A flood simulation method that makes full use of terrain data

Abstract

The application discloses a flood simulation method fully utilizing terrain data, and belongs to the technical field of water conservancy engineering flood simulation and flood control and disaster mitigation, and comprises the following steps: step 1, terrain data gridding processing; step 2, non-structure grid division; step 3, analysis of spatial topological relationship between grids and meshes; step 4, solution of water level-storage capacity relationship of non-structure grid units; step 5, calculation of grid node elevations; and step 6, construction of discrete format of a flood simulation model. The method disclosed by the application can fully utilize all high-precision terrain data without increasing calculation amount, completely depict local micro-terrain and water storage capacity inside each unit cell, improve flood simulation precision, and provide a scientific basis for flood control and disaster mitigation.

Description

Technical Field

[0001] This invention belongs to the field of flood simulation and flood control and disaster reduction technology in water conservancy projects, and in particular relates to a flood simulation method that makes full use of topographic data. Background Technology

[0002] Two-dimensional hydrodynamic models are the mainstream method for simulating surface floods. The main idea is to use numerical methods such as the finite volume method and the finite difference method to discretize and solve the two-dimensional shallow water equations. Currently, the mainstream two-dimensional flood simulation method uses the unstructured mesh finite volume method model. Two-dimensional models using unstructured meshes typically divide the study area into several unstructured meshes according to a certain size, and assign topography (i.e., underlying surface elevation data) to the mesh cell nodes (sloping bottom mode) or the mesh cell center point (flat bottom mode).

[0003] The application of technologies such as drones and satellite remote sensing has simplified terrain surveying, resulting in higher resolution terrain data compared to traditional methods, reaching meter-level or even centimeter-level accuracy. However, for high-resolution terrain data, regardless of the type of unstructured grid used (triangular, quadrilateral, or a mixture of types), data utilization is insufficient, leading to wasted data resources. Traditional methods define elevation at the center point or nodes. For sub-meter elevation data, the grid size needs to be controlled at the sub-meter level to fully utilize the terrain data. However, sub-meter grid sizes often result in an excessively large number of grids, significantly reducing model computation efficiency and the efficiency of data storage and display. Using conventional grid sizes (e.g., a 10-meter quadrilateral grid with an average area of ​​approximately 100 square meters), if the terrain is meter-level (assuming 1 meter), a single grid may contain 121 elevation points. If a flat-bottom pattern is used, a single grid can only set a maximum of one elevation data point; if a sloping-bottom pattern is used, a single grid can only utilize a maximum of four elevation data points, failing to effectively reflect the micro-topography within the grid cell. Therefore, how to fully utilize topographic data in flood simulation methods is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to provide a flood simulation method that makes full use of topographic data to solve the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention discloses a flood simulation method that fully utilizes topographic data, the method comprising the following steps:

[0007] Step 1: Rasterization of terrain data: Obtain high-precision terrain data of the study area. The high-precision terrain data is meter-level or higher resolution terrain data. Without reducing the data resolution, the terrain data is processed into raster type data.

[0008] Step 2, Unstructured grid division: Divide the study area into a number of unstructured grids according to a certain size. The grid size is larger than the topographic data resolution, and the grid coordinate system is consistent with the topographic data coordinate system.

[0009] Step 3: Grid and mesh spatial topology analysis: Perform spatial topology analysis on all grid cells and grid terrain data of the study area; specifically, based on spatial location, analyze each grid cell (assuming it is numbered R). i What percentage of the area is represented (assuming it is R)? i,j Located in a specific grid (assuming the grid number is C) j If the raster R i Completely fall into grid C j Then R i,j =1, if half of them fall into the grid, then R i,j =0.5;

[0010] Step 4: Solving the water level-storage relationship in unstructured grid cells: Solve for the maximum possible water storage within the grid range under all characteristic water levels to form the water level-storage relationship curve; assuming grid C... j If there are n grids within the range, then the characteristic water level values ​​are the elevation values ​​of these n grids, assumed to be... 1. 2、...、 n The characteristic water level Z is calculated using formula (1). k Below, grid cell C j Storage capacity:

