Water quality sampling frequency design method and evaluation system based on Newton-Costa closed integral error formula

Abstract

The invention discloses a water quality sampling frequency design method based on a Newton-Costa closed integral error formula in the technical field of water environment monitoring. The water quality sampling frequency design method comprises the following steps: step 1) determining a maximum acceptable error limit Em of a pollutant output load estimation result; 2) carrying out high-frequency hydrology and water quality monitoring, and measuring a local flow process and a pollutant concentration process; 3) determining key parameters of a pollutant load output process according to an actual hydrology and water quality monitoring result; and 4) according to a Newton-Costa closed integral error formula, calculating the appropriate water quality sampling frequency considering the given load estimation error upper limit, and through theoretical analysis of the pollutant output load estimation error, providing the appropriate water quality sampling frequency design method oriented to the given error upper limit.

Description

Technical Field

[0001] The present invention relates to the technical field of water environment monitoring and management, and in particular to a water quality sampling frequency design method and an evaluation system. Background Art

[0002] In recent years, countries around the world have invested a lot of manpower and material resources to carry out river water quality monitoring in order to finely evaluate river water quality, identify pollutant sources, and provide data support for water environment management. Among them, improving water environment quality requires first accurately describing the pollutant output load and its spatiotemporal dynamic characteristics. An inappropriate sampling system may introduce a large number of errors in pollutant load estimation. Therefore, how to design a reasonable sampling interval is one of the keys to reducing the uncertainty of pollutant output load.

[0003] With the development of online water quality monitoring technology, it is becoming easier and easier to obtain high-frequency hydrological and water quality data, which helps to accurately estimate the pollutant output load. However, in many monitoring scenarios, due to the randomness and uncertainty of rainfall events, continuous monitoring generally faces technical, human and economic difficulties. Therefore, how to recommend appropriate sampling frequencies based on high-frequency water quality data and accuracy requirements has become a research hotspot. Previous studies on sampling frequency mainly used the Monte Carlo resampling method, and there were few theoretical studies on pollutant load estimation errors. Therefore, based on high-frequency hydrological and water quality monitoring, it is necessary to propose a set of water quality sampling frequency calculation methods for a given error upper limit based on the theoretical analysis of pollutant load estimation errors. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a water quality sampling frequency design method and evaluation system based on the Newton-Costa closed form integral error formula. Through theoretical analysis of the pollutant output load estimation error, a suitable water quality sampling frequency design method for a given error upper limit is proposed.

[0005] The object of the present invention is achieved in this way: a water quality sampling frequency design method based on the Newton-Costa closed-form integral error formula, comprising the following steps:

[0006] Step 1) Determine the maximum acceptable error limit Em of the pollutant output load estimation result;

[0007] Step 2) Conduct high-frequency hydrological and water quality monitoring to measure local flow processes and pollutant concentration processes;

[0008] Step 3) Determine the key parameters of the pollutant load output process based on the actual hydrological and water quality monitoring results;

[0009] Step 4) Calculate the appropriate water quality sampling frequency considering the upper limit of the given load estimation error based on the Newton-Costa closed-form integral error formula.

[0010] Furthermore, step 2) conducts high-frequency hydrological and water quality monitoring to determine the local flow process q(t) and pollutant concentration process c(t), including: high-frequency hydrological and water quality monitoring is carried out at a constant frequency, and its frequency varies from region to region. If there is no local recommended high-frequency monitoring frequency, the interval between two adjacent monitoring points shall not exceed four hours.

[0011] Furthermore, in step 3), the key parameters of the pollutant load output process are determined based on the actual hydrological and water quality monitoring results, including:

[0012] The starting point Ta and end point Tb of hydrological and water quality monitoring data

[0013] The total pollutant output load I obtained from hydrological and water quality data;

[0014] The maximum value D of the second-order derivative of the pollutant load output process.

[0015] Furthermore, the calculation formula for the total pollutant output load I obtained from the hydrological and water quality data is:

[0016]

[0017] Among them, T a With T b are the starting point and end point of the monitoring data, respectively. f(t) is the pollutant output process during the monitoring period. The calculation process is as follows:

[0018]

[0019] Among them, q(t) and c(t) are the flow process and pollutant concentration process of high-frequency water quality monitoring, respectively;

[0020] The calculation formula for the maximum value D of the second-order derivative of the pollutant load output process is:

[0021]

[0022] Among them, ξ i is the interval [T i , T i+1 ], T i is the sampling time of the i-th water quality data, is the second derivative of f(t).

