A method and system for simulating total phosphorus concentration in cryosphere watersheds

Abstract

This invention belongs to the field of total phosphorus concentration simulation, and provides a method and system for simulating total phosphorus concentration in cryospheric watersheds. The method involves acquiring meteorological temperature, runoff, and total phosphorus concentration within a certain time period in the cryospheric watershed; preprocessing the acquired data; constructing a dynamic phosphorus simulation model considering the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryospheric watershed; using a multi-objective optimization algorithm to optimize the constructed dynamic phosphorus simulation model, with the objectives of maximizing the correlation coefficient and Nash efficiency coefficient, iteratively calculating the optimal solution for the parameters of the dynamic phosphorus simulation model; based on the obtained optimal solution, cross-validation and validity verification are performed on the optimized dynamic phosphorus simulation model to obtain the final dynamic phosphorus simulation model; and finally, using the final dynamic phosphorus simulation model, total phosphorus concentration simulation is achieved. This invention improves the model's adaptability and prediction accuracy in various regions.

Description

Technical Field

[0001] This invention belongs to the field of total phosphorus concentration simulation, specifically relating to a method and system for simulating total phosphorus concentration in cryosphere watersheds. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the ongoing impacts of climate change, the dynamics of phosphorus in the cryosphere have undergone significant changes, particularly in terms of phosphorus availability and mobility. Rising temperatures and the melting of glaciers and permafrost in cold regions alter the processes of phosphorus formation, transport, and deposition, thereby affecting nutrient flows in freshwater systems. Increased phosphorus runoff driven by these changes can lead to eutrophication, which in turn degrades water quality and impacts aquatic ecosystems. Therefore, understanding these changes is crucial for the effective management of water resources in the context of global warming.

[0004] However, current models used to simulate phosphorus dynamics in cold regions have limitations in accurately capturing the complex processes driving phosphorus release and transport. These models often fail to account for characteristics specific to cold regions, such as thermodynamic processes, sediment availability, and the dynamic mechanisms of phosphorus storage depletion. Consequently, these models frequently exhibit significant errors in predicting phosphorus flows in regions affected by rapid hydrological and climate change.

[0005] On the other hand, existing models for simulating phosphorus dynamics in cold regions generally employ single-objective optimization, which easily overlooks the Pareto trade-off between model parameters, leading to results trapped in local optima. Moreover, existing models lack validation for the hysteresis effect of extreme hydrological events (such as the phenomenon of phosphorus concentration leading runoff peak during snowmelt), resulting in insufficient predictive ability in extreme hydrological events and affecting water quality management and decision-making. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a method and system for simulating total phosphorus concentration in cryosphere watersheds. This invention incorporates the unique thermodynamic processes and freeze-thaw cycle mechanism of the cryosphere, employs multi-objective optimization, and introduces a modeling method for the hysteresis effect of extreme hydrological events. This enhances the model's adaptability and prediction accuracy across various regions, thereby improving phosphorus availability and transport forecasting, and providing a more valuable reference for water resource management in the context of climate change.

[0007] According to some embodiments, the present invention adopts the following technical solution:

[0008] A method for simulating total phosphorus concentration in a cryosphere watershed includes the following steps:

[0009] Obtain meteorological temperature, runoff, and total phosphorus concentration in a cryosphere basin over a specific period of time;

[0010] The acquired data is preprocessed;

[0011] Considering the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin, a dynamic phosphorus simulation model is constructed.

[0012] Using at least some of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, a multi-objective optimization algorithm is used to optimize the constructed phosphorus dynamic simulation model. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model.

[0013] Using another portion of the preprocessed meteorological temperature, runoff, and total phosphorus concentration data as the validation dataset, the optimized phosphorus dynamics simulation model is cross-validated and validated based on the optimal solution of the obtained parameters, resulting in the final phosphorus dynamics simulation model.

[0014] Meteorological temperature and runoff of the cryosphere basin within the target time period are obtained and preprocessed. The final phosphorus dynamics simulation model is then used to simulate the total phosphorus concentration.

[0015] As an alternative implementation, the meteorological temperature and runoff are obtained on a daily basis.

