Boundary detection and positioning method suitable for trans-boundary water pollution

Abstract

The invention discloses a boundary detection and positioning method suitable for trans-boundary water pollution, and relates to the technical field of river water quality monitoring. According to data obtained at the longitudinal and transverse positions of a river channel of each monitoring point of a selected drainage basin, a two-dimensional hydrodynamic model of the selected drainage basin is established; then, combining with the obtained target pollutant concentration to construct a diffusion model of the target pollutant, identifying and integrating a to-be-positioned region set in each time period, and screening out the concentration abrupt change regions which are spatially adjacent and consistent in concentration gradient change trend through clustering analysis by utilizing the spatial distribution positions and concentration gradient values of the concentration abrupt change regions; and the boundary contour of the pollutant is generated by fitting in combination with the direction information of the flow velocity field. According to the method, after concentration abrupt change areas identified in each time period are integrated, clustering analysis is carried out according to spatial distribution and gradient change trends of the concentration abrupt change areas, pollution boundary contour fitting is optimized in combination with flow velocity field direction information, and pollution boundary detection requirements in a complex water area environment are met.

Description

Technical Field

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

[0002] The issue of transboundary environmental governance is the key and challenge of regional coordinated development, and the boundary effect is an important factor affecting the development of transboundary regions. Existing environmental governance policies have varying degrees of "boundary failure" in practical applications. Taking the typical transboundary water environment as an example, due to the fluidity of water bodies, the diffusion and concentration distribution of pollutants have significant spatio-temporal dynamic characteristics, which often plunge the transboundary water environment in this region into a long-term repeated governance dilemma from "turbid and polluted water" to "clear and sweet water".

[0003] In actual river basins, pollution boundaries can shift significantly in space due to factors such as water flow velocity, direction, and seasonal hydrological changes. For example, during the flood season, the pollution boundary within the river basin may expand downstream with the water flow; during the dry season, the reduced flow velocity causes pollutants to accumulate in specific areas, resulting in the boundary contracting or local accumulation occurring. The shape and scope of the pollutant boundary change over time, and these hydrological dynamics lead to non-linear changes in the pollutant diffusion path and distribution range, 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 influence range of pollutants will continuously change in shape over time and with the water flow distribution.

[0004] Therefore, to comprehensively understand the spatio-temporal variation characteristics of pollutant diffusion, it is necessary to pay attention to the dynamic boundary changes during the pollutant diffusion process, thereby enhancing the pertinence and effectiveness of transboundary river basin environmental governance. Summary of the Invention

[0005] I. Technical Problems to be Solved The present invention provides a method for boundary detection and location applicable to transboundary water pollution, which can fit the pollution boundary region by calculating the spatial change rate of pollutant concentration.

[0006] II. Technical Solutions To achieve the above object, the present invention provides the following technical solutions: A method for boundary detection and location applicable to transboundary water pollution, including: According to the topographic information and river cross-section data of the selected river basin, monitoring points are set at the upstream and downstream boundary points of the selected river basin and at the entrances and exits of each tributary. At the longitudinal and transverse directions of the river channel at each monitoring point, the target pollutant concentration, water flow rate, and water flow velocity are respectively obtained; Using the topographic data, river cross-section data of the selected river basin, and the water flow rate and water flow velocity obtained at each monitoring point, a two-dimensional hydrodynamic model of the selected river basin is established to describe the velocity field and flow distribution of the water body in the horizontal direction; Based on the flow velocity field and flow rate 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 basin; Set multiple time periods based on time series. Within each time period, according to the concentration distribution of the target pollutant described by the simulation of the diffusion model, calculate the concentration change gradient value of the pollutant in the selected basin, and identify the regions with steep concentration changes from them; Among the regions with steep concentration changes identified within each time period, screen out the regions with steep concentration changes having continuous spatial distribution characteristics within any adjacent time periods, and integrate them into a set of regions to be located; Utilize the spatial distribution positions and concentration gradient values of the regions with steep concentration changes in the set of regions to be located, screen out the regions with steep concentration changes that are spatially adjacent and have the same trend of concentration gradient change through cluster analysis, and combine with the flow velocity field direction information to fit and generate the boundary contour of the pollutant.

