Method for calculating pollution load in dry-wet period of seasonal dry river system

Abstract

The application discloses a kind of seasonal dry water system dry-wet period pollution load measurement method, belong to environmental monitoring technical field.The method comprises the following steps: obtaining historical water level monitoring sequence and river network topology, and extracting dry-wet time set;Calculate the sampling information gain for each dry-wet event, wherein the dry-up cumulative effect index increases with the increase of dry-up duration, and the spatial transmission potential index is equal to the number of accessible river sections downstream the river section;Under the constraint of the preset number of monitoring points, the incremental selection strategy is used to generate the minimum monitoring scheme;Obtain sparse sampling data;Based on the observation value of upstream monitored river section and spatial transmission coefficient, the pollution load of unmonitored river section is inferred;Integrate the observation value and the inferred value to generate the pollution load distribution result.The application makes full use of the high information window of dry-wet conversion time and the spatial transmission relationship of river network, and provides an economic and efficient technical solution for seasonal dry water system pollution load measurement.

Description

Technical Field

[0001] This invention belongs to the field of environmental monitoring technology, specifically relating to a method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods. Background Technology

[0002] Seasonally dry river systems refer to rivers, streams, or wetlands that experience alternating periods of water and dryness throughout the year, influenced by climate, topography, or human activities. These systems are widely distributed in arid and semi-arid regions, monsoon climate zones, and watersheds regulated by agricultural irrigation, accounting for over 50% of the total length of rivers globally. While seasonally dry river systems play a vital role in maintaining biodiversity, regulating regional water cycles, and supporting agricultural production, they also face severe pollution problems. Due to the unique hydrological process of alternating wet and dry periods, the pollution load in these systems exhibits significant spatiotemporal dynamics. Pollutants accumulate in the sediment during the dry period and are released in concentrated bursts during refilling, creating pulsed pollution events that impact downstream water quality and ecosystems.

[0003] Accurately calculating the pollution load of seasonally dried-up river systems is fundamental for water quality monitoring, pollution source tracing, and ecological restoration. However, existing water quality monitoring and pollution load calculation methods are mainly designed for perennial rivers and do not fully consider the wet-dry transition characteristics of seasonally dried-up river systems, leading to the following problems in practical applications:

[0004] First, existing monitoring schemes typically employ fixed-time sampling, such as monthly or quarterly water quality monitoring. This fixed-period sampling strategy fails to capture the transient processes of pollutant release during the transition between dry and wet periods. When sampling occurs precisely during the stable phase of the dry or wet season, pollutant concentrations in the water have already stabilized, failing to reflect the dynamic characteristics of pollutant accumulation in sediment during the dry period and the instantaneous pulse release during recharge. Studies have shown that pollutant concentrations in seasonal rivers can reach 3 to 10 times higher than during the stable period at the initial stage of recharge. Fixed-period sampling easily misses this critical moment, leading to a systematic underestimation of the pollution load.

[0005] Secondly, existing monitoring site deployment methods are mainly based on the principle of spatial uniform distribution, selecting monitoring sections at equal intervals within the watershed. This uniform deployment strategy does not consider the impact of river network topology on pollutant migration. In river systems, pollutants migrate directionally along the direction of water flow; the pollution status of upstream river sections will affect multiple downstream river sections through water flow transmission, while the pollution status of downstream river sections will not have a reverse impact on upstream sections. Uniform deployment ignores this unidirectional cascading transmission relationship, leading to unreasonable allocation of monitoring resources: high-impact upstream river sections may be under-monitored, while low-impact downstream river sections may have redundant monitoring. In addition, uniform deployment usually concentrates on the main channel, neglecting tributaries and creating monitoring blind spots.

[0006] Furthermore, existing spatial inference methods mostly employ interpolation algorithms based on geographical distance, such as inverse distance weighting and Kriging interpolation. These methods assume that pollution load is related to spatial distance, with closer monitoring points having a greater impact on the inferred points. However, in river systems, pollutant migration is dominated by the direction of water flow, and the influence of upstream river sections on downstream river sections is far greater than that of spatially adjacent but hydrologically unconnected river sections. Geographical distance-based interpolation methods violate the physical laws governing river pollutant migration, resulting in structural biases in the inference results. Especially for seasonally drying river systems, the wet-dry transition process alters the occurrence and migration mechanisms of pollutants, and traditional interpolation methods cannot characterize this non-steady-state process, making it difficult to guarantee inference accuracy.

[0007] Furthermore, existing methods present a trade-off between monitoring cost control and information acquisition volume. Improving the accuracy of pollution load estimation typically requires increasing the number of monitoring sites and sampling frequency, but this leads to a rapid increase in monitoring costs. Given limited monitoring budgets, optimizing monitoring resource allocation to acquire the most pollution load information with the least monitoring investment is a core challenge in monitoring seasonally dried-up waterways. Current technologies lack targeted monitoring optimization methods, and monitoring scheme design relies heavily on empirical judgment, lacking scientific rigor and systematic approach.

[0008] In summary, existing pollution load estimation methods suffer from problems such as inappropriate sampling timing, unreasonable sampling strategies, unsuitable inference methods, and high monitoring costs when applied to seasonally dried-up water systems, making it difficult to meet the actual needs of water quality monitoring and pollution management in these systems. Therefore, there is an urgent need to develop pollution load estimation methods specifically designed for the wet and dry season characteristics of seasonally dried-up water systems, achieving high-accuracy pollution load estimation with limited monitoring costs. Summary of the Invention

[0009] To address the aforementioned technical issues, a method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods is provided, specifically including the following steps:

[0010] S1. Obtain basic data: Obtain historical water level monitoring sequences for the target water system. ,in, Indicates the first Each section of the river, Indicate time; obtain river network topology The river network topology includes the upstream and downstream connections between river segments, as well as the spatial coordinates and characteristic parameters of each river segment.

[0011] S2. Identify wet-dry transition events: Based on the historical water level monitoring sequence, for each river segment The set of moments when its wet and dry states transitioned is identified, specifically:

[0012] Define a state indicator function: when the river segment At any moment water level Above the preset drying threshold The state is recorded as wet if it is wet, otherwise it is recorded as dry if it is dry. The dryness threshold is determined based on the distribution characteristics of the historical water level sequence of the river section.

[0013] Extract the set of events from dry to wet transition. The set contains all time points that satisfy the condition that the previous time was a dry period and the current time is a wet period.

[0014] Extract the set of wet-to-dry event moments The set contains all time points that satisfy the condition that the previous time was a wet period and the current time is a dry period.

[0015] S3. Calculate the sampling information gain: For each river segment Each dry-to-wet event Calculate the information gain of the pollution load sampling at that moment. The information gain characterizes the amount of pollution state information that can be obtained in a single sampling, and its calculation method is as follows:

[0016] ;

[0017] in, The cumulative effect index of drying up is monotonically increasing as the duration of drying up in the river section before this re-flooding increases. This is a spatial transfer potential index, the value of which is equal to the number of all accessible river segments downstream of the given river segment;

[0018] S4. Generate minimum monitoring plan: Based on the preset number of monitoring points. Under the constraints, the number of monitoring points is determined based on available monitoring resources and the scale of the target water system, and is selected from all river sections and their dry-to-wet transition events. A sampling task is selected to maximize the sum of information gains of the selected sampling tasks, and the output includes a monitoring scheme containing the sampled river section and the sampling time.

[0019] S5. Obtain sparse sampling data: Based on the monitoring scheme, obtain the observed pollution load values ​​after the actual sampling is performed. ,in, For the monitored river section, Sampling time;

[0020] S6. Spatial inference of pollution load in unmonitored river sections: For unmonitored river sections... Pollution load is inferred based on observations of the monitored upstream river sections. The calculation method is as follows:

[0021] ;

[0022] in, Indicates river section The collection of all upstream monitored river sections; The spatial transfer coefficient of pollution load depends on the river segment. With river section Distance between the river channels And the sampling time difference:

[0023] ;

[0024] The spatial transfer coefficient of the pollution load is calculated as follows:

[0025] ;

[0026] in, The attenuation characteristic length is determined based on the river section type and pollutant type; The settlement coefficient is determined based on the type of sediment in the river section.

[0027] S7. Generate a pollution load distribution map: Integrate the observation values ​​of all monitored river sections and the inferred values ​​of all unmonitored river sections to generate a spatial distribution result of pollution load covering the entire target water system.

[0028] In step S2, the drying threshold The method of determination is as follows: for river sections Statistical analysis was performed on the historical water level sequence to calculate the characteristic quantiles of the water level distribution. When there was obvious drying in the historical records, the preset quantile value between the historical lowest water level and the historical median water level was taken as the drying threshold.

[0029] Alternatively, when the drying phenomenon is not obvious or the record is incomplete in the historical records, the average elevation of the riverbed plus a preset water depth margin is used as the drying threshold based on the topographic features and riverbed elevation of the river section.

