Plain polder area water system connectivity calculation method based on network flow

Abstract

The invention discloses a plain polder area water system connectivity calculation method based on network flow, and the method comprises the steps: carrying out the topology of an in-polder water system structure based on the remote sensing image data and field survey data of a plain polder area, carrying out the generalization of an intersection point between a riverway boundary and a riverway into a node, and carrying out the generalization of the riverway into an edge; collecting the drainage modulus and the corresponding control water level of each drainage station in polder, and establishing a drainage scene; establishing a one-dimensional hydrodynamic model, and calculating node water levels and river water flow directions and flows under different drainage scenes by setting corresponding initial water levels and boundary conditions; the method comprises the following steps: establishing a directed river network graph model under a corresponding drainage scene, generalizing intersection points between riverway boundaries and riverways as source points, generalizing nodes of drainage stations needing to be opened as sink points, generalizing the riverways as edges, and constructing a weighted adjacency matrix with the peak flow of the riverways as weights; and constructing a node maximum flow matrix based on a maximum flow algorithm, and further calculating the plain polder area total water system connectivity by integrating the water system connectivity under each drainage scene.

Description

Technical Field

[0001] The invention relates to the technical field of water resources, and in particular to a method for calculating the connectivity of a plain polder water system based on network flow. Background Art

[0002] The polder area is an artificial water collection unit formed by building embankments and reclaiming land in the low-lying areas of the plain in order to resist flood disasters and expand production and living space. The river channel gradient within the polder is small, and the river flow is almost zero when the drainage station is not opened. Under the joint dispatching scenario of drainage stations at different locations and ranges, the river flow and flow direction are also different.

[0003] At present, there are two main methods for calculating the connectivity of river systems in plain river networks. One is based on the river network topology, calculating the number of nodes, ring degree and other structural indexes to characterize the static connectivity level of the river network. This type of method only considers the structural connectivity of the river network, and does not consider functional connectivity indicators such as flow direction and flow rate; the other is the connectivity calculation method based on graph theory, which usually introduces water flow resistance or flow rate to characterize the flow capacity of the river channel. However, due to the characteristics of the uncertain flow direction of rivers in plain river networks, the existing graph theory methods mostly construct the river network water system as an undirected graph model. The above methods are less applicable in plain polder areas because the flow direction and flow rate of the river channel in the polder area are mainly affected by hydraulic structures such as sluice pumps. If its connectivity is to be discussed, the changes in the hydrodynamics of the river channel under the joint dispatch of different hydraulic structures must be considered. Summary of the invention

[0004] The present invention provides a method for calculating the connectivity of a plain polder water system based on network flow, so as to solve the problem that the existing method for calculating the connectivity of a plain polder water system does not consider functional connectivity indicators such as flow direction and flow rate, and has poor applicability in plain polder water systems.

[0005] The present invention provides a method for calculating the connectivity of a plain polder water system based on network flow, comprising: Step 1: Based on the remote sensing image data and field survey data of the plain polder area, the water system structure in the polder is topologically analyzed, the river boundary and the intersection points between the river channels are generalized as nodes, and the river channels are generalized as edges; Step 2: Collect the drainage modulus and corresponding controlled water level of each drainage station in the dike to establish a drainage scenario; Step 3: Establish a one-dimensional hydrodynamic model, and calculate the node water level, river water flow direction, and flow rate under different drainage scenarios by setting the corresponding initial water level and boundary conditions; Step 4: Establish a directed river network model under the corresponding drainage scenario, generalize the intersection points between river boundaries and river channels as source points, generalize the drainage station nodes that need to be opened as sink points, and generalize the river channels as edges, and construct a weighted adjacency matrix with the peak flow of the river channel as the weight; Step 5: Based on the maximum flow algorithm, a node maximum flow matrix is ​​constructed, and the water system connectivity under various drainage scenarios is comprehensively considered to further calculate the total water system connectivity of the plain embankment area.

[0006] Furthermore, in step 2, the average water level in the dike Refers to the average water level at each node. The water level control station in the dike has a total of Simulate the highest water level in the dike Start, then , … The water levels of the drainage stations are controlled from high to low, and the simulation is divided into In a flood drainage scenario, the water level is Down to , Down to ...until the water level drops to the lowest limit , calculate the river flow and direction for each drainage scenario separately; In the drainage scenario, the drainage water depth for:

[0007] In the formula, is the upper limit water level of this drainage scenario, is the lower limit water level of the drainage scenario, 0<y≤m; Total drainage depth H for:

[0008] In the formula, It is the highest water level in the dike. The lowest water level.

