A calculation method for the water system connectivity of plain polder areas based on network flow

Abstract

The present invention discloses a method for calculating the water system connectivity of plain polder areas based on network flow. The method includes topologizing the water system structure within the polder based on remote sensing image data and field survey data of the plain polder area, generalizing the intersection points between the river channel boundaries and the river channels into nodes, and generalizing the river channels into edges; collecting the drainage modulus and the corresponding control water level of each drainage pumping station within the polder to establish a drainage scenario; establishing a one-dimensional hydrodynamic model, and calculating the node water level, the water flow direction and flow rate of the river channel under different drainage scenarios by setting the corresponding initial water level and boundary conditions; establishing a directed river network graph model under the corresponding drainage scenario, generalizing the intersection points between the river channel boundaries and the river channels into source points, generalizing the nodes of the drainage pumping stations to be opened into sink points, generalizing the river channels into edges, and constructing a weighted adjacency matrix with the peak flow rate of the river channel as the weight; constructing a node maximum flow matrix based on the maximum flow algorithm, and further calculating the total water system connectivity of the plain polder area by integrating the water system connectivity under each drainage scenario.

Description

Technical Field

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

[0002] A polder area is an artificial water collection unit formed by building dikes and reclaiming land in the low-lying areas of the plain to resist flood disasters and expand production and living spaces. The river gradient inside the polder is small, and the river flow is almost zero when the drainage pump stations are not opened. Under the combined dispatching scenarios of drainage pump stations with different positions and capacities, the river flow and direction are also different.

[0003] Currently, there are mainly two types of methods for calculating the water system connectivity of plain river network areas. One is to calculate structural indices such as the number of nodes and cyclomatic number based on the river network topological structure 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 indices 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 river's flow capacity. Due to the characteristics of the uncertain river flow direction in the plain river network area, the existing graph theory methods mostly construct the river network water system as an undirected graph model. The above methods have poor applicability in plain polder areas because the water flow direction and flow rate in the polder rivers are mainly affected by hydraulic structures such as sluices and pumps. If we want to discuss their connectivity, we must consider the hydrodynamic changes of the river channels under the combined dispatching of different hydraulic structures. Summary of the Invention

[0004] The present invention provides a method for calculating the water system connectivity of plain polder areas based on network flow to solve the problem that the existing methods for calculating the water system connectivity of plain polder areas do not consider functional connectivity indices such as flow direction and flow rate and have poor applicability in plain polder areas.

[0005] The present invention provides a method for calculating the water system connectivity of plain polder areas based on network flow, including:

[0006] Step 1: Based on the remote sensing image data and field survey data of the plain polder area, topologize the water system structure inside the polder, generalize the intersections between the river boundaries and the rivers as nodes, and generalize the rivers as edges.

[0007] Step 2: Collect the drainage modulus and corresponding control water levels of each drainage pump station inside the polder to establish a drainage scenario.

[0008] Step 3: Establish a one-dimensional hydrodynamic model, and calculate the node water levels, river water body flow directions and flow rates under different drainage scenarios by setting corresponding initial water levels and boundary conditions.

[0009] Step 4: Establish a directed river network graph model under the corresponding drainage scenario, generalize the intersections between the river boundaries and the rivers as source points, generalize the nodes of the drainage pump stations to be opened as sink points, generalize the rivers as edges, and construct a weighted adjacency matrix with the peak river flow rate as the weight.

[0010] Step 5: Construct a node maximum flow matrix based on the maximum flow algorithm, and further calculate the total water system connectivity of the plain polder area by integrating the water system connectivity under each drainage scenario.

[0011] Furthermore, in Step 2, the average water level inside the polder refers to the average water level at each node. Suppose there are a total of water level control levels of drainage pumping stations inside the polder. Starting from the highest water level inside the polder, then , … are the water level control levels of the drainage pumping stations from high to low respectively. Simulate drainage scenarios. The water level drops from to , drops to …… until it drops to the lowest lower limit water level . Calculate the river flow and flow direction for each drainage scenario separately; in the th drainage scenario, the drainage water depth is:

[0012]

[0013] In the formula, is the upper limit water level of this drainage scenario, is the lower limit water level of this drainage scenario, 0 < y ≤ m;

[0014] The total drainage water depth H is:

[0015]

[0016] In the formula, is the highest water level inside the polder, is the lowest lower limit water level.