[0016] As an alternative implementation, the preprocessing process includes identifying mutation points in the data using a mutation point detection method and removing the mutation points;

[0017] The acquired meteorological temperatures are segmented by a threshold, and data below the set temperature is removed.

[0018] As an alternative implementation method, the construction of a phosphorus dynamics simulation model is based on the premise that the daily variation of soil temperature has a limited impact on phosphorus activity, the snowmelt process is equivalent to an increase in runoff, the phosphorus concentration in the river is assumed to be uniform and continuous in time and space, phosphorus availability has a feedback effect on phosphorus transport dynamics, and the interaction between sediment and phosphorus plays a key role in phosphorus dynamics.

[0019] As an alternative implementation method, the constructed phosphorus dynamic simulation model is as follows:

[0020] ;

[0021] in, This represents the total phosphorus concentration. An index characterizing the long-term phosphorus storage depletion effect is calculated based on the cumulative changes in daily runoff and phosphorus transport. Daily weather temperature, This represents the two-day increase in runoff. Here are the coefficient parameters, where i is 1, 2, or 3. Here, j represents the coefficient parameter, where j is 1, 2, 3, 4, or 5. Flow rate, unit is m 3 / s.

[0022] As an alternative implementation method, in the process of multi-objective optimization of the constructed phosphorus dynamic simulation model, a multi-objective frog-leap algorithm is used for multi-objective optimization, specifically including:

[0023] Suppose that within a convex-dimensional search space, random generation... A frog population consists of only one frog. i A frog is represented as The fitness function is used as the heuristic function of the algorithm to measure the performance of the frogs, and the fitness function value of each frog is calculated. The frogs were then sorted according to their fitness values, and the entire frog population was divided into... m There are several ethnic groups, and each ethnic group has... n There are 10 frogs, with the first frog assigned to the first group, the second frog assigned to the second group, and so on. m Only one frog was assigned to the first m The first ethnic group, m+1 Only one frog is assigned to the first group, and so on, assuming... Y k For the first k The distribution process of a set of frog populations is described by the following formula:

[0024] ;

[0025] ;

[0026] For each population, a local depth-first search is performed; that is, in one iteration, within each population, selects... q Create a subpopulation of frogs and find the worst-performing frog in that subpopulation. Optimal Frog And the best frog in the entire population. Then only for Perform the update operation, with the update strategy as follows:

[0027] ;

[0028] In the formula, S This represents the adjustment vector for the worst-performing frog; min and max are functions for finding the minimum and maximum values, respectively; for discrete integer variables, rounding is required. r It is a random number between [0,1]. This represents the maximum step size that the frog is allowed to change.

[0029] If the frog is updated Its fitness value is better than Then replace If the fitness value does not improve, then use replace Repeat the update strategy, and check again whether the fitness value has improved after this update. If there is still no improvement, randomly generate a frog to replace it. Repeat this operation until the required number of iterations is reached;

[0030] when m After each population completes a local depth search, all green plots within the population are reordered according to their fitness, global information is exchanged, and then they are divided into... m For each population, perform a local depth search, repeating this operation until the required number of iterations or a stopping condition is met.

[0031] As an alternative implementation method, in the process of multi-objective optimization aiming to maximize the correlation coefficient and the Nash efficiency coefficient, the correlation coefficient... Nash efficiency coefficient / ,in, For the i-th measured value, For the first i One simulated value; n The length of the data sequence. This is the average value of the measured values. This is a simulated average value; when the simulated value and the measured value are equal, =1 indicates a match, when The value <1 indicates a lower degree of data consistency.

[0032] As an alternative implementation method, the process of cross-validation and validity verification of the optimized phosphorus dynamic simulation model includes dividing the acquired data into multiple parts, selecting one part as the training dataset and the other part as the validation dataset each time, and performing multiple validations. The division of the training dataset and the validation dataset is different each time. In each validation process, the average error and variance analysis method of cross-validation are used to evaluate the stability of the model. By calculating the index of each cross-validation, it is confirmed whether the model has good generalization ability. Through cross-validation, it is identified whether the model has overfitting.

[0033] A system for simulating total phosphorus concentration in a cryosphere watershed includes:

[0034] The data acquisition module is configured to acquire meteorological temperature, runoff, and total phosphorus concentration within a certain time period in the cryosphere basin;

[0035] The data preprocessing module is configured to preprocess the acquired data;

[0036] The model building module is configured to construct a dynamic phosphorus simulation model that takes into account the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin.

