A sandy beach cusp morphological feature analysis method based on unmanned aerial vehicle technology

Abstract

The application discloses a sandy beach cusp morphological feature analysis method based on a UAV technology, relates to the technical field of data analysis, and comprises the following steps: S1, collecting aerial photography data by using a UAV, processing the data, and generating DSM data; S2, performing smoothing processing on the DSM data, and extracting a first optimal convex part bottom end control point, a second optimal convex part bottom end control point, an optimal concave part top end control point and an optimal concave part bottom end control point; and S3, determining morphological parameters of the cusp according to the first optimal convex part bottom end control point, the second optimal convex part bottom end control point, the optimal concave part top end control point and the optimal concave part bottom end control point. The application completely innovates a traditional cusp landform monitoring method, realizes objectification, quantification and processization of cusp boundary control point identification by fusing a high-precision aerial surveying technology of a UAV.

Description

Technical Field

[0001] This invention relates to the field of data analysis technology, specifically to a method for analyzing the morphological characteristics of sandy beach corners based on unmanned aerial vehicle (UAV) technology. Background Technology

[0002] Beach promontory is one of the most perplexing rhythmic topographic features observed on beaches. Shaped by wave action, beach promontory is a typical rhythmic landform, and its morphological characteristics and dynamic evolution are crucial for understanding coastal erosion-deposition processes, sediment transport mechanisms, and geomorphic stability. Beach promontory typically exhibits a rhythmic structure of alternating sharp angles (convexities) protruding seaward and shallow channels (concaveities) inland. It is one of the most important characteristic topographic features on the coastline, a product of the coupling effects of nearshore sediment, hydrodynamics, and topography. Traditional beach promontory monitoring mainly relies on ground measurements or remote sensing imagery, but limitations in resolution, cost, and timeliness make it difficult to accurately capture micro-topographic changes on the beach surface, especially the dynamic response during rapid evolution phases.

[0003] A review of previous research indicates that the formation mechanism and topographic changes of beach promontory have been extensively studied. For example, Giovanni Coco et al. conducted field measurements of three beach promontory developments on a barrier island near Dac, North Carolina, exploring the mechanism by which tides influence beach promontory development and directions for model improvement. Li Zhiqiang et al. conducted topographic measurements and hydrodynamic observations of beach promontory on the western beach of Jieshi Bay in eastern Guangdong under normal wave conditions. Javier Benavente et al. studied the medium-term behavior and evolution of beach promontory systems, comparing marginal wave theory and self-organization theory. Sayyida Ali et al. used beach profile measurement methods to study the morphodynamics of beach promontory on microtidal exposed beaches, analyzing factors influencing beach promontory formation and changes. Li Zhiqiang et al. used field piling measurements of beach promontory topography to study the spatiotemporal characteristics of beach promontory topographic changes under normal wave conditions. Giovanni Coco et al. conducted numerical simulations using a self-organization model and compared relevant theories with field observation data to study the relationship between marginal waves and beach promontory formation. Li Zhiqiang et al. used cellular automata models to numerically simulate the formation and development of beach promontory and analyzed the simulation results to explore the causes of beach promontory formation. However, previous studies mainly focused on the analysis of theoretical models and relied on traditional ground monitoring methods to monitor topographic changes at beach promontory, resulting in a lack of empirical research on non-equilibrium beach promontory evolution and difficulty in obtaining high spatiotemporal resolution topographic evolution sequences. In recent years, UAV aerial surveying technology has provided an innovative approach to coastal micro-topographic monitoring due to its advantages of centimeter-level resolution, flexible operation, and low cost; however, its application in the dynamic capture of beach promontory morphological features is still limited. Summary of the Invention

[0004] To address the above problems, this invention proposes a method for analyzing the morphological characteristics of sandy beach corners based on unmanned aerial vehicle (UAV) technology.

[0005] The technical solution of this invention is: a method for analyzing the morphological characteristics of sandy beach corners based on unmanned aerial vehicle (UAV) technology, comprising the following steps: S1. Use drones to collect aerial photography data, process it, and generate DSM data; S2. Smooth the DSM data and extract the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part. S3. Determine the morphological parameters of the beach angle based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part.

[0006] Furthermore, S2 includes the following sub-steps: S21. Use Gaussian filtering to smooth the DSM data; S22. Based on the smoothed DSM data, place several boundary control points on several contour lines; S23. Based on several boundary control points, extract the coordinate points in the discrete point sequence and calculate the curvature of each coordinate point; S24. Based on the curvature of each coordinate point, determine the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S25. Determine the optimal control point at the top of the concave section based on the curvature of each coordinate point; S26. Determine the optimal bottom control point of the concave part based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, and the optimal top control point of the concave part.