[0009] Furthermore, in step three, a one-dimensional hydrodynamic model is constructed to calculate the water level of the water system nodes in the dike and the water flow of the river channel, where the water level calculation point is located at the node, and the water flow calculation point of the river channel is located at the midpoint section of the river channel. The basic equation of the one-dimensional hydrodynamic model is as follows:

[0010]

[0011] In the formula, is the flow rate, in units of ; is the lateral inflow, in units of ; is the water flow area, in units of ; is the acceleration due to gravity; is the water level in ; is the hydraulic radius, in units of ; is Xiecai coefficient; is the momentum correction factor; In a certain drainage scenario, the river boundary where the drainage station needs to be opened in this drainage scenario is set as an open boundary and assigned a corresponding outflow. The outflow is the drainage modulus of the drainage station, and the remaining boundary nodes are all closed boundaries. The initial water level is set to the upper limit water level in this drainage scenario until the average water level in the dike drops to the lower limit water level in this drainage scenario. The change of the average water level in the dike and the flow direction and flow of the river water body in this drainage scenario are calculated. After the calculation is completed, the boundary conditions are reset to simulate the next drainage scenario.

[0012] Furthermore, in step 4, the intersection points between river boundaries and river channels are generalized as source points, the drainage station nodes that need to be opened are generalized as sinks, and the river channels are generalized as edges to establish a river network model. ,in is a node set, represents the sink set, represents the source point set; represents the edge set, Nodes represent the direction of water flow Flow to Node The river channel, for the directed graph ; is the weighted adjacency matrix of the graph, and the edge weights are calculated as follows:

[0013] In the formula, For the river of peak flow.

[0014] Furthermore, in step 5, the node maximum flow matrix is ​​constructed , Indicates that the source To the meeting point The maximum flow of is used to characterize the source point Capacity to reach the exit point of the polder water system; The connectivity of the water system under this drainage scenario The calculation is done using the following formula:

[0015] Total water system connectivity Calculated as:

[0016] In the formula, is the drainage depth under the yth drainage scenario, is the total drainage water depth, is the water system connectivity under the yth drainage scenario.

[0017] The present invention has the following beneficial effects: a method for calculating the connectivity of a plain polder water system based on network flow is provided. Based on remote sensing images and field surveys, the water system structure in the dike is topologically constructed; drainage scenarios are set according to the drainage modulus and corresponding control water level of each drainage station in the dike; a one-dimensional hydrodynamic model is established, and the node water level and the flow direction and flow of the river water body under different drainage scenarios are calculated by setting the corresponding initial water level and boundary conditions; a directed river network graph model under the corresponding drainage scenario is established, and a weighted adjacency matrix with the peak flow of the river as the weight is constructed; the node maximum flow matrix is ​​constructed based on the maximum flow algorithm, and the total water system connectivity of the dike area is further calculated by comprehensively considering the water system connectivity under various drainage scenarios; the network flow theory can incorporate the directionality and flow size of the river water flow into the connectivity analysis, and the combined scheduling effect of multiple hydraulic structures can be considered in conjunction with the hydrodynamic model. The combination of the two can accurately simulate the flow path and flow distribution under different scheduling schemes, and comprehensively considers the structural connectivity and functional connectivity under actual hydrodynamic conditions. This quantitative ability enables the model to be used to compare the effects of different scheduling schemes, and then optimize the management strategy, which has important practical value for flood risk assessment and drainage system design in plain dike areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0019] Figure 1 It is a flow chart of a method for calculating the connectivity of a plain polder water system based on network flow in an embodiment of the present invention; Figure 2 This is an example of a river network model in an embodiment of the present invention; Figure 3 It is a generalized schematic diagram of a river network map in an embodiment of the present invention; Figure 4 A schematic diagram of a flood drainage scenario in an embodiment of the present invention; Figure 5 The river network graph model and adjacency matrix of each flood drainage scenario in the embodiment of the present invention; Figure 6 This is a generalized diagram of the river network after the water system connection project is implemented in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The technical solutions provided by the embodiments of the present invention are described in detail below in conjunction with the drawings.

[0021] See also Figures 1 to 6 The present invention provides a method for calculating the connectivity of a plain polder water system based on network flow, taking a plain polder as an example, comprising the following steps: Step 1: Based on the remote sensing image data and field survey data of the plain embankment area, the water system structure within the embankment is topologically analyzed, the river boundaries and intersections between river channels are generalized as nodes, and the river channels are generalized as edges.

