A method, system and device for predicting pollutants in a tidal river network

Abstract

The application discloses a kind of tidal river network pollutant prediction method, system and equipment, it is related to water environment pollution detection technical field.The method comprises the following steps: based on tidal river network topology and boundary data, a hydrodynamic field mathematical model is constructed;Based on this, the convection-diffusion attenuation equation and the bifurcation mass conservation condition are established, and a pollutant coupling transport model is constructed;According to the spatial dispersion and time step analysis of pollution source parameters, the concentration space-time distribution is obtained;Key time indicators are analyzed and visualized to predict distribution. The technical problems that the simulation precision of the pollutant migration and diffusion process of the sudden water pollution accident in the complex tidal river network area of the prior art is low, the calculation speed is slow, it is difficult to quickly and accurately predict the influence time and range of pollutants on downstream sensitive targets, and cannot meet the emergency warning demand are solved, the technical effects of quickly and accurately simulating the pollutant transport of tidal river network are realized, and the pollutant front arrival time, peak concentration and over-standard duration are effectively predicted.

Description

Technical Field

[0001] This invention relates to the field of water environment pollution detection technology, specifically to a method, system, and equipment for predicting pollutants in tidal river networks. Background Technology

[0002] Tidal river networks are typically located near river estuaries, where the combined effects of runoff and tides result in complex and variable hydrological conditions. For example, the Pearl River Delta is a typical tidal river network region, characterized by a dense network of over 100 major river branches, totaling approximately 1600 km in length, with a river network density as high as 0.81 km / km². 2 The area receives water from the three rivers, with an annual runoff exceeding 300 billion cubic meters. At the same time, it is affected by tides at the outlets, resulting in a non-constant reciprocating flow. Some river sections experience repeated flow during the dry season, making the migration and transport patterns of pollutants extremely complex.

[0003] Research on water quality prediction and forecasting models has evolved from the mass balance principle to stochastic theory, grey theory, and fuzzy theory. Foreign countries started earlier in this field, with models such as BLTM, QUAL series models, WASP model systems, MIKE series models, and Delft3D models, which have achieved water quality simulation for rivers, lakes, estuaries, and reservoirs. Significant progress has also been made domestically in recent years, such as the decision support system for comprehensive water environment management based on GIS technology and tidal river network hydrodynamic water quality models, and the Hwqnow model.

[0004] However, existing technologies are mainly designed for routine water quality simulations, and their capabilities for rapid early warning and prediction of sudden water pollution incidents remain significantly insufficient. In recent years, the frequency of sudden water pollution incidents has been increasing. Statistical analysis shows that transportation, production and storage, and abnormal sewage discharge are the main risk sources for sudden urban water source pollution events, accounting for over 80% in total. Organic toxic substances, oils, and organic oxygen-consuming substances are the main pollutants. Sudden water pollution incidents are characterized by three main features: uncertainty, urgency, and the need for rapid and effective response. The randomness of the time and location of the incident, the uncertainty of the type, quantity, and discharge method of pollutants, and the various unpredictable hydrological and meteorological conditions at the time of the incident pose significant challenges to the simulation and prediction of pollution incidents. Especially in tidal river network areas, the influence of tidal backflow extends the pollutant transport time, causing the pollution band to ripple through the river channel, potentially affecting water intake safety for extended periods. Existing water quality prediction technologies have significant limitations when dealing with complex boundary conditions in tidal river networks: on the one hand, traditional models are slow to calculate, making it difficult to meet the time requirements for emergency response to sudden incidents; on the other hand, their simulation accuracy for phenomena such as tidal flow reversal and pollutant backwashing is insufficient, making it impossible to accurately predict the warning time and impact time at downstream water plant intakes. Furthermore, most models have complex and highly specialized parameter settings, making them difficult to apply quickly in emergency scenarios and unable to intuitively demonstrate the spatiotemporal evolution of pollutants, hindering decision-makers from quickly understanding the incident situation and formulating emergency plans. Summary of the Invention

[0005] This application provides a method, system, and equipment for predicting pollutants in tidal river networks. It solves the technical problems of existing technologies, such as low accuracy and slow calculation speed in simulating the migration and diffusion process of pollutants in sudden water pollution accidents in complex tidal river network areas, making it difficult to quickly and accurately predict the impact time and range of pollutants on downstream sensitive targets and failing to meet emergency early warning needs. It achieves rapid and accurate simulation of pollutant transport in tidal river networks, effectively predicts the arrival time of pollutant fronts, peak concentrations, and duration of exceedances, and intuitively displays pollution risks through visualization, providing reliable technical support for emergency decision-making and the protection of sensitive targets in sudden water pollution accidents.

[0006] The first aspect of this application provides a method for predicting pollutants in tidal river networks, the method comprising: Based on the topology of tidal river networks and hydrodynamic data of tidal boundaries, a hydrodynamic field mathematical model is constructed. Based on this model, a pollutant convection-diffusion-attenuation control equation is established, and mass conservation connection conditions are established at the river network inlets to construct a pollutant coupling transport model applicable to complex tidal river network structures. Spatial discretization and time-stepping analysis are performed using the pollutant coupling transport model based on pollution source emission parameters to obtain the spatiotemporal distribution of pollutant concentrations. Based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed using a spatial visualization heatmap for pollution risk early warning of sensitive targets associated with the river network.

[0007] A second aspect of this application provides a pollutant prediction system for tidal river networks, the system comprising: The mathematical model construction module constructs a hydrodynamic field mathematical model based on the topology of the tidal river network and hydrodynamic data of the tidal boundary. The coupled model construction module establishes a pollutant convection-diffusion-attenuation control equation based on the hydrodynamic field mathematical model, and establishes mass conservation connection conditions at the river network inlets to construct a pollutant coupled transport model applicable to complex tidal river network structures. The emission analysis module performs spatial discretization and time-stepping analysis based on the pollutant emission parameters using the coupled transport model to obtain the spatiotemporal distribution results of pollutant concentrations. The prediction and analysis module predicts and analyzes the pollutant front arrival time, maximum concentration time, and duration of exceedance based on the spatiotemporal distribution results of pollutant concentrations, and displays the prediction results in a spatial visualization heatmap for pollution risk early warning of sensitive targets associated with the river network.

[0008] A third aspect of this application provides an electronic device, comprising: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement a pollutant prediction method for a tidal river network provided in this application.

[0009] One or more technical solutions provided in this application have at least the following technical effects or advantages: Based on the topology of tidal river networks and hydrodynamic data of tidal boundaries, a hydrodynamic field mathematical model is constructed. Subsequently, based on this model, a pollutant convection-diffusion-attenuation control equation is established, and mass conservation connectivity conditions are established at the river network distributary nodes to construct a pollutant coupled transport model applicable to complex tidal river network structures. Then, based on pollution source emission parameters, spatial discretization and temporal step analysis are performed using the pollutant coupled transport model to obtain the spatiotemporal distribution of pollutant concentrations. Finally, based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed using spatial visualization heatmaps for pollution risk early warning of sensitive targets associated with the river network. This technology addresses the technical challenges of existing methods in simulating pollutant migration and diffusion processes during sudden water pollution incidents in complex tidal river networks. These challenges include low accuracy, slow computation speed, difficulty in quickly and accurately predicting the impact time and extent of pollutants on downstream sensitive targets, and inability to meet emergency early warning requirements. This new technology enables rapid and accurate simulation of pollutant transport in tidal river networks, effectively predicting the arrival time of pollutant fronts, peak concentrations, and duration of exceedances. Furthermore, it provides a visual and intuitive representation of pollution risks, offering reliable technical support for emergency decision-making and the protection of sensitive targets during sudden water pollution incidents. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic flowchart of a pollutant prediction method for a tidal river network provided in an embodiment of this application.

[0012] Figure 2 This is a schematic diagram of a pollutant prediction system for a tidal river network provided in an embodiment of this application.

[0013] Figure 3 This is a schematic diagram of the structure of an exemplary electronic device of this application.

[0014] Figure reference numerals: Mathematical model building module 11, Coupled model building module 12, Emission analysis module 13, Prediction and analysis module 14, Processor 21, Memory 22, Input device 23, Output device 24. Detailed Implementation

[0015] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0016] Example 1 like Figure 1 As shown in the embodiment of this application, a method for predicting pollutants in a tidal river network is provided, wherein the method includes: Based on the topology of the tidal river network and the hydrodynamic data of the tidal boundary, a mathematical model of the hydrodynamic field is constructed.