[0007] Furthermore, in S23, the coordinate points curvature The expression is: ; ; ; ; ; in, Coordinates The first derivative of the x-coordinate with respect to the parameter. Coordinates The first derivative of the ordinate with respect to the parameter at the given position. Coordinates The second derivative of the x-coordinate with respect to the parameter, Coordinates The second derivative of the ordinate with respect to the parameter at the given position. To be located at the current point in the contour point sequence The x-coordinate of the previous position. To be located at the current point in the contour point sequence The y-coordinate of the previous position. To be located at the current point in the contour point sequence The x-coordinate of the next location. To be located at the current point in the contour point sequence The y-coordinate of the next position. Coordinates x-coordinate Coordinates The vertical coordinate is [value].

[0008] Furthermore, in S24, the two local maxima of curvature on the contour lines of the seaward protrusion in the beach corner unit are respectively used as the first optimal bottom control point of the protrusion and the second optimal bottom control point of the protrusion in the beach corner unit.

[0009] Furthermore, in S25, the local maximum curvature point of each coordinate point on the contour line of the protruding part in the direction of the shore in the beach corner unit is taken as the optimal concave top control point in the beach corner unit.

[0010] Furthermore, the local maxima of curvature are determined by an adaptive curvature threshold; the adaptive curvature threshold... The expression is: ; ; ; in, The mean curvature of the contour lines. For the standard deviation of curvature, To adjust the coefficient, This represents the number of points on the current contour line. Coordinates The curvature.

[0011] Furthermore, S26 includes the following sub-steps: S261. Calculate the normal vector of the line connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S262. Establish the equation of a straight line that passes through the optimal concave top control point and is parallel to the normal vector, and use it as the first straight line equation. S263. Establish the equation of the line segment connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part, and use it as the equation of the second line. S264. Solve for the parameters based on the equations of the first and second lines; S265. Based on the solved parameters, determine the coordinates of the optimal control point at the bottom of the concave section.

[0012] Furthermore, in S262, the expression for the equation of the first straight line is: ; in, Let x be the x-coordinate of any point on the concave axis AC. Let be the ordinate value of any point on the concave axis AC. Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S263, the expression for the equation of the second line is: .

[0013] Furthermore, in S264, the parameters to be solved... The expression is: ; in, Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S265, the expression for the coordinates of the optimal concave bottom control point is: ; ; in, Let x be the x-coordinate of the optimal concave bottom control point. The coordinates of the control point at the bottom of the optimal concave section are given.

[0014] Furthermore, in S3, the horizontal distance between the first optimal convex bottom control point and the second optimal convex bottom control point is taken as the beach angle spacing, the horizontal distance between the optimal concave top control point and the optimal concave bottom control point is taken as the beach angle depth, and the elevation difference between the optimal concave top control point and the optimal concave bottom control point is taken as the beach angle height.

[0015] The beneficial effects of this invention are: (1) This invention completely revolutionizes the traditional beach corner landform monitoring method. By integrating high-precision aerial survey technology of UAVs, it realizes the objectification, quantification and process of beach corner boundary control point identification.

[0016] (2) This invention utilizes curvature extreme value analysis and adaptive threshold determination to eliminate subjective bias in visual interpretation and ensure the repeatability of results; furthermore, through a rigorous vertical projection geometric model, it accurately defines the position of the bottom end point of the beach corner concave part, so that the morphological parameter measurement has a unified mathematical basis and clear geometric meaning, which significantly improves the standardization and comparability of the data.

[0017] (3) This invention provides unprecedented technical support for capturing the high-frequency dynamic evolution of micro-topography at the beach corner and exploring its self-organized evolution mechanism, which has powerfully promoted the development of coastal geomorphology research towards standardization, precision and intelligence. Attached Figure Description

[0018] Figure 1 A flowchart of a method for analyzing the morphological characteristics of sandy beach angles based on UAV technology; Figure 2 (a) Sentinel-2 global remote sensing imagery as of January 6, 2025; Figure 2 (b) An aerial orthophoto taken on January 15, 2025; Figure 3 (a) is a schematic diagram of wind speeds during the study period; Figure 3 (b) is a schematic diagram of wave direction during the study period; Figure 3 (c) is a schematic diagram of the significant wave height during the study period; Figure 3 (d) is a schematic diagram of the wave period during the study period; Figure 4 (a) is a schematic diagram of a two-dimensional model of the morphological parameters of the beach corner; Figure 4 (b) is a schematic diagram of the three-dimensional model of the beach corner morphological parameters; Figure 5 This is a schematic diagram of the wave period frequency; Figure 6 A schematic diagram of the beachhead topography and its changes; Figure 7 A schematic diagram of the morphological parameters of the beachhead; Figure 8 A schematic diagram illustrating the correlation between beach corner morphological parameters; Figure 9 A schematic diagram showing the correlation analysis results among the morphological parameters of various beach corners; Figure 10 This is a schematic diagram comparing the actual and theoretical values ​​of the beach angle distance; Figure 11 (a) An orthophoto of the beachhead terrain taken by an unmanned aerial vehicle; Figure 11 (b) is a side view of the beachhead terrain. Figure 11 (c) is another side view of the beach corner terrain. Detailed Implementation

[0019] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0020] like Figure 1 As shown, this invention provides a method for analyzing the morphological characteristics of sandy beach corners based on UAV technology, including the following steps: S1. Use drones to collect aerial photography data, process it, and generate DSM data; S2. Smooth the DSM data and extract the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part. S3. Determine the morphological parameters of the beach angle based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part.

