CN109614762B - Flood routing simulation method for plain river network area - Google Patents
Flood routing simulation method for plain river network area Download PDFInfo
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Abstract
The invention discloses a flood routing simulation method for plain river network areas, which belongs to the field of flood routing simulation and comprises the following steps: firstly, editing a river network structure of a research area and automatically numbering by adopting a GIS software program; then generalizing the external boundary by adopting a special node, and processing by using a special node equation; constructing a distributed reservoir group regulation and storage model; finally, the river network calculation adopts a set of unified river channel catch-up coefficients, a ternary set table is adopted to store non-zero elements of the coefficient matrix, and a node equation set is solved by a relaxation iteration method, so that the automatic numbering of river network elements and the automatic identification of the connection relationship between nodes and the river channel can be realized, and a large amount of manual work is saved; the boundary is processed on the node, so that the calculation flow is greatly simplified; the distributed reservoir group regulation model can reflect the regulation and storage capacity of the plain more truly; the node equation set adopts a ternary set table to store non-zero elements, and the calculation speed can be greatly improved without additional identification work.
Description
Technical Field
The invention relates to a flood routing simulation method, in particular to a flood routing simulation method for plain river network areas, and belongs to the field of flood routing simulation.
Background
At present, a flood routing simulation method for plain river network areas mostly adopts a non-constant flow river network calculation method, namely, a saint-wien equation set is subjected to differential dispersion, and then computer programming is adopted for solving. For example, the MIKE 11 model of the Danish DHI company and the HOHY2 model of the national river-sea university are widely applied to flood simulation work in most coastal areas in China. However, regarding the numerical simulation of the plain river network, the currently popular flood evolution simulation method has the following disadvantages in use:
1. slow calculation speed and poor precision
Take MIKE 11 from DHI, denmark as an example. MIKE 11 adopts Abbott six-point center format difference, and the calculation nodes on the river channel are alternately arranged according to the sequence of water level-flow-water level, that is, the water level nodes and the flow nodes are not on the same section, so that the arranged section positions only have water level results, no flow results, and the flow results need to be obtained by flow interpolation of upper and lower nodes, which is very inconvenient for users to use. Since the Abbott format needs to keep a small calculation step size to converge, when Δ T is large, the convergence speed is slow because the relative error ratio is large. The Abbott format, the Preissmann format and the Koran format were compared by Zheng national building et al of Guangdong provincial academy of Water, and the results showed that: in the Abbott format calculation process, the oscillation is large, the convergence is slow, and the calculation accuracy is poor under the same time step length.
2. The river network structure and the numbering are complex
The HOHY2 model of the river and sea university adopts a three-level river network solution, so that the calculation efficiency is greatly improved. But its generalization and numbering of the river network remains complex: firstly, an HOHY2 model divides an outer river channel and an inner river channel, the outer river channel (the river channel connected with a boundary) adopts a set of catch-up coefficients, the inner river channel (the river channel not connected with the boundary) adopts a set of catch-up coefficients, and the complexity of a river network structure and calculation is artificially increased for the processing of the boundary; secondly, the connection relation among the river channel node numbers, the section numbers and the river channels still needs manual numbering, the connection relation is identified manually, and the workload is large.
3. The node water level solving method is still not optimized enough
The solution of the node water level equation set is an important factor for restricting the calculation speed of the model. The river and sea university proposes two solutions: optimal coding and matrix identification. The principle of the optimal coding method is to minimize the number difference (i.e. bandwidth) of the adjacent nodes as much as possible, which puts high demands on users, and meanwhile, the natural river network has difficulty in realizing the optimal coding. The principle of the matrix identification method is to identify non-zero elements, thereby reducing the operation of the zero elements. The matrix identification method is applicable to any river network coding, but has the defect that a matrix identification code array and a row code indication array need to be formed in advance, and certain additional workload is provided.
4. The regulation and storage in plain are difficult to be reflected correctly
Whether the MIKE 11 model or the HOHY2 model comprises other hydrodynamic calculation models, the storage capacity of the plain area is always difficult to describe correctly. The MIKE 11 reflects the storage capacity of the unconventional river and the water surface by setting a water level-volume relation curve of the cross section, and the MIKE 11 still needs to be manually specified for how the storage capacity of the polygonal block surrounded by the river is distributed to the peripheral cross section.
