CN109784568B - Method for predicting lake water quality model through multi-target uncertainty analysis - Google Patents
Method for predicting lake water quality model through multi-target uncertainty analysis Download PDFInfo
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Abstract
The invention discloses a method for predicting a lake water quality model through multi-target uncertainty analysis, which comprises the following steps of: determining a model for water quality prediction and parameters thereof; (2) determining the value range and distribution characteristics of the model parameters; (3) Determining a plurality of objective functions for parameter uncertainty analysis; (4) determining the value of the objective function under the corresponding condition; (5) Comparing and obtaining a dominant parameter set corresponding to the pareto set under the target function; (6) performing two-parameter uncertainty analysis: (7) Estimating and drawing the density distribution of each parameter in the domination set by using a kernel function, wherein the value corresponding to the highest probability density is the model parameter calibration result; (8) And collecting boundary conditions required by prediction and substituting the boundary conditions and the calibrated parameters into the model to predict the water quality. The method can simultaneously give uncertainty and parameter calibration of the water quality model parameters and predict the parameters, can greatly save the time required by the application of the model, and provides reference information and basis for lake water quality management.
Description
Technical Field
The invention relates to a method for predicting a lake water quality model through multi-target uncertainty analysis, and belongs to the field of lake water quality management.
Background
Under the influence of industrial and agricultural pollution discharge, the water quality conditions of most lakes in China tend to be worsened, and the pollution problem is frequent. In order to protect the water quality and ecological safety of lakes, pollution prediction by using a lake water quality model is a necessary means. In the process of predicting by using the lake water quality model, uncertainty analysis and calibration of parameters of the model are extremely important steps. At present, uncertainty analysis of a water quality model is mostly but target uncertainty analysis is not enough to reflect diversity of lake water quality and ecology; the existing multi-target uncertainty analysis needs to be converted into single-target analysis through the weight, so the selection of the weight is very subjective and random. In addition, at present, the parameter calibration of the water quality model and the parameter uncertainty analysis are separated from each other, and the parameter calibration needs to be optimized after the uncertainty analysis is completed, so that the calculation cost of model application is greatly increased, and the popularization and application of model prediction are greatly hindered.
Disclosure of Invention
The invention aims to solve the problems and overcome the defects in the prior art, and provides a method for predicting a lake water quality model through multi-target uncertainty analysis. The method can objectively carry out multi-target uncertainty analysis on the parameters of the water quality model and simultaneously complete the parameter calibration work, thereby greatly reducing the calculation workload of the lake water quality model prediction.
The invention aims to realize the method for predicting the lake water quality model through multi-target uncertainty analysis, which is characterized by comprising the following steps of:
(1) Collecting monitoring data of lakes and boundary rivers with water quality to be predicted, and determining a model for predicting the water quality and parameters thereof;
(2) Determining the value range and distribution characteristics of the model parameters, and extracting m groups of parameter values in the value range according to respective distribution characteristics, wherein m is greater than or equal to 10000;
(3) Determining n objective functions for model parameter uncertainty analysis, wherein n is greater than or equal to 2;
(4) Substituting the values of m groups of model parameters, the monitoring data of the boundary river and the monitoring data of the lake into the water quality model for calculation to determine m groups of values of the objective function;
(5) Comparing and obtaining dominant parameter sets corresponding to the pareto sets under the objective function, wherein the number d of the parameter sets in the parameter dominant sets is not less than 500; if d is less than 500, increasing the number m of the parameter sets extracted in the step (2), and repeatedly executing the steps (2) - (4);
(6) Drawing a double-parameter joint probability density function of the dominant parameter set, and carrying out double-parameter uncertainty analysis;
(7) Estimating and drawing the probability density distribution of each parameter in the dominance set by using a kernel function, wherein the value corresponding to the highest probability density is used as a model parameter calibration result;
(8) And collecting and predicting the monitoring data of the boundary river required by prediction and substituting the collected and predicted model parameters into the water quality model to predict the water quality.
