CN106295135B - Piecewise regression catastrophe point determines shallow lake water quality management goal approach - Google Patents
Piecewise regression catastrophe point determines shallow lake water quality management goal approach Download PDFInfo
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Abstract
Shallow lake water quality management goal approach is determined the invention discloses a kind of piecewise regression catastrophe point, is comprised the following steps：(1) collect it needs to be determined that the concentration Z of the shallow lake n group chlorophyll as of water quality management targeti, total phosphorus concentration XiAnd total nitrogen concentration YiValue, obtains corresponding value logZi、logXiAnd logYi；(2) total phosphorus catastrophe point is primarily determined that；(3) the accurate catastrophe point for determining total phosphorus；(4) total phosphorus concentration is replaced with total nitrogen concentration, repeat step (2) and (3) accurately determine the catastrophe point of total nitrogen；(5) shallow lake candidate's nutritive salt water quality management target is determined；(6) determine water quality required by shallow lake water body purposes and compared with candidate's nutritive salt water quality management target, finally determine specific Lakes in Nutrition salt water quality management objectives.The statistics catastrophe point showed naturally in objective observation data has been fully utilized in the present invention, accurate to determine that water grade is interval, it is easy to be promoted the use of in the determination of various polluted shallow lake water quality management targets.
Description
Technical field
Shallow lake water quality management goal approach is determined the present invention relates to piecewise regression catastrophe point, belongs to lake field.
Background technology
China's major part freshwater lake is all shallow lake and eutrophication problem is more serious, and water quality aggravates；And
Nitrogen and phosphorus are topmost nutritive salt in water body in lake, and the content of nitrogen and phosphorus is for reduction in the particularly shallow lake of control lake
Lake Eutrophication, protection water body in lake quality has conclusive effect.Formulate appropriate nitrogen and phosphorous nutrient water quality pipe
Reason target is the precondition of effective protection shallow lake quality of water environment, is had for protection shallow lake water environment very heavy
The meaning wanted.At present, the formulation of shallow lake nutritive salt water quality objective is most makes decisions by the experience of expert and leader, its
It is artificial subjective；This Lakes in Nutrition salt water quality management objectives for causing to formulate departs from the actual conditions of lake water quality often.
In fact, being unfavorable for Water Environment In Lakes protection if shallow lake water environment management target is excessively loose, shallow lake is caused to enter
One step eutrophication, water quality more deteriorates；It is not only unnecessary if management objectives are excessively strict that to may interfere with local economy again social
Development.
The content of the invention
Goal of the invention：In order to overcome the deficiencies in the prior art, it is true that the present invention provides a kind of piecewise regression catastrophe point
Determine shallow lake water quality management goal approach, the statistics catastrophe point showed naturally in objective observation data has been fully utilized, accurately
Determination water grade it is interval, it is easy to promoted the use of in the determination of various polluted shallow lake water quality management targets.
Technical scheme：In order to solve the above technical problems, a kind of piecewise regression catastrophe point of the present invention determines shallow lake water
Matter management objectives method, comprises the following steps：
(1) collect it needs to be determined that the concentration of the shallow lake n group chlorophyll as of water quality management target, total phosphorus concentration and always
Nitrogen concentration, n is the integer more than 50, Zi、XiAnd YiConcentration, total phosphorus concentration and the total nitrogen concentration of i-th group of chlorophyll a are represented respectively
Value, the concentration of unified chlorophyll a, the unit of total phosphorus concentration and total nitrogen concentration；And by the concentration of chlorophyll a, total phosphorus concentration with
And total nitrogen concentration is taken respectively from the logarithm that right logarithm e is bottom, obtains corresponding value logZi、logXiAnd logYi；
(2) the log concentration value using chlorophyll a is done nonparametric by independent variable of total phosphorus concentration logarithm value and returned as dependent variable
Return, and primarily determine that total phosphorus catastrophe point；
(3) using chlorophyll-a concentration logarithm value as dependent variable, piecewise linearity is done by independent variable of total phosphorus concentration logarithm value and is returned
Return, it is accurate to determine total phosphorus catastrophe point with the total phosphorus catastrophe point determined in step (2) as initial value is solved；
(4) total phosphorus concentration is replaced with total nitrogen concentration, repeat step (2) and (3) accurately determine the catastrophe point of total nitrogen；
(5) according to total nitrogen catastrophe point and total phosphorus catastrophe point and the socio-economic development situation of lake region and national water
Matter standard, determines shallow lake candidate's nutritive salt water quality management target；
(6) determine water quality required by shallow lake water body purposes and compared with candidate's nutritive salt water quality management target, finally
It is determined that specific Lakes in Nutrition salt water quality management objectives.