[0023] Furthermore, in step 4), according to the Newton-Costa closed-form integral error formula, the appropriate water quality sampling frequency considering the upper limit of the given load estimation error is calculated, including:

[0024] According to the Newton-Costa closed integral error formula, the trapezoidal formula is used to estimate the relative sampling error E of the integral rel , can be calculated by the following formula:

[0025]

[0026] Among them, E sum is the cumulative error in pollutant load estimation, E i is the error of the ith data point, ΔT is the sampling interval, n is the total number of data points, ξ i is the interval [T i , T i+1 ] at some point between .

[0027] Furthermore, the cumulative error obtained in step 4) according to the Newton-Costa closed-form integral error formula has the following general rules:

[0028] The relative sampling error is proportional to the cube of ΔT;

[0029] The relative sampling error is related to the value of the second-order derivative f′′(x);

[0030] The relative sampling error is linear with the number n of calculation intervals.

[0031] Furthermore, when the relative sampling error has a given upper limit E m , then:

[0032]

[0033] After sorting, we can get:

[0034]

[0035] Furthermore, when the second-order derivative f"(x) is in [T a , T b ] has a maximum value D in the range, then:

[0036]

[0037] because , we can further get:

[0038]

[0039] Furthermore, according to the Newton-Costa closed-form integral error formula, the appropriate water quality sampling frequency (ΔT m ), and its calculation formula is:

[0040]

[0041] A water quality sampling frequency evaluation system based on the Newton-Costa closed form integral error formula is used to implement a water quality sampling frequency design method based on the Newton-Costa closed form integral error formula, comprising:

[0042] An upper error limit input module is used to input a given upper error limit of pollutant load estimation;

[0043] High-frequency hydrological and water quality data processing module, used to calculate the pollutant output process based on high-frequency monitoring;

[0044] The pollutant load output key parameter determination module is used to identify the key parameters that affect the water quality sampling frequency;

[0045] The appropriate sampling frequency design module calculates the appropriate water quality sampling frequency based on the given error limit and the derived formula.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] Based on high-frequency hydrological and water quality monitoring, this paper starts from the theoretical analysis of pollutant load estimation errors, quantifies the analytical relationship between water quality sampling frequency and pollutant load estimation errors without assuming the distribution characteristics of monitoring data, and proposes a non-parametric estimation method for suitable pollutant sampling frequency. The research results are expected to provide a theoretical basis and technical reference for optimizing water quality monitoring programs and non-point source pollution prevention and control. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0049] Figure 1 It is a flow chart of the present invention.

[0050] Figure 2 : It is the test site location and the distribution map of high-frequency hydrological and water quality data sampling points in the embodiment.

[0051] Figure 3 It is the high-frequency hydrological and water quality data in the embodiment. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Example 1

[0054] like Figure 1 A water quality sampling frequency design method based on the Newton-Costa closed-form integral error formula is shown, comprising the following steps:

[0055] Step 1) Determine the maximum acceptable error limit E of the pollutant output load estimate m Its physical meaning is the maximum value of the ratio between the pollutant monitoring load error and the actual pollutant output load. The specific data is determined according to the different water environment quality requirements in different places.

[0056] Step 2) Conduct high-frequency hydrological and water quality monitoring to measure the local flow process q(t) and pollutant concentration process c(t), including: high-frequency hydrological and water quality monitoring is carried out at a constant frequency, which varies from region to region. If there is no local recommended high-frequency monitoring frequency, the interval between two adjacent monitoring points shall not exceed four hours;

[0057] Step 3) Based on the actual hydrological and water quality monitoring results, determine the key parameters of the pollutant load output process, including:

[0058] Starting point T for hydrological and water quality monitoring data a With the end point T b

[0059] The total pollutant output load I obtained from hydrological and water quality data; its calculation formula is:

[0060]

[0061] Among them, T a With T b are the starting point and end point of the monitoring data, respectively. f(t) is the pollutant output process during the monitoring period. The calculation process is as follows:

[0062]

[0063] Among them, q(t) and c(t) are the flow process and pollutant concentration process of high-frequency water quality monitoring, respectively;

[0064] The maximum value D of the second-order derivative of the pollutant load output process; its calculation formula is:

[0065]

[0066] Among them, ξ i is the interval [T i , T i+1 ], T i is the sampling time of the i-th water quality data, is the second derivative of f(t).

