CN113158428B - Method for determining river water quality transition zone length based on shape control inverse problem - Google Patents
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Abstract
The invention discloses a method for determining the length of a river water quality transition area based on a shape control inverse problem, which comprises the following steps of: carrying out hydrological frequency analysis to judge whether the river water flow is constant uniform flow or non-constant uniform flow; calculating to obtain the length of the water quality transition area; judging the flow direction of water flow, if the water flow is unidirectional flow, converting the problem determined by the length L of the water quality transition area into a shape inverse problem, establishing a water quality transition area length inversion model based on the shape inverse problem, and determining the length of the water quality transition area; if the water flow is a bidirectional tidal river, turning to the next step; the following steps are adopted to calculate the length of the water quality transition area of the bidirectional tidal river. The method provides key technical support and scientific basis for dividing the water area range of the secondary protection area of the river-type water source area, and can be popularized and applied to planning, designing, researching and managing works such as water source area protection, water function zoning, water environment comprehensive treatment, water safety pattern optimization, effective protection and reasonable utilization of water resources and the like.
Description
Technical Field
The invention belongs to the technical field of water environment planning and management, relates to a river drinking water source protection area range division technology, and particularly relates to a method for determining the length of a river water quality transition area based on a shape control inverse problem.
Background
The safety problem of drinking water sources is a big matter which is related to the health and life safety of people, the social stability and the livelihood of people. The water source protection area setting is a surface water source planning and management technology which is applied more at home and abroad at present. The drinking water source protection area can be divided into an earth surface water source protection area and an underground water source protection area according to the water body characteristics, the earth surface water source protection area can be divided into a reservoir water source protection area, a lake water source protection area and a river water source protection area, and the division mode and experience are mostly obtained from the underground water source protection area. Since the foreign drinking water source mainly comprises underground water, the division research of the underground water source protection area is relatively sufficient, but the surface water source in China has a large proportion, and particularly in plain areas, the surface water source is the main water supply source. Because the division research results of the surface water source protection area are relatively few, and foreign experience which can be referred is relatively lacking, the division of the surface water source protection area in China has the characteristics of random division and poor scientificity at present, most of the surface water source protection areas are not subjected to scientific calculation, and the function of the protection area cannot be fully exerted. Therefore, the national environmental protection agency promulgates technical specifications for division of drinking water source protection areas (hereinafter referred to as specifications) in 2007, and unifies basic methods for division of surface water drinking water source protection areas and underground water drinking water source protection areas. According to the "norm", the river-type protection zone is provided with three types of protection zones with different requirements, namely, a primary protection zone, a secondary protection zone and a quasi-protection zone, as shown in fig. 1. The range of the primary protection area is specified clearly, the quasi-protection area is set as required, the range determination method can refer to the division method of the secondary protection area, and meanwhile, the width of the protection area is specified clearly in the 'standard', so that the length of the water area of the secondary protection area is not specified clearly, and related division technologies need to be developed. The main bases for determining the water area length of the secondary protection area of the river-type water source are as follows:
(1) the water quality in the water area length range meets the requirements of GB3838-2002 III water quality standards, and the water quality flowing into the primary protection area is ensured not to be lower than the requirements of the primary protection area water quality standards;
(2) the distance from the upstream boundary of the secondary protection area to the upstream boundary of the primary protection area is larger than the distance required by the pollutants to be attenuated from the GB3838-2002 class III water quality standard concentration level to the class II water quality standard concentration.
(3) In general river water source, the length of the secondary protection area extends from the upstream boundary of the primary protection area to the upstream side and is not less than 2000m, and the downstream side outer boundary is not less than 200m from the boundary of the primary protection area.
Therefore, the division of the secondary protection area is carried out, the distance required for the transition from the type III water quality to the type II water quality is firstly determined, the distance is not called the length of the water quality transition area, and the water quality flowing into the primary protection area is ensured not to be lower than the type II water quality. Theoretically, the larger the scope of the protection area is, the more obvious the protection effect on the water source area is, but the local government wants to define the protection area as small as possible due to the restriction of land use, economic development and other factors. The actual defined protective area range is therefore often based on a minimum range which meets the water quality transition requirements. The calculation of the distance of the water quality transition area is the basic work for determining the range of the water source secondary protection area and is an important basis for determining the length of the water source secondary protection area. For a unidirectional river, the downstream water quality does not affect the upstream water quality, the length of the secondary protection area is mainly determined by the length of the secondary protection area I, namely the distance from the upstream side boundary of the secondary protection area to the upstream boundary of the primary protection area, so that the length of the water quality transition area at the upstream of the primary protection area of the water intake port only needs to be calculated. For tidal rivers, because the water flow is bidirectional, the lengths of the water quality transition areas upstream and downstream of the primary protection area need to be determined respectively, and fig. 2 is referred to. Therefore, a corresponding water quality transition region length determination method needs to be provided according to the difference of river hydrological characteristics.