[0017] In one embodiment, a structured model of the tidal river network is first constructed based on historical monitoring data, river cross-sectional data, and the actual distribution of the river system. This model clarifies the spatial location, length, cross-sectional form, and interconnections of each river segment, identifies the main channel, tributaries, and distributary nodes, and distinguishes different types of nodes such as upstream inflow boundaries, downstream tidal control boundaries, and closed boundaries, thus establishing a complete river network topology model. Subsequently, combining measured or predicted tidal process lines, flow process lines, or water level-flow curves, time-varying hydrodynamic boundary conditions are set at each boundary cross-section. Continuous time-varying boundary functions are constructed using interpolation methods, enabling the model to accurately reflect the dynamic characteristics of alternating high and low tides. Then, one-dimensional hydrodynamic control equations are established for each river segment of the river network. The continuous river segments are spatially discretized, and calculations are performed progressively over time to solve for the flow, water level, and velocity distributions at each time step. To accommodate the periodic reversal of flow direction in tidal river networks, a flow direction discrimination mechanism can be introduced during the calculation process. This mechanism dynamically identifies the high or low tide stage based on changes in water level gradient or flow sign between adjacent time steps and adjusts the flow direction parameters accordingly. Finally, through the above solution process, the flow field, velocity field, and water level field covering the entire tidal river network are obtained, forming a hydrodynamic mathematical model that reflects the spatiotemporal variation characteristics of water flow under the influence of tides, providing driving conditions for subsequent pollutant transport calculations.

[0018] Furthermore, based on the topology of the tidal river network and the hydrodynamic data of the tidal boundary, a mathematical model of the hydrodynamic field is constructed, including: Based on historical river network monitoring data, tidal boundary identification is performed to establish the topology of the tidal river network and determine the connection relationships and boundary node types of each river segment. Time-varying boundary conditions are set for each boundary section of the tidal river network based on the topology. These time-varying boundary conditions include at least one of tidal level procedural lines, flow procedural lines, or water level-flow relationship curves, and continuous boundary functions are constructed through time interpolation. Based on the topology and the time-varying boundary conditions, a one-dimensional hydrodynamic control equation is established, and discrete solutions are performed for each river segment of the river network to calculate the flow field, velocity field, and water level field at each time step, thus establishing the hydrodynamic field mathematical model. Furthermore, a dynamic tidal phase identification mechanism is introduced during the hydrodynamic field calculation process. By comparing the changes in water level gradient direction or flow sign between adjacent time steps, it is determined whether the current river segment is in the rising or falling tidal phase, and the flow direction calculation parameters are adjusted based on the determination results.

[0019] Preferably, the outer edge of the river network and key control sections are first selected as candidate boundary sections. Historical water level and flow monitoring data of the river network over multiple consecutive tidal cycles are read. Each candidate section is preprocessed to remove missing data and outliers and is aligned with a unified time reference. Then, the tidal characteristics of the water level sequence of the section are calculated, including the rate of change of water level obtained by the difference between adjacent time points, the peak and trough values ​​and amplitudes within a single cycle, and the period length between adjacent peaks. Furthermore, the water level sequence of the candidate section is compared with the tidal control station downstream or the tidal sequence in the open sea using correlation coefficient and phase difference analysis. If the candidate section shows stable periodic fluctuations, significant amplitudes, and a high correlation with the tidal control sequence or has an explainable phase lag, then the section is determined to be a tidal control boundary. For sections with more complete flow monitoring, the flow sign is simultaneously analyzed to see whether positive and negative alternation occurs within the tidal cycle and the consistency of the alternation frequency with the tidal cycle. If there is periodic positive and negative reversal corresponding to water level fluctuations, then the section is considered a tidal boundary with backflow hydrodynamic characteristics.

[0020] After identifying the tidal boundaries, the river channel is coded by segment, with each segment defined as a directed or reversible edge connecting two nodes. Distributaries, confluences, branching points, and boundary sections are uniformly abstracted as nodes, and attribute type identifiers are established for each node, including at least upstream inflow boundary nodes, downstream tidal boundary nodes, ordinary internal connection nodes, and distributary nodes. Subsequently, an adjacency table is established based on spatial connectivity, clarifying the set of incoming and outgoing edges connected to each node. Geometric and hydraulic information for each river segment is recorded, such as length, cross-sectional parameters, roughness, riverbed elevation, cross-sectional area, and water level relationships. The topology is then validated for consistency, ensuring the absence of broken segments, duplicate connections, or incorrect direction definitions, thus forming a river network topology model suitable for numerical solutions. After the topology is defined, time-varying boundary conditions are set for each boundary section. For boundary sections identified as tidal-controlled, their tidal process line is selected as the boundary input. If the tidal data is a discrete time sequence, it is interpolated into a continuous function η(t) according to the model time step Δt. Interpolation can be piecewise linear, spline, or other monotonic interpolation methods, ensuring that the interpolated tidal level does not produce non-physical oscillations near the peak and trough. For upstream boundary sections identified as inflow-controlled, the flow process line Q(t) is selected as the boundary input, and the discrete observation sequence is also interpolated into a continuous function according to Δt. When some boundary sections only have a water level-flow relationship, a relationship curve of Q=f(H) is established with water level as the independent variable, and the required Q for the boundary is calculated in real time according to the current solution variable during the calculation process. If the same boundary has both tidal and flow information, it is configured according to the priority of the boundary type. For example, the downstream is mainly controlled by tidal level, and the upstream is mainly controlled by flow, and consistency constraints are used to ensure that the boundary conditions do not conflict when necessary. After the boundary conditions are constructed, the boundary functions are then bound to the topology. That is, the η(t), Q(t), or HQ relationship is attached to the corresponding boundary nodes to form a callable input of "node-continuous boundary function-time" so that the boundary values ​​can be directly read when solving at each time step.

[0021] Subsequently, a one-dimensional unsteady hydrodynamic governing equation system is established for each river segment. Variables typically include water level H(x,t), flow rate Q(x,t), and velocity U(x,t), where velocity can be calculated using U=Q / A(H). Each river segment is then divided into several grid nodes according to a spatial step Δx, forming a discrete node sequence along the river. For each discrete node, cross-sectional hydraulic relationships are configured, such as cross-sectional area A(H), hydraulic radius R(H), roughness coefficient n, or drag coefficient, so that parameters A and R are updated by H during iterative solutions. A step-by-step approach is adopted in the time dimension, calculating backwards from the initial time t0 with Δt. Initial conditions can be assigned from the monitored initial water level and flow field, or obtained through steady-state pre-running. At the beginning of each time step, the current boundary tidal level or flow rate value is read from the continuous boundary function and written into the discrete equation system as the constraint condition for the boundary node. Next, global equations are assembled for the nodes within the river network according to their topological connections. The discrete equations of each river segment are coupled with the continuity conditions of the nodes, such as consistent water levels and flow conservation, to form solvable algebraic equations. Then, appropriate numerical solution strategies, such as explicit / implicit progression and iterative solutions, are used to calculate the unknowns at that time step. After the solution is completed, the water level field H and flow field Q of the entire river network at that time step are obtained, and the velocity field U is calculated from the cross-sectional relationships. To ensure the reliability of the results, basic physical verification is performed after each time step is solved. For example, it checks whether the water level changes are continuous, whether the flow is conserved at the distributary nodes, and whether there are non-physical negative cross-sectional areas or excessive water levels. If anomalies are found, they are corrected by adjusting the time step size, iterative convergence threshold, or boundary smoothing, thereby steadily advancing to the end of the full-time calculation. Finally, a mathematical model of the hydrodynamic field covering the entire time period and the entire river network is output, namely, a spatiotemporal dataset of H(x,t), Q(x,t), and U(x,t) that varies with time.

[0022] Furthermore, to adapt to the characteristics of alternating high and low tides and periodic reversals of flow direction in tidal river networks, a dynamic identification mechanism for tidal phases is introduced during the hydrodynamic field calculation process and used to adjust the flow direction calculation parameters. Specifically, before solving each time step, the discriminant for each river segment is calculated for adjacent time steps. If water level gradient discrimination is used, the water level difference ΔH between discrete nodes upstream and downstream of the river segment is taken and its sign or direction change between t and t-Δt is observed. If the direction of ΔH indicates that the water surface slope changes from pointing downstream to pointing upstream, the river segment is considered to have entered a tidal phase opposite to the previous time step. If flow sign discrimination is used, the Q value of the river segment in adjacent time steps is directly read. When Q changes from positive to negative or from negative to positive, the flow direction is determined to have reversed, and the river segment is marked as either high tide-dominated or low tide-dominated. After the stage judgment is completed, the judgment result is applied to update the calculation parameters related to the flow direction: on the one hand, it ensures consistency with the current flow direction in terms of convection direction, friction term direction, or numerical format. For example, the positive direction defined above as upstream-downstream is automatically switched with the flow direction. On the other hand, during the assembly of river network connection nodes, the identity of the river segment as an incoming or outgoing edge is updated synchronously, so that the node conservation equations still maintain physical consistency when the flow direction reverses. At the same time, reversal protection rules can be set. For example, a small threshold band is used to avoid frequent jitter at the moment of reversal when the flow is close to zero, or a short-term smooth transition is used for the flow direction switch to improve the calculation stability. Through the closed-loop mechanism of "judgment-marking-synchronous update-stability control", the hydrodynamic field model can continuously track the changes in the high and low tide stages throughout the entire calculation period, accurately output the flow field, velocity field, and water level field that evolve dynamically with the tide, and provide driving conditions consistent with the actual flow direction for subsequent pollutant transport calculations.