[0007] Further, construct the two-dimensional hydrodynamic model based on the shallow water equations. Among them, the shallow water equations include the continuity equation and the momentum equation. Specifically: Combine the topographic information and river cross-section data of the selected basin to discretize the shallow water equations, and divide the selected basin into multiple computational grids; According to the water flow rate and water flow velocity obtained at the longitudinal and transverse directions of the river at each monitoring point, associate their positions with the corresponding grids according to the position relationship to initialize the two-dimensional hydrodynamic model; The two-dimensional hydrodynamic model preliminarily simulates the flow velocity field of the water body in the horizontal direction of the target basin, the flow rate magnitude passing through each cross-section of the river per unit time, and the water flow turbulence intensity; among them, the simulation results are all based on the physical parameters within the grid and the hydrodynamic interaction between adjacent grids; Compare the preliminary simulation results of the two-dimensional hydrodynamic model with the monitored water flow rate and water flow velocity data, and correct the model using the error minimization method.

[0008] Further, construct the diffusion model of the target pollutant 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 basin, and its equation form is: Among them, is the concentration of the target pollutant, and is also expressed as a function of time and two-dimensional space ; is the water flow velocity in the transverse direction of the river, is the water flow velocity in the longitudinal direction of the river Flow velocity of water; among which, and both come from the simulation results of the two-dimensional hydrodynamic model; is the diffusion coefficient in the transverse direction of the river channel and is the diffusion coefficient in the longitudinal direction of the river channel ; is the attenuation coefficient of the target pollutant; is the source term, representing the degradation rate of the target pollutant.

[0009] Furthermore, the diffusion model of the target pollutant receives the flow velocity data of the constructed two-dimensional hydrodynamic model, and receives the target pollutant concentrations obtained respectively at the longitudinal and transverse directions of the river channel at each of the monitoring points, so as to simulate the diffusion path and concentration distribution of the target pollutant in the selected basin.

[0010] Furthermore, the simulation results of the diffusion model of the target pollutant are compared with the target pollutant concentration data obtained at each of the monitoring points, so as to update the diffusion coefficients and in different two-dimensional spaces.

[0011] Furthermore, according to the diffusion path and concentration distribution of the target pollutant described by the diffusion model in the selected basin, the concentration change gradient value of the pollutant in the selected basin is calculated within each of the time periods. Specifically: Through the simulated concentration distribution, the pollutant concentration values of each grid in the basin are extracted within each time period; The pollutant concentration values of any adjacent grids are compared, and the grids with concentration gradient values greater than the preset gradient value are screened out and merged into one area, which is defined as the concentration abrupt change area.

[0012] Furthermore, based on the concentration abrupt change areas identified within each time period, through spatial and temporal continuity screening, the screened concentration abrupt change areas are integrated into the set of areas to be located. Specifically: Obtain the grid position distribution of the concentration abrupt change areas identified within any adjacent time periods; Set the regional proximity condition, for the concentration abrupt change areas that meet the proximity condition, mark their continuity according to the time series, and screen out the concentration abrupt change areas that continuously appear in multiple time periods, and integrate them into the set of areas to be located.

[0013] Further, extract the spatial positions and corresponding concentration gradient values of each concentration abrupt change region from the set of regions to be located, calculate the concentration gradient change directions of each concentration abrupt change region, and perform clustering analysis on the extracted concentration abrupt change region data, that is, compare the directionality and change amplitude of the concentration gradients between regions, and screen out the concentration abrupt change regions with consistent gradient directions and change amplitudes within a set range.

[0014] Further, for each concentration abrupt change region screened after clustering, according to the flow velocity field direction, preferentially fit the extension path of the boundary along the water flow direction to ensure that the boundary contour is consistent with the water flow distribution trend, and then use the curve fitting method to construct the outer envelope contour of the concentration gradient distribution, thereby generating the boundary of the target pollutant.

[0015] (III) Beneficial effects: Compared with the prior art, the invention has the following beneficial effects: By introducing a two-dimensional hydrodynamic model and a pollutant diffusion model, combining the topographic data and cross-section characteristics of the selected river basin to obtain the flow velocity field, flow distribution and target pollutant concentration distribution information within the river basin, and setting multiple time periods based on time series, calculating the concentration gradients of the pollutant diffusion process within each time period, and identifying the concentration abrupt change regions, the dynamic characteristics of the change of the pollutant concentration range with time and water flow can be reflected.