[0037] The model optimization module is configured to use at least a portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, and to perform multi-objective optimization on the constructed phosphorus dynamic simulation model using a multi-objective optimization algorithm. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model.

[0038] The model validation module is configured to use another portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as the validation dataset. Based on the optimal solution of the obtained parameters, it performs cross-validation and validity verification on the optimized phosphorus dynamics simulation model to obtain the final phosphorus dynamics simulation model.

[0039] The simulation module is configured to acquire meteorological temperature and runoff of the cryosphere basin within the target time period, perform preprocessing, and use the final phosphorus dynamic simulation model to simulate total phosphorus concentration.

[0040] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] This invention introduces the unique thermodynamic processes and freeze-thaw cycle mechanism of the cryosphere during the model construction process, which improves the model's adaptability and prediction accuracy in high-altitude and cold regions. It solves the problem that existing simulation models cannot accurately simulate the dynamic changes of phosphorus in high-altitude and cold regions, leading to deviations in prediction results.

[0043] In the process of model optimization, this invention adopts a multi-objective optimization method, considers the Pareto trade-off between model parameters, improves optimization efficiency, overcomes the limitations of traditional single-objective optimization, can consider multiple performance indicators at the same time, improves parameter calibration efficiency, can not only obtain more accurate model parameters, but also avoid local optima caused by over-focusing on a single objective.

[0044] In the process of model validation, this invention introduces a hysteresis effect modeling method to improve the model's predictive ability in extreme hydrological events.

[0045] Through experiments, the simulation results of this invention improve the Nash efficiency coefficient (NSE) by 15%~20%, are applicable to complex hydrological conditions in cryosphere watersheds, shorten parameter calibration time by 30%, support rapid iteration, reduce the average cross-validation error to within ±5%, and significantly enhance model stability, which is helpful for cryosphere environmental management.

[0046] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0047] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0048] Figure 1 This is a schematic diagram of the overall process of one embodiment;

[0049] Figure 2 This is a schematic diagram illustrating the solution process of the frog-jumping algorithm in one embodiment.

[0050] Figure 3 This is a schematic diagram of the effect of a simulation model in one embodiment, wherein (a) is a Taylor plot comparing the model used by the method provided by the present invention with other methods, wherein (b) is a comparison diagram of the simulated values ​​and observed values ​​of the method provided by the present invention and the traditional method, and wherein (c) is a schematic diagram of the time series comparison of the simulated values ​​and observed values ​​of the method provided by the present invention and the traditional method.

[0051] Figure 4 This is a schematic diagram illustrating the effects of different methods in one embodiment on analyzing the relationship between runoff and total phosphorus concentration over time. (a) is a schematic diagram of the effect of clockwise hysteresis in event 1, (b) is a schematic diagram of the effect of counterclockwise hysteresis in event 2, (c) is a schematic diagram of the effect of figure-eight hysteresis in event 3, and (d) is a schematic diagram of the effect of clockwise hysteresis in event 4. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. 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 invention pertains.

[0054] 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 scope of exemplary embodiments according to the invention. 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.

[0055] Where there is no conflict, the embodiments and features described in this application may be combined with each other.

[0056] Example 1

[0057] A method for simulating total phosphorus concentration in cryosphere watersheds, such as Figure 1 As shown, it includes the following steps:

[0058] Obtain meteorological temperature, runoff, and total phosphorus concentration in a cryosphere basin over a specific period of time;

[0059] The acquired data is preprocessed;

[0060] Considering the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin, a dynamic phosphorus simulation model is constructed.

[0061] Using at least some of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, a multi-objective optimization algorithm is used to optimize the constructed phosphorus dynamic simulation model. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model.

[0062] Using another portion of the preprocessed meteorological temperature, runoff, and total phosphorus concentration data as the validation dataset, the optimized phosphorus dynamics simulation model is cross-validated and validated based on the optimal solution of the obtained parameters, resulting in the final phosphorus dynamics simulation model.

[0063] Meteorological temperature and runoff of the cryosphere basin within the target time period are obtained and preprocessed. The final phosphorus dynamics simulation model is then used to simulate the total phosphorus concentration.