The water source protection area setting is a surface water source planning and management technology which is applied more at home and abroad at present. The river type water source is a main water supply source type in plain areas of China, and although technical requirements that the distance from the upstream side boundary of the secondary protection area to the upstream boundary of the primary protection area is larger than the distance required by the pollutants to be attenuated from GB 3838-. The reason is mainly that the actual river flow conditions are complex, the length of the water quality transition area is difficult to determine, and an effective technical method is lacked.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the problems of strong subjectivity and insufficient scientificity in the range division of the secondary protection area of the existing water source area in the prior art, the method for determining the length of the river water quality transition area based on the shape control inverse problem is provided, can provide key technical support and scientific basis for the division of the water area range of the secondary protection area of the river flow type water source area, and can be popularized and applied to planning, designing, researching and managing work such as water source area protection, water function division, water environment comprehensive treatment, water safety pattern optimization, effective protection and reasonable utilization of water resources and the like.
The technical scheme is as follows: in order to achieve the aim, the invention provides a method for determining the length of a river water quality transition area based on a shape control inverse problem, which comprises the following steps:
s1: collecting hydrological data of the river length series, carrying out hydrological frequency analysis, judging whether the river water flow is constant uniform flow or non-constant uniform flow, if the river water flow is constant uniform flow, switching to a step S2, and if the river water flow is non-constant uniform flow, switching to a step S3;
s2: the length of the water quality transition area is calculated by adopting the following formula:
in the formula, CIIIIs a standard value of class III water quality, CIIIs a standard value of class II water quality, u is the river flow rate, K1Is the pollutant degradation coefficient;
s3: judging the flow direction of water flow, if the water flow is unidirectional flow, converting the problem determined by the length L of the water quality transition area into a shape inverse problem, establishing a water quality transition area length inversion model based on the shape inverse problem, and determining the length of the water quality transition area; if the water flow is a bidirectional tidal river, the process goes to step S4;
s4: the length of the water quality transition area of the bidirectional tidal river is calculated by the following steps:
a1: selecting a design hydrological condition;
a2: according to the selected design hydrological conditions, a tidal river flow model is applied to simulate and calculate the average maximum flow velocity of the boundary section of the transition region of the rising current and the falling current;
a3: calculating the initial length L of the water quality transition area I by using the formula of the step S2 according to the average maximum flow velocity of the boundary section of the falling current transition areaI0(ii) a According to the tidal current transition regionCalculating the initial length L of the water quality transition zone II by using the formula of the step S2II0；
A4: according to the initial length LI0And an initial length LII0Positioning the initial ranges of the water quality transition zone I and the transition zone II;
a5: respectively calculating the length L of the water quality transition region I by adopting a water quality transition region length inversion model based on the inverse shape problem according to the initial ranges of the water quality transition region I and the transition region III(t) and length L of water quality transition zone IIII(t)；
A6: summary LI(t) and LII(t), at the time of falling tide LII(t) 0, tidal range LIAnd (t) is 0, namely the dynamic change process of the length of the water transition zone under the designed hydrological condition is obtained.
Further, if the water flow is a unidirectional flow in step S3, the method for determining the length of the water quality transition area includes:
b1: the water quality transition area range is set as [ a, b ], and the problem of determining the pollutant distribution in the range is as follows:
the determination of the water quality transition zone range can be converted into the following inverse problem of shape: the water quality at the position where the lower boundary x ═ b of the transition zone is known to meet a certain water quality standard CdThe position of the upper boundary x ═ a is estimated. According to the principle of dividing the water source protection area in China, the farther the water intake is, the lower the water quality standard is, so that CuIs in a ratio of CdThe water quality standard of the first grade is lower. In the division of the secondary protection area of the drinking water source, the range of the water quality transition area is equivalent to the distance required for the transition from the GB3838-2002 III water quality standard concentration level to the II water quality standard concentration.