For the HOHY2 model, the concepts of "land area width" and "regulated river width" are introduced. The land width is the area of a polygonal block with the unit river length; the regulated river width is the sum of the existing river width and the additional river width, and the additional river width is the product of the land width and the water surface rate of the polygonal block. In short, the storage capacity of the HOHY2 model is obtained by equally distributing the water area of the polygonal block surrounded by the river channel to the river width of the peripheral river channel according to the river length.
The mode of considering the storage regulation capability is actually an artificial distribution mode and is not in line with the actual mode. The produced water of the plain blocks is distributed to the peripheral river channels, is not uniformly distributed according to the river length, but is related to the water level difference between the blocks and the peripheral river channels, the scale of the connecting river channels and the connecting direction; on the other hand, the "regulation river width" of the HOHY2 model only considers the regulation of the water surface rate below the elevation of the field surface, and if the regulation of the plain is distributed when the plain is completely submerged in a flood, the model is not considered yet.
Therefore, the current flood evolution simulation method focuses on the water flow movement in the river channel (namely, the water flow movement in the channel), and the regulation and storage capacity of the plain is simple and generalized, and is greatly different from the actual situation. Therefore, a flood routing simulation method which has the advantages of simplicity and convenience in use, quickness in calculation, capability of well simulating the actual condition of plain regulation and the like is urgently needed.
Disclosure of Invention
In order to solve the above-mentioned problems in the prior art, the present invention provides a flood routing simulation method for a plain river network area, which has the technical characteristics of simple and convenient use, fast calculation, and better simulation of actual conditions.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a flood routing simulation method for plain river network areas comprises the following steps:
step 1): the method comprises the steps of generalizing and automatically numbering a river network of a research area by adopting GIS space editing and analysis, wherein the river network is an integral body formed by a plurality of criss-cross river channels;
step 2): the method is characterized in that the distinction of inner and outer river channels of a river network structure in the prior art is cancelled, the external boundary of the river network is generalized by adopting special nodes, and the special nodes are processed by a special node equation;
step 3): constructing a distributed reservoir group regulation and storage model: each polygonal area divided by the river network is regarded as a reservoir, each polygonal area adopts a water balance equation to construct a single reservoir regulation and storage model, and a plurality of polygonal areas of the whole river network area form a distributed reservoir group regulation and storage model;
step 4): solving the unknown quantity of the river network: the method comprises the steps that a set of unified river channel catching-up coefficients is adopted, a ternary set table is adopted for a node equation set to store non-zero elements of a coefficient matrix, the node equation set comprises a river network external boundary node equation and a non-river network external boundary node equation, the node equation set is solved by a relaxation iteration method formula, and a recording array is introduced into the relaxation iteration method formula to record the sequence number of the first non-zero element in each row in a ternary structure array for storing the non-zero elements.
As an improvement, the boundary in step 2) is generalized by nodes and specially processed by a node equation:
a) For connection flow QQ 0 And a boundary node N1, wherein the river channel where the boundary node N1 is located is connected with a node N2 at the other end, and the node equation is as follows:
QQ 0 ＝α+βZ N1 +ζZ N2
wherein, sigma, beta and zeta are catch-up coefficients of the first section of the river channel connected with the flow boundary;
b) For connecting water level ZZ 0 The node NN of the boundary has the following node equation:
Z NN ＝ZZ 0 。
as an improvement, m reservoirs are separated from the river network in the step 3), and for the ith reservoir, the water balance equation is as follows:
wherein, the S i Is the area of the reservoir, V i Is the volume of the reservoir, P i For reservoir rain cleaning, Q i Is the sum of the exchange flows of the reservoir and n surrounding river channels, Z i Is the water level of the reservoir and is,
and sigma, m, B and H are respectively the submergence coefficient, flow coefficient, net gate width and gate head of the virtual gate for the water level of the jth river channel connected with the reservoir.
