Regional lake and reservoir nutritive salt reference setting method based on Bayesian hierarchical model

Abstract

The invention discloses a regional lake and reservoir nutritive salt benchmark making method based on a Bayesian hierarchical model, and the method comprises the following steps: S1, collecting different forms of nitrogen and phosphorus index monitoring data of a regional lake and reservoir, and constructing a regional lake and reservoir nutritive salt benchmark making database; s2, establishing a Bayesian hierarchical model for the nutritive salt in a specific form to simulate the concentration of the nutritive salt in the lake and reservoir; s3, according to monitoring data in a regional lake and reservoir nutritive salt benchmark formulating database, performing parameter estimation on the Bayesian hierarchical model to obtain posterior distribution of each parameter in the model; s4, according to a parameter estimation result, obtaining the distribution of the regional lake and reservoir nutritive salt concentration; s5, deducing a nutritive salt standard value according to a quantile set by a reference state method; the method is direct and easy to use, has obvious advantages in quantifying the balance of generality and difference of the region, can accurately and scientifically formulate the regional lake and reservoir nutritive salt reference, provides effective support for lake and reservoir water environment management, and has obvious advantages and application value.

Description

Technical Field

[0001] The invention belongs to the technical field of water quality monitoring and water body management, and specifically relates to a method for formulating a regional lake nutrient salt benchmark based on a Bayesian hierarchical model. Background Art

[0002] Lake eutrophication is an important challenge in global water environment issues. The increase in the concentration of nutrients such as nitrogen and phosphorus not only easily leads to the degradation of aquatic ecosystems, but also may cause water quality problems such as algal blooms and dissolved oxygen deficiency, which in turn affects biodiversity and threatens the safety of water resources. Therefore, establishing a scientific and reasonable nutrient benchmark, especially its application in regional lake and reservoir water quality management, has become an important task for water resource management and environmental protection in various countries.

[0003] The current method for establishing nutrient benchmarks for lakes and reservoirs generally adopts the reference state method and the pressure-response model. This method often faces a "similarity dilemma" due to the heterogeneity of regional lakes and reservoirs. Lakes and reservoirs in the region have significant spatial differences in nutrient background values ​​due to differences in natural conditions and human activity intensity, while traditional methods rely on unified reference lakes and reservoirs or fixed quantiles, which easily ignore sub-regional specificity. As an emerging method, the Bayesian hierarchical model can integrate data from different lakes and reservoirs, not only considering the differences within a single lake or reservoir, but also paying attention to the similarities between lakes and reservoirs in different regions.

[0004] In summary, the present invention proposes a method for formulating regional lake and reservoir nutrient salt benchmarks based on a Bayesian hierarchical model, aiming to overcome the limitations of the existing technology and more accurately set nutrient salt standard values ​​suitable for each region to promote the protection and restoration of lake and reservoir ecosystems. Summary of the invention