[0017] Furthermore, in Step 3, construct a one-dimensional hydrodynamic model to calculate the water levels of the water system nodes inside the polder and the water flow of the river channels. The water level calculation points are located at the nodes, and the water flow calculation points of the river channels are located at the mid-section of the river channels. The basic equations of the one-dimensional hydrodynamic model are as follows:

[0018]

[0019]

[0020] In the formula, is the flow rate, with the unit of ; is the lateral inflow, with the unit of ; is the cross-sectional area, with the unit of ; is the acceleration due to gravity; is the water level, with the unit of ; is the hydraulic radius, with the unit of ; is the Chezy coefficient; is the momentum correction coefficient;

[0021] In a certain drainage scenario, set the river boundary where the drainage station needs to be opened in this drainage scenario as an open boundary and assign the corresponding discharge. The discharge is the drainage modulus of the drainage station, and the remaining boundary nodes are all closed boundaries. The initial water level is set as the upper limit water level in this drainage scenario until the average water level in the polder drops to the lower limit water level in this drainage scenario. Calculate the change of the average water level in the polder and the flow direction and flow rate of the river water body in this drainage scenario. After the calculation, reset the boundary conditions to simulate the next drainage scenario.

[0022] Furthermore, in step four, generalize the intersection points between the river boundary and the river as source points, generalize the nodes of the drainage stations to be opened as sink points, and generalize the river as edges to establish a river network graph model , where is the node set, represents the sink point set, represents the source point set; represents the edge set, represents that the water body flow direction is from node to node of the river. For the directed graph ; is the weighted adjacency matrix of the graph, and the edge weight value is calculated as follows:

[0023]

[0024] In the formula, is the peak flow rate of the river .

[0025] Furthermore, in step five, construct the node maximum flow matrix , represents the maximum flow from the source point to the sink point , which is used to characterize the ability of the source point to the outlet point of the polder water system;

[0026] The water system connectivity in this drainage scenario is calculated using the following formula:

[0027]

[0028] Total water system connectivity Calculated as:

[0029]

[0030] In the formula, is the drainage depth under the y-th drainage scenario, is the total drainage depth, is the water system connectivity under the y-th drainage scenario.

[0031] The present invention has the following beneficial effects: A method for calculating the water system connectivity of a plain polder area based on network flow according to the present invention topologizes the water system structure within the polder based on remote sensing images and field investigations; sets drainage scenarios according to the drainage modulus and corresponding control water levels of each drainage pump station within the polder; establishes a one-dimensional hydrodynamic model, and calculates the node water levels, water flow directions and flows in the river channels under different drainage scenarios by setting corresponding initial water levels and boundary conditions; establishes a directed river network graph model under the corresponding drainage scenario, and constructs a weighted adjacency matrix with the peak flow of the river channel as the weight; constructs a node maximum flow matrix based on the maximum flow algorithm, and further calculates the total water system connectivity of the polder area by synthesizing the water system connectivity under each drainage scenario; the network flow theory can incorporate the directionality and flow magnitude of the river channel water flow into the connectivity analysis, and the hydrodynamic model can consider the combined dispatching effect of multiple hydraulic structures. The combination of the two can accurately simulate the water flow paths and flow distributions under different dispatching schemes, comprehensively consider the structural connectivity and functional connectivity under actual hydrodynamic conditions. This quantification ability enables the model to be used to compare the effects of different dispatching schemes, and then optimize the management strategy, which has important practical value for flood risk assessment and drainage system design in plain polder areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0033] Figure 1 is a flowchart of a method for calculating the water system connectivity of a plain polder area based on network flow in an embodiment of the present invention;

[0034] Figure 2 is an example of a river network graph model in an embodiment of the present invention;

[0035] Figure 3 is a schematic diagram of the generalization of the river network graph in an embodiment of the present invention;

[0036] Figure 4 is a schematic diagram of a drainage scenario in an embodiment of the present invention;

[0037] Figure 5 The river network diagram model and adjacency matrix for each drainage scenario in the embodiments of the present invention;

[0038] Figure 6 The generalized river network diagram after implementing the water system connection project in the embodiments of the present invention. Detailed implementation manners

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. The technical solutions provided by each embodiment of the present invention will be described in detail below with reference to the drawings.

[0040] Please refer to Figures 1 to 6 , a method for calculating the water system connectivity of a plain polder area based on network flow provided by the present invention. Taking a certain plain polder area as an example, it includes the following steps:

[0041] Step 1, based on the remote sensing image data and field survey data of the plain polder area, topologize the water system structure within the polder, generalize the intersections between the river boundaries and the rivers into nodes, and generalize the rivers into edges.

[0042] Based on the remote sensing image and field survey, topologize the water system structure within the polder, generalize the river boundaries, the intersections between the rivers, and the boundaries where the drainage pumping stations are located into nodes, generalize the rivers into edges, and vectorize the water system structure for subsequent model simulation. Figure 3 In (a) is an example diagram before generalization, and (b) is an example diagram after generalization.