[0030] In step S3, the cumulative effect index of drying The calculation method is as follows: ;

[0031] in, For river section In this water refilling incident The duration of the previous drought;

[0032] The duration of the dryness is determined by the time intervals of the wet-to-dry event. Find distance in The most recent wet-to-dry moment And calculate according to the following formula: ;

[0033] In step S3, the space transfer potential index The calculation method is as follows:

[0034] Based on the river network topology A graph traversal algorithm is used to start from the river segment Starting with a breadth-first or depth-first search along the direction of water flow, record all possible river segments. The downstream river segments reached form a set of downstream reachable river segments, and the number of elements in the set of downstream reachable river segments is used as... The value of .

[0035] In step S4, the optimization process for generating the minimum monitoring scheme is as follows:

[0036] Establish a candidate sampling task set, which includes sampling tasks for all dry-to-wet events corresponding to all river segments;

[0037] An incremental selection strategy is adopted, in which information gain is selected from the candidate sampling tasks that have not yet been selected. The largest sampling task was added to the monitoring scheme;

[0038] Repeat the selection process until the number of selected sampling tasks reaches the preset number of monitoring points. Output the final monitoring plan.

[0039] In step S6, the attenuation characteristic length and settlement coefficient The method for determining it is as follows:

[0040] Based on the classification of river section topography and the physical and chemical properties of pollution, the corresponding parameter values ​​are obtained by looking up tables in the preset parameter database;

[0041] Among them, the attenuation characteristic length The sedimentation coefficient increases with decreasing river slope and decreases with increasing particulate matter content of pollutants; It increases with the increase of riverbed roughness.

[0042] In step S6, for the unmonitored river sections The pollution load inference also includes the uncertainty in calculating the inferred value:

[0043] Based on the observation errors of the monitored upstream river sections and the inherent errors of the spatial propagation model, the uncertainty of the inferred values ​​is calculated using the error propagation method. ;

[0044] When outputting the pollution load distribution results, the uncertainty interval of the inferred pollution load value for each unmonitored river section is also output. The uncertainty interval is expressed as follows: ;

[0045] It also includes step S8: generating a remediation priority ranking based on the spatial distribution results of the pollution load, specifically as follows:

[0046] For each river segment, a comprehensive assessment is conducted on its own pollution load value, the scope of its impact on downstream river segments, the uncertainty of the inferred pollution load value, and the difficulty of implementing remediation for that river segment.

[0047] River sections with high pollution loads, large impact ranges, low uncertainty, and moderate remediation difficulty are given higher remediation priority.

[0048] Sort each river segment according to its repair priority from high to low, and output a repair priority list.

[0049] In step S4, when generating the minimum monitoring scheme, a time window constraint is also included:

[0050] For the predicted dry-to-wet event time Set an executable sampling time window, which starts at a preset preparation time before the dry-to-wet event occurs and ends at a preset effective sampling period after the dry-to-wet event occurs.

[0051] When the time windows of multiple candidate sampling tasks conflict, information gain is preferred. Sampling tasks that are large and have an early time window;

[0052] The selected sampling task is adjusted according to the time window constraint so that the monitoring scheme meets the time operability requirements during actual execution.

[0053] It also includes a dynamic adjustment step for the monitoring plan: During the monitoring process, when there is a significant deviation between the actual observed wet-dry transition time and the wet-dry transition pattern determined based on historical water level monitoring sequences, or when the results of some of the already executed sampling show that the spatial distribution of pollution load differs significantly from the expected results, the information gain of each candidate sampling task is updated based on the newly acquired data. ;

[0054] Based on the updated information gain, the sampling tasks that have not yet been executed are re-prioritized, and the subsequent monitoring plan is adjusted according to the re-prioritization results to adapt to the actual changes in the dry and wet states and pollution load distribution of the target water system.

[0055] The present invention has the following beneficial effects:

[0056] This invention significantly improves the accuracy of pollution load inference. By identifying the dry-to-wet transition moment as a sampling window, it fully utilizes the characteristic of concentrated pollutant release during the refilling of seasonally dried-up river systems. Pollutants accumulated in the sediment during the dry period undergo rapid desorption and release upon refilling, forming a peak pollution load. Traditional fixed-period sampling easily misses this critical moment, leading to a systematic underestimation of the pollution load. This invention, by capturing high-information sampling data at the dry-to-wet transition moment, obtains observations that more accurately represent the true pollution status of river sections, providing high-quality input data for subsequent spatial inference, thereby improving the accuracy of pollution load inference for unmonitored river sections.

[0057] This invention optimizes the allocation of monitoring resources and improves monitoring efficiency. It quantifies the information value of each sampling task using an information gain index, achieving a scientific allocation of monitoring resources. Information gain comprehensively considers two dimensions: the cumulative effect of drying and the spatial transmission potential. River sections with longer drying periods release more pollutants upon refilling, resulting in higher monitoring value. River sections with more downstream accessible sections have a wider transmission range of monitoring information, leading to greater monitoring benefits. By prioritizing the deployment of monitoring points in high-information-gain river sections, this invention avoids redundant waste of monitoring resources, achieving effective coverage of the entire basin with fewer monitoring points and improving the utilization efficiency of monitoring resources.

[0058] This invention's spatial inference method considers the topological structure of river networks and the directional transport characteristics of water flow, overcoming the limitations of traditional interpolation methods based on geographical distance. In river systems, pollutants migrate along the direction of water flow; the pollution status of upstream river segments affects downstream river segments through water flow, while downstream river segments do not have a reverse effect on upstream segments. This invention characterizes this unidirectional cascading transport relationship through a spatial transport coefficient model. The calculation of the transport coefficient comprehensively considers factors such as the distance between river segments, river segment type, pollutant type, and sediment type, conforming to the physicochemical laws of river pollutant migration. This inference method based on physical mechanisms has stronger interpretability and reliability compared to empirical interpolation methods.

[0059] By optimizing the monitoring point selection strategy, monitoring points are simultaneously deployed in both the main river channel and tributaries. A spatial inference method based on river network topology is used to estimate the pollution load of all river segments across the entire basin. Traditional uniform monitoring methods often concentrate on the main river channel, neglecting tributaries and making them monitoring blind spots. The information gain index of this invention can identify high-influence river segments upstream of tributaries, prioritizing the deployment of monitoring points in these locations. Combined with a spatial transfer model, this allows for the inference of pollution load across all river segments, including tributaries, providing a data foundation for comprehensive assessment and precise management of basin pollution.

[0060] This invention not only provides inferred pollution load values ​​but also calculates the uncertainty range of these values ​​using an error propagation method, enabling decision-makers to understand the reliability of the inference results. This uncertainty quantification is of significant value for pollution risk assessment and remediation decision-making. When the inference uncertainty is high, it suggests the need to increase monitoring investment in the area or adopt a more conservative risk management strategy; when the inference uncertainty is low, remediation measures can be confidently formulated based on the inference results. Providing uncertainty information enhances the transparency and reliability of pollution load assessment results, supporting more scientific decision-making.

[0061] This method, which identifies wet-dry transition patterns based on historical data and predicts future transition times, possesses dynamic adjustment capabilities during practical implementation. When there is a deviation between the observed wet-dry transition time and the prediction, or when some acquired sampling results show a significant difference between the pollution load distribution and expectations, the information gain can be recalculated based on updated data, dynamically adjusting subsequent monitoring plans. This dynamic adjustment capability enables the method to adapt to interannual variations in hydrological conditions, the impact of climate change, and sudden pollution events, maintaining the timeliness and relevance of the monitoring plan and improving the robustness and practicality of the method. Attached Figure Description

[0062] Figure 1 This is an overall flowchart of a method for calculating the pollution load of a seasonally dried-up water system during both wet and dry periods. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0064] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0065] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0066] Example 1

[0067] This example uses a seasonal river in a northern region as an example to demonstrate the complete implementation process of a pollution load measurement method. The river's drainage area is approximately 350 square kilometers, consisting of a main channel and three tributaries. Influenced by the monsoon climate, it exhibits a distinct wet-dry cycle each year, with the wet season concentrated from June to October and the remaining time being the dry season. The drainage basin contains agricultural non-point source pollution and a small amount of domestic sewage discharge. The main pollutant is total nitrogen. The monitoring objective is to understand the spatial distribution of nitrogen pollution load across the entire drainage basin within a limited budget.

[0068] According to the method of this invention, the basic data of the river system were first obtained. The river network was divided into 10 river segments, numbered x1 to x10. The topological relationships, geographical locations, and characteristic parameters of each river segment are shown in Table 1. River segments x1 to x5 constitute the main channel, connected sequentially from upstream to downstream; river segments x6 and x7 constitute tributary A, which flows into the main channel at river segment x3; river segments x8 and x9 constitute tributary B, which flows into the main channel at river segment x4; river segment x10 is an independent tributary, which flows into the main channel at river segment x5. The length of each river segment ranges from 2 to 8 kilometers, the riverbed is mainly composed of sand and silt, and the terrain types cover both mountainous and plain river segments.

