Calculation method for balance profile form of beach with multiple sand dams

Abstract

The invention relates to the field of coastal topographic survey and coastal zone protection utilization and management, in particular to a calculation method of a multi-sand-dam beach balance profile form. Comprising the following steps: S1, constructing a standardized profile matrix; s2, variational mode decomposition is carried out on the standardized profile matrix constructed in the step S1; s3, describing a baseline form of the multi-sand-dam beach section in a power function form; s4, describing a beach shoulder-groove-sand dam curve form of the multi-sand-dam beach profile in a trigonometric function form; and S5, adding the trigonometric functions in the step S3 and the step S4 to obtain the multi-sand-dam beach balance profile morphological function. The calculation method for the balance profile form of the multi-sand-dam beach provided by the invention is applied to the multi-sand-dam beach with a relatively stable near-shore hydrodynamic environment, the beach terrain is estimated under the condition of data scarcity, and a powerful tool is provided for the fields of protection, utilization and management of a coastal zone; the expression form is simple and easy to understand, convenient to apply and wide in coverage.

Description

Technical Field

[0001] This invention relates to the fields of coastal topographic surveying, coastal zone protection, utilization and management, and more specifically to a method for calculating the equilibrium profile morphology of multi-sandbar beaches. Background Technology

[0002] The foundation of coastal zone protection, utilization and management lies in understanding local nearshore hydrodynamics and morphological dynamics. Currently, manual handheld RTK-GPS point-by-point elevation measurement from the shore to the sea is still the main way to obtain measured water depth or topographic data of the intertidal zone. Therefore, there is a general lack of intertidal topographic or water depth data. Estimating based on beach equilibrium profiles is a way to supplement relevant information.

[0003] Sandy coasts commonly exhibit intertidal or subtidal sandbars under wave action (especially swells). Despite seasonal variations and migration, these sandbars generally maintain a stable morphology. Ignoring sandbars can lead to significant deviations in predictions of nearshore hydrodynamics (such as wave breaking and coastal currents). Therefore, the sandbar system is a fundamental element that must be considered when extracting equilibrium profiles of multi-sandbar beaches.

[0004] Currently available beach equilibrium profile models are mainly divided into three categories: (1) Traditional model, namely a concave profile with monotonically decreasing elevation from the shore to the sea, has expressions in the form of power function, exponential function, logarithmic function and their composite function, but none of them can reflect the ubiquitous sandbar landform; (2) The equilibrium profile formula for a beach with a single sandbar is expressed by a piecewise function, and the morphology of each segment is described by power function, exponential function, hyperbolic function and their composite function; (3) The beach equilibrium profile with sandbar system only has the composite function expression composed of trigonometric and power functions proposed by Leont'ev in his paper, but only the underwater part is given and the shape of the beach shoulder is not included. Summary of the Invention

[0005] This invention addresses the problems mentioned in the background art by providing a method for calculating the equilibrium profile morphology of multi-sandbar beaches. By analyzing limited profile measurement data, this invention provides a functional expression for the equilibrium profile morphology of multi-sandbar beaches, thus offering effective information on beach topography.

[0006] The technical solution adopted by this invention to solve this problem is: a method for calculating the equilibrium profile morphology of multi-sandbar beaches, specifically including the following steps: Step S1: Construct a standardized profile matrix based on the multi-sandbar beach profile measurement data; Step S2: Perform variational mode decomposition on the standardized profile matrix constructed in step S1 to obtain the baseline matrix and the beach shoulder-ditch-sandbar curve matrix of the multi-sandbar beach profile. Step S3: Based on the baseline matrix of Step S2, describe the baseline morphology of the multi-sandbar beach profile in the form of a power function. Step S4: Based on the beach shoulder-sandbar-ditch curve matrix from Step S2, describe the beach shoulder-ditch-sandbar curve morphology of the multi-sandbar beach profile in trigonometric function form. Step S5: The power function of the baseline morphology in Step S3 is added to the trigonometric function of the beach shoulder-ditch-sandbar curve morphology in Step S4, which is the equilibrium profile morphology function of the multi-sandbar beach.