In the step (1):
a. the collected monitoring data of the lake and the boundary river with the predicted water quality are continued for at least 2 months and averagely 1 time per week, and the monitoring data comprise the water quality monitoring data of the predicted lake, the water quality monitoring data of the lake boundary river and the flow data of the boundary river;
b. determining a model for predicting the water quality of the lake according to the collected water quality indexes and indexes needing prediction in the monitoring data of the lake and the boundary rivers with the water quality to be predicted, and determining parameters of the model according to the model structure.
The step (2) specifically comprises the following steps:
a. determining the value ranges and the distribution of the model parameters, and assuming that the model parameters are uniformly distributed in the respective value ranges;
b. generating m random numbers by a random number generation program in the respective value range of each parameter according to the distribution form of each parameter, wherein m is more than or equal to 10000;
c. and grouping the generated parameter random values according to the model requirements, ensuring that each parameter in each group has 1 value, and forming m groups of parameter groups which can be used for driving the model.
The step (3) specifically comprises the following steps:
a. analyzing the water quality prediction requirement;
b. determining n target functions for parameter uncertainty analysis according to the analysis requirement result, wherein n is greater than or equal to 2; the objective function may be an average relative error RE between the model simulation value S and the monitored value O of different environmental indicators, and a root mean square error RMSE thereof, specifically as follows:
wherein O is i Is the ith monitor value, S i Is with O i Corresponding model simulation values, T is the total number of monitored values.
The step (4) specifically comprises the following steps:
a. substituting the values of m groups of model parameters and the corresponding monitoring data of the boundary river into the water quality model for calculation to determine the simulation values S of m groups of environmental indexes i ,i＝1,2,3...T；
b. Monitoring data O combined with lake i I =1,2,3.. T, the values of each set of objective functions are calculated for m sets.
The step (5) specifically comprises the following steps:
a. distinguishing the properties of the target function, and dividing the properties into two categories, namely, the larger the target function is, the better the simulation result is represented, and the smaller the target function is, the better the simulation result is represented; adding a negative sign in front of one type of target function with the larger target function and the better target function, and unifying the two types of target functions to ensure that the smaller target function represents the better simulation result;
b. defining that n objective functions corresponding to the parameter group u are all larger than n objective functions corresponding to the parameter group v; then the parameter set u is considered to be dominated by the parameter set v;
c. comparing the objective functions corresponding to the m groups of parameters, and removing all the parameter groups which are dominated by any group of parameters under the definition of the step b; the rest set of the d groups of objective function values is called a pareto set, and d is not less than 500;
d. extracting a parameter group corresponding to the pareto set to obtain a dominant parameter set composed of d groups of parameters;
e. if d is less than 500, the number m of parameter sets extracted in step (2) is increased, and steps (2) to (4) are repeatedly executed.
The step (6) specifically comprises the following steps:
a. drawing a two-parameter joint probability density function of the dominant parameter set;
b. carrying out double-parameter uncertainty analysis by a visual inspection method: the uncertainty of the local parameters with high probability density is small, and the uncertainty of the local parameters with low probability density is large.
The step (7) specifically comprises the following steps:
a. estimating and drawing the probability density distribution of each parameter in the dominance set by using the kernel function; wherein the kernel function adopts a Gaussian kernel function;
b. selecting a value corresponding to the highest probability density as a model parameter calibration result;
the step (8) specifically comprises the following steps:
a. sorting and calibrating the finished model parameters;
b. and collecting and predicting the monitoring data of the boundary river required by prediction and substituting the collected and predicted model parameters into the water quality model to predict the water quality.