[0021] In this embodiment of the invention, S2 includes the following sub-steps: S21. Use Gaussian filtering to smooth the DSM data; S22. Based on the smoothed DSM data, place several boundary control points on several contour lines; S23. Based on several boundary control points, extract the coordinate points in the discrete point sequence and calculate the curvature of each coordinate point; S24. Based on the curvature of each coordinate point, determine the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S25. Determine the optimal control point at the top of the concave section based on the curvature of each coordinate point; S26. Determine the optimal bottom control point of the concave part based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, and the optimal top control point of the concave part.

[0022] In this embodiment of the invention, in S23, the coordinate points curvature The expression is: ; ; ; ; ; in, Coordinates The first derivative of the x-coordinate with respect to the parameter. Coordinates The first derivative of the ordinate with respect to the parameter at the given position. Coordinates The second derivative of the x-coordinate with respect to the parameter, Coordinates The second derivative of the ordinate with respect to the parameter at the given position. To be located at the current point in the contour point sequence The x-coordinate of the previous position. To be located at the current point in the contour point sequence The y-coordinate of the previous position. To be located at the current point in the contour point sequence The x-coordinate of the next location. To be located at the current point in the contour point sequence The y-coordinate of the next position. Coordinates x-coordinate Coordinates The vertical coordinate is [value].

[0023] In this embodiment of the invention, in S24, two local maxima of curvature on the contour line of the seaward protrusion in the beach corner unit are respectively used as the first optimal bottom control point of the protrusion and the second optimal bottom control point of the protrusion in the beach corner unit.

[0024] In this embodiment of the invention, in S25, the local maximum curvature point of each coordinate point on the contour line of the protruding part in the direction of the shore in the beach corner unit is taken as the optimal concave top control point in the beach corner unit.

[0025] In this embodiment of the invention, the local maxima of curvature are determined by an adaptive curvature threshold; the adaptive curvature threshold... The expression is: ; ; ; in, The mean curvature of the contour lines. For the standard deviation of curvature, To adjust the coefficient, This represents the number of points on the current contour line. Coordinates The curvature.

[0026] when At this time, the sensitivity is moderate, and the detection rate and false detection rate are balanced; when When the sensitivity is high, it tends to detect more potential feature points; when At this time, the sensitivity is low, and only the most significant feature points are detected.

[0027] In this embodiment of the invention, S26 includes the following sub-steps: S261. Calculate the normal vector of the line connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S262. Establish the equation of a straight line that passes through the optimal concave top control point and is parallel to the normal vector, and use it as the first straight line equation. S263. Establish the equation of the line segment connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part, and use it as the equation of the second line. S264. Solve for the parameters based on the equations of the first and second lines; S265. Based on the solved parameters, determine the coordinates of the optimal control point at the bottom of the concave section.

[0028] In this embodiment of the invention, in S262, the expression for the equation of the first straight line is: ; in, Let x be the x-coordinate of any point on the concave axis AC. Let be the ordinate value of any point on the concave axis AC. Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S263, the expression for the equation of the second line is: .

[0029] In embodiment S264 of the present invention, the parameters to be solved The expression is: ; in, Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S265, the expression for the coordinates of the optimal concave bottom control point is: ; ; in, Let x be the x-coordinate of the optimal concave bottom control point. The coordinates of the control point at the bottom of the optimal concave section are given.

[0030] In this embodiment of the invention, in S3, the horizontal distance between the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part is taken as the beach angle spacing, the horizontal distance between the optimal top control point of the concave part and the optimal bottom control point of the concave part is taken as the beach angle depth, and the elevation difference between the optimal top control point of the concave part and the optimal bottom control point of the concave part is taken as the beach angle height.

[0031] The following description is based on specific embodiments.

[0032] The technical solution of this invention is not limited to this embodiment; it is also applicable to geological studies of other terrains. This study takes a sandy beach in a certain area as the research object, and systematically analyzes the spatial differentiation characteristics and dynamic evolution of beach head morphology through a combination of UAV aerial surveys and RTK-GNSS ground measurements. By verifying the accuracy and applicability of UAV monitoring technology for beach head micro-topography monitoring, the study reveals the spatiotemporal differentiation patterns of beach head erosion-deposition processes within the monitoring period, and explores the correlation between beach head morphological parameters to reveal the evolutionary patterns of beach head. The research results can provide data support for the evolution mechanism of sandy coastal landforms and provide a scientific basis for coastal zone protection and management decisions.