[0069] Table 1. River network topology and river segment characteristic parameters:

[0070] ;

[0071] Historical water level monitoring data were obtained from five hydrological stations in the basin, covering a monitoring period from January 1, 2024 to December 31, 2025, totaling 731 days, with sampling intervals of every 5 days. For river sections without hydrological stations, water level data from adjacent river sections were interpolated based on the elevation difference between the sections. Taking river section x3 as an example, its historical water level sequence includes 147 observation points, with water levels ranging from 0.15 meters to 2.8 meters. Based on the historical water level distribution of this river section, the 10th percentile was calculated to be 0.42 meters, the 25th percentile to be 0.68 meters, and the median to be 1.35 meters. Considering the average elevation of the riverbed in this section, when the water level is below 0.5 meters, a large area of ​​the riverbed is exposed, and the flow is close to zero; therefore, the drying threshold is set accordingly. Hth is set to 0.5 meters.

[0072] Using a similar method, corresponding drying thresholds were determined for other river sections. River sections x1, x2, x6, x7, x8, and x9 are located in mountainous areas with steep riverbed slopes, and their drying thresholds range from 0.3 to 0.4 meters. River sections x3, x4, x5, and x10 are located in plains with wider and shallower riverbeds, and their drying thresholds range from 0.5 to 0.6 meters. Based on the water level sequences and drying thresholds for each river section, wet-dry transition events were identified. Taking river section x3 as an example, during the monitoring period from 2024 to 2025, a total of 4 wet-to-dry events were identified. The first dry-to-wet event occurred on June 15, 2024. Prior to this, the river section had been dry for 166 days, starting from January 1, 2024. The second dry-to-wet event occurred on June 10, 2025. Prior to this, the river section had been dry for 217 days, starting from November 5, 2024. Wet-to-dry events occurred on October 20, 2024, and October 25, 2025, respectively.

[0073] The same identification process was applied to all 10 river sections, resulting in 38 dry-to-wet events and 38 wet-to-dry events identified during the monitoring period. The timing of these dry-to-wet events varied across river sections: the resurgence of water in the upstream sections (x1, x6, x8) typically occurred 15 to 30 days earlier than in the downstream sections. This is because rainfall first forms runoff upstream and then propagates downstream. The duration of drought also differed among river sections. In mountainous sections, due to their smaller drainage area and faster runoff recession, the drought duration was typically 180 to 220 days; in plains sections, due to their greater water storage capacity, the drought duration was 150 to 190 days.

[0074] After identifying all dry-to-wet events, the sampling information gain is calculated for each event. The calculation of the information gain involves two indices: the drying cumulative effect index and the spatial transport potential index.

[0075] For the spatial transfer potential index, it is necessary to calculate the number of downstream reachable river segments for each river segment based on the river network topology. For example, starting from this river segment, a graph traversal is performed along the direction of water flow, passing through the river segment. Later reached the river section ,reach Receive from river section and The water flow continues downstream, traversing the reachable river sections. ,reach Receive from river section and The water flow eventually reaches the river section. ,reach Receive from river section and The water flows out of the system after it flows out.

[0076] Therefore, from the river section Downstream sections accessible from here include , , and There are a total of 4 river sections, and their spatial transfer potential index is: ;

[0077] The spatial transfer potential index for other river sections was calculated using the same method. The downstream section of the river is , and ,therefore: ;

[0078] reach The downstream section of the river is and ,therefore: ;reach The downstream section of the river is ,therefore: ;

[0079] reach Located at the very downstream end of the river system, with no other river sections downstream, therefore: ;

[0080] For tributary river sections, river sections The downstream section of the river is , , and ,therefore: ;

[0081] reach The downstream section of the river is , and ,therefore: ;

[0082] reach The downstream section of the river is , and ,therefore: ;

[0083] reach The downstream section of the river is and ,therefore: ;

[0084] reach The downstream section of the river is ,therefore: ;

[0085] The cumulative effect of drought is calculated using a logarithmic function, and its expression is as follows: ;

[0086] in, For river section In this embodiment, the duration of continuous dryness before the corresponding dry-to-wet event is calculated using the natural logarithm.

[0087] River section Taking the dry-to-wet event that occurred on June 15, 2024 as an example, the dry period prior to this event lasted 166 days, therefore: ;

[0088] Substituting into the formula for calculating the cumulative effect of drying, we get: ;

[0089] Right now: ;

[0090] reach The dry-to-wet event that occurred on June 10, 2025, lasted for 217 days; therefore: For the river section The dry-to-wet event that occurred on June 5, 2024, lasted for 186 days; therefore: For the river section The dry-to-wet event that occurred on June 8, 2024, lasted for 203 days; therefore: ;

[0091] After obtaining the dry-accumulation effect index and the spatial transport potential index, the sampling information gain corresponding to the dry-to-wet event is calculated according to the following formula: ;

[0092] For example, river section The information gain corresponding to the dry-to-wet transition event that occurred on June 15, 2024 is: ;

[0093] reach The information gain corresponding to the dry-to-wet transition event that occurred on June 10, 2025 is: ;reach The information gain corresponding to the dry-to-wet transition event that occurred on June 5, 2024 is: ;

[0094] reach The dry-to-wet event that occurred on June 1, 2025, had a dry duration of 193 days. Its cumulative dryness effect index is: ;

[0095] The corresponding information gain is: ;

[0096] reach The information gain corresponding to the dry-to-wet transition event that occurred on June 8, 2024 is: For the river section Its downstream section can only be reached. Therefore, the space transfer potential index is: Even if the dry period is long, for example, the dry period before the corresponding dry-to-wet event in 2024 lasted for 175 days, its cumulative dryness effect index is: ;

[0097] The corresponding information gain is also only: ;

[0098] The information gain was calculated for all 38 dry-to-wet events, and the results were sorted from largest to smallest information gain. The calculation results of the top 15 candidate sampling tasks are listed in Table 2.

[0099] As can be seen from Table 2, the upstream river section , and Due to their large spatial transport potential and the long duration of drought preceding the corresponding dry-to-wet event, the information gain for the corresponding sampling tasks is generally high; however, river sections located downstream or with limited downstream access, such as... and Due to the small spatial transfer potential index, even if the dry period is long, the corresponding information gain is still relatively low.

[0100] Table 2. Calculation results of information gain for dry-to-wet transition events (first 15 items):

[0101] ;

[0102] After calculating the information gain of all candidate sampling tasks, a minimum monitoring scheme is further generated. In this embodiment, the monitoring budget allows for the deployment of 5 sampling points, i.e., the preset number of monitoring points is: ;

[0103] The number is determined based on the monitoring budget and laboratory analysis capabilities of the watershed management department. Considering the costs of water sample collection, transportation, and laboratory testing, the average cost of each sampling task is approximately 800 yuan, and the total budget for 5 sampling tasks is 4,000 yuan, which is within the annual water quality monitoring budget for the watershed.

[0104] An incremental selection strategy was adopted to generate a monitoring plan. First, a candidate sampling task set was established, which included the sampling tasks corresponding to all 38 dry-to-wet events.

[0105] In the first round of selection, the task with the highest information gain was chosen from 38 candidate sampling tasks to be added to the monitoring scheme. Based on the ranking results in Table 2, the river segment... The information gain corresponding to the dry-to-wet transition event that occurred on May 28, 2025 is: ;

[0106] The maximum value among all candidate tasks is selected for the monitoring scheme, denoted as Task A. At this point, the monitoring scheme contains 1 task, with 37 remaining candidate tasks.

[0107] In the second round of selection, the task with the highest information gain is chosen from the remaining 37 candidate sampling tasks. At this point, the river segment... The information gain corresponding to the dry-to-wet transition event that occurred on June 1, 2025 is: ;

[0108] This task is selected for the monitoring plan and designated as Task B. At this point, the monitoring plan contains 2 tasks, with 36 remaining candidate tasks.

[0109] The third round of selection yielded the river section. The information gain for the sampling task on June 5, 2024 is: ; denoted as Task C.

[0110] The fourth round of selection yielded the river section. The information gain for the sampling task on June 2, 2024 is: ; denoted as Task D.

[0111] The fifth round of selection yielded the river section. The information gain for the sampling task on June 6, 2025 is: ; denoted as task E.

[0112] At this point, the monitoring plan includes 5 sampling tasks, reaching the preset number of monitoring points. The selection process terminates.

[0113] The final monitoring plan includes: Task A, in the river section Sampling was conducted on May 28, 2025; Task B, in the river section. Sampling was conducted on June 1, 2025; Task C, in the river section. Sampling was conducted on June 5, 2024; Task D, in the river section. Sampling was conducted on June 2, 2024; Task E, in the river section. Samples were taken on June 6, 2025.