[0011] (1)

[0012] In the formula: This is the raster elevation value with grid number i, where i is the raster number, indicating that it falls within grid cell C. j The grid, i.e. ;

[0013] Formula (1) can be further rewritten as the water level-depth relationship curve:

[0014] (2)

[0015] (3)

[0016] In the formula: The water level of the grid cell is The corresponding water depth value, in meters; m is the area of ​​the grid cell. 2 ; The maximum value among the characteristic water levels;

[0017] Step 5, Calculate the elevation of grid nodes: First, calculate the ratio of the grid element size l to the grid resolution w, assuming it is P. CR Then according to P CR The size is determined by the number of the nearest grid cells around the node, let's say M. R Finally, M was adopted. R The average elevation of each grid cell is used to calculate the elevation of each grid node; P CR The calculation formula is:

[0018] (4)

[0019] In the formula: l s The length of the s-th edge of the grid; m is the total number of grid edge elements;

[0020] Step 6: Construction of the Discrete Scheme for the Flood Simulation Model: An improved two-dimensional shallow water control equation is adopted, and the bottom slope term is solved using line integrals to construct the discrete scheme for the flood simulation model. The specific formula is as follows:

[0021] (5)

[0022]

[0023] (6)

[0024] In the formula: It is a time variable; and Coordinates; For water depth; and They are respectively and Flow velocity in the direction; S is the acceleration due to gravity. b Indicates the bottom slope term, where and The bottom slope components are in the x and y directions, respectively; S f Represents the friction term, where and These are the friction components in the x and y directions, respectively;

[0025] The source terms caused by the bottom slope term are as follows:

[0026] (7)

[0027] Integrating equation (7) over the grid cells and converting it to a line integral, we get:

[0028] (8)

[0029] In the formula: Water level; b s To find the bottom elevation of the s-th edge of the grid, take the average of the elevations of the nodes at both ends of the edge. The node elevations are calculated using the method described in step 5; n x n y These represent the outward normal unit vectors in the x and y directions, respectively;

[0030] The flood simulation model constructed based on the above discrete format and method is used to perform flood simulation calculations.

[0031] Furthermore, the unstructured mesh mentioned in step 2 can be any type of unstructured mesh, including quadrilaterals, triangles, and mixed meshes of different types.

[0032] Furthermore, in step 5, M R The value can be:

[0033] When P CR >10, M R =21;

[0034] When 5 < P CR ≤10, M R =9;

[0035] When 2 < P CR ≤5, M R =4;

[0036] When 1 < P CR ≤2, M R =1.

[0037] The beneficial effects of this invention are: the flood simulation method that makes full use of topographic data described in this invention, based on the concept of "water level-storage capacity", can make full use of all high-precision topographic data without increasing the amount of calculation, fully depict the local micro-topography and water storage capacity inside each cell, improve the accuracy of flood simulation, and provide a scientific basis for flood prevention and disaster reduction.

[0038] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the method flow described in this invention;

[0040] Figure 2This is a schematic diagram of unstructured grid subdivision and terrain data rasterization in Example 1;

[0041] Figure 3 This is a schematic diagram of the spatial topology of the grid cells and grid terrain in Example 1;

[0042] Figure 4 This is a schematic diagram of the water level-storage / water depth relationship curve in Example 1;

[0043] Figure 5 This is a schematic diagram of the spatial relationship between grid nodes and grid terrain in Example 1. Detailed Implementation

[0044] This invention discloses a flood simulation method that fully utilizes topographic data, such as... Figure 1 As shown, the method includes the following steps:

[0045] Step 1: Rasterization of terrain data:

[0046] To construct a two-dimensional hydrodynamic model of the study area, high-precision topographic data of the area is required first, which should be meter-level or higher resolution. Without reducing data resolution and accuracy, the acquired topographic data is processed into raster type (assuming a single raster size of w, in meters). If the topographic data is already in raster format, rasterization is unnecessary.