[0023] Based on the aforementioned hydrodynamic field mathematical model, a pollutant convection-diffusion-attenuation control equation is established, and a mass conservation connection condition is established at the river network inlet node to construct a pollutant coupling transport model applicable to complex tidal river network structures.

[0024] In one embodiment, after constructing the mathematical model of the hydrodynamic field of the tidal river network, the output flow field, velocity field, and water level field at each time step are used as the driving basis for pollutant transport calculation. Based on this, a pollutant convection-diffusion-attenuation control equation is established for each river segment. The convection term characterizes the migration process of pollutants with the direction and velocity of the water flow, the diffusion term describes the longitudinal dispersion effect of pollutants in the water body, and the attenuation term reflects the attenuation process of pollutants under natural conditions, such as degradation, transformation, or adsorption and sedimentation. The diffusion coefficient can be determined according to the river segment's flow velocity, cross-sectional morphology, and hydraulic conditions, while the attenuation coefficient is set according to the pollutant type. In complex tidal river networks, each river segment is interconnected through multiple distributary nodes, and the flow direction may reverse with the tides. To ensure the continuity and rationality of pollutant transport between different river segments, a mass conservation connection condition is established at each distributary node, meaning the total mass of pollutants flowing into the node is equal to the total mass of pollutants flowing out of the node. Pollutant concentrations at nodes are weighted and allocated according to the real-time flow ratios of each connecting river segment. When the flow direction of a river segment changes, the concentration allocation direction is adjusted synchronously to ensure that the model can accurately reflect backpropagation and superposition phenomena. By establishing convection-diffusion-attenuation equations within a single river segment and applying mass conservation constraints at the river network distributary nodes, the calculation results of each river segment are coupled under a unified framework to form a pollutant coupled transport model suitable for complex tidal river network structures. This enables a holistic description of the dynamic concentration field of pollutants, thereby improving the accuracy and stability of pollutant transport prediction in tidal river networks.

[0025] Furthermore, constructing a pollutant coupled transport model applicable to complex tidal river network structures includes: Based on the hydrodynamic parameters obtained from the aforementioned hydrodynamic field mathematical model, including the flow field, velocity field, and water level field, these hydrodynamic parameters are used as driving conditions for pollutant transport calculations. Based on these driving conditions, a pollutant convection-diffusion-attenuation control equation is established, including convection, longitudinal diffusion, and attenuation terms. Corresponding diffusion and attenuation coefficients are set according to the pollutant type. Mass conservation connection conditions are established at the river network distributary nodes, and the pollutant concentration distribution ratio is determined by flow-weighted calculation of pollutant concentrations in each tributary to ensure the continuity of pollutant transport in the tidal river network. This constructs the pollutant coupled transport model to describe the dynamic concentration field of pollutants in the tidal river network.

[0026] Preferably, after obtaining the hydrodynamic parameters calculated from the hydrodynamic field mathematical model, the flow field Q, velocity field U, and water level field H corresponding to each time step and each river segment are first organized into a directly callable driving dataset, and bound one-to-one with the river network topology. In this way, for each river segment and each discrete node in the river network, the corresponding Q(x,t), U(x,t), and H(x,t) can be read at any time t. At the same time, parameters such as cross-sectional area A(x,t), water depth, and wetted perimeter are calculated based on the water level H and cross-sectional relationship, providing complete hydrodynamic input for subsequent transport calculations. Subsequently, on each river segment, the cross-sectional average concentration C(x,t) is used as the state variable, and the spatial coordinates of the river segment are discretized into several calculation units, and a unified time step Δt is selected for progressive advancement. At the beginning of each time step, the hydrodynamic parameters of each calculation unit at that time step are read first, and the actual mainstream direction of the river segment at that moment is determined based on the sign of the velocity U or flow Q, thereby determining the propagation direction of the convection term and the position of the upstream boundary unit. Next, a convection-diffusion-attenuation control equation for pollutants is constructed. This equation includes a convection term, a longitudinal diffusion term, and an attenuation term, as well as diffusion and attenuation coefficients set according to the pollutant type. The convection term describes the translational transport of pollutants with the overall movement of the water body, and its computational cost is determined by U, A, and the concentration difference between adjacent units. The longitudinal diffusion term describes the smoothing of the concentration gradient caused by longitudinal dispersion in the river channel, and its diffusion coefficient E is determined according to the hydrodynamic and cross-sectional characteristics of the river section, usually varying with flow velocity and water depth. The attenuation term describes the natural degradation, volatilization, or biochemical consumption of pollutants in the water body, and its attenuation coefficient k is set according to the pollutant type, and the concentration is updated exponentially or linearly over time. In actual calculations, the concentration increment caused by three parts is calculated for each computational unit within the same time step: first, the pollutant flux from the upstream unit is carried into the downstream unit according to the mainstream direction to complete the convection update; then, the diffusion exchange is calculated according to the concentration gradient of adjacent units to complete the diffusion update; finally, the updated concentration is deducted according to the attenuation coefficient to obtain the transient concentration results of each unit within the river segment at that time step. When the hydrodynamic calculation shows that the flow direction has reversed, the upstream-downstream relationship of the convection term automatically reverses in the next time step, allowing pollutants to propagate in the opposite direction and superimpose with the original residual concentration during the return flow. At the same time, in order to ensure that the pollutant transport at the distributary nodes of multiple river segments is continuous and satisfies mass conservation, node coupling calculation is performed for each distributary node at each time step. In this process, the flow direction of the hydrodynamic field at that moment is used to determine which connected river segments are inflows and which are outflows. Then, the pollutant mass flux brought into the node by all inflow river segments is summed, that is, the concentration C of each inflow river segment near the node is taken. in,i With the corresponding inflow rate Q i This forms the inflow pollutant mass flux Σ(Q) i ·Cin,i ), and use it as the total pollutant input that can be allocated to that node.

[0027] Then, the outflow segments are proportionally allocated according to their outflow volume, and the concentration C to be assigned to each outflow segment at the node is calculated. out,j , such that Σ(Q j ·C out,j )=Σ(Q i ·C in,i To establish this, a common practice is to first determine the nodal mixing concentration C. m =Σ(Q i ·C in,i ) / Σ(Q i Then, set the concentration at each outflow node equal to C. m Alternatively, when it is necessary to consider the differences in flow distribution, a weighted allocation can be performed based on a preset allocation coefficient or cross-sectional differences, provided that the conservation principle is met. When a tributary changes from outflow to inflow or from inflow to outflow at a given time step, the node calculation synchronously updates its role and recalculates Σ(Q). i ·C in,i The concentration distribution ratio is determined to ensure that the conservation constraint of inflow mass equaling outflow mass is strictly satisfied even under tidal reversal conditions, preventing non-physical concentration jumps or mass loss. After completing the concentration coupling at the nodes, the outflow concentration obtained at the node end is used as the boundary concentration condition for the next unit of the corresponding river segment, assembled together with the convection-diffusion-attenuation discrete equations within the river segment, and advanced to the next time step. This cycle of "reading hydrodynamics - determining flow direction - calculating convection-diffusion attenuation within the river segment - performing mass conservation distribution at the distributaries - updating boundary and unit concentrations" is repeated throughout the entire river network. Finally, a pollutant coupled transport model suitable for complex tidal river network structures is constructed and run, outputting the dynamic concentration field of pollutants evolving over time in the river network, thereby achieving accurate characterization and stable simulation of the spatiotemporal evolution of pollutants in complex tidal river networks.

[0028] Furthermore, the convection term describes the parameters of pollutant migration with the water flow; the longitudinal diffusion term describes the parameters of pollutant spatial dispersion, wherein the diffusion coefficient is determined based on the river flow velocity and cross-sectional characteristics; and the attenuation term describes the parameters of the natural attenuation process of pollutants, wherein the attenuation coefficient is set according to the pollutant type.