The problem of determining the length of the water quality transition area is solved as the following inverse problem:
the concentration and the position of the lower boundary and the concentration of the upper boundary are known, and the position x of the upper boundary is calculated;
for the river water quality simulation problem, the control equation is as follows:
in the formula: q is a cross-sectional flow, m3S; c is the concentration of pollutants, mg/L; a is a cross-sectional area, m2；ExIs the longitudinal dispersion coefficient, m2S; k is the comprehensive degradation coefficient, s-1(ii) a S is a pollution source item, g/m/S.
B2: converting the inverse shape problem into an optimization problem, wherein the optimization target is simulated concentration values C (x ═ b) and C at a lower boundary (x ═ b)IIThe distance is minimum;
b3: initial value x for boundary position x on given transition zone0In [ x ]0，b]Dispersing river reach in the interval, carrying out numerical value dispersion on the unsteady flow control equation by adopting a finite difference method, and establishing a river one-dimensional water quality model;
as the cross section area of the river changes along the longitudinal direction, the flow speed and the water depth also change along the way, and a numerical solution is needed to be adopted for solving the control equation. And taking the upper end position of the first-stage protection area as the lower boundary of the water quality transition area, namely the lower boundary of the river research range. Taking the point as the origin, carrying out space dispersion to the upstream to divide the river research range into L lengthsn、Ln-1、.....、L2、L1The pollutant concentration of the upper boundary section of the corresponding river reach is respectively C1、C2、......、Cn-1、Cn；Cu、CdThe water quality standard concentration of the upper boundary and the water quality standard concentration of the lower boundary of the water quality transition area are respectively set; l is the length of the water quality transition zone.
The equation is discretized in an implicit windward difference format, where each term is discretized as follows:
the discrete equation set and the boundary conditions of the upstream and the downstream can form a tri-diagonal equation set, and the solution can be realized by a catch-up method.
B4: c is to beIIIAs the incoming water concentration, C (x ═ b) was calculated by a water quality forward model, and C (x ═ b) and C were addedIIComparing and judging the objective function phi (X) to min | Cb-CIIIf the | meets the precision requirement, the step B6 is carried out, and if the | does not meet the precision requirement, the step B5 is carried out;
b5: automatically modifying an inversion variable x by adopting an optimization algorithm, dispersing the river reach by adopting a moving grid or fixed grid method, and turning to step B4 to continuously reduce the distance between the calculated value and the standard value until the requirement is met; or setting the maximum iteration step number, and terminating after the iteration step number is reached;
b6: and outputting the current inversion variable value x as the boundary position a on the transition region, wherein the difference between b and a is the length of the transition region.
Further, in the step B5, since the boundary on the transition region is unknown, the dynamic boundary problem needs to be handled, and there are two processing methods: a dynamic grid method and a fixed grid method.
The process of dispersing the river reach by the dynamic grid method comprises the following steps: when the upper boundary changes, the number of discrete river reach in the transition area is unchanged, the length of each river reach is changed, namely the space step length is changed, and space dispersion is carried out once every iteration; the process of dispersing the river reach by the grid fixing method comprises the following steps: when the upper boundary changes, the spatial dispersion of the whole river keeps unchanged, namely the spatial step size is unchanged, and the search is carried out by depending on the boundary end point.
Further, the optimization method in step B2 adopts a differential evolution algorithm. The Differential Evolution Algorithm (DEA) is a simple and effective algorithm for solving a continuous variable global optimization problem proposed by Rainer store and Kenneth Price in 1995, and is a great progress made in the algorithm aspect since the generation of the evolution algorithm. In 1996 the algorithm participated in the First ICEO evolution algorithm (First International content on evolution computer 1stICEO), which proved the fastest among all the participating algorithms. The DEA is a random search method simulating natural evolution and evolving according to probability, and has good convergence performance on many problems compared with other evolutionary algorithms.
Further, the selected method for designing the hydrological conditions in the step a1 is as follows: the hydrological change process of the upper and lower boundaries corresponding to the dry season and the big tide is used as a designed hydrological condition, namely, the probability statistical analysis is carried out according to the change rule of the tide and the characteristic high tide data of the long series, and the designed tide type change process with the set guarantee rate is provided as the designed hydrological condition for researching the river.