Preferably, the step (2) specifically includes following steps：
A. according to the observation data bulk n of lake total phosphorus concentration and the concentration of chlorophyll a, h=n is used-1/5Calculate optimal
Bandwidth value h；
B. 1000 numerical value uniformly are taken as independent variable logM value in the span of total phosphorus concentration logarithm value
logMp, i.e. logM1、logM2、logM3...logM1000；
C. from logM1Start calculating to obtain all meeting condition logXi≤logM1+ 3h and logXi≥logM1- 3h total phosphorus
Logarithm value logXi, the logX of condition is met to eachiAnd logM1Calculate corresponding kernel function K (logXi-logM1), as
logXiIn point logM1On weight, be unsatisfactory for condition logXi≤logM1+ 3h and logXi≥logM1- 3h logXiWeight is
0；Wherein：
D. using existing numerical method, to logM1Two groups of real number a (logM are solved successively1), b (logM1)；It is specific i.e.
Seek a (logM1), b (logM1) make following formula minimum,
E. repeat step c and d, successively by logM2、logM3...logM1000Replace logM1Calculate two groups of real number a
(logMp), b (logMp)；
F. regression equation logZ=a (logM are drawnp)+b(logMp) logM curve, wherein logZ represents regression equation
Dependent variable, logM is the independent variable of regression equation；Note again that a (logMp), b (logMp) be regression equation coefficient, be with
Independent variable logM value logMpDifferent and different two group real number, observation equation logZ=a (logMp)+b(logMp)
Turning point in logM curve, and the corresponding values of catastrophe point log γ of the variable are recorded as piecewise regression solution iteration
Initial value, if any multiple total phosphorus catastrophe points, takes the total phosphorus catastrophe point of minimum.
Preferably, the method for solving of the step (3) is to solve for four real number β0, β1, δ andMake following formula minimum, ask
The visible bibliography of solution method (Ulm, 1991)：
WhereinIt is indicative function, namely meets following formula：
Equation can be iterated to calculate with existing standard nonlinear regression solver above,The total phosphorus of as required solution
Accurate catastrophe point,The quality of iterative calculation initial value directly affects the efficiency of solution and the accuracy of result；By log γ
Substitute into equation conductIteration initial value can improve the accuracy of computational efficiency and result well.Initial value be
logγ。
Preferably, step (5) step specifically includes following steps：
A. according to the indicator of economic development of lake region, the Regional Economic Development grade, China's each department warp are determined
Ji development grade includes：
A. developed regions：Region GNP per capita exceedes 2 times of national GNP per capita, i.e. people from region
Equal gross national product substantially exceeds national GNP per capita, and people's lives are plentiful；
B. comparatively developed regions：Region GNP per capita is 1.3 times to 2 times of national GNP per capita,
I.e. region GNP per capita exceedes national GNP per capita, and people's lives are more plentiful；
C. medium area：Region GNP per capita is 0.8 to 1.3 times of national GNP per capita, i.e.,
With national GNP per capita almost, living standards of the people are medium for region GNP per capita；
D. backward areas：Region GNP per capita is less than national 0.8 times of GNP per capita, i.e. people from region
Equal gross national product is significantly less than national GNP per capita, and people's lives are poorer.
B. by the mutation point value of total nitrogen, total phosphorus and chlorophyll a and country《Water environment quality standard (GB3838-
2002)》Compare, water grade is interval where determining catastrophe point；
C. developed regions should formulate tightened up shallow lake nutritive salt management objectives, therefore on the basis of mutation point value
On, a grade is raised as the candidate of nutritive salt water quality management target；Water grade area where comparatively developed regions take catastrophe point
Between the corresponding high-grade candidate as nutritive salt water quality management target；Water grade interval is right where medium area takes catastrophe point
The inferior grade answered as nutritive salt water quality management target candidate；Backward areas are on the basis of catastrophe point, and one grade of reduction is made
For the candidate of nutritive salt water quality management target.