[0007] Compared with the prior art, the present invention has the following beneficial effects: 1. The calculation method for the equilibrium profile morphology of multi-sandbar beaches proposed in this invention is applied to multi-sandbar beaches with relatively stable nearshore hydrodynamic environment. Based on limited profile measurement data, the functional expression of its equilibrium profile morphology can be given. The beach topography can be estimated in the case of scarce data, providing a powerful tool for the field of coastal zone protection, utilization and management. 2. The expression is simple and easy to understand, convenient to use, and can reflect the common sandbar landforms, providing a more comprehensive description; 3. Beach balance profiles with sandbar systems not only depict the underwater portion but also include the morphology of the beach shoulders, providing broad coverage. Attached Figure Description

[0008] To more clearly illustrate the technical solution and specific embodiments of the present invention, the following description is provided with reference to the accompanying drawings: Figure 1 Flowchart of the calculation method of this invention Figure 2 The original beach profile measurement data of the embodiment and the standardized interpolation results of its application step S1 Figure 3 The beach normalized profile matrix of the embodiment is applied to the calculation results of variational mode decomposition in step S2. Figure 4 Example: Calculation process and results of the baseline morphology function for the fitted profile in step S3 of the beach application. Figure 5 Example: Beach application step S4 - Calculation process and results of the beach shoulder-ditch-sandbar curve morphology function fitting profile. Figure 6 Example: Beach application step S5 calculates the equilibrium profile morphology function and evaluates its representativeness. Detailed Implementation

[0009] The invention will now be described in detail with reference to the accompanying drawings.

[0010] The method for calculating the equilibrium profile morphology of multi-sandbar beaches disclosed in this invention specifically includes the following steps: Step S1: Construct a standardized profile matrix based on the multi-sandbar beach profile measurement data; Step S2: Perform variational mode decomposition on the standardized profile matrix constructed in step S1 to obtain the baseline matrix and the beach shoulder-ditch-sandbar curve matrix of the multi-sandbar beach profile. Step S3: Based on the baseline matrix of Step S2, describe the baseline morphology of the multi-sandbar beach profile in the form of a power function. Step S4: Based on the beach shoulder-sandbar-ditch curve matrix from Step S2, describe the beach shoulder-ditch-sandbar curve morphology of the multi-sandbar beach profile in trigonometric function form. Step S5: The power function of the baseline morphology in Step S3 is added to the trigonometric function of the beach shoulder-ditch-sandbar curve morphology in Step S4, which is the equilibrium profile morphology function of the multi-sandbar beach.

[0011] As a preferred approach, in step S1, regarding the profile measurement of the beach with multiple sandbars, considering a relatively stable shoreline without artificial sand replenishment or coastal engineering construction, a fixed shoreline base and the same elevation datum are used to perform n measurements of the beach profile, serving as the basis for constructing a standardized profile matrix. The method for constructing the standardized profile matrix is ​​as follows: First, establish a coordinate system. The horizontal coordinate axis is the x-axis, with the shore base station as the 0 point and the seaward direction as positive; the vertical coordinate axis is the z-axis, with the measurement elevation datum as the 0 point and the upward direction as positive; let i represent the number of measurements (i = 1,2,…,n), then the i-th measurement yields a set of profile data. The x-value represents the distance from the shore (starting from the shoreline). The endpoint of the measurement is the maximum value. (Unit: m), data z is the corresponding elevation value (unit: m), subscript k is the data point sequence number, and the maximum value of k is the total number of data points in the i-th measurement; Secondly, create a standardized X Mesh accuracy is x has m grids and m+1 nodes. The first node of the grid is taken as the location of the shore base. The nearest measurement endpoint from the shore is selected from the 1st to nth profile measurement data, i.e., the array. minimum value Based on the position of the last node in the computational grid, i.e. x, then forms a grid matrix X;

[0012] Finally, based on the grid matrix X Profile data were obtained from each measurement. Interpolation calculations are performed to obtain standardized profile elevation data corresponding to grid points X.

[0013] The elevation data after interpolation of all n measured profile data are arranged in order to form a standardized profile matrix Z for the multi-sandbar beach.