[0064] The specific details are described in detail below.

[0065] First, this embodiment acquires input data and verification data within a certain period of time as the initial dataset.

[0066] Input data includes:

[0067] Meteorological data: Daily temperature (°C): used to reflect the impact of climate change on phosphorus dynamics in cold regions.

[0068] Hydrological data: Daily runoff Q (m³) 3 / s): As a direct driver of phosphorus transport, changes in runoff are closely related to phosphorus loss.

[0069] Validation data:

[0070] Total phosphorus concentration (TPC) (mg / L): Monitoring changes in phosphorus concentration is a key indicator for simulating phosphorus flow and dynamics, and is used for model calibration and validation.

[0071] The next step is preprocessing, which includes:

[0072] Outlier removal:

[0073] This embodiment employs the Pettitt mutation detection method to identify mutation points in the data. This method can effectively detect abrupt changes in the data, ensuring the temporal consistency and authenticity of the data, and preventing outliers from interfering with model training and parameter optimization.

[0074] Standardization process:

[0075] This embodiment uses a -4°C threshold for temperature segmentation. Below this temperature, phosphorus release activity is assumed to be zero because low temperatures inhibit microbial activity and reduce phosphorus release. This standardization process ensures that the influence of soil temperature on phosphorus release has a reasonable physical basis.

[0076] A dynamic phosphorus simulation model, namely the SAT-P model, was constructed.

[0077] Model assumptions:

[0078] (1) The diurnal variation of soil temperature has a limited effect on phosphorus activity.

[0079] We assume that the diurnal variation of soil temperature has a limited impact on phosphorus activity. Therefore, the model only considers the effect of long-term average temperature on phosphorus adsorption-desorption processes in the soil. This assumption acknowledges that, despite diurnal temperature variation, overall climatic conditions dominate phosphorus dynamics.

[0080] (2) Snowmelt is equivalent to an increase in runoff.

[0081] We assume that snowmelt can be represented by an increase in runoff, and that there is no significant difference between snowmelt and rainfall in their phosphorus scouring capacity. This simplification allows the model to treat the two forms of water input uniformly, facilitating the assessment of phosphorus mobilization during hydrological events.

[0082] (3) Phosphorus concentration in the river is assumed to be uniform and continuous in time and space.

[0083] This study assumes that phosphorus concentrations in rivers are uniform and continuous in both time and space. This assumption simplifies the modeling of phosphorus dynamics by treating rivers as homogeneous systems, facilitating the calculation of transport and dilution effects. However, it also acknowledges the possibility of local variations due to factors such as point source emissions or sediment interactions.

[0084] (4) Phosphorus availability has a feedback effect on its transportation dynamics.

[0085] The model incorporates a feedback mechanism, meaning that phosphorus availability influences its transport dynamics. Specifically, during events such as snowmelt or rainfall, while phosphorus is mobilized downstream, it may affect future phosphorus availability through changes in sediment dynamics and nutrient storage within the watershed.

[0086] (5) The interaction between sediments and phosphorus is crucial to phosphorus dynamics.

[0087] This hypothesis assumes that sediment transport significantly influences phosphorus binding and release, thereby affecting the overall phosphorus concentration in water bodies. This hypothesis underscores the crucial role of sediments in phosphorus dynamics.

[0088] Model structure:

[0089] The SAT-P model, based on the coupling mechanism of sediment availability and transport, combines thermodynamic and hydrological processes to simulate phosphorus dynamics in cold-region environments. By integrating dynamic changes in temperature, runoff, and phosphorus storage depletion, the model accurately predicts phosphorus concentration variations under different environmental and climatic conditions. The specific formulas are as follows:

[0090] ;

[0091] Meaning of key parameters:

[0092] An index characterizing the depletion effect of long-term phosphorus reserves. This parameter is used to calculate the depletion process of phosphorus in sediments, reflecting the gradual reduction of phosphorus reserves. The value is calculated based on the cumulative changes in daily runoff and phosphorus transport, and can dynamically update the phosphorus storage status.

[0093] The temperature of the study area on that day is expressed in °C. Temperature is a key factor affecting phosphorus release; increased temperature can enhance microbial activity and promote phosphorus dissolution and release. Therefore, Tᵢ directly affects the phosphorus release rate and phosphorus availability in the model.