[0043] Step 2, collect the drainage modulus and corresponding control water levels of each drainage pumping station within the polder to establish a drainage scenario.

[0044] The opening and closing of the drainage pumping stations in the polder area are determined by their control water levels. When the average water level within the polder exceeds the control water level of the drainage pumping station, the drainage pumping station starts to drain water outside the polder; when the average water level within the polder is lower than the control water level of the drainage pumping station, the drainage pumping station stops operating. Establish a drainage scenario, starting from the highest water level within the polder, with the control water level of the drainage pumping station as the boundary, until it drops to the lower limit water level, that is, there is no drainage pumping station operating at this water level. Through the above drainage scenario setting method, the whole-process drainage mode of the plain polder area is quantified. The average water level within the polder refers to the average value of the water levels at each node.

[0045] The average water level within the polder refers to the average value of the water levels at each node. Suppose there are a total of control water levels of the drainage pumping stations within the polder, and the simulation starts from the highest water level within the polder, then , … are the drainage station control water levels from high to low respectively, simulating drainage scenarios, the water level drops from to , to …… until it drops to the lowest lower limit water level . For each drainage scenario, calculate its river channel flow and flow direction separately; in the th drainage scenario, the drainage water depth is:

[0046]

[0047] In the formula, is the upper limit water level of this drainage scenario, is the lower limit water level of this drainage scenario, 0 < y ≤ m;

[0048] The total drainage water depth H is:

[0049]

[0050] In the formula, is the highest water level in the polder, is the lowest lower limit water level.

[0051] In this embodiment, there are 3 drainage stations in the exemplary polder, and there are 3 corresponding control water levels. Simulate starting from the highest water level in the polder, , , are the drainage station control water levels from high to low respectively, then the drainage water depth:

[0052]

[0053]

[0054]

[0055] The total drainage water depth is:

[0056]

[0057] Simulate 3 scenarios, that is, the average water level in the polder drops from to , to , to . For each scenario, calculate its river channel flow and flow direction separately. See the schematic diagram of the drainage scenario inFigure 4 , the drainage modulus and control water level of each drainage pumping station are shown in Table 1.

[0058] Table 1 Drainage modulus and control water level of each drainage pumping station

[0059]

[0060] Step 3: Establish a one-dimensional hydrodynamic model. By setting the corresponding initial water level and boundary conditions, calculate the node water level, river water body flow direction and flow rate under different drainage scenarios;

[0061] Construct a one-dimensional hydrodynamic model to calculate the water level of the water system nodes in the polder and the river channel flow rate. The water level calculation point is located at the node, and the river channel flow rate calculation point is located at the mid-section of the river channel. The basic equations of the one-dimensional hydrodynamic model are as follows:

[0062]

[0063]

[0064] In the formula, is the flow rate, ; is the lateral inflow, ; is the cross-sectional area of flow, ; is the acceleration due to gravity; is the water level, ; is the hydraulic radius, ; is the Chezy coefficient; is the momentum correction coefficient;

[0065] In a certain drainage scenario, set the nodes where the drainage pumping stations need to be opened in this scenario as open boundaries and assign the corresponding outflows, that is, the drainage modulus of the drainage pumping stations. The remaining boundary nodes are all closed boundaries. The initial water level is set as the upper limit water level in this scenario until the average water level in the polder drops to the lower limit water level in this scenario, and calculate the change of the average water level in the polder and the flow direction and flow rate of the river water body in this scenario. After the calculation is completed, reset the boundary conditions to conduct the simulation of the next scenario.

[0066] In this embodiment, the initial water level in the polder is set as the maximum value, that is , at this time, all three drainage pumping stations need to be opened. Set the nodes of Drainage Pumping Stations No. 1, 2, and 3 in this scenario as open boundaries and assign the corresponding discharge, that is, the drainage modulus of the pumping station. The remaining boundary nodes are all closed boundaries. Calculate the change in the average water level inside the polder and the flow direction and flow rate of the river water in this scenario until the average water level inside the polder drops to the lower limit water level of this scenario, that is, when the average water level inside the polder drops to 3.75 m, the simulation of Drainage Scenario 1 ends; then close Drainage Pumping Station No. 3 and continue drainage until the average water level inside the polder drops to 3.5 m, and the simulation of Drainage Scenario 2 ends; finally, close Drainage Pumping Stations No. 2 and 3, and only open Drainage Pumping Station No. 1 until the average water level inside the polder drops to 3.3 m. At this time, the drainage ends and all drainage pumping stations are closed.

