Basin management method

Abstract

This invention relates to the field of watershed management technology, specifically to a watershed management method. The method includes: obtaining a pollution source contribution allocation vector corresponding to a target watershed and a nitrogen load allocation vector corresponding to each hydrological transport path in the target watershed; constructing a transport cost matrix based on the landscape connectivity index of pollutants corresponding to each pollution source; the landscape connectivity index is used to determine the smoothness of pollutant flow in the target watershed; constructing a target optimization function constrained by information entropy based on the pollution source contribution allocation vector, nitrogen load allocation vector, and transport cost matrix; solving the target optimization function to obtain the target source-path coupling matrix corresponding to the target watershed; and determining the target management scheme corresponding to the target watershed based on the target source-path coupling matrix. This achieves precise policy implementation for each source and path, customizing control measures from both the source and migration process perspectives, thereby improving the targeting of watershed nitrogen pollution management.

Description

Technical Field

[0001] This invention relates to the field of watershed management technology, and more specifically to watershed management methods. Background Technology

[0002] Non-point source pollution has become the primary factor restricting the improvement of water quality in watersheds, especially in watersheds in urban-rural transition zones. The pollution sources in these watersheds are complex, with chemical fertilizers, livestock manure, domestic sewage, and atmospheric precipitation coexisting; hydrological transport pathways are intertwined, with surface runoff, interflow, and baseflow all carrying nitrogen output. This high degree of coupling between pollution sources and transport pathways poses a fundamental challenge to the accurate tracing and targeted treatment of nitrogen pollution in watersheds.

[0003] Currently, source apportionment and pathway analysis, primarily based on Bayesian mixture models using stable isotopes, can quantify the contributions of each source. However, these models treat the watershed as a black box, failing to reveal the transport pathways of pollutants reaching the water body. Consequently, they cannot achieve a shift from total emission control to pathway-targeted precise management, thus hindering the comprehensive water environment management needs of watersheds in urban-rural transition zones. Summary of the Invention

[0004] This invention provides a watershed management method to address the problem of being unable to shift from total quantity control to path-targeted precise management, thus meeting the needs of comprehensive water environment management in watersheds in urban-rural transition zones.

[0005] In a first aspect, the present invention provides a watershed management method, comprising: obtaining a pollution source contribution allocation vector corresponding to a target watershed and a nitrogen load allocation vector corresponding to each hydrological transmission path corresponding to the target watershed; the pollution sources include chemical fertilizers, rainfall, domestic sewage, and livestock manure; the hydrological transmission paths include surface runoff transmission paths, interflow transmission paths, and baseflow transmission paths; constructing a transmission cost matrix based on the landscape connectivity index of pollutants corresponding to each pollution source; the landscape connectivity index is used to determine the smoothness of pollutant flow in the target watershed; constructing a target optimization function constrained by information entropy based on the pollution source contribution allocation vector, the nitrogen load allocation vector, and the transmission cost matrix; solving the target optimization function to obtain the target source-path coupling matrix corresponding to the target watershed; and determining the target management scheme corresponding to the target watershed based on the target source-path coupling matrix.

[0006] The watershed management method provided in this application obtains pollution source contribution allocation vectors and nitrogen load allocation vectors. It quantitatively decomposes nitrogen pollution from two dimensions: pollution sources and hydrological transport paths, clarifying the contribution proportions of various pollution sources and the load-bearing structure of different runoff paths. This provides a dual-boundary quantitative constraint basis for subsequent coupled analysis, avoiding singular and one-sided governance judgments. A transport cost matrix is ​​constructed based on the landscape connectivity index. The differences in pollutant migration resistance across multiple paths (surface, interflow, and baseflow) are quantified, transforming natural conditions such as topography, soil, and hydrogeology into calculable cost indicators. This objectively reflects the actual transport patterns in the watershed, improving the scientific rigor of source-path matching. An information entropy-constrained objective optimization function is constructed. With transport minimization as the core and information entropy regularization as the constraint, this approach aligns with the objective law of preferential low-resistance pollutant migration while avoiding extreme and fragmented allocation results. It ensures balanced and reasonable solution results that conform to the actual characteristics of multi-path mixed transport. Solving the optimization function yields the objective source-path coupling matrix. This approach achieves precise two-way coupling and quantification of pollution sources and hydrological pathways, quantifying the nitrogen output ratio of different pollution sources through various runoff channels, accurately identifying key pollution transport combinations, and overcoming the limitations of traditional single-source tracing that cannot distinguish transport pathways. Targeted remediation solutions are determined based on the coupling matrix. High-contribution dominant coupling units are targeted, enabling precise policy implementation for each source and pathway. Control measures are customized from both the source and migration process perspectives, improving the targeting, precision, and efficiency of watershed nitrogen pollution control and the utilization of remediation resources.

[0007] In one optional implementation, obtaining the pollution source contribution allocation vector corresponding to the target watershed includes: obtaining the source endmember dual isotope signals and initial watershed nitrate concentration data for each pollution source corresponding to the target watershed; the source endmember dual isotope signals include source-end nitrate nitrogen isotope signals and source-end nitrate oxygen isotope signals; obtaining the section dual isotope signals and section nitrate concentration data corresponding to each preset monitoring section in the target watershed; wherein, each preset monitoring section meets preset monitoring conditions; the section dual isotope signals include section nitrate nitrogen isotope signals and The cross-sectional nitrate oxygen isotope signal; based on the cross-sectional dual isotope signal and nitrate concentration data of each preset monitoring section in the target watershed, the target denitrification fractionation coefficient of the target watershed is determined; based on the source end-member dual isotope signal, the initial watershed nitrate concentration data, the cross-sectional dual isotope signal and nitrate concentration data of each preset monitoring section, and the target denitrification fractionation coefficient, the posterior contribution probability distribution of each pollution source is determined; based on the posterior contribution probability distribution of each pollution source, the pollution source contribution allocation vector of each pollution source is determined.

[0008] The watershed management method provided in this application acquires dual isotope signals of the source endmembers of various pollution sources and initial watershed nitrate concentration data. It accurately establishes a dedicated isotope fingerprint database for various pollution sources, locking in the background characteristics of pollution sources and providing standard prior data for subsequent source tracing modeling, ensuring the uniqueness of the source analysis benchmark. It acquires dual isotope signals and nitrate concentration data from monitoring sections. Based on compliant monitoring sections, it forms an in-situ measured dataset of the watershed, fully capturing the actual isotope characteristics and concentration changes of nitrogen in the water body, truly reflecting the current state of mixed pollution in the watershed, and ensuring that the analysis results are consistent with reality. It determines the target denitrification fractionation coefficient. It quantitatively characterizes the isotope fractionation law of source transformation within the watershed, effectively correcting the isotope signal shift caused by denitrification, eliminating interference from natural transformation, and improving the accuracy of pollution source identification. Combining multiple types of data and fractionation coefficients, it solves the posterior contribution probability distribution of each pollution source. By leveraging dual isotope coupling and probabilistic inversion mechanisms, this method achieves probabilistic quantitative analysis of multiple pollution sources, avoiding the qualitative ambiguity, large errors, and uncertainty in quantification results inherent in traditional methods. Based on the posterior contribution probability distribution, a pollution source contribution allocation vector is determined. The probabilistic source tracing results are transformed into standardized quantitative allocation weights, enabling a structured expression of the contribution proportions of various pollution sources. This provides reliable source-level quantitative support for subsequent path coupling simulation and regional pollution control.

[0009] In one optional implementation, the target denitrification fractionation coefficient for the target watershed is determined based on the cross-sectional dual isotope signals and nitrate concentration data corresponding to each preset monitoring section in the target watershed. This includes: calculating the nitrogen isotope fractionation coefficient for the target watershed based on the linear relationship between the cross-sectional nitrogen isotope signals and the cross-sectional nitrate concentration data corresponding to each preset monitoring section; calculating the oxygen isotope fractionation coefficient for the target watershed based on the linear relationship between the cross-sectional oxygen isotope signals and the cross-sectional nitrate concentration data corresponding to each preset monitoring section; and generating the target denitrification fractionation coefficient for the target watershed based on the nitrogen isotope fractionation coefficient and the oxygen isotope fractionation coefficient.

[0010] The watershed management method provided in this application calculates the nitrogen isotope fractionation coefficient based on the linear relationship between nitrogen isotope and nitrate concentrations at cross-sections. Relying on the objective variation patterns of in-situ monitoring data, it accurately quantifies the degree of nitrogen isotope enrichment caused by denitrification, truly reflecting the fractionation response characteristics of the watershed nitrogen transformation process. Based on the linear relationship between oxygen isotope and nitrate concentrations at cross-sections, it calculates the oxygen isotope fractionation coefficient. It supplements the fractionation characteristics at the oxygen isotope level, improves the dual-index fractionation characterization system, overcomes the limitations of single isotope analysis, and enhances the completeness of the endogenous transformation process characterization. It couples the nitrogen and oxygen isotope fractionation coefficients to generate the target denitrification fractionation coefficient. By integrating the synergistic fractionation characteristics of dual isotopes, it forms a comprehensive fractionation parameter specific to the watershed, effectively correcting signal biases caused by hydrological transformation, and significantly improving the accuracy and reliability of subsequent pollution source contribution analysis and quantitative calculation.

[0011] In one optional implementation, based on the source end-member dual isotope signal, initial watershed nitrate concentration data, cross-sectional dual isotope signals corresponding to each preset monitoring section, cross-sectional nitrate concentration data, and target denitrification fractionation coefficient, the posterior contribution probability distribution corresponding to each pollution source is determined. This includes: calculating the remaining nitrate proportion corresponding to each preset monitoring section based on the initial watershed nitrate concentration data and the cross-sectional dual isotope signals corresponding to each preset monitoring section; and for each preset monitoring section, correcting the cross-sectional nitrate nitrogen isotope signal corresponding to the preset monitoring section based on the remaining nitrate proportion, cross-sectional nitrate nitrogen isotope signal, and nitrogen isotope fractionation coefficient to obtain the cross-sectional corrected nitrate. Nitrogen isotope signals; based on the residual nitrate ratio, nitrate oxygen isotope signals, and oxygen isotope fractionation coefficients corresponding to preset monitoring sections, the nitrate oxygen isotope signals of the preset monitoring sections are corrected to obtain the corrected nitrate oxygen isotope signals; it is verified that the source end-member dual isotope signals corresponding to each pollution source conform to a normal distribution, and the correspondence between pollution source type and isotope fingerprint parameters is obtained; based on the source end nitrate nitrogen isotope signals, source end nitrate oxygen isotope signals, corrected nitrate nitrogen isotope signals, and corrected nitrate oxygen isotope signals, dual isotope simultaneous equations are constructed; based on the Markov chain Monte Carlo algorithm, the posterior contribution probability distribution corresponding to each pollution source is solved.

[0012] The watershed management method provided in this application calculates the remaining proportion of nitrate at each monitoring section. It quantitatively characterizes the residual level of nitrate degradation in the watershed, quantifies the degree of denitrification consumption, and provides core proportional parameters for isotope signal bias correction. It corrects the nitrogen isotope signal of nitrate at the monitoring sections by eliminating interference from nitrogen isotope enrichment caused by denitrification fractionation, restoring the original nitrogen isotope background characteristics of the mixed water body, and improving the authenticity of the source tracing data. It also corrects the oxygen isotope signal of nitrate at the monitoring sections by simultaneously correcting oxygen isotope fractionation offset, improving the dual isotope correction system, and eliminating signal distortion caused by endogenous transformation. It verifies the normal distribution of source end-member isotopes and establishes fingerprint correspondence. It clarifies the prior distribution characteristics of isotopes from various pollution sources, ensuring compliance with Bayesian model input requirements and guaranteeing reasonable and standardized prior parameter settings. It constructs a dual isotope simultaneous equation. Based on nitrogen and oxygen dual isotope constraints, it establishes a mass balance equation, restricting the solution interval in multiple dimensions to reduce ambiguity and error in multi-source analysis. The MCMC algorithm is used to solve the posterior contribution probability distribution. It enables probabilistic inversion of pollution source contributions, quantifies the uncertainty of analysis results, breaks through the limitations of traditional fixed-value calculation, and makes the source tracing results more scientific and robust.

[0013] In one optional implementation, obtaining the nitrogen load allocation vector corresponding to each hydrological transmission path of the target watershed includes: obtaining initial continuous daily flow data and daily discrete nitrogen concentration data corresponding to the outlet of the target watershed within a preset time period; separating the initial continuous daily flow data to determine the target surface flow data, target base flow data, and target soil flow data; selecting daily discrete nitrogen concentration data with a target base flow data ratio greater than a first preset ratio and daily nitrogen concentration fluctuation less than a preset fluctuation threshold as baseflow nitrogen concentration end-members; baseflow-specific nitrogen concentration end-members are used to characterize the nitrogen concentration samples corresponding to baseflow components formed entirely by groundwater recharge; selecting the target surface flow... Daily discrete nitrogen concentration data with a proportion less than the second preset ratio are used as end-members of interflow nitrogen concentration. Daily discrete nitrogen concentration data with a proportion greater than or equal to the third preset ratio and satisfying preset selection events are selected as end-members of surface runoff nitrogen concentration. Based on the target surface flow data and the baseflow nitrogen concentration end-members, the daily nitrogen load sequence of baseflow is calculated. Based on the target interflow data and the interflow nitrogen concentration end-members, the daily nitrogen load sequence of interflow is calculated. Based on the target surface flow data and the surface runoff nitrogen concentration end-members, the daily nitrogen load sequence of surface runoff is calculated. Based on the daily nitrogen load sequence of baseflow, the daily nitrogen load sequence of interflow, and the daily nitrogen load sequence of surface runoff, the nitrogen load allocation vector corresponding to the target watershed is determined.