[0016] By performing clustering analysis on the spatial distribution and gradient change trend of the concentration abrupt change regions, and optimizing the fitting of the pollution boundary contour in combination with the flow velocity field direction information, the deviation caused by local anomalies is reduced while the accuracy of boundary positioning is improved, meeting the pollution boundary detection requirements in complex water environment. Brief description of the drawings

[0017] Figure 1 It is a method flow chart of a boundary detection and positioning method for transboundary water pollution provided by an embodiment of the present invention; Figure 2 It is a flow chart of establishing a two-dimensional hydrodynamic model in a boundary detection and positioning method for transboundary water pollution provided by an embodiment of the present invention; Figure 3 It is a schematic diagram of identifying concentration abrupt change regions in a boundary detection and positioning method for transboundary water pollution provided by an embodiment of the present invention; Figure 4 It is a schematic diagram of the model simulation boundary in a boundary detection and positioning method for transboundary water pollution provided by an embodiment of the present invention. Detailed implementation manners

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0019] In the description of the present invention, it should be understood that the terms "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It is 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 thus should not be construed as a limitation to the present invention.

[0020] In addition, terms such as "first" and "second" are only used for distinguishing descriptions and should not be construed as indicating or implying relative importance.

[0021] It should be noted that the features in the embodiments of the present invention may be combined with each other without conflict.

[0022] Water pollution monitoring and tracking is an important topic in modern environmental protection. Especially in transboundary water pollution, pollutants may migrate from one basin or region to another, involving complex hydraulic conditions and pollution diffusion laws. However, the existing monitoring and tracking technologies have obvious deficiencies in solving the problem of transboundary water pollution, which are mainly reflected in the following aspects.

[0023] In the treatment of transboundary water pollution, there have been a large number of studies on the existence and impact degree of boundary pollution, but the revelation of the spatio-temporal evolution characteristics and action mechanism of boundary pollution is still insufficient. This is because boundary pollution is not only closely related to the pollutant emission intensity, land use change, and basin terrain characteristics, but also related to the hydrological flow information in the basin. Ignoring the dynamics, it is difficult to accurately evaluate the true impact range of pollutants on the transboundary regional environment. It can also be understood that without a spatio-temporal continuous description of the dynamic changes of pollutants in the whole basin, it is difficult to comprehensively reflect the diffusion characteristics and evolution process of pollutants at the boundary.

[0024] To solve the above problems, in combination with Figures 1 to 4As shown in the figure, an embodiment of the present invention proposes a method for boundary detection and location applicable to transboundary water pollution. This method makes full use of hydrodynamic, pollutant migration and diffusion theories, and statistical optimization technologies, taking into account the mechanistic analysis of pollutant diffusion and the complexity of the actual river environment. Its efficient, accurate and dynamic characteristics make it an important technical means to solve the problems of transboundary water pollution boundary detection and tracing, providing a scientific basis and practical support for water pollution control and regional cooperation.

[0025] Specifically, first, perform S10: According to the topographic information and river cross-section data of the selected basin, set up monitoring points at the upstream and downstream boundary points of the selected basin and the entrances and exits of each tributary. At the longitudinal and transverse directions of the river at each monitoring point, obtain the target pollutant concentration, water flow rate, and water velocity respectively. Selecting monitoring points within the basin scope is the key to this step. Here, refer to Figure 3 , the monitoring points include:

[0026] Upstream and downstream boundary points, located at the upstream and downstream junctions of the basin scope, are used to monitor the input and output of pollutants to ensure that the monitoring covers the impact range of the entire basin.

[0027] Tributary inlet points, selected at the inlets of tributaries with relatively high pollution risks, such as industrial wastewater discharge points or domestic sewage centralized discharge areas, to monitor the impact of tributaries on the water quality of the main river.

[0028] Key river cross-sections, according to the velocity and flow rate changes of the river within the basin, set up monitoring points at key cross-sections, such as river bends or areas with drastic flow rate changes.

[0029] Taking a certain transboundary 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, a tributary monitoring point can be set up near the centralized sewage discharge outlet in the middle reaches of the town, and a boundary monitoring point can be set up at the transboundary provincial boundary in the lower reaches to form a monitoring network covering the entire upstream and downstream.

[0030] The key water quality parameters to be monitored include basic water quality parameters, target pollutant concentrations, and hydrological parameters, specifically as follows.

[0031] Target pollutant concentration: According to the actual pollution situation, select the concentration of specific pollutants (such as heavy metals, ammonia nitrogen, petroleum) at each monitoring point for monitoring and obtain pollutant concentration data.

[0032] Hydrological parameters: At the longitudinal and transverse directions of the river at each monitoring point, obtain the water flow rate and water velocity respectively.

[0033] Among them, longitudinal river monitoring can reflect the path and rate of pollutant diffusion along the main flow direction. Long-distance pollution diffusion is often dominated by longitudinal velocity and flow rate. Mastering longitudinal data helps to simulate the macroscopic laws of pollutant diffusion process and is an important basis for pollution source identification and location.

