Flood simulation method fully utilizing topographic data

Abstract

The invention discloses a flood simulation method fully utilizing topographic data, and belongs to the technical field of hydraulic engineering flood simulation and flood control and disaster reduction. The method comprises the following steps: step 1, rasterizing topographic data; step 2, dividing an unstructured grid; step 3, analyzing a topological relation between grids and a grid space; 4, solving a water level-storage capacity relation of the unstructured grid units; 5, calculating the elevation of a grid node; and step 6, constructing a discrete format of the flood simulation model. According to the method, on the basis of the idea of'water level-storage capacity ', all high-precision topographic data can be fully utilized to completely describe the local microtopography and the water storage capacity in each cell under the condition that the calculation amount is not increased, the flood simulation precision is improved, and a scientific basis is provided for flood control and disaster reduction.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of flood simulation and flood control and disaster reduction of water conservancy projects, and particularly relates to a flood simulation method capable of fully utilizing terrain data. BACKGROUND

[0002] A two-dimensional hydrodynamic model is a mainstream method for simulating surface flood, and the main idea is to discretely solve two-dimensional shallow water equations by using numerical methods such as finite volume method and finite difference method. The mainstream flood two-dimensional simulation method is a finite volume method model using unstructured grids. The two-dimensional model using unstructured grids usually divides the research area into a plurality of unstructured grids according to a certain size, and assigns the terrain (i.e. the underlying surface elevation data) to the grid cell node (oblique bottom mode) or the grid cell center point (flat bottom mode).

[0003] Due to the application of unmanned aerial vehicle and satellite remote sensing technologies, terrain measurement has become simpler, and the obtained terrain data has higher resolution than traditional technical means, which can reach meter level or even centimeter level. For high-resolution terrain data, no matter which type of unstructured grid (triangle, quadrilateral or mixed type) is used, the data is not fully utilized, resulting in waste of data resources. According to the traditional method, the elevation is defined at the center point or the node. For sub-meter elevation data, the grid discrete size needs to be controlled at sub-meter level to fully utilize the terrain data, but the sub-meter grid size often leads to a large number of grids, thereby greatly reducing the model calculation efficiency and result data storage and display efficiency. If the grid is divided according to the conventional size (such as 10-meter quadrilateral grid, the average area of the grid is about 100 square meters), if the terrain is meter level (assuming 1 meter), there may be 121 elevation points in the range of a single grid, if the flat bottom mode is used, a single grid can set at most 1 elevation data, if the oblique bottom mode is used, a single grid can utilize at most 4 elevation data, and the micro-terrain inside the grid cell cannot be effectively reflected. Therefore, how to fully utilize the terrain data in the flood simulation method is a technical problem to be solved in the field. SUMMARY

[0004] The application aims to provide a flood simulation method capable of fully utilizing terrain data to solve the above technical problems.

[0005] To achieve the above object, the application provides the following technical scheme:

[0006] The application discloses a flood simulation method capable of fully utilizing terrain data, which comprises the following steps:

[0007] Step 1, terrain data rasterization processing: obtain high-precision terrain data of the study area, and process the terrain data into raster type data without reducing the data resolution;

[0008] Step 2, division of unstructured grid: divide the study area into a certain number of unstructured grids according to a certain size, and the grid division size is greater than the terrain data resolution, and the grid coordinate system is consistent with the terrain data coordinate system;

[0009] Step 3, analysis of spatial topological relationship between grid and grid: spatial topological analysis is performed on all grid cells and raster terrain data in the study area; specifically, based on the spatial position, analyze how many area proportions (assuming R i,j ) of each grid (assuming the number is R i ) are located in a specific grid (assuming the number is C j ), if the grid R i falls completely into the grid C j , then R i,j =1, if half of it falls into the grid, then R i,j =0.5;

[0010] Step 4, solution of water level-storage relationship of unstructured grid cell: solve the maximum possible water storage in the grid range under all characteristic water levels, and form the water level-storage relationship curve; assuming that there are n grids in the grid C j , then the characteristic water level values are the elevation values of these n grids, which are assumed to be 1、 2、...、 n ; the storage of the grid cell C j under a certain characteristic water level Z k is calculated by formula (1):

[0011] (1)

[0012] In the formula: is the elevation value of the grid numbered i, i is the grid serial number, which represents the grid falling into the grid cell C j , that is, ;

[0013] Further rewriting formula (1) as the water level-water depth relationship curve is:

[0014] (2)

[0015] (3)

[0016] In the formula: is the water level of the grid cell 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 2Fig. 1 is a schematic diagram of unstructured grid division and terrain data rasterization in Example 1;

[0041] Figure 3 Fig. 2 is a schematic diagram of grid cell and raster terrain spatial topological relationship in Example 1;