[0014] The watershed management method provided in this application acquires daily flow and daily nitrogen concentration data at the watershed outlet. It unifies cross-sections and synchronously collects hydrological and water quality data over time, ensuring data source matching and providing a complete basic data source for runoff segmentation and multi-path concentration and load analysis. Initial continuous daily flow is segmented into multiple components. This achieves refined breakdown of total flow, accurately distinguishing between surface runoff, interflow, and baseflow hydrological transport paths, and clarifying the differences in water volume proportions of different runoff generation mechanisms. Samples from stable periods are selected to construct baseflow nitrogen concentration end-members. This avoids interference from rainfall and short-term hydrological disturbances, purifies the background concentration characteristics of groundwater, and ensures the purity and representativeness of baseflow concentration samples. Samples with low surface area ratios are selected to construct interflow nitrogen concentration end-members. This eliminates interference from surface scour pollution, accurately reflects the inherent nitrogen concentration level of lateral interflow in the soil, and achieves independent characterization of mid-level path concentrations. Samples with high surface area ratios and rainfall events are selected to construct surface runoff end-members. By identifying typical slope runoff and scour periods, the characteristics of surface runoff non-point source pollution concentrations are accurately depicted, aligning with the actual patterns of pollution transport during heavy rainfall. Daily nitrogen load of baseflow is calculated using baseflow and concentration end-members. The long-term stable nitrogen pollution load from groundwater is quantitatively quantified, enabling time-series accounting of pollution output along the baseflow path. Daily nitrogen load of interflow is calculated using interflow and concentration end-members. The nitrogen load from lateral migration in the middle soil layer is accurately calculated, improving the quantitative accounting system for intermediate hydrological pathways. Daily nitrogen load of surface runoff is calculated using surface flow and concentration end-members. Short-term surface pollution load driven by rainfall scour is effectively quantified, reconstructing key pollution output characteristics during the flood season. Multi-path loads are aggregated to determine the nitrogen load allocation vector. The standardized quantification of the nitrogen load proportions of surface, interflow, and baseflow forms a quantitative constraint vector along the path dimension, providing reliable boundary conditions for subsequent source-path coupling optimization modeling.

[0015] In one optional implementation, a transport cost matrix is ​​constructed based on the landscape connectivity index of pollutants corresponding to each pollution source. This includes: determining the landscape contribution area corresponding to each pollution source within the target watershed based on the spatial distribution characteristics of each pollution source; the landscape contribution area characterizes all catchment areas within the target watershed where pollutants from each pollution source can be stably transported to the receiving water body via surface runoff, interflow, or groundwater under constraints of natural hydrological and topographical conditions; for each landscape contribution area, calculating the landscape connectivity index corresponding to the pollutants from the corresponding pollution source in the surface runoff transport path, interflow transport path, and baseflow transport path; calculating the transport cost corresponding to each landscape connectivity index; and constructing a transport cost matrix based on each transport cost.

[0016] The watershed management method provided in this application delineates the landscape contribution areas corresponding to each pollution source. It accurately delineates the effective catchment area of ​​pollutants by combining topographic and hydrological connectivity, eliminating ineffective closed areas and clarifying the actual pollution generation and transport spatial range of various pollution sources, avoiding calculation bias caused by generalization of spatial ranges. It calculates the landscape connectivity indices for surface, interflow, and baseflow along different pathways. From multiple dimensions of topography, soil, and hydrogeology, it quantifies the smoothness of pollutant migration along the three hydrological pathways, objectively reflecting the differences in natural barriers and connectivity among different transport channels. The transport cost of each pathway is derived from the landscape connectivity index. This achieves a quantitative transformation of connectivity characteristics into resistance costs, unifies the quantification standard, and intuitively represents the strength of migration resistance of pollutants along different transport pathways. A source-path dimension transport cost matrix is ​​constructed. This forms a structured and standardized resistance dataset, fully representing the matching resistance relationship between multiple pollution sources and multiple hydrological pathways, providing a precise quantitative foundation for subsequent optimization model construction and coupling analysis.

[0017] In one optional implementation, the landscape connectivity indices corresponding to surface runoff transport paths, interflow transport paths, and baseflow transport paths are respectively the surface runoff connectivity index, interflow connectivity index, and baseflow connectivity index. For each landscape contribution area, the landscape connectivity indices corresponding to the pollutants from the pollution sources in the corresponding landscape contribution areas in the surface runoff transport paths, interflow transport paths, and baseflow transport paths are calculated, including: for each pollution source corresponding to the landscape contribution area, based on the runoff accumulation, weighted slope, and land use resistance coefficient of the landscape contribution area, calculating the surface runoff connectivity index of the pollutants from the pollution sources in the surface runoff transport path; for each pollution source corresponding to the landscape contribution area, based on the unit catchment area, topographic slope, and soil saturated hydraulic conductivity of the landscape contribution area, calculating the interflow connectivity index of the pollutants from the pollution sources in the interflow transport path. For each pollution source corresponding to the landscape contribution area, based on the aquifer permeability coefficient, effective aquifer thickness and groundwater gradient of the corresponding landscape contribution area, the baseflow connectivity index of the pollutants corresponding to the pollution source in the baseflow transport path is calculated.

[0018] The watershed management method provided in this application calculates the surface runoff connectivity index. By coupling topographic runoff, slope potential energy, and underlying surface barrier conditions, it accurately quantifies the unimpeded flow capacity of surface pollutants and objectively reflects the natural endowment differences in surface pathway pollution transport. It also calculates the interflow connectivity index. Combining catchment conditions, topographic gradient, and soil infiltration properties, it scientifically characterizes the level of pollutant migration and connectivity in lateral soil water flow, filling the gap in the quantitative characterization of interflow pathways. Finally, it calculates the baseflow connectivity index. Based on key hydrogeological parameters, it quantifies groundwater dynamics and infiltration transport conditions, accurately depicts the characteristics of long-term underground pollution migration, and improves the comprehensive evaluation system for multi-pathway connectivity.

[0019] In one optional implementation, based on the pollution source contribution allocation vector, the nitrogen load allocation vector, and the transmission cost matrix, a target optimization function constrained by information entropy is constructed, including: Construct an initial source-path coupling matrix; the initial source-path coupling matrix represents each pollution source, and its columns are surface runoff transport paths, interflow transport paths, and baseflow transport paths; the elements in the initial source-path coupling matrix... The nitrogen load contribution ratio from pollution source i via hydrological path j is represented. Based on the pollution source contribution allocation vector, nitrogen load allocation vector, transmission cost moment, and initial source-path coupling matrix, an objective optimization function is constructed with information entropy as a constraint and minimizing transmission cost as the objective. The objective optimization function is: ; The constraints are: ; in, For information entropy constraints, Π is the initial source-path coupling matrix. These are the elements in the initial source-path coupling matrix; Let λ be the transmission cost matrix, and λ be the regularization coefficient.

[0020] The watershed management method provided in this application constructs an initial source-path coupling matrix. A two-dimensional correlation framework between pollution sources and hydrological pathways is established, quantifying the initial nitrogen load allocation ratio and providing a basic variable carrier for coupled optimization solutions, thus realizing a structured expression of multi-source and multi-path relationships. An entropy constraint and cost minimization objective optimization function are constructed. Minimizing migration resistance aligns with natural transport patterns, while information entropy constraints prevent extreme allocation results. Furthermore, combining bidirectional total quantity conservation constraints significantly improves the rationality and solution stability of the nitrogen load coupled allocation results.

[0021] In one optional implementation, solving the objective optimization function to obtain the target source-path coupling matrix corresponding to the target watershed includes: transforming the objective optimization function into a solvable convex optimization function; transforming the transmission cost matrix into an exponential probability transition kernel matrix; determining initial row scaling factors and initial column scaling factors based on the initial source-path coupling matrix; setting a preset iteration stopping condition; adjusting the initial row scaling factors based on the pollution source contribution allocation vector of the exponential probability transition kernel matrix; adjusting the initial column scaling factors based on the exponential probability transition kernel matrix and the nitrogen load allocation vector; until the preset iteration stopping condition is reached, obtaining the target row scaling factors and target column scaling factors; and obtaining the target source-path coupling matrix based on the target row scaling factors and target column scaling factors.

[0022] The watershed management method provided in this application transforms the objective optimization function into a convex optimization function. This eliminates local optima, ensures the existence of a unique global optimum in the optimization model, and improves solution stability and result reliability. The transmission cost matrix is ​​converted into an exponential probability transition kernel matrix. Migration resistance is transformed into a probabilistic correlation, smoothing numerical differences, adapting to the iterative algorithm's operational logic, and reducing numerical solution errors. Initial row and column scaling factors are determined. This provides an initial correction benchmark for bidirectional equilibrium iteration, establishes a foundation for coordinated correction of sources and paths, and ensures orderly iteration startup. Preset iteration stop conditions are set. The number of iteration operations and convergence accuracy are reasonably controlled, balancing computational efficiency and simulation accuracy, and avoiding invalid loop operations. The initial row scaling factor is iteratively adjusted. Iteratively adjusting the initial column scaling factor, matching the total pollution source constraints, and correcting the source allocation weights to achieve source load conservation constraints. The initial column scaling factor is iteratively adjusted. Matching the load carrying capacity upper limit of each hydrological path, correcting the path allocation ratio, and ensuring the balance constraint of the total transport path. The target row and column scaling factors are obtained through iterative convergence. Continuous bidirectional iterative correction gradually reduces computational deviations, enabling the model results to quickly and stably converge to an equilibrium state. The source-path coupling matrix of the target is obtained by solving the problem. The optimal nitrogen load allocation ratio for multiple pollution sources and multiple hydrological pathways is accurately output, and the differential nitrogen transport coupling law is fully revealed, providing quantitative support for precise pollution control.

[0023] In one optional implementation, determining the target governance scheme for the target watershed based on the target source-path coupling matrix includes: sorting the coupling elements in the target source-path coupling matrix in descending order; calculating the proportion of each coupling element to the total nitrogen output of the target watershed; comparing the proportion of each coupling element to the total nitrogen output of the target watershed with a preset proportion threshold; identifying coupling elements with proportions greater than the preset proportion threshold as dominant coupling units; determining the initial governance scheme for the target watershed based on each dominant coupling unit; simulating each initial governance scheme to determine the nitrogen load reduction amount corresponding to each initial governance scheme; and determining the target governance scheme for the target watershed based on the nitrogen load reduction amount corresponding to each initial governance scheme.

[0024] The watershed management method provided in this application sorts the coupling elements in descending order. It quickly identifies the differences in the combined contributions of various pollution sources and hydrological pathways, highlighting key transport combinations to facilitate subsequent screening and analysis. It calculates the total nitrogen output percentage of each coupling element. It quantifies the pollution contribution weight of different source-path combinations, achieving quantitative differentiation of pollution contributions and avoiding subjective judgment. The coupling percentage is compared with a preset threshold. A unified screening standard is established to achieve graded identification of pollution combinations and accurately delineate primary and secondary pollution transport units. The dominant coupling unit is screened and determined. It accurately identifies high-contribution pollution sources and dominant migration pathways in the watershed, grasping the key points of core pollution control. An initial management plan is formulated based on the dominant coupling unit. It targets and matches key pollution combinations, customizing differentiated control measures to achieve site-specific and precise adaptation of the management plan. The nitrogen load reduction of each plan is simulated and calculated. The emission reduction efficiency of different management measures is quantified, using data to support plan evaluation and abandoning experience-based approaches. The final target management plan is determined based on the reduction amount. The management plan with the best emission reduction effect and comprehensive benefits is selected to improve the scientific nature and implementation effectiveness of watershed nitrogen pollution management. Attached Figure Description

[0025] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the first process of a watershed management method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a second process for a watershed management method according to an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0029] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0030] According to an embodiment of the present invention, a watershed management method embodiment is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0031] This embodiment provides a watershed management method that can be used in electronic devices, such as mobile phones and tablets. Figure 1 This is a flowchart of a watershed management method according to an embodiment of the present invention, such as... Figure 1 As shown, the process includes the following steps: Step S101: Obtain the pollution source contribution allocation vector corresponding to the target watershed and the nitrogen load allocation vector corresponding to each hydrological transmission path of the target watershed.

[0032] Pollution sources include chemical fertilizers, rainfall, domestic sewage, and livestock manure. Hydrological transport pathways include surface runoff transport pathways, interflow transport pathways, and baseflow transport pathways. The nitrogen load allocation vector is a one-dimensional numerical vector composed of the proportion of total nitrogen load carried by each hydrological transport pathway within the target watershed, normalized and quantified according to a fixed pathway sorting rule. It characterizes the nitrogen transport carrying capacity and background pollution load allocation weight of each of the three types of hydrological pathways: surface runoff, interflow, and baseflow. It is a fixed-path constraint vector in the source-path optimal transport model.

[0033] Specifically, the electronic device can receive the pollution source contribution allocation vector corresponding to the target watershed and the nitrogen load allocation vector corresponding to each hydrological transmission path of the target watershed, which are input by the user. It can also receive the pollution source contribution allocation vector corresponding to the target watershed and the nitrogen load allocation vector corresponding to each hydrological transmission path of the target watershed sent by other devices.

[0034] This step will be explained in detail below.

[0035] Step S102: Construct a transmission cost matrix based on the landscape connectivity index of pollutants corresponding to each pollution source.

[0036] Among them, the landscape connectivity index is used to measure the smoothness of pollutant flow in the target watershed.

[0037] Specifically, for each type of pollution source, electronic devices can calculate the landscape connectivity index by combining spatial elements such as land use, topographic slope, vegetation cover, ditches and water systems, and landscape patterns of the target watershed. The physical meaning of this landscape connectivity index is: the smoothness of the diffusion, transport, and flow of nitrogen pollutants between landscape units in the watershed. The higher the connectivity, the easier it is for pollutants to be transported across units.

[0038] Then, based on the inverse correlation between the landscape connectivity index and the transmission cost, a transmission cost matrix is ​​constructed.

[0039] This step will be explained in detail below.

[0040] Step S103: Based on the pollution source contribution allocation vector, nitrogen load allocation vector, and transmission cost matrix, construct an objective optimization function constrained by information entropy.

