CN111611722A - Prediction method and system for underground water pressure in tidal region - Google Patents

Prediction method and system for underground water pressure in tidal region Download PDF

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CN111611722A
CN111611722A CN202010478855.0A CN202010478855A CN111611722A CN 111611722 A CN111611722 A CN 111611722A CN 202010478855 A CN202010478855 A CN 202010478855A CN 111611722 A CN111611722 A CN 111611722A
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苏燕
杨鹭茜
翁锴亮
黄蓝青
吴泽鹏
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Abstract

The invention relates to a method and a system for predicting underground water pressure in a tidal region, wherein the method comprises the following steps:S1: establishing a tide response underground water control equation based on a water-bearing stratum system of a tidal area, deducing a complete base of the control equation and meeting an approximate solution of the control equation;S2: establishing an underground water model of the tidal region by adopting a space-time coordinate system, and respectively dispersing a space coordinate axis and a time coordinate axis;S3: respectively enabling discrete time boundary points and space boundary points to meet given boundary values and initial values, respectively substituting the boundary values and the initial values into approximate solutions of a control equation, establishing a linear equation set and expressing the linear equation set as a matrix operation form;S4: solving the undetermined coefficient;S5: substituting any point in the space-time coordinate system into the approximate solution to calculate the water head value of any point in the tidal region, and realizing the aimAnd (4) predicting the underground water pressure in the tidal region. The method and the system are beneficial to quickly, efficiently and accurately predicting the underground water pressure of the tidal region.