[0042] Figure 4 Fig. 3 is a schematic diagram of water level-storage / water depth relationship curve in Example 1;

[0043] Figure 5 Fig. 4 is a schematic diagram of grid node and raster terrain spatial relationship in Example 1. DETAILED DESCRIPTION

[0044] The present application discloses a flood simulation method fully utilizing terrain data, as shown in the following steps: Figure 1

[0045] Step 1, terrain data rasterization processing:

[0046] In order to construct a two-dimensional hydrodynamic model of the study area, high-precision terrain data of the study area needs to be obtained, wherein the high-precision terrain data is terrain data with a resolution of meters or higher. On the basis of not reducing the data resolution and accuracy, the obtained terrain data is processed into a grid type (assuming that the size of a single grid is w, in meters). If the terrain data itself is in a grid form, no rasterization processing is needed.

[0047] Step 2, division of unstructured grid:

[0048] Considering the requirements of calculation efficiency and simulation accuracy, the study area is discretized into a plurality of unstructured grids with a certain size; the unstructured grid can be any type of unstructured grid, including quadrilateral, triangular and mixed grids of different types; the grid division size is greater than the terrain data resolution, and the grid coordinate system is consistent with the terrain data coordinate system.

[0049] Step 3, analysis of spatial topological relationship between grid and terrain data:

[0050] Spatial topological analysis is performed on all grid cells and raster terrain data of the study area. Based on the spatial position, it is analyzed how many area proportions (assuming R i ) of each grid (assuming the number is R i,j ) are located in a specific grid (assuming the number is C j ). If the grid R i is completely located in the grid C j , then R i,j =1, and if half of it is located in the grid, then R i,j =0.5.

[0051] ​Step 4, non-structural grid cell water level-storage relationship solution:

[0052] Solve the maximum possible storage in the grid range under all characteristic water levels to form the water level-storage relationship curve. Assume that grid C j has n grids, then the characteristic water level values are the elevation values of these n grids, which are assumed to be 1, 2,..., n The storage of grid cell C k under water level Z j is calculated as follows:

[0053] (1)

[0054] In the formula: is the elevation value of grid No. i, i is the grid serial number, and only the grids falling into grid cell C j , i.e. , are considered.

[0055] For some models, direct application of the water level-storage relationship may be difficult, and the above formula can be further modified to the water level-water depth relationship curve:

[0056] (2)

[0057] (3)

[0058] In the formula: is the water depth value corresponding to grid water level , m; is the area of the grid, m 2 ; is the maximum value in the characteristic water level.

[0059] Among them, the construction of water level-storage or water level-water depth relationship only needs to be calculated once in the model preprocessing stage, combined with the relationship curve, the water depth can be interpolated according to the water level or the water level can be interpolated according to the water depth, especially when the grid water level is higher than the highest point (Z ), the water level and the water depth are in a linear relationship, only simple addition and subtraction operations are needed, which is consistent with the calculation amount of the traditional method.

[0060] Step 5, calculation of grid node elevation:

[0061] The grid node elevation is the basis for calculating the grid edge element flux. First, calculate the ratio of grid edge element size l to grid resolution w, which is assumed to be P CR , then according to P CR ​The size determination adopts the number of the nearest grids around the node, assuming M R , and finally the grid node elevation is calculated by averaging the elevations of M R grids. CR The calculation formula of P

[0062] (4)

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

[0064] According to practical experience, the value of M R may refer to Table 1:

[0065] Table 1 Value reference of M R

[0066]

[0067] Step 6, construction of the discrete format of the flood simulation model:

[0068] In theory, the method proposed in the application is based on the consideration of the elevations of three points or four nodes in the traditional inclined bottom model, and further considers all the elevation point data in the grid element, and other spatial or temporal discrete methods do not need to be specially processed, so that any finite volume method discrete format that can maintain harmony can be used with the above idea, and the following is one of them: an improved two-dimensional shallow water control equation is used, specifically as shown in formula (5) and formula (6), and a line integral solving bottom slope term is used, specifically as shown in formula (7) and formula (8), to construct the discrete format of the flood simulation model. The combination of the two can strictly guarantee the harmony of the model, and the edge element flux calculation can use HLLC, ROE and other formats.

[0069] (5)

[0070]

[0071] (6)

[0072] In the formula, t is a time variable; and x are coordinates; is water depth; and u are flow velocities in x and y directions, respectively; is gravitational acceleration; and S b represents a bottom slope term, wherein and ​the bottom slope term component in x and y direction respectively; S f represents the friction term, wherein and the friction term component in x and y direction respectively.