[0022] Based on remote sensing images and field surveys, the water system structure within the dike was topologically analyzed. The boundaries of the river channels, the intersections between the channels, and the boundaries of the drainage stations were generalized as nodes, the rivers were generalized as edges, and the water system structure was vectorized to facilitate subsequent model simulation. Figure 3 (a) is an example image before generalization, and (b) is an example image after generalization.

[0023] Step 2: Collect the drainage modulus and corresponding controlled water level of each drainage station within the dike to establish a drainage scenario.

[0024] The opening and closing of the drainage station in the polder area is determined by the controlled water level. When the average water level in the polder exceeds the controlled water level of the drainage station, the drainage station starts to drain water outside the polder; when the average water level in the polder is lower than the controlled water level of the drainage station, the drainage station stops operating. A drainage scenario is established, starting from the highest water level in the polder and the controlled water level of the drainage station as the boundary, until it drops to the lower limit water level, that is, no drainage station will operate under this water level. The above drainage scenario setting method is used to quantify the full process drainage mode of the plain polder area. Average water level in the polder Refers to the average water level at each node.

[0025] Average water level in the dike Refers to the average water level at each node. The water level control station in the dike has a total of Simulate the highest water level in the dike Start, then , … The water levels of the drainage stations are controlled from high to low, and the simulation is divided into In a flood drainage scenario, the water level is Down to , Down to ...until the water level drops to the lowest limit , calculate the river flow and direction for each drainage scenario separately; In the drainage scenario, the drainage water depth for:

[0026] In the formula, is the upper limit water level of this drainage scenario, is the lower limit water level of the drainage scenario, 0<y≤m; Total drainage depth H for:

[0027] In the formula, It is the highest water level in the dike. The lowest water level.

[0028] In this embodiment, there are 3 drainage stations in the example embankment, and there are 3 corresponding control water levels. start, , , The water levels of the drainage stations are controlled from high to low, and the drainage water depth is:

[0029]

[0030]

[0031] The total drainage depth is:

[0032] The simulation is divided into three scenarios, namely, the average water level in the dike is Down to , Down to , Down to , the river flow and flow direction are calculated separately for each scenario. Figure 4 The drainage modulus and controlled water level of each drainage station are shown in Table 1.

[0033] Table 1 Drainage modulus and controlled water level of each drainage station

[0034] Step 3: Establish a one-dimensional hydrodynamic model, and calculate the node water level, river water flow direction, and flow rate under different drainage scenarios by setting the corresponding initial water level and boundary conditions; A one-dimensional hydrodynamic model is constructed to calculate the water level of the water system nodes and the river flow in the dike. The water level calculation point is located at the node, and the river flow calculation point is located at the midpoint section of the river. The basic equation of the one-dimensional hydrodynamic model is as follows:

[0035]

[0036] In the formula, For flow, ; For lateral inflow, ; is the water-passing area, ; is the acceleration due to gravity; is the water level, ; is the hydraulic radius, ; is Xiecai coefficient; is the momentum correction factor; In a certain drainage scenario, the nodes where the drainage station needs to be opened in this scenario are set as open boundaries and assigned corresponding outflows, i.e., the drainage modulus of the drainage station. The remaining boundary nodes are all closed boundaries, and the initial water level is set as the upper limit water level in this scenario until the average water level in the dike drops to the lower limit water level in this scenario. The changes in the average water level in the dike and the flow direction and flow of the river water body in this scenario are calculated. After the calculation is completed, the boundary conditions are reset to simulate the next scenario.

[0037] In this embodiment, the initial water level in the dike is set to the maximum value, that is, At this time, all three drainage stations need to be opened. The nodes of drainage stations 1, 2, and 3 in this scenario are set as open boundaries and assigned corresponding outflows, i.e., the drainage modulus of the drainage station. The remaining boundary nodes are all closed boundaries. The changes in the average water level in the dike and the flow direction and flow of the river water body in this scenario are calculated until the average water level in the dike drops to the lower limit of this scenario, that is, when the average water level in the dike drops to 3.75m, the simulation of drainage scenario 1 ends; next, drainage station No. 3 is closed to continue drainage until the average water level in the dike drops to 3.5m, and the simulation of drainage scenario 2 ends; finally, drainage stations No. 2 and 3 are closed, and only drainage station No. 1 is opened until the average water level in the dike drops to 3.3m. At this time, drainage ends and all drainage stations are closed.