[0029] Optionally, in the calculation of the convection term, the velocity U(x,t) and flow rate Q(x,t) of each calculation unit in the corresponding river segment are first read at each time step, and the current main propagation direction is determined based on the flow rate sign or velocity direction. Then, using the cross-sectional average concentration C(x,t) as a variable, the pollutant mass flux between adjacent units is calculated. Specifically, the concentration of the upstream unit is multiplied by the instantaneous flow rate of the cross-section to obtain the pollutant mass transported through the cross-section per unit time. This mass flux is then converted into the concentration change within that time step according to the time step Δt. If the flow direction is positive, the upstream unit concentration is used as input; if the flow direction reverses, the upstream unit concentration in the opposite direction is automatically used in the calculation. Through this flux update method based on real-time flow direction determination, a quantitative description of pollutant migration with the water flow is achieved, enabling the convection term to accurately reflect the bidirectional transport characteristics under alternating high and low tide conditions. In the calculation of the longitudinal diffusion term, the diffusion coefficient E is determined based on hydrodynamic parameters such as the current river segment's velocity, water depth, cross-sectional area, and hydraulic radius. The diffusion coefficient can be determined based on empirical relationships or as a function of flow velocity. For example, the diffusion coefficient can be appropriately increased at higher flow velocities to reflect the enhanced turbulence effect, and decreased at lower flow velocities to reflect the weakened dispersion characteristics. Simultaneously, E is corrected based on geometric features such as cross-sectional width and water depth to reflect river segment differences. Next, the concentration gradient between adjacent cells is calculated in the spatially discrete grid. This is achieved by dividing the concentration difference between the current cell and the cells before and after it by the spatial step size Δx to obtain the rate of concentration change. This gradient is then multiplied by the diffusion coefficient to obtain the diffusion flux per unit time. By integrating the diffusion flux over the time step, the concentration increase or decrease caused by dispersion is calculated and superimposed with the convection update results, thus characterizing the smooth diffusion and mixing process of pollutants in space. In the attenuation term, a corresponding attenuation coefficient k is pre-set according to the pollutant type. Different pollutants can be classified and set according to their physicochemical properties, biodegradability, or volatility characteristics. For example, a larger attenuation coefficient is set for easily degradable organic matter, and a smaller attenuation coefficient is set for stable pollutants. Within each time step, based on the concentration value of the current computational unit, the decay amount within that time step is calculated according to the decay law, and updated using an exponential decay or linear approximation form. That is, after convection and diffusion updates are completed, the concentration is updated according to... Alternatively, it can be corrected using an equivalent discrete form. This treatment ensures that pollutants exhibit natural decay effects simultaneously during transport. Through time-step calculation and superposition updates of the convection, longitudinal diffusion, and decay terms, the pollutant concentration within each computational unit is simultaneously affected by the combined effects of water flow migration, spatial dispersion, and natural degradation, thus forming a dynamic concentration change process consistent with the hydrodynamic characteristics of tidal river networks.

[0030] Furthermore, establishing mass-conserving connectivity conditions at river network distributary nodes also includes: The mass conservation connection condition satisfies that the total mass of pollutants flowing into the inlet node is equal to the total mass of pollutants flowing out of the inlet node. When the river flow direction reverses, the concentration distribution direction of the river network inlet node is adjusted synchronously.

[0031] Optionally, during the operation of the pollutant coupled transport model, mass-conserving connectivity calculations are performed on all distributary nodes in the river network at each time step. Specifically, at the current time step, the instantaneous flow rate Q and node-end concentration C of each river segment connected to the distributary node are read, and each river segment is determined to be either inflow or outflow at that moment based on the flow rate sign. When Q > 0 (defined according to a pre-defined direction) and points to the node, it is identified as an inflow segment; when Q < 0 or the flow direction is outflow from the node, it is identified as an outflow segment. After completing the inflow and outflow classification, the pollutant mass flux entering the node in that time step is calculated for each inflow segment, i.e., M. i =Q i ×C i , where Q i C represents the absolute value of the instantaneous flow rate pointing to the node in that river segment. i Let M be the concentration of pollutants near the node in this river segment. Summing all inflow mass fluxes yields the total pollutant input mass M at the node at the current time step. in Subsequently, to satisfy the mass conservation condition, the total mass of pollutants flowing out of this node must equal the total mass of pollutants flowing in, i.e., M. out =M in Therefore, concentration allocation is performed for all outflow segments according to their instantaneous outflow proportions. Specifically, the total flow rate Q of all outflow segments is first calculated. out Then calculate the node mixing concentration C. m =M in / Q out and C m This serves as the initial concentration allocated to each outflow segment at this node. If differences in hydraulic conditions across different segments are considered, or if a preset diversion coefficient exists, then Σ(Q) is satisfied. j ×C j )=M in Under the premise of [unclear], the allocation is adjusted according to the weighting coefficient. After the allocation is completed, the concentration C at the node end of each outflow section is [unclear]. j The cells corresponding to the river segment are written into the system for convection-diffusion calculations at the current or next time step. When the flow direction of a river segment reverses in an adjacent time step—that is, when a river segment changes from outflow to inflow or from inflow to outflow—the system re-determines the inflow or outflow status based on the updated flow sign before proceeding to the next time step calculation. Simultaneously, it adjusts the role of the river segment in the nodal conservation equations and recalculates M. in Q out and C mThis avoids using the distribution direction of the previous time step, thus ensuring that during the transition between high and low tides, the mass of pollutants at the nodes always satisfies the conservation relationship that the total mass of inflow equals the total mass of outflow, without generating false accumulation or non-physical loss, and realizing the node concentration distribution process that couples dynamic flow direction changes with mass conservation under tidal river network conditions.

[0032] Based on the emission parameters of the pollution source, spatial discretization and time step analysis are performed using the pollutant coupling transport model to obtain the spatiotemporal distribution results of pollutant concentration.

[0033] In one embodiment, after constructing the pollutant coupled transport model, pollutant source emission parameters are introduced into the model as source term conditions. These emission parameters include information such as the location of the pollution source, emission intensity, emission duration, and emission mode. These parameters are converted into corresponding mathematical expressions based on different emission forms and superimposed on the governing equations of the corresponding river segments. Subsequently, each river segment of the river network is spatially discretized, dividing the continuous river segment into several computational units. This allows pollutant concentrations to be expressed spatially as discrete nodes. A progressive time-stepping method is used in the time dimension, performing iterative calculations for each time step. Within each time step, hydrodynamic parameters at the corresponding moment are read, including flow rate, velocity, and water level information. The propagation direction of the convection term is determined based on the real-time flow direction, and the migration, dispersion, and attenuation of pollutants in each computational unit are calculated using diffusion and attenuation coefficients. At the river network distributary nodes, the concentration distribution relationship is updated based on the real-time flow ratio. When a flow direction reversal occurs, reverse propagation and concentration superposition calculations are performed simultaneously. By continuously iterating the time stepping process, the pollutant concentration values ​​of each calculation unit are dynamically updated, and finally the spatiotemporal distribution results of pollutant concentration covering the entire tidal river network are obtained, thus forming a dynamic concentration field of pollutants at different times and in different river sections, providing basic data for subsequent risk analysis and early warning.

[0034] Furthermore, based on the pollution source emission parameters, spatial discretization and time-stepping analysis are performed using the aforementioned pollutant coupled transport model to obtain the spatiotemporal distribution results of pollutant concentrations, including: Based on the pollution source emission location, emission intensity, and emission mode in the pollution source emission parameters, the pollution source term is introduced into the pollutant coupled transport model. The river network segments are spatially discretized, and continuous river segments are divided into several computational units. A step-by-step time-incremental calculation is performed. At each time step, the hydrodynamic parameters corresponding to each computational unit are read. The flow direction and main propagation direction of the current river segment are analyzed based on the hydrodynamic parameters. The direction of the convection term is updated based on the analyzed flow direction. The migration amount of pollutants within each computational unit is calculated, and the concentration changes caused by the diffusion and attenuation terms are calculated. At the river network distributary nodes, the concentration distribution is updated according to the real-time flow ratio. When the flow direction of a river segment reverses, the pollutant reverses propagation and concentration superposition is performed. The dynamic spatiotemporal distribution of pollutant concentration in the tidal river network is obtained by updating the processing based on the concentration changes at each time step.

