Method for determining maximum limit value of total phosphorus in lake and evaluating uncertainty

Abstract

The invention discloses a method for determining the maximum limit value of total phosphorus in a lake and evaluating uncertainty in the technical field of lake management. The method comprises the following steps: 1) collecting observation values of algae chlorophyll a and total phosphorus in the lake of which the maximum limit value of total phosphorus needs to be determined; supplementing and collecting algae samples; 2) measuring the content of algal toxin, obtaining a relationship with chlorophyll a, and determining a limit value of the chlorophyll a; 3) taking total phosphorus as a dependent variable and chlorophyll a as an independent variable, and establishing a regression relationship between the total phosphorus and the chlorophyll a under different quantiles; 4) calculating 95% confidence intervals of regression coefficients of different quantiles, and determining that the regression coefficients can pass through a significance test minimum quantile; 5) selecting a corresponding regression relationship to obtain the maximum limit value of the total phosphorus of the lake, and 6) determining the uncertainty of the maximum limit value. The method determines the maximum limit value and the uncertainty of the total phosphorus of the lake by using the relationship among algal toxin, total phosphorus and chlorophyll a in the lake, and is easy to be used in the determination of water quality management targets of various polluted shallow lakes.

Description

Technical Field

[0001] The invention relates to the technical field of lake management, and in particular to a method for determining a maximum limit of total phosphorus in a lake and evaluating uncertainty. Background Art

[0002] Phosphorus is the most important nutrient in lake water. Controlling the growth of lake algae plays a decisive role in reducing the concentration of lake algae and protecting the quality of lake water. Formulating an appropriate maximum limit for total phosphorus is a prerequisite for effectively improving the quality of lake water environment and is of great significance for protecting the lake water environment. At present, the formulation of the maximum limit for total phosphorus in lakes is highly subjective; this leads to the fact that the maximum limit for total phosphorus in lakes is often out of touch with the actual water quality of the lakes. In fact, if the maximum limit for total phosphorus in lakes is too high, it will be detrimental to the protection of the lake water environment and may easily lead to further deterioration of the water quality of the lake; if the maximum limit is too low, it is unnecessary and may hinder local economic and social development. Summary of the invention

[0003] In view of the deficiencies in the prior art, the present invention provides a method for determining the maximum limit of total phosphorus in lakes and evaluating uncertainty. The relationship between algal toxins, total phosphorus and chlorophyll a in lakes is used to determine the maximum limit of total phosphorus in lakes and its uncertainty, which can be easily promoted and used in determining water quality management objectives for various polluted shallow lakes.

[0004] The object of the present invention is achieved in this way: a method for determining the maximum limit of total phosphorus in a lake and evaluating uncertainty comprises the following steps:

[0005] Step 1) Collect historical observations of algae chlorophyll a and total phosphorus in lakes where the maximum limit of total phosphorus needs to be determined; and collect algae samples and their chlorophyll a values ​​at the same time;

[0006] Step 2) Determine the algae toxin content in the lake and obtain its relationship with chlorophyll a to determine the limit value of chlorophyll a;

[0007] Step 3) Taking the historical observations of total phosphorus as the dependent variable and the historical observations of chlorophyll a as the independent variable, a regression relationship between the two at different quantiles is established;

[0008] Step 4) Calculate the 95% confidence interval of the regression coefficient at different quantiles and determine the minimum quantile at which the regression coefficient can pass the significance test;

[0009] Step 5) Select the regression relationship corresponding to the quantile obtained in step 4) to obtain the maximum limit of total phosphorus in the lake;

[0010] Step 6) Determine the uncertainty in the maximum limit for total phosphorus in the lake.

[0011] Further, step 1) specifically includes the following steps:

[0012] Step 1-1) Collect the historical total phosphorus (i.e., TP) observation values of n groups of lakes for which the maximum total phosphorus limit needs to be determined, denoted as TP i ; and the simultaneously monitored chlorophyll a (i.e., Chla), and the observation value is denoted as Chla i ; where n is an integer greater than 500, and i = 1, 2, 3... n;

[0013] Step 1-2) Supplementary sampling is carried out in the lake to determine the concentration TOX of microcystin in m groups of algal samples S and the corresponding chlorophyll a value Chla s ; where m is an integer greater than 10, and s = 1, 2, 3... m.