[0014]

[0015] As a preferred option, grid accuracy The value of x depends on the dimensions (depth, width, height, and width) of the beach trenches and sandbars. The principle is to obtain standardized profile data for beaches with multiple sandbars after interpolation, which can accurately describe the morphological characteristics of the smallest trenches and sandbars. Typically... Applicable to most beach profiles.

[0016] As a preferred option, in step S2, variational mode decomposition is performed on the standardized profile matrix of the multi-sandbar beach, wherein the variational mode decomposition adopts the Variational Mode Decomposition (VMD) method proposed by Konstantin Dragomiretskiy and Dominique Zosso in their paper. Variational mode decomposition of the standardized profile matrix refers to performing variational mode decomposition on each column of the data matrix Z with the same settings, including: The penalty factor alpha = m+1, which is the number of grid nodes; Noise tolerance tau=0; The number of modes in the decomposition is K=4; DC component DC=0; Initialize the center frequency init = 0; Convergence criterion tolerance tol = 1e-6; This yields the data matrix. The decomposition result is Where zmj represents the elevation component of mode j, and according to VMD theory, the standardized profile elevation data It equals the sum of all modal elevation components decomposed, i.e. .

[0017]

[0018] The first modal elevation component from each column of the standardized profile data matrix Z is used to form matrix A, matrix B, matrix C, and matrix D, respectively.

[0019]

[0020]

[0021]

[0022] Thus, we obtain: Data matrix A is the baseline matrix of the multi-sandbar beach profile; data matrix B is the beach shoulder-ditch-sandbar curve matrix; data matrix C is the short-term elevation change of the multi-sandbar beach profile; and data matrix D is the elevation deviation at the level of profile measurement error.

[0023] As a preferred option, in step S3, the power function form used is: , Calculate the average value of each row of the baseline matrix A to obtain the average baseline matrix.

[0024]

[0025] Using the grid matrix X as the variable, the average baseline matrix By fitting the dependent variable, the values ​​of coefficients a, b, and c are obtained, which are the baseline morphology functions of the multi-sandbar beach profile.

[0026] As a preferred option, in step S4, the trigonometric function form used is: , Calculate the average value of each row in the beach-ditch-sandbar curve matrix B to obtain the average beach-ditch-sandbar curve matrix.

[0027]

[0028] Using the grid matrix X as the variable, the average beach shoulder-ditch-sandbar curve matrix By fitting the dependent variable, the values ​​of coefficients p, q, d, e, f, g, and h are obtained, which are the beach shoulder-ditch-sandbar curve morphology functions of the multi-sandbar beach profile.

[0029] As a preferred option, in step S5, the equilibrium profile morphology function of the multi-sandbar beach is:

[0030] The values ​​of each coefficient in the formula are based on the matrix. and The results are obtained in steps S3 and S4, respectively.

[0031] The present invention will now be described in detail with reference to specific embodiments.

[0032] The implementation process of the calculation method of this invention is as follows: Figure 1 As shown, the method requires at least one beach profile measurement data. The corresponding multi-sandbar beach equilibrium profile morphology function expression is obtained by calculating in sequence according to the steps of this invention.

[0033] Taking Qinhuangdao Aka Beach as an example of the present invention, in this embodiment, step S1 is implemented as follows: Figure 2 As shown, the original measurement data (unit: meters) of the four profiles collected in spring, summer, autumn, and winter are known, i.e., the number of measurements. , Figure 2 The middle circles represent the data points for these measurements. The original measurement data for the 1st to 4th measurements are as follows: First measurement (spring measurement, 59 data points)

[0034] Second measurement (summer measurement, 199 data points)

[0035] Third measurement (autumn measurement, 193 data points)

[0036] Fourth measurement (winter measurement, 200 data points)

[0037] Create a standardized X-mesh with a precision of [precision value missing]. The grid starts at the shore base location. Furthermore, the measurement endpoint closest to the shore in the four profile measurement data... ,according to x, find If grid X has 1991 cells and 1992 nodes, then it forms a grid matrix X;