Preferably, step (6) step specifically includes following steps：
A. water body in lake purposes and required water quality are determined：It can be divided into conservation of nature according to national water standard water body purposes
Area, potable water source district, fishery, industrial and agriculture five major class；Be corresponding in turn in《Water environment quality standard (GB3838-
2002)》In I, II, III, IV and V class water；
B. candidate's nutritive salt water quality management target is compared with water quality required by the water body in lake purposes, finally takes two
In person water quality more strict result as specific Lakes in Nutrition salt water quality management target.
In the present invention, the research of environmentology is pointed out, leading indicator chlorophyll-a concentration and the battalion of shallow lake eutrophication
Support and there is substantial connection between salt total nitrogen, total phosphorus concentration；And there is catastrophe point in relation each other in these envirment factors.The present invention
According to view of the above, the catastrophe point in total nitrogen, total phosphorus and chlorophyll a relation is accurately determined using piecewise linear regression method；Knot
Close the specific use of national water environment quality standard, the socio-economic development situation of shallow lake region and water body in lake
On the way it is objective it is accurate determination shallow lake nutritive salt water quality management mesh calibration method.The present invention combines lake local economy social development
Level and water body in lake particular use, objective accurate determination shallow lake water quality management mesh calibration method.This method can help ring
Border administrative department determines correct objectively management objectives, and water resources in lake can be made full use of by reaching, be that socio-economic development is carried
It can effectively be protected again for necessary condition and improve lake water quality, reduce shallow lake Eutrophic Extent.
Beneficial effect：The piecewise regression catastrophe point of the present invention determines shallow lake water quality management goal approach, is fully utilized
The statistics catastrophe point and the standard of national authority showed naturally in objective observation data, almost nobody is Subjective Intervention
Step, overcomes existing method subjectivity and the stronger shortcoming of human intervention, can accurately determine the water standard of lake region,
And considered socio-economic development, water body in lake purposes factor, it is easy in various polluted shallow lake water quality management mesh
Target is promoted the use of in determining.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is total phosphorus-chlorophyll a local linear smoothing figure；
Fig. 3 is total phosphorus-chlorophyll a piecewise linear regression figure；
Fig. 4 is total nitrogen-chlorophyll a local linear smoothing figure；
Fig. 5 is total nitrogen-chlorophyll a piecewise linear regression figure.
Embodiment
The present invention is further described with east China shallow lake actual observation data below in conjunction with the accompanying drawings.
(1) according to flow chart shown in Fig. 1, the shallow lake total phosphorus, total nitrogen and leaf are obtained from document and actual measurement first green
Totally 151 groups of plain a concentration value；The unit of total nitrogen and total phosphorus concentration is mg/litre, chlorophyll-a concentration unit be generally microgram/
Rise, by the unified numerical value consistent with total nitrogen, total phosphorus concentration unit after itself divided by 1000.
(2) concentration of total phosphorus, total nitrogen and chlorophyll a is taken the logarithm value, while by n=151, substituting into h=n-1/5Managed
By optimum bandwidth h=0.366, h=0.37 is taken in this calculating.
The number of the independent variable to be calculated in the span for being set in total phosphorus logarithm value point, for the part finally shown
The tropic is relatively smooth, and this uniformly takes 1000 numerical value conducts in the span -4.6 to -0.5 of total phosphorus logarithm value
LogMp, as logM1、logM2、logM3…logM1000, for each logMpContrast the logarithm logX of total phosphorus observationi,
It is all to meet condition logXi≤logMp+ 3h and logXi≥logMp- 3h logXi, kernel function K (logX are calculated respectivelyi-
logMp), wherein：
Solve a (logMp), b (logMp) make following formula value minimum：
This is solved is completed with existing Newton tangential methods, for each logMp, meeting above formula and minimum bar
One group of a (logM is obtained under partp), b (logMp), equation logZ=a (logM are drawn as shown in Figure 2p)+b(logMp) logM song
Line, the transverse and longitudinal coordinate of this curve represent respectively have on the logarithm value of total phosphorus concentration and the logarithm value of corresponding chlorophyll a, figure compared with
Obvious multiple catastrophe points, for the purpose of protection lake environment, its aimed concn should be smaller, so total phosphorus value should be taken most
Small catastrophe point, the corresponding total phosphorus value of catastrophe point is about 0.045 mg/litre in this example, and the value of chlorophyll a is about
0.0037 mg/litre.