Further, the method for positioning the initial ranges of the water-quality transition region I and the transition region II in the step A1 comprises the following steps: taking the fixed boundary of the high-standard transition area as a base point, and drawing a length L upstreamI0The river reach is the initial range of the transition area I; the length of the downstream is defined as LII0The river reach of (1) is the initial range of the transition zone (II).
Further, the length L of the water-quality transition region I in the step A5IThe calculation method of (t) is as follows: taking the lower boundary (the upper boundary of the primary protection area of the water source area) of the transition area I as a reference, and extracting the falling current hydrological conditions; taking the initial range of the transition region I as a research range, drawing up a space step length and a time step length according to the requirement of simulation calculation precision, dividing a calculation unit grid of a research river, and calculating the length L of the water quality transition region I in the time interval by adopting a water quality transition region length inversion model based on the inverse shape problemI(t)；
Length L of water quality transition zone IIIIThe calculation method of (t) is as follows: taking the upper boundary of the transition region II (the lower boundary of the primary protection region of the water source region) as a reference, and extracting the tidal current hydrological conditions; taking the initial range of the transition region II as a research range, dividing time step length and space step length, and adopting a water quality transition region length inversion model calculation model based on the inverse shape problemAnd calculating the length of the water quality transition region I in the time period.
The inverse shape problem mainly refers to the inverse shape control problem, the positive shape control problem is to influence the characteristics of the system through the change of the boundary geometry of the region, and the inverse shape control problem is to reversely calculate the boundary shape of the region according to the system target, which is also called as the inverse geometry problem. The inverse shape problem is the most difficult of the five inverse problems because it inevitably involves a moving boundary problem. The inverse problem of one-dimensional shape is to determine the location of the end point; the inverse problem of two-dimensional and three-dimensional shapes is to determine the shape of a region curve or curved surface. In the field of environmental hydraulics, the determination of an unknown boundary of an area is a typical inverse shape problem, and the determination of the length of a water quality transition area in a secondary protection area of a drinking water source is one of the problems. Because the shape inverse problem has strong unsuitability, no one can determine the length of the water quality transition area from the angle of solving the inverse problem at present.
The invention is based on the idea of inverse problem, and the problem of determining the length of the water quality transition area in the range division of the secondary protection area of the water source area is solved as the inverse problem of environmental hydraulics shape control. The finite difference numerical value dispersion method is combined with a differential evolution algorithm, a dispersion-optimization method is adopted to solve the one-dimensional shape inverse problem, two technical means of a dynamic grid and a fixed grid are utilized to process the dynamic boundary problem, and the reliability of the method is verified through an example. The whole process of the invention can be completed by computer programming, the manual intervention is less, the invention is suitable for both steady-state water flow conditions and unsteady-state water flow conditions, is suitable for both unidirectional rivers and tidal bidirectional rivers, and provides key technical support for scientifically and reasonably determining the water area range of the secondary protection area of the river water source.
Has the advantages that: compared with the prior art, the method realizes the determination of the length of the water quality transition area by the inverse problem solving angle, and has the following advantages:
(1) aiming at constant uniform flow, non-constant unidirectional flow and non-constant bidirectional flow, the method for determining the length of the water quality transition area is correspondingly provided, the application range is wide, and the problem that the length of the water quality transition area of a river with complicated hydrodynamic conditions such as a tidal river is difficult to determine is solved;
(2) based on the idea of inverse problem, firstly solving the problem of determining the length of the water source water quality transition region as the inverse problem of environmental hydraulics shape control, combining a finite difference numerical value discrete method with a differential evolution algorithm, processing the problem of dynamic boundary by using two technical means of a dynamic grid and a fixed grid, and verifying the reliability of the method by a calculation example;
(3) according to the method flow, all processes can be completed by a computer, so that less manual intervention is performed, and the calculation precision is improved;
(4) the method not only provides key technical support and scientific basis for rationality analysis, feasibility demonstration and optimization adjustment of secondary protection area range division of the river water source area and for correctly processing coordination relationship between water source area protection and social and economic development, but also can be popularized and applied to planning, designing, researching and managing work such as water function division, water environment comprehensive regulation, water source area optimization configuration, effective protection and reasonable utilization of water resources and the like.