[0005] To solve the above problems, the present invention proposes a method for formulating regional lake and reservoir nutrient benchmarks based on the Bayesian hierarchical model. The method is direct and easy to use, has obvious advantages in quantifying the balance between regional commonalities and differences, can accurately and scientifically formulate regional lake and reservoir nutrient benchmarks, and provide effective support for lake and reservoir water environment management. It has significant advantages and application value.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A method for establishing a regional lake nutrient benchmark based on a Bayesian hierarchical model includes the following steps: S1. Collect monitoring data on different forms of nitrogen and phosphorus indicators in regional lakes and reservoirs, and build a database for the formulation of nutrient salt benchmarks in regional lakes and reservoirs; S2. For specific forms of nutrients, a Bayesian hierarchical model is established to simulate the nutrient concentration in lakes and reservoirs; The specific process of step S2 is: S21, performing logarithmic transformation on the concentration values ​​in the monitoring data; wherein, for zero-value data, the zero-value data is replaced with half of the detection limit according to the standard of water quality monitoring; S22. Use the regional lake nutrient benchmark database data to train the Bayesian hierarchical model. The model formula is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; It is the location of lakes and reservoirs; The sequence of monitoring values ​​for a particular lake or reservoir; is the regional overall mean of the concentration of a specific form of nutrient salt; For lakes and reservoirs Deviation from the overall mean of the region; For lakes and reservoirs In the The residual error of the second monitoring; S23. Use monitoring data of different forms of nitrogen and phosphorus indicators as input variables to simulate the nutrient concentration of lakes and reservoirs and realize the construction of Bayesian hierarchical model; S3. According to the monitoring data in the database of regional lake nutrient salt benchmark, the parameters of the Bayesian hierarchical model are estimated to obtain the posterior distribution of each parameter in the model; S4. Based on the parameter estimation results, the distribution of nutrient concentrations in regional lakes and reservoirs is obtained; S5. Derive the standard value of nutrient salts according to the quantiles set by the reference state method; The specific process of step S5 is: S51. Select reference quantiles from the probability density function of the overall distribution of nutrient concentrations in regional lakes and reservoirs; where the 25% reference quantile is selected for areas with pollution greater than the threshold, and the 75% reference quantile is selected for areas with protection greater than the threshold; S52. Using the posterior distribution of the Bayesian hierarchical model, samples are extracted and the concentration values ​​of the selected quantiles are calculated to obtain the standard values ​​of nutrient concentrations in regional lakes and reservoirs.

[0007] Preferably, the specific process of step S1 is: S11. Collect monitoring data on different forms of nitrogen and phosphorus indicators in lakes and reservoirs in multiple regions; S12, processing the outliers of the collected monitoring data, and then using the Kalman filter method to improve the accuracy of the state estimation by fusing the measured value and the state estimation, and completing the missing value filling; S13. Store and manage data to build a regional lake and reservoir nutrient benchmark database.

[0008] Preferably, the monitoring data in step S1 includes total nitrogen data, ammonia nitrogen data, nitrate nitrogen data, nitrite nitrogen data, organic nitrogen data, total phosphorus data, dissolved phosphorus data, particulate phosphorus data and organic phosphorus data.

[0009] Preferably, the abnormal value processing in step S12 includes eliminating non-numeric data and eliminating duplicate data; the non-numeric data includes characters and null values; and the elimination of duplicate data is to eliminate data with duplicate timestamps.

[0010] Preferably, the Kalman filtering method in step S12 includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle.

[0011] Preferably, the specific process of step S3 is: S31. Set the prior distribution for the parameters in the Bayesian hierarchical model. The prior distribution of the parameters is: , , ,in, and is a constant; is a variable and follows the Gamma distribution; ,in, and is a priori hyperparameter of a known distribution; S32. The prior distribution defined is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; S33. Using the Markov Chain Monte Carlo algorithm to estimate parameters, sampling is performed from a defined prior distribution through the Markov Chain Monte Carlo algorithm to construct a Markov chain, so as to make the stationary distribution of the Markov chain the posterior distribution of the parameters.

[0012] Preferably, the specific process of step S33 is: S331. For each parameter , , and , update the parameter value by acceptance-rejection sampling or conditional distribution sampling according to the current value and prior distribution; S332. Through multiple sampling, a large number of samples are generated from the prior distribution. The goal of the Markov Chain Monte Carlo algorithm is to gradually approach the posterior distribution of the target parameter through continuous iterative sampling; S333. Use diagnostic tools to check the convergence of the Markov chain; perform multiple sampling until the Markov chain converges, and use the posterior distribution to perform parameter estimation and inference; the diagnostic tools include Gelman-Rubin diagnosis and trajectory diagram.

[0013] Preferably, the specific process of step S4 is: S41. Using the posterior distribution samples in the Bayesian hierarchical model, the nutrient concentration of each lake is calculated using the Bayesian hierarchical model formula. The predicted value of S42. For the concentration distribution samples of all lakes and reservoirs, repeated calculations are performed based on the posterior distribution of the Bayesian method to generate concentration prediction values ​​under multiple posterior samples, which are used to reflect the different performances of nutrient concentrations under different environmental conditions and constitute multi-dimensional samples of concentration distribution; S43. Integrate the concentration distributions obtained from all posterior samples to obtain the overall distribution of nutrient concentrations in regional lakes and reservoirs. The overall distribution of nutrient concentrations in regional lakes and reservoirs can be used to reflect the concentration variation range and uncertainty of each lake and reservoir in the region under different time and environmental conditions, providing a basis for the formulation of regional nutrient standards.