(3) mg/litre of total phosphorus 0.045 for trying to achieve previous step, is used as catastrophe pointThe initial value of iterationSubstitute intoIn, solve β0, β1, δ andMake this and most
Small, specific method for solving refers to Ulm, K., 1991.A statistical method for assessing a threshold
in epidemiological studies.Statistics in medicine 10,341-349；WhereinIt is indicative function, namely following formula：
Corresponding piecewise linear regression equation is：
Such as Fig. 3, in this example, the value of each parameter is finally obtained：β0=-6.12；β1=-0.32；δ=0.50；It is most important
It is that the total phosphorus catastrophe point accurately estimated is 0.061 mg/litre.
(4) as shown in Figure 4 and Figure 5, research object is changed to total nitrogen-chlorophyll a repeat step (2)-(3) and obtains total nitrogen
Catastrophe point corresponding concentration is 0.71 mg/litre.
(5) compare《Water environment quality standard (GB3838-2002)》It can be found that 0.061 milligram of total phosphorus catastrophe point/
Rise, between Group III water and IV class water quality standards；And the mg/litre of total nitrogen catastrophe point 0.71 is located at II classes water and Group III water quality standard
Between.The shallow lake is located in the Suzhou and the districts under city administration of Wuxi two of South of Jiangsu Province, and the region GNP per capita is far high
In national GNP per capita, (region GNP per capita exceedes 2 times of national GNP per capita, the people
Life is plentiful), people's lives are rich, are one of most economically developed regions of China.Therefore, raise a grade and be used as nutritive salt
Candidate's water quality management of the candidate of water quality management target, i.e. total nitrogen are targeted by I class water water standards, the water quality management mesh of total phosphorus
It is demarcated as II class water.
(6) it is agricultural and fishery water through investigating the main purposes in the lake, its corresponding water standard is Group III water；
Therefore, compared by the total nitrogen with candidate and total phosphorus water quality management target, the total nitrogen water quality management target in the final lake is I classes
Water water standard, the water quality management of total phosphorus is targeted by II class water water standards.
The statistics catastrophe point showed naturally in objective observation data and the standard of national authority has been fully utilized in the present invention,
The step of almost nobody is Subjective Intervention, overcomes existing method subjectivity and the stronger shortcoming of human intervention, can be accurate
Really set the goal the water standard in region, is easy to the water quality management of target area.This method to data used without it is any it is special will
Ask, and considered socio-economic development, water body in lake purposes factor, it is easy in various polluted shallow lake water quality managements
Promoted the use of in the determination of target.
Described above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (4)
1. a kind of piecewise regression catastrophe point determines shallow lake water quality management goal approach, it is characterised in that comprise the following steps：
(1) collect it needs to be determined that the concentration of the shallow lake n group chlorophyll as of water quality management target, total phosphorus concentration and total nitrogen are dense
Degree, n is the integer more than 50, Zi、XiAnd YiThe value of concentration, total phosphorus concentration and the total nitrogen concentration of i-th group of chlorophyll a is represented respectively,
Unify the unit of concentration, total phosphorus concentration and the total nitrogen concentration of chlorophyll a；And by the concentration of chlorophyll a, total phosphorus concentration and total nitrogen
Concentration is taken respectively from the logarithm that right logarithm e is bottom, obtains corresponding value logZi、logXiAnd logYi；
(2) the log concentration value using chlorophyll a does non parametric regression by independent variable of total phosphorus concentration logarithm value as dependent variable, and
Primarily determine that total phosphorus catastrophe point；
(3) the log concentration value using chlorophyll a does piecewise linear regression as dependent variable using total phosphorus concentration logarithm value as independent variable,
It is accurate to determine total phosphorus catastrophe point with the total phosphorus concentration catastrophe point determined in step (2) as initial value is solved；
(4) total phosphorus concentration is replaced with total nitrogen concentration, repeat step (2) and (3) accurately determine the catastrophe point of total nitrogen；
(5) according to total nitrogen catastrophe point and total phosphorus catastrophe point and the socio-economic development situation of lake region and national water quality mark
Standard, determines shallow lake candidate's nutritive salt water quality management target；
(6) determine water quality required by shallow lake water body purposes and compared with candidate's nutritive salt water quality management target, it is final to determine
Specific Lakes in Nutrition salt water quality management objectives；
The step (2) specifically includes following steps：