Drawings
FIG. 1 is a schematic diagram of a river water source protection area grading;
FIG. 2 is a schematic view of the transition region of a tidal river;
FIG. 3 is a schematic flow chart of the present invention;
fig. 4 is a schematic diagram of a river segmentation discrete study.
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
The invention provides a river water quality transition zone length determination method based on a shape control inverse problem, which comprises the following steps as shown in figure 3:
s1: collecting hydrological data of the river length series, carrying out hydrological frequency analysis, judging whether the river water flow is constant uniform flow or non-constant uniform flow, if the river water flow is constant uniform flow, then switching to step S2, and if the river water flow is non-constant uniform flow, then switching to step S3.
S2: the length of the water quality transition area is calculated by adopting the following formula:
in the formula, CIIIIs a standard value of class III water quality, CIIIs a standard value of class II water quality, u is the river flow rate, K1Is the pollutant degradation coefficient;
s3: judging the flow direction of water flow, if the water flow is unidirectional flow, converting the problem determined by the length L of the water quality transition area into a shape inverse problem, establishing a water quality transition area length inversion model based on the shape inverse problem, and determining the length of the water quality transition area; if the water flow is a bidirectional tidal river, the process goes to step S4;
s4: the length of the water quality transition area of the bidirectional tidal river is calculated by the following steps:
a1: selecting a design hydrological condition;
a2: according to the selected design hydrological conditions, a tidal river flow model is applied to simulate and calculate the average maximum flow velocity of the boundary section of the transition region of the rising current and the falling current;
a3: calculating the initial length L of the water quality transition area I by using the formula of the step S2 according to the average maximum flow velocity of the boundary section of the falling current transition areaI0(ii) a Calculating the initial length L of the water quality transition region II by using the formula of the step S2 according to the average maximum flow velocity of the boundary section of the tidal current transition regionII0；
A4: according to the initial length LI0And an initial length LII0Positioning the initial ranges of the water quality transition zone I and the transition zone II;
a5: respectively calculating the length L of the water quality transition region I by adopting a water quality transition region length inversion model based on the inverse shape problem according to the initial ranges of the water quality transition region I and the transition region III(t) and length L of water quality transition zone IIII(t)；
A6: summary LI(t) and LII(t), at the time of falling tide LII(t) 0 at tidal altitudeLIAnd (t) is 0, namely the dynamic change process of the length of the water transition zone under the designed hydrological condition is obtained.
In the step S3, if the water flow is unidirectional, the method for determining the length of the water quality transition area is as follows:
b1: the water quality transition area range is set as [ a, b ], and the problem of determining the pollutant distribution in the range is as follows:
the determination of the water quality transition zone range can be converted into the following inverse problem of shape: the water quality at the position where the lower boundary x ═ b of the transition zone is known to meet a certain water quality standard CdThe position of the upper boundary x ═ a is estimated. According to the principle of dividing the water source protection area in China, the farther the water intake is, the lower the water quality standard is, so that CuIs in a ratio of CdThe water quality standard of the first grade is lower. In the division of the secondary protection area of the drinking water source, the range of the water quality transition area is equivalent to the distance required for the transition from the GB3838-2002 III water quality standard concentration level to the II water quality standard concentration.
The problem of determining the length of the water quality transition area is solved as the following inverse problem:
the concentration and the position of the lower boundary and the concentration of the upper boundary are known, and the position x of the upper boundary is calculated;
for the river water quality simulation problem, the control equation is as follows:
in the formula: q is a cross-sectional flow, m3S; c is the concentration of pollutants, mg/L; a is a cross-sectional area, m2；ExIs the longitudinal dispersion coefficient, m2S; k is the comprehensive degradation coefficient, s-1(ii) a S is a pollution source term, g/m/s。
B2: converting the inverse shape problem into an optimization problem, wherein the optimization target of the differential evolution algorithm is simulated concentration values C (x ═ b) and C (x ═ b) at a lower boundary (x ═ b)IIThe distance is minimum;
b3: initial value x for boundary position x on given transition zone0In [ x ]0,b]Dispersing river reach in the interval, carrying out numerical value dispersion on the unsteady flow control equation by adopting a finite difference method, and establishing a river one-dimensional water quality model;
as the cross section area of the river changes along the longitudinal direction, the flow speed and the water depth also change along the way, and a numerical solution is needed to be adopted for solving the control equation. And taking the upper end position of the first-stage protection area as the lower boundary of the water quality transition area, namely the lower boundary of the river research range. Taking the point as the origin, carrying out space dispersion to the upstream to divide the river research range into L lengthsn、Ln-1、.....、L2、L1The pollutant concentration of the upper boundary section of the corresponding river reach is respectively C1、C2、......、Cn-1、Cn；Cu、CdThe water quality standard concentration of the upper boundary and the water quality standard concentration of the lower boundary of the water quality transition area are respectively set; l is the length of the water quality transition zone, as shown in fig. 4.