[0067] Step 4) Calculate the appropriate water quality sampling frequency considering the upper limit of the given load estimation error based on the Newton-Costa closed-form integral error formula, including:

[0068] According to the Newton-Costa closed integral error formula, the trapezoidal formula is used to estimate the relative sampling error E of the integral rel , can be calculated by the following formula:

[0069]

[0070] Among them, E sum is the cumulative error in pollutant load estimation, E i is the error of the ith data point, ΔT is the sampling interval, n is the total number of data points, ξ i is the interval [T i , T i+1 ] at some point between .

[0071] The cumulative error obtained according to the Newton-Costa closed-form integral error formula has the following general rules:

[0072] The relative sampling error is proportional to the cube of ΔT;

[0073] The relative sampling error is related to the value of the second-order derivative f′′(x);

[0074] The relative sampling error is linear with the number n of calculation intervals.

[0075] When the relative sampling error has a given upper limit E m , then:

[0076]

[0077] After sorting, we can get:

[0078]

[0079] When the second-order derivative f"(x) is in [T a , T b ] has a maximum value D in the range, then:

[0080]

[0081] because , we can further get:

[0082]

[0083] Calculate the appropriate water quality sampling frequency (ΔT) considering the upper limit of the error of the given load estimation m ), and its calculation formula is:

[0084]

[0085] Example 2

[0086] A water quality sampling frequency evaluation system based on the Newton-Costa closed-form integral error formula, used to implement Example 1, includes:

[0087] An upper error limit input module is used to input a given upper error limit of pollutant load estimation;

[0088] High-frequency hydrological and water quality data processing module, used to calculate the pollutant output process based on high-frequency monitoring;

[0089] The pollutant load output key parameter determination module is used to identify the key parameters that affect the water quality sampling frequency;

[0090] The appropriate sampling frequency design module calculates the appropriate water quality sampling frequency based on the given error limit and the derived formula.

[0091] The following is combined with Figure 2~3 The water quality sampling frequency with a given upper error limit is designed based on the measured data to verify the beneficial effects of the present invention.

[0092] Specifically, the hydrological and water quality data of an irrigation area in Yangzhou City, Jiangsu Province was selected as a case study. Figure 2 The location of the test site and the layout of sampling points.

[0093] Furthermore, the present invention carried out high-frequency hydrological and water quality monitoring during the flooding period of rice-wheat rotation farmland in the study area, mainly monitoring the farmland drainage process and the change process of nitrate nitrogen concentration. Figure 3 The monitoring interval of the drainage process was 15 minutes, and the interval of nitrate nitrogen concentration was 1 hour; in order to facilitate subsequent analysis, the nitrate nitrogen concentration was interpolated to the 15-minute monitoring interval.

[0094] Furthermore, the present invention calculates the nitrogen output process ( Figure 3 ), the calculation formula is as follows:

[0095]

[0096] Furthermore, the present invention obtains key parameters describing the change of nitrate nitrogen according to the nitrogen output process, and the results are shown in Table 1.

[0097] Table 1 Key parameters describing the nitrate nitrogen output process

[0098] parameter Data starting point (Ta) Data endpoint (Tb) Pollutant output load (I) Maximum value of second derivative (D) Numeric 2024 / 6 / 8 10:00 2024 / 6 / 9 2:00 0.905 0.0454

[0099] Furthermore, the present invention calculates the sampling intervals corresponding to different given error limits based on the key parameters describing the nitrate nitrogen output process, and the results are shown in Table 2. When the given error limit is 10%, the corresponding water quality sampling interval should be no more than 1.22 hours; when the given error limit is 50%, the water quality sampling interval should be no more than 2.73 hours.