[0035] Optionally, after obtaining the coupled hydrodynamic field and pollutant transport model, the pollution source emission location, emission intensity, and emission mode are first read. The pollution source emission location is the river segment and mileage to which the pollution source belongs; the emission intensity is typically the mass flow rate; and the emission mode is either continuous or instantaneous. Subsequently, the location of the pollution source is matched with the river network topology and spatial grid to determine its corresponding computational unit number. If the pollution source is located between two discrete units, it is allocated to adjacent units according to distance ratio. For continuous emission sources, the emission intensity is converted into a mass increment ΔM per unit time step according to the time step Δt within its emission period, and then converted into a concentration increment and superimposed on the corresponding computational unit. For instantaneous emission sources, the pollutant mass is added all at a specified time step and used as the initial input condition for subsequent transport calculations. Next, each river segment of the river network is spatially discretized, and each continuous river segment is divided into several computational units according to a preset spatial step Δx. Each unit stores the concentration value C of the current time step and the corresponding hydrodynamic parameter index. A unified time step Δt is set in the time dimension, progressively advancing from the start time to the prediction end time, forming a two-dimensional computational framework of spatial grid-time step. At the beginning of each time step, the hydrodynamic parameters corresponding to the current time are read, including the flow rate Q, velocity U, and water level H of the river segment where each computational unit is located. The flow direction and main propagation direction of the current river segment are determined based on the flow rate sign or water level gradient. When Q is positive, propagation is in the preset forward direction; when Q is negative, it is determined to be reverse propagation, thus determining the upstream and downstream unit relationships of the convection term within that time step. After clarifying the flow direction, pollutant migration calculations are performed on each computational unit. In this process, the mass flux of pollutants transported from upstream to downstream (or in the reverse direction) within the time step Δt is calculated based on the convection term, and the unit concentration is updated accordingly. The longitudinal diffusion flux is calculated based on the concentration gradient of adjacent units. The concentration change caused by diffusion is obtained based on the diffusion coefficient E and the spatial step Δx, and superimposed on the convection update result. Then, the attenuation amount within that time step is calculated based on the pollutant attenuation coefficient k, and attenuation correction is performed on the updated concentration. After the combined effects of the above three parts are completed, the transient concentration results of each calculation unit within the river section are obtained.

[0036] After completing the internal update of the river segment, mass conservation allocation calculations are performed on all distributary nodes. Based on the real-time flow ratio of each connected river segment at the current time step, the inflow and outflow river segments are determined. The pollutant mass flux of all inflow river segments is summed to obtain the total input mass of the node, and the node mixing concentration or weighted concentration is calculated according to the outflow flow ratio, and allocated to the node end of each outflow river segment as its boundary concentration. When the flow direction of a river segment reverses at the current time step, its inflow or outflow status in the node is adjusted accordingly, and the mass flux and allocation ratio are recalculated according to the new flow direction. At the same time, pollutants are allowed to propagate in the reverse direction in the internal calculation of the river segment and superimposed on the original concentration field to reflect the reverse transport and accumulation effect under tidal backflow conditions. The above process of "reading hydrodynamics - determining flow direction - calculating convective diffusion attenuation - performing node conservation allocation - updating concentration field" is repeated at each time step, and the concentration results of the entire river network at each step are stored. As the time step progresses, the dynamic concentration evolution of pollutants in the entire tidal river network can be obtained, forming a complete spatiotemporal distribution dataset, including spatial concentration distribution maps at any time section and any computational unit. This allows us to obtain the spatiotemporal distribution results of the dynamic concentration of pollutants in the tidal river network, improving the accuracy and reliability of pollutant transport prediction.

[0037] Furthermore, the spatiotemporal distribution of pollutant dynamic concentrations in the tidal river network is obtained by updating the processing based on concentration changes at each time step, and also includes: In the time-step analysis process, a pollutant propagation link identification mechanism is introduced to identify and record the hydrodynamic parameters, propagation paths, and concentration changes of pollutants in each calculation unit, constructing a pollutant concentration change update space. Based on the concentration change update space, at the end of each time step, the total mass of pollutants is checked for mass consistency to determine whether the concentration result of the current time step meets the mass conservation condition. When a mass deviation is detected to exceed a preset threshold, the concentration of the corresponding calculation unit is corrected for error. When the river flow direction reverses or pollutants are backflowed and superimposed, a weight correction factor is introduced for the superimposed concentration to avoid concentration deviation caused by repeated calculations. Based on the concentration change update space, the global concentration distribution within the same time step is corrected for consistency, and the time step deviation is located and analyzed. The pollutant concentration distribution is corrected according to the deviation location results to determine the spatiotemporal distribution result of the dynamic concentration change of pollutants.

[0038] Optionally, in order to make the propagation process of pollutants in the complex tidal river network traceable, accountable, and correctable throughout the time step calculation, in addition to the conventional convection-diffusion-attenuation update and the conservation allocation of the distributary nodes, a pollutant propagation link identification mechanism and a concentration change update space are also introduced at each time step. Specifically, firstly, a time-updated record structure is established for each computational unit in the river network. This structure includes at least a snapshot of the hydrodynamic parameters used by the unit at the current time step, the main current direction identifier of the unit at this time step, the numbers of adjacent units with which it exchanged mass, and the component decomposition record of the concentration change of the unit. For each mass flux, a source-destination-flux magnitude link identifier is established. This link identifier can be recorded in the format (source unit ID → target unit ID, flux M, direction dir, time step t), allowing for complete tracking of which river segments the pollutants travel along, which distributaries they pass through, and at which time steps they undergo backpropagation and superposition. For example, in the 12th time step, the link identifier could be (R3-05 → R3-06, M = 2.35 kg, dir = forward, t = 12). Thus, the parameters, links, and component increments of all units are uniformly summarized within the same time step, forming the pollutant concentration change update space for that time step.

[0039] After constructing the pollutant concentration change update space, a quality consistency check is performed at the end of each time step; that is, the updated concentration C of each computational unit is taken. new Multiplying this by the water volume corresponding to that time step yields the pollutant mass m within the unit. i The total mass M within the domain is obtained by summing over all elements. domain (t). Simultaneously, the theoretical mass balance is calculated based on the external inputs and outputs recorded in the update space at this time step. The external inputs include the mass ΔM injected by the pollution source at this time step. src The upstream boundary carries in the mass ΔM at this time step with the inflow. in，以及 Other terms are defined as external inputs; external outputs include the mass ΔM carried away by the downstream boundary with the outflow at this time step. out Other items defined as outflow losses; attenuation losses are summarized as ΔM through attenuation component records. decay Subsequently, a mass balance relationship is constructed, which theoretically should satisfy M. domain (t)=M domain (t-Δt)+ΔM src +ΔM in -ΔM out -ΔM decayThe actual mass obtained from the concentration field integration on the left is compared with the theoretical mass derived from the source-sink ledger on the right to calculate the mass deviation ε. This deviation is then compared with a preset threshold to determine whether the result at this time step meets the mass conservation requirement. When the mass deviation exceeds the preset threshold, the error correction process begins. At this point, global scaling is not performed directly; instead, the source of the error is located based on the propagation link identifier and component records. In this process, the net mass change contribution Δm of each unit at this time step is first calculated from the update space. i The contribution of this net mass change is obtained by summing up the convection, diffusion, source term, node allocation, and attenuation components, and checking for any obvious anomalies, such as inconsistencies between the convection input of some cells and the convection output of adjacent cells, mismatch between the inflow quality and outflow quality of the tributary node, and the failure of the flux direction of the flow reversal cell to switch synchronously, resulting in duplicate counting.

[0040] Next, abnormal units are assigned deviation responsibility tags, forming a set of units requiring correction. When performing error correction on units within the set, a local conservation backfill method is used. If the deviation manifests as a loss of mass, the missing mass is backfilled according to the weight of the main propagation path of each unit in this time step, for example, distributed among relevant units according to the inflow volume. If the deviation manifests as an artificial increase in mass, the same principle is applied to the abnormal link to ensure that the corrected local link satisfies the consistency of output = input ± source-sink. For deviations caused by distributary nodes, the mixing concentration and distribution concentration of this time step are recalculated at the node level to ensure that the outflow mass of the node is strictly equal to the inflow mass of the node. The corrected node-end concentration is then written back to the boundary units of the connected river segments, triggering a linkage update of the concentration of related adjacent units to avoid chain inconsistencies caused by modifying only one unit.

[0041] In scenarios where the river flow direction reverses or pollutants are superimposed due to backflow, a weighting correction factor for the superimposed concentration is introduced to avoid the same pollutant being repeatedly counted in the numerical format or node allocation during forward propagation, reverse backflow, and subsequent forward propagation. Specifically, when a cell in the update space is identified as acting as both the receiver of one link and the backflow receiver of another link within the same time step, or when a link loop is superimposed after backflow in adjacent time steps, the superposition amount ΔC is calculated separately for the backflow superposition portion. back The result is multiplied by a weighting factor ω and then incorporated into the final concentration update. ω can be set based on the backflow duration, the backflow flow ratio, and the numerical stability index of the unit at this time step. At the same time, the superimposed update is recorded as a backflow superimposed item in the link ledger so that it can be correctly included and tracked during subsequent quality verification. This preserves the physical meaning of backflow accumulation and suppresses the non-physical concentration overestimation caused by overlapping calculation links.

[0042] After completing local error correction and backflow weight correction, the global concentration distribution within the same time step is consistently corrected based on the concentration change update space. This correction aims to ensure global quality closure, local link conservation, and concentration non-negativity and smoothness. First, the global quality is calculated and the deviation is reduced to within a threshold. Then, a spot check or full check is performed to verify the input-output matching of key links in the ledger. Subsequently, constraints are applied to potentially local negative concentrations or unreasonable spikes. For example, concentrations less than zero are truncated, and the resulting quality difference is compensated according to the diffusion weights of adjacent units to maintain conservation. Simultaneously, the time step deviation is analyzed for location. That is, the final residual deviation of this time step is decomposed by link type and refined to specific river segments or nodes, forming a deviation source-location-magnitude location result. This is used to determine whether the next correction should focus on a specific distributary node, a type of flow reversal river segment, or certain high-gradient diffusion areas.