[0038] Based on the grid matrix X, interpolation calculations are performed on the profile data obtained from the 1st to 4th measurements. The interpolation results are arranged from left to right to form the standardized beach profile matrix Z corresponding to grid X. A graph is plotted with grid X as the x-axis and the columns of matrix Z from left to right as the y-axis. Figure 2 The solid black lines in (a), (b), (c), and (d);

[0039] In this embodiment, step S2 is performed as follows: Figure 3 As shown, the variational mode decomposition is the Variational Mode Decomposition (VMD) method proposed by Konstantin Dragomiretskiy and Dominique Zosso. The authors have publicly released the VMD program in MATLAB and Python versions. Step S2 of this invention directly uses this program for calculation.

[0040] Step S2, performing variational mode decomposition on the standardized profile matrix Z, refers to performing variational mode decomposition on each column of the data matrix Z with the same settings, including: The penalty factor (also known as the balance parameter) alpha = 1992, which is the number of grid nodes; Noise tolerance tau=0; The number of modes in the decomposition is K=4; DC component DC=0; Initialize the center frequency init = 0; The convergence criterion tolerance is tol = 1e-6.

[0041] The first column of the normalized profile matrix Z For example (the interpolation results from the first spring measurement), the decomposition results are as follows: ,matrix The columns from left to right represent the elevation components of mode 1, mode 2, mode 3, and mode 4, as follows: Figure 3 The first row contains (a1), (b1), (c1), and (d1). Figure 3 Rows 2, 3, and 4 correspond to columns 2, 3, and 4 of matrix Z (i.e., ... , , The decomposition results of ).

[0042]

[0043] According to VMD theory, the sum of the elevation components of the four modes equals the profile elevation, i.e., the elevation of the first row and first column of Z ( The first data point equals The sum of the data in the first row can be similarly extended to the second, third, and fourth columns of Z.

[0044] The first modal elevation component from each column of the standardized beach profile data matrix Z forms matrix A, matrix B, matrix C, and matrix D.

[0045]

[0046]

[0047]

[0048] Plotting a graph with grid X as the x-axis and each column of matrix A from left to right as the y-axis, is equivalent to... Figure 3 The first column (a1)-(a4) contains black solid lines; plot the graph with grid X as the x-axis and each column of matrix B from left to right as the y-axis, which is... Figure 3 The black solid lines in column 2 (b1)-(b4); plot the graph with grid X as the x-axis and each column of matrix C from left to right as the y-axis, that is... Figure 3 The black solid lines in column 3 (c1)-(c4); plot the graph with grid X as the x-axis and each column of matrix D from left to right as the y-axis, that is... Figure 3 The solid black lines in column 4 (d1)-(d4).

[0049] In a physical sense, data matrix A represents the baseline of a multi-bar beach profile, data matrix B represents the shoulder-ditch-bar curve, data matrix C represents the short-term elevation changes on the profile, and data matrix D corresponds to the elevation deviation at the level of profile measurement error. According to VMD theory, the beach profile Z is the sum of the four sets of elevation components A, B, C, and D. Therefore, the baseline plus the shoulder-ditch-bar curve constitutes the equilibrium profile of a multi-bar beach. Consequently, A is called the baseline matrix, and B is called the shoulder-ditch-bar curve matrix.

[0050] Step S3 as follows Figure 4 As shown, based on the first mode elevation component matrix A obtained in step S2, in Figure 4 In (a), the scattered points represented by circles, plus signs, triangles, and crosses (corresponding to columns 1-4 of A, respectively) are used to calculate the average value of each row of the baseline matrix A, thus obtaining the average baseline matrix.

[0051]

[0052] With grid X as the x-axis, Plotting the vertical axis is equivalent to... Figure 4 The black solid lines in (a) and (b) use power functions. , The black solid line is fitted, and the fitting result is: , , Coefficient of determination Root mean square error m, the fitted curve is Figure 4(b) Red dashed line.