The invention discloses a method for predicting a lake water quality model through multi-target uncertainty analysis, which can objectively give out multi-target uncertainty of parameters of the lake water quality model by applying the concept of a pareto set and give out a result of model parameter calibration while analyzing the uncertainty. The method comprises the following steps: (1) Collecting monitoring data of lakes and boundary rivers to be predicted for water quality, and determining a model for predicting water quality and main parameters of the model; (2) Determining the value range and distribution characteristics of the main parameters according to experience, and extracting multiple groups of parameter values according to respective distribution characteristics in the value range; (3) Determining a plurality of objective functions for parameter uncertainty analysis; (4) Substituting the values of all the groups of parameters, the boundary conditions and the monitoring data of the water body into the eutrophication model for calculation, and determining the value of the objective function under the corresponding condition; (5) Comparing and obtaining a dominance parameter set corresponding to the pareto set under the objective function; (6) Drawing a double-parameter joint probability density function of the dominant parameter set, and carrying out double-parameter uncertainty analysis: (7) Estimating and drawing the density distribution of each parameter in the dominating set by using a kernel function, wherein the value corresponding to the highest probability density is the calibration result of the model parameters; (8) And collecting boundary conditions required by prediction and substituting the boundary conditions and the calibrated parameters into the model to predict the water quality. The method can simultaneously give uncertainty and parameter calibration of the water quality model parameters and predict the parameters, can greatly save the time required by the application of the model, and provides reference information and basis for lake water quality management.
Has the advantages that: a method for predicting a lake water quality model through multi-target uncertainty analysis can objectively give out multi-target uncertainty analysis results of lake water quality model parameters and give out model parameter calibration results at the same time, so that subjectivity and arbitrariness in the multi-target uncertainty analysis of the lake water quality model parameters are greatly reduced, and huge calculation amount required by the model for prediction is reduced.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a graph of two-parameter joint probability densities and respective kernel function estimated probability densities for KTB and BMR.
FIG. 3 is a graph of two-parameter joint probability densities and respective kernel function estimated probability densities for PM and KESS.
FIG. 4 shows model prediction results.
Detailed Description
The invention will be further described with reference to the accompanying drawings and the practical situation of a lake in the east of this country.
(1) According to the flow chart shown in fig. 1, the step (1) includes:
a. blue algae and ammonia nitrogen of the lake from 7 months to 9 months of a certain station in a certain year are collected, and the blue algae and ammonia nitrogen are used for 1 time per week
Nitrate nitrogen
And phosphoric acid
11 sets of monitored values. Simultaneously obtains the flow of main 8 river channels of the lake and the blue algae and ammonia nitrogen thereof in the period
Nitrate nitrogen
And phosphoric acid
Monitoring data of main environmental indexes, wherein the data can be used as boundary conditions to participate in model calculation;
b. and determining an Environmental hydrodynamic Code (EFDC) model for prediction according to the collected water quality index and the condition of mainly predicting the biomass of the blue-green algae. The model has 4 parameters, and the specific meanings are shown in the following table:
(2) As shown in the flow chart, the step (2) includes:
a. the value ranges of the main parameters are determined as shown in the following table, and the main parameters are assumed to be uniformly distributed in the respective ranges;
b. generating 11000 random numbers by using a random number generation program in the respective value range of each parameter according to the distribution form of each parameter;
c. and randomly taking the generated parameters according to the requirements of the model, and grouping the parameters to ensure that each parameter in each group has only 1 value and the parameters form 11000 groups of parameters.
(3) As shown in the flowchart, step (3) includes:
a. analyzing the water quality prediction requirement: the main target of the prediction is the biomass of the blue algae;
b. according to the analysis requirement result, determining the target function for carrying out parameter uncertainty analysis as blue algae and ammonia nitrogen
Nitrate nitrogen
And phosphoric acid
The relative error RE of the simulation results is calculated using the following equation:
wherein O is i Is the ith monitor value, S i Is with O i The corresponding model simulation value, T is the total number of monitored values, here equal to 11.
(4) As shown in the flow chart, the step (4) includes:
a. substituting 11000 groups of parameters and corresponding boundary conditions into the eutrophication model for calculation to determine 11000 groups of blue algae and ammonia nitrogen
Nitrate nitrogen
And phosphoric acid
Calculated value S of i ,i＝1,2,3...T；
b. Monitoring data O combined with water body i I =1,2,3.. T, 11000 sets of values of relative error were calculated.
