of each concentration-change region are extracted from the aforementioned set of areas to be located. The concentration-change regions are then classified after the direction of concentration gradient change is calculated. Cluster analysis is then performed on the extracted concentration-change region data, comparing the directionality and variation of concentration gradients between regions, and screening for concentration-change regions with consistent gradient directions and variation within a set range. By calculating the spatial variation rate of pollutant concentration, combined with threshold judgment, cluster analysis, and other methods, the diffusion boundaries of pollutants in water bodies can be effectively identified.

[0117] By comparing the gradient directions and variation ranges of different concentration abrupt change areas, areas with consistent directions and variation ranges within a certain range can be classified into one category, and abnormal areas with excessively large differences in direction or variation range can be eliminated. Among them, the calculation of the concentration gradient value can refer to the above-mentioned spatial difference method, the calculation of the gradient direction consistency, in some embodiments, the direction consistency between the two areas can be calculated based on the cosine similarity of the extracted concentration gradient direction. Identifying areas with abrupt concentration changes helps to quickly locate pollution sources, determine the diffusion range of pollutants, and provide a scientific basis for pollution control and water quality monitoring. This step is of great significance for tracing the source of pollutants and formulating control strategies.

[0118] Finally, proceed to S60: using the spatial distribution position and concentration gradient value of the concentration steep change area in the set of areas to be located, screen out the concentration steep change areas that are spatially adjacent and have the same concentration gradient change trend through cluster analysis, and combine the velocity field direction information to fit and generate the boundary contour of the pollutant. The main goal of this step is to infer the preliminary position of the pollution source through the reverse convection diffusion model. After the pollutants enter the water body from the source, they will diffuse to different positions according to the water flow and diffusion process. By monitoring the pollutant concentrations at different positions in the water body and combining the reverse deduction of the water flow and diffusion model, the boundary position of the pollutant can be inferred. The key to this step is to use the spatial distribution characteristics and gradient change information of the concentration steep change area, and generate the pollutant boundary contour through the fusion of cluster analysis and velocity field direction.

[0119] It can be understood that the grid in areas of abrupt concentration changes exhibits specific geometric distribution characteristics in two-dimensional space, and its center or boundary can be described by positional coordinates. Gradient variations reflect the direction and intensity of pollutant concentration diffusion within a local area. Consistency in gradient trends between adjacent areas suggests that pollutants likely share the same diffusion boundary. The direction of the velocity field influences the pollutant diffusion path. Incorporating velocity field information can avoid excessive or unreasonable extrapolation during boundary fitting.

[0120] More specifically, the spatial coordinates (e.g., grid center points) and corresponding concentration gradient values ​​of each concentration abrupt change region in the set of regions to be located are inversely obtained, and the velocity field direction information is imported from the two-dimensional hydrodynamic model.

[0121] In some embodiments, the above-extracted set of localized regions is clustered using a spatial clustering algorithm, such as DBSCAN or a density-based clustering method, based on the spatial location (e.g., longitude and latitude coordinates) and concentration gradient values ​​of the regions to be located. Spatial location ensures that the proximity between the regions to be located conforms to actual distribution characteristics, while the concentration gradient value reflects the intensity of pollution concentration changes, helping to distinguish between areas of varying pollution intensities.

[0122] It can be understood that the cluster analysis in this step is based on the gradient consistent areas screened out in the first step, and further screening is performed in combination with the direction of the velocity field. Its purpose is to use cluster analysis to analyze the flow direction consistency in the area with a sudden concentration change, ensure that the starting point and extension direction of the boundary fitting are consistent with the water flow trend, and finally generate the outer contour through curve fitting.

[0123] The clustering results are initially screened using the velocity field direction information to retain regions with consistent or similar velocity directions. For example, the velocity field direction vector can be compared with the concentration gradient direction to screen out regions where the velocity and gradient directions are consistent. In some embodiments, an angle between the velocity direction vector and the gradient direction vector can be set. If this angle is within a preset range or less than a threshold, the region is defined as consistent, and discrete regions that do not fall within this definition are eliminated.