[0047] Step 2, Generating unstructured meshes:

[0048] Taking into account both computational efficiency and simulation accuracy requirements, the study area is discretized into a number of unstructured grids of a certain size; the unstructured grids can be of any type, including quadrilaterals, triangles, and mixed grids of different types; the grid size is larger than the resolution of the terrain data, and the grid coordinate system is consistent with the terrain data coordinate system.

[0049] Step 3: Analyze the spatial topology of the raster and mesh:

[0050] Spatial topology analysis was performed on all grid cells and raster terrain data of the study area. Based on spatial location, each raster (assuming its number is R) was analyzed. i What percentage of the area is represented (assuming it is R)? i,j Located in a specific grid (assuming the grid number is C) j If the raster R i Completely fall into grid C j Then R i,j =1, if half of them fall into the grid, then R i,j =0.5.

[0051] Step 4: Solving for the water level-storage relationship in unstructured grid cells:

[0052] Solve for the maximum possible water storage within the grid range under all characteristic water levels to form a water level-storage relationship curve. Assume grid C. j If there are n grids within the range, then the characteristic water level values ​​are the elevation values ​​of these n grids, assumed to be... 1. 2、...、 n The characteristic water level Z is calculated using the following formula. k Below, grid cell C j storage capacity for:

[0053] (1)

[0054] In the formula: This is the raster elevation value with grid number i, where i is the raster number, indicating that only the value falling within grid cell C needs to be considered. j The grid, i.e. .

[0055] For some models, directly applying the water level-storage relationship may be difficult. The above equation can be further rewritten as a water level-depth relationship curve:

[0056] (2)

[0057] (3)

[0058] In the formula: The grid water level is The corresponding water depth value, in meters; m is the area of ​​the grid. 2 ; This represents the maximum value among the characteristic water levels.

[0059] The construction of the water level-storage or water level-depth relationship only needs to be calculated once in the model preprocessing stage. Based on this relationship curve, the water depth can be interpolated according to the water level or vice versa, especially when the grid water level is higher than the highest point. The water level and water depth have a linear relationship, requiring only simple addition and subtraction operations, with the same amount of calculation as traditional methods.

[0060] Step 5: Calculate the elevation of grid nodes:

[0061] Grid node elevation is fundamental to calculating grid element flux. First, the ratio of grid element size l to raster resolution w is calculated, assuming it to be P. CR Then according to P CRThe size is determined by the number of the nearest grid cells around the node, let's say M. R Finally, M was adopted. R The average elevation of each raster is used to calculate the elevation of each grid node. CR The calculation formula is:

[0062] (4)

[0063] In the formula: l s is the length of the s-th edge of the grid; m is the total number of grid edge elements.

[0064] Based on practical experience, M R The values ​​can be found in Table 1:

[0065] Table 1 M R Value Reference

[0066]

[0067] Step 6: Constructing the Discrete Format of the Flood Simulation Model:

[0068] Theoretically, the method proposed in this invention, based on the traditional sloping bottom model which considers the elevations of three or four nodes, further considers the elevation data of all elevation points within the grid cell. Other spatial or temporal discretization methods do not require special processing. Therefore, any finite volume method discretization scheme that can maintain harmony can use the above approach. One such scheme is as follows: an improved two-dimensional shallow water control equation is adopted, specifically Equations (5) and (6), and the bottom slope term is solved by line integrals, specifically Equations (7) and (8), to construct the discretization scheme of the flood simulation model. The combination of the two can strictly guarantee the harmony of the model. HLLC, ROE, and other formats can be used for edge element flux calculation.

[0069] (5)

[0070]

[0071] (6)

[0072] In the formula: It is a time variable; and Coordinates; For water depth; and They are respectively and Flow velocity in the direction; S is the acceleration due to gravity. b Indicates the bottom slope term, where and The bottom slope components are in the x and y directions, respectively; S f Represents the friction term, where and These are the friction components in the x and y directions, respectively.