[0041] Specifically, electronic devices can be designed with the goal of minimizing the overall transport cost of nitrogen pollutants across the entire watershed. Information entropy regularization constraints are introduced to control the dispersion and uniformity of the source-path coupling allocation results. Then, based on the pollution source contribution allocation vector, the nitrogen load allocation vector, and the transport cost matrix, an objective optimization function is constructed.

[0042] This step will be explained in detail below.

[0043] Step S104: Solve the objective optimization function to obtain the target source-path coupling matrix corresponding to the target watershed.

[0044] Specifically, the electronic device can solve the target optimization function based on a preset solution algorithm to obtain the target source-path coupling matrix corresponding to the target watershed.

[0045] This step will be explained in detail below.

[0046] Step S105: Based on the target source-path coupling matrix, determine the target governance scheme corresponding to the target watershed.

[0047] Specifically, electronic devices can rely on the quantitative attribution results of the target source-path coupling matrix to delineate differentiated and targeted governance schemes and determine the target governance schemes corresponding to the target watersheds.

[0048] This step will be explained in detail below.

[0049] The watershed management method provided in this application obtains pollution source contribution allocation vectors and nitrogen load allocation vectors. It quantitatively decomposes nitrogen pollution from two dimensions: pollution sources and hydrological transport paths, clarifying the contribution proportions of various pollution sources and the load-bearing structure of different runoff paths. This provides a dual-boundary quantitative constraint basis for subsequent coupled analysis, avoiding singular and one-sided governance judgments. A transport cost matrix is ​​constructed based on the landscape connectivity index. The differences in pollutant migration resistance across multiple paths (surface, interflow, and baseflow) are quantified, transforming natural conditions such as topography, soil, and hydrogeology into calculable cost indicators. This objectively reflects the actual transport patterns in the watershed, improving the scientific rigor of source-path matching. An information entropy-constrained objective optimization function is constructed. With transport minimization as the core and information entropy regularization as the constraint, this approach aligns with the objective law of preferential low-resistance pollutant migration while avoiding extreme and fragmented allocation results. It ensures balanced and reasonable solution results that conform to the actual characteristics of multi-path mixed transport. Solving the optimization function yields the objective source-path coupling matrix. This approach achieves precise two-way coupling and quantification of pollution sources and hydrological pathways, quantifying the nitrogen output ratio of different pollution sources through various runoff channels, accurately identifying key pollution transport combinations, and overcoming the limitations of traditional single-source tracing that cannot distinguish transport pathways. Targeted remediation solutions are determined based on the coupling matrix. High-contribution dominant coupling units are targeted, enabling precise policy implementation for each source and pathway. Control measures are customized from both the source and migration process perspectives, improving the targeting, precision, and efficiency of watershed nitrogen pollution control and the utilization of remediation resources.

[0050] This embodiment provides a watershed management method that can be used in electronic devices, such as mobile phones and tablets. Figure 2 This is a flowchart of a watershed management method according to an embodiment of the present invention, such as... Figure 2 As shown, the process includes the following steps: Step S201: Obtain the pollution source contribution allocation vector corresponding to the target watershed and the nitrogen load allocation vector corresponding to each hydrological transmission path of the target watershed.

[0051] The sources of pollution include chemical fertilizers, rainfall, domestic sewage, and livestock manure. Hydrological transport pathways include surface runoff transport pathways, interflow transport pathways, and baseflow transport pathways.

[0052] Specifically, the step S201 above, "obtaining the pollution source contribution allocation vector corresponding to the target watershed," may include the following steps: Step S2011: Obtain the source end-member dual isotope signals of each pollution source corresponding to the target watershed and the initial watershed nitrate concentration data.

[0053] Among them, the source end-member dual isotope signal includes the source end-nitrate nitrogen isotope signal and the source end-nitrate oxygen isotope signal.

[0054] Specifically, electronic devices can delineate four typical pollution sources in the target watershed: chemical fertilizers, livestock and poultry manure, domestic sewage, and atmospheric precipitation, each as an independent pollution source, and conduct separate sample collection and indicator detection.

[0055] For each type of pollution source, electronic equipment can collect pure end-member samples that are representative of the source and have not been mixed with other pollutants, thus avoiding cross-contamination. For chemical sources: samples of mainstream fertilizers applied in the watershed and leaching solutions from the surface of farmland are collected; for livestock and poultry manure sources: fresh manure from large-scale farms and raw wastewater from livestock farming are collected; for domestic sewage sources: raw septic tank solutions from rural areas and in-situ water samples of domestic sewage from villages and towns are collected. Regarding the sources of atmospheric precipitation: collect natural precipitation samples from the entire watershed and remove interference from dry deposition impurities.

[0056] For each type of source-end component sample, electronic equipment can uniformly perform professional isotope detection, measuring the source-end nitrate nitrogen isotope signal (δ¹⁸O₁₀). 15 N); source-end nitrate oxygen isotope signal (δ) 18 O). Electronic devices can aggregate and organize the nitrogen and oxygen isotope detection results corresponding to the four types of pollution sources to form a source-specific dual isotope signal dataset for each pollution source, which can be used as the isotope fingerprint feature of the pollution source.

[0057] Electronic equipment can collect background water samples from pristine, clean sections upstream of a target watershed where significant denitrification has not occurred and where human interference is minimal. The equipment can then determine the nitrate content in the water samples using methods such as ion chromatography, obtaining initial watershed nitrate concentration data. This initial watershed nitrate concentration data represents the background nitrate concentration under natural conditions and is used for subsequent calculations of denitrification levels and isotope correction.

[0058] Step S2012: Obtain the dual isotope signals and nitrate concentration data of each preset monitoring section in the target watershed.

[0059] Each preset monitoring section meets the preset monitoring conditions; the dual isotope signal of the section includes the nitrate nitrogen isotope signal and the nitrate oxygen isotope signal of the section.

[0060] Specifically, electronic equipment can be used to deploy several pre-set monitoring sections in the main stream, tributaries, and catchment outlets of the target watershed, taking into account the distribution of the water system, the boundaries of sub-basins, and the migration paths of pollutants. The conditions corresponding to the pre-set monitoring sections include: complete cross-section confluence, coverage of the entire hydrological transport process, simultaneous monitoring of water quality and quantity, minimal instantaneous human interference, and continuous and stable sampling. Qualified sections are selected as pre-set monitoring sections.

[0061] Within a unified monitoring cycle, water samples are collected synchronously at each pre-set monitoring section to ensure uniformity in sampling time, sampling depth, and sampling method, thereby ensuring sample representativeness and accurately reflecting the pollution characteristics of the mixed water body at the section.

[0062] The electronic equipment can uniformly detect the mixed water samples collected from each preset monitoring section using an isotope mass spectrometer, and obtain the nitrate nitrogen isotope signal and the nitrate oxygen isotope signal of the section respectively.

[0063] Electronic equipment can integrate the detection results of all preset monitoring sections to form a multi-point, systematic dual isotope signal dataset, which characterizes the comprehensive isotopic features of the mixed water body after migration and transformation.

[0064] The electronic equipment can also simultaneously measure the real-time nitrate concentration of water samples from the same batch of preset monitoring sections, obtaining nitrate concentration data for each preset monitoring section. This nitrate concentration data can intuitively reflect the nitrogen pollution load level in different river sections, providing key basic parameters for subsequent fractionation coefficient fitting, quantitative calculation of denitrification intensity, and Rayleigh model correction.

[0065] Step S2013: Based on the dual isotope signals and nitrate concentration data of each preset monitoring section in the target watershed, determine the target denitrification fractionation coefficient corresponding to the target watershed.

[0066] Specifically, step S2013 above may include the following steps: Step a1: Based on the linear relationship between the nitrate nitrogen isotope signal and the nitrate concentration data of each preset monitoring section, calculate the nitrogen isotope fractionation coefficient corresponding to the target watershed.

[0067] Specifically, based on the decay law of denitrifying substances in the watershed, the electronic equipment defines the remaining nitrate ratio as the ratio of the current residual nitrate to the initial background nitrate, and calculates the remaining nitrate ratio at each preset monitoring section: ;in, The remaining nitrate percentage at the i-th preset monitoring section; This represents the nitrate concentration data corresponding to the i-th preset monitoring section; its physical meaning is to characterize the degree of residual nitrate relative to the initial background after denitrification consumption. This refers to the initial nitrate concentration data corresponding to the target watershed.

[0068] The electronic device calculates the natural logarithm of the remaining nitrate percentage for each preset monitoring section: .

[0069] Additional explanation: Within the same river basin... Under certain conditions, lnf and lnC have a linear equivalent relationship. In actual engineering calculations, lnCi can be directly used to replace lnfi for regression fitting without changing the slope (fractionation coefficient) result.

[0070] Then, the electronic device, with isotope response as the dependent variable and concentration logarithm as the independent variable, was paired cross-section by cross-section: independent variable (or Dependent variable This results in multiple sets of standardized sample pairs: .

[0071] The electronic device was fitted with a linear regression using the logarithm of nitrate concentration as the independent variable and the cross-sectional nitrate nitrogen isotope signal as the dependent variable, resulting in the following linear fitting equation: In the formula: C is the nitrate concentration at the cross section. b1 is the fitting slope, and b1 is the fitting intercept.

[0072] Finally, the slope in the linear fitting equation was determined as the nitrogen isotope fractionation coefficient corresponding to the target watershed. .

[0073] Step a2: Based on the linear relationship between the nitrate oxygen isotope signal and the nitrate concentration data of each preset monitoring section, calculate the oxygen isotope fractionation coefficient of the target watershed.

[0074] Specifically, all preset monitoring section samples that have been screened and quality controlled in step a1 are reused to ensure that the data source, sampling period and monitoring conditions are completely consistent, to avoid systematic errors and to ensure that the calculation caliber of the two types of fractionation coefficients is consistent.

[0075] The logarithmic processing of concentration was completed simultaneously using the same method as the calculation of nitrogen isotope concentration logarithm to ensure consistency of independent variable parameters and the effectiveness of cross-sectional comparison.

[0076] A linear regression model of oxygen isotopes was established with the logarithm of nitrate concentration as the independent variable and the cross-sectional nitrate oxygen isotope signal δ0 as the metric. 18 With O as the dependent variable, a linear regression equation for oxygen isotopes was obtained through fitting: In the formula: is the slope of the oxygen isotope fitting, and b2 is the corresponding intercept.

[0077] The slope of the regression equation directly characterizes the rate of change in oxygen isotope enrichment; the fitted slope is determined as the oxygen isotope fractionation coefficient. The oxygen isotope fractionation coefficient was solved.

[0078] Step a3: Based on the nitrogen isotope fractionation coefficient and the oxygen isotope fractionation coefficient, generate the target denitrification fractionation coefficient corresponding to the target watershed.

[0079] Specifically, the nitrogen isotope fractionation coefficient obtained in step a1 of electronic device integration The oxygen isotope fractionation coefficient obtained in step a2 This forms a set of matching fractionation parameters for the denitrification process in the watershed.

[0080] Electronic equipment can combine watershed hydrological conditions, denitrification environmental characteristics, and existing research experience to measure nitrogen isotope fractionation coefficients. and oxygen isotope fractionation coefficient Perform a rationality check; eliminate abnormal parameters that deviate from reasonable thresholds, and optimize parameters through mean correction and interval constraints when necessary to ensure that the fractionation coefficient conforms to the actual denitrification enrichment law of the watershed.

[0081] Finally, the validated nitrogen isotope fractionation coefficient and oxygen isotope fractionation coefficient are coupled and bound together to form the target denitrification fractionation coefficient corresponding to the target watershed. The target denitrification fractionation coefficient is a binary parameter combination that includes fractionation characteristics in both nitrogen and oxygen dimensions, uniformly characterizing the isotope enrichment and fractionation patterns of the overall denitrification process in the target watershed. The target denitrification fractionation coefficient parameter set is used for subsequent cross-sectional dual isotope signal correction and pollution source Bayesian source tracing calculations, providing core correction parameters for solving the posterior contribution probability of pollution sources.

[0082] Step S2014: Based on the source end-member dual isotope signal, the initial watershed nitrate concentration data, the cross-sectional dual isotope signal corresponding to each preset monitoring section, the cross-sectional nitrate concentration data, and the target denitrification fractionation coefficient, determine the posterior contribution probability distribution corresponding to each pollution source.

[0083] Specifically, step S2014 above may include the following steps: Step b1: Based on the initial nitrate concentration data of the watershed and the dual isotope signals of each preset monitoring section, calculate the remaining nitrate ratio of each preset monitoring section.

[0084] Specifically, based on the decay law of denitrifying substances in the watershed, the electronic equipment defines the remaining nitrate ratio as the ratio of the current residual nitrate to the initial background nitrate, and calculates the remaining nitrate ratio at each preset monitoring section: .in, The remaining nitrate percentage at the i-th preset monitoring section; This represents the nitrate concentration data corresponding to the i-th preset monitoring section; its physical meaning is to characterize the degree of residual nitrate relative to the initial background after denitrification consumption. This refers to the initial nitrate concentration data corresponding to the target watershed.

[0085] The electronic device completes the calculation for each preset monitoring section, forming a dataset of the remaining nitrate ratio corresponding to each preset monitoring section, providing core parameters for subsequent isotope calibration.

[0086] Step b2: For each preset monitoring section, based on the remaining nitrate ratio, nitrate nitrogen isotope signal, and nitrogen isotope fractionation coefficient of the preset monitoring section, the nitrate nitrogen isotope signal of the section is corrected to obtain the corrected nitrate nitrogen isotope signal of the section.

[0087] Specifically, electronic devices can cause nitrogen isotope enrichment during the denitrification process. The increase in enrichment due to fractionation needs to be subtracted in reverse to reduce the original isotope background signal before the reaction. The correction formula is as follows: .in, The corrected nitrate isotope signal of the cross section represents the true original nitrogen isotope signal of nitrate in the water body after eliminating the interference of denitrification fractionation; that is, the initial isotope fingerprint of the watershed before microbial denitrification consumption, which is the true and effective input for source tracing modeling. The nitrate nitrogen isotope signal for the preset monitoring section is already affected by denitrification isotope enrichment, resulting in a systematic shift that cannot be directly used for pollution source analysis. Electronic equipment can perform calculations on all preset monitoring sections one by one, eliminating the isotope shift caused by denitrification fractionation, and obtaining the corrected nitrate nitrogen isotope signal for each section, characterizing the true nitrogen isotope features before denitrification occurred.