[0043] Finally, for errors identified as node allocation errors, the allocation is redistributed and rewritten at the node level; for errors identified as repeated counting due to flow reversal, the backflow weight factor is adjusted or the link direction identifier is corrected and the link flux is recalculated; for errors identified as diffusion numerical errors, the dispersion form of diffusion flux is adjusted or flux is limited for high-gradient units and the corrected concentration is rewritten; for errors identified as source term mapping errors, the pollution source injection mass is reassigned according to the grid distance ratio. After a closed-loop process of "record-verify-locate-correct-re-verify," the final spatiotemporal distribution result of pollutant dynamic concentration changes is obtained, which satisfies mass conservation, maintains consistent propagation links, and reflects the superposition characteristics of tidal backflow. The updated space and correction record of this time step are archived together for continued tracking and rolling updates in subsequent time steps, thereby reducing numerical errors caused by flow reversal and backflow superposition, improving the stability and accuracy of concentration prediction results, and thus enhancing the reliability of pollutant spatiotemporal distribution analysis and risk warning.

[0044] Based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed in a spatially visualized heat map for pollution risk warning of sensitive targets associated with the river network.

[0045] In one embodiment, after obtaining the dynamic spatiotemporal distribution of pollutant concentrations in the tidal river network, the concentration change curves of each sensitive section are first extracted over continuous time steps. The time point when the pollutant concentration first reaches or exceeds a preset threshold is identified, and this time is determined as the arrival time of the pollutant front, used to determine when the pollution impact begins. Subsequently, extreme value analysis is performed on the concentration time series to determine the time when the concentration reaches its peak and the corresponding maximum concentration value, reflecting the most severe stage of the pollution impact. Simultaneously, the concentration curves are compared with water quality standard limits, and the time intervals during which the concentration is continuously higher than the standard limits are statistically analyzed to calculate the duration of exceedance, used to measure the persistence of pollution risk. Based on this, key indicators such as the arrival time of the front, the time of maximum concentration, and the duration of exceedance are mapped onto the spatial structure of the river network. Combined with the spatial location of each river segment and node, a dynamic and visualized heat map or cloud map is generated to intuitively display the pollutant diffusion path, propagation timeline, and concentration evolution trend. By continuously updating the prediction results under changing tidal conditions, the impact of pollution on downstream water intakes, ecologically sensitive areas, and other related targets can be assessed in real time, thereby providing decision support for pollution risk early warning and emergency response.

[0046] Furthermore, based on the spatiotemporal distribution of the pollutant concentration, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed as a spatially visualized heatmap for pollution risk early warning of sensitive targets associated with the river network, including: Based on the spatiotemporal distribution of pollutant concentrations, time series analysis is performed on each sensitive section to identify the time point when pollutant concentrations first exceed the threshold and determine the arrival time of the pollutant front. Extreme value analysis is performed on the concentration time series to determine the time of occurrence of the maximum concentration and the corresponding concentration value, and the duration interval of concentration exceeding the preset standard value is calculated to obtain the duration of exceedance. The arrival time of the front, the time of maximum concentration, and the duration of exceedance are mapped onto the river network spatial structure to generate a dynamic thermal cloud map of pollutant concentration distribution, determine the timeline of pollutant diffusion and propagation and the trajectory of concentration evolution, and based on the dynamic changes of tidal conditions in the tidal river network, rolling predictions are updated for subsequent time periods to generate pollution risk warning results for sensitive targets.

[0047] Preferably, after obtaining the spatiotemporal distribution results of pollutant concentrations, the locations of sensitive targets requiring key protection or early warning are first identified in the river network space. These include, for example, sections where water plant intakes are located, control sections of backup water sources, ecologically sensitive river sections, and boundary sections of functional zones with water quality requirements. These sensitive sections are then mapped one-to-one with specific nodes or computational units in the river network topology. Subsequently, the concentration time series C(t) for each sensitive section is extracted from the spatiotemporal distribution results in a section-time manner. This series is consistent with the model's time step, covering the entire process from the start of pollution source emissions to the end of the prediction. When analyzing the arrival time of the front, a threshold is first set for each type of sensitive target. This threshold can be an incremental threshold relative to the background concentration or a direct early warning trigger threshold. Then, C(t) is scanned step by step along the time axis. When the concentration first jumps from below the threshold to above the threshold, this time point is recorded as the arrival time of the front. To avoid misjudgments caused by short-term fluctuations due to tidal cycles, a continuous confirmation rule can be introduced. This means that the arrival of the leading edge is only confirmed after a certain number of consecutive time steps have passed below a threshold, or after the cumulative duration exceeding the threshold within a small time window reaches a set proportion. Simultaneously, to better reflect actual response needs, the arrival time of the leading edge can be further converted into a lead time from the current moment to determine whether the minimum preparation time for emergency actions such as switching water sources, shutting down water intake, and scheduling gate pumps is met.

[0048] When analyzing the time of maximum concentration and the duration of exceedance, extreme value analysis is performed on the same concentration time series, that is, the maximum value C(t) is found for the entire time period. max and its corresponding time t max , will t max Record the time of maximum concentration occurrence and set C max This serves as a peak risk indicator for the sensitive target. If multiple peaks exist under tidal conditions, such as a secondary peak caused by backflow, the output will retain information on both the primary and secondary peaks, and label the corresponding tidal stage. Then, a preset standard value C is used. std As a criterion for judging whether the value exceeds the limit, all cases satisfying C(t) > C on the time axis are identified. std A continuous interval, recording the starting point t of each interval. start With the endpoint t end The system calculates the duration ΔTt. When multiple exceedance intervals exist, the duration of each interval is output separately, along with the cumulative exceedance duration. This helps determine how long the water plant or other water-using targets need to take protective or alternative measures throughout the event. For more refined management indicators, derived results such as the first exceedance time, the longest consecutive exceedance duration, and the number of exceedances can also be provided to differentiate between short-term fluctuations and long-term exposure risk patterns.

[0049] After extracting the time-related indicators, the arrival time of the leading edge, the time of maximum concentration, and the duration of exceeding the standard are mapped back into the river network spatial structure to form a spatialized risk layer. Specifically, each river segment, each calculation unit, or key section of the river network is assigned a corresponding indicator value to form renderable spatial attribute data. Then, the concentration field is represented by a cloud map that is plotted and played continuously at each time step. That is, at each predicted time t, the concentration values ​​of all units in the river network are used as the spatial field input, and the pollutant distribution concentration cloud map at that time is rendered on the river network space through color gradients or contour lines. Then, the cloud maps of t0, t1, t2, etc. are played continuously in time sequence to obtain a dynamic thermal cloud map with dynamic evolution effect. This dynamic thermal cloud map provides a clear visual understanding of the complete evolutionary trajectory of pollutants, from their initial emission point along the main river channel, through diversion or convergence at tributaries, backflow during high tide, and subsequent discharge during low tide. Spatial markers of sensitive targets can be overlaid on the map; when a high-concentration area approaches or covers a marker, the system can visually demonstrate the impact of the pollution cloud on the target. To more clearly represent the propagation timeline, an arrival time contour map can be generated based on the cloud map. This involves rendering the arrival time of the leading edge at each spatial location as a numerical field, forming a time band from near to far, thus obtaining the timeline of pollutant diffusion and propagation. Similarly, the maximum concentration time and the duration of exceedance can be rendered as independent layers to show spatial patterns such as where the pollutants are most affected, where the risk peak occurs latest, and where exceedances are prolonged.

[0050] In terms of rolling forecast updates, the system incorporates the dynamic changes in tidal conditions into the continuous update mechanism. Whenever a new boundary tide forecast or new measured water level and flow data is obtained, the hydrodynamic field is updated using the latest boundary conditions. Based on this, a preset prediction window is pushed forward from the current moment to recalculate the spatiotemporal distribution of pollutant concentrations. During rolling updates, the current concentration field is retained as the new initial field, and the flow direction and node allocation are automatically adjusted in conjunction with the latest tidal stage identification results to ensure that the prediction always aligns with the actual tidal evolution. Then, the updated concentration spatiotemporal results are analyzed again for front arrival, peak time, and duration of exceedance, and the cloud map sequence is refreshed synchronously to ensure that the warning results are not delayed due to changes in tidal forecasts or measured deviations. Finally, the system generates pollution risk warning results centered on sensitive targets. When a forecast indicates that a leading edge will arrive at a water plant's intake at a specific future time, or that the peak concentration will exceed the warning threshold, or that the duration of the exceedance will exceed the tolerable duration, an early warning message will be automatically output. The message will include at least the name of the affected target, the expected arrival time of the leading edge, the expected peak time and peak concentration, the expected start and end times of the exceedance, and the total duration. The affected area and propagation path will be prominently displayed on the dynamic heat map of the river network. A countdown timer indicating how long until the leading edge arrives will be provided, along with suggested response windows. This allows water plants or other areas with water source requirements to take measures in advance, such as switching water intakes, scheduling gate pumps, strengthening monitoring, or activating emergency plans. This enables visualized, resolvable, and continuously updated pollution risk warnings for complex tidal river networks, thereby improving the accuracy and timeliness of pollution warnings for water plant intakes and other sensitive areas.