(5) As shown in the flowchart, step (5) includes:
a. distinguishing the properties of the target function, and dividing the properties into two categories, namely representing the simulation result as the larger the target function is, and representing the simulation result as the smaller the target function is; adding a negative sign in front of the first class of target function with the larger target function better, so that the two classes of target functions are unified that the smaller the target function is, the better the simulation result is;
in this calculation, a smaller relative error represents a better simulation result, and therefore no conversion is required.
b. Defining that all 4 relative errors corresponding to the parameter group u are larger than 4 relative errors corresponding to the parameter group v; the parameter group u is considered to be dominated by the parameter group v;
c. comparing 11000 groups of parameters with corresponding objective functions, and removing all parameter groups which are defined in the step b and have a certain group of parameter groups dominance; the remaining set of 600 sets of relative errors is called the pareto set;
d. and extracting the parameter group corresponding to the pareto set, and obtaining 600 more groups of parameters to form an optimal parameter set.
(6) As shown in the flowchart, step (6) includes:
a. drawing a two-parameter joint probability density function of the dominant parameter set; the results are shown in FIGS. 2 and 3;
b. carrying out double-parameter uncertainty analysis by a visual inspection method: the uncertainty of the local parameters with high probability density is small, and the uncertainty of the local parameters with low probability density is large. As can be seen from the figure, the probability density is large where the 4 parameters are relatively large, i.e., the uncertainty is small here; while at the rest of the distribution the uncertainty is smaller.
(7) As shown in the flowchart, step (7) includes:
a. estimating and drawing the probability density distribution of each parameter in the dominance set by using the kernel function; wherein the kernel function adopts a Gaussian kernel function; the results are shown in FIGS. 2 and 3;
b. selecting the value corresponding to the highest probability density position as a model parameter calibration result, wherein the result is shown in the following table:
(8) As shown in the flowchart, step (8) includes:
a. sorting and calibrating the finished model parameters;
b. and collecting boundary conditions required by prediction and substituting the boundary conditions and the calibrated parameters into the model to predict the water quality. The blue algae biomass prediction result is shown in figure 4.
Claims (7)
1. A method for predicting a lake water quality model through multi-target uncertainty analysis is characterized by comprising the following steps:
(1) Collecting monitoring data of lakes and boundary rivers with water quality to be predicted, and determining a model for predicting the water quality and model parameters thereof;
(2) Determining the value range and distribution characteristics of the model parameters, and extracting m groups of parameter values in the value range according to respective distribution characteristics, wherein m is greater than or equal to 10000;
(3) Determining n objective functions for model parameter uncertainty analysis, wherein n is greater than or equal to 2; the method specifically comprises the following steps:
a. analyzing the water quality prediction requirement;
b. determining n objective functions for parameter uncertainty analysis according to the analysis requirement result, wherein n is greater than or equal to 2; the objective function is the average relative error RE of the model simulation value S and the monitoring value O of different environmental indexes and the root mean square error RMSE thereof, and is specifically shown in the following two formulas:
wherein O is i Is the ith monitor value, S i Is with O i Corresponding model simulation values, T is the total number of monitoring values;
(4) Substituting the values of m groups of model parameters, the monitoring data of the boundary river and the monitoring data of the lake into the water quality model for calculation to determine m groups of values of the objective function; the method specifically comprises the following steps:
a. substituting the values of m groups of model parameters and the corresponding monitoring data of the boundary river into the water quality model for calculation to determine the simulation values S of m groups of environmental indexes i ,i＝1,2,3...T；
b. Monitoring data O combined with lake i I =1,2,3.. T, calculating values of each group of objective functions, for a total of m groups;
(5) Comparing and obtaining dominant parameter sets corresponding to the pareto sets under the objective function, wherein the number d of the parameter sets in the parameter dominant sets is not less than 500; if d is less than 500, increasing the number m of the parameter sets extracted in the step (2), and repeatedly executing the steps (2) - (4);
(6) Drawing a double-parameter joint probability density function of the dominant parameter set, and carrying out double-parameter uncertainty analysis;
(7) Estimating and drawing the probability density distribution of each parameter in the domination set by using a kernel function, wherein the value corresponding to the highest probability density is used as a model parameter calibration result;
(8) And collecting monitoring data of the boundary river required for prediction and substituting the collected monitoring data and the calibrated model parameters into the water quality model to predict the water quality.