[0067] Step 4: Establish a directed river network graph model for the corresponding drainage scenario. Generalize the intersection points between the river boundaries and the rivers into source points, and generalize the nodes of the drainage pumping stations to be opened into sink points. Generalize the rivers into edges, and construct a weighted adjacency matrix with the peak flow rate of the river as the weight;

[0068] Generalize the intersection points between the river boundaries and the rivers into "source points", generalize the nodes of the drainage pumping stations to be opened into "sink points", generalize the rivers into edges, and establish a river network graph model , where is the node set, represents the sink point set, represents the source point set. In the river network graph model, sink points are represented by triangles and source points are represented by circles; represents the edge set, represents that the water flow direction is from node to node of the river; is the weighted adjacency matrix of the graph, and the edge weight value is calculated as follows:

[0069]

[0070] In the formula, is the peak flow rate of the river . When and only when nodes and are directly connected by an edge and the water flow direction of the river is from to , ; when nodes and are not directly connected by an edge or the water flow direction of the river is not from to , .

[0071] Taking Figure 2Taking the generalized river network graph model as an example, it has a total of 2 sink nodes (m = 2), 5 source nodes (n = 5), and a weighted adjacency matrix is as follows:

[0072]

[0073] In network flow theory, the maximum flow refers to the maximum possible flow that can be transmitted from the source node (source point) to the sink node (sink point) in a network. The network consists of nodes (nodes represent points or locations) and directed edges connecting the nodes (representing paths or channels), and 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 the source node to the sink node while ensuring that the flow of each edge in the network does not exceed its capacity.

[0074] Step 5: Construct a node maximum flow matrix based on the maximum flow algorithm, and further calculate the total water system connectivity of the plain polder area by integrating the water system connectivity in each drainage scenario.

[0075] In Step 5, construct a node maximum flow matrix , represents the maximum flow from the source point to the sink point , and is used to characterize the ability of the source point to the water system outlet point of the polder area. In Step 5, with the source points as rows and the sink points as columns, construct an n-row and m-column node maximum flow matrix , represents the maximum flow from the source point to the sink point , and is used to characterize the ability of the source point to the water system outlet point of the polder area. Calculate the results using the Ford-Fulkerson method based on Python programming.

[0076] Taking Figure 2 the generalized river network graph model as an example, and as the sink points, and the remaining nodes as the source points, represents the maximum flow between the source point and the sink point . There are a total of 2 paths from to , namely Path 1 ( ) and Path 2 ( ), which can be divided into 3 sections, namely Section 1 ( ), Section 2 ( ), and Section 3 ( ). Sections 1 and 2 are single sections, with , , and Section 2 can be further divided into Section 2-1 ( ) and section 2-2 ( ), section 2-1 is composed of edges (6, 4) and (4, 3), and the flow-through volume is restricted by the minimum-weight edge (6, 4), and there is ; section 2-2 is composed of edges (6, 5) and (5, 3), and the flow-through volume is restricted by the minimum-weight edge (6, 5), and there is = 6; section 2-1 and section 2-2 meet at node 3, so . Combining with the maximum flow theory, we have: , and similarly, the maximum node flow from other "source points" to "sink points" can be obtained, and the maximum node flow matrix of the river network graph model shown in Figure 2 is:

[0077]

[0078] Figure 5 are the river network graph models and their respective maximum flow matrices for each of the three drainage scenarios. Among them, (a) is h 0 —h 1 ， (b) is h 1 —h 2, and (c) is h 2 —h 3.

[0079] The water system connectivity under this drainage scenario is defined as the sum of the maximum node flows from each "source point" to the "sink point". The water system connectivity IC under a certain drainage scenario is calculated using the following formula:

[0080]

[0081] Taking Figure 2 the generalized river network graph model as an example, the water system connectivity under this scenario is the sum of all elements of the maximum node flow matrix, and the calculated value is 64.

[0082] Table 2 Water system connectivity for each drainage scenario

[0083]

[0084] Total water system connectivity comprehensively reflects the structural connectivity and functional connectivity of the polder water system during the drainage process, and the calculation is as follows:

[0085]

[0086] In the formula, is the drainage water depth in the y-th scenario, is the total drainage water depth, is the water system connectivity under the y-th scenario. Through the above calculations, the water system connectivity of this polder area is 48.75.