A. according to the observation data bulk n of lake total phosphorus concentration and the concentration of chlorophyll a, h=n is used-1/5Calculate optimum bandwidth value
h；
B. 1000 numerical value uniformly are taken as independent variable logM value logM in the span of total phosphorus concentration logarithm valuep, i.e.,
logM1、logM2、logM3...logM1000；
C. from logM1Start calculating to obtain all meeting condition logXi≤logM1+ 3h and logXi≥logM1- 3h total phosphorus logarithm
Value logXi, the logX of condition is met to eachiAnd logM1Calculate corresponding kernel function K (logXi-logM1), it is used as logXi
In point logM1On weight, be unsatisfactory for condition logXi≤logM1+ 3h and logXi≥logM1- 3h logXiWeight is 0；Its
In：
D. using existing numerical method, to logM1Two groups of real number a (logM are solved successively1), b (logM1)；It is specific to require a
(logM1), b (logM1) make following formula minimum,
E. repeat step c and d, successively by logM2、logM3...logM1000Replace logM1Calculate two groups of real number a (logMp), b
(logMp)；
F. regression equation logZ=a (logM are drawnp)+b(logMp) logM curve, wherein logZ represent regression equation because become
Amount, logM is the independent variable of regression equation；Note again that a (logMp), b (logMp) be regression equation coefficient, be with from become
Measure logM value logMpDifferent and different two group real number, observation equation logZ=a (logMp)+b(logMp) logM
Turning point in curve, and record the initial value that the corresponding values of catastrophe point log γ of the variable solve iteration as piecewise regression,
If any multiple total phosphorus catastrophe points, the total phosphorus concentration catastrophe point of minimum is taken.
2. piecewise regression catastrophe point determines shallow lake water quality management goal approach according to claim 1, it is characterised in that：
The method for solving of the step (3) is to solve for four real number β0, β1, δ andMake following formula minimum,
WhereinIt is indicative function, namely meets following formula：
β0, β1, δ initial value is 0,Initial value be log γ.
3. piecewise regression catastrophe point determines shallow lake water quality management goal approach according to claim 1, it is characterised in that：
The step (5) specifically includes following steps：
A. according to the indicator of economic development of lake region, the Regional Economic Development grade, China's Regional Economic hair are determined
Exhibition grade includes：
A. developed regions：Region GNP per capita exceedes 2 times of national GNP per capita, and people's lives are rich
Foot；
B. comparatively developed regions：Region GNP per capita is 1.3 to 2 times of national GNP per capita, people's people's livelihood
Work is more plentiful；
C. medium area：Region GNP per capita is 0.8 to 1.3 times of national GNP per capita, people's people's livelihood
Running water is put down medium；
D. backward areas：Region GNP per capita is less than national 0.8 times of GNP per capita, and people's lives are leaner
It is tired.
B. by the mutation point value of total nitrogen, total phosphorus and chlorophyll a and country《Water environment quality standard (GB3838-2002)》Than
Compared with water grade is interval where determining catastrophe point；
C. developed regions should formulate tightened up shallow lake nutritive salt management objectives, and one grade of rise is used as nutritive salt water quality
The candidate of management objectives；Water grade where comparatively developed regions take catastrophe point is interval corresponding high-grade as nutritive salt water quality pipe
Manage the candidate of target；The interval corresponding inferior grade of water grade where medium area takes catastrophe point is as nutritive salt water quality management mesh
Target candidate；Backward areas reduce a grade as the candidate of nutritive salt water quality management target on the basis of catastrophe point.
4. piecewise regression catastrophe point determines shallow lake water quality management goal approach according to claim 1, it is characterised in that：
The step (6) specifically includes following steps：
A. water body in lake purposes and required water quality are determined：According to national water standard water body purposes can be divided into nature reserve area,
Potable water source district, fishery, industrial and agriculture five major class；Be corresponding in turn in《Water environment quality standard (GB3838-2002)》
In I, II, III, IV and V class water；
B. candidate's nutritive salt water quality management target is compared with water quality required by the water body in lake purposes, finally taken in both
Water quality more strict result as specific Lakes in Nutrition salt water quality management target.
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| CN108492042B (en) * | 2018-03-29 | 2022-04-08 | 河海大学 | Method for determining acceptable range and accessibility risk of lake water quality management target |
| CN109346134B (en) * | 2018-11-09 | 2022-05-10 | 扬州大学 | Determination method for key control variable and target value of black and odorous water body |
| CN117347327B (en) * | 2022-11-22 | 2024-10-01 | 中国环境科学研究院 | System and method for evaluating shallow lake steady state by utilizing chlorophyll a and submerged plants |
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