[0034] Lateral monitoring of river channels can reflect the spatial distribution characteristics of pollutant concentrations within a basin, especially in areas with low flow velocities, such as riverbanks or recirculation zones, where pollutant accumulation or diffusion blind spots may form. Regarding lateral flow, such as lateral recirculation or tributary inflows, it has an important impact on the diffusion shape and boundary contour of pollutants. Obtaining lateral data helps improve the accuracy of pollutant boundary fitting.

[0035] At the entrance of a tributary near an industrial park, monitor the concentrations of heavy metals (such as lead and cadmium), and simultaneously monitor parameters such as DO, COD, and flow rate at upstream and downstream points to analyze the pollution diffusion situation.

[0036] It can be understood that by obtaining the spatio-temporal distribution information of water quality at key locations within the basin, it provides basic data for subsequent model construction. Combining the actual spatio-temporal monitoring point layout and parameter acquisition methods can ensure the accurate positioning and full coverage of water quality problems within a transboundary basin, laying a data foundation for pollution boundary identification and source tracing analysis.

[0037] After obtaining data at the monitoring points, perform S20: Using the topographic data of the selected basin, river channel cross-section data, and water flow rate and water velocity obtained at each monitoring point, establish a two-dimensional hydrodynamic model of the selected basin to describe the velocity field and flow distribution of the water body in the horizontal direction. The purpose of this step is to establish a two-dimensional hydrodynamic model based on basin topography, river channel cross-section, and velocity flow rate data to simulate the flow characteristics of the water body, such as velocity field, flow rate, turbulence intensity, etc., providing a physical basis for the analysis of pollutant migration and diffusion laws and pollution boundary identification.

[0038] The two-dimensional hydrodynamic model is based on the shallow water equations and is suitable for simulating the flow characteristics in shallow water bodies such as rivers and lakes. Its mathematical form consists of the following two core equations, namely the mass conservation equation (continuity equation) and the momentum conservation equation (two-dimensional momentum equation).

[0039] Specifically, the mass conservation equation describes the mass conservation relationship of the water body, representing the change in water level height per unit time, and its formula is: where is the water depth unit: m ), that is, the water level height; is the velocity component of the water flow in the direction (unit: m / s ), is the water flow direction velocity component (unit: m / s ).

[0040] The momentum conservation equation describes the momentum change of fluid on a horizontal plane, which is affected by factors such as fluid inertia, gravity, and bottom friction. Its formula is: Among them, and are the components of the external force in the x and directions; and are the driving forces caused by the water level gradient.

[0041] By solving these two equations above, the flow characteristics of the water body at any time on the plane can be simulated.

[0042] Specifically, a digital elevation model is adopted to describe the terrain undulation of the basin, and the cross-sectional information of the river channel, including width, depth, and slope shape, is obtained by using surveying and mapping data. The dynamic parameters such as flow velocity, flow rate, and water depth in the basin are collected as initial conditions and boundary conditions. The research area is divided into two-dimensional grids, and the water depth is stored at each grid node. The shallow water equations are discretized using the finite difference method, finite volume method, or finite element method, and the partial differential equations are transformed into algebraic equations for easy computer solution. Physical quantities such as flow velocity. The grids can be regular rectangular grids or unstructured triangular grids based on the actual terrain.

[0043] Regarding the setting of boundary conditions, in some embodiments, specifically: At the upstream boundary, the inflowing water volume or flow velocity is set; At the downstream boundary, the water level or free outflow condition is set; At the boundary nodes, the no-slip condition is set to simulate the influence of the river bank on the flow velocity.

[0044] Through iterative algorithms, such as the explicit Euler method and implicit finite difference method, the water depth and flow velocity at each grid point are gradually updated to simulate the dynamic evolution process of the water body.

[0045] For example, in a certain cross-provincial basin (such as the middle and lower reaches of a certain section of the Yangtze River), the following data is used to establish a two-dimensional hydrodynamic model: The terrain data is the DEM data with a resolution of 30m in the basin obtained from remote sensing data; The river channel cross-section is obtained by hydrological measurement equipment for the river channel width, depth, and slope; The hydrological data is the time series data of flow velocity and flow rate obtained by a buoy current meter, and a time step of 5 minutes is set to simulate the flow change within 1 hour.