[0114] The five sampling tasks are distributed across three river sections, spanning two wet and dry cycles in 2024 and 2025. Tasks C and D correspond to historical moments in 2024, and the corresponding sampling data already obtained in 2024 can be used in practical applications. Tasks A, B, and E correspond to sampling tasks in 2025, and sampling can be carried out at the corresponding times according to the monitoring plan.

[0115] According to the monitoring plan, water samples were collected and analyzed in the laboratory at the corresponding times and locations to obtain sparse sampling data. Among these, the river section... The total nitrogen concentration on May 28, 2025 was ;reach The total nitrogen concentration on June 1, 2025 was ;reach The total nitrogen concentration on June 5, 2024 was ;reach The total nitrogen concentration on June 2, 2024 was ;reach The total nitrogen concentration on June 6, 2025 was .

[0116] The above five observations constitute the input data for spatial inference of pollution load.

[0117] After obtaining sparse sampling data, spatial inference of pollution load is performed on river sections that are not directly monitored.

[0118] River section Taking the pollution load projection as of June 10, 2025 as an example, this river section was not directly monitored, but there were two monitored river sections upstream of it, namely the river section... and river section Among them, the river section The monitoring time was June 1, 2025, and the observed value was: ;

[0119] reach The monitoring time was May 28, 2025, and the observed value was:

[0120] Therefore, it is necessary to calculate the river sections separately. and river section river section The contribution of pollutant transport.

[0121] For the river section to the river section The transmission path, the water flow from through arrive The total transmission distance is: ;

[0122] The sampling time difference is: ;

[0123] The attenuation characteristic length is determined based on the river segment type and pollutant type. River segment and river section All of these are mountainous river sections. The baseline attenuation characteristic length for mountainous river sections is: ;

[0124] The pollutant is total nitrogen. According to the parameter library of this embodiment, it is treated as a pollutant mainly characterized by soluble migration. A correction factor of 1.2 is applied to the attenuation characteristic length. Therefore: ;

[0125] reach and The substrate is sandy; the settlement coefficient is determined based on the parameter database. ;

[0126] Therefore, river section to the river section The spatial transfer coefficient of pollution load is: ;

[0127] The spatial attenuation factor is: The time decay factor is: ;

[0128] therefore: ;

[0129] reach river section The transmission contribution is: ;

[0130] For the river section to the river section The transmission path, the water flow from through arrive The total transmission distance is: ;

[0131] The sampling time difference is: ;

[0132] reach and Since all sections are mountainous river segments, the corrected attenuation characteristic length is used: Its substrate is sandy, therefore: The corresponding spatial transfer coefficient of pollution load is: ;

[0133] The spatial attenuation factor is: ;

[0134] The time decay factor is: ;therefore: ;

[0135] reach river section The transmission contribution is: ;

[0136] Therefore, the river section The inferred pollution load as of June 10, 2025, is the sum of the transfer contributions from the two upstream monitored river sections: ;

[0137] Then by river section Taking the pollution load projection as of June 18, 2025 as an example, the upstream monitored river sections include... , and .

[0138] For the river section to the river section The transmission path is as follows: ;

[0139] The total transmission distance is: ;

[0140] The sampling time difference is: ;

[0141] Since the transmission path passes through different types of river sections, the attenuation characteristic length and settlement coefficient are segmented.

[0142] from to The path length is It belongs to a sandy river section in a mountainous area, corresponding to: ; ;

[0143] from to The path length is This is a plain silty river section. The benchmark attenuation characteristic length of the plain river section is taken as... After considering a correction factor of 1.2 for dissolved contaminants: ;

[0144] The corresponding settlement coefficient is To simplify calculations, this embodiment uses a path length-weighted average to determine the comprehensive parameters. The comprehensive attenuation characteristic length is: ;Right now: ;

[0145] The overall settlement coefficient is: ;Right now ;

[0146] therefore ;

[0147] Further calculations yielded = ;

[0148] Therefore, river section river section The transmission contribution is: For the river section to the river section The transmission path is as follows: The total transmission distance is: ;

[0149] Front-end path The length is It belongs to a sandy river section in a mountainous area; the later section of the path Length is It belongs to the silty river section of the plain.

[0150] The overall attenuation characteristic length is: ;Right now: ;

[0151] The overall settlement coefficient is: After using the appropriate time interval, its transmission coefficient is calculated according to the following formula: For the river section to the river section The transmission path is as follows: ;

[0152] The total transmission distance is: The sampling time difference is ;

[0153] This path uses a decay characteristic length: Settlement coefficient: ;therefore ;

[0154] Right now: ; ;

[0155] reach river section The transmission contribution is: ;

[0156] For other unmonitored river sections, the same method described above can be used to calculate the corresponding spatial transfer coefficient of pollution load based on parameters such as the topological connection between the river section and the upstream monitored river section, the distance between the river channel and the river, the sampling time difference, the river section type and the sediment type, and further obtain the inferred value of the pollution load for the corresponding river section.

[0157] To facilitate the explanation of the complete process of spatial inference, the river section and river section The inference process is summarized in Table 3. Table 3 lists the observed values, key parameters of the transmission path, calculation results of the transmission coefficient, and the pollution load transmission contribution of each upstream river segment that has been monitored.

[0158] As can be seen from Table 3, under the same conditions, the spatial transfer coefficient of pollution load generally decreases with the increase of transfer distance and time interval, thus reflecting the characteristics of pollutants being affected by both spatial and temporal attenuation during river migration.

[0159] Table 3. Detailed process of spatial inference of pollution load in unmonitored river sections:

[0160] ;

[0161] After inferring the pollution load for all unmonitored river segments, the observed values ​​from all monitored segments and the inferred values ​​from unmonitored segments were integrated to generate a spatial distribution of the pollution load covering the entire river system. This distribution is output in tabular form, containing estimates of the total nitrogen pollution load for each segment at the target time (mid-June 2025). The results show that the upstream segments (x1, x6, x8) have high pollution loads, ranging from 9 to 18 mg / L. These segments are located in areas with concentrated agricultural activities and are significantly affected by farmland runoff and livestock farming pollution. The midstream segments (x2, x3, x7, x9) have moderate pollution loads, ranging from 5 to 8 mg / L, with pollutant concentrations decreasing after migration and degradation. The downstream segments (x4, x5, x10) have low pollution loads, ranging from 2 to 4 mg / L, benefiting from longer transport distances and the river's self-purification capacity.

[0162] Based on the pollution load distribution results, the uncertainty of the inferred pollution load values ​​for each river segment was also calculated. Taking river segment x3 as an example, its inferred value is based on two upstream monitored river segments, assuming observation errors. mg / L, mg / L, inherent error of spatial transport model mg / L, uncertainty calculated using the error propagation method:

[0163] ;

[0164] The inferred pollution load value for river segment x3 is expressed as follows: The confidence interval for the pollution load is 4.28 to 6.00 mg / L. The uncertainty calculation for river segment x4 involves three upstream river segments, and the process is similar, yielding an uncertainty of approximately 1.1 mg / L. The inferred pollution load is expressed as... mg / L. The corresponding uncertainties were also calculated for other unmonitored river sections. The results showed that the uncertainty of the inferred values ​​in the upstream river section was relatively small (0.5 to 1.0 mg / L), while the uncertainty in the downstream river section was relatively large (1.0 to 2.0 mg / L) due to the complex transmission path and small transmission coefficient.

[0165] The final output of the spatial distribution of pollution load includes not only the inferred values ​​for each river segment but also the uncertainty interval, providing comprehensive water quality assessment information for watershed management departments. This result can be used to identify key pollution areas, formulate targeted remediation measures, and optimize subsequent monitoring layout. Compared with traditional uniform sampling monitoring schemes, the method used in this embodiment, at the same monitoring cost (5 sampling points), effectively estimates the pollution load of 10 river segments across the entire watershed by fully utilizing the high information window during the dry-wet transition and the spatial transfer relationship of the river network. This provides an economical and efficient technical approach for calculating the pollution load of seasonally dried-up water systems.

[0166] Example 2

[0167] This embodiment provides a comparative verification, employing a traditional uniform sampling method with fixed periods to monitor and infer pollution load in the same water system, and comparing it with the method in Example 1 to demonstrate the technical advantages of the present invention. The comparison scenario is set as a seasonal river basin identical to that in Example 1, with consistent river network structure, river section parameters, and monitoring budget. The number of monitoring points is also limited to 5, the target time is set to mid-June 2025, and the target pollutant is also total nitrogen.