[0014] After adopting the above technical scheme, the present invention has the following beneficial effects: the method for formulating the regional lake nutrient salt benchmark based on the Bayesian hierarchical model of the present invention is direct and easy to use. In the data quality control stage, the abnormal data is identified and the missing value is interpolated to reduce the impact of abnormal data on the model construction and precision evaluation process; the concentration is logarithmically transformed and the zero value is replaced by 1 / 2 of the detection limit, which can solve the skewed distribution problem in the data and ensure the rationality of the statistical analysis; the Bayesian hierarchical model, as a probability generation model, is significantly superior to the traditional frequency school statistical model (such as linear regression, mixed distribution) and static empirical method in benchmark formulation, and the benchmark value is directly output in combination with adjustable quantiles (such as 25% or 75%), breaking through the traditional method's dependence on a single distribution assumption and data independence. Therefore, the method for formulating the regional lake nutrient salt benchmark based on the Bayesian hierarchical model of the present invention has obvious advantages in quantifying the balance between regional commonalities and differences, and can accurately and scientifically formulate the regional lake nutrient salt benchmark, providing effective support for lake water environment management, and has significant advantages and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the present invention; Figure 2 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0017] like Figure 1 and Figure 2 As shown, a method for establishing a regional lake nutrient benchmark based on a Bayesian hierarchical model includes the following steps: S1. Collect monitoring data on different forms of nitrogen and phosphorus indicators in regional lakes and reservoirs, and build a database for the formulation of nutrient salt benchmarks in regional lakes and reservoirs; The monitoring data in step S1 includes total nitrogen data, ammonia nitrogen data, nitrate nitrogen data, nitrite nitrogen data, organic nitrogen data, total phosphorus data, dissolved phosphorus data, particulate phosphorus data and organic phosphorus data; The specific process of step S1 is: S11. Collect monitoring data on different forms of nitrogen and phosphorus indicators in lakes and reservoirs in multiple regions; S12, processing the outliers of the collected monitoring data, and then using the Kalman filter method to improve the accuracy of the state estimation by fusing the measured value and the state estimation, and completing the missing value filling; The abnormal value processing in step S12 includes eliminating non-numeric data and eliminating duplicate data; the non-numeric data includes characters and null values; the elimination of duplicate data is to eliminate data with duplicate timestamps; The Kalman filter method in step S12 includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle; S13. Store and manage data to build a regional lake nutrient benchmark database; S2. For specific forms of nutrients, a Bayesian hierarchical model is established to simulate the nutrient concentration in lakes and reservoirs; The specific process of step S2 is: S21, performing logarithmic transformation on the concentration values ​​in the monitoring data; wherein, for zero-value data, the zero-value data is replaced with half of the detection limit according to the standard of water quality monitoring; S22. Use the regional lake nutrient benchmark database data to train the Bayesian hierarchical model. The model formula is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; It is the location of lakes and reservoirs; The sequence of monitoring values ​​for a particular lake or reservoir; is the regional overall mean of the concentration of a specific form of nutrient salt; For lakes and reservoirs Deviation from the overall mean of the region; For lakes and reservoirs In the The residual error of the second monitoring; S23. Use monitoring data of different forms of nitrogen and phosphorus indicators as input variables to simulate the nutrient concentration of lakes and reservoirs and realize the construction of Bayesian hierarchical model; S3. According to the monitoring data in the database of regional lake nutrient salt benchmark, the parameters of the Bayesian hierarchical model are estimated to obtain the posterior distribution of each parameter in the model; The specific process of step S3 is: S31. Set the prior distribution for the parameters in the Bayesian hierarchical model. The prior distribution of the parameters is: , , ,in, and is a constant; is a variable and follows the Gamma distribution; ,in, and is a priori hyperparameter of a known distribution; S32. The prior distribution defined is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; S33, using a Markov chain Monte Carlo algorithm to perform parameter estimation, sampling from a defined prior distribution through the Markov chain Monte Carlo algorithm, constructing a Markov chain, and making the stationary distribution of the Markov chain the posterior distribution of the parameter; The specific process of step S33 is: S331. For each parameter , , and , update the parameter value by acceptance-rejection sampling or conditional distribution sampling according to the current value and prior distribution; S332. Through multiple sampling, a large number of samples are generated from the prior distribution. The goal of the Markov Chain Monte Carlo algorithm is to gradually approach the posterior distribution of the target parameter through continuous iterative sampling; S333, using diagnostic tools to check the convergence of the Markov chain; sampling multiple times until the Markov chain converges, and using the posterior distribution to perform parameter estimation and inference; the diagnostic tools include Gelman-Rubin diagnosis and trajectory diagram; S4. Based on the parameter estimation results, the distribution of nutrient concentrations in regional lakes and reservoirs is obtained; The specific process of step S4 is: S41. Using the posterior distribution samples in the Bayesian hierarchical model, the nutrient concentration of each lake is calculated using the Bayesian hierarchical model formula. The predicted value of S42. For the concentration distribution samples of all lakes and reservoirs, repeated calculations are performed based on the posterior distribution of the Bayesian method to generate concentration prediction values ​​under multiple posterior samples, which are used to reflect the different performances of nutrient concentrations under different environmental conditions and constitute multi-dimensional samples of concentration distribution; S43. Integrate the concentration distributions obtained from all posterior samples to obtain the overall distribution of nutrient concentrations in regional lakes and reservoirs; through the overall distribution of nutrient concentrations in regional lakes and reservoirs, reflect the concentration variation range and uncertainty of each lake and reservoir in the region under different time and environmental conditions, and provide a basis for the formulation of regional nutrient standards; S5. Derive the standard value of nutrient salts according to the quantiles set by the reference state method; The specific process of step S5 is: S51. Select reference quantiles from the probability density function of the overall distribution of nutrient concentrations in regional lakes and reservoirs; where the 25% reference quantile is selected for areas with pollution greater than the threshold, and the 75% reference quantile is selected for areas with protection greater than the threshold; S52. Using the posterior distribution of the Bayesian hierarchical model, samples are extracted and the concentration values ​​of the selected quantiles are calculated to obtain the standard values ​​of nutrient concentrations in regional lakes and reservoirs.