[0088] Step b3: Based on the remaining nitrate ratio, nitrate oxygen isotope signal and oxygen isotope fractionation coefficient of the preset monitoring section, the nitrate oxygen isotope signal of the section is corrected to obtain the corrected nitrate oxygen isotope signal of the section.

[0089] Specifically, the electronic equipment can use the same cross-sectional sample and the same residual ratio that are completely consistent with the nitrogen isotope correction. Electronic equipment can acquire the original nitrate oxygen isotope signal δ from the cross-section. 18 O mix Oxygen isotope fractionation coefficient .

[0090] Electronic devices can use the same principle of reverse correction to deduct the enrichment shift of oxygen isotopes caused by denitrification. The correction formula is as follows: .in, The corrected section nitrate oxygen isotope signal represents the true original oxygen isotope signal of nitrate in the water body after eliminating the interference of denitrification fractionation; that is, the initial isotope fingerprint of the watershed before microbial denitrification consumption, which is the true and effective input for source tracing modeling. The nitrate oxygen isotope signal of the monitoring section was preset. However, the nitrate oxygen isotope signal of this section has been affected by the enrichment of denitrification isotopes and has a systematic shift, so it cannot be directly used for pollution source analysis.

[0091] The electronic equipment completes oxygen isotope signal correction at each preset monitoring section to obtain the corrected nitrate oxygen isotope signal. After dual-index synchronous correction, the dual isotope data of the section completely eliminates the source transformation interference in the watershed and can be directly used for multi-source mixed source tracing modeling.

[0092] Step b4 verifies that the source endmember dual isotope signals corresponding to each pollution source all conform to a normal distribution, and obtains the correspondence between pollution source type and isotope fingerprint parameters.

[0093] Specifically, electronic devices can process source-end-member dual isotope measured sample data from four major pollution sources: chemical fertilizers, livestock and poultry manure, domestic sewage, and atmospheric precipitation. For each type of pollution source, the δ¹⁸O₅... 15 N, δ 18 Normality tests (Shapiro-Wilk test and KS test) were performed to verify that the isotope signals of various source sources conform to a normal distribution, satisfying the prior distribution assumptions of the Bayesian mixture model. Then, the electronic equipment calculated the mean and standard deviation of the isotope indicators for each pollution source. , .

[0094] Electronic devices can be categorized by pollution source type and bound to the corresponding isotope mean and standard deviation parameters to form a one-to-one correspondence between pollution source type and isotope fingerprint parameters, which can then be used as prior constraint inputs for the model.

[0095] Step b5: Based on the source-end nitrate nitrogen isotope signal, the source-end nitrate oxygen isotope signal, the cross-section corrected nitrate nitrogen isotope signal, and the cross-section corrected nitrate oxygen isotope signal, construct a dual isotope simultaneous equation.

[0096] Specifically, the electronic device can use cross-sectionally corrected nitrate nitrogen isotope signals and cross-sectionally corrected nitrate oxygen isotope signals as mixed observations, use the characteristics of nitrate nitrogen isotope signals and nitrate oxygen isotope signals at each source as end-member components, and use the contribution ratio of each pollution source as the weight parameter to be determined to construct a weighted mixed equilibrium relationship.

[0097] Specifically, let p k The contribution ratio of the k-th pollution source satisfies the physical constraints: .

[0098] Then, the electronic device, combining the nitrogen and oxygen isotope indices, establishes a dual-constraint simultaneous equation: in To represent the detection error and unexplained variation in the model residuals that conform to a normal distribution, electronic devices can combine watershed emission statistics and previous source apportionment results to add interval prior constraints on the contribution ratio of some pollution sources, thus completing a fully solvable dual-isotope Bayesian simultaneous equation system.

[0099] Step b6: Based on the Markov chain Monte Carlo algorithm, solve for the posterior contribution probability distribution corresponding to each pollution source.

[0100] Specifically, before solving the Bayesian model, the electronic equipment is pre-standardized with a complete set of iterative operation parameters to avoid problems such as initial value interference, insufficient sample size, and incomparable results, thus laying the foundation for stable sampling.

[0101] Specifically, a certain number of preheating iterations are preset in the early stage. The sampling data generated in this stage is not included in the final statistics and result calculation. The core function is to discard the bias caused by the initial random assignment of the model, weaken the interference of the initial parameters on the calculation results, and allow the Markov chain to gradually enter a stable iterative state. After the preheating stage, a sufficient number of formal sampling times are set to continuously collect effective samples. A sufficient number of effective samples can ensure the integrity of the posterior distribution statistical characteristics, reduce random sampling errors, and ensure the accuracy of subsequent probability statistics and interval estimation. Multiple independent Markov chains are run simultaneously, each chain using different initial values ​​for synchronous iteration. The parallel operation of multiple chains provides a data foundation for subsequent convergence testing and result stability verification, avoiding the randomness of results caused by single-chain iteration.

[0102] After parameter configuration, the electronic device can load the core constraints and observational data required for source tracing modeling into the model, constructing a complete solution boundary. The electronic device inputs the dual-isotope normal distribution parameters of four pollution sources: fertilizer, livestock manure, domestic sewage, and atmospheric precipitation, including the mean and standard deviation of nitrogen and oxygen isotopes, as prior information for the model, limiting the reasonable range of isotope fingerprint values ​​for each pollution source. It loads the cross-sectional corrected nitrogen and oxygen isotope data after denitrification fractionation correction, serving as the actual observed true values ​​for the model and the core basis for model fitting and inverse solving. It inputs basic and artificial prior constraints on contribution ratios, including non-negative contribution ratio constraints, normalized global proportion constraints, and source interval constraints based on watershed surveys, ensuring that the solved pollution source contribution ratios conform to actual physical laws and avoiding non-physical interpretations.

[0103] Then, based on the core principles of the MCMC algorithm, and combined with random sampling and a probabilistic acceptance-rejection mechanism, continuous iterative calculations are performed. Starting with the initial contribution ratio, the electronic device, combined with prior distribution and isotopic mixing equations, randomly generates the pollution contribution ratio p for each group. kCandidate samples are selected. Based on the Bayesian posterior probability criterion, the model fitting error corresponding to the candidate samples is compared, and the acceptance probability of the candidate parameters is calculated. An acceptance-rejection mechanism is used to determine whether to retain or discard the current candidate sample, and the sampling sequence of the contribution ratio of each pollution source is continuously updated and iterated. As the iteration continues, the Markov chain gradually deviates from the random initial state and continuously approaches and converges to the true posterior probability distribution of each contribution ratio parameter.

[0104] Finally, after iteration, the Gelman-Rubin test is used to determine the convergence of multiple independent Markov chains, ensuring the reliability of the results. The electronic device can calculate the within-group and between-group variances of multiple independent chains separately, quantifying the parameter dispersion between different chains; and calculate the Gelman-Rubin statistic R, which characterizes the consistency of the multi-chain distribution. The judgment criteria are: when R < 1.1, it proves that the distribution characteristics of the multiple independent chains tend to be uniform, the iteration process is stable and converges, and the sampling results are valid and usable; if R ≥ 1.1, the chain is determined to have not converged, and the iteration count needs to be increased, the parameters adjusted, and the calculation repeated.

[0105] Under the premise of model convergence and valid sampling, electronic equipment performs statistical analysis on all valid sampled data to quantify the contribution characteristics of pollution sources. All valid sampled data for each type of pollution source contribution ratio are aggregated to form a continuous sample dataset. Based on large-sample statistics, core quantitative indicators are calculated, including the mean, median, 25th percentile, 75th percentile, and 95% confidence interval of the contribution ratio. Probability density curves are plotted based on the sample distribution characteristics to intuitively reflect the probability levels corresponding to different contribution ratios. Finally, a complete posterior contribution probability distribution for each type of pollution source is output, which can determine the most likely contribution ratio and quantify the uncertainty of the results, achieving a precise probabilistic and quantitative analysis of multi-source nitrogen pollution in the watershed.

[0106] Step S2015: Based on the posterior contribution probability distribution of each pollution source, determine the pollution source contribution allocation vector corresponding to each pollution source.

[0107] Specifically, after the MCMC algorithm iteratively converges and completes the sampling analysis, the electronic device extracts complete statistical samples of the posterior contribution probability distributions corresponding to the four pollution sources: chemical fertilizers, livestock and poultry manure, domestic sewage, and atmospheric precipitation. For each type of pollution source, valid sampling sequences are screened, all valid contribution ratio sample sets after convergence are retained, and invalid data during the warm-up period are removed to ensure the objectivity and validity of the samples.

[0108] For each type of pollution source, a unified characterization index is selected to represent the overall contribution level of that pollution source based on its posterior contribution probability distribution. The mean of the posterior distribution is typically used as the core characterization value. ,in, This represents the average contribution percentage of the k-th pollution source. This value comprehensively reflects the overall concentration level of the posterior distribution and weakens the impact of random sampling fluctuations.

[0109] Then, the electronic device can arrange the characterization contribution values ​​of the four types of pollution sources in sequence according to a preset fixed sorting rule (chemical fertilizer → livestock and poultry manure → domestic sewage → atmospheric precipitation) to form an initial one-dimensional array: This array represents the unstandardized raw contribution combination, and the sum of its elements is not necessarily strictly equal to 1. To conform to the total pollution source balance law, a normalization calculation is performed on the initial array to eliminate total bias: In the formula: q k The normalized contribution coefficient for the k-th pollution source is given; the denominator is the sum of the characteristic contribution values ​​of the four pollution sources; after normalization, it strictly satisfies: .

[0110] Finally, the electronic equipment arranges the normalized contribution coefficients of each pollution source in a unified order to construct a structured and standardized pollution source contribution allocation vector: The vector dimension corresponds one-to-one with the number of pollution sources, and each vector element uniquely corresponds to the quantitative contribution weight of a type of pollution source. Then, the electronic device stores and solidifies the generated pollution source contribution allocation vector, which serves as the fixed source-end constraint input for subsequent construction of the transmission cost matrix, establishment of the information entropy-constrained objective optimization function, and solution of the source-path coupling matrix, thereby realizing the standardized transformation of isotopic posterior analysis results into spatial coupling allocation parameters.

[0111] Specifically, the step S201 above, "obtaining the nitrogen load allocation vector corresponding to each hydrological transmission path corresponding to the target watershed," may include the following steps: Step S2016: Obtain the initial continuous daily flow data and the daily discrete nitrogen concentration data corresponding to the outlet of the target watershed within a preset time period.

[0112] Specifically, electronic devices can collect two types of basic data at the outlet of the target watershed: initial continuous daily flow data and total daily flow monitoring data (unit: m³) over a preset period (e.g., 1 year). 3 / s), reflecting the continuous changes in watershed runoff (such as a surge in flow during the rainy season and a stable flow during the dry season). Daily discrete nitrogen concentration data: Nitrogen concentration data (unit: mg / L) obtained by fixed-point sampling within a preset time period. The sampling frequency is usually monthly or quarterly (e.g., once a month, for a total of 12 discrete data points), reflecting the periodic characteristics of nitrogen concentration.

[0113] Step S2017: Separate the initial continuous daily flow data to determine the target surface flow data, target base flow data, and target soil flow data within the initial continuous daily flow data.

[0114] Specifically, the electronic device can acquire the watershed type corresponding to the target watershed. Based on the watershed type, it extracts the corresponding watershed characteristic parameters. These parameters include geomorphological parameters, land use parameters, and hydrological parameters. Based on these parameters, the first and second initial filtering core parameters are calculated using a mapping model. These parameters are then corrected based on a preset parameter range to obtain the first and second target initial filtering core parameters. Finally, based on these parameters, the initial continuous daily flow data is separated to determine the target surface flow data, target subsurface flow data, and target soil flow data within the initial continuous daily flow data.

[0115] The specific details of this step are existing technology and will not be elaborated here.

[0116] Step S2018: Select daily discrete nitrogen concentration data that has a target base flow data ratio greater than the first preset ratio and a daily nitrogen concentration fluctuation less than the preset fluctuation threshold, as the base flow nitrogen concentration end element.

[0117] Among them, the baseflow-specific nitrogen concentration endmember is used to characterize the nitrogen concentration sample corresponding to the baseflow component that is entirely recharged by groundwater.

[0118] Specifically, the electronic device can use initial continuous daily flow data as a basis to filter date periods where the target base flow percentage is greater than a first preset proportion. During these periods, the watershed hydrology is mainly characterized by slow groundwater recharge, with minimal interference from rapid surface runoff. Then, concentration screening conditions are simultaneously overlaid to filter daily discrete nitrogen concentration data where the daily fluctuation of nitrogen concentration is less than a preset fluctuation threshold, eliminating samples with abnormal concentration fluctuations caused by rainfall erosion, temporary sewage discharge, and short-term hydrological disturbances.

[0119] Electronic equipment can uniformly define daily nitrogen concentration samples that simultaneously meet the baseflow proportion threshold condition and concentration stability condition as baseflow nitrogen concentration end-members. This baseflow nitrogen concentration end-member is used to characterize the background nitrogen concentration characteristics of baseflow components from stable groundwater recharge, excluding the mixing interference of surface runoff and interflow, and serves as a dedicated concentration benchmark for baseflow load calculation.

[0120] For example, the first preset ratio is 80%, and the preset fluctuation threshold for nitrogen concentration is ±0.2 mg / L. The first preset ratio and the preset fluctuation threshold can be set according to actual conditions.

[0121] Step S2019: Select daily discrete nitrogen concentration data with a target surface flow data ratio less than the second preset ratio as end-members of soil interflow nitrogen concentration.