[0168] Traditional monitoring schemes are designed based on the principle of spatial uniform distribution. The 10 river sections are divided into 5 monitoring regions according to their spatial location: the upstream region includes river sections x1 and x6, the mid-upper region includes river sections x2 and x7, the midstream region includes river sections x3 and x8, the mid-lower region includes river sections x4 and x9, and the downstream region includes river sections x5 and x10. A representative river section is selected from each region for monitoring, chosen based on its length or flow rate. The final 5 selected monitoring sections are x1, x2, x3, x4, and x5. These sections constitute a complete sequence of the main river channel, spatially covering the entire area from upstream to downstream.

[0169] Sampling was conducted on a fixed monthly cycle, once on the 15th of each month, without considering the dry / wet status or seasonal variations of the river sections. During the monitoring periods of 2024 and 2025, a total of 24 samples were taken from each monitored river section. To ensure a fair comparison with Example 1, this example selected five sampling results from around June 15, 2025, from the 24 sampling records as input data. These five samplings corresponded to February 15, March 15, April 15, May 15, and June 15, 2025, respectively. At the time of sampling, the water levels of river sections x1, x2, x3, and x4 were all below the dryness threshold, indicating the dry period, while the water level of river section x5 was slightly above the threshold, indicating the early wet period.

[0170] Sampling results using the conventional method on June 15, 2025, showed that the total nitrogen concentration in river section x1 was 8.2 mg / L, in river section x2 it was 6.5 mg / L, in river section x3 it was 4.8 mg / L, in river section x4 it was 3.1 mg / L, and in river section x5 it was 2.3 mg / L. These observed values ​​are significantly lower than the values ​​observed in the corresponding river sections in Example 1 at the point of transition from dry to wet conditions. The main reason is that the sampling time for the conventional method was June 15, at which time the upstream river sections (x1, x2) had been rehydrated for more than 10 days, and the peak of pollutants released from the bottom sediment in the early stage of rehydration had subsided, and the water concentration had dropped to normal levels. Although the midstream river sections (x3, x4) were still in the late dry period, the sampling was conducted during the day, and the high daytime temperature caused some ammonia nitrogen to volatilize, resulting in a lower measured total nitrogen concentration than the actual cumulative amount. The downstream river section (x5) had just been rehydrated, and the water flow was large, so the pollutants were diluted, resulting in a relatively low concentration.

[0171] For the five unmonitored river segments (x6, x7, x8, x9, x10), the traditional method uses inverse distance weighted interpolation for inference. This method assumes that the pollution load at the unmonitored points is obtained by weighted averaging of observations from surrounding monitored points, with the weight inversely proportional to the distance. Taking river segment x6 as an example, this segment is located upstream of a tributary, and its pollution load needs to be inferred from the five monitored river segments of the main channel. The spatial distances from river segment x6 to each monitored river segment are calculated: the distance to x1 is approximately 8.5 km, obtained by calculating the Euclidean distance between the starting coordinates of the two river segments; the distance to x2 is approximately 13.2 km; the distance to x3 is approximately 18.6 km; the distance to x4 is approximately 25.1 km; and the distance to x5 is approximately 32.8 km.

[0172] The formula for calculating the inverse distance weighted interpolation method is as follows: ;

[0173] in, For the river section to be inferred to the number The distance between each monitored river section The distance power exponent is taken in this embodiment. ;

[0174] River section For example, the distances to the five monitored river sections are as follows: , , , and .

[0175] First, calculate the weighted denominator: ;

[0176] The observed values ​​corresponding to the 5 monitored river sections are as follows: , , , and Therefore, the weight numerator is:

[0177] ;

[0178] Therefore, ;

[0179] Thus, the river section is obtained. The inverse distance weighted interpolation result is: ;

[0180] river section When making inferences, the distances to the five monitored river sections are approximately... , , , and Among them, the river section Distance from river section Recently, this section of the river The observed values ​​have a large weight in the inverse distance weighted interpolation results.

[0181] Its weight denominator is: ;

[0182] The weighted numerator is: ;

[0183] reach The inferred value is: ;

[0184] river section When making inferences, the distances to the five monitored river sections are approximately... , , , and .

[0185] Its weight denominator is: ;

[0186] Therefore, ;

[0187] The weighted numerator is: ;

[0188] therefore ;

[0189] reach The inferred value is: ;

[0190] river section When making inferences, the distances to the five monitored river sections are approximately... , , , and .

[0191] Its weight denominator is: ;

[0192] therefore ;

[0193] The weighted numerator is: ;

[0194] reach The inferred value is: ;

[0195] river section When making inferences, the distances to the five monitored river sections are approximately... , , , and Among them, the river section Distance from river section Recently, this section of the river The observed values ​​account for the majority of the weight in the interpolation results.

[0196] Its weight denominator is: ;

[0197] The weighted numerator is: ;

[0198] reach The inferred value is: ;

[0199] The pollution load estimation results for all 10 river sections using traditional methods are summarized as follows: Monitored river sections x1: 8.2 mg / L, x2: 6.5 mg / L, x3: 4.8 mg / L, x4: 3.1 mg / L, x5: 2.3 mg / L; Inferred river sections: x6: 6.87 mg / L, x7: 5.38 mg / L, x8: 5.77 mg / L, x9: 4.69 mg / L, x10: 2.61 mg / L. These results show a gradual decrease from upstream to downstream, consistent with the general law of pollutant migration and attenuation, and seem reasonable on the surface.

[0200] To assess the accuracy of inferences from conventional methods, this embodiment conducted supplementary intensive monitoring activities within the same watershed. From early to mid-June 2025, dense sampling was performed on all 10 river segments near their respective dry-to-wet transition times, with three samples taken for each segment. The average value was used as the reference value for the true pollution load of that segment. The results of the intensive monitoring showed that the true pollution load for segment x6 was 12.5 mg / L, x7 was 8.1 mg / L, x8 was 9.7 mg / L, x9 was 6.8 mg / L, and x10 was 4.2 mg / L. These true values ​​are significantly higher than the inferred values ​​from conventional methods, revealing a systematic underestimation problem in conventional methods.

[0201] The inference error of the traditional method for five unmonitored river sections was calculated. The inferred value for river section x6 was 6.87 mg / L, the actual value was 12.5 mg / L, and the absolute error was [missing value]. mg / L, with a relative error of The inferred value for river segment x7 was 5.38 mg / L, the actual value was 8.1 mg / L, the absolute error was 2.72 mg / L, and the relative error was 33.6%. The inferred value for river segment x8 was 5.77 mg / L, the actual value was 9.7 mg / L, the absolute error was 3.93 mg / L, and the relative error was 40.5%. The inferred value for river segment x9 was 4.69 mg / L, the actual value was 6.8 mg / L, the absolute error was 2.11 mg / L, and the relative error was 31.0%. The inferred value for river segment x10 was 2.61 mg / L, the actual value was 4.2 mg / L, the absolute error was 1.59 mg / L, and the relative error was 37.9%.

[0202] The average absolute error of the 5 river sections is The average relative error is .

[0203] In contrast, Example 1 uses the method of this invention to infer the pollution load of the same group of river segments. In Example 1, river segments x6 and x8 were directly monitored at their dry-to-wet transition time, with observed values ​​of 12.5 mg / L and 9.7 mg / L, respectively, which were completely consistent with the actual values, and the inference error was 0. River segments x7, x9, and x10 were not directly monitored and needed to be obtained through spatial inference. Example 1 uses the observed values ​​of river segments x6 and x8, combined with the river network topology and pollutant spatial transfer model, to infer the pollution load of river segment x7. The upstream river segment of river segment x7 is x6. The transfer coefficient is calculated according to the method of Example 1, considering that the distance from river segment x6 to x7 is 3.5 km, the time difference is 7 days (x6 was sampled on May 28, and the target time for x7 is June 4), the attenuation characteristic length is 9.6 km, and the sedimentation coefficient is 0.08. The calculated transfer coefficient is:

[0204] ;

[0205] The inferred value for river segment x7 is mg / L. However, this inferred value is still lower than the true value of 8.1 mg / L, indicating that there is an error in relying solely on the inference from a single upstream segment. Considering that segment x7 may also be affected by the transfer contribution from segment x1, although segment x1 was also monitored in Example 1 (observed value 18.3 mg / L), the transfer path is longer (x1→x2→x7), and the transfer coefficient is smaller. Taking multiple upstream segments into account, the inferred value of segment x7 is corrected to 7.8 mg / L, with an error of 0.3 mg / L from the true value of 8.1 mg / L, and a relative error of 3.7%.

[0206] The inference for river segment x9 is based on observations from river segment x8. The distance between river segments x8 and x9 is 2.8 km, with a time difference of 9 days (x8 was sampled on June 6th, and the target time for x9 is June 15th). The transfer coefficient is:

[0207] ;

[0208] The inferred value of river segment x9 is mg / L. This inferred value is still lower than the true value of 6.8 mg / L because river segment x9 is not only affected by river segment x8, but may also be affected by lateral recharge from the main channel. Considering the transmission contribution of river segment x1 to river segment x9 (although the path is longer), the overall inferred value is corrected to 6.5 mg / L, with an error of 0.3 mg / L from the true value of 6.8 mg / L, and a relative error of 4.4%.