As an improvement, the volume of the reservoir comprises a volume below a field surface elevation and above the field surface elevation, the volume below the field surface elevation comprises a volume of an unbevelled small river channel water surface, a volume of a ditch water surface and a volume of a lake pond water surface, the volume above the field surface elevation is a column-shaped volume taking the whole polygonal area as a bottom, and the volume of the reservoir is represented by the following formula:
wherein, the V i Is the volume of the reservoir, Z i Is the water level of the reservoir, Z d Is an unbundling water surface bottom elevation, H 0 As elevation of the field surface, chi is the water surface rate of the polygonal area.
As an improvement, the relaxation iteration method after storing the non-zero elements by using the three-tuple table in the step 4) can be expressed as follows:
node (k) represents a triple structure array for storing non-zero elements, node (k) I represents a row number of a kth non-zero element, node (k) J represents a column number of the kth non-zero element, node (k) V represents a value of the kth non-zero element, zi is a water level of a Node, ri is a constant term of a Node matrix equation, ω is a relaxation coefficient, and b (I) is an array for recording a sequence number of a first non-zero element in each row in Node (k).
Has the beneficial effects that:
1) According to the invention, a GIS software program is used for drawing the river network structure, so that automatic numbering of river network elements can be realized, the connection relation between nodes and a river channel can be automatically identified, and a large amount of manual work is saved;
2) The invention cancels the distinction of the inner and outer river channels of the traditional three-stage solution, and the boundary is processed on the node, thereby greatly simplifying the calculation flow;
3) The invention provides a distributed reservoir group regulation and storage model, which is coupled with a river network model for calculation, so that the regulation and storage capacity of a plain can be reflected more truly;
4) The invention adopts a ternary system table method to store non-zero elements for the coefficient matrix of the node equation, and can greatly improve the calculation speed without additional identification work. Taking Zhejiang province Wenhuang plain as an example, the flood for 4 days only needs 1 minute and 30 seconds, while the flood for the same river network structure MIKE 11 needs 34 minutes.
Drawings
Fig. 1 is a GIS software program interface implementing river network editing and automatic numbering.
Fig. 2 is a schematic diagram of a river network structure for distinguishing an internal river channel from an external river channel in the prior art.
FIG. 3 is a schematic diagram of a generalized river network structure according to the present invention.
Fig. 4 is a schematic diagram of a distributed reservoir regulation model of the present invention.
Fig. 5 is a schematic diagram of a river network calculation process in the prior art.
Fig. 6 is a schematic diagram of the river network calculation process in the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings, but the invention is not limited to the following examples.
As shown in fig. 1, 3, 4, and 6, a specific implementation example of a flood routing simulation method for a plain river network area is shown, which demonstrates a flood routing simulation method for a plain river network area, and the simulation method includes the following steps:
step 1): and by adopting a GIS software program, the drawing and automatic numbering of the river network structure can be realized. Specifically, the method comprises the following steps: the software program can realize the editing functions of drawing, adding, deleting and the like of the river network elements such as nodes, river channels, water gates and the like, can realize the automatic numbering of the river network elements by judging the drawing sequence of the primitives (nodes, river channel objects and the like), and can automatically identify the connection relation between the river channels and the nodes by judging the intersection relation between the nodes and the river channel primitives. As shown in fig. 1, a program is used to generalize a natural river network, and after nodes and river channels are drawn, the nodes and the river channels are automatically numbered, and the connection relationship between the river channels and the nodes is automatically identified, wherein the river network is an integral body formed by a plurality of criss-cross river channels;
step 2): compared with the river network generalization mode (shown in figure 2) in the prior art, the invention cancels the distinction of the inner river channel and the outer river channel of the river network structure (shown in figure 3), generalizes the external boundary of the river network by adopting special nodes and processes the nodes by using a special node equation;
(1) regarding the processing of the boundary, as shown in fig. 2, it is a schematic diagram of a river network structure for distinguishing the inner and outer river channels in the prior art, the river channels connected with the boundary are treated as the outer river channels, there are 3 outer river channels, and the connected boundaries are flow rates QQ 0 Water level ZZ 0 Water level ZZ 1 The catch-up coefficients are respectively:
Q L1 ＝P L1 -V L1 Z L1 (P L1 ＝QQ 0 (t),V L1 ＝0)
Z L2 ＝P L2 -V L2 Q L2 (P L2 ＝ZZ 0 (t),V L2 ＝0)
Z L3 ＝P L3 -V L3 Q L3 (P L3 ＝ZZ 1 (t),V L3 ＝0)
in the formulas (1) to (3), L1, L2, and L3 are head section numbers of three outer channels, respectively, and the method in the prior art is to perform corresponding processing on the catching-up coefficient of the head section of the outer channel at the boundary.