[0073] The source terms caused by the bottom slope term are as follows:

[0074] (7)

[0075] Integrating equation (7) on the grid and converting it to a line integral, we get:

[0076] (8)

[0077] In the formula: Water level; b s For the bottom elevation of the s-th edge of the grid, take the average of the elevations of the nodes at both ends of the edge (the node elevations are calculated using the method in step 5); s n is the length of the s-th edge of the grid; x n y These represent the outward normal unit vectors in the x and y directions, respectively.

[0078] Using the model constructed based on the above discrete format and method to perform flood simulation calculations can make full use of high-precision terrain data.

[0079] The flood simulation model mentioned in this invention is generally applicable to flood simulation with high-precision terrain data, and the grid size is larger than the terrain data resolution. For grid sizes that are the same as the terrain data resolution, or grid sizes that are smaller than the terrain data resolution, the traditional simulation method can be used to assign values ​​to the grid elevation directly.

[0080] Example 1

[0081] This embodiment is an application example of the above method.

[0082] This embodiment discloses a flood simulation method that fully utilizes topographic data, including the following steps:

[0083] Step 1: Rasterization of Terrain Data: In this embodiment, 5m resolution raster terrain data is selected, i.e., a single raster size w=5m. No rasterization processing is required. Figure 2 As shown.

[0084] Step 2: Unstructured Mesh Generation: Considering both computational efficiency and simulation accuracy requirements, an unstructured mesh is generated for the study area. In this embodiment, the study area is 10.9 km². 2 A 30-meter grid size was used, dividing the study area into 12,174 unstructured grids, such as... Figure 2 As shown, the coordinate system for the grid file and terrain data is CGCS2000_3_Degree_GK_CM_117E.

[0085] Step 3: Raster and Grid Spatial Topology Analysis: Perform spatial topology analysis on all grid cells and raster terrain data in the study area to... Figure 3 Taking the medium grid C1 as an example, there are a total of 49 associated grids (C). 1,1 -C 1,49 ), corresponding area ratio R 1,j As shown in Table 2.

[0086] Table 2 Statistical Table of Calculation Results

[0087]

[0088]

[0089] Step 4: Solving the water level-storage relationship in unstructured grid cells: Calculate the corresponding storage of all associated grid cells within the grid at the characteristic water level. Taking a characteristic water level of 20m as an example, grid C... 1,1 Elevation 21.6m , ; Grid C 1,15 Elevation 18.0m , The storage capacity calculation results for each grid cell are detailed in Table 2. Summing the storage capacity results for each grid cell yields the grid storage capacity at the characteristic water level:

[0090] .

[0091] The calculated water level-storage relationship is converted into a water level-depth relationship using formulas (2) and (3). In this embodiment... Substitute into formula (3) to calculate the corresponding When the characteristic water level is 20m-24m, , When the characteristic water level is 25m, , .

[0092] Among them, the water level-water depth relationship or the water level-storage relationship (such as...) Figure 4 The construction of (as shown) only needs to be completed once during the model preprocessing stage. Subsequent calculations can be based on this relationship curve to determine relevant parameters as needed. When the water level in a cell is below the highest point ( The calculation is performed using curve interpolation, as shown in this embodiment. The corresponding water level at that time When the water level in a cell is higher than the highest point ( The calculation only requires simple addition and subtraction of parameters, as in this embodiment. The corresponding water level at that time .

[0093] Step 5, Calculate the elevation of grid nodes: Figure 5 Taking node N1 as an example, the length of each mesh edge element is 30m, and the grid resolution is 5m. Therefore According to the M provided in

[0018] R Experience value statistics table Take the 21 nearest cells to the node (e.g.) Figure 5 The average elevation of node N1 is taken as the elevation value of node N1, as shown in the figure. .