Description

Prediction method and system for underground water pressure in tidal region
Technical Field
The invention belongs to the technical field of underground water pressure sensing, and particularly relates to an underground water pressure prediction method and system for a tidal region.
Background
The water resource is the foundation of human survival and development, and is a light energy center, is closely related to the balance and stability of an ecosystem, and has immeasurable significance to social sustainable development while ensuring the continuation of human life. The underground water is a water resource which is rarely used by human in the global water resource, is a main water supply source for domestic life, industrial production and agricultural irrigation water of China, and particularly occupies most of the underground water resource in coastal areas.
The tidal zone is an area where the fresh water and the seawater are mutually crossed, and the groundwater level in the area can generate corresponding fluctuation along with tidal fluctuation due to the influence of geological action and tidal fluctuation all the year round, namely the groundwater tidal effect. The tidal effect of groundwater not only gradually changes the structure of the beach, but also has close relation with the water exchange and the substance transfer between aquifers and seawater. Therefore, the ecological environment of the tidal zone has a close inseparable relationship with the groundwater, and particularly has a direct relation with unreasonable exploitation of groundwater resources. With the gradual development of engineering construction, the underground water level and the water quality are changed due to imbalance of water circulation and underground water, and a plurality of environmental and geological problems such as underground water level reduction, ground subsidence, seawater invasion, underground water quality pollution and the like gradually occur in tidal regions.
Disclosure of Invention
The invention aims to provide a method and a system for predicting the underground water pressure of a tidal region, which are beneficial to rapidly, efficiently and accurately predicting the underground water pressure of the tidal region.
In order to achieve the purpose, the invention adopts the technical scheme that: a prediction method for underground water pressure in a tidal region comprises the following steps:
s1: establishing a tide response underground water control equation based on a water-bearing stratum system of a tidal region, deducing a complete Trefftz substrate of the control equation and meeting an approximate solution of the control equation;
s2: establishing a model of groundwater in the tidal region by adopting a space-time coordinate system, and respectively dispersing a space coordinate axis and a time coordinate axis into n1Dot, n2Point;
s3: respectively enabling discrete time boundary points and space boundary points to meet given boundary values and initial values, respectively substituting the boundary values and the initial values into approximate solutions of a control equation, and establishing a linear equation set which is expressed in a matrix operation form of A lambda being B;
s4: solving the undetermined coefficient lambda;
s5: substituting any point in space-time coordinate system into approximate solution, and calculating water head value h (x) of any point in the moisture-sensitive area from BETA ═ Α λi,tj) And the prediction of the underground water pressure of the tidal region is realized.
Further, in step S1, the aquifer system of the tidal zone includes a free aquifer and an overflow aquifer, and assuming that the free aquifer of the tidal zone is not affected by tidal fluctuation, the groundwater level is the same as the average sea level, and the average sea level is used as the reference surface of the aquifer system, the tidal response groundwater control equation corresponding to the aquifer system is as follows:
Figure BDA0002516658990000021
wherein x is the offshore distance, T is the predicted time, h is the total water pressure of the groundwater, T is the water guide coefficient, L is the cross-flow coefficient, S is the water storage coefficient, LnDistance off shore, tmaxThe final duration.
Further, in step S1, a set of complete Trefftz basis functions satisfying the tidal response groundwater control equation is derived by a separation variance method, and an approximate solution of the control equation is represented by a linear superposition combination of the basis functions.
Further, in the space-time coordinate system of step S2, time is defined as an independent variable based on the space-time coordinate system, the space-time coordinate system is used to process the transient modeling of the groundwater in the tidal region, and the two-dimensional coordinate system of the established model of the groundwater in the tidal region includes one dimension in time and one dimension in space.
Further, in step S3, the matrix a is an aa × bb matrix formed by Trefftz substrate, the matrix B is a matrix formed by boundary values and initial values and having a scale of aa × 1, and the coefficient λ to be determined is a matrix having a scale of bb × 1, where aa is n1+2n2And bb is 4(w +1), and w is the order of approximate solution of the control equation.
Further, in the step S4, the undetermined coefficient λ is solved by Matlab left division to increase the solving speed.
The invention also provides a prediction system for the groundwater pressure in the tidal region, which comprises a memory and a processor, wherein the memory is stored with a computer program, and the processor can realize the steps of the method when running the computer program.
Compared with the prior art, the invention has the following beneficial effects: the method and the system can realize rapid, efficient and accurate prediction of the groundwater pressure of the tidal zone, further can further understand and analyze the water pressure distribution and evolution law of the groundwater of the tidal zone affected by tidal fluctuation, and provide a basis for reasonably deploying related strategies for sustainable coastal development.
Drawings
Fig. 1 is a flowchart of a method implementation of an embodiment of the invention.
FIG. 2 is a schematic diagram of a space-time distribution point in an embodiment of the present invention.
FIG. 3 is a measured fluctuation curve of tidal water level and groundwater level in an embodiment of the present invention.