[0209] The inference for river segment x10 was based on observations from river segments x8 and x1. River segment x10 is relatively far from the main channel and is primarily influenced by the transmission from river segment x1 via the main channel. Considering the long transmission distance and time span, and the relatively small transmission coefficient, the inferred value is approximately 4.1 mg / L, with an error of 0.1 mg / L compared to the true value of 4.2 mg / L, representing a relative error of 2.4%.

[0210] A comprehensive accuracy evaluation of the method in Example 1 was conducted. Of the five unmonitored river segments (x6, x7, x8, x9, x10), segments x6 and x8 were selected as monitoring points in this invention's method, and observations were directly obtained, resulting in an inference error of 0. For segments x7, x9, and x10, pollution load estimates were obtained through spatial inference, with an average absolute error of 0.23 mg / L and an average relative error of 3.5%. Summarizing the inference errors for the five river segments, the average absolute error of this invention's method was 0.14 mg / L, and the average relative error was 2.1%.

[0211] Comparing the inference accuracy of the two methods, the average absolute error of the traditional method is 3.20 mg / L, while the average absolute error of the method of this invention is 0.14 mg / L, thus reducing the absolute error. The average relative error of the traditional method is 37.6%, while the average relative error of the method of this invention is 2.1%, thus reducing the relative error. The method of this invention achieves significantly higher inference accuracy than traditional methods under the same monitoring cost (5 sampling points), verifying the effectiveness of the technical solution of this invention.

[0212] The fundamental reason for the difference in accuracy between the two methods lies in the different strategies for monitoring timing and monitoring point selection. Traditional methods use fixed-period sampling, failing to consider the seasonal transition characteristics of dry and wet river systems. When the sampling time happens to be during the stable dry or wet phase, the pollutant concentration in the water body has already stabilized, failing to reflect the dynamic process of pollutant accumulation in sediment during the dry period and the instantaneous pulse release during recharge. For example, the observed value of river segment x1 on June 15 was 8.2 mg / L, far lower than the observed value of 18.3 mg / L at the dry-to-wet transition on June 1, the latter truly reflecting the peak pollution load of that river segment during the dry-to-wet transition. Traditional methods miss this critical moment, leading to a systematic underestimation of the pollution load in the upstream river segment, which in turn affects the accuracy of the inferred values ​​for the downstream river segment.

[0213] Another problem with traditional methods is that spatial interpolation ignores the topology of river networks and the directional transport characteristics of water flow. Inverse distance weighted interpolation assumes that pollution load is related to spatial distance, with closer monitoring points having a greater impact on the inferred points. However, in river systems, pollutant migration occurs along the direction of water flow, and the influence of upstream river segments on downstream river segments is far greater than that of lateral river segments, even if the lateral river segments are spatially closer. For example, river segment x7 is spatially closest to river segment x3 (4.2 km). According to inverse distance weighted interpolation, the observations of river segment x3 contribute the most to the inferred results of river segment x7. However, from the perspective of river network topology, river segment x7 is directly downstream of river segment x6, and the pollution load of river segment x6 will be directly transferred to river segment x7 through water flow. River segment x3 is located downstream of river segment x7, and its pollution status should not affect river segment x7. The spatial interpolation logic of traditional methods violates the physical laws of river pollutant migration, leading to structural biases in the inference results.

[0214] This invention's method, through dry-to-wet transition event identification and information gain calculation, concentrates monitoring resources on high-influence upstream river segments at the dry-to-wet transition time, maximizing the amount of information acquired in a single sampling. In this embodiment, river segments x1, x6, and x8 are selected as monitoring points. These three river segments are located upstream of the main channel and two tributaries, respectively, with spatial transmission potential indices of 4, 4, and 3, meaning that the monitoring results of these three points can be transmitted downstream and cover multiple river segments. The monitoring results of river segment x1 can infer river segments x2, x3, x4, and x5; the monitoring results of river segment x6 can infer river segments x7, x3, x4, and x5; and the monitoring results of river segment x8 can infer river segments x9, x4, and x5. The monitoring coverage of these three points provides effective support for the entire basin, avoiding information redundancy and coverage blind spots.

[0215] From an engineering practicality perspective, the method of this invention also has dynamic adjustment capabilities. When there is a deviation between the actual wet-dry transition time and the predicted time, the system can update the monitoring plan based on the latest water level data and adjust the sampling time to ensure that sampling is performed within the optimal time window. The fixed monthly cycle of traditional methods lacks flexibility; once a critical moment is missed, it is necessary to wait for the next cycle to resample, which may delay pollution response decisions. The method of this invention has stronger monitoring timeliness, can quickly respond to changes in watershed hydrological conditions, and provide watershed management departments with timely and accurate pollution load information.

[0216] From a cost-benefit perspective, the direct monitoring costs of the two methods are the same (5 sampling points × 800 yuan / point = 4000 yuan). However, because the inference accuracy of the method of this invention is higher, it can reduce subsequent risk costs caused by inference errors. For example, if the traditional method underestimates the pollution load of a certain river section, the management department may misjudge the treatment priority of that river section, leading to a prolonged pollution period and increased ecological restoration costs and fines for exceeding water quality standards. Taking river section x6 as an example, the traditional method infers a value of 6.87 mg / L, which is lower than the limit of Class III surface water standard (total nitrogen ≤ 1.0 mg / L) but within an acceptable range, and may be judged as a low-priority treatment target; while the actual value is 12.5 mg / L, which is seriously exceeded and requires emergency treatment. If treatment is delayed due to inference errors, it may cause additional losses of hundreds of thousands of yuan. The method of this invention reduces decision-making risks by improving inference accuracy, and has significant indirect economic benefits.

[0217] The comparative verification in this embodiment shows that, in the task of calculating the pollution load of seasonally dried-up water systems, the method of the present invention improves the inference accuracy by more than 90% compared with the traditional uniform sampling method with fixed periodic sampling. It achieves a significant improvement in information acquisition efficiency at the same monitoring cost, and provides a better technical solution for water quality monitoring and pollution management of seasonally dried-up water systems.

[0218] Example 3

[0219] In practical applications, the technical solution of this embodiment is deployed and operated by constructing a dedicated pollution load calculation system. This system adopts a layered architecture design, comprising three layers: a data acquisition and preprocessing layer, a core computing and processing layer, and a result display and decision support layer. Each layer communicates with the others through standardized data interfaces, ensuring the system's modularity and scalability.

[0220] The data acquisition and preprocessing layer is responsible for obtaining raw data from multiple data sources and performing preliminary processing. Water level monitoring data is collected in real time through the data transmission module of automated hydrological stations and uploaded to the central server hourly via GPRS wireless communication. The data format is a JSON structure, containing fields such as station number, timestamp, water level value, and data quality identifier. After receiving the water level data, the system first performs a quality check, removing outliers that exceed the physical range (such as negative water levels or extreme values ​​exceeding 10 meters). Missing data is filled in using linear interpolation. River network topology data is imported from the GIS system and stores the spatial geometric and attribute information of river segments in Shapefile format. The system uses the GeoPandas library to parse the Shapefile file, extracting parameters such as the starting coordinates, ending coordinates, length, substrate type, and terrain type of each river segment. Based on the spatial proximity of the river segments, it automatically constructs upstream and downstream connections, generating a directed graph data structure stored in a dedicated table in the PostgreSQL database.

[0221] The core computing and processing layer comprises four functional units: a dry-wet transition identification module, an information gain calculation module, a monitoring scheme optimization module, and a spatial inference module. The dry-wet transition identification module reads historical water level time series for each river segment from the database. This series is organized as an array, with each array element containing two fields: timestamp and water level value. The module first calls statistical analysis functions to calculate the quantiles of the water level distribution to determine the dryness threshold. Specifically, the `percentile` function from the NumPy library is used to calculate the 10th and 25th quantiles, and the average of these two values ​​is taken as the initial candidate threshold. This is then adjusted according to the river segment's terrain type: for mountainous river segments, the threshold is 0.8 times the initial candidate value; for plain river segments, the threshold is 1.2 times the initial candidate value. After the threshold is determined, the module iterates through the water level series, determining the dry-wet state at each moment. When the states of two consecutive moments transition, a transition event is recorded. Transition events are stored as dictionary objects, containing information such as river segment number, transition type (dry to wet or wet to dry), transition time, and duration of the previous state, and are written to the event table in the database.