[0122] Specifically, the electronic device can use daily flow structure proportion data to set a second preset proportion as the upper limit threshold for surface flow proportion. The electronic device can filter daily periods where the target surface flow proportion is less than the second preset proportion; these daily periods have no heavy rainfall slope runoff, and the contribution of rapid surface runoff is extremely low. Under these hydrological conditions, watershed runoff and pollutant transport are mainly characterized by interflow through the soil layer, and the hydrological environment is relatively stable.

[0123] The daily discrete nitrogen concentration data corresponding to this type of time period are identified as endmembers of soil interflow nitrogen concentration to characterize the inherent nitrogen concentration characteristics of the soil mid-layer hydrological pathway.

[0124] For example, the second preset ratio is 15% (the upper limit of surface flow ratio). On a given day, the surface flow ratio is less than 15%, there is no heavy rainfall and slope runoff, and the watershed runoff is mainly caused by lateral soil flow. The second preset ratio can be set according to the actual situation.

[0125] Step S20110: Select daily discrete nitrogen concentration data that have a target surface flow data ratio greater than or equal to the third preset ratio and meet the preset selection event, as the surface runoff nitrogen concentration end-member.

[0126] Specifically, the electronic device can set a third preset ratio as the lower limit threshold of the surface flow proportion, and prioritize the screening of strong runoff dates where the target surface flow proportion is greater than or equal to the third preset ratio. Then, preset selection event constraints are superimposed, with typical preset selection events being surface-driven hydrological processes such as rainfall events, confluence events, and slope runoff events.

[0127] During periods when both conditions are met simultaneously, the watershed is dominated by overland runoff and rapid river confluence, and is significantly affected by surface source erosion and surface pollutant migration. Electronic devices can extract daily discrete nitrogen concentration data corresponding to these periods as end-members of surface runoff nitrogen concentration, characterizing the pollution concentration features of rapid surface transport paths.

[0128] Step S20111: Based on the target surface flow data and the baseflow nitrogen concentration endmember, calculate the daily nitrogen load sequence of the baseflow.

[0129] Specifically, the electronic equipment can uniformly use the segmented daily target base flow as the hydrological flow parameter. Then, the screened and determined baseflow nitrogen concentration endmember is introduced as a fixed concentration value to represent the stable pollutant concentration level along the baseflow path.

[0130] Electronic equipment can perform load calculations on a daily basis according to the classical hydrological load calculation formula: In the formula: Q 基流,i Let C be the target base flow rate on day i; 基 L represents the base current nitrogen concentration endmember concentration. 基流,i The daily nitrogen load of the baseflow on day i corresponding to the target baseflow is calculated continuously by electronic equipment to form a long-term series of daily nitrogen load of the baseflow, quantifying the total nitrogen pollution load output by the groundwater pathway each day.

[0131] Step S20112: Based on the target soil flow data and the soil flow nitrogen concentration endmember, calculate the daily nitrogen load sequence of the soil flow.

[0132] Specifically, the electronic device can extract daily target subsurface flow data after runoff segmentation as subsurface flow hydrological input conditions. Then, it matches the pre-screened subsurface flow nitrogen concentration endmembers as subsurface flow path characteristic concentrations.

[0133] Electronic equipment can use the same-caliber load calculation method to calculate the interflow nitrogen load in the soil daily: In the formula, Q 壤中,i For the target soil flow data on day i, C 壤中 The end-member concentration of nitrogen in the soil interflow, L 壤中,i Let be the daily nitrogen load of the interflow on the i-th day.

[0134] Electronic equipment performs continuous time-series calculations to obtain the daily nitrogen load sequence of soil interflow and quantifies the daily nitrogen output load of soil lateral transport paths.

[0135] Step S20113: Calculate the daily nitrogen load sequence of surface runoff based on the target surface flow data and the nitrogen concentration end-member of surface runoff.

[0136] Specifically, the electronic device can retrieve daily target surface flow data, corresponding to the rapid runoff volume driven by rainfall. Then, it substitutes the selected surface runoff nitrogen concentration end-members to characterize the pollutant concentration under surface scour conditions.

[0137] Daily calculation of nitrogen pollution load in surface runoff using electronic equipment: In the formula, Q 地表,i For the target surface flow data on day i, C 地表 L represents the end-member concentration of nitrogen in surface runoff. 地表,i Let be the daily nitrogen load of the surface runoff on day i.

[0138] Electronic devices perform continuous time-series calculations to generate daily nitrogen load sequences of surface runoff, which fully reflect the nitrogen pollution output patterns of surface paths during the rainfall confluence stage.

[0139] Step S20114: Based on the daily nitrogen load sequence of baseflow, daily nitrogen load sequence of interflow, and daily nitrogen load sequence of surface runoff, determine the nitrogen load allocation vector corresponding to the target watershed.

[0140] Specifically, the electronic equipment can perform time-series aggregation of the daily nitrogen load sequences of the three types of hydrological pathways, and calculate the total load within the period, using the following formula: ; L 总地表 For the periodic surface runoff nitrogen load, L 总壤中 For the interflow nitrogen load in the soil during the cycle, L 总基流 The nitrogen load is a periodic base flow.

[0141] Then, the electronic equipment calculates the total nitrogen load of the three hydrological pathways in the watershed: ; among which, L 总 The total nitrogen load corresponding to the target watershed.

[0142] Then, the electronic equipment calculates the normalized percentage of total nitrogen load for the three pathways, using the following formula: ; Wherein, v1 is the proportion of nitrogen load distribution in surface runoff during the period, v2 is the proportion of nitrogen load distribution in soil during the period, and v3 is the proportion of nitrogen load distribution in base flow during the period.

[0143] Finally, the electronic devices construct a one-dimensional standardized nitrogen load allocation vector, V=[v1,v2,v3], according to a fixed sequence of "surface runoff—interflow—baseflow". This nitrogen load allocation vector is the nitrogen load allocation vector for the target watershed, satisfying the constraints of summation of 1 and non-negativity. It quantifies the nitrogen pollution load allocation weights of the three types of hydrological transport paths, providing path-end constraints for the subsequent source-path coupling optimization model.

[0144] Step S202: Construct a transmission cost matrix based on the landscape connectivity index of pollutants corresponding to each pollution source.

[0145] Among them, the landscape connectivity index is used to measure the smoothness of pollutant flow in the target watershed.

[0146] Specifically, step S202 above may include the following steps: Step S2021: Based on the spatial distribution characteristics of each pollution source, determine the landscape contribution area corresponding to each pollution source within the target watershed.

[0147] Among them, the landscape contribution area is used to characterize the entire catchment area of ​​the receiving water body where pollutants from each pollution source can be stably transported to the receiving water body through surface runoff, interflow, or groundwater runoff within the target watershed under the constraints of natural hydrological and topographical conditions.

[0148] Specifically, the electronic device can receive spatial distribution characteristics of various pollution sources input by the user, and can also receive spatial distribution characteristics of various pollution sources sent by other devices. Based on the spatial distribution characteristics of each pollution source, the electronic device can determine the spatial location and distribution patterns of four types of pollution sources within the target watershed, and extract the spatial attributes corresponding to each pollutant. For example, chemical fertilizers are concentrated in agricultural land units such as arable land, orchards, and farmland, exhibiting a concentrated, patchy distribution; livestock and poultry manure is distributed in large-scale farms, free-range farms, and areas surrounding manure piles, exhibiting a point-like and small-area-like distribution; domestic sewage is concentrated in village and town settlements, residential areas, and urban and rural living spaces; atmospheric precipitation is evenly distributed throughout the entire area, representing a non-point source pollution input across the entire area.

[0149] Electronic devices can simultaneously collect basic spatial data of the target watershed. This basic spatial data includes land use types, pollution source location vectors, topographic elevation, slope, aspect, water system network, gully distribution, sub-watershed boundaries, and confluence paths, providing a spatial basis for zoning. The landscape contribution area refers to the entire confluence control area where pollutants from a certain type of pollution source can stably migrate, converge, and ultimately flow into the receiving water body of a river, under the constraints of topography, terrain, and natural hydrological connectivity. This excludes isolated areas with topographic barriers, low-lying and enclosed terrain, no connected water systems, and no lateral confluence conditions; only areas with effective pollutant transport capacity are retained.

[0150] Electronic equipment can perform watershed hydrological analysis based on a Digital Elevation Model (DEM), specifically including: depression filling, flow direction calculation, runoff accumulation calculation, drainage system extraction, and sub-watershed delineation. Then, using the topographic runoff direction as the core, it determines the runoff destination, migration path, and connectivity of incoming channels for each spatial grid or plot. The electronic equipment can also delineate the smallest runoff response units within the watershed, ensuring that each unit has a clearly defined downstream water transport channel.

[0151] For a single pollution source, electronic devices can pinpoint the land area to which the pollution source belongs and surrounding related landscape units. Based on surface connectivity, soil lateral infiltration conditions, and groundwater hydraulic connections, it can be determined whether surrounding plots can achieve stable transport of pollutants to the river channel via: lateral scouring transport by surface runoff; lateral infiltration transport by interflow; or groundwater recharge transport via groundwater base flow. Areas with topographic barriers, enclosed depressions, areas outside watersheds, and isolated plots without hydrological connectivity are excluded, as pollutants in these areas cannot flow into receiving water bodies and are not included in the contributing area.

[0152] Next, electronic devices can start from the core distribution area of ​​the pollution source and extend outward along natural runoff paths, waterways, slope runoff zones, and soil infiltration connectivity zones. All runoff spaces that can be controlled by the pollution source and possess hydrological transport connectivity are merged and their boundaries are standardized. This forms an independent, clearly defined spatial range for each type of pollution source, which is the landscape contribution area corresponding to that pollution source.

[0153] Finally, the electronic equipment obtained the following landscape contribution areas: fertilizer landscape contribution area, livestock and poultry manure landscape contribution area, domestic sewage landscape contribution area, and atmospheric precipitation landscape contribution area. Each area is independent of each other or spatially superimposed and compatible, and corresponds to the effective production and runoff space of its respective pollutants, providing accurate spatial calculation units for subsequent calculation of landscape connectivity index and construction of transmission cost matrix.

[0154] Step S2022: For each landscape contribution area, calculate the landscape connectivity index corresponding to the pollutants from the corresponding pollution sources in the surface runoff transport path, interflow transport path, and baseflow transport path.

[0155] Specifically, the landscape connectivity indices corresponding to surface runoff transport pathways, interflow transport pathways, and baseflow transport pathways are the surface runoff connectivity index, interflow connectivity index, and baseflow connectivity index, respectively; specifically, step S2022 above may include the following steps: Step c1: For each pollution source corresponding to the landscape contribution area, calculate the surface runoff connectivity index of the pollutants in the surface runoff transmission path based on the runoff accumulation, weighted slope and land use resistance coefficient of the landscape contribution area.

[0156] Specifically, the electronic equipment extracts core basic parameters for the landscape contribution areas corresponding to each pollution source. These core basic parameters include: runoff accumulation: characterizing the surface water flow collection capacity of the area; the higher the value, the stronger the surface water collection conditions; weighted slope: the weighted average slope within the landscape contribution area; the steeper the slope, the stronger the surface flow potential energy; and land use resistance coefficient: the resistance coefficient of different underlying surfaces (cultivated land, construction land, forest land, etc.) to the migration of surface pollutants; the stronger the underlying surface barrier, the higher the resistance coefficient. Then, based on the extracted runoff accumulation, the electronic equipment can calculate the average runoff accumulation of the landscape contribution area; based on the extracted weighted slope, it can calculate the corresponding weighted average slope of the landscape contribution area; and based on the land use resistance coefficients corresponding to forest land, grassland, cultivated land, and construction land, it assigns different values ​​to the land use resistance coefficients corresponding to forest land, grassland, cultivated land, and construction land respectively, to calculate the comprehensive land use resistance coefficient.

[0157] Then, the electronic device can construct the calculation logic with surface water flow dynamics as the positive driving factor and land use resistance as the negative limiting factor: the higher the runoff accumulation and the greater the weighted slope, the faster the surface runoff convergence speed, the stronger the slope transport capacity, and the higher the landscape connectivity; the greater the land use resistance coefficient, the stronger the obstacle to the migration of surface pollutants and the lower the surface connectivity.

[0158] Finally, the electronic device can calculate the surface runoff connectivity index based on the average cumulative runoff volume of the landscape contribution area, the weighted average slope of the landscape contribution area, and the comprehensive land use resistance coefficient of the landscape contribution area, as calculated above, using the following formula: ; in, ; ; ; in, This is a standardized index of cumulative inflow. The weighted slope standardization index, Standardize the land use resistance coefficient; I surf The surface runoff connectivity index indicates that the higher the value, the smoother the surface transport of pollutants; A acc A represents the average cumulative runoff in the landscape contribution area. acc,min This represents the minimum cumulative runoff volume across the entire watershed; it is the minimum benchmark value for the cumulative runoff volume of all spatial units within the entire watershed, used for range normalization. A acc,max S represents the maximum cumulative runoff volume across the entire basin. w The weighted average slope of the landscape contribution area reflects the driving force of slope runoff; S min S represents the minimum slope across the entire target watershed. max R represents the maximum slope across the entire target watershed.land The comprehensive land use resistance coefficient, R, for the landscape contribution area min R represents the minimum land use resistance coefficient for the entire watershed. max This represents the maximum value of the land use resistance coefficient for the entire watershed. , , These are fixed weighting coefficients for runoff accumulation, slope, and land use resistance, respectively, and their sum is 1.

[0159] Step c2: For each pollution source corresponding to the landscape contribution area, based on the unit catchment area, topographic slope and soil saturated hydraulic conductivity of the landscape contribution area, calculate the soil connectivity index corresponding to the pollutant transport path in the soil for each pollution source.

[0160] Specifically, for each pollution source corresponding to a landscape contribution area, electronic devices can extract the unit catchment area, topographic slope, and soil saturated hydraulic conductivity of the landscape contribution area.

[0161] Then, the electronic device can calculate the standardized index per unit catchment area based on the unit catchment area, using the following formula: ,in, The unit catchment area of ​​the landscape contribution zone reflects the scale of interflow recharge. The maximum value per unit catchment area in the landscape contribution area. Minimum catchment area per unit of water area contributing to the landscape.