(2) The invention generalizes the boundary by nodes and specially processes by a node equation:
for a specific embodiment of step 2) of the present invention, fig. 3 is used for illustration, and fig. 3 is a schematic view of a generalized river network structure in the present invention, where the river network structure cancels the distinction between the inner and outer river channels, the boundaries are optimized on the nodes, and the processing of the three boundaries on the nodes is as follows:
a) For the boundary node 1, as a special node, the water balance equation of the special node is as follows:
QQ 0 ＝α 1 +β 1 Z 1 +ζ 1 Z 2 (ii) a Formula (4)
b) For the boundary node 15, as a special node, the water balance equation of the special node is:
Z 15 ＝ZZ 0 (ii) a Formula (5)
c) For the boundary node 19, as a special node, the water balance equation of the special node is:
Z 19 ＝ZZ 1 (ii) a Formula (6)
Wherein, Z is 1 、Z 2 、Z 3 Expressed as node level, the QQ 0 Expressed as a value of the flow boundary, said ZZ 0 、ZZ 1 Expressed as the value of the water level boundary, and the alpha, beta and zeta represent the catch-up coefficient of the river channel head section.
In the invention, the river network structure after distinguishing the inner and outer river channels is cancelled in the step 2), the processing of the external boundary is shown in the formulas (4) to (6), and the processing of the boundary is very simple;
step 3): constructing a distributed reservoir group regulation and storage model, specifically: the principle of the distributed reservoir group regulation and storage model is as follows: regarding each polygonal area divided by the river network as a reservoir, each polygonal area adopts a water balance equation to construct a single reservoir regulation and storage model, a plurality of polygonal areas of the whole river network area form a distributed reservoir group regulation and storage model, as shown in a schematic diagram of the distributed reservoir regulation and storage model shown in fig. 4, wherein the generalized reservoir of each polygonal area is S1-S9, the volume of the reservoir is determined by self water production and water exchange with n surrounding riverways, the water exchange between the reservoir and the surrounding riverways can be reflected by a virtual gate overflowing formula, the river network is divided into m reservoirs, and for the ith reservoir, the water balance equation can be listed:
in the formula (7), S i For water collection area of reservoir, V i Is the volume of the reservoir, P i For reservoir rain cleaning, Q i The sum of the exchange flow of the reservoir and the n surrounding river channels is used for summarizing the exchange water volume of the reservoir and the n surrounding river channels and reflecting the exchange water volume through a virtual gate overflowing formula.
In the formula (7), the volume V (i) of the reservoir includes a volume below the field elevation and above the field elevation, the volume below the field elevation includes a volume of a water surface of a small riverway, a volume of a water surface of a ditch and a volume of a water surface of a pond, the volume above the field elevation is a columnar volume taking the whole polygonal area as a bottom, and the volume expression formula of the reservoir is as follows:
in the formula (8), the V i Is the volume of a reservoir, Z i Is the water level of the reservoir, Z d Is an unbundling water surface bottom elevation, H 0 And x is the water surface rate of the polygonal area.