[0014] Further, step 2) specifically includes the following steps:

[0015] Step 2-1) Taking the microcystin concentration TOX determined by m groups of supplementary sampling as the independent variable and the corresponding chlorophyll a value Chla as the dependent variable, establish a linear regression relationship between the two using the least squares method:

[0016] ;

[0017] where d is the regression coefficient of the microcystin concentration and e is the intercept of the regression equation

[0018] Step 2-2) Substitute the maximum content of microcystin specified in the sanitary standard for domestic drinking water, which is 1 μg / L, into the above regression relationship to obtain the maximum limit Chla of the corresponding chlorophyll a max .

[0019] Further, step 3) specifically includes the following steps:

[0020] Step 3-1) Select a quantile p, 0 < p < 1. Taking all the historical observation values TP of total phosphorus as the dependent variable and all the historical observation values Chla of chlorophyll a as the independent variable, establish a regression relationship between the two at the p quantile:

[0021] ;

[0022] where is the regression coefficient corresponding to the p quantile regression relationship, is the intercept corresponding to the p quantile regression relationship; in the regression relationship , can be obtained by minimizing the following formula:

[0023] ;

[0024] Step 3-2) In step 3-1), p is initialized to 0.05 and the step length is repeated until p = 0.95.

[0025] Furthermore, the step 4) specifically includes the following steps:

[0026] Step 4-1) From the n groups of total phosphorus and chlorophyll a observation values, 100 groups of observation data are extracted with replacement to form a subset of observation values. Based on the observation values ​​in this subset, step 3 is repeated);

[0027] Step 4-2) For each fixed p, repeat step a 1000 times to obtain 1000 sets of and ;

[0028] Step 4-3) For each specified p, the 1000 Arrange from small to large and determine its 25th value and the 975th value ;

[0029] Step 4-4) Calculate If the value of is greater than 0, and at least one of the values ​​is greater than 0, then the regression coefficient can pass the significance test at the p quantile; otherwise, the regression coefficient cannot pass the significance test at the p quantile;

[0030] Step 4-5) Determine the regression coefficients The smallest p that can pass the significance test min .

[0031] Furthermore, the step 5) specifically includes the following steps:

[0032] Step 5-1) Determine p from the results obtained in step 3) min The corresponding quantile regression relationship is:

[0033] ;

[0034] Step 5-2) Substitute the maximum limit value of chlorophyll a obtained in step 2) into max Substitute Chla into the above relationship to obtain the corresponding total phosphorus value, recorded as TP v .

[0035] Step 5-3) The maximum limit of total phosphorus in the lake TP max Calculated by the following formula:

[0036] .

[0037] Furthermore, the step 6) specifically includes the following steps:

[0038] Step 6-1) for step 4) min The corresponding 1000 groups and , repeatedly calculate the following formula to obtain the corresponding 1000 sets of TPd (d=1,2,…,1000):

[0039] ;

[0040] Step 6-2) Arrange the 1000 groups of TPd from smallest to largest and determine their 25th value and the 975th value ;

[0041] Step 6-3) The lower limit of the maximum limit of total phosphorus in the lake TP d,min yes:

[0042] ;

[0043] Step 6-4) Maximum limit of total phosphorus TP for the lake d,max The upper bound of is:

[0044] ;

[0045] Step 6-5) Determine the uncertainty TP of the maximum limit of total phosphorus in the lake u for:

[0046] .

[0047] In the present invention, environmental studies have pointed out that there is a close relationship between the concentration of chlorophyll a and the total phosphorus concentration in lakes, and there is a relationship between the concentration of algae toxins and the concentration of chlorophyll a, and algae toxins are difficult to remove through water treatment processes; related medical studies have pointed out that algae toxins are extremely harmful to humans and may cause poisoning, so algae toxins in water need to be strictly controlled. Based on the above viewpoints, the present invention uses linear regression and other methods to determine the maximum limit of total phosphorus in lakes and its uncertainty.

[0048] Compared with the prior art, the beneficial effects of the present invention are: the present invention utilizes the statistical relationship of objective observation data and national authoritative standards, and has almost no steps of subjective human intervention, thus overcoming the shortcomings of the existing methods of subjectivity and strong human intervention, and can accurately determine the maximum limit of total phosphorus in lakes, and can be easily promoted and used in determining water quality management objectives for various polluted shallow lakes. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] 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.

[0050] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0051] 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.