[0124] For each clustering result, a boundary fitting technique is used to form a preliminary outline of the pollution boundary. In some embodiments, the clustering results are first fitted into a closed polygon representing the pollution boundary using an alpha shape algorithm or a minimum convex hull technique. The alpha shape algorithm can adapt to complex boundary features and avoid the overly smooth boundaries that may be produced by the minimum convex hull. During the boundary fitting process, the velocity field direction information is combined with the boundary stretching or constraint direction to make the fitting result more consistent with the actual laws of pollution diffusion under the hydrodynamic model.

[0125] To further improve the accuracy and rationality of the boundary, the fitted boundary is optimized by combining the pollutant diffusion model with the velocity field data. In some embodiments, after fitting the above-mentioned boundary contour, the concentration distribution within the boundary area is simulated to verify whether the concentration difference inside and outside the boundary is consistent with the actual monitoring data. Abnormal concentration distribution areas or redundant areas that significantly deviate from the flow direction are removed. Based on the pollution diffusion dynamics of multiple time periods, the boundary results of different time periods are superimposed to screen out the boundaries of areas with stable spatiotemporal distribution, further refining the pollution boundary range.

[0126] Finally, the optimized boundary contours are used to generate a visual pollution boundary map, showing the distribution range of the polluted area and its concentration variation characteristics. A boundary data file is also generated to provide technical support for the subsequent design of pollution control plans.

[0127] In summary, this method combines pollutant concentration data, velocity field information, and watershed grid data to comprehensively describe the characteristics of pollution diffusion under complex hydrological conditions. From concentration gradient analysis to boundary fitting, it fully utilizes information from monitoring points and computational grids. By calculating gradient values ​​and screening for spatial distribution consistency, it prioritizes key areas with steep concentration changes, reducing the amount of computation while improving the accuracy of boundary positioning. The introduction of velocity field direction information dynamically adjusts the boundary contour, taking into account the directionality of water flow and helping to more accurately reflect the evolution of the pollution range over time. In summary, this method, from concentration gradient calculation and identification of steep change areas to final boundary contour generation, can be gradually refined to more accurately reflect the diffusion patterns and boundary characteristics of pollutants under complex hydrological conditions.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. The scope of patent protection of the present invention shall be based on the claims. Any equivalent structural changes made using the description and drawings of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A boundary detection and positioning method suitable for transboundary water pollution, characterized in that: include: Based on the topographic information and river cross-section data of the selected watershed, monitoring points are set up at the upstream and downstream boundary points of the selected watershed and at the entrances and exits of each tributary. The target pollutant concentration, water flow rate, and water flow rate are obtained at each monitoring point in the longitudinal and transverse directions of the river; Using the topographic data of the selected watershed, the river section data, and the water flow and water velocity obtained at each of the monitoring points, a two-dimensional hydrodynamic model of the selected watershed is established to describe the velocity field and flow distribution of the water body in the horizontal direction; wherein, the two-dimensional hydrodynamic model is constructed based on the shallow water equation group, and the shallow water equation group is discretized in combination with the topographic information and river section data of the selected watershed, and the selected watershed is divided into a plurality of calculation grids. Based on the water flow and water velocity obtained in the longitudinal and transverse directions of the river channel at each monitoring point, they are positionally associated with the corresponding grids according to the positional relationship, and the two-dimensional hydrodynamic model is initialized. The preliminary simulation results of the two-dimensional hydrodynamic model are compared with the monitored water flow and water velocity data, and the model is corrected using an error minimization method; Based on the velocity field and flow rate distribution provided by the two-dimensional hydrodynamic model and the target pollutant concentrations obtained at various monitoring points, a diffusion model of the target pollutant is constructed to describe the diffusion path and concentration distribution of the target pollutant in the selected watershed; Setting multiple time periods based on a time sequence, calculating the concentration gradient of the pollutant in the selected watershed according to the concentration distribution of the target pollutant described by the diffusion model simulation in each time period, and identifying the area with abrupt concentration changes; In the concentration sudden change areas identified in each time period, the concentration sudden change areas with continuous spatial distribution characteristics in any adjacent time periods are screened out and integrated into a set of areas to be located; The spatial distribution positions and concentration gradient values ​​of the concentration steep change areas in the set of areas to be located are used to screen out the concentration steep change areas that are spatially adjacent and have consistent concentration gradient change trends through cluster analysis, and the boundary contours of the pollutants are fitted and generated in combination with the flow velocity field direction information.