[0018] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for establishing a regional lake nutrient benchmark based on a Bayesian hierarchical model, characterized in that: The following steps are involved: S1. Collect monitoring data on different forms of nitrogen and phosphorus indicators in regional lakes and reservoirs, and build a database for the formulation of nutrient salt benchmarks in regional lakes and reservoirs; S2. For specific forms of nutrients, a Bayesian hierarchical model is established to simulate the nutrient concentration in lakes and reservoirs; The specific process of step S2 is: S21, performing logarithmic transformation on the concentration values ​​in the monitoring data; wherein, for zero-value data, the zero-value data is replaced with half of the detection limit according to the standard of water quality monitoring; S22. Use the regional lake nutrient benchmark database data to train the Bayesian hierarchical model. The model formula is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; It is the location of lakes and reservoirs; The sequence of monitoring values ​​for a particular lake or reservoir; is the regional overall mean of the concentration of a specific form of nutrient salt; For lakes and reservoirs Deviation from the overall mean of the region; For lakes and reservoirs In the The residual error of the second monitoring; S23. Use monitoring data of different forms of nitrogen and phosphorus indicators as input variables to simulate the nutrient concentration of lakes and reservoirs and realize the construction of Bayesian hierarchical model; S3. According to the monitoring data in the database of regional lake nutrient salt benchmark, the parameters of the Bayesian hierarchical model are estimated to obtain the posterior distribution of each parameter in the model; S4. Based on the parameter estimation results, the distribution of nutrient concentrations in regional lakes and reservoirs is obtained; S5. Derive the standard value of nutrient salts according to the quantiles set by the reference state method; The specific process of step S5 is: S51. Select reference quantiles from the probability density function of the overall distribution of nutrient concentrations in regional lakes and reservoirs; where the 25% reference quantile is selected for areas with pollution greater than the threshold, and the 75% reference quantile is selected for areas with protection greater than the threshold; S52. Using the posterior distribution of the Bayesian hierarchical model, samples are extracted and the concentration values ​​of the selected quantiles are calculated to obtain the standard values ​​of nutrient concentrations in regional lakes and reservoirs.

2. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 1, characterized in that: The specific process of step S1 is: S11. Collect monitoring data on different forms of nitrogen and phosphorus indicators in lakes and reservoirs in multiple regions; S12, processing the outliers of the collected monitoring data, and then using the Kalman filter method to improve the accuracy of the state estimation by fusing the measured value and the state estimation, and completing the missing value filling; S13. Store and manage data to build a regional lake and reservoir nutrient benchmark database.

3. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 1, characterized in that: The monitoring data in step S1 include total nitrogen data, ammonia nitrogen data, nitrate nitrogen data, nitrite nitrogen data, organic nitrogen data, total phosphorus data, dissolved phosphorus data, particulate phosphorus data and organic phosphorus data.

4. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 2, characterized in that: The abnormal value processing in step S12 includes eliminating non-numeric data and eliminating duplicate data; the non-numeric data includes characters and null values; and the elimination of duplicate data is to eliminate data with duplicate timestamps.

5. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 2, characterized in that: The Kalman filtering method described in step S12 includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle.

6. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 1, characterized in that: The specific process of step S3 is: S31. Set the prior distribution for the parameters in the Bayesian hierarchical model. The prior distribution of the parameters is: , , ,in, and is a constant; is a variable and follows the Gamma distribution; ,in, and is a priori hyperparameter of a known distribution; S32. The prior distribution defined is: ,in, is the specific nutrient in lakes and reservoirs after logarithmic transformation No. Secondary monitoring value; S33. Using the Markov Chain Monte Carlo algorithm to estimate parameters, sampling is performed from a defined prior distribution through the Markov Chain Monte Carlo algorithm to construct a Markov chain, so as to make the stationary distribution of the Markov chain the posterior distribution of the parameters.

7. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 6, characterized in that: The specific process of step S33 is: S331. For each parameter , , and , update the parameter value by acceptance-rejection sampling or conditional distribution sampling according to the current value and prior distribution; S332. Through multiple sampling, a large number of samples are generated from the prior distribution. The goal of the Markov Chain Monte Carlo algorithm is to gradually approach the posterior distribution of the target parameter through continuous iterative sampling; S333. Use diagnostic tools to check the convergence of the Markov chain; perform multiple sampling until the Markov chain converges, and use the posterior distribution to perform parameter estimation and inference; the diagnostic tools include Gelman-Rubin diagnosis and trajectory diagram.

8. A method for establishing a regional lake nutrient salt benchmark based on a Bayesian hierarchical model as claimed in claim 1, characterized in that: The specific process of step S4 is: S41. Using the posterior distribution samples in the Bayesian hierarchical model, the nutrient concentration of each lake is calculated using the Bayesian hierarchical model formula. The predicted value of S42. For the concentration distribution samples of all lakes and reservoirs, repeated calculations are performed based on the posterior distribution of the Bayesian method to generate concentration prediction values ​​under multiple posterior samples, which are used to reflect the different performances of nutrient concentrations under different environmental conditions and constitute multi-dimensional samples of concentration distribution; S43. Integrate the concentration distributions obtained from all posterior samples to obtain the overall distribution of nutrient concentrations in regional lakes and reservoirs. The overall distribution of nutrient concentrations in regional lakes and reservoirs can be used to reflect the concentration variation range and uncertainty of each lake and reservoir in the region under different time and environmental conditions, providing a basis for the formulation of regional nutrient standards.

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