[0162] Electronic devices can calculate the terrain slope standardization index based on the terrain slope, using the following formula: ,in, The standardized index of terrain slope. The comprehensive topographic slope of the soil layer in the landscape contribution area, calculated using the landscape contribution area corresponding to each pollution source as the statistical unit, is the core topographic driving factor controlling the lateral migration of interflow. The maximum slope of the soil layer across the entire target watershed. The minimum topographic slope of the soil layer is defined as the value within the entire target watershed.

[0163] Electronic devices can calculate the standardized index of soil saturated hydraulic conductivity based on the soil's saturated hydraulic conductivity, using the following formula: ,in, The standardized index of soil saturated hydraulic conductivity. The measured or average value of saturated hydraulic conductivity of soil in the landscape contribution area reflects soil pore development and permeability, and determines the lateral flow of soil water and the infiltration and migration capacity of nitrogen pollutants. The minimum saturated hydraulic conductivity of the soil across the entire target watershed in the landscape contribution area. The maximum value of saturated hydraulic conductivity of the soil in the entire target watershed.

[0164] Then, based on the calculated standardized index of unit catchment area, standardized index of topographic slope, and standardized index of soil saturated hydraulic conductivity, the electronic device calculates the soil flow connectivity index, using the following formula: ,in, Let λ1, λ2, and λ3 be the distribution weights of unit catchment area, topographic slope, and saturated hydraulic conductivity, respectively, satisfying λ1+λ2+λ3=1.

[0165] Step c3: For each pollution source corresponding to the landscape contribution area, calculate the baseflow connectivity index of the pollutants in the baseflow transport path based on the aquifer permeability coefficient, effective aquifer thickness and groundwater gradient of the corresponding landscape contribution area.

[0166] Specifically, for each pollution source's corresponding landscape contribution area, the electronic device can extract the aquifer permeability coefficient, effective aquifer thickness, and groundwater gradient of that area. Then, it calculates the standardized indices of the aquifer permeability coefficient, effective aquifer thickness, and groundwater gradient. The process for calculating these indices is similar to the process for calculating the standardized index of the unit catchment area, topographic slope, and soil saturated hydraulic conductivity described above, and will not be repeated here.

[0167] Then, the electronic device can calculate the baseflow connectivity index based on the calculated aquifer permeability coefficient normalization index, aquifer effective thickness normalization index, and groundwater gradient normalization index, using the following formula: Among them, I gw It is the fundamental connectivity index. The standardized index of aquifer permeability coefficient. The standardized index of the effective thickness of the aquifer. The groundwater gradient standardization index. , , The weighting coefficients for aquifer permeability coefficient, effective thickness, and hydraulic gradient are 1.

[0168] Step S2023: Calculate the transmission cost corresponding to each landscape connectivity index based on each landscape connectivity index.

[0169] Specifically, the electronic device can use the landscape contribution areas of each of the four pollution sources (chemical fertilizers / livestock manure / domestic sewage / atmospheric precipitation) as the calculation unit. It retrieves the previously obtained surface connectivity index, subsurface flow connectivity index, and baseflow connectivity index. Then, it calculates the transmission cost corresponding to each landscape connectivity index based on the following formula:

[0170] Among them, C s Cost of surface runoff transport along pathways; C r For the cost of transport along the interflow path; C g For the basestream path transmission cost, I surf It is the surface runoff connectivity index. I is the soil connectivity index. gw It is the fundamental connectivity index. This is the correction factor corresponding to the surface runoff connectivity index; This is the correction coefficient corresponding to the soil connectivity index; This is the correction coefficient corresponding to the basic current connectivity index.

[0171] Step S2024: Construct a transmission cost matrix based on each transmission cost.

[0172] Specifically, each set of "source-path" transmission costs calculated in step S2023 is sequentially filled into the corresponding positions in the matrix to obtain the transmission cost matrix:

[0173] Where, any element C in the matrix jk This represents the comprehensive transport cost of pollutants from pollution source j transported via hydrological pathway k.

[0174] Step S203: Based on the pollution source contribution allocation vector, nitrogen load allocation vector, and transmission cost matrix, construct an objective optimization function constrained by information entropy.

[0175] Specifically, step S203 above may include the following steps: Step S2031: Construct the initial source-path coupling matrix.

[0176] The initial source-path coupling matrix represents the pollution sources, with columns indicating surface runoff transport paths, interflow transport paths, and baseflow transport paths. The elements in the initial source-path coupling matrix... Characterizes the proportion of nitrogen load contribution from pollution source i through hydrological pathway j.

[0177] Specifically, electronic devices can construct a two-dimensional coupled matrix framework with pollution sources as rows and hydrological transmission paths as columns: Matrix row i: corresponds to 4 types of pollution sources in sequence: i=1 chemical fertilizer, i=2 livestock and poultry manure, i=3 domestic sewage, i=4 atmospheric precipitation; Matrix column j: corresponds to 3 types of hydrological transmission paths in sequence: j=1 surface runoff, j=2 interflow, j=3 baseflow.

[0178] Then, the electronic device constructs an initial coupling matrix: .

[0179] Matrix elements The nitrogen load contribution ratio of the i-th type of pollution source through the j-th type of hydrological transport path represents the initial allocation correlation between pollution source and hydrological path.

[0180] Electronic devices can use uniform initial values, prior experience-based initial values, or initial values ​​matched to spatial landscapes; the initial values ​​are only the starting point for iteration and do not represent the final actual allocation result; the requirement of non-negative initial values ​​must be met. ≥0, providing an initial solution variable space for subsequent optimization iterations.

[0181] Step S2032: Based on the pollution source contribution allocation vector, nitrogen load allocation vector, transmission cost moment and initial source-path coupling matrix, construct an objective optimization function with information entropy as constraint and minimum transmission cost as objective.

[0182] The objective function is: ; The constraints are: ; in, For information entropy constraints, Π is the initial source-path coupling matrix. These are the elements in the initial source-path coupling matrix; Let λ be the transmission cost matrix, and λ be the regularization coefficient.

[0183] Specifically, electronic devices can introduce four types of core inputs: source-side constraint vectors: Pollution source contribution allocation vector; path-end constraint vector: Nitrogen load allocation vector resistance cost matrix: Source-path transmission cost matrix. Variable to be determined: Source-path coupling matrix Π.

[0184] Electronic devices can prioritize minimizing the overall transport cost of all pollution sources via various hydrological pathways, reflecting the objective law that watershed pollutants preferentially migrate along low-resistance, highly connected pathways. Then, an information entropy regularization term is introduced as a constraint to control the dispersion of the allocation results. A higher entropy value results in a more balanced allocation across pathways, avoiding excessive concentration of results in a single channel; it also prevents model overfitting and extreme allocation results, improving the rationality and stability of the coupled allocation. Finally, a multi-objective single-substitution optimization function is formed using the minimum cost + entropy regularization smoothing constraint.

[0185] The standard form of the objective function is: ; in,

[0186] Among them, the first item The total transmission cost across the entire domain is represented, and the optimization direction is to minimize it. H(Π) is the source-path allocation structure information entropy; λ is the entropy regularization coefficient, balancing the weights of the cost term and the entropy constraint term; the negative sign indicates that maximizing the information entropy is equivalent to subtracting the entropy term in the minimum value model.

[0187] The constraints are: ; Article 1: Source of Constraints and Constraints The sum of the proportions of the same pollution source allocated to the three pathways equals the overall contribution percentage q of that pollution source. i ; Ensure that the total output load at the source is kept constant and that the total amount at the source does not become distorted.

[0188] The second constraint path list and constraints The sum of the distribution ratios of all pollution sources along the same path is equal to the nitrogen load ratio p of that hydrological path. j To ensure the conservation of the total hydrological load and match the actual hydrological load structure of the basin.

[0189] Article 3 Non-negativity Constraint The allocation ratio of any pollution source-path coupling is not negative, thus eliminating non-physical phenomena such as negative contributions and reverse transport.

[0190] Under the constraints of source and path conservation and non-negative hard boundary allocation, electronic devices aim to minimize the overall transport resistance of pollutants. By weakening extreme allocations and optimizing structural rationality through information entropy regularization, a closed, solvable, and watershed-compliant constrained optimization model is constructed. This optimization function provides a complete mathematical model for subsequent iterative solutions to the optimal source-path coupling matrix, enabling accurate calculations from single-source contribution and single-path load to bidirectional quantitative coupling allocation between sources and paths.

[0191] Step S204: Solve the objective optimization function to obtain the target source-path coupling matrix corresponding to the target watershed.

[0192] Specifically, step S204 above may include the following steps: Step S2041: Transform the objective optimization function into a solvable convex optimization function.

[0193] Specifically, electronic devices can transform maximizing information entropy into minimizing negative entropy, thus unifying the "minimization" optimization paradigm: .

[0194] Then, a regularization coefficient λ is introduced to balance the weights of "minimum cost" and "entropy balance": the larger λ is, the more uniform and smooth the distribution results; the smaller λ is, the more the results are concentrated on low-cost paths.

[0195] Electronic devices can utilize the smooth and differentiable properties of the entropy function to make the objective function continuous, first-order differentiable, and second-order strictly positive definite within the feasible region, thus completely eliminating piecewise abrupt changes and non-convex oscillatory components.

[0196] Final standard convex optimization form: By combining linear equality constraints with nonnegativity constraints, a strict convex optimization standard normal form with linear constraints is formed.

[0197] Step S2042: Convert the transmission cost matrix into an exponential probability transition kernel matrix.

[0198] Specifically, the electronic device can retrieve the source-path transmission cost matrix C. ij Based on the classical transformation rule of entropy regular optimal transmission, and using exponential decay mapping, the cost matrix is ​​transformed into a kernel matrix: Among them, C ij Let λ represent the source-path transmission cost, and λ be the information entropy regularization coefficient. The higher the cost, the smaller the exponential result, and the lower the corresponding coupling allocation probability. Based on the above formula, electronic devices can obtain the exponential probability transition kernel matrix K. The exponential probability transition kernel matrix represents the inherent transition probability basis of different pollution sources migrating to hydrological paths and is the core operation matrix of the Sinkhorn iteration.

[0199] Step S2043: Based on the initial source-path coupling matrix, determine the initial row scaling factor and the initial column scaling factor.

[0200] Specifically, the line scaling factor u i Characterizing the proportional correction factor for each pollution source; column scaling factor v j The proportional correction coefficients represent the corresponding hydrological transmission paths.

[0201] Electronic devices can use the initial source-path coupling matrix Πij Based on this, and combined with the prior boundaries of the source contribution vector and path load vector, initialize a set of uniform or unit initial values: , The initial scaling factor is the starting correction factor for iterative calculations, used to continuously adjust the weighting of sources and paths to achieve bidirectional total balance.

[0202] Step S2044: Set the preset iteration stop condition.

[0203] Specifically, the electronic device can pre-set a preset iteration stop condition. This preset iteration stop condition could be: the maximum deviation between the row coefficients and column coefficients of two consecutive iterations is less than a convergence threshold (e.g., 10). -6 ); The overall change in the source-path coupling matrix elements is less than the preset error; a maximum number of iterations is set to prevent infinite loops; the iteration is terminated when any condition is met, ensuring a balance between computational efficiency and solution accuracy.

[0204] Step S2045: Adjust the initial row scaling factor based on the pollution source contribution allocation vector of the exponential probability transition kernel matrix and the sum of the two matrices.

[0205] Specifically, electronic devices can be configured based on the exponential probability transition kernel matrix K and the pollution source contribution allocation vector q. i Current column scaling factor v j Based on the Sinkhorn row balancing iteration formula, the correction coefficients for each pollution source row are updated sequentially: By using the proportion of total contribution from each pollution source as a constraint, the row coefficient is adjusted to ensure that the sum of all path allocations matches the upper limit of the total source load, thus achieving the source load conservation constraint.

[0206] Step S2046: Adjust the initial column scaling factor based on the exponential probability transition kernel matrix and the nitrogen load allocation vector.

[0207] Specifically, the electronic device can transfer the kernel matrix K based on the exponential probability transfer and the nitrogen load allocation vector p. j Updated row scaling factor u i Perform a column balancing iteration update to adjust the initial column scaling factor, using the following formula: Using the nitrogen load carrying capacity ratio of each hydrological path as a constraint, correction coefficients are applied to ensure that the sum of the proportions of all pollution sources flowing into the path matches the total path load, thus achieving the load conservation constraint at the hydrological path ends.

[0208] Step S2047 continues until the preset iteration stop condition is met, obtaining the target row scaling factor and the target column scaling factor.

[0209] Specifically, the electronic device alternately updates row and column coefficients in a loop. Each iteration continuously reduces the computational deviation, gradually approaching a bidirectional equilibrium state. The iteration stops when the coefficient fluctuations and matrix changes meet the convergence requirements. Finally, the target row scaling coefficients after convergence and stabilization are output. scaling factor of target column .

[0210] Step S2048: Based on the target row scaling factor and the target column scaling factor, obtain the target source-path coupling matrix.

[0211] Specifically, the electronic device can calculate the optimal coupling allocation ratio by element-wise multiplication based on the target row scaling factor and the target column scaling factor: The target source-path coupling matrix is ​​obtained. This target source-path coupling matrix fully satisfies the three constraints: .

[0212] This target source-path coupling matrix fully quantifies the nitrogen load distribution ratio of four types of pollution sources through surface runoff, interflow, and baseflow, achieving both optimal transmission cost and stable distribution structure, and providing a quantitative basis for differentiated watershed management solutions.

[0213] Step S205: Based on the target source-path coupling matrix, determine the target governance scheme corresponding to the target watershed.

[0214] Specifically, step S205 above may include the following steps: Step S2051: Sort the coupling elements in the target source-path coupling matrix in descending order.

[0215] Specifically, electronic devices can extract all coupling elements in the target source-path coupling matrix. Each element uniquely corresponds to the nitrogen load coupling allocation ratio of a pollution source i and a hydrological transport path j.