[0046] In summary, it can be understood that the construction and solution of the two-dimensional hydrodynamic model lay the foundation for the accurate simulation of water flow characteristics. The model fully considers the basin topography, river cross-section, and dynamic hydrological characteristics, and can provide high-resolution kinetic data support for the subsequent pollutant diffusion model, thereby improving the accuracy and scientific nature of pollution source tracing and boundary identification.

[0047] After that, perform S30: According to the velocity field and flow distribution provided by the two-dimensional hydrodynamic model, and combined with the target pollutant concentrations obtained at each monitoring point, construct a diffusion model for the target pollutant to describe the diffusion path and concentration distribution of the target pollutant in the selected basin. By combining the physicochemical properties of the target pollutant and dynamically correcting the model based on the monitoring data, the accuracy of pollutant diffusion simulation is improved, and further support is provided for pollution source tracing and pollution boundary identification.

[0048] Specifically, the convection-diffusion equation is the basic equation describing the migration and diffusion of pollutants in water, mainly considering two main forces: convection and diffusion. Among them, convection is the migration of pollutants with the movement of water, and the velocity of the water directly affects the propagation speed of pollutants. Diffusion is the gradual diffusion of pollutants from high-concentration areas to low-concentration areas due to the random movement between molecules, and the diffusion coefficient reflects the diffusion ability of pollutants.

[0049] Generally, the convection-diffusion equation can be written as where is the concentration of the target pollutant, representing a function of time and space (unit: mg / L ).

[0050] is the flow velocity of the water in the direction (unit: m / s ), is the flow velocity of the water in the direction (unit: m / s ), both of which come from the output results of the two-dimensional hydrodynamic model.

[0051] is the diffusion coefficient in the direction, is the diffusion coefficient in the direction, reflecting the diffusion degree of pollutants in water (unit: m² / s ), and usually can be divided into molecular diffusion and turbulent diffusion.

[0052] is the attenuation coefficient of the target pollutant; is the source term (such as the impact of emission sources, rainfall, etc.), representing the generation or consumption of pollutants per unit volume.

[0053] Since the migration and diffusion characteristics of each pollutant are different, its physical and chemical properties such as solubility, diffusion coefficient, and reaction rate are specifically 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 of target pollutants (such as heavy metals, organic compounds, etc.) can be adjusted according to their molecular weights and water temperatures.

[0054] For different pollutants, different empirical formulas can be used to estimate their diffusion coefficients. Common formulas are as follows:

[0055] Molecular diffusion coefficient : where is the temperature, is the viscosity of water, is a constant, usually determined according to different pollutants.

[0056] Turbulent diffusion coefficient , and the turbulent diffusion coefficient usually depends on the flow velocity and turbulence intensity of the fluid, and can be estimated by numerical simulation or empirical formula.

[0057] By continuously collecting water quality monitoring data (such as concentration data) and comparing it with the prediction results of the model, the parameters of the model (such as diffusion coefficient, source term, etc.) are dynamically adjusted. In some embodiments, the Kalman wave filtering method or the least squares method is used. Among them, the Kalman wave filtering method dynamically adjusts parameters such as diffusion coefficient and flow velocity by estimating the difference between the error and the model prediction results, making the model more conform to the actual data.

[0058] Use numerical methods such as the finite difference method, finite element method, and finite difference method to discretize the convection-diffusion equation and solve it through a computer program to simulate the migration and diffusion process of pollutants.

[0059] Still 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 , and its water flow velocity is u = 0.3 m / s . At a certain moment, the ammonia nitrogen concentration at the midpoint of the river channel is = 5 mg / L . By solving the propagation situation of this pollutant in the river channel through numerical methods, it can be expected that:

[0060] In a given time period, the distribution of pollutant concentration at different locations is obtained by numerically solving the convection-diffusion equation.

[0061] Based on actual water quality data collected regularly (e.g., data from continuous monitoring sites), a dynamic correction is performed using the least squares method to adjust the diffusion coefficient and correct the model bias.

[0062] In summary, through the establishment of the convection-diffusion equation and the dynamic correction of monitoring data, this step can accurately simulate the migration and diffusion process of pollutants in water bodies, and adjust the model parameters according to the actual monitoring data, thereby improving the prediction ability of the model. Ultimately, it can provide a scientific basis for locating pollution sources, identifying pollution boundaries, and water quality management.

[0063] Then proceed to S40: set multiple time periods based on the time series, simulate the concentration distribution of the target pollutant described by the diffusion model in each time period, calculate the concentration change gradient value of the pollutant in the selected watershed, and identify the concentration sudden change area. And S50: in the concentration sudden change area identified in each time period, screen out the concentration sudden change area with continuous spatial distribution characteristics in any adjacent time period, and integrate it 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 pollutant boundaries. Through this method, the precise pollution boundary can be initially determined, which further provides a basis for pollution source tracking and pollution control.