[0053] In this embodiment, step S4 is as follows: Figure 5 As shown, based on the second mode elevation component matrix B obtained in step S2, in Figure 5 In (a), the scattered points represented by circles, plus signs, triangles, and crosses (corresponding to columns 1-4 of B, respectively) are used to calculate the average value of each row in the beach-ditch-sandbar curve matrix B, thus obtaining the average beach-ditch-sandbar curve matrix.

[0054]

[0055] With grid X as the x-axis, Plotting the vertical axis is equivalent to... Figure 5 The black solid lines in (a), (b), and (d) show that the curve exhibits significant fluctuations, with both amplitude and frequency gradually decreasing along the x-direction. Therefore, the following trigonometric functions are used. , The black solid line is fitted as follows: First, extract the points across 0 on the curve, such as... Figure 5 (b) The red circles and triangles; secondly, the valleys and peaks of the curve can be easily found by crossing the zero point, such as Figure 5 (b) Black rice flowers; Then, the amplitude of the curve is calculated based on the valley and peak points, i.e. Figure 5 (b) shows the elevation difference between two adjacent valleys and peaks, but this amplitude only represents the fluctuation characteristics of this small distance between two adjacent valleys and peaks. Therefore, the midpoint between two adjacent valleys and peaks is taken as the x-axis. Figure 5 (b) can be obtained from the 9 valleys and peaks. Figure 5 (c) uses 8 amplitude points to fit the linear part of the trigonometric function. The fitting result is , ; Finally, the obtained p and q values ​​are substituted into the selected trigonometric function to fit the black solid line, and the fitting result is: , , , , Coefficient of determination Root mean square error m, the fitted curve is Figure 5 (d) The red dashed line.

[0056] It is important to note during the fitting process that fluctuations with an amplitude less than 0.10m are insufficient to be considered as trenches or sandbars. Therefore, the 7th zero-crossing point was selected as the cutoff point. Figure 5 (b) The red triangle at the cutoff point represents a region with a significant beach-ditch-sandbar curve towards the shore, and a straight region towards the sea. Therefore... Figure 5 (d) The red dashed line exists only on the shore side of the cutoff point.

[0057] In this embodiment, step S5 is as follows: Figure 6 As shown, based on the function fitting results obtained in steps S3 and S4, and the cutoff point positions extracted in step S4 ( Figure 6 (a) The triangle), at the cutoff point towards the shore (nearshore part), according to VMD theory, the fitting functions of steps S3 and S4 are added together to obtain the equilibrium profile function expression. , correspond Figure 6 (a) The solid red line from the central triangle point to the shore; On the seaward side (outer sea portion) of the cutoff point, the equilibrium profile function expression is the baseline function of step S3. , correspond Figure 6 (a) The black solid line on the seaward side of the central triangle point; The above is the expression for the equilibrium profile function of the multi-sandbar beach calculated by this invention.

[0058] Further analysis revealed the correlation between the balanced profile of this invention and the four measurement profiles in the example, such as... Figure 6 As shown in (b), the range of determination coefficients between the equilibrium profile calculated by this invention and the four measurements. Root mean square error range m indicates that the equilibrium profile calculated by this invention is highly representative of the local sandbar beaches.

Claims

1. A method for calculating the equilibrium profile morphology of a multi-sandbar beach, characterized in that: Specifically, the following steps are included: Step S1: Construct a standardized profile matrix based on the multi-sandbar beach profile measurement data; Step S2: Perform variational mode decomposition on the standardized profile matrix constructed in step S1 to obtain the baseline matrix and the beach shoulder-ditch-sandbar curve matrix of the multi-sandbar beach profile. Step S3: Based on the baseline matrix of Step S2, describe the baseline morphology of the multi-sandbar beach profile in the form of a power function. Step S4: Based on the beach shoulder-sandbar-ditch curve matrix from Step S2, describe the beach shoulder-ditch-sandbar curve morphology of the multi-sandbar beach profile in trigonometric function form. Step S5: The power function of the baseline morphology in Step S3 is added to the trigonometric function of the beach shoulder-ditch-sandbar curve morphology in Step S4, which is the equilibrium profile morphology function of the multi-sandbar beach.