2. The boundary detection and positioning method for transboundary water pollution according to claim 1, characterized in that: The shallow water equations include the continuity equation and the momentum equation. The two-dimensional hydrodynamic model preliminarily simulates the horizontal velocity field of the water body in the target basin, the flow rate through each section of the river per unit time, and the turbulence intensity of the water flow; wherein the simulation results are all based on the physical parameters within the grid and the hydrodynamic interaction between adjacent grids.

3. The boundary detection and positioning method for transboundary water pollution according to claim 1, characterized in that: The diffusion model of the target pollutants is constructed using the convection-diffusion equation. The convection-diffusion equation is used to describe the diffusion and migration behavior of the target pollutants in the selected watershed. The equation form is: in, is the concentration of the target pollutant, also expressed as time and two-dimensional space function; For the horizontal The water flow rate, For the longitudinal direction of the river The water flow rate is: and All are derived from the simulation results of the two-dimensional hydrodynamic model; For the horizontal The diffusion coefficient, For the longitudinal direction of the river The diffusion coefficient of is the attenuation coefficient of the target pollutant; is the source term, which represents the degradation rate of the target pollutant.

4. The boundary detection and positioning method for transboundary water pollution according to claim 1, characterized in that: The diffusion model of the target pollutant receives the water flow rate data of the constructed two-dimensional hydrodynamic model, and receives the target pollutant concentration obtained in the longitudinal and transverse directions of the river channel at each monitoring point, so as to simulate the diffusion path and concentration distribution of the target pollutant in the selected watershed.

5. The boundary detection and positioning method for transboundary water pollution according to claim 4, characterized in that: The simulation results of the diffusion model of the target pollutant are compared with the target pollutant concentration data obtained at each monitoring point, so as to Diffusion coefficient and to update.

6. The boundary detection and positioning method for transboundary water pollution according to claim 2, characterized in that: According to the diffusion path and concentration distribution of the target pollutant in the selected watershed described by the diffusion model, the concentration change gradient value of the pollutant in the selected watershed is calculated in each time period, specifically: Extracting the pollutant concentration value of each grid in the watershed in each time period through the simulated concentration distribution; The pollutant concentration values ​​of any adjacent grids are compared, and grids with concentration gradient values ​​greater than a preset gradient value are screened out according to the gradient calculation formula and merged into one area, which is defined as the concentration sudden change area.

7. The boundary detection and positioning method for transboundary water pollution according to claim 6, characterized in that: Based on the concentration sudden change areas identified in each time period, the screened concentration sudden change areas are integrated into the set of areas to be located through spatial and temporal continuity screening. Specifically: Obtaining the grid position distribution of the concentration sudden change area identified in any adjacent time period; A region proximity condition is set, and for the concentration sudden change regions that meet the proximity condition, their continuity is marked according to the time series, and the concentration sudden change regions that appear continuously in multiple time periods are screened out and integrated into the set of regions to be located.

8. The boundary detection and positioning method for transboundary water pollution according to claim 1, characterized in that: The spatial position and corresponding concentration gradient value of each concentration steep change area are extracted from the set of areas to be located, the concentration gradient change direction of each concentration steep change area is calculated, and cluster analysis is performed on the extracted concentration steep change area data, that is, the directionality and change amplitude of the concentration gradient between areas are compared, and the concentration steep change areas with consistent gradient direction and change amplitude within the set range are screened.

9. The boundary detection and positioning method for transboundary water pollution according to claim 8, characterized in that: For each area of ​​steep concentration change screened after clustering, the extension path of the boundary is preferentially fitted along the direction of the water flow according to the direction of the velocity field to ensure that the boundary contour is consistent with the water flow distribution trend. Then, the outer contour of the concentration gradient distribution is constructed by curve fitting to generate the boundary of the target pollutant.

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