[0064] First, it is necessary to collect pollutant concentration data at multiple monitoring sections, calculate the rate of change of pollutant concentration at each section, and compare the concentration differences at different sections. After that, by calculating the gradient of pollutant concentration at different sections, identify the areas with the most dramatic concentration changes, which are the possible boundaries of pollutants. By gathering these abrupt change areas, the diffusion range of pollutants can be determined, and a scientific basis can be provided for subsequent pollution source tracing, monitoring and governance.

[0065] More specifically, the concentration gradient refers to the rate of change of the pollutant concentration in space. The concentration gradient can be calculated by simple difference method or differential method.

[0066] For the concentration data on a monitoring section, its concentration gradient It can be calculated as follows: 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.

[0067] In a continuous water body model, the concentration gradient can be more precisely expressed in a differential manner as: In the numerical models of some embodiments, the finite difference method or other numerical methods are often used to estimate such gradients.

[0068] To accurately identify the regions of rapid change in concentration, it is first necessary to calculate the concentration gradient at multiple cross-sections (such as the cross-sections of different river basins or multiple monitoring points).

[0069] Calculate the rate of change of concentration between adjacent cross-sections to identify the steep change regions along the river basin: where, is the rate of change of concentration between cross-sections, and are the average concentrations of adjacent cross-sections respectively, is the distance between cross-sections.

[0070] Calculate the rate of change of concentration with respect to position at each cross-section. If the rate of change is greater than a certain threshold, then this region is considered a region of steep concentration change. This threshold can be set by empirical or statistical methods. For example, it can be set as the region where the rate of change of concentration is greater than a certain multiple of the standard deviation, or the threshold can be set by the quantiles of the dataset.

[0071] By analyzing the rates of change of concentration at multiple cross-sections, all regions with large concentration gradients are identified. These regions are the places where the pollutant concentration changes the fastest and usually represent the diffusion boundaries of pollutants. Combining information such as the water flow characteristics of the river channel and the diffusion pattern of pollutants, the farthest boundary position of pollutant diffusion is determined. For example, pollutants may spread downstream with the movement of the water flow. Determine the downstream steep change region and predict the further diffusion range of pollutants. In addition, in some cases, clustering algorithms (such as the K-means algorithm, DBSCAN, etc.) can be used to perform spatial clustering analysis on the regions of steep concentration change, so as to more clearly determine the scope and boundary of the pollution source.

[0072] It can be understood that the spatial positions and corresponding concentration gradient values of each region of steep concentration change are extracted from the above-mentioned set of regions to be located, and after calculating the direction of change of the concentration gradient for each region of steep concentration change, the regions of steep concentration change are classified. Cluster analysis is performed on the extracted data of the regions of steep concentration change, that is, the directionality and change amplitude of the concentration gradients between regions are compared, and the regions of steep concentration change with consistent gradient directions and change amplitudes within the set range are screened. By calculating the spatial rate of change of pollutant concentration and combining methods such as threshold judgment and cluster analysis, the diffusion boundary of pollutants in the water body can be effectively identified.

[0073] 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 extracted concentration gradient direction can be used to calculate the directional consistency between the two areas based on the cosine similarity. 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.

[0074] Finally, perform 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 concentration 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.

[0075] It can be understood that the grid in the area of ​​abrupt concentration changes has specific geometric distribution characteristics in two-dimensional space, and its center point or boundary can be described by position coordinates. Gradient changes reflect the diffusion direction and intensity of pollutant concentration in the local area. The consistency of gradient trends between adjacent areas indicates that pollutants may belong to the same diffusion boundary, and the direction of the velocity field affects the diffusion path of pollutants. Combined with velocity field information, excessive or unreasonable extrapolation in the boundary fitting process can be avoided.

[0076] More specifically, the spatial coordinates (eg, 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.

[0077] In some embodiments, for the set of localized areas formed by the above extraction set, a spatial clustering algorithm, such as DBSCAN or a density-based clustering method, is used to perform cluster analysis on the localized areas according to the spatial position (such as longitude and latitude coordinates) and concentration gradient value of the localized areas. The spatial position ensures that the proximity between the localized areas conforms to the actual distribution characteristics, while the concentration gradient value reflects the intensity of the change in pollution concentration, which helps to distinguish pollution areas of different intensities.