The equation is discretized in an implicit windward difference format, where each term is discretized as follows:
the discrete equation set and the boundary conditions of the upstream and the downstream can form a tri-diagonal equation set, and the solution can be realized by a catch-up method.
B4: c is to beIIIAs the incoming water concentration, C (x ═ b) was calculated by a water quality forward model, and C (x ═ b) and C were addedIIComparing and judging the objective function phi (X) to min | Cb-CIIIf the | meets the precision requirement, the step B6 is carried out, and if the | does not meet the precision requirement, the step B5 is carried out;
b5: automatically modifying an inversion variable x by adopting an optimization algorithm, dispersing the river reach by adopting a moving grid or fixed grid method, and turning to step B4 to continuously reduce the distance between the calculated value and the standard value until the requirement is met; or setting the maximum iteration step number, and terminating after the iteration step number is reached;
b6: and outputting the current inversion variable value x as the boundary position a on the transition region, wherein the difference between b and a is the length of the transition region.
In the step B5, since the boundary on the transition region is unknown, the problem of the dynamic boundary needs to be handled, and there are two methods: a dynamic grid method and a fixed grid method.
The process of dispersing the river reach by the dynamic grid method comprises the following steps: when the upper boundary changes, the number of discrete river reach in the transition area is unchanged, the length of each river reach is changed, namely the space step length is changed, and space dispersion is carried out once every iteration; the process of dispersing the river reach by the grid fixing method comprises the following steps: when the upper boundary changes, the spatial dispersion of the whole river keeps unchanged, namely the spatial step size is unchanged, and the search is carried out by depending on the boundary end point.
The method for selecting the hydrological conditions in the step A1 comprises the following steps: the hydrological change process of the upper and lower boundaries corresponding to the heavy tide in the dry season is used as a designed hydrological condition, namely, probability statistical analysis is carried out according to the change rule of the tide and the characteristic high tide data of the long series, and the designed tidal type change process with 90% guarantee rate is provided as the designed hydrological condition for researching the river.
The method for positioning the initial ranges of the water-quality transition region I and the transition region II in the step A1 comprises the following steps: taking the fixed boundary of the high-standard transition area as a base point, and drawing a length L upstreamI0The river reach of (1) is the initial range of the transition zone I; the length of the downstream is defined as LII0The river section of (a) is the initial range of the transition zone (II).
Length L of water-quality transition zone I in the above step A5IThe calculation method of (t) is as follows: extracting the falling current by taking the lower boundary (the upper boundary of the primary protection area of the water source area) of the transition area I as a referenceHydrologic conditions; taking the initial range of the transition region I as a research range, drawing up a space step length and a time step length according to the requirement of simulation calculation precision, dividing a calculation unit grid of a research river, and calculating the length L of the water quality transition region I in the time period by adopting a water quality transition region length inversion model based on the inverse shape problemI(t)；
Length L of water quality transition zone IIIIThe calculation method of (t) is as follows: taking the upper boundary of the transition region II (the lower boundary of the primary protection region of the water source region) as a reference, and extracting the tidal current hydrological conditions; and taking the initial range of the transition zone II as a research range, dividing time step length and space step length, and calculating and simulating the length of the water quality transition zone I in the time period by adopting a water quality transition zone length inversion model based on the inverse shape problem.
The embodiment also provides a system for determining the length of the river water quality transition area based on the shape control inverse problem, which comprises a network interface, a memory and a processor; the network interface is used for receiving and sending signals in the process of receiving and sending information with other external network elements; a memory for storing computer program instructions executable on the processor; a processor for performing the steps of the above method when executing the computer program instructions.