2. The method for model prediction of lake water quality through multi-objective uncertainty analysis according to claim 1, wherein in the step (1):
a. the collected monitoring data of the lake and the boundary river with the predicted water quality are continued for at least 2 months and averagely 1 time per week, and the monitoring data comprise the water quality monitoring data of the predicted lake, the water quality monitoring data of the lake boundary river and the flow data of the boundary river;
b. determining a model for predicting the water quality of the lake according to the collected water quality indexes and indexes needing prediction in the monitoring data of the lake and the boundary rivers with the water quality to be predicted, and determining parameters of the model according to the model structure.
3. The method for performing model prediction of lake water quality through multi-objective uncertainty analysis according to claim 1, wherein the step (2) comprises the following steps:
a. determining the value ranges and the distribution of the model parameters, and assuming that the model parameters are uniformly distributed in the respective value ranges;
b. generating m random numbers by a random number generation program in the respective value range of each parameter according to the distribution form of each parameter, wherein m is more than or equal to 10000;
c. and grouping the generated parameters randomly according to model requirements, ensuring that each parameter in each group has only 1 value, and forming m groups of parameter groups which can be used for driving the model.
4. The method for lake water quality model prediction through multi-objective uncertainty analysis according to claim 1, wherein the step (5) comprises the following steps:
a. distinguishing the properties of the target function, and dividing the properties into two categories, namely, the larger the target function is, the better the simulation result is represented, and the smaller the target function is, the better the simulation result is represented; adding a negative sign in front of the first class of target function with the larger target function better, so that the two classes of target functions are unified that the smaller the target function is, the better the simulation result is;
b. defining that n objective functions corresponding to the parameter group u are all larger than n objective functions corresponding to the parameter group v; the parameter group u is considered to be dominated by the parameter group v;
c. comparing the objective functions corresponding to the m groups of parameters, and removing all the parameter groups which are dominated by any group of parameters under the definition of the step b; the rest set of the d groups of objective function values is called a pareto set, and d is not less than 500;
d. extracting parameter groups corresponding to the pareto sets, and obtaining d groups of parameters to form an optimal parameter set;
e. and (4) if d is less than 500, increasing the number m of the parameter sets extracted in the step (2), and repeatedly executing the steps (2) - (4).
5. The method for performing model prediction of lake water quality through multi-objective uncertainty analysis according to claim 1, wherein the step (6) comprises the following steps:
a. drawing a dual-parameter joint probability density function of the dominant parameter set;
b. carrying out double-parameter uncertainty analysis by a visual inspection method: the uncertainty of the local parameters with high probability density is small, and the uncertainty of the local parameters with low probability density is large.
6. The method for lake water quality model prediction through multi-objective uncertainty analysis according to claim 1, wherein the step (7) comprises the following steps:
a. estimating and drawing the probability density distribution of each parameter in the dominance set by using the kernel function; wherein the kernel function adopts a Gaussian kernel function;
b. selecting a value corresponding to the highest probability density as a model parameter calibration result;
7. the method for lake water quality model prediction through multi-objective uncertainty analysis according to claim 1, wherein the step (8) comprises the following steps:
a. sorting and calibrating the finished model parameters;
b. and collecting monitoring data of the boundary river required for prediction and substituting the collected monitoring data and the calibrated model parameters into the water quality model to predict the water quality.
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