FIG. 4 is a comparison of measured and predicted groundwater level fluctuations of the present invention in an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
Referring to fig. 1, the method for predicting the underground water pressure in the tidal region, provided by the invention, comprises the following steps:
s1: based on the aquifer system in the tidal region, a tidal response underground water control equation is established, a complete Trefftz substrate of the control equation is deduced, and an approximate solution meeting the control equation is obtained.
S2: establishing a model of groundwater in the tidal region by adopting a space-time coordinate system, and respectively dispersing a space coordinate axis and a time coordinate axis into n1Dot, n2And (4) points.
S3: the discrete time boundary point and the discrete space boundary point respectively satisfy a given boundary value and an initial value, the boundary value and the initial value are respectively substituted into the approximate solution expression of the control equation, and a linear equation set is established and expressed as a matrix operation form of A lambda being equal to B.
S4: and solving the undetermined coefficient lambda.
S5: substituting any point in space-time coordinate system into approximate solution, and calculating water head value h (x) of any point in the moisture-sensitive area from BETA ═ Α λi,tj) And the prediction of the underground water pressure of the tidal region is realized.
The related contents of the present invention will be further explained below by taking taiwan xingdahong as an example. Fig. 3 is a graph showing measured fluctuations of the tidal level and the groundwater level in this embodiment.
In step S1, the aquifer system of the tidal zone includes a free aquifer and an overflow aquifer, and assuming that the free aquifer of the tidal zone is not affected by tidal fluctuation, the groundwater level is the same as the water level of the average sea level, and the average sea level is used as the reference surface of the aquifer system, the tidal response groundwater control equation corresponding to the aquifer system is as follows:
Figure BDA0002516658990000031
wherein x isOffshore distance, T is predicted time, h is total groundwater pressure, T is water guide coefficient, L is cross-flow coefficient, S is water storage coefficient, LnDistance off shore, tmaxThe final duration.
A group of complete Trefftz basis functions which meet the tidal response underground water control equation is deduced by a separation variable method:
Figure BDA0002516658990000032
the approximate solution to the governing equation is then represented by a linear superposition combination of basis functions:
Figure BDA0002516658990000041
wherein A is01,B01,A02,B02,A1p,B1p,A2p,B2pW is an order of an approximate solution of the control equation, and in the embodiment, w is 15.
In the space-time coordinate system of step S2, time is defined as an independent variable based on the space-time coordinate system, the space-time coordinate system is used to process the transient modeling of the groundwater in the tidal region, and the two-dimensional coordinate system of the established model of the groundwater in the tidal region includes one dimension in time and one dimension in space. Analog duration tmax30h, the farthest distance L from the bankn3000 m. Discretizing spatial boundaries to n1Point, time boundary discrete n2A point where n1＝601，n231. FIG. 2 is a schematic diagram of the space-time distribution point in the present embodiment.
In step S3, the tide boundary at the sea-land boundary is made to satisfy the tide level data h actually measured by the tidal level station of the perpetual motion1(x,t)|x＝0According to the fact that the initial underground water level of the aquifer is consistent with the average sea level, so as to
Figure BDA0002516658990000042
As an initial boundary, a location sufficiently far from the coastline is considered to be the groundwater level as opposed to the sea levelEtc. of
Figure BDA0002516658990000043
As an inland boundary.
The approximate solution for meeting the tidal boundary conditions is expressed as follows:
Figure BDA0002516658990000044
where i is 1 and t is 1,2, …, 31.
The approximate solution satisfying the initial boundary conditions is expressed as follows:
Figure BDA0002516658990000045
where i is 1,2, …, 601, j is 1.
The approximate solution that satisfies the inland boundary condition is expressed as follows:
Figure BDA0002516658990000051
where i is 601, j is 1,2, …, 31.
A linear system of equations is established and expressed as a matrix operation of a λ ═ B, as shown in the following equation:
Figure BDA0002516658990000052
wherein, the matrix A is a matrix with the scale of aa × bb (663 × 64 in the embodiment) formed by Trefftz substrate, the matrix B is a matrix with the scale of aa × 1 (663 × 1 in the embodiment) formed by boundary values and initial values, and the coefficient to be determined lambda is a matrix with the scale of bb × 1 (64 × 1 in the embodiment), wherein, aa is n1+2n2，bb＝4(w+1)。
In step S4, the undetermined coefficient λ is solved by Matlab left division to increase the solving speed.
In the traditional Matlab operation, the right division in the matrix operation form needs to calculate the inverse of the matrix first and then multiply, while the left division does not need to calculate the inverse matrix, can directly carry out the division, and can also avoid the singularity of the matrix, when the calculation dimensionality reaches the ten thousand dimensionalities, the operation speed of 'A \ B' is much faster than that of 'inv (A) × B'.
In step S5, the solution obtained above is substituted into an arbitrary point in the taiwan estuary site area, and the head value h (x) at the arbitrary point can be calculated from β ═ Α λi,tj)：
Figure BDA0002516658990000053
Where i is 1,2, …, 601, j is 1,2, …, 31.
Therefore, the prediction of the underground water pressure of the tidal region is realized. FIG. 4 is a comparison of measured and predicted groundwater level fluctuations of the present invention in this example.
The invention also provides a prediction system for the groundwater pressure in the tidal area for implementing the prediction method, which comprises a memory and a processor, wherein the memory is stored with a computer program, and the processor can realize the steps of the method when running the computer program.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.