[0052] like Figure 1 A method for determining a maximum limit for total phosphorus in lakes and assessing uncertainty is shown, including the following steps:

[0053] Step (1) collecting historical observation values ​​of algae chlorophyll a and total phosphorus in the lake for which the maximum limit of total phosphorus needs to be determined; and collecting algae samples and their chlorophyll a values ​​at the same time; specifically comprising the following steps:

[0054] a. Collect n groups of historical total phosphorus observations for lakes for which the maximum limit of total phosphorus needs to be determined, recorded as TP i And the chlorophyll a obtained by simultaneous monitoring, denoted as Chla i ; Where n is an integer greater than 500, i=1,2,3…n;

[0055] b. Take additional samples from the lake to determine the concentration of algal toxins in group m algae samples (TOX) S and the corresponding chlorophyll a value Chla s ; Wherein, m is an integer greater than 10, and s=1,2,3…m.

[0056] Step (2) determines the algal toxin content in the lake and obtains its relationship with chlorophyll a to determine the limit value of chlorophyll a, which specifically includes the following steps:

[0057] a. Take the algae toxin concentration TOX measured by the supplementary sampling of group m as the independent variable and the corresponding chlorophyll a value Chla as the dependent variable, and use the least squares method to establish the linear regression relationship between the two:

[0058]

[0059] b. Substitute the maximum content of microcystin, which is 1 μg / L as stipulated in the national hygienic standard for domestic drinking water, into the above regression relationship to obtain the maximum limit value Chla of the corresponding chlorophyll a. max 。

[0060] Step (3): Use the historical observed values of total phosphorus as the dependent variable and the historical observed values of chlorophyll a as the independent variable to establish the regression relationship between the two at different quantiles; specifically, it includes the following steps:

[0061] a. Select a quantile p (0 < p < 1), use all the historical observed values TP of total phosphorus as the dependent variable, and all the historical observed values Chla of chlorophyll a as the independent variable to establish the regression relationship between the two at the p - quantile:

[0062]

[0063] where, is the regression coefficient corresponding to the p - quantile regression relationship, is the intercept corresponding to the p - quantile regression relationship.

[0064] In the regression relationship, , can be obtained by minimizing the following formula:

[0065]

[0066] b. In step a, p uses 0.05 as the initial value and step size, and repeats until p = 0.95.

[0067] Step (4): Calculate the 95% confidence interval of the regression coefficients at different quantiles, and determine the minimum quantile at which the regression coefficient can pass the significance test; specifically, it includes the following steps:

[0068] a. From the n groups of observed values of total phosphorus and chlorophyll a, draw 100 groups of observed data with replacement to form a subset of observed values, and based on the observed values in this subset, repeat step (3).

[0069] b. For each fixed p, step a is repeated 1000 times to obtain 1000 groups of and 。

[0070] c. Arrange the 1000 corresponding to each specified p in ascending order, and determine its 25th value and the 975th value 。

[0071] d. Calculate If the value of is greater than 0, and at least one of the values ​​is greater than 0, then the regression coefficient can pass the significance test at the quantile p; otherwise, the regression coefficient cannot pass the significance test at the p quantile.

[0072] e. Determine the regression coefficient The smallest p that can pass the significance test min .

[0073] Step (5) selects the regression relationship corresponding to the quantile obtained in step (4) to obtain the maximum limit of the total phosphorus in the lake; specifically, it includes the following steps:

[0074] a. Determine p from the result obtained in step (3) min The corresponding quantile regression relationship is:

[0075]

[0076] b. The maximum limit value of chlorophyll a obtained in step (2) max Substitute Chla into the above relationship to obtain the corresponding total phosphorus value, recorded as TP v .

[0077] c. The maximum limit of total phosphorus in the lake TP max Calculated by the following formula:

[0078] .

[0079] Step (6) determines the uncertainty of the maximum limit of total phosphorus in the lake; specifically includes the following steps:

[0080] a. For step (4) p min The corresponding 1000 groups and , repeatedly calculate the following formula to obtain the corresponding 1000 sets of TPd (d=1,2,…,1000):

[0081]

[0082] b. Arrange the 1000 groups of TPd from small to large and determine their 25th value and the 975th value .

[0083] c. The lower limit of the maximum limit of total phosphorus in the lake TP d,min yes:

[0084]

[0085] The maximum limit of total phosphorus in the lake is TP d,max The upper bound of is:

[0086]

[0087] e. Uncertain TP for determining the maximum limit of total phosphorus in the lake u for:

[0088] .