[0100] Table 2 Sampling intervals corresponding to some given error limits

[0101] Error limit (%) 5 10 20 30 40 50 Sampling interval (hours) 0.86 1.22 1.73 2.12 2.45 2.73

[0102] The above embodiments are only used to help understand the method and core idea of ​​the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A water quality sampling frequency design method based on the Newton-Costa closed form integral error formula, characterized in that: The following steps are involved: Step 1) Determine the maximum acceptable error limit Em of the pollutant output load estimation result; Step 2) Conduct high-frequency hydrological and water quality monitoring to measure local flow processes and pollutant concentration processes; Step 3) Determine the key parameters of the pollutant load output process based on the actual hydrological and water quality monitoring results; Step 4) Calculate the appropriate water quality sampling frequency considering the upper limit of the given load estimation error based on the Newton-Costa closed-form integral error formula.

2. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 1 is characterized in that: Step 2) Conduct high-frequency hydrological and water quality monitoring to determine the local flow process q(t) and pollutant concentration process c(t), including: High-frequency hydrological and water quality monitoring is carried out at a constant frequency, and the frequency varies from region to region. If there is no recommended high-frequency monitoring frequency in the local area, the interval between two adjacent monitoring points shall not exceed four hours.

3. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 1 or 2, characterized in that: In step 3), the key parameters of the pollutant load output process are determined based on the actual hydrological and water quality monitoring results, including: The starting point Ta and end point Tb of hydrological and water quality monitoring data; The total pollutant output load I obtained from hydrological and water quality data; The maximum value D of the second-order derivative of the pollutant load output process.

4. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 3 is characterized in that: The calculation formula for the total pollutant output load I obtained from the hydrological and water quality data is: ； Among them, T a With T b are the starting point and end point of the monitoring data, respectively. f(t) is the pollutant output process during the monitoring period. The calculation process is as follows: ； Among them, q(t) and c(t) are the flow process and pollutant concentration process of high-frequency water quality monitoring, respectively; The calculation formula for the maximum value D of the second-order derivative of the pollutant load output process is: ； Among them, ξ i is the interval [T i , T i+1 ], T i is the sampling time of the i-th water quality data, is the second derivative of f(t).

5. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 1 or 2, characterized in that: In step 4), according to the Newton-Costa closed-form integral error formula, the appropriate water quality sampling frequency considering the upper limit of the given load estimation error is calculated, including: According to the Newton-Costa closed integral error formula, the trapezoidal formula is used to estimate the relative sampling error E of the integral rel , can be calculated by the following formula: ； Among them, E sum is the cumulative error in pollutant load estimation, E i is the error of the ith data point, ΔT is the sampling interval, n is the total number of data points, ξ i is the interval [T i , T i+1 ] at some point between .

6. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 1 or 2, characterized in that: The cumulative error obtained in step 4) according to the Newton-Costa closed-form integral error formula has the following general rules: The relative sampling error is proportional to the cube of ΔT; The relative sampling error is related to the value of the second-order derivative f′′(t); The relative sampling error is linear with the number n of calculation intervals.

7. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 6 is characterized in that: When the relative sampling error has a given upper limit E m , then: ； After sorting, we can get: 。 8. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 1 is characterized in that: When the second-order derivative f"(x) is in [T a , T b ] has a maximum value D in the range, then: ； because , we can further get: 。 9. The water quality sampling frequency design method based on the Newton-Costa closed form integral error formula according to claim 8 is characterized in that: The Newton-Costa closed-form integral error formula is used to calculate the appropriate water quality sampling frequency (ΔT) considering the upper limit of the given load estimation error. m ), and its calculation formula is: 。 10. A water quality sampling frequency evaluation system based on the Newton-Costa closed form integral error formula, used to implement the water quality sampling frequency design method based on the Newton-Costa closed form integral error formula described in any one of claims 1 to 9, characterized in that: include: An upper error limit input module is used to input a given upper error limit of pollutant load estimation; High-frequency hydrological and water quality data processing module, used to calculate the pollutant output process based on high-frequency monitoring; The pollutant load output key parameter determination module is used to identify the key parameters that affect the water quality sampling frequency; The appropriate sampling frequency design module calculates the appropriate water quality sampling frequency based on the given error limit and the derived formula.

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