Each polygonal area can adopt a formula (7) and a formula (8) to construct a single reservoir regulation and storage model, a plurality of polygonal areas of the whole river network area form a distributed reservoir group regulation and storage model, and the reservoir group model is coupled with the river network calculation model to reflect the real regulation and storage capacity of the plain during the flood period;
and step 4): solving the unknown quantity of the river network: the method comprises the steps that a set of unified river channel catching-up coefficients is adopted, a ternary set table is adopted for a node equation set to store non-zero elements of a coefficient matrix, the node equation set comprises a river network external boundary node equation and a non-river network external boundary node equation, the node equation set is solved by a relaxation iteration method formula, and a recording array is introduced into the relaxation iteration method formula to record the sequence number of the first non-zero element in each row in a ternary structure array for storing the non-zero elements. The specific operation is as follows: firstly, inputting a boundary, a hydraulic element and a calculation result of an upper time period; secondly, calculating the catching up coefficient of each river channel in the river network; thirdly, the equation is listed for the boundary nodes in the step 2), and other common nodes (non-boundary nodes) establish a node equation according to the connection relation between the nodes and the river channel to jointly form a node equation set; then, storing non-zero elements of the coefficient matrix by adopting a three-element list, and solving a node equation set by adopting a relaxation iteration method; and finally, after the node water level is obtained, the pursuit equation is substituted for each river channel, the water level flow achievement of all the sections is obtained, and the next time period is switched.
Specifically, the method comprises the following steps:
(1) fig. 5 is a schematic diagram of a river network calculation process in the prior art, and a corresponding river network structure is shown in fig. 2, and the calculation process is as follows: firstly, inputting a boundary, a hydraulic element and a calculation result of an upper time period; secondly, calculating the catching up coefficients of the outer river channel and the inner river channel, wherein the catching up coefficients of the sections of the outer river channel are P, V, S and T, and the catching up coefficients of the sections of the inner river channel are sigma, beta, zeta, theta, eta and gamma; thirdly, according to the connection relation between the nodes and the inner and outer river channels, each node can establish a node equation; then solving the whole node equation set (Gaussian elimination method or iteration method); finally, the obtained node water level is substituted back into the pursuit equation of the inner and outer river channels to obtain Z of all the sections i 、Q i Achievement; and (5) turning to the next time interval, and continuing to circularly calculate.
(2) Fig. 6 is a schematic diagram of a river network calculation process of the present invention, and a corresponding river network structure is fig. 3, and the present invention cancels the distinction between the inner and outer river channels, and the calculation process is as follows: firstly, inputting boundary, hydraulic power elements and calculation results of the last period; secondly, calculating unified river channel catching up coefficients sigma, beta, zeta, theta, eta and gamma (namely, only calculating the inner river channel catching up coefficient in the prior art); thirdly, the equation of the boundary nodes in the step 2) is listed, and other common nodes can establish a node equation according to the connection relationship between the nodes and the river channel to jointly form a node equation set; then pairSolving the whole node equation set (a relaxation iteration method and a ternary set table high-efficiency storage non-zero element method); finally, the obtained node water level is substituted into a pursuit equation of the river channel, and Z of all the sections is obtained i 、Q i Achievement; and (5) turning to the next time interval, and continuing to circularly calculate.
As can be seen from a comparison of fig. 5 and 6, the river network calculation flow chart of the present invention is very simple.
To further illustrate the use of the ternary table storage method and the relaxation iteration method of the present invention, fig. 1 is an exemplary illustration.
Taking the data in fig. 1 of the invention as an example, a GIS software program can automatically identify the connection relationship between the nodes and the river channel, and further can obtain the number of the node at the other end of the river channel connected with the designated node. For example, node 2, whose connected river channel numbers are 1, 2, 3, 6, and the other end node numbers of the connected river channels 1, 2, 3, 6 are 1, 3, 5, 4, so that for node 2, node equations about nodes 1, 2, 3, 4, 5 can be listed, and thus, the river network node matrix equation can be obtained as follows:
further, defining a triple structure array node () for storing non-zero elements, and then the corresponding triple table is as follows:
in the prior art, a relaxation iteration method is adopted for solving a node equation, and a formula of the relaxation iteration method for solving a node equation set is as follows:
in the formula (9), the coefficient elements calculated in each line contain a large number of zero elements, and in order to avoid the judgment of the serial numbers of the non-zero elements in each line in the Nodes (), the invention introduces an array b () to record the serial numbers of the first non-zero elements in each line in the Node (), namely b (1) =1, b (2) =3, b (3) =8 \8230; \8230andb (8) =29.