[0033] like Figure 2 As shown in (a), the study area is located on a beach on the north side of a certain place, such as Figure 2As shown in (b), the study area is approximately 1200m long and 150m wide. The beach is a long, narrow strip, generally oriented north-south, measuring 28km in length and 150-300m in width, and is a sandy coast. The sea waves are mainly wind-driven, resulting in wave-dominated landforms. The sea area experiences irregular semi-diurnal tides. Located in a low-latitude region bordering the South China Sea, the average annual temperature is around 23.5℃, and the annual precipitation is between 1400-1700mm. The area exhibits significant tidal phenomena; during high tide, the seawater submerges part of the beach, and during low tide, it exposes it again. This ebb and flow of the seawater erodes and deposits sediment on the beach surface, creating a rhythmic topographical undulation over time. The area features numerous regularly spaced shallow channels that indent towards the sea and sharp angles that protrude towards the sea, forming a series of alternating promontory topography. Therefore, this area provides favorable conditions for studying the morphological characteristics of promontory beach features and the grain size distribution of sediments.

[0034] The analysis was based on hourly reanalysis data from the European Centre for Medium-Range Weather Forecasts (ERA5) with a resolution of 1 hour. The specific station analyzed was the closest point to the adjacent sea area (21°N, 110.55°E). During the monitoring period, the wind direction in the study area was predominantly southerly, with wind speeds generally greater than 4 m / s, and a maximum wind speed reaching 7 m / s. Figure 3 As shown in (a), the wave direction is mainly concentrated between 80° and 95° (east of southeast). In the week leading up to November 30, 2024, on December 14, 2024, and January 11, 2025, the wave direction briefly shifted from 80° to 95° to 50° to 70°, as shown in (a). Figure 3 As shown in (b), the significant wave height generally fluctuated between 0.6 and 0.9 m during the monitoring period. The maximum significant wave height occurred around December 21, 2024, reaching 1 m, while the minimum significant wave height occurred around December 28, 2024, at 0.35 m. Figure 3 As shown in (c), the wave period remained generally between 4 and 6 seconds during the monitoring period. Before December 21, 2024, the wave period remained around 5 seconds, with a minimum wave period of 3.9 seconds. After December 21, 2024, the wave period generally remained above 5 seconds, with a maximum wave period of 8 seconds. Figure 3 As shown in (d).

[0035] The study area is characterized by typical sandy coastal landforms, with its beach promontory exhibiting a rhythmic topography consisting of alternating shallow channels (concave sections) and sharp promontory (convex sections) facing sea. Based on the spatial morphological characteristics of the beach promontory, boundary control points are defined as follows: Figure 4 (a) and Figure 4As shown in (b), the top of the concave part of the beach promontory (A), the bottom of the convex part of the beach promontory (B, D), and the bottom of the concave part of the beach promontory (C) are defined as follows: the part of the beach promontory that bulges outward towards the sea is the convex part of the beach promontory; the part between adjacent convex parts of the beach promontory that bulges inland is the concave part of the beach promontory; the horizontal distance between the bottoms of adjacent convex parts of the beach promontory (B and C) is the beach promontory spacing (L); the horizontal distance between the top of the concave part of the beach promontory (A) and the bottom of the concave part of the beach promontory (C) is the beach promontory depth (W); and the difference between the elevation of the top of the concave part of the beach promontory (A) and the elevation of the bottom of the concave part of the beach promontory (C) is the beach promontory height (H).

[0036] The data acquisition method for this study combined UAV aerial photography and ground-based GNSS RTK measurements. Aerial monitoring of the study area was conducted at low tide levels on November 24, 2024, and January 15, 2025 (early to mid-winter period). Details of the UAV platform and photographic parameters are shown in Table 1. The CGCS2000 coordinate system was used for both aerial monitoring sessions. To ensure the accuracy, reliability, and consistency of the DSM (Discrete Scale Mapping) data from the two aerial surveys, 10 verification points were established on the ground in the third group of areas of the study area during the aerial photography process. The coordinates and elevation data of these points were measured using Qianxun Location X Plus GNSS RTK (CGCS2000 coordinate system). The verification points were numbered sequentially from land to sea, from 1 to 10, and their distribution is shown in Table 1. Figure 2 (b).

[0037] Table 1

[0038] In the process of verifying the accuracy of aerial photography data, the absolute error between the RTK-GNSS measured elevation value and the DSM elevation value of the verification point is calculated. ) and (RMSE, Root Mean Squared Error) and coefficient of determination ( The accuracy of the DSM is measured using the following formula: ; ; ; In the formula, R represents the absolute error between the RTK-GNSS measured elevation value and the DSM elevation value. RMSE is the root mean square absolute error. 2 As the coefficient of determination, To verify the RTK-GNSS measurements at the verification point, To verify the DSM elevation value of the point, To verify the average of the measured RTK-GNSS elevation values ​​at the point, Number of verification points. (UAV data accuracy verification) This study uses DJI Terra software to process drone aerial data, generating orthophotos and a digital stenography (DSM). The DSM is then imported into ArcMap software for further processing. A Gaussian filter algorithm is used to smooth the DSM and reduce noise interference. The filter window size is 3×3 pixels, and the formula is as follows: ; In the formula: This indicates that the position coordinates within the filtering window are... The Gaussian filter weight value. This value is a dimensionless weight coefficient, ranging from 0 to 1, used to calculate the contribution of this location to the smoothing result of the center pixel. This indicates the horizontal (eastward) offset distance of the current pixel within the filter window relative to the center pixel of the window, expressed in pixels. This indicates the offset distance of the current pixel within the filter window in the vertical direction (north direction) relative to the center pixel of the window, expressed in pixels. The constant value of pi is 3.14. The standard deviation parameter of the Gaussian distribution, expressed in pixels.