[0051] In summary, the embodiments of this application have at least the following technical effects: Based on the topology of tidal river networks and hydrodynamic data of tidal boundaries, a hydrodynamic field mathematical model is constructed. Based on this model, a pollutant convection-diffusion-attenuation control equation is established, and mass conservation connection conditions are established at the river network inlets to construct a pollutant coupling transport model applicable to complex tidal river network structures. Spatial discretization and time-stepping analysis are performed using the pollutant coupling transport model based on pollution source emission parameters to obtain the spatiotemporal distribution of pollutant concentrations. Based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed using a spatial visualization heatmap for pollution risk early warning of sensitive targets associated with the river network. This technology addresses the technical challenges of existing methods in simulating pollutant migration and diffusion processes during sudden water pollution incidents in complex tidal river networks. These challenges include low accuracy, slow computation speed, difficulty in quickly and accurately predicting the impact time and extent of pollutants on downstream sensitive targets, and inability to meet emergency early warning requirements. This new technology enables rapid and accurate simulation of pollutant transport in tidal river networks, effectively predicting the arrival time of pollutant fronts, peak concentrations, and duration of exceedances. Furthermore, it provides a visual and intuitive representation of pollution risks, offering reliable technical support for emergency decision-making and the protection of sensitive targets during sudden water pollution incidents.

[0052] Example 2 Based on the same inventive concept as the pollutant prediction method for a tidal river network in the foregoing embodiments, such as Figure 2 As shown, this application provides a pollutant prediction system for tidal river networks, wherein the system includes: Mathematical model construction module 11: Based on the topology of the tidal river network and the hydrodynamic data of the tidal boundary, a hydrodynamic field mathematical model is constructed; Coupled model construction module 12: Based on the hydrodynamic field mathematical model, a pollutant convection-diffusion-attenuation control equation is established, and a mass conservation connection condition is established at the river network inlet nodes to construct a pollutant coupled transport model applicable to complex tidal river network structures; Emission analysis module 13: Based on the emission parameters of the pollution sources, spatial discretization and time step analysis are performed through the pollutant coupled transport model to obtain the spatiotemporal distribution results of pollutant concentrations; Prediction and analysis module 14: Based on the spatiotemporal distribution results of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed, and the prediction results are displayed in a spatial visualization heat map for pollution risk early warning of sensitive targets associated with the river network.

[0053] Furthermore, the mathematical model construction module 11 is used to perform the following methods: Based on historical river network monitoring data, tidal boundary identification is performed to establish the topology of the tidal river network and determine the connection relationships and boundary node types of each river segment. Time-varying boundary conditions are set for each boundary section of the tidal river network based on the topology. These time-varying boundary conditions include at least one of tidal level procedural lines, flow procedural lines, or water level-flow relationship curves, and continuous boundary functions are constructed through time interpolation. Based on the topology and the time-varying boundary conditions, a one-dimensional hydrodynamic control equation is established, and discrete solutions are performed for each river segment of the river network to calculate the flow field, velocity field, and water level field at each time step, thus establishing the hydrodynamic field mathematical model. Furthermore, a dynamic tidal phase identification mechanism is introduced during the hydrodynamic field calculation process. By comparing the changes in water level gradient direction or flow sign between adjacent time steps, it is determined whether the current river segment is in the rising or falling tidal phase, and the flow direction calculation parameters are adjusted based on the determination results.

[0054] Furthermore, the coupling model construction module 12 is used to perform the following methods: Based on the hydrodynamic parameters obtained from the aforementioned hydrodynamic field mathematical model, including the flow field, velocity field, and water level field, these hydrodynamic parameters are used as driving conditions for pollutant transport calculations. Based on these driving conditions, a pollutant convection-diffusion-attenuation control equation is established, including convection, longitudinal diffusion, and attenuation terms. Corresponding diffusion and attenuation coefficients are set according to the pollutant type. Mass conservation connection conditions are established at the river network distributary nodes, and the pollutant concentration distribution ratio is determined by flow-weighted calculation of pollutant concentrations in each tributary to ensure the continuity of pollutant transport in the tidal river network. This constructs the pollutant coupled transport model to describe the dynamic concentration field of pollutants in the tidal river network.

[0055] Furthermore, the coupling model construction module 12 is used to perform the following methods: The convection term describes the parameters of pollutant migration with water flow; the longitudinal diffusion term describes the parameters of pollutant spatial dispersion, wherein the diffusion coefficient is determined based on the river flow velocity and cross-sectional characteristics; the attenuation term describes the parameters of the natural attenuation process of pollutants, wherein the attenuation coefficient is set according to the pollutant type.

[0056] Furthermore, the coupling model construction module 12 is used to perform the following methods: The mass conservation connection condition satisfies that the total mass of pollutants flowing into the inlet node is equal to the total mass of pollutants flowing out of the inlet node. When the river flow direction reverses, the concentration distribution direction of the river network inlet node is adjusted synchronously.

[0057] Furthermore, the emission analysis module 13 is used to perform the following methods: Based on the pollution source emission location, emission intensity, and emission mode in the pollution source emission parameters, the pollution source term is introduced into the pollutant coupled transport model. The river network segments are spatially discretized, and continuous river segments are divided into several computational units. A step-by-step time-incremental calculation is performed. At each time step, the hydrodynamic parameters corresponding to each computational unit are read. The flow direction and main propagation direction of the current river segment are analyzed based on the hydrodynamic parameters. The direction of the convection term is updated based on the analyzed flow direction. The migration amount of pollutants within each computational unit is calculated, and the concentration changes caused by the diffusion and attenuation terms are calculated. At the river network distributary nodes, the concentration distribution is updated according to the real-time flow ratio. When the flow direction of a river segment reverses, the pollutant reverses propagation and concentration superposition is performed. The dynamic spatiotemporal distribution of pollutant concentration in the tidal river network is obtained by updating the processing based on the concentration changes at each time step.

[0058] Furthermore, the emission analysis module 13 is used to perform the following methods: In the time-step analysis process, a pollutant propagation link identification mechanism is introduced to identify and record the hydrodynamic parameters, propagation paths, and concentration changes of pollutants in each calculation unit, constructing a pollutant concentration change update space. Based on the concentration change update space, at the end of each time step, the total mass of pollutants is checked for mass consistency to determine whether the concentration result of the current time step meets the mass conservation condition. When a mass deviation is detected to exceed a preset threshold, the concentration of the corresponding calculation unit is corrected for error. When the river flow direction reverses or pollutants are backflowed and superimposed, a weight correction factor is introduced for the superimposed concentration to avoid concentration deviation caused by repeated calculations. Based on the concentration change update space, the global concentration distribution within the same time step is corrected for consistency, and the time step deviation is located and analyzed. The pollutant concentration distribution is corrected according to the deviation location results to determine the spatiotemporal distribution result of the dynamic concentration change of pollutants.

[0059] Furthermore, the prediction parsing module 14 is used to perform the following method: Based on the spatiotemporal distribution of pollutant concentrations, time series analysis is performed on each sensitive section to identify the time point when pollutant concentrations first exceed the threshold and determine the arrival time of the pollutant front. Extreme value analysis is performed on the concentration time series to determine the time of occurrence of the maximum concentration and the corresponding concentration value, and the duration interval of concentration exceeding the preset standard value is calculated to obtain the duration of exceedance. The arrival time of the front, the time of maximum concentration, and the duration of exceedance are mapped onto the river network spatial structure to generate a dynamic thermal cloud map of pollutant concentration distribution, determine the timeline of pollutant diffusion and propagation and the trajectory of concentration evolution, and based on the dynamic changes of tidal conditions in the tidal river network, rolling predictions are updated for subsequent time periods to generate pollution risk warning results for sensitive targets.

[0060] Example 3, Figure 3 This is a schematic diagram of the structure of an electronic device provided in Embodiment 3 of the present invention, showing a block diagram of an exemplary electronic device suitable for implementing the embodiments of the present invention. Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the present invention. Figure 3 As shown, the electronic device includes a processor 21, a memory 22, an input device 23, and an output device 24; the number of processors 21 in the electronic device can be one or more. Figure 3 Taking a processor 21 as an example, the processor 21, memory 22, input device 23, and output device 24 in an electronic device can be connected via a bus or other means. Figure 3 Taking the example of a connection between China and Israel via a bus.