The invention also provides a computer storage medium storing a computer program which, when executed by a processor, is operable to carry out the method described above. The computer-readable medium may be considered tangible and non-transitory. Non-limiting examples of a non-transitory tangible computer-readable medium include a non-volatile memory circuit (e.g., a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), a volatile memory circuit (e.g., a static random access memory circuit or a dynamic random access memory circuit), a magnetic storage medium (e.g., an analog or digital tape or hard drive), and an optical storage medium (e.g., a CD, DVD, or blu-ray disc), among others. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also comprise or rely on stored data. The computer programs may include a basic input/output system (BIOS) that interacts with the hardware of the special purpose computer, a device driver that interacts with specific devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, and the like.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Based on the above scheme, the embodiment applies the method as an example, specifically as follows:
the river flow in this example is 10m3The river length is 30km, the flow velocity is distributed along the way as u is 0.1+0.0001x, and the longitudinal dispersion coefficient of the river is 50m2And s. COD is used as a control index, and the degradation coefficient is 0.3d-1And the length of a transition zone required for the water quality to transition from the class III to the class II is calculated.
The specific process is as follows:
(1) according to the hydrological characteristics of the river, the water flow is unidirectional non-uniform flow and should be calculated by the step S3.
(2) According to the environmental quality Standard of surface Water, Water quality index CIII(COD)＝20mg/l，CII(COD) 15 mg/l. And (3) solving the problem of determining the water quality transition area as an inverse shape problem, namely controlling the concentration of the downstream boundary of the river to be 15mg/l and solving the position of the upstream boundary of the transition area reversely.
(3) And establishing a river water quality forward model by using a finite difference method.
(4) The finite difference method is combined with a water quality forward model to establish an inversion model, the inversion model is utilized to solve the shape inverse problem, and the iteration process comprises two methods, namely a moving grid method and a fixed grid method.
(5) And when the distance between the calculated downstream boundary concentration value and the standard value is 15mg/l, outputting the upstream boundary position x, wherein the distance between the upstream boundary position x and the downstream boundary is the length of the transition zone.
In the embodiment, the inversion result of the water quality transition region by adopting the dynamic grid method and the fixed grid method is shown in table 1. As can be seen from the table, the calculation results of the two methods are not very different. Since the dynamic grid method needs to perform grid division once per iteration, the time consumption is high, and therefore, the fixed grid method is recommended.
TABLE 1 inversion results of water quality transition zone length
Claims (7)
1. A river water quality transition zone length determination method based on shape control inverse problem is characterized by comprising the following steps:
s1: performing hydrological frequency analysis, judging whether the river water flow is constant uniform flow or non-constant uniform flow, if the river water flow is constant uniform flow, turning to the step S2, and if the river water flow is non-constant uniform flow, turning to the step S3;
s2: the length of the water quality transition area is calculated by adopting the following formula:
in the formula, CIIIIs a standard value of class III water quality, CIIIs a standard value of class II water quality, u is the river flow rate, K1Is the pollutant degradation coefficient;
s3: judging the flow direction of water flow, if the water flow is unidirectional flow, converting the problem determined by the length L of the water quality transition area into a shape inverse problem, establishing a water quality transition area length inversion model based on the shape inverse problem, and determining the length of the water quality transition area; if the water flow is a bidirectional tidal river, the process goes to step S4;
s4: the length of the water quality transition area of the bidirectional tidal river is calculated by the following steps:
a1: selecting a design hydrological condition;
a2: according to the selected design hydrological conditions, a tidal river flow model is applied to simulate and calculate the average maximum flow velocity of the boundary section of the transition region of the rising current and the falling current;
a3: calculating the initial length L of the water quality transition area I by using the formula of the step S2 according to the average maximum flow velocity of the boundary section of the falling current transition areaI0(ii) a According to the average maximum flow velocity of the boundary section of the tidal current transition region, the method of step S2 is usedCalculating the initial length L of the water quality transition zone IIII0；
A4: according to the initial length LI0And an initial length LII0Positioning the initial ranges of the water quality transition zone I and the transition zone II;
a5: respectively calculating the length L of the water quality transition region I by adopting a water quality transition region length inversion model based on the inverse shape problem according to the initial ranges of the water quality transition region I and the transition region III(t) and length L of water quality transition zone IIII(t)；
A6: summary LI(t) and LII(t), at the time of falling tide LII(t) 0, tidal range LIAnd (t) is 0, namely the dynamic change process of the length of the water transition zone under the designed hydrological condition is obtained.