[0094] This represents the two-day runoff increase, in meters. 3 / s. This parameter reflects the scouring effect of snowmelt or rainfall events on phosphorus. Increased runoff causes phosphorus to be mobilized from sediments and transported into the water body; therefore, The value directly affects the change in phosphorus concentration;

[0095] Q represents flow rate, measured in meters (m). 3 / s.

[0096] Here are the coefficient parameters, where i is 1, 2, or 3. is the coefficient parameter, where j is 1, 2, 3, 4, or 5.

[0097] The model is mainly divided into the following parts:

[0098] Long-term phosphorus storage depletion effect: Considering the depletion process of long-term phosphorus storage and the impact of hydrological events (such as snowmelt and rainfall) on phosphorus release.

[0099] Temperature-phosphorus release relationship: Soil temperature drives the release and adsorption of phosphorus by influencing microbial activity and phosphorus solubility.

[0100] Runoff-phosphorus scour relationship: simulating the mobilization and transport of phosphorus by changes in runoff (especially snowmelt and rainfall).

[0101] In the SAT-P model, parameter calibration is a crucial step in improving model accuracy. To optimize model parameters, MOSFLA (Multi-Objective Frog Leaping Algorithm) is employed for multi-objective optimization. This algorithm combines meme evolution-based algorithms with swarm optimization-based algorithms, offering high computational efficiency and excellent global search capabilities. It is characterized by its simple concept, minimal parameter adjustments, fast computation speed, strong global search optimization ability, and ease of implementation. The basic process is as follows: Figure 2 As shown, the mathematical description of the frog-jumping algorithm is as follows:

[0102] Suppose that within a convex-dimensional search space, random generation... A frog population consists of only one frog. i A frog is represented as The fitness function is used as the heuristic function of the algorithm to measure the performance of the frogs, and the fitness function value of each frog is calculated. The frogs were then sorted according to their fitness values, and the entire frog population was divided into... m There are several ethnic groups, and each ethnic group has... n There are 10 frogs, with the first frog assigned to the first group, the second frog assigned to the second group, and so on. m Only one frog was assigned to the first m The first ethnic group, m+1 Only one frog is assigned to the first group, and so on, assuming... Y k For the first k The distribution process of a set of frog populations is described by the following formula:

[0103] ;

[0104] ;

[0105] For each population, a local depth-first search is performed; that is, in one iteration, within each population, selects... q Create a subpopulation of frogs and find the worst-performing frog in that subpopulation. Optimal Frog And the best frog in the entire population. Then only for Perform the update operation, with the update strategy as follows:

[0106] ;

[0107] In the formula, S This represents the adjustment vector for the worst-performing frog; min and max are functions for finding the minimum and maximum values, respectively; for discrete integer variables, rounding is required. r It is a random number between [0,1]. This represents the maximum step size that the frog is allowed to change.

[0108] If the frog is updated Its fitness value is better than Then replace If the fitness value does not improve, then use replace Repeat the update strategy, and check again whether the fitness value has improved after this update. If there is still no improvement, randomly generate a frog to replace it. Repeat this operation until the required number of iterations is reached;

[0109] when m After each population completes a local depth search, all green plots within the population are reordered according to their fitness, global information is exchanged, and then they are divided into... m For each population, perform a local depth search, repeating this operation until the required number of iterations or a stopping condition is met.

[0110] Of course, in other embodiments, multi-objective particle swarm optimization algorithm can also be used to solve multi-objective optimization problems.

[0111] The objective functions are the correlation coefficient R. 2 The Nash efficiency coefficient (NSE) is used to evaluate the applicability of the model and find the optimal model parameter values ​​and ranges.

[0112] R 2 It is widely used as an accuracy evaluation indicator; the closer its value is to 1, the higher the accuracy. Correlation coefficient Nash efficiency coefficient / ,in, For the i-th measured value, For the first i One simulated value; n The length of the data sequence. This is the average value of the measured values. This is a simulated average value; when the simulated value and the measured value are equal, =1 indicates a match, when The value <1 indicates a lower degree of data consistency.