2. The method for calculating the equilibrium profile morphology of multi-sandbar beaches according to claim 1, characterized in that: In step S1, the profile measurement of the beach with multiple sandbars is carried out n times using a fixed shore base station and the same elevation datum, which serves as the basis for constructing a standardized profile matrix. The method for constructing the standardized profile matrix is ​​as follows: First, establish a coordinate system. The horizontal coordinate axis is the x-axis, with the shore base station as the 0 point and the seaward direction as positive; the vertical coordinate axis is the z-axis, with the measurement elevation datum as the 0 point and the upward direction as positive; let i represent the number of measurements (i = 1,2,…,n), then the i-th measurement yields a set of profile data. The x-value represents the distance from the shore (starting from the shoreline). The endpoint of the measurement is the maximum value. (Unit: m), data z is the corresponding elevation value (unit: m), subscript k is the data point sequence number, and the maximum value of k is the total number of data points in the i-th measurement; Secondly, create a standardized X Mesh accuracy is Let x be a grid with m cells and m+1 nodes. The first node of the grid is taken as the location of the shoreline. The position of the last node of the grid is calculated based on the nearest measurement endpoint from the shore in the 1st to nth profile measurement data. x, then forms a grid matrix X; ， Finally, based on the grid matrix X Profile data were obtained from each measurement. Interpolation calculations are performed to obtain standardized profile elevation data corresponding to grid points X. ， The elevation data from all n interpolated measurement profiles are arranged sequentially to form a standardized profile matrix Z for the multi-sandbar beach. 。 3. The method for calculating the equilibrium profile morphology of multi-sandbar beaches according to claim 2, characterized in that: Mesh accuracy The value of x depends on the shape and size of the beach trenches and sandbars. The principle is to obtain standardized profile data of beaches with multiple sandbars after interpolation.

4. The method for calculating the equilibrium profile morphology of a multi-sandbar beach according to claim 1, characterized in that: In step S2, variational mode decomposition is performed on the standardized profile matrix of the multi-sandbar beach, where the variational mode decomposition adopts the VMD method. Variational mode decomposition of the standardized profile matrix refers to performing variational mode decomposition on each column of the data matrix Z with the same settings, including: The penalty factor alpha = m+1, which is the number of grid nodes; Noise tolerance tau=0; The number of modes in the decomposition is K=4; DC component DC=0; Initialize the center frequency init = 0; Convergence criterion tolerance tol = 1e-6; This yields the data matrix. The decomposition result is Where zmj represents the elevation component of mode j, and according to VMD theory, the standardized profile elevation data It equals the sum of all modal elevation components decomposed, i.e. , ， The first mode elevation component from each column of the standardized profile data matrix Z is used to form matrix A, and the second mode elevation component is used to form matrix B. ， ， Thus, data matrix A is the baseline matrix of the multi-sandbar beach profile, and data matrix B is the beach shoulder-ditch-sandbar curve matrix.

5. The method for calculating the equilibrium profile morphology of a multi-sandbar beach according to claim 4, characterized in that: In step S3, the power function form used is: ， Calculate the average value of each row of the baseline matrix A to obtain the average baseline matrix. , ， Using the grid matrix X as the variable, the average baseline matrix By fitting the dependent variable, the values ​​of coefficients a, b, and c are obtained, which are the baseline morphology functions of the multi-sandbar beach profile.

6. The method for calculating the equilibrium profile morphology of a multi-sandbar beach according to claim 5, characterized in that: In step S4, the trigonometric function form used is: ， Calculate the average value of each row in the beach-ditch-sandbar curve matrix B to obtain the average beach-ditch-sandbar curve matrix. , ， Using the grid matrix X as the variable, the average beach shoulder-ditch-sandbar curve matrix By fitting the dependent variable, the values ​​of coefficients p, q, d, e, f, g, and h are obtained, which are the beach shoulder-ditch-sandbar curve morphology functions of the multi-sandbar beach profile.

7. The method for calculating the equilibrium profile morphology of a multi-sandbar beach according to claim 6, characterized in that: In step S5, the equilibrium profile morphology function of the multi-sandbar beach is: 。

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