[0089] The present invention will be further described below in conjunction with specific examples.

[0090] A method for determining a maximum limit for total phosphorus in lakes and assessing uncertainty includes the following steps:

[0091] Step (1) According to the requirements of this manual, 960 sets of historical total phosphorus observation values ​​and corresponding chlorophyll a observation values ​​of the lake were collected; at the same time, 15 sets of algae status samples and their corresponding chlorophyll a status samples were collected in the lake.

[0092] Step (2) determines the concentration of algae toxin TOX and the corresponding concentration of chlorophyll a Chla in the supplementary algae status sample, and uses the least squares method to determine the regression relationship between the two:

[0093] ;

[0094] Substituting the maximum limit of algae toxin concentration of 1 μg / L into the above formula, we obtain the maximum limit of chlorophyll a concentration in this lake to be 15.59 μg / L.

[0095] Step (3) Select 0.05 as the quantile, take all historical observations of total phosphorus TP as the dependent variable, and all historical observations of chlorophyll a Chla as the independent variable, and minimize the following formula:

[0096]

[0097] The relationship between chlorophyll a and total phosphorus at the 0.05 quantile is:

[0098]

[0099] The above steps were repeated with a step size of 0.05 to obtain the relationship between chlorophyll a and total phosphorus at 0.10, 0.15, …, 0.95 quantiles, the regression coefficient of chlorophyll a, and the corresponding intercept.

[0100] Step (4) The first step is to randomly select 100 groups of observation data from the 960 groups of historical observation data of chlorophyll a and total phosphorus with replacement to form a subset of observation data for the 0.05 quantile. Based on the data in this subset, repeat step (3). This step is repeated 1000 times to obtain the regression coefficients and corresponding intercepts of 1000 groups of chlorophyll a at the 0.05 quantile.

[0101] In the second step, the above steps are performed for each quantile of 0.05, 0.10…, 0.95 to obtain the regression coefficients of 1000 groups of chlorophyll a at each quantile.

[0102] The third step is to arrange the 1000 chlorophyll a regression coefficients obtained for each quantile from small to large to obtain the 25th and 975th regression coefficients; and multiply them.

[0103] Step 4: If the multiplication result is greater than or equal to 0, and at least one of the two regression coefficients is greater than 0, the regression coefficient at this quantile can pass the significance test and the corresponding quantile is recorded.

[0104] Step 5: Repeat steps 1 to 4 for each quantile, record each quantile that can pass the significance test, and sort them to get the smallest quantile. In this example, the smallest quantile is 0.65.

[0105] Step (5) Obtain the relationship between chlorophyll a and total phosphorus corresponding to the 0.65 quantile from step (3):

[0106]

[0107] Substituting the maximum limit of chlorophyll a obtained in step (2), 15.59 μg / L, into the above formula, we obtain the maximum limit of total phosphorus in the lake, 0.27 mg / L.

[0108] Step (6) The first step is to substitute the maximum limit of chlorophyll a, 15.59 μg / L, into the relationship between chlorophyll a and total phosphorus for 1000 groups at the 0.65 quantile in step (4) to calculate the total phosphorus value for 1000 groups.

[0109] In the second step, the 1000 groups of total phosphorus values ​​are arranged from small to large, and the corresponding values ​​of the 25th and 975th are taken out.

[0110] In the third step, the above two values ​​are compared with 0 respectively, and the larger one is taken, and the uncertainty of the maximum limit of total phosphorus in the lake is obtained as [0.013, 0.039] mg / L.

[0111] The present invention fully utilizes the statistical relationship of objective observation data and national authoritative standards, and has almost no steps of subjective human intervention. It can accurately determine the maximum limit of total phosphorus in the target lake, which is convenient for water quality management in the target area. The method has no special requirements for the data used and is easy to promote and use in determining water quality management targets for various polluted shallow lakes.