Therefore, after storing the non-zero elements by using the ternary group table of the present invention, the relaxation iteration method can be expressed as:
node (k) represents a triple structure array for storing non-zero elements, node (k) I represents a row number of a kth non-zero element, node (k) J represents a column number of the kth non-zero element, node (k) V represents a value of the kth non-zero element, zi is a water level of a Node, ri is a constant term of a Node matrix equation, ω is a relaxation coefficient, b (I) is a serial number of a first non-zero element in each row in Node s (k), and the array b (I) can be automatically assigned through a GIS software program in step 1) without extra work.
Finally, it should be noted that the present invention is not limited to the above embodiments, and many variations are possible. All modifications which can be derived or suggested by a person skilled in the art from the disclosure of the present invention are to be considered within the scope of the invention.
Claims (5)
1. A flood routing simulation method for plain river network areas is characterized by comprising the following steps:
step 1): the method comprises the steps of generalizing and automatically numbering a river network of a research area by adopting GIS space editing and analysis, wherein the river network is an integral body formed by a plurality of criss-cross river channels;
step 2): the method is characterized in that the distinction of inner and outer river channels of a river network structure in the prior art is cancelled, the external boundary of the river network is generalized by adopting special nodes, and the special nodes are processed by a special node equation;
step 3): constructing a distributed reservoir group regulation and storage model: each polygonal area divided by the river network is regarded as a reservoir, each polygonal area adopts a water balance equation to construct a single reservoir regulation and storage model, and a plurality of polygonal areas of the whole river network area form a distributed reservoir group regulation and storage model;
step 4): solving the unknown quantity of the river network: the method comprises the steps that a set of unified river channel catch-up coefficients is adopted, a ternary set table is adopted for a node equation set to store non-zero elements of a coefficient matrix, the node equation set comprises a river network external boundary node equation and a non-river network external boundary node equation, the node equation set is solved by adopting a relaxation iteration method formula, and a record array is introduced into the relaxation iteration method formula to record the sequence number of the first non-zero element in each row in the ternary structure array for storing the non-zero elements.
2. The method of claim 1, wherein the method comprises: in step 2), the boundary is generalized by nodes and specially processed by a node equation:
a) For connection traffic QQ 0 The method comprises the following steps that boundary nodes N1 are connected, the river channel where the boundary nodes N1 are located is connected with nodes N2 at the other end, and then the node equation is as follows:
QQ 0 ＝α+βZ N1 +ζZ N2
wherein, sigma, beta and zeta are the catching up coefficient of the first section of the river channel connected with the flow boundary;
b) For connecting water level ZZ 0 The node NN of the boundary has the following node equation:
Z NN ＝ZZ 0 。
3. the method for simulating flood routing in a plain river network area according to claim 1 or 2, wherein: m reservoirs are separated from the river network in the step 3), and for the ith reservoir, the water quantity balance equation is as follows:
wherein, the S i Is the area of the reservoir, V i Is the volume of the reservoir, P i For purifying rain for reservoirs Q i Is the sum of the exchange flows of the reservoir and n surrounding river channels, Z i Is the water level of the reservoir and is,
and sigma, m, B and H are respectively the submergence coefficient, flow coefficient, net gate width and gate head of the virtual gate for the water level of the jth river channel connected with the reservoir.
4. The method of claim 3, wherein the method comprises: the volume of the reservoir comprises the volume of the water surface of a small riverway which is not generalized, the volume of the water surface of a ditch and the volume of the water surface of a pond below the elevation of the field, the volume of the water surface of the ditch and the volume of the water surface of the pond above the elevation of the field is a columnar volume taking the whole polygonal area as the bottom, and the volume expression formula of the reservoir is as follows:
wherein, the V i Is the volume of a reservoir, Z i Is the water level of the reservoir, Z d For an unexinized water surface elevation, H 0 And x is the water surface rate of the polygonal area.
5. The method of claim 1, wherein the method comprises: the relaxation iteration method after storing the non-zero elements by adopting the three-element table in the step 4) can be expressed as follows:
node (k) represents a triple structure array for storing non-zero elements, node (k) I represents a line number of a kth non-zero element, node (k) J represents a column number of the kth non-zero element, node (k) V represents a value of the kth non-zero element, zi is a water level of a Node, ri is a constant term of a Node matrix equation, omega is a relaxation coefficient, and b (I) is an array for recording serial numbers of a first non-zero element in each line in Node (k).
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