[0113] The accuracy of the simulation can be judged based on the value of NSE. The general classification is as follows: (1) Excellent: 0.75 < NSE ≤1.00; (2) Good: 0.65< NSE <0.75; (3) Qualified: 0.50< NSE <0.65; (4) Unqualified: NSE ≤0.50.

[0114] Optimization objective: To maximize R simultaneously 2 The MOSFLA algorithm maximizes NSE to ensure high accuracy and stability of the model. It selects the optimal parameter combination from multiple solutions through fast non-dominated sorting and crowding calculation.

[0115] Determining the optimal parameters: After several generations of optimization, MOSFLA can find a set of optimal parameter values ​​in the multidimensional solution space. These parameter values ​​will be applicable to the studied watershed, taking into account the unique hydrological and climatic conditions of the watershed.

[0116] Determine the parameter range: By using the Pareto front of the algorithm, determine the appropriate range of each parameter, thereby providing actionable guidance for the application of the model.

[0117] To ensure the generalization ability and stability of the SAT-P model, this embodiment uses a ten-cross-validation method to verify the model's effectiveness. Cross-validation is a commonly used model validation method that can effectively avoid overfitting.

[0118] Dataset partitioning: The entire dataset is randomly divided into 10 parts. Nine parts are selected each time for model training, and the remaining part is used for validation. In this way, the model will be evaluated over 10 different training and testing iterations.

[0119] Training and Testing: During each cross-validation, the training and validation sets are divided differently to ensure the model's performance on different subsets of data. This allows the model to be validated for stability and reliability under varying sample conditions.

[0120] Validation Results: The stability of the model was evaluated using the mean error and analysis of variance (ANOVA) method for cross-validation. The NSE, RMSE, and R-squared values ​​were calculated for each cross-validation step. 2 These indicators will be used to further confirm whether the model has good generalization ability.

[0121] Overfitting detection: Cross-validation can identify whether a model is overfitting. If the model performs well on the training set but poorly on the validation set, it indicates potential overfitting, requiring model adjustment or optimization.

[0122] To verify the applicability of the SAT-P model in cryosphere watersheds, this embodiment will also compare it with the traditional CQ model. By comparing the simulation results of different models, the most suitable model for this watershed will be selected.

[0123] The CQ model is a traditional phosphorus concentration prediction model that assumes a linear relationship between flow rate and concentration. This model will be used for basic simulations, and the simulation results will be compared with those of the SAT-P model.

[0124] Error metric evaluation: Based on the results of cross-validation, error metrics (such as NSE, ...) are used. The simulation accuracy of different models is quantified using metrics such as RMSE (Real-Time Errors). These metrics are used to evaluate the superiority of the SAT-P model over the CQ model.

[0125] Selecting the optimal model: Based on cross-validation results and error indices, select the model that best suits the watershed and research conditions. The SAT-P model, which performs better on multiple error indices, will be selected as the optimal model, providing a tool for predicting phosphorus dynamics under future climate change.

[0126] like Figure 3 As shown in (a)-(c), the method provided by the present invention has better performance than existing methods in terms of standard error, total phosphorus simulation effect and simulation accuracy.

[0127] In other embodiments, leave-one-out cross-validation can be used instead of ten cross-validations, which is suitable for small sample scenarios.

[0128] like Figure 4 As shown in (a)-(d), this embodiment also selects runoff growth events (ranging from 3 to 15 days) to analyze the relationship between runoff and total phosphorus concentration over time and make comparisons. The method provided in this embodiment can effectively simulate the hysteresis relationship of runoff growth events (such as clockwise, counterclockwise, figure-eight, and reverse figure-eight), while traditional methods cannot simulate this process.

[0129] Example 2

[0130] A system for simulating total phosphorus concentration in a cryosphere watershed includes:

[0131] The data acquisition module is configured to acquire meteorological temperature, runoff, and total phosphorus concentration within a certain time period in the cryosphere basin;

[0132] The data preprocessing module is configured to preprocess the acquired data;

[0133] The model building module is configured to construct a dynamic phosphorus simulation model that takes into account the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin.

[0134] The model optimization module is configured to use at least a portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, and to perform multi-objective optimization on the constructed phosphorus dynamic simulation model using a multi-objective optimization algorithm. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model.