[0039] Subsequently, using the "Contour" tool in "Spatial Analyst Tools," contour lines (with a contour line spacing of 0.5m) were generated for the beach corner region. Four boundary control points were defined: the top of the beach corner concave area (A), the bottom of the beach corner convex area (B, D), and the bottom of the beach corner concave area (C).

[0040] The contour line extraction method can make full use of DSM data to effectively and accurately extract the beach corner outline. By analyzing the direction and closure of contour lines, the boundary control points of the beach corner are placed visually: the top of the concave part of the beach corner (A), the bottom of the convex part of the beach corner (B, D), and the bottom of the concave part of the beach corner (C).

[0041] The method for placing boundary control points at the top of the concave part of the beach promontory (A) and the bottom of the convex part of the beach promontory (B, D) is to determine the optimal placement of the boundary control points based on the curvature of multiple boundary control points on the contour lines. The specific steps are as follows: First, place multiple boundary control points along the shoreline at the most convex part of multiple contour lines. For the placed boundary control points, use the "Add XY Coordinates" tool in the "Spatial Analyst Tools" of ArcMap software to extract their coordinates from the discrete point sequence. =( , ), =1,2,...,m. Calculate each point. curvature .point The curvature at a point is a dimensionless geometric quantity, the magnitude of which reflects the degree of curvature of the contour line at that point. The larger the value, the more severe the curvature at that point. and These are the east and north coordinates in the CGCS2000 coordinate system, respectively. and Points coordinates and The first derivative with respect to the parameter (approximately the arc length) describes the direction of the tangent at that point. and Points coordinates and The second derivative with respect to the parameter describes the rate of change of the tangent direction at that point, i.e., the curvature of the curve.

[0042] For discrete point sequences, the first and second derivatives are numerically estimated using the central difference method, and the calculation formulas are as follows: ; ; ; ; In the formula, Adjacent points and The average step size between these steps can be approximated as a constant. In this study, the sequence density was relatively high, so we assume... =1, which simplifies the above formula.

[0043] Visual interpretation is used to determine the convex and concave sections of the beach angles on the contour lines (the parts convex towards the sea are convex, and the parts convex towards the shore are concave). The values ​​at each point are then calculated using the above method. curvature Then, find each point on the contour line of the seaward protrusion within each beach corner unit. Local maxima of curvature ( Within a beach angle unit, points significantly larger than their neighbors are designated as the optimal control points for the bottom of the convex portion (points B and D) within that unit. Similarly, each point on the contour line of the protruding portion towards the shore within each beach angle unit is considered a control point. The local maximum point of curvature is then used as the control point for the optimal concave apex (point A) within the beach corner unit. This invention will set an adaptive curvature threshold. Find local maxima of curvature.

[0044] Adaptive curvature threshold The mechanism of action is to avoid measurement noise causing slight fluctuations in contour lines, which would generate pseudo-curvature extrema. By setting a reasonable threshold, these minor fluctuations caused by noise are filtered out. Simultaneously, feature saliency is assessed, revealing differences in the degree of curvature among different beach corner units. It can adaptively acquire the truly significant curvature features in the current contour lines, excluding minor fluctuations. After determining the local maxima of curvature using the above method, the maxima need to be classified as follows: maxima located on the seaward convex arc of the contour lines are classified as the bottom of the convex part (points B and D); maxima located on the landward concave arc of the contour lines are classified as the top of the concave part (point A).

[0045] After determining the top of the concave part of the beach promontory (point A) and the bottom of the adjacent convex part (points B and D) through curvature analysis, this invention further proposes a precise geometric positioning method for the bottom of the concave part of the beach promontory (point C) based on vertical projection. First, point C is defined as the perpendicular intersection of the horizontal line passing through point A and line segment BD. This geometric relationship ensures that line segment AC is perpendicular to line segment BD, conforming to the basic principle in beach promontory morphology that the axis of the concave part is perpendicular to the shoreline (approximately represented by BD). Given the coordinates of point A: ( , Point B: () , Point D: ( , The second step is to calculate the direction vector of the line connecting lines BD. With normal vector The calculation formula is as follows: ; ; The third step is to establish the equation of a straight line passing through point A and parallel to the normal vector N. This straight line equation represents the direction of the concave axis AC.

[0046] The fourth step is to establish the equation of the line containing line segment BD.

[0047] The fifth step is to substitute formula (16) into formula (15) to solve for the parameters. .

[0048] The sixth step will yield the result. Substituting into equation (16), the coordinates of point C can be obtained.