[0038] Step 4: Establish a directed river network model under the corresponding drainage scenario, generalize the intersection points between river boundaries and river channels as source points, generalize the drainage station nodes that need to be opened as sink points, and generalize the river channels as edges, and construct a weighted adjacency matrix with the peak flow of the river channel as the weight; The intersection points between river boundaries and river channels are generalized as "source points", the nodes of drainage stations that need to be opened are generalized as "sink points", and the river channels are generalized as edges to establish a river network model. ,in is a node set, represents the sink set, Indicates the source point set. In the river network model, the sink point is represented by a triangle and the source point is represented by a circle. represents the edge set, Nodes represent the direction of water flow Flow to Node of the river; is the weighted adjacency matrix of the graph, and the edge weights are calculated as follows:

[0039] In the formula, For the river The peak flow of . If and only if the node and There are edges directly connected and rivers The water flow direction is Flow direction hour, ; When the node and No direct connection or river The water flow is not Flow direction hour, .

[0040] by Figure 2 Take the generalized river network model as an example. It has 2 sinks (m=2), 5 source points (n=5), and the weighted adjacency matrix for:

[0041] In network flow theory, maximum flow refers to the maximum possible flow that can be transmitted from a source node (source point) to a sink node (sink point) in a network. A network consists of nodes (nodes represent points or locations) and directed edges (representing paths or channels) connecting nodes. Each edge has a capacity (representing the maximum flow that this path can accommodate). The maximum flow problem can be described as calculating the maximum flow that can be achieved from a source node to a sink node while ensuring that the flow of each edge in the network does not exceed its capacity.

[0042] Step 5: Based on the maximum flow algorithm, a node maximum flow matrix is ​​constructed, and the water system connectivity under various drainage scenarios is comprehensively considered to further calculate the total water system connectivity of the plain embankment area.

[0043] In step 5, construct the node maximum flow matrix , Indicates that the source To the meeting point The maximum flow of is used to characterize the source point In step 5, the node maximum flow matrix with n rows and m columns is constructed with source points as rows and sink points as columns. , Indicates that the source To the meeting point The maximum flow of is used to characterize the source point The capacity of the water system exit point in the polder area is calculated using the Ford-Fulkerson method based on Python programming.

[0044] by Figure 2 Taking the generalized river network model as an example, and is the sink, and the rest of the nodes are source points. Indicates the source point To the meeting point The maximum flow between arrive There are two paths, path 1 ( ) and path 2 ( ), which can be divided into 3 sections, namely Section 1 ( ), Section 2 ( ), Section 3 ( ), sections 1 and 2 are single sections, , , where Section 2 can be further divided into Section 2-1 ( ) and Section 2-2 ( ), section 2-1 consists of edges (6, 4) and (4, 3), and the flow rate is limited by the minimum weight edge (6, 4), so ; Section 2-2 consists of the edges (6, 5) and (5, 3). The flow rate is limited by the minimum weight edge (6, 5). =6; Section 2-1 and Section 2-2 intersect at node 3, so . Combined with the maximum flow theory, we have: Similarly, we can get the maximum flow from other "source points" to "sink points", and get Figure 2 The node maximum flow matrix of the river network model shown is:

[0045] Figure 5 are the river network models and their respective maximum flow matrices for the three drainage scenarios. Among them, (a) is h 0 —h 1 ， (b) h 1 —h 2, (c) ish 2 —h 3.

[0046] The water system connectivity under this drainage scenario is defined as the sum of the maximum flows from each "source point" to the "sink point". The water system connectivity under a drainage scenario is IC The calculation is done using the following formula:

[0047] by Figure 2 Taking the generalized river network model as an example, the water system connectivity in this scenario is the sum of all elements of the node maximum flow matrix, which is calculated to be 64.

[0048] Table 2 Water system connectivity under various drainage scenarios

[0049] Total water system connectivity The structural connectivity and functional connectivity of the water system in the polder area during the drainage process are comprehensively reflected and calculated as follows:

[0050] In the formula, is the drainage depth in the yth scenario, is the total drainage water depth, is the water system connectivity under the yth scenario. According to the above calculation, the water system connectivity of the polder area is 48.75.