[0135] The model validation module is configured to use another portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as the validation dataset. Based on the optimal solution of the obtained parameters, it performs cross-validation and validity verification on the optimized phosphorus dynamics simulation model to obtain the final phosphorus dynamics simulation model.

[0136] The simulation module is configured to acquire meteorological temperature and runoff of the cryosphere basin within the target time period, perform preprocessing, and use the final phosphorus dynamic simulation model to simulate total phosphorus concentration.

[0137] Example 3

[0138] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method provided in Embodiment 1.

[0139] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).

[0140] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0141] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0142] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0143] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simulating total phosphorus concentration in cryosphere watersheds, characterized in that, Includes the following steps: Obtain meteorological temperature, runoff, and total phosphorus concentration in a cryosphere basin over a specific period of time; The acquired data is preprocessed; Considering the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin, a dynamic phosphorus simulation model is constructed. Using at least some of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, a multi-objective optimization algorithm is used to optimize the constructed phosphorus dynamic simulation model. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model. Using another portion of the preprocessed meteorological temperature, runoff, and total phosphorus concentration data as the validation dataset, the optimized phosphorus dynamics simulation model is cross-validated and validated based on the optimal solution of the obtained parameters, resulting in the final phosphorus dynamics simulation model. Meteorological temperature and runoff of the cryosphere basin within the target time period are obtained and preprocessed. The final phosphorus dynamics simulation model is then used to simulate the total phosphorus concentration. When constructing the phosphorus dynamics simulation model, the following premises are assumed: the daily variation of soil temperature has a limited impact on phosphorus activity; the snowmelt process is equivalent to an increase in runoff; the phosphorus concentration in the river is assumed to be uniform and continuous in time and space; phosphorus availability has a feedback effect on phosphorus transport dynamics; and the interaction between sediment and phosphorus plays a key role in phosphorus dynamics. The constructed phosphorus dynamic simulation model is as follows: ； in, This represents the total phosphorus concentration. An index characterizing the long-term depletion effect of phosphorus storage, used to calculate the depletion process of phosphorus in sediments, reflecting the gradual reduction of phosphorus reserves, and calculated based on the cumulative changes in daily runoff and phosphorus transport. Daily weather temperature directly affects the phosphorus release rate and phosphorus availability in the model. This represents the two-day runoff increase, used to reflect the ability of snowmelt or rainfall events to wash away phosphorus, directly affecting changes in phosphorus concentration. Here are the coefficient parameters, where i is 1, 2, or 3. Here, j represents the coefficient parameter, where j is 1, 2, 3, 4, or 5. For traffic.

2. The method for simulating total phosphorus concentration in a cryosphere watershed as described in claim 1, characterized in that, The meteorological temperature and runoff data are obtained on a daily basis.

3. The method for simulating total phosphorus concentration in a cryosphere watershed as described in claim 1, characterized in that, The preprocessing process includes identifying mutation points in the data using a mutation point detection method and removing mutation points; The acquired meteorological temperatures are segmented by a threshold, and data below the set temperature is removed.

4. The method for simulating total phosphorus concentration in a cryosphere watershed as described in claim 1, characterized in that, In the process of multi-objective optimization of the constructed phosphorus dynamic simulation model, a multi-objective frog-leap algorithm is used for multi-objective optimization, specifically including: Suppose that within a convex-dimensional search space, random generation... A frog population consists of only one frog. i A frog is represented as The fitness function is used as the heuristic function of the algorithm to measure the performance of the frogs, and the fitness function value of each frog is calculated. The frogs were then sorted according to their fitness values, and the entire frog population was divided into... m There are several ethnic groups, and each ethnic group has... n There are 10 frogs, with the first frog assigned to the first group, the second frog assigned to the second group, and so on. m Only one frog was assigned to the first m The first ethnic group, m +1 frog is assigned to the first group, and so on, assuming... Y k For the first k The distribution process of a set of frog populations is described by the following formula: ； ； For each population, a local depth-first search is performed; that is, in one iteration, within each population, selects... q Create a subpopulation of frogs and find the worst-performing frog in that subpopulation. Optimal Frog And the best frog in the entire population. Then only for Perform the update operation, with the update strategy as follows: ； In the formula, S This represents the adjustment vector for the worst-performing frog; min and max are functions for finding the minimum and maximum values, respectively; for discrete integer variables, rounding is required. r It is a random number between [0,1]. This represents the maximum step size that the frog is allowed to change. If the frog is updated Its fitness value is better than Then replace If the fitness value does not improve, then use replace Repeat the update strategy, and check again whether the fitness value has improved after this update. If there is still no improvement, randomly generate a frog to replace it. Repeat this operation until the required number of iterations is reached; when m After each population completes a local depth search, all green plots within the population are reordered according to their fitness, global information is exchanged, and then they are divided into... m For each population, perform a local depth search, repeating this operation until the required number of iterations or a stopping condition is met.