[0216] Electronic devices can aggregate all elements of a two-dimensional matrix into a one-dimensional dataset, and then sort them in descending order of value. This allows for the placement of high-contribution coupling units at the beginning and low-contribution units at the end, providing a sorting basis for selecting key coupling relationships.

[0217] Step S2052: Calculate the proportion of each coupling element in the total nitrogen output of the target watershed.

[0218] Specifically, electronic equipment can statistically analyze the total nitrogen output load across the entire target watershed as a baseline for total output.

[0219] For each "pollution source-hydrological pathway" coupling unit, electronic devices can be paired one by one based on the coupling ratio and the corresponding load level. Calculate its actual proportion in the total nitrogen output load of the entire watershed: Among them, R ij L represents the nitrogen output percentage of the ij-th coupling unit; ij L represents the actual nitrogen load output corresponding to this source-path combination. total The total nitrogen output load of the target watershed is used. The pollution contribution weight of different coupling combinations is quantified by proportion to distinguish the primary and secondary transport relationships.

[0220] Step S2053: Compare the proportion of each coupling element in the total nitrogen output of the target watershed with the preset proportion threshold.

[0221] Specifically, electronic devices can pre-set a preset percentage threshold based on watershed management requirements and pollution load classification standards. This preset percentage threshold serves as a critical value for classifying the strength of pollution contribution and is used to screen key control units.

[0222] The electronic device can calculate the proportion R of each coupling unit obtained in step S2052. ij Each element is compared to a preset threshold for size judgment. A hierarchical screening of all source-path coupling combinations is completed, dividing units into high-proportion and low-proportion units.

[0223] Step S2054: Determine the coupling elements whose proportion is greater than the preset proportion threshold as the dominant coupling units.

[0224] Specifically, electronic devices can define source-path coupling elements whose nitrogen output percentage exceeds a preset threshold as dominant coupling units. A dominant coupling unit is the combination of "critical pollution sources and critical transport pathways" that contributes the most to nitrogen pollution output and has the greatest impact on overall water quality within the target watershed. Low-percentage, non-dominant coupling units are treated as secondary control targets and are not included in the core governance scope, thus achieving precise focus.

[0225] Step S2055: Based on each dominant coupling unit, determine the initial governance scheme corresponding to the target watershed.

[0226] Specifically, electronic devices can analyze the binary combination relationship of each dominant coupling unit to identify the core pollution source type and the dominant hydrological transport pathway.

[0227] Differentiated initial remediation plans are matched for different combinations. For example, for agricultural fertilizers – dominated by surface runoff: ecological ditches, farmland buffer zones, and reduced fertilizer application control; for livestock and poultry manure – dominated by interflow: manure resource utilization, soil improvement, and seepage prevention measures; for domestic sewage – dominated by baseflow: interception and collection of sewage, groundwater pollution prevention, and in-situ remediation. Targeted control measures are matched around all dominant coupling units to form multiple initial remediation plans. The initial plans are preliminary plans for targeted measures, focusing on high-contribution pollution combinations.

[0228] Step S2056: Simulate each initial treatment scheme to determine the nitrogen load reduction corresponding to each initial treatment scheme.

[0229] Specifically, electronic devices can first rely on existing watershed spatial data, hydrological monitoring data, and pollution source tracing results to construct a comprehensive, coupled watershed nitrogen load simulation system. This system establishes a unified model framework, defines simulation boundaries, computational units, and time scales, clarifies the overall calculation rules for nitrogen generation, migration, transformation, and output, and provides a unified operating platform for multi-scheme simulations, ensuring complete consistency in the comparison criteria between different treatment schemes. The specific process of constructing the comprehensive, coupled watershed nitrogen load simulation system is not the subject of this application and is existing technology in the field; therefore, it will not be described in detail here.

[0230] Then, the electronic equipment can input three core basic parameters into the simulation system based on actual watershed monitoring data, experimental parameters, and industry standard parameters, completing the configuration of the model's basic database. These include hydrological parameters such as daily flow, base flow, soil flow, surface runoff, topographic slope, soil properties, aquifer characteristics, and runoff patterns, simulating the natural runoff and water transport processes of the watershed; pollution input parameters such as emission intensity of various pollution sources, source nitrogen output baseline, pollution background concentration in each landscape contribution area, and source contribution ratio, characterizing the initial input level of nitrogen pollution; and migration and transformation parameters such as nitrogen deposition, adsorption and desorption, nitrification and denitrification, seepage migration, along-path attenuation, and river degradation, reconstructing the natural attenuation and biochemical transformation patterns of nitrogen in the surface, soil, and groundwater through multiple pathways. Through the input of all parameters, the model's baseline conditions are accurately reproduced, ensuring that the simulation results closely match the actual situation of the watershed.

[0231] For each initial treatment plan formulated based on the dominant coupling unit, the core control indicators of the plan are extracted and uniformly substituted into the nitrogen load simulation model: control intensity parameters are entered, such as the pollution reduction ratio at the source, the reduction in fertilizer application, the sewage collection rate, the intensity of livestock control, and the intensity of non-point source control; engineering measure parameters are entered, such as the buffer zone interception coefficient, the purification efficiency of the ecological ditch, the leakage blocking intensity, the groundwater remediation coefficient, and the removal capacity of the interception project; the control effect of different treatment measures is quantified into calculation parameters that the model can recognize, so as to realize the digital and model-based expression of the measures.

[0232] Under the premise of keeping hydrological, climatic, and natural transformation conditions constant, the controlled variable method was used for separate calculations. The control parameters corresponding to each initial treatment scheme were activated separately, simulating the changes throughout the entire process after the implementation of treatment measures, including nitrogen source emission reduction, interception and blockage along the route, pathway migration disruption, and enhanced biochemical purification. The changes in nitrogen transport along three transport pathways—surface runoff, interflow, and baseflow—were quantitatively extrapolated, fully reproducing the differences in pollution transport before and after treatment.

[0233] Next, the electronic equipment compares the simulation results of the untreated baseline conditions with the post-treatment conditions of each scheme, and performs quantitative calculations item by item. The total nitrogen output load before treatment is calculated by subtracting the total nitrogen output load after treatment to obtain the absolute reduction volume; the relative reduction ratio is calculated based on the current baseline load; at the same time, the reduction effects of different pollution sources and different hydrological pathways are distinguished to clarify the targeted emission reduction capabilities of each measure.

[0234] Finally, through horizontal comparison of multiple schemes, the adaptability and actual effectiveness of different types of governance measures were quantified. The interception and emission reduction capacity of ecological interception and non-point source control measures for surface runoff-dominant units was assessed; the blocking and emission reduction effects of soil improvement and infiltration blocking measures for interflow-dominant units were assessed; and the long-term purification level of source interception and groundwater remediation measures for baseflow-dominant units was assessed. Data quantification replaced subjective experience-based judgments, eliminating the defects of experience-based and qualitative policy implementation, and ensuring that governance measures matched the key coupled pollution characteristics of the watershed.

[0235] Step S2057: Based on the nitrogen load reduction amount corresponding to each initial treatment scheme, determine the target treatment scheme corresponding to the target watershed.

[0236] Specifically, electronic devices can collect multi-dimensional indicators such as nitrogen load reduction, treatment cost, implementation difficulty, and ecological benefits for each initial treatment scheme. Nitrogen reduction capacity is used as the core evaluation indicator, while also considering engineering feasibility and economic rationality. Treatment combinations with the optimal reduction effect and highest overall benefits are compared and selected. This integration and optimization forms the final target watershed treatment scheme that coordinates the overall situation and targets key coupled units. This achieves a closed-loop process from pollution source tracing and pathway analysis → key unit identification → differentiated policy implementation → effect optimization.

[0237] The watershed management method provided in this application acquires dual isotope signals from the source components of various pollution sources and initial watershed nitrate concentration data. It accurately establishes a dedicated isotope fingerprint database for various pollution sources, locking in the background characteristics of pollution sources and providing standard prior data for subsequent source tracing modeling, ensuring the uniqueness of the source analysis benchmark. It acquires dual isotope signals and nitrate concentration data from monitoring sections. Based on compliant monitoring sections, it forms an in-situ measured dataset for the watershed, fully capturing the actual isotope characteristics and concentration changes of nitrogen in the water body, truly reflecting the current state of mixed pollution in the watershed, and ensuring that the analysis results are consistent with reality. Based on the linear relationship between nitrogen isotopes and nitrate concentrations at the sections, it calculates the nitrogen isotope fractionation coefficient. Based on the objective change patterns of the in-situ monitoring data, it accurately quantifies the degree of nitrogen isotope enrichment caused by denitrification, truly reflecting the fractionation response characteristics of the nitrogen transformation process in the watershed. Based on the linear relationship between oxygen isotopes and nitrate concentrations at the sections, it calculates the oxygen isotope fractionation coefficient. This study supplements oxygen isotope fractionation characteristics, improves the dual-index fractionation characterization system, overcomes the limitations of single isotope analysis, and enhances the completeness of the endogenous transformation process characterization. It couples nitrogen and oxygen isotope fractionation coefficients to generate target denitrification fractionation coefficients. By integrating dual isotope synergistic fractionation characteristics, it forms a basin-specific comprehensive fractionation parameter, effectively correcting signal biases caused by hydrological transformation and significantly improving the accuracy and reliability of subsequent pollution source contribution analysis and quantitative calculations. Then, it calculates the remaining nitrate proportion at each monitoring section. This quantitatively characterizes the residual nitrate degradation level in the basin, quantifies the degree of denitrification consumption, and provides core proportional parameters for isotope signal bias correction. It corrects the nitrate nitrogen isotope signal at the monitoring section. It eliminates nitrogen isotope enrichment interference caused by denitrification fractionation, restores the original nitrogen isotope background characteristics of the mixed water body, and improves the authenticity of the source tracing data. It also corrects the nitrate oxygen isotope signal at the monitoring section. Simultaneously, it corrects oxygen isotope fractionation offset issues, improves the dual isotope correction system, and eliminates signal distortion caused by endogenous transformation. Verify the normal distribution of isotopes at the source and establish fingerprint correspondences. Clarify the prior distribution characteristics of isotopes for various pollution sources, ensuring they meet the input requirements of Bayesian models and that prior parameter settings are reasonable and standardized. Construct dual-isotope simultaneous equations. Establish a mass balance equation based on nitrogen and oxygen dual isotope constraints, limiting the solution interval in multiple dimensions to reduce ambiguity and error in multi-source analysis. Use the MCMC algorithm to solve for the posterior contribution probability distribution. Achieve probabilistic inversion of pollution source contributions, quantify the uncertainty of analysis results, overcome the limitations of traditional fixed-value calculations, and make source tracing results more scientific and robust.

[0238] Then, daily flow and daily nitrogen concentration data at the watershed outlet were acquired. Hydrological and water quality data were collected synchronously at unified cross-sections to ensure data source matching, providing a complete basic data source for runoff segmentation and multi-path concentration and load analysis. Initial continuous daily flow was segmented into multiple components. This achieved refined breakdown of total flow, accurately distinguishing between surface runoff, interflow, and baseflow hydrological transport pathways, and clarifying the differences in water volume proportions of different runoff generation mechanisms. Baseflow nitrogen concentration end-members were constructed by selecting samples from stable periods. To avoid interference from rainfall and short-term hydrological disturbances, the background concentration characteristics of groundwater were purified, ensuring the purity and representativeness of baseflow concentration samples. Interflow nitrogen concentration end-members were constructed by selecting samples with low surface area ratios. This eliminated interference from surface scour pollution, accurately reflecting the inherent nitrogen concentration level of lateral interflow in the soil, and achieving independent characterization of mid-level pathway concentrations. Surface runoff end-members were constructed by selecting samples with high surface area ratios and rainfall events. By identifying typical slope runoff and scour periods, the characteristics of surface runoff non-point source pollution concentrations are accurately depicted, aligning with the actual patterns of pollution transport during heavy rainfall. Daily nitrogen load of baseflow is calculated using baseflow and concentration end-members. The long-term stable nitrogen pollution load from groundwater is quantitatively quantified, enabling time-series accounting of pollution output along baseflow pathways. Daily nitrogen load of interflow is calculated using interflow and concentration end-members. The nitrogen load from lateral migration in the middle soil layer is accurately calculated, improving the quantitative accounting system for intermediate hydrological pathway pollution. Daily nitrogen load of surface runoff is calculated using surface flow and concentration end-members. Short-term surface pollution load driven by rainfall scour is effectively quantified, reconstructing key pollution output characteristics during the flood season. Multi-path loads are aggregated to determine the nitrogen load allocation vector. The proportions of nitrogen load from surface, interflow, and baseflow are standardized and quantified, forming a quantitative constraint vector along the pathway dimension, providing reliable boundary conditions for subsequent source-path coupling optimization modeling. Landscape contribution areas corresponding to each pollution source are delineated. By combining topographic and hydrological connectivity, the effective catchment area of ​​pollutants is accurately delineated, ineffective closed areas are eliminated, and the actual pollution generation and transport spatial range of various pollution sources is clearly defined, avoiding calculation bias caused by generalization of spatial range. Landscape connectivity indices for surface, interflow, and baseflow are calculated for each path. From multiple dimensions of topography, soil, and hydrogeology, the smoothness of pollutant migration in three types of hydrological paths is quantified, objectively reflecting the differences in natural barriers and connectivity among different transport channels. The transport cost of each path is derived from the landscape connectivity index. This achieves a quantitative transformation of connectivity characteristics into resistance costs, unifies the quantification standard, and intuitively represents the strength of migration resistance of pollutants along different transport paths. A source-path dimension transport cost matrix is ​​constructed. A structured and standardized resistance dataset is formed, fully representing the matching resistance relationship between multiple pollution sources and multiple hydrological paths, providing a precise quantitative foundation for subsequent optimization model construction and coupling analysis.