[0078] It is understandable that the clustering analysis in this step is based on the gradient-consistent regions selected in the first step and further screened in combination with the flow velocity field direction. The purpose is to ensure the consistency of the flow direction of the concentration steep change regions through clustering analysis, so as to ensure that the starting point and extension direction of the boundary fitting are consistent with the water flow trend, and finally generate an outer envelope contour through curve fitting.

[0079] The clustering results are preliminarily screened by combining the flow velocity field direction information, and the regions with consistent or close flow velocity directions are retained. For example, the direction vector of the flow velocity field can be compared with the concentration gradient direction to screen out the regions where the flow velocity direction and the gradient direction are consistent. In some embodiments, the included angle between the flow velocity direction vector and the gradient direction vector can be set, and if the included angle is within a preset range or less than a threshold, it is defined as a region meeting the consistency, and the discrete regions that do not belong to its definition are removed.

[0080] For each clustering result, boundary fitting technology is used to form a preliminary contour of the pollution boundary. In some embodiments, first, the Alpha shape algorithm or the minimum convex hull technology is used to fit the clustering result into a closed polygon of the pollution boundary. Among them, the Alpha shape algorithm can adapt to the boundary characteristics of complex shapes and avoid the over-smooth boundary situation that may occur in the minimum convex hull. During the boundary fitting process, in combination with the flow velocity field direction information, by setting the boundary stretching or constraint direction, the fitting result can be made more in line with the actual law of pollution diffusion under the hydrodynamic model.

[0081] Considering further improving the accuracy and rationality of the boundary, the fitting boundary is optimized by combining the pollutant diffusion model and the flow velocity field data. In some embodiments, after the above-mentioned boundary contour is fitted, the concentration distribution within the boundary region is simulated to verify whether the concentration difference inside and outside the boundary is consistent with the actual monitoring data, and the regions with abnormal concentration distribution or redundant regions that deviate significantly from the flow velocity direction are removed. According to the dynamic pollution diffusion in multiple time periods, the boundary results of different time periods are superimposed, and the region boundary with stable spatio-temporal distribution is screened out to further accurately define the pollution boundary range.

[0082] Finally, the optimized boundary contour is used to generate a visualized pollution boundary map to display the distribution range of the pollution area and its concentration change characteristics. At the same time, a boundary data file is generated to provide technical support for the subsequent design of pollution control plans.

[0083] In summary, this method combines pollutant concentration data, flow velocity field information, and watershed grid data, and can comprehensively describe the pollution diffusion characteristics under complex hydrological conditions. From the entire process of concentration gradient analysis to boundary fitting, it fully utilizes the information of monitoring points and computational grids. Through gradient value calculation and spatial distribution consistency screening, it preferentially locates key regions with steep concentration changes, reduces the computational amount, and at the same time improves the accuracy of boundary positioning. By introducing the flow velocity field direction information to dynamically adjust the boundary contour, it not only takes into account the directionality of water body flow but also helps to more accurately reflect the evolution of the pollution range over time. It can be summarized that from the calculation of concentration gradient, identification of steep change regions to the generation of the final boundary contour, this method can be gradually refined and can more accurately reflect the diffusion law and boundary characteristics of pollutants under complex hydrological conditions.

[0084] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. The patent protection scope of the present invention is subject to the claims. Any equivalent structural changes made by using the description and drawings of the present invention should, by the same token, be included in the protection scope of the present invention.