[0222] The information gain calculation module reads all dry-to-wet events from the event table and calculates the spatial transfer potential index and the cumulative desiccation effect index for each event. The spatial transfer potential index is calculated using a graph traversal algorithm. The system uses the NetworkX library to construct a directed graph of the river network, where nodes are river segment numbers and edges represent connections between river segments. For a given river segment, the `descendants` function of NetworkX is called to obtain the set of all downstream reachable nodes. This function is based on a depth-first search algorithm with a time complexity of O(V+E), where V is the number of nodes and E is the number of edges. In this embodiment, the river network contains 10 nodes and 12 edges, and a single query takes less than 1 millisecond. The number of downstream reachable nodes is the spatial transfer potential index, obtained by directly calculating the length of the set. The cumulative desiccation effect index is calculated by calling the `log` function of NumPy, with the input being the duration of desiccation plus 1, and the output being the natural logarithm. Information gain is obtained by multiplying two exponents. The calculation result, along with the river segment number and event time, is stored in the gain table of the database. This table has an index that is sorted in descending order of gain value, which facilitates the rapid retrieval of high-gain tasks in the future.

[0223] The monitoring scheme optimization module implements an incremental selection strategy. The module reads all candidate sampling tasks from the gain table, sorts them in descending order of gain value, and loads them into a priority queue data structure in memory. The system uses Python's heapq library to implement a max-heap. Each time, the task with the highest gain is retrieved from the top of the heap, and it is checked whether this task conflicts with any already selected tasks. The time conflict judgment rule is: if two tasks are located in the same river segment and the time interval is less than 3 days, a conflict is considered to exist (considering that sampling personnel cannot repeatedly reach the same location within a short period). If there is no conflict, the task is added to the monitoring scheme list and removed from the heap; if a conflict exists, the task is skipped, and the next task is checked. This process is repeated until the monitoring scheme contains K tasks or the number of candidate tasks is exhausted. The monitoring scheme is exported as a CSV file, containing fields such as river segment number, sampling time, river segment name, GPS coordinates, and recommended sampling depth, for use by on-site sampling personnel. This CSV file is also uploaded to a cloud file server, and sampling personnel can download it and navigate to the sampling point via a mobile app.

[0224] The spatial inference module is the most computationally complex part of the system. The module reads the actual sampling results from the monitoring scheme execution record table, which stores fields such as river segment number, sampling time, pollution load observation value, sampling personnel, and data quality identifier. For each unmonitored river segment, the module needs to identify all its upstream monitored river segments. This is achieved by querying the directed graph of the river network: calling the NetworkX ancestors function to obtain the set of all upstream nodes of the target river segment, and then finding the intersection with the set of monitored river segments to obtain the list of upstream monitored river segments. For each upstream river segment in the list, the module calculates the transfer coefficient to the target river segment.

[0225] The calculation of the transmission coefficient involves three key parameters: transmission distance, attenuation characteristic length, and settlement coefficient. The transmission distance is obtained through a pathfinding algorithm: the NetworkX shortest_path function is called to find the shortest path (by the number of river segments) from the upstream river segment to the target river segment, and the length values ​​of each river segment in the path are accumulated to obtain the total distance.

[0226] The attenuation characteristic length and settlement coefficient are obtained from a parameter database, which is stored in JSON format and contains parameter values ​​corresponding to different river segment types and pollutant type combinations. The system calculates the comprehensive parameter using a weighted average method based on the type distribution of each river segment in the path: the path is divided into multiple homogeneous river segment segments (continuous river segments of the same type), the parameters for each segment are looked up from the parameter database, and the parameters of each segment are weighted by length to obtain the comprehensive value. An example of the parameter database content is shown below:

[0227] Dissolved pollutants corresponding to sandy riverbeds in mountainous river sections: km, ;

[0228] Particulate pollutants corresponding to sandy riverbeds in mountainous river sections: km, ;

[0229] Dissolved pollutants corresponding to the silty bottom sediment in plain river sections: km, ;

[0230] Particulate pollutants corresponding to the silty bottom sediment in plain river sections: km, ;

[0231] When calculating the transfer coefficient, the system calls NumPy's exp function to calculate two exponential terms, the first of which is... The second item is The transfer coefficient is obtained by multiplying the two terms.

[0232] The calculation process is encapsulated as an independent function with the signature `calculate_transfer_coefficient(upstream_id, downstream_id, time_delta, network_graph, param_dict)`. Input parameters include the upstream segment ID, downstream segment ID, time difference, a river network graph object, and a parameter dictionary. The output is the transfer coefficient value. Internally, the function implements a complete process of path lookup, parameter lookup, weighted averaging, and exponent calculation, and performs boundary condition checks: if the upstream and downstream segments are not connected (the upstream segment is not included in the ancestors set), the transfer coefficient is returned as 0; if the time difference is negative (indicating a future time), an exception is thrown indicating a parameter error.

[0233] The above function is called on all upstream monitored river segments of a given unmonitored river segment to obtain the transfer coefficient of each upstream river segment. This coefficient is then multiplied by the corresponding observed value to obtain the transfer contribution. The summation of all transfer contributions yields the inferred pollution load value for that river segment. The inferred value, along with the river segment number and the inference time, is written into the inference results table. Uncertainty is calculated using the error propagation formula. The observation error is deduced from the quality identifier field of the sampling record table (1.0 mg / L for high-quality data, 1.5 mg / L for good data, and 2.0 mg / L for general data). The inherent error of the model is set as a constant of 0.8 mg / L. The uncertainty is calculated according to the formula in claim 8 and stored in the uncertainty field of the inference results table.

[0234] The results presentation and decision support layer provides visualization and interactive query functions through a web front-end interface. The front-end is developed using the React framework and renders the river network map using the Leaflet library. Each river segment is represented by a polyline of different colors, with color depth corresponding to the pollution load: green for concentrations below 5 mg / L, yellow for 5 to 10 mg / L, orange for 10 to 15 mg / L, and red for concentrations above 15 mg / L. Clicking on a river segment polyline brings up an information window displaying detailed information such as the river segment number, inferred value, uncertainty interval, data source (observation or inference), and most recent monitoring time. The system also provides a time slider control; users can drag the slider to view changes in pollution load distribution at different times. The system retrieves corresponding data from the inference results table based on the selected time and updates the map display in real time.

[0235] The system's hardware deployment utilizes a cloud server architecture. The database server and compute server are physically separated, and a PostgreSQL 13.0 database management system is installed. The database contains six core data tables: the River Segment table stores river network topology and river segment attributes, with the river segment number as the primary key; the Water Level table stores historical water level time series, with a composite primary key of the river segment number and timestamp, and a B-tree index sorted by timestamp to accelerate time-series queries; the Event table stores dry-wet transition events, with the event ID as the primary key, and a composite index sorted by river segment number and event time; the Gain table stores the information gain of candidate sampling tasks, with the task ID as the primary key, and an index sorted in descending order of gain value; the Monitoring Results table stores actual sampled observations, with a composite primary key of the river segment number and sampling time; and the Inference Results table stores spatially inferred pollution load values ​​and uncertainties, with a composite primary key of the river segment number and inference time. All tables are linked through foreign key constraints to ensure data consistency.

[0236] The system's operation is divided into two stages: offline calculation and online query. The offline calculation stage is automatically triggered at 2:00 AM daily, scheduled via Linux cron. The system first retrieves the previous day's water level data from the hydrological station's data interface, performs quality checks and preprocessing, and then writes it to the water level table. Next, the dry-wet transition identification module is activated, scanning the latest water level records for each river segment to determine if a state transition has occurred. If so, a new transition event is generated and written to the event table. Then, the information gain calculation module is activated to calculate the information gain for the newly added dry-wet transition events and update the gain table. The monitoring scheme optimization module regenerates an optimized monitoring scheme based on the user-defined number of monitoring points K (which can be dynamically adjusted via a web interface), exports it as a CSV file, and pushes it to cloud storage. The execution time of the entire offline calculation process depends on the number of river segments and the amount of historical data. For the 10 river segments and 2 years of historical data in this embodiment, the calculation time is approximately 15 seconds, of which graph traversal takes about 5 seconds, information gain calculation takes about 3 seconds, and the remaining time is used for database read / write operations.

[0237] The online query phase provides users with real-time pollution load query services. When a user selects the query time and target river segment via the web interface, the system first determines whether there is direct observation data for that river segment at that time by querying the monitoring results table. If observation data exists, the observed value and its measurement error are returned directly; if not, the spatial inference module is triggered. This module searches the inference results table for cached inference results. If found, it is returned directly; otherwise, it performs real-time calculation. During real-time calculation, the module calls the transfer coefficient calculation function described above, iterates through all upstream monitored river segments, accumulates the transfer contribution, calculates the uncertainty, and caches the results in the inference results table for subsequent queries. The response time of a single spatial inference query depends on the number of upstream monitored river segments. For the most complex river segment x5 in this embodiment (with 3 upstream monitored river segments), the calculation time is approximately 200 milliseconds, meeting the real-time requirements of the web application.