[0239] Next, an initial source-path coupling matrix is ​​constructed. A two-dimensional correlation framework between pollution sources and hydrological pathways is established to quantify the initial nitrogen load allocation ratio, providing a basic variable carrier for coupled optimization solutions and realizing a structured expression of multi-source and multi-path relationships. An entropy constraint and cost minimization objective optimization function is constructed. Minimizing migration resistance aligns with natural transport patterns, while information entropy constraints prevent extreme allocation results. Furthermore, combining bidirectional total quantity conservation constraints significantly improves the rationality and solution stability of the nitrogen load coupled allocation results.

[0240] The objective optimization function is transformed into a convex optimization function. This eliminates local optima, ensures the existence of a unique global optimum in the optimization model, and improves solution stability and result reliability. The transmission cost matrix is ​​converted into an exponential probability transition kernel matrix. Migration resistance is transformed into a probabilistic correlation, smoothing numerical differences, adapting to the iterative algorithm's operational logic, and reducing numerical solution errors. Initial row and column scaling factors are determined. This provides an initial correction benchmark for bidirectional equilibrium iteration, establishes a foundation for coordinated correction of sources and paths, and ensures orderly iteration startup. Preset iteration stop conditions are set. The number of iteration operations and convergence accuracy are reasonably controlled, balancing computational efficiency and simulation accuracy, and avoiding invalid loop operations. The initial row scaling factor is iteratively adjusted. Adapting to the total pollution source constraints, the source allocation weights are corrected successively to achieve source load conservation constraint matching. The initial column scaling factor is iteratively adjusted. Matching the load carrying capacity upper limit of each hydrological path, the path allocation ratio is corrected to ensure the total transport path balance constraint. The target row and column scaling factors are obtained through iterative convergence. Continuous bidirectional iterative correction gradually reduces computational deviations, enabling the model results to quickly and stably converge to an equilibrium state. The target source-path coupling matrix is ​​obtained by solving. It accurately outputs the optimal nitrogen load allocation ratio for multiple pollution sources and multiple hydrological pathways, fully reveals the coupling law of differentiated nitrogen transport, and provides quantitative support for precise pollution control.

[0241] Finally, the coupling elements are sorted in descending order. This quickly identifies the differences in the combined contributions of various pollution sources and hydrological pathways, highlighting key transport combinations to facilitate subsequent screening and analysis. The total nitrogen output percentage of each coupling element is calculated. The pollution contribution weight of different source-pathway combinations is quantified to achieve quantitative differentiation of pollution contributions and avoid subjective judgment. The coupling percentage is compared with a preset threshold. A unified screening standard is established to achieve graded identification of pollution combinations and accurately delineate primary and secondary pollution transport units. The dominant coupling unit is screened and determined. High-contribution pollution sources and dominant migration pathways in the watershed are accurately identified, grasping the key points of core pollution control. Initial treatment plans are developed based on the dominant coupling units. Targeted matching of key pollution combinations is used to customize differentiated control measures, achieving site-specific and precise adaptation of treatment plans. The nitrogen load reduction of each plan is simulated and calculated. The emission reduction efficiency of different treatment measures is quantified to support plan evaluation with data, abandoning experience-based approaches. The final target treatment plan is determined based on the reduction amount. The treatment plan with the best emission reduction effect and the best overall benefits is selected to improve the scientific nature and implementation effectiveness of watershed nitrogen pollution control.

[0242] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A watershed management method, characterized in that, The method includes: Obtain the pollution source contribution allocation vector corresponding to the target watershed and the nitrogen load allocation vector corresponding to each hydrological transport path of the target watershed; the pollution sources include chemical fertilizers, rainfall, domestic sewage and livestock manure; the hydrological transport paths include surface runoff transport paths, interflow transport paths and baseflow transport paths. A transport cost matrix is ​​constructed based on the landscape connectivity index of the pollutants corresponding to each pollution source; the landscape connectivity index is used to determine the smoothness of the flow of the pollutants in the target watershed. Based on the pollution source contribution allocation vector, the nitrogen load allocation vector, and the transmission cost matrix, a target optimization function constrained by information entropy is constructed. Solving the objective optimization function yields the target source-path coupling matrix corresponding to the target watershed; Based on the target source-path coupling matrix, the target governance scheme corresponding to the target watershed is determined.

2. The method according to claim 1, characterized in that, The process of obtaining the pollution source contribution allocation vector corresponding to the target watershed includes: Acquire the source end-member dual isotope signals corresponding to each pollution source in the target watershed and the initial watershed nitrate concentration data; the source end-member dual isotope signals include source end-nitrate nitrogen isotope signals and source end-nitrate oxygen isotope signals; The cross-sectional dual isotope signals and nitrate concentration data of each preset monitoring section in the target watershed are obtained; wherein each preset monitoring section meets preset monitoring conditions; the cross-sectional dual isotope signals include cross-sectional nitrate nitrogen isotope signals and cross-sectional nitrate oxygen isotope signals. Based on the dual isotope signals and nitrate concentration data of each preset monitoring section in the target watershed, the target denitrification fractionation coefficient corresponding to the target watershed is determined. Based on the source end-member dual isotope signal, the initial watershed nitrate concentration data, the section dual isotope signal corresponding to each of the preset monitoring sections, the section nitrate concentration data, and the target denitrification fractionation coefficient, the posterior contribution probability distribution corresponding to each of the pollution sources is determined. Based on the posterior contribution probability distribution corresponding to each pollution source, the pollution source contribution allocation vector corresponding to each pollution source is determined.

3. The method according to claim 2, characterized in that, The determination of the target denitrification fractionation coefficient for the target watershed based on the cross-sectional dual isotope signals and nitrate concentration data of each preset monitoring section in the target watershed includes: Based on the linear relationship between the nitrogen isotope signal of nitrate at each preset monitoring section and the nitrate concentration data at the section, the nitrogen isotope fractionation coefficient of the target watershed is calculated. Based on the linear relationship between the nitrate oxygen isotope signal and the nitrate concentration data of each preset monitoring section, the oxygen isotope fractionation coefficient of the target watershed is calculated. Based on the nitrogen isotope fractionation coefficient and the oxygen isotope fractionation coefficient, the target denitrification fractionation coefficient corresponding to the target watershed is generated.

4. The method according to claim 2, characterized in that, The determination of the posterior contribution probability distribution corresponding to each pollution source based on the source end-member dual isotope signal, the initial watershed nitrate concentration data, the section dual isotope signal corresponding to each of the preset monitoring sections, the section nitrate concentration data, and the target denitrification fractionation coefficient includes: Based on the initial watershed nitrate concentration data and the dual isotope signals of each preset monitoring section, the remaining nitrate ratio of each preset monitoring section is calculated. For each of the preset monitoring sections, based on the remaining nitrate ratio, the nitrate nitrogen isotope signal of the section, and the nitrogen isotope fractionation coefficient corresponding to the preset monitoring section, the nitrate nitrogen isotope signal of the section is corrected to obtain the corrected nitrate nitrogen isotope signal of the section. Based on the remaining nitrate ratio, the oxygen isotope signal of nitrate at the preset monitoring section, and the oxygen isotope fractionation coefficient, the oxygen isotope signal of nitrate at the preset monitoring section is corrected to obtain the corrected oxygen isotope signal of nitrate at the section. The source endmember dual isotope signals corresponding to each pollution source were verified to conform to a normal distribution, and the correspondence between pollution source type and isotope fingerprint parameters was obtained. Based on the source-end nitrate nitrogen isotope signal, the source-end nitrate oxygen isotope signal, the cross-section corrected nitrate nitrogen isotope signal, and the cross-section corrected nitrate oxygen isotope signal, a dual isotope simultaneous equation is constructed. Based on the Markov chain Monte Carlo algorithm, the posterior contribution probability distribution corresponding to each pollution source is solved.

5. The method according to claim 1, characterized in that, Obtaining the nitrogen load allocation vector corresponding to each hydrological transport path of the target watershed includes: Acquire the initial continuous daily flow data and the daily discrete nitrogen concentration data corresponding to the outlet of the target watershed within a preset time period; The initial continuous daily flow data is separated to determine the target surface flow data, target base flow data, and target soil flow data within the initial continuous daily flow data. The daily discrete nitrogen concentration data that accounts for a greater than a first preset proportion and whose daily nitrogen concentration fluctuation is less than a preset fluctuation threshold are selected as the baseflow nitrogen concentration end-member; the baseflow-specific nitrogen concentration end-member is used to characterize the nitrogen concentration sample corresponding to the baseflow component that is entirely recharged by groundwater. The daily discrete nitrogen concentration data with a proportion of the target surface flow data that is less than the second preset proportion are selected as the end-member of the soil interflow nitrogen concentration. The daily discrete nitrogen concentration data that accounts for a proportion greater than or equal to a third preset proportion and satisfies a preset selection event are selected as the surface runoff nitrogen concentration end-member. Based on the target surface flow data and the baseflow nitrogen concentration endmember, calculate the daily nitrogen load sequence of the baseflow. Based on the target soil flow data and the soil flow nitrogen concentration endmember, the daily nitrogen load sequence of the soil flow is calculated. Based on the target surface flow data and the surface runoff nitrogen concentration end-member, calculate the daily nitrogen load sequence of surface runoff; Based on the daily nitrogen load sequence of the baseflow, the daily nitrogen load sequence of the interflow, and the daily nitrogen load sequence of the surface runoff, the nitrogen load allocation vector corresponding to the target watershed is determined.

6. The method according to claim 1, characterized in that, The step of constructing a transport cost matrix based on the landscape connectivity index of the pollutants corresponding to each pollution source includes: Based on the spatial distribution characteristics of each pollution source, a landscape contribution area corresponding to each pollution source is determined within the target watershed. The landscape contribution area is used to characterize the entire catchment area of ​​the receiving water body within the target watershed, under the constraints of natural hydrological and topographical conditions, where pollutants from each pollution source can be stably transported to the receiving water body through surface runoff, interflow, or groundwater runoff. For each of the aforementioned landscape contribution areas, calculate the landscape connectivity index corresponding to the pollutants from the pollution sources in the corresponding landscape contribution areas in the surface runoff transport path, interflow transport path, and baseflow transport path, respectively. Based on each of the aforementioned landscape connectivity indices, calculate the transmission cost corresponding to each of the aforementioned landscape connectivity indices; Based on each of the aforementioned transmission costs, the transmission cost matrix is ​​constructed.

7. The method according to claim 6, characterized in that, The landscape connectivity indices corresponding to the surface runoff transport pathway, interflow transport pathway, and baseflow transport pathway are respectively the surface runoff connectivity index, interflow connectivity index, and baseflow connectivity index; the calculation of the landscape connectivity indices corresponding to the pollutants of the pollution source in each landscape contribution area in the surface runoff transport pathway, interflow transport pathway, and baseflow transport pathway includes: For each pollution source corresponding to the landscape contribution area, the surface runoff connectivity index of the pollutants in the surface runoff transport path corresponding to the pollution source is calculated based on the runoff accumulation, weighted slope and land use resistance coefficient of the landscape contribution area. For each pollution source corresponding to the landscape contribution area, based on the unit catchment area, topographic slope and soil saturated hydraulic conductivity of the landscape contribution area, the soil flow connectivity index of the pollutant corresponding to the pollution source in the soil flow transport path is calculated; For each pollution source corresponding to the landscape contribution area, based on the aquifer permeability coefficient, effective aquifer thickness, and groundwater gradient of the corresponding landscape contribution area, the baseflow connectivity index of the pollutant corresponding to the pollution source in the baseflow transport path is calculated.

8. The method according to claim 1, characterized in that, The step of constructing an objective optimization function constrained by information entropy based on the pollution source contribution allocation vector, the nitrogen load allocation vector, and the transmission cost matrix includes: Construct an initial source-path coupling matrix; the columns of the initial source-path coupling matrix represent the pollution sources, and the columns represent surface runoff transport paths, interflow transport paths, and baseflow transport paths; the elements in the initial source-path coupling matrix... Characterize the proportion of nitrogen load contribution from pollution source i through hydrological pathway j; Based on the pollution source contribution allocation vector, the nitrogen load allocation vector, the transmission cost moment, and the initial source-path coupling matrix, the objective optimization function is constructed with information entropy as a constraint and the goal of minimizing transmission cost. The objective optimization function is: ; The constraints are: ； in, For information entropy constraints, Π is the initial source-path coupling matrix. These are the elements in the initial source-path coupling matrix; Let λ be the transmission cost matrix, and λ be the regularization coefficient.

9. The method according to claim 8, characterized in that, Solving the objective optimization function to obtain the target source-path coupling matrix corresponding to the target watershed includes: The objective optimization function is transformed into a solvable convex optimization function; The transmission cost matrix is ​​converted into an exponential probability transition kernel matrix; Based on the initial source-path coupling matrix, determine the initial row scaling factor and the initial column scaling factor; Set a preset iteration stop condition; Based on the exponential probability transition kernel matrix and the pollution source contribution allocation vector, the initial row scaling factor is adjusted; The initial column scaling factor is adjusted based on the exponential probability transfer kernel matrix and the nitrogen load allocation vector. The process continues until the preset iteration stop condition is met, at which point the target row scaling factor and the target column scaling factor are obtained. Based on the target row scaling factor and the target column scaling factor, the target source-path coupling matrix is ​​obtained.

10. The method according to claim 1, characterized in that, The step of determining the target governance scheme corresponding to the target watershed based on the target source-path coupling matrix includes: Sort the coupling elements in the target source-path coupling matrix in descending order; Calculate the proportion of each of the aforementioned coupling elements in the total nitrogen output of the target watershed; The proportion of each coupling element in the total nitrogen output of the target watershed is compared with a preset proportion threshold. Coupled elements whose proportion is greater than the preset proportion threshold are identified as dominant coupling units; Based on each of the dominant coupling units, the initial governance scheme corresponding to the target watershed is determined; Simulations were performed on each of the initial treatment schemes to determine the nitrogen load reduction corresponding to each initial treatment scheme. Based on the nitrogen load reduction amount corresponding to each of the initial treatment schemes, the target treatment scheme corresponding to the target watershed is determined.

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