[0094] Step 6: Construction of the discrete format of the flood simulation model: Calculate the water depth and node elevation of all grids according to the above method, substitute them into formulas (5) to (8), adopt the improved two-dimensional shallow water control equation, and use the method of solving the bottom slope term by line integral to construct the discrete format of the flood simulation model and carry out flood simulation calculation.

[0095] Finally, it should be noted that the above description is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred arrangement, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A flood simulation method that fully utilizes topographic data, characterized in that, The method includes the following steps: Step 1: Rasterization of terrain data: Obtain high-precision terrain data of the study area. The high-precision terrain data is meter-level or higher resolution terrain data. Without reducing the data resolution, the terrain data is processed into raster type data. Step 2, Unstructured grid division: Divide the study area into a number of unstructured grids according to a certain size. The grid size is larger than the topographic data resolution, and the grid coordinate system is consistent with the topographic data coordinate system. Step 3: Grid and Mesh Spatial Topology Analysis: Perform spatial topology analysis on all grid cells and grid terrain data of the study area; specifically, based on spatial location, analyze the proportion of each grid's area located within a specific grid. If grid R... i Completely fall into grid C j Then the area ratio R i,j =1, if half of the area falls into the grid, then the area ratio R is 1. i,j =0.5; Step 4: Solving the water level-storage relationship in unstructured grid cells: Solve for the maximum possible water storage within the grid range under all characteristic water levels to form the water level-storage relationship curve; Grid C j If there are n grids within the range, then the characteristic water level values ​​are the elevation values ​​of these n grids, respectively.

1. 2、...、 n The characteristic water level Z is calculated using formula (1). k Below, grid cell C j Storage capacity: （1） In the formula: This is the raster elevation value with grid number i, where i is the raster number, indicating that it falls within grid cell C. j The grid, i.e. ; Formula (1) can be further rewritten as the water level-depth relationship curve: （2） （3） In the formula: The water level of the grid cell is The corresponding water depth value, in meters; m is the area of ​​the grid cell. 2 ; The maximum value among the characteristic water levels; Step 5, Calculate the elevation of grid nodes: First, calculate the ratio of the grid element size l to the grid resolution w, assuming it is P. CR Then according to P CR The size is determined by the number of the nearest grid cells around the node, let's say M. R Finally, M was adopted. R The average elevation of each grid cell is used to calculate the elevation of each grid node; P CR The calculation formula is: （4） In the formula: l s The length of the s-th edge of the grid; m is the total number of grid edge elements; Step 6: Construction of the Discrete Scheme for the Flood Simulation Model: An improved two-dimensional shallow water control equation is adopted, and the bottom slope term is solved using line integrals to construct the discrete scheme for the flood simulation model. The specific formula is as follows: （5） （6） In the formula: It is a time variable; and Coordinates; For water depth; and They are respectively and Flow velocity in the direction; S is the acceleration due to gravity. b Indicates the bottom slope term, where and The bottom slope components are in the x and y directions, respectively; S f Represents the friction term, where and These are the friction components in the x and y directions, respectively; The source terms caused by the bottom slope term are as follows: （7） Integrating equation (7) over the grid cells and converting it to a line integral, we get: （8） In the formula: Water level; b s To find the bottom elevation of the s-th edge of the grid, take the average of the elevations of the nodes at both ends of the edge. The node elevations are calculated using the method described in step 5; n x n y These represent the outward normal unit vectors in the x and y directions, respectively; The flood simulation model constructed based on the above discrete format and method is used to perform flood simulation calculations.

2. The flood simulation method that fully utilizes topographic data according to claim 1, characterized in that, The unstructured mesh mentioned in step 2 can be any type of unstructured mesh, including quadrilaterals, triangles, and mixed meshes of different types.

3. The flood simulation method that fully utilizes topographic data according to claim 1, characterized in that, In step 5, M R The value can be: When P CR >10, M R =21; When 5 < P CR ≤10, M R =9; When 2 < P CR ≤5, M R =4; When 1 < P CR ≤2, M R =1.

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