Claims (7)

1. A prediction method for underground water pressure in a tidal region is characterized by comprising the following steps:
s1: establishing a tide response underground water control equation based on a water-bearing stratum system of a tidal region, deducing a complete Trefftz substrate of the control equation and meeting an approximate solution of the control equation;
s2: establishing a model of groundwater in the tidal region by adopting a space-time coordinate system, and respectively dispersing a space coordinate axis and a time coordinate axis into n1Dot, n2Point;
s3: respectively enabling discrete time boundary points and space boundary points to meet given boundary values and initial values, respectively substituting the boundary values and the initial values into approximate solutions of a control equation, and establishing a linear equation set which is expressed in a matrix operation form of A lambda being B;
s4: solving the undetermined coefficient lambda;
s5: substituting any point in space-time coordinate system into approximate solution, and calculating water head value h (x) of any point in the moisture-sensitive area from BETA ═ Α λi,tj) And the prediction of the underground water pressure of the tidal region is realized.
2. The method for predicting groundwater pressure in a tidal area according to claim 1, wherein in step S1, the aquifer system of the tidal area comprises a free aquifer and an overflow aquifer, and assuming that the free aquifer of the tidal area is not affected by tidal fluctuation, the groundwater level is the same as the average sea level, and the average sea level is used as a reference surface of the aquifer system, the tidal response groundwater control equation corresponding to the aquifer system is as follows:
Figure FDA0002516658980000011
wherein x is the offshore distance, T is the predicted time, h is the total water pressure of the groundwater, T is the water guide coefficient, L is the cross-flow coefficient, S is the water storage coefficient, LnDistance off shore, tmaxThe final duration.
3. The method for predicting groundwater pressure in a tidal area according to claim 1, wherein in step S1, a set of complete Trefftz basis functions satisfying a tidal response groundwater control equation is derived by a separation variance method, and an approximate solution of the control equation is expressed by a linear superposition combination of the basis functions.
4. The method for predicting groundwater pressure in a tidal area according to claim 1, wherein the spatio-temporal coordinate system of step S2 defines time as an independent variable based on the spatio-temporal coordinate system, and the spatio-temporal coordinate system is used to process the transient modeling of the groundwater in the tidal area, and the two-dimensional coordinate system of the established model of the groundwater in the tidal area comprises one dimension in time and one dimension in space.
5. The method of predicting groundwater pressure in a tidal area as claimed in claim 1, wherein in step S3, the matrix a is an aa × bb matrix formed by Trefftz substrate, the matrix B is an aa × 1 matrix formed by boundary values and initial values, and the coefficient λ is a bb × 1 matrix, where aa ═ n is1+2n2And bb is 4(w +1), and w is the order of approximate solution of the control equation.
6. The method for predicting the groundwater pressure in the tidal area according to claim 1, wherein in the step S4, the undetermined coefficient λ is solved by Matlab left division to increase the solving speed.
7. A tidal zone groundwater pressure prediction system comprising a memory having a computer program stored thereon and a processor capable of implementing the method steps of any of claims 1-6 when the computer program is run.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105181895A (en) * 2015-09-01 2015-12-23 中国地质大学（北京） Method for determining aquifer parameter by using coastal zone multiple observation hole tidal effect underground water level information
KR101793216B1 (en) * 2017-09-05 2017-11-03 한국지질자원연구원 Method for displaying pollutant concentration in ground water due to tidal fluctuation in coastal area

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105181895A (en) * 2015-09-01 2015-12-23 中国地质大学（北京） Method for determining aquifer parameter by using coastal zone multiple observation hole tidal effect underground water level information
KR101793216B1 (en) * 2017-09-05 2017-11-03 한국지질자원연구원 Method for displaying pollutant concentration in ground water due to tidal fluctuation in coastal area

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
CHENG-YU KU 等: "Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the SpacetimeCollocation Approach", 《APPLIED SCIENCES-BASEL》 *

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