[0112] 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 method for determining the maximum limit of total phosphorus in lakes and assessing uncertainty, characterized in that: It includes the following steps: Step 1) Collect historical observation values of algal chlorophyll a and total phosphorus in the lake for which the maximum limit of total phosphorus needs to be determined; and supplement the values of the simultaneously collected algal samples and their chlorophyll a; Step 2) Measure the content of algal toxins in the lake and obtain the relationship between them and chlorophyll a to determine the limit value of chlorophyll a; Step 3) Take the historical observation values of total phosphorus as the dependent variable and the historical observation values of chlorophyll a as the independent variable to establish the regression relationship between the two at different quantiles; Step 4) Calculate the 95% confidence interval of the regression coefficients at different quantiles and determine the minimum quantile at which the regression coefficients can pass the significance test; Step 5) Select the regression relationship corresponding to the quantile obtained in Step 4) to obtain the maximum limit value of total phosphorus in the lake; Step 6) Determine the uncertainty of the maximum limit value of total phosphorus in the lake.

2. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 1, characterized in that: Step 1) Specifically includes the following steps: Step 1-1) Collect n groups of historical total phosphorus (TP) observations for lakes for which the maximum TP limit is to be determined, denoted as TP i ; and the chlorophyll a (Chla) obtained by simultaneous monitoring, the observed value is recorded as Chla i ; Where n is an integer greater than 500, i=1,2,3…n; Step 1-2) Take additional samples from the lake to determine the concentration of algal toxins in group m algae samples S and the corresponding chlorophyll a value Chla s ; Wherein, m is an integer greater than 10, and s=1,2,3…m.

3. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 2, characterized in that: The said Step 2) Specifically includes the following steps: Step 2-1) Take the algal toxin concentration TOX measured by m groups of supplementary sampling as the independent variable and the corresponding chlorophyll a value Chla as the dependent variable, and establish the linear regression relationship between the two by the least squares method: ； where d is the regression coefficient of the algal toxin concentration and e is the intercept of the regression equation Step 2-2) Substitute the maximum algae toxin content of 1 μg / L specified in the drinking water hygiene standard into the above regression relationship to obtain the corresponding maximum limit value of chlorophyll a, Chla max .

4. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 3, characterized in that: The said Step 3) Specifically includes the following steps: Step 3-1) Select a quantile p, 0 < p < 1, take all the historical observation values TP of total phosphorus as the dependent variable and all the historical observation values Chla of chlorophyll a as the independent variable to establish the regression relationship between the two at the p quantile: ； in, is the regression coefficient corresponding to the p-quantile regression relationship, is the intercept corresponding to the p-quantile regression relationship; , It can be obtained by minimizing the following formula: ； Step 3-2) In Step 3-1), p takes 0.05 as the initial value and step size, and repeats until p = 0.

95.

5. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 4, characterized in that: The said Step 4) Specifically includes the following steps: Step 4-1) From n groups of total phosphorus and chlorophyll a observation values, draw 100 groups of observation data with replacement to form a subset of observation values, and based on the observation values in this subset, repeat Step 3); Step 4-2) For each fixed p, repeat step a 1000 times to obtain 1000 sets of and ; Step 4-3) For each specified p, the 1000 Arrange from small to large and determine its 25th value and the 975th value ; Step 4-4) Calculate If the value of is greater than 0, and at least one of the values ​​is greater than 0, then the regression coefficient can pass the significance test at the p quantile; otherwise, the regression coefficient cannot pass the significance test at the p quantile; Step 4-5) Determine the regression coefficients The smallest p that can pass the significance test min .

6. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 5, characterized in that: The said Step 5) Specifically includes the following steps: Step 5-1) Determine p from the results obtained in step 3) min The corresponding quantile regression relationship is: ； Step 5-2) Substitute the maximum limit value of chlorophyll a obtained in step 2) into max Substitute Chla into the above relationship to obtain the corresponding total phosphorus value, recorded as TP v ; Step 5-3) The maximum limit of total phosphorus in the lake TP max Calculated by the following formula: 。 7. A method for determining the maximum limit of total phosphorus in a lake and assessing uncertainty according to claim 6, characterized in that: The said Step 6) Specifically includes the following steps: Step 6-1) for step 4) min The corresponding 1000 groups and , repeatedly calculate the following formula to obtain the corresponding 1000 sets of TPd (d=1,2,…,1000): ； Step 6-2) Arrange the 1000 groups of TPd from smallest to largest and determine their 25th value and the 975th value ; Step 6-3) The lower limit of the maximum limit of total phosphorus in the lake TP d,min yes: ； Step 6-4) Maximum limit of total phosphorus TP for the lake d,max The upper bound of is: ； Step 6-5) Determine the uncertainty TP of the maximum limit of total phosphorus in the lake u for: 。

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