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

[0074] (7)

[0075] Integrating formula (7) on the grid and converting it into a line integral, we can obtain:

[0076] (8)

[0077] In the formula: is the water level; b s is the bottom elevation of the s-th edge of the grid, taking the average value of the elevations of the two end nodes of the grid edge (the node elevation is calculated by the method in step 5); l s is the length of the s-th edge of the grid; n x , n y represent the x-direction and y-direction external normal unit vectors respectively.

[0078] The model constructed according to the above discrete format and method is used for flood simulation and simulation calculation, which can fully utilize high-precision terrain data.

[0079] The flood simulation model mentioned in the application is generally applicable to flood simulation and simulation with high-precision terrain data, and the grid division size is greater than the terrain data resolution. For the same grid size and terrain data resolution, or the grid size is smaller than the terrain data resolution, the traditional simulation method is directly used to assign the grid elevation.

[0080] Example 1

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

[0082] This embodiment discloses a flood simulation method which fully utilizes terrain data, comprising the following steps:

[0083] Step 1, terrain data gridding processing: this embodiment selects 5m precision grid terrain data, i.e. the size of a single grid w=5m, without grid processing, as shown in Figure 2 .

[0084] Step 2, division of unstructured grid: considering the requirements of calculation efficiency and simulation accuracy, the unstructured grid of the study area is divided. In this embodiment, the study area with an area of 10.9km 2 is divided into 12174 unstructured grids with a grid size of 30m, as shown inFigure 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 makes full use of terrain data, characterized by, The method comprises the following steps: Step 1, terrain data rasterization processing: obtaining high-precision terrain data of a research area, the high-precision terrain data being meter-level or higher resolution terrain data, and the terrain data being processed into raster type data without reducing the data resolution; Step 2, division of non-structural grids: dividing the research area into a plurality of non-structural grids according to a certain size, the grid division size being greater than the terrain data resolution, and the grid coordinate system being consistent with the terrain data coordinate system; Step 3, analysis of the topological relationship between the grid and the mesh space: spatial topological analysis is performed on all mesh units and grid terrain data in the study area; specifically, based on the spatial position, analyze how many area proportions (assuming R i,j ) of each grid (assuming the number is R i ) are located in a specific mesh (assuming the number is C j ). If the grid R i falls completely into the mesh C j , then R i,j =1, and if half of it falls into the mesh, then R i,j =0.5; Step 4: Solve the water level-storage relationship of the unstructured grid cell: Solve the maximum possible storage in the grid range under all characteristic water levels to form the water level-storage relationship curve; assume that the grid C j There are n grids in the range, and the characteristic water level values are the elevation values of the n grids, which are assumed to be 1、 2,..., n The storage of the grid cell C k under a certain characteristic water level Z j is calculated by formula (1): （1） In the formula: is the grid elevation value for the grid number i, i is the grid number, indicating the grid falling into the grid cell C j , that is ; The formula (1) is further rewritten as a water level-water depth relationship curve: （2） （3） In the formula: is the water depth value corresponding to the water level of the grid cell , m; is the area of the grid cell, m 2 ; is the maximum value in the characteristic water level; Step 5, grid node elevation calculation: first, calculate the ratio of grid element size l and grid resolution w, assume P CR Then, according to the size of P CR , determine the number of the nearest grids around the node, assume M R , finally, take the average of M R grid elevations to calculate the grid node elevation; the calculation formula of P CR is: （4） where: l s is the length of the s-th edge of the grid; m is the total number of grid edge elements; Step 6, construction of a discrete format of the flood simulation model: adopting an improved two-dimensional shallow water control equation and a solving bottom slope term mode which is linear integration, a discrete format of the flood simulation model is constructed, and a specific formula is as follows: （5） （6） where: is a time variable; and are coordinates; is a water depth; and are respectively and directional flow velocities; is a gravitational acceleration;S b denotes a bed slope term, where and are respectively x and y directional bed slope term components;S f denotes a friction term, where and are respectively x and y directional friction term components; A source term caused by the bottom slope term is as follows: （7） Integrating the formula (7) on the grid unit and converting into linear integration, the following is obtained: （8） In the formula: is the water level; b s is the bottom elevation of the s-th edge of the grid, which is the average of the elevations of the two end nodes of the edge, and the node elevation is calculated by the method in step 5; n x , n y respectively represent the x-direction and y-direction external normal unit vectors; The flood simulation model constructed according to the above discrete format and method is used for flood simulation and calculation.

2. The flood simulation method using terrain data according to claim 1, wherein, The non-structural grid in step 2 is any type of non-structural grid, including quadrilaterals, triangles and mixed grids of different types.

3. The flood simulation method of fully utilizing terrain data according to claim 1, wherein, M in step 5 R takes the value: 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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