[0061] The memory 22, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules, such as the program instructions / modules corresponding to the pollutant prediction method for a tidal river network in this embodiment of the invention. The processor 21 executes various functional applications and data processing of the electronic device by running the software programs, instructions, and modules stored in the memory 22, thereby realizing the aforementioned pollutant prediction method for a tidal river network.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting pollutants in tidal river networks, characterized in that, include: Based on the topology of the tidal river network and the hydrodynamic data of the tidal boundary, a mathematical model of the hydrodynamic field is constructed. Based on the aforementioned hydrodynamic field mathematical model, a pollutant convection-diffusion-attenuation control equation is established, and a mass conservation connection condition is established at the river network distributary nodes to construct a pollutant coupling transport model applicable to complex tidal river network structures. Based on the emission parameters of the pollution source, spatial discretization and time step analysis are performed using the pollutant coupling transport model to obtain the spatiotemporal distribution results of pollutant concentrations. Based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed in a spatially visualized heat map for pollution risk warning of sensitive targets associated with the river network.

2. The pollutant prediction method for tidal river networks according to claim 1, characterized in that, Based on the topology of the tidal river network and hydrodynamic data of the tidal boundary, a mathematical model of the hydrodynamic field is constructed, including: Based on historical river network monitoring data, tidal boundaries are identified, the topological structure of the tidal river network is established, and the connection relationships and boundary node types of each river segment are determined. Based on the topology, time-varying boundary conditions are set for each boundary section of the tidal river network. The time-varying boundary conditions include at least one of tidal level process line, flow process line or water level-flow relationship curve, and a continuous boundary function is constructed by time interpolation. Based on the aforementioned topology and time-varying boundary conditions, a one-dimensional hydrodynamic control equation is established. The equations are then discretely solved for each river segment of the river network to calculate the flow field, velocity field, and water level field at each time step, thus establishing the hydrodynamic field mathematical model. Secondly, a dynamic identification mechanism for tidal phases is introduced into the hydrodynamic field calculation process. By comparing the changes in water level gradient direction or flow sign in adjacent time steps, it is determined whether the current river section is in the high tide or low tide phase, and the flow direction calculation parameters are adjusted according to the determination results.

3. The pollutant prediction method for tidal river networks according to claim 1, characterized in that, Constructing a pollutant coupled transport model applicable to complex tidal river network structures, including: The hydrodynamic parameters obtained from the hydrodynamic field mathematical model include the flow field, velocity field, and water level field. These hydrodynamic parameters are used as the driving conditions for pollutant transport calculations. Based on the aforementioned driving conditions, a pollutant convection-diffusion-attenuation control equation is established, which includes a convection term, a longitudinal diffusion term, and an attenuation term. The corresponding diffusion coefficient and attenuation coefficient are set according to the pollutant type. Mass conservation connection conditions are established at the river network inlet nodes. The pollutant concentration distribution ratio is determined by flow weighting calculation of the pollutant concentration of each tributary to ensure the continuity of pollutant transmission in the tidal river network. The pollutant coupled transport model is constructed to describe the dynamic concentration field of pollutants in the tidal river network.

4. The pollutant prediction method for tidal river networks according to claim 3, characterized in that, The convection term describes the parameters of pollutant migration with water flow; the longitudinal diffusion term describes the parameters of pollutant spatial dispersion, wherein the diffusion coefficient is determined based on the river flow velocity and cross-sectional characteristics; the attenuation term describes the parameters of the natural attenuation process of pollutants, wherein the attenuation coefficient is set according to the pollutant type.

5. The pollutant prediction method for tidal river networks according to claim 3, characterized in that, Establishing mass-conserving connectivity conditions at river network distributary nodes also includes: The mass conservation connection condition satisfies that the total mass of pollutants flowing into the inlet node is equal to the total mass of pollutants flowing out of the inlet node. When the river flow direction reverses, the concentration distribution direction of the river network inlet node is adjusted synchronously.

6. The pollutant prediction method for tidal river networks according to claim 5, characterized in that, Based on the pollution source emission parameters, spatial discretization and time step analysis are performed using the pollutant coupled transport model to obtain the spatiotemporal distribution results of pollutant concentrations, including: Based on the pollution source emission location, emission intensity and emission mode in the pollution source emission parameters, the pollution source term is introduced into the pollutant coupling transport model. The river network segments are spatially discretized, and continuous river segments are divided into several calculation units. In the time dimension, a step-by-step calculation is performed using a progressive approach. At each time step, read the hydrodynamic parameters corresponding to each computational unit; The flow direction and main propagation direction of the current river section are analyzed based on the hydrodynamic parameters. The direction of convection is updated based on the flow direction obtained from the analysis. The amount of pollutant migration in each calculation unit is calculated, and the concentration changes caused by the diffusion and attenuation terms are calculated. At river network inlets, the concentration allocation is updated based on the real-time flow ratio. When the river flow direction reverses, the pollutants are reversed and the concentration is calculated by superposition. The dynamic spatiotemporal distribution of pollutant concentrations in the tidal river network is obtained by updating the processing based on the concentration changes at each time step.

7. The pollutant prediction method for tidal river networks according to claim 6, characterized in that, The spatiotemporal distribution of pollutant dynamic concentrations in the tidal river network is obtained by updating the concentration changes at each time step, and also includes: During the time-step analysis, a pollutant propagation link identification mechanism is introduced to identify and record the hydrodynamic parameters, propagation paths, and concentration changes of pollutants in each calculation unit, thereby constructing a pollutant concentration change update space. Based on the concentration change update space, at the end of each time step, the total mass of pollutants is checked for mass consistency to determine whether the concentration result of the current time step meets the mass conservation condition. When a quality deviation is detected to exceed a preset threshold, error correction processing is performed on the concentration of the corresponding calculation unit; When the flow direction of a river section reverses or pollutants are backflowed and superimposed, a weighting correction factor is introduced for the superimposed concentration to avoid concentration deviation caused by double calculation. Based on the concentration change update space, the global concentration distribution within the same time step is corrected for consistency, and the time step deviation is located and analyzed. Based on the deviation positioning results, the pollutant concentration distribution is corrected to determine the spatiotemporal distribution of the dynamic concentration changes of pollutants.

8. The pollutant prediction method for tidal river networks according to claim 1, characterized in that, Based on the spatiotemporal distribution of pollutant concentrations, the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceedance are predicted and analyzed. The prediction results are then displayed as a spatially visualized heatmap for pollution risk early warning of sensitive targets associated with river networks, including: Based on the spatiotemporal distribution of pollutant concentrations, time series analysis is performed on each sensitive section to identify the time point when the pollutant concentration first exceeds the threshold and to determine the arrival time of the pollutant front. Extreme value analysis was performed on the concentration time series to determine the time when the maximum concentration occurred and the corresponding concentration value, and the duration range of the concentration exceeding the preset standard value was calculated to obtain the duration of the exceedance. The arrival time of the leading edge, the time of maximum concentration, and the duration of exceeding the standard are mapped onto the spatial structure of the river network to generate a dynamic thermal cloud map of pollutant concentration distribution. The timeline of pollutant diffusion and propagation and the trajectory of concentration evolution are determined. Based on the dynamic changes of tidal conditions in the tidal river network, rolling predictions are made for subsequent time periods to generate pollution risk warning results for sensitive targets.

9. A pollutant prediction system for tidal river networks, characterized in that, A pollutant prediction method for implementing any one of claims 1-8 in a tidal river network includes: Mathematical model construction module: Based on the topology of the tidal river network and the hydrodynamic data of the tidal boundary, a mathematical model of the hydrodynamic field is constructed; Coupled model construction module: Based on the hydrodynamic field mathematical model, establish the pollutant convection-diffusion-attenuation control equation, and establish mass conservation connection conditions at the river network distributary nodes to construct a pollutant coupled transport model applicable to complex tidal river network structures; Emissions analysis module: Based on the emission parameters of the pollution source, spatial discretization and time step analysis are performed through the pollutant coupling transport model to obtain the spatiotemporal distribution results of pollutant concentration; Prediction and analysis module: Based on the spatiotemporal distribution results of the pollutant concentration, it predicts and analyzes the arrival time of the pollutant front, the time of maximum concentration, and the duration of exceeding the standard, and displays the prediction results in a spatial visualization heat map for pollution risk early warning of sensitive targets associated with the river network.

10. An electronic device, characterized in that, The electronic device includes: Memory, used to store executable instructions; A processor, when executing executable instructions stored in the memory, implements a pollutant prediction method for a tidal river network according to any one of claims 1-8.

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