[0049] Finally, verify the validity of the intersection point. If point C lies on line segment BD, then it is a valid solution. If point C is located on the extension of BD, then the identification of points A, B, and D should be checked to see if they are accurate.

[0050] The coordinates of four boundary control points can be obtained using the above method. These four control points can then be used to create three lines: the beach angle spacing (horizontal distance between points BD and AC), the beach angle depth (horizontal distance between points AC and AC), and the beach angle height (elevation difference between points AC and AC). Then, the "Extract Values ​​to Points" tool in ArcMap's "Spatial Analyst Tools" and the "Add XY Coordinates" tool in "Data Management Tools" are used to extract the coordinate and elevation information of the boundary control points at the beach angles. The coordinate system for the point coordinates is the CGCS2000 coordinate system, and the elevation datum for the point elevation information is the CGCS2000 geodetic height. The point coordinate information is used to calculate the beach angle spacing and depth, while the point elevation information is used to calculate the beach angle height. The formulas are as follows: ; ; In the formula, Horizontal distance The difference between the north coordinates of the two points. The difference between the eastern coordinates of the two points. This is the elevation difference (i.e., the height of the beach angle). Let A be the elevation value. Here is the elevation value of point C. (Beachhead extraction method) To quantitatively reveal the intrinsic correlation among the morphological features of beach corners in the study area, this invention selects beach corner spacing (L), beach corner depth (W), and beach corner height (H) as core analytical variables, and uses the Pearson correlation coefficient to quantify the linear correlation among these three variables. The Pearson correlation coefficient is suitable for measuring the degree of linear correlation between two continuous variables, with a value range of [-1, 1]. The closer the absolute value is to 1, the stronger the linear correlation between the variables; a positive value indicates a positive correlation, a negative value indicates a negative correlation, and a value close to 0 indicates a weak or no significant linear correlation. The calculation formula is as follows: ; In the formula, Represents the Pearson correlation coefficient; The number of samples; and These represent two different beach angle morphology parameters (such as beach angle spacing and beach angle depth, beach angle spacing and beach angle height, and beach angle depth and beach angle height). This represents the sum of the products of the corresponding observations of two variables; and Each represents the sum of the observed values ​​of the two variables; and Each represents the sum of the squares of the observed values ​​of the two variables; and These represent the squares of the sum of the observed values ​​of the two variables.

[0051] Subsequently, statistical analysis software was used to pair the three sets of parameter data, and Pearson correlation coefficients were calculated between beach angle distance and beach angle depth, beach angle distance and beach angle height, and beach angle depth and beach angle height, respectively. Significance analysis was performed using t-tests, with significance levels set at α=0.01 and α=0.05. If the calculated P-value was less than the set significance level, the linear correlation between the two variables was considered statistically significant; otherwise, the correlation was considered insignificant.

[0052] According to edge wave theory, there is a close relationship between beach angle spacing and wave period. Based on wave type, edge waves can be divided into schuomodal edge waves and synchronous edge waves. Beach angle spacing The relationship with the incident wave and the beach head topography can be expressed as: ; In the formula, g is the acceleration due to gravity, which is usually taken as 9.81 m / s². 2 Where T is the incident wave period (s), tanβ is the beach angle slope, and m = 1.0 or 0.5 corresponds to the subharmonic edge wave and the synchronous edge wave, respectively. The beach angle slope tanβ is defined as the ratio of the beach angle height to the beach angle depth, and the calculation formula is as follows: ; In the formula, The height of the beach corner, This refers to the depth of the beach head.

[0053] Based on the wind speed and wave characteristics during the monitoring period (November 24, 2024 to January 15, 2025) Figure 3 The wave period frequency of the nearshore waters in the study area was statistically analyzed, and the wave period frequency results are as follows: Figure 5 As shown. Therefore, the incident wave period at the beach angle in the study area is taken as 6s. The beach angle morphology parameters are taken from data on January 15, 2025 (since the marginal wave theory is for the isostatic state of sandy and gravelly beaches, the beach angle morphology is selected from the later period of the study period for morphology parameter estimation), and the estimated value of the beach angle distance is calculated.

[0054] Before using UAV data to analyze the dynamic changes in beachhead terrain, it is essential to ensure the accuracy, reliability, and consistency of the UAV data. Therefore, the accuracy of the verification points established during UAV aerial photography was first verified. This study will use UAV data from November 24, 2024, and RTK measured data for accuracy verification. The verification results are detailed in Table 2. The results show that, through comparison and verification between RTK measured data and UAV modeling data (RMSE=0.1087m, R...), the accuracy of the verification points is satisfactory.2 =0.9956), confirming that the elevation reconstruction error of the digital surface model (DSM) is significantly lower than the interannual variation threshold of beach corner topography (typically >0.5m). In particular, the minimum absolute error reaches the centimeter level (0.0275m), indicating that UAV point cloud data can achieve centimeter-level spatial resolution in areas with no vegetation disturbance, such as bare beach surfaces. This provides technical support for capturing micro-topographic evolution such as beach erosion and deposition.