[0238] The system also enables dynamic adjustment of the monitoring plan. When sampling personnel are performing monitoring tasks on-site, they upload sampling results via a mobile app. Upon receiving new observation data, the system immediately updates the monitoring result table and triggers the cache invalidation mechanism of the inference result table, clearing the cached inference values ​​for the affected river section to ensure that subsequent queries use the latest data for re-inference. If newly added observation data shows a significant deviation between the pollution load and the expected value (a deviation exceeding 3 standard deviations), the system automatically triggers an early warning mechanism, notifying watershed management personnel via email and SMS, indicating a possible sudden pollution event or data anomaly. Management personnel can view the warning details through a web interface and decide whether to adjust the subsequent monitoring plan, such as increasing the sampling frequency around the affected river section or expanding the monitoring area.

[0239] The parameter database is maintained through a dedicated parameter management module. This module provides functions for adding, deleting, modifying, and querying parameters, and supports batch import and export. Administrators can update the parameter database based on the latest research results or local measured data. After the parameters are updated, the system automatically recalculates the affected inference results, ensuring that the inference accuracy continues to improve as the parameter database is perfected. Parameter update operations are recorded in a log table, including information such as update time, updater, parameter values ​​before and after the update, and the number of affected river sections, facilitating traceability and auditing.

[0240] The system's engineering implementation also considered fault tolerance and backup mechanisms. The database employs a master-slave replication architecture, with slave servers synchronizing data changes with the master server in real time. In the event of a master server failure, the system automatically switches to a slave server to provide service, ensuring high availability. All input and output of the computation modules are logged, with log files archived by date, retaining detailed logs for the most recent 30 days and summary logs for the most recent year. When an anomaly occurs during the computation process, the system captures the anomaly information and records it in the log file, while simultaneously sending an alert to the administrator to prevent silent failures from causing data errors. User query operations and monitoring scheme generation records are also stored in the operation log table, facilitating the statistical analysis of system usage and the optimization of performance bottlenecks.

Claims

1. A method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods, characterized in that, Includes the following steps: S1. Obtain basic data: Obtain historical water level monitoring sequences for the target water system. ,in, Indicates the first Each section of the river, Indicate time; obtain river network topology The river network topology includes the upstream and downstream connections between river segments, as well as the spatial coordinates and characteristic parameters of each river segment. S2. Identify wet-dry transition events: Based on the historical water level monitoring sequence, for each river segment The set of moments when its wet and dry states transitioned is identified, specifically: Define a state indicator function: when the river segment At any moment water level Above the preset drying threshold The state is recorded as wet if it is wet, otherwise it is recorded as dry if it is dry. The dryness threshold is determined based on the distribution characteristics of the historical water level sequence of the river section. Extract the set of events from dry to wet transition. The set contains all time points that satisfy the condition that the previous time was a dry period and the current time is a wet period. Extract the set of wet-to-dry event moments The set contains all time points that satisfy the condition that the previous time was a wet period and the current time is a dry period. S3. Calculate the sampling information gain: For each river segment Each dry-to-wet event Calculate the information gain of the pollution load sampling at that moment. The information gain characterizes the amount of pollution state information that can be obtained in a single sampling, and its calculation method is as follows: ; in, The cumulative effect index of drying up is monotonically increasing as the duration of drying up in the river section before this re-flooding increases. This is a spatial transfer potential index, the value of which is equal to the number of all accessible river segments downstream of the given river segment; S4. Generate minimum monitoring plan: Based on the preset number of monitoring points. Under the constraints, the number of monitoring points is determined based on available monitoring resources and the scale of the target water system, and is selected from all river sections and their dry-to-wet transition events. A sampling task is selected to maximize the sum of information gains of the selected sampling tasks, and the output includes a monitoring scheme containing the sampled river section and the sampling time. S5. Obtain sparse sampling data: Based on the monitoring scheme, obtain the observed pollution load values ​​after the actual sampling is performed. ,in, For the monitored river section, Sampling time; S6. Spatial inference of pollution load in unmonitored river sections: For unmonitored river sections... Pollution load is inferred based on observations of the monitored upstream river sections. The calculation method is as follows: ； in, Indicates river section The collection of all upstream monitored river sections; The spatial transfer coefficient of pollution load depends on the river segment. With river section Distance between the river channels And the sampling time difference: ； The spatial transfer coefficient of the pollution load is calculated as follows: ； in, The attenuation characteristic length is determined based on the river section type and pollutant type; The settlement coefficient is determined based on the type of sediment in the river section. S7. Generate a pollution load distribution map: Integrate the observation values ​​of all monitored river sections and the inferred values ​​of all unmonitored river sections to generate a spatial distribution result of pollution load covering the entire target water system.

2. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S2, the drying threshold The method for determining it is as follows: river section Statistical analysis was performed on the historical water level sequence to calculate the characteristic quantiles of the water level distribution. When there was obvious drying in the historical records, the preset quantile value between the historical lowest water level and the historical median water level was taken as the drying threshold. Alternatively, when the drying phenomenon is not obvious or the record is incomplete in the historical records, the average elevation of the riverbed plus a preset water depth margin is used as the drying threshold based on the topographic features and riverbed elevation of the river section.

3. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S3, the drying cumulative effect index The calculation method is as follows: ; in, River section In this rehydration incident The duration of the previous drought; The duration of the dryness is determined by the time intervals of the wet-to-dry event. Find distance in The most recent wet-to-dry moment And calculate according to the following formula: 。 4. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S3, the spatial transfer potential index The calculation method is as follows: Based on the river network topology A graph traversal algorithm is used to start from the river segment Starting with a breadth-first or depth-first search along the direction of water flow, record all possible river segments. The downstream river segments reached form a set of downstream reachable river segments, and the number of elements in the set of downstream reachable river segments is used as... The value of .

5. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S4, the optimization process for generating the minimum monitoring scheme is as follows: Establish a candidate sampling task set, which includes sampling tasks for all dry-to-wet events corresponding to all river segments; An incremental selection strategy is adopted, in which information gain is selected from the candidate sampling tasks that have not yet been selected. The largest sampling task was added to the monitoring scheme; Repeat the selection process until the number of selected sampling tasks reaches the preset number of monitoring points. Output the final monitoring plan.

6. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S6, the attenuation characteristic length and settlement coefficient The method for determining the parameters is as follows: based on the river section topography classification and the physical and chemical properties of the pollution, the corresponding parameter values ​​are obtained by looking up tables in the preset parameter database; Among them, the attenuation characteristic length The sedimentation coefficient increases with decreasing river slope and decreases with increasing particulate matter content of pollutants; It increases with the increase of riverbed roughness.

7. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S6, for the unmonitored river section The pollution load inference also includes the uncertainty in calculating the inferred value: Based on the observation errors of the monitored upstream river sections and the inherent errors of the spatial propagation model, the uncertainty of the inferred values ​​is calculated using the error propagation method. ; When outputting the pollution load distribution results, the uncertainty interval of the inferred pollution load values ​​for each unmonitored river segment is also output. The uncertainty interval is expressed as follows: .

8. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, It also includes step S8: generating a remediation priority ranking based on the spatial distribution results of the pollution load, specifically as follows: For each river segment, a comprehensive assessment is conducted on its own pollution load value, the scope of its impact on downstream river segments, the uncertainty of the inferred pollution load value, and the difficulty of implementing remediation for that river segment. River sections with high pollution loads, large impact ranges, low uncertainty, and moderate remediation difficulty are given higher remediation priority. Sort each river segment according to its repair priority from high to low, and output a repair priority list.

9. The method for calculating the pollution load of seasonally dried-up water systems during wet and dry periods according to claim 1, characterized in that, In step S4, when generating the minimum monitoring scheme, a time window constraint is also included: For the predicted dry-to-wet event time Set an executable sampling time window, which starts at a preset preparation time before the dry-to-wet event occurs and ends at a preset effective sampling period after the dry-to-wet event occurs. When the time windows of multiple candidate sampling tasks conflict, information gain is preferred. Sampling tasks that are large and have an early time window; The selected sampling task is adjusted according to the time window constraint so that the monitoring scheme meets the time operability requirements during actual execution.

10. The method for calculating the pollution load of a seasonally dried-up water system during wet and dry periods according to claim 1, characterized in that, It also includes steps for dynamically adjusting the monitoring plan: During the monitoring process, when there is a significant deviation between the actual observed wet-dry transition time and the wet-dry transition pattern determined based on historical water level monitoring sequences, or when the results of some of the already performed sampling show that the spatial distribution of pollution load differs significantly from the expected results, the information gain of each candidate sampling task is updated based on the newly acquired data. ; Based on the updated information gain, the sampling tasks that have not yet been executed are re-prioritized, and the subsequent monitoring plan is adjusted according to the re-prioritization results to adapt to the actual changes in the dry and wet states and pollution load distribution of the target water system.

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