[0051] In order to further prove the practicality of the present invention, a water system connection project in the embankment area is proposed. The water level and drainage modulus of the drainage station remain unchanged. The generalized river network diagram after the water system connection project is shown in Figure 6 , repeat the above steps to calculate the connectivity of the water system in the Houwei area, see Table 3: Table 3 Water system connectivity under various drainage scenarios after the water system connection project

[0052] Total water system connectivity after the connection project Calculated as:

[0053] After connecting to the rear area, the total water connectivity increased to 63.61, an increase of 30.5% over the original water connectivity.

[0054] The above-described embodiments of the present invention do not limit the protection scope of the present invention.

Claims

1. A method for calculating the connectivity of water systems in plain polder areas based on network flow, characterized in that: include: Step 1: Based on the remote sensing image data and field survey data of the plain polder area, the water system structure in the polder is topologically analyzed, the river boundary and the intersection points between the river channels are generalized as nodes, and the river channels are generalized as edges; Step 2: Collect the drainage modulus and corresponding controlled water level of each drainage station in the dike to establish a drainage scenario; Step 3: Establish a one-dimensional hydrodynamic model, and calculate the node water level, river water flow direction, and flow rate under different drainage scenarios by setting the corresponding initial water level and boundary conditions; Step 4: Establish a directed river network model under the corresponding drainage scenario, generalize the intersection points between river boundaries and river channels as source points, generalize the drainage station nodes that need to be opened as sink points, and generalize the river channels as edges, and construct a weighted adjacency matrix with the peak flow of the river channel as the weight; Step 5: Based on the maximum flow algorithm, a node maximum flow matrix is ​​constructed, and the water system connectivity under various drainage scenarios is comprehensively considered to further calculate the total water system connectivity of the plain embankment area.

2. A method for calculating the connectivity of a plain polder water system based on network flow as claimed in claim 1, characterized in that: In step 2, the average water level in the dike Refers to the average water level at each node. The water level control station in the dike has a total of Simulate the highest water level in the dike Start, then , … The water levels of the drainage stations are controlled from high to low, and the simulation is divided into In a flood drainage scenario, the water level is Down to , Down to ...until the water level drops to the lowest limit , calculate the river flow and direction for each drainage scenario separately; In the drainage scenario, the drainage water depth for: In the formula, is the upper limit water level of this drainage scenario, is the lower limit water level of the drainage scenario, 0<y≤m; Total drainage depth H for: In the formula, It is the highest water level in the dike. The lowest water level.

3. A method for calculating the connectivity of a plain polder water system based on network flow as claimed in claim 1, characterized in that: In step three, a one-dimensional hydrodynamic model is constructed to calculate the water level of the water system nodes in the dike and the water flow of the river. The water level calculation point is located at the node, and the water flow calculation point of the river is located at the midpoint section of the river. The basic equation of the one-dimensional hydrodynamic model is as follows: In the formula, is the flow rate, in units of ; is the lateral inflow, in units of ; is the water flow area, in units of ; is the acceleration due to gravity; is the water level in ; is the hydraulic radius, in units of ; is Xiecai coefficient; is the momentum correction factor; In a certain drainage scenario, the river boundary where the drainage station needs to be opened in this drainage scenario is set as an open boundary and assigned a corresponding outflow. The outflow is the drainage modulus of the drainage station, and the remaining boundary nodes are all closed boundaries. The initial water level is set to the upper limit water level in this drainage scenario until the average water level in the dike drops to the lower limit water level in this drainage scenario. The change of the average water level in the dike and the flow direction and flow of the river water body in this drainage scenario are calculated. After the calculation is completed, the boundary conditions are reset to simulate the next drainage scenario.

4. The method for calculating the connectivity of a plain polder water system based on network flow according to claim 1, characterized in that: In step 4, the intersection points between river boundaries and river channels are generalized as source points, the drainage station nodes that need to be opened are generalized as sinks, and the river channels are generalized as edges to establish a river network model. ,in is a node set, represents the sink set, represents the source point set; represents the edge set, Nodes represent the direction of water flow Flow to Node The river channel, for the directed graph ; is the weighted adjacency matrix of the graph, and the edge weights are calculated as follows: In the formula, For the river of peak flow.

5. The method for calculating the connectivity of a plain polder water system based on network flow according to claim 1, characterized in that: In step 5, construct the node maximum flow matrix , Indicates that the source To the meeting point The maximum flow of is used to characterize the source point Capacity to reach the exit point of the polder water system; The connectivity of the water system under this drainage scenario The calculation is done using the following formula: Total water system connectivity Calculated as: In the formula, is the drainage depth under the yth drainage scenario, is the total drainage water depth, is the water system connectivity under the yth drainage scenario.

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