[0055] Table 2

[0056] like Figure 6 As shown, by observing the digital surface model (DSM) and contour line distribution on November 24, 2024 and January 15, 2025, the number and distribution of beach cape systems show obvious evolutionary characteristics. In the early stage, beach cape systems were characterized by their sparse number and irregular spatial distribution, while in the later stage, the number of beach capes increased significantly and their distribution became more regular.

[0057] like Figure 6 As shown, analysis of topographic change maps from two digital surface models (DSM) on November 24, 2024, and January 15, 2025, reveals a unique topographic evolution pattern in the beach cape system. During this monitoring period, the DSM topographic change maps show that significant siltation and uplift were generally observed in the convex portion (the seaward-facing end) of the beach cape along the coast, while no significant elevation changes were observed in the concave portion (the bay crest on the landward side). Notably, the lower part of the beach cape (the seaward extension of the convex portion) exhibits a large-scale striped pattern of alternating erosion and siltation, with alternating localized siltation areas (blue patches) and localized siltation areas (red patches).

[0058] according to Figure 7 Based on the morphological parameters of the beach corners shown in Table 3, significant differences and evolutionary characteristics of the beach corner morphology between November 24, 2024, and January 15, 2025, can be observed. Regarding the distance between beach corners, the average heights of the two observations are similar (26.52 m in November; 26.47 m in January), indicating that the overall spatial scale of the beach corner system remains relatively stable. However, the number of statistically significant data points in January increased significantly (from 25 to 48), and the standard deviation decreased from 7.22 m to 5.00 m, while the relative dispersion decreased from 27% to 19%, indicating that the distribution of beach corner distances became more uniform and concentrated in the later period, and spatial variability was significantly reduced.

[0059] Table 3

[0060] The beach angle depth parameter showed a clear decreasing trend. The average beach angle depth in November was 12.73m (range 6.88~24.48m), while the average beach angle depth in January dropped to 9.94m (range 7.28~12.34m), a decrease of about 22%. At the same time, the dispersion of the January data decreased significantly (standard deviation decreased from 4.39m to 1.33m; relative dispersion decreased from 35% to 13%), indicating that the vertical erosion of the beach angle tended to be more uniform in the later period. Meanwhile, the beach angle height also showed a slight decrease and stronger uniformity: the average height decreased slightly from 1.32m in November (range 0.62~2.10m) to 1.13m in January (range 0.80~1.29m), the standard deviation decreased significantly from 0.41m to 0.12m, and the relative dispersion decreased significantly from 31% to 10%.

[0061] In summary, the three morphological parameters all showed lower data dispersion and stronger spatial homogeneity in the results from January 15, 2025, reflecting the systematic characteristics of the beach headland landform in this area becoming more regular and more uniformly developed over time during this monitoring period.

[0062] like Figure 8 and Figure 9 As shown, the correlations among the morphological parameters of the beach angles reveal significant temporal evolution characteristics. The linear correlation coefficients between the distance between beach angles and their depth at two different periods were 0.57 and 0.27, respectively. The correlation was significant at the 0.01 confidence level (two-sided) in the earlier period (November 24, 2024, the same below), while the correlation was not significant in the later period (January 15, 2025, the same below). The linear correlation coefficients between the distance between beach angles and their height were 0.35 and -0.01, respectively, with no significant correlation between the two periods. The linear correlation coefficients between the depth of beach angles and their height were 0.88 and 0.49, respectively, with significant correlations between the two periods at the 0.01 confidence level.

[0063] From the perspective of changes, the correlation between morphological parameters in the early and late stages underwent a systematic transformation. The positive correlation between beach angle spacing and depth weakened significantly (correlation coefficient changed from 0.57 to 0.27), indicating that the response mechanism of depth increasing with spacing in the early stage essentially disappeared. Beach angle spacing and height became uncorrelated (r=-0.01, p=0.958), and its horizontal distribution pattern y=1.14-0.0002x indicates complete decoupling between the two. Although the positive correlation between beach angle depth and height remained significant, the correlation weakened significantly (correlation coefficient changed from 0.88 to 0.49), reflecting a decrease in the control effectiveness of beach angle depth on height. Overall, the correlation between beach angle morphological parameters generally weakened from the early to the late stage.

[0064] Based on edge wave theory, the theoretical value of the beach angle spacing was calculated using the beach angle morphology parameters on January 15, 2025. As shown in Table 4, the calculated theoretical value of the beach angle spacing under the action of disharmonic edge waves was 12.94 m, which differs significantly from the average value of the actual beach angle spacing (26.47 m). Furthermore, the theoretical and actual values ​​were not statistically significant at the 0.01 and 0.05 confidence levels (p=0.09>0.01; p=0.09>0.05). Figure 10 A comparison of the actual and theoretical values ​​of the beach angle distance (actual value / theoretical value) shows that the ratio of the actual to the theoretical value is only 52% within the range of 0.5 to 2. Therefore, the actual and theoretical values ​​of the beach angle distance exhibit a significant difference.