Claims

1. A boundary detection and positioning method applicable to transboundary water pollution, characterized in that Including: According to the topographic information and river cross-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. At the longitudinal and transverse directions of the river at each monitoring point, the concentration of target pollutants, water flow rate, and water flow velocity are respectively obtained; Using the topographic data, river cross-section data of the selected basin, and the water flow rate and water flow velocity obtained at each monitoring point, a two-dimensional hydrodynamic model of the selected basin is established to describe the velocity field and flow distribution of the water body in the horizontal direction; According to the velocity field and flow distribution provided by the two-dimensional hydrodynamic model, combined with the concentration of the target pollutants obtained at each monitoring point, a diffusion model of the target pollutants is constructed to describe the diffusion path and concentration distribution of the target pollutants in the selected basin; Based on the time series, multiple time periods are set. In each time period, according to the concentration distribution of the target pollutants described by the simulation of the diffusion model, the concentration change gradient value of the pollutants in the selected basin is calculated, and the concentration abrupt change area is identified therefrom; In the concentration abrupt change areas identified in each time period, the concentration abrupt 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; Using the spatial distribution position and concentration gradient value of the concentration abrupt change areas in the set of areas to be located, the concentration abrupt change areas with adjacent space and consistent concentration gradient change trends are screened out through cluster analysis, and combined with the direction information of the velocity field, the boundary contour of the pollutants is fitted and generated; 2. The boundary detection and location method for transboundary water pollution according to claim 1, characterized in that The two-dimensional hydrodynamic model is constructed based on the shallow water equations. Among them, the shallow water equations include a continuity equation and a momentum equation. Specifically: Combined with the topographic information and river cross-section data of the selected basin, the shallow water equations are discretized, and the selected basin is divided into multiple computational grids; According to the water flow rate and water flow velocity obtained at the longitudinal and transverse directions of the river at each monitoring point, they are positionally associated with the corresponding grids according to the positional relationship, and the initialization of the two-dimensional hydrodynamic model is carried out; The two-dimensional hydrodynamic model preliminarily simulates the velocity field of the water body in the horizontal direction of the target basin, the flow rate passing through each cross-section of the river per unit time, and the water flow turbulence intensity; among them, the simulation results are all based on the physical parameters within the grid and the hydrodynamic interaction between adjacent grids; The preliminary simulation results of the two-dimensional hydrodynamic model are compared with the monitored water flow rate and water flow velocity data, and the model is corrected by the error minimization method; 3. A 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 basin, and its equation form is: Among them, is the concentration of the target pollutant, and is also expressed as a function of time and two-dimensional space ; is the water flow velocity in the lateral direction of the river channel ; is the water flow velocity in the longitudinal direction of the river channel ; Among them, and both come from the simulation results of the two-dimensional hydrodynamic model; is the diffusion coefficient in the lateral direction of the river channel ; is the diffusion coefficient in the longitudinal direction of the river channel ; is the attenuation coefficient of the target pollutant; is the source term, indicating the degradation rate of the target pollutant.

4. A boundary detection and location method for transboundary water pollution according to claim 1, characterized in that, The diffusion model of the target pollutants receives the water flow velocity data of the constructed two-dimensional hydrodynamic model, and receives the concentration of the target pollutants respectively obtained at the longitudinal and transverse directions of the river at each monitoring point, so as to simulate the diffusion path and concentration distribution of the target pollutants in the selected basin; 5. A boundary detection and positioning method for transboundary water pollution according to claim 4, characterized in that, Compare the simulation results of the diffusion model of the target pollutant with the target pollutant concentration data obtained at each of the monitoring points, so as to update the diffusion coefficients in different two-dimensional spaces of the diffusion coefficient and for updating 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 pollutants in the selected basin described by the diffusion model, the concentration change gradient value of the pollutants in the selected basin is calculated in each time period. Specifically: Extract the pollutant concentration values of each grid in the basin for each time period based on the simulated concentration distribution; Compare the pollutant concentration values of any two adjacent grids, and screen out the grids with a concentration gradient value greater than the preset gradient value according to the gradient calculation formula, and merge them into one area, which is defined as the concentration abrupt change area.

7. A boundary detection and location method for transboundary water pollution according to claim 6, characterized in that, Based on the concentration abrupt change areas identified in each time period, through spatial and temporal continuity screening, integrate the screened concentration abrupt change areas into the set of areas to be located. Specifically: Obtain the grid position distributions of the concentration abrupt change areas identified in any two adjacent time periods; Set the regional proximity condition, for the concentration abrupt change areas that meet the proximity condition, mark their continuity according to the time series, screen out the concentration abrupt change areas that continuously appear in multiple time periods, and integrate them into the set of areas to be located.

8. A boundary detection and positioning method for transboundary water pollution according to claim 1, wherein, Extract the spatial positions and corresponding concentration gradient values of each concentration abrupt change area from the set of areas to be located, calculate the concentration gradient change direction of each concentration abrupt change area, and perform cluster analysis on the extracted concentration abrupt change area data, that is, compare the directionality and change amplitude of the concentration gradients between regions, and screen out the concentration abrupt change areas with the same gradient direction and the change amplitude within the set range.

9. The boundary detection and positioning method for transboundary water pollution according to claim 8, characterized in that, For each concentration abrupt change area screened after clustering, according to the flow velocity field direction, first fit the extension path of the boundary along the water flow direction to ensure that the boundary contour is consistent with the water flow distribution trend, and then use the curve fitting method to construct the outer contour of the concentration gradient distribution, thereby generating the boundary of the target pollutant.

Images