5. The method for simulating total phosphorus concentration in a cryosphere watershed as described in claim 1, characterized in that, In the process of multi-objective optimization with the objectives of maximizing the correlation coefficient and the Nash efficiency coefficient, the correlation coefficient... Nash efficiency coefficient / ,in, For the i-th measured value, For the first i One simulated value; n The length of the data sequence. This is the average value of the measured values. This is a simulated average value; when the simulated value and the measured value are equal, =1 indicates a match, when The value <1 indicates a lower degree of data consistency.

6. The method for simulating total phosphorus concentration in a cryosphere watershed as described in claim 1, characterized in that, The process of cross-validation and validity verification of the optimized phosphorus dynamic simulation model includes dividing the acquired data into multiple parts, selecting one part as the training dataset and the other part as the validation dataset for each validation, and performing multiple validations. The division of the training and validation datasets is different each time. In each validation process, the average error and variance analysis method of cross-validation are used to evaluate the stability of the model. By calculating the index of each cross-validation, it is confirmed whether the model has good generalization ability. Cross-validation is used to identify whether the model has overfitting.

7. A total phosphorus concentration simulation system for cryosphere watersheds, characterized in that, include: The data acquisition module is configured to acquire meteorological temperature, runoff, and total phosphorus concentration within a certain time period in the cryosphere basin; The data preprocessing module is configured to preprocess the acquired data; The model building module is configured to construct a dynamic phosphorus simulation model that takes into account the phosphorus storage depletion effect, temperature-phosphorus release relationship, and runoff-phosphorus scour relationship in the cryosphere basin. The model optimization module is configured to use at least a portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as training datasets, and to perform multi-objective optimization on the constructed phosphorus dynamic simulation model using a multi-objective optimization algorithm. The multi-objective optimization aims to maximize the correlation coefficient and the Nash efficiency coefficient, and iteratively calculates the optimal solution of the parameters of the phosphorus dynamic simulation model. The model validation module is configured to use another portion of the preprocessed meteorological temperature, runoff and total phosphorus concentration data as the validation dataset. Based on the optimal solution of the obtained parameters, it performs cross-validation and validity verification on the optimized phosphorus dynamics simulation model to obtain the final phosphorus dynamics simulation model. The simulation module is configured to acquire meteorological temperature and runoff of the cryosphere basin within the target time period, perform preprocessing, and use the final phosphorus dynamic simulation model to simulate total phosphorus concentration. When constructing the phosphorus dynamics simulation model, the following premises are assumed: the daily variation of soil temperature has a limited impact on phosphorus activity; the snowmelt process is equivalent to an increase in runoff; the phosphorus concentration in the river is assumed to be uniform and continuous in time and space; phosphorus availability has a feedback effect on phosphorus transport dynamics; and the interaction between sediment and phosphorus plays a key role in phosphorus dynamics. The constructed phosphorus dynamic simulation model is as follows: ； in, This represents the total phosphorus concentration. An index characterizing the long-term depletion effect of phosphorus storage, used to calculate the depletion process of phosphorus in sediments, reflecting the gradual reduction of phosphorus reserves, and calculated based on the cumulative changes in daily runoff and phosphorus transport. Daily weather temperature directly affects the phosphorus release rate and phosphorus availability in the model. This represents the two-day runoff increase, used to reflect the ability of snowmelt or rainfall events to wash away phosphorus, directly affecting changes in phosphorus concentration. Here are the coefficient parameters, where i is 1, 2, or 3. Here, j represents the coefficient parameter, where j is 1, 2, 3, 4, or 5. For traffic.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-6.

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