2. The method for determining the length of the water quality transition zone of a river based on the inverse problem of shape control as claimed in claim 1, wherein if the water flow is unidirectional flow in step S3, the method for determining the length of the water quality transition zone comprises:
b1: the water quality transition area range is set as [ a, b ], and the problem of determining the pollutant distribution in the range is as follows:
the problem of determining the length of the water quality transition area is solved as the following inverse problem:
the concentration and the position of the lower boundary and the concentration of the upper boundary are known, and the position x of the upper boundary is calculated;
b2: converting the inverse shape problem into an optimization problem, wherein the optimization target is a simulated concentration value C at a lower boundary x-bx＝bAnd CIIThe distance is minimum;
b3: initial value x for boundary position x on given transition zone0In [ x ]0,b]Dispersing river reach in the interval, carrying out numerical value dispersion on the unsteady flow control equation by adopting a finite difference method, and establishing a river one-dimensional water quality model;
b4: c is to beIIIAs the incoming water concentration, C is calculated by using a water quality forward modelx＝bMixing C withx＝bAnd CIIComparing and judging the objective function phi (X) to min | Cb-CHIf the | meets the precision requirement, the step B6 is carried out, and if the | does not meet the precision requirement, the step B5 is carried out;
b5: automatically modifying an inversion variable x by adopting an optimization algorithm, dispersing the river reach by adopting a moving grid or fixed grid method, and turning to step B4 to continuously reduce the distance between the calculated value and the standard value until the requirement is met; or setting the maximum iteration step number, and terminating after the iteration step number is reached;
b6: and outputting the current inversion variable value x as the boundary position a on the transition region, wherein the difference between b and a is the length of the transition region.
3. The method for determining the length of the river water quality transition area based on the shape control inverse problem as claimed in claim 2, wherein the process of discretizing the river reach by the dynamic grid method in the step B5 is as follows: when the upper boundary changes, the number of discrete river reach in the transition area is unchanged, the length of each river reach is changed, namely the space step length is changed, and space dispersion is carried out once every iteration; the process of dispersing the river reach by the grid fixing method comprises the following steps: when the upper boundary changes, the spatial dispersion of the whole river keeps unchanged, namely the spatial step size is unchanged, and the search is carried out by depending on the boundary end point.
4. The method for determining the length of the river water quality transition region based on the shape control inverse problem as claimed in claim 2, wherein the optimization method in the step B2 adopts a differential evolution algorithm.
5. The method for determining the length of the river water quality transition region based on the shape control inverse problem as claimed in claim 1, wherein the method for selecting the hydrological conditions in the step A1 is as follows: the hydrological change process of the upper and lower boundaries corresponding to the dry season and the big tide is used as a designed hydrological condition, namely, the probability statistical analysis is carried out according to the change rule of the tide and the characteristic high tide data of the long series, and the designed tide type change process with the set guarantee rate is provided as the designed hydrological condition for researching the river.
6. The method for determining the length of the river water quality transition zone based on the shape control inverse problem as claimed in claim 1, wherein the method for positioning the initial ranges of the water quality transition zone I and the transition zone II in the step A1 comprises the following steps: taking the fixed boundary of the high-standard transition area as a base point, and drawing a length L upstreamI0The river reach is the initial range of the transition area I; the length of the downstream is defined as LII0The river reach of (1) is the initial range of the transition zone (II).
7. The method for determining the length of the river water quality transition region based on the shape control inverse problem as claimed in claim 1, wherein the length L of the water quality transition region I in the step A5IThe calculation method of (t) is as follows: taking the lower boundary of the transition region I as a reference, and extracting the falling tide hydrological conditions; taking the initial range of the transition area I as a research range, drawing up a space step length and a time step length according to the requirement of simulation calculation precision, dividing a calculation unit grid of a research river, and calculating the length L of the water quality transition area I in a tide falling period by adopting a water quality transition area length inversion model based on a shape inverse problemI(t)；
Length L of water quality transition zone IIIIThe calculation method of (t) is as follows: taking the upper boundary of the transition region II as a reference, and extracting the tidal current hydrological conditions; and taking the initial range of the transition area II as a research range, dividing time step length and space step length, and calculating the length of the water quality transition area I in the flood period by adopting a water quality transition area length inversion model based on the inverse shape problem.
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