[0087] To further prove the practicability of the present invention, a water system connectivity project for this polder area is formulated. The control water level and drainage modulus of the drainage pumping station remain unchanged. The generalized river network diagram after the water system connectivity project is shown in Figure 6 , repeat the above steps, and the calculated water system connectivity of the polder area after connectivity is shown in Table 3:

[0088] Table 3 Water system connectivity under each drainage scenario after the water system connectivity project

[0089]

[0090] The total water system connectivity after the connectivity project The calculation is as follows:

[0091]

[0092] The total water system connectivity of the polder area after connectivity is increased to 63.61, which is a 30.5% increase compared to the original water system connectivity.

[0093] The embodiments of the present invention described above do not constitute a limitation on the protection scope of the present invention.

Claims

1. A method for calculating the water system connectivity of plain polder areas based on network flow, characterized in that Including: Step 1: Based on the remote sensing image data and field survey data of the plain polder area, topologize the water system structure within the polder, generalize the intersection points between the river boundaries and the rivers into nodes, and generalize the rivers into edges; Step 2: Collect the drainage modulus and corresponding control water levels of each drainage pumping station within the polder to establish drainage scenarios; Step 3: Establish a one-dimensional hydrodynamic model. By setting the corresponding initial water level and boundary conditions, calculate the node water levels, the flow direction and flow rate of the river water body under different drainage scenarios; In Step 3, construct a one-dimensional hydrodynamic model to calculate the water levels of the water system nodes within the polder and the flow rate of the river water body. The water level calculation points are located at the nodes, and the river water body flow rate calculation points are located at the mid-section of the river. The basic equations of the one-dimensional hydrodynamic model are as follows: In the formula, is the flow rate, with the unit of ; is the lateral inflow, with the unit of ; is the cross-sectional area of flow, with the unit of ; is the acceleration due to gravity; is the water level, with the unit of ; is the hydraulic radius, with the unit of ; is the Chezy coefficient; is the momentum correction coefficient; Under a certain drainage scenario, set the river boundary where the drainage pumping station needs to be opened in this drainage scenario as an open boundary and assign the corresponding outflow. The outflow is the drainage modulus of the drainage pumping station. The remaining boundary nodes are all closed boundaries. Set the initial water level as the upper limit water level in this drainage scenario until the average water level within the polder drops to the lower limit water level of this drainage scenario, calculate the change of the average water level within the polder and the flow direction and flow rate of the river water body in this drainage scenario. After the calculation is completed, reset the boundary conditions to simulate the next drainage scenario; Step 4: Establish a directed river network graph model under the corresponding drainage scenario. Generalize the intersection points between the river boundaries and the rivers into source points, generalize the nodes of the drainage pumping stations that need to be opened into sink points, generalize the rivers into edges, and construct a weighted adjacency matrix with the peak flow rate of the river as the weight; Step 5: Based on the maximum flow algorithm, construct a node maximum flow matrix, and further calculate the total water system connectivity of the plain polder area by integrating the water system connectivity under each drainage scenario.

2. The method for calculating the water system connectivity of plain polder areas based on network flow according to claim 1, wherein, In Step 2, the average water level inside the polder refers to the average water level at each node. Suppose there are pumping stations for drainage control inside the polder. Starting from the highest water level inside the polder, , … are the drainage control water levels from high to low respectively. There are drainage scenarios simulated. The water level drops from to , drops to … until it drops to the lowest lower limit water level . The river flow rate and direction are calculated separately for each drainage scenario. In the th drainage scenario, the drainage water depth is: In the formula, is the upper water level of the drainage scenario, is the lower water level of the drainage scenario, 0 < y ≤ m; Total drainage depth H is as follows: In the formula, is the highest water level inside the polder, is the lowest lower limit water level.

3. The calculation method of the water system connectivity of the plain polder area based on network flow according to claim 1, characterized in that, In Step 4, the intersections between the river boundaries and the river are generalized as source points, the drainage pumping station nodes to be opened are generalized as sink points, and the river is generalized as an edge to establish a river network graph model , where is the node set, represents the sink point set, represents the source point set; represents the edge set, represents that the water body flow direction is from node to node of the river. For the directed graph ; is the weighted adjacency matrix of the graph, and the edge weight value is calculated as follows: In the formula, is the river channel peak discharge.

4. A method for calculating the water system connectivity of plain polder areas based on network flow as described in claim 1, characterized in that, In step five, construct the node maximum flow matrix , denotes the maximum flow from the source point to the sink point , and is used to characterize the ability of the source point to the outlet point of the polder water system; The water system connectivity under this waterlogging drainage scenario It is calculated using the following formula: Total water system connectivity Calculated as: In the formula, is the drainage depth under the y-th drainage scenario, is the total drainage depth, is the water system connectivity under the y-th drainage scenario.

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