[0065] Table 4

[0066] This invention utilizes a combination of UAV aerial surveying technology and ground-based GNSS RTK measurements to conduct aerial monitoring of the study area during high and low tides, acquiring abundant data. Compared to traditional monitoring methods, this combined approach significantly improves data acquisition efficiency, enabling the acquisition of data from a large area of ​​the beach promontory in a short time, providing a sufficient data foundation for subsequent analysis. UAV aerial surveying technology can accurately locate topographic changes in different areas, clearly identifying the specific locations of erosion and deposition. It is more efficient and precise than traditional monitoring methods (such as on-site manual cross-section measurement and planar measurement), capturing subtle topographic changes and providing reliable data support for the study of beach promontory evolution.

[0067] In monitoring the topographic evolution of beachheads, the digital surface model (DSM) generated from UAV aerial survey data exhibits extremely high accuracy. Table 2 shows that, through a comparative analysis of the RTK-GNSS measured elevation values ​​and the DSM elevation values ​​at the verification points, the results indicate that RMSE = 0.1087m, R... 2 =0.9956, with a minimum absolute error reaching the centimeter level (0.0275m). This indicates that UAV aerial surveying technology can achieve centimeter-level spatial resolution in areas with no vegetation disturbance, such as exposed beaches, and can clearly capture micro-topographical evolution such as beach erosion and siltation.

[0068] Another important value of drones in beachhead monitoring lies in their ability to track dynamic changes in beachhead topography in real time. Understanding the patterns of topographic change at different stages is crucial for studying the development process of beachheads, as this is essential for explaining their formation mechanisms. Therefore, to more effectively study the micro-topographic changes and morphological characteristics of beachheads, future research should focus on increasing the frequency and multi-time-period coverage of drone monitoring of the beachhead topography in this study area.

[0069] This invention analyzes the correlation between morphological parameters of beach corners at two different periods. The results show that all three sets of correlations among beach corner morphological parameters exhibit temporal decay (the correlations between depth and spacing, height and depth, and height and spacing are systematically weakened).

[0070] The significant weakening of the correlation between beach angle spacing and depth (r value decreased from 0.57 to 0.27) may reveal a shift in the control of the erosion base level. In the early stages, the depth of the trough incision was controlled by the flow path length (spacing), resulting in a linear response of depth with increasing spacing. As lower erosion releases a large amount of sediment (…),… Figure 6 The DSM topographic change map shows localized erosion at the lower part of the beach promontory. Material is continuously transported to the promontory convexity, causing rapid accumulation and uplift. This leads to the rapid development and stabilization of the promontory convexity, resulting in a stable beach promontory spacing. Consequently, the depth of the troughs gradually deviates from the spacing constraint and becomes dominated by the homogenized erosion base level. This process is later characterized by a rapid contraction of the beach promontory depth (the maximum value decreased from 24.48 m to 12.34 m, and the average value decreased from 12.73 m to 9.94 m). The original spatial control mechanism is replaced by negative feedback dominated by sedimentary flux, leading to the collapse of statistical correlations.

[0071] The complete decoupling of the correlation between beach angle spacing and height (r value changes from 0.35 to -0.01) highlights the morphological independence of mature beach angles. In the early stages, spacing indirectly affects protrusion growth by modulating wave energy focusing intensity. After the beach angle system completes spatial reorganization through source redistribution, the homogenized array (later stage) causes each unit to achieve similar flow separation efficiency, and the control of spacing on wave energy distribution is eliminated. At this point, protrusion height growth mainly responds to local dynamic-sedimentary equilibrium and is independent of the surrounding spatial configuration. This independence manifests as a complete decoupling of height parameters from system-level variables (spacing, depth). This transformation, along with the proliferation of beach angles and the reduction in dispersion (Table 3), constitutes a marker of the system entering a dynamic equilibrium state.

[0072] The decrease in the correlation between beach angle depth and height (r value decreased from 0.88 to 0.49) reflects the maturation of the protrusion growth mechanism. The early "depth-controlled height" reflects the physical limitations imposed on protrusion formation by the erosion source in the trough. When the protrusion accumulation reaches a critical height, its leading-edge eddies form a self-sustaining depositional system: the backflow generated by wave separation at the protrusion tip can autonomously capture suspended sediment, significantly reducing dependence on the trough source. Simultaneously, the regularization of the beach angle array leads to a homogeneous distribution of wave energy flow, weakening the control of depth over height, thus manifesting as a decrease in the correlation between depth and height. This shift marks a change in the vertical development of the beach angle from "source-driven" to "morphodynamic self-regulation."

[0073] In summary, this systematic evolution is consistent with the maturation process of beach cape landforms: the strong correlation between morphological parameters in the early stage reflects the morphological synergy constraints in the early development phase, while the general weakening of correlation in the later stage marks the system entering a homogenized and stable stage. In particular, the increased independence of height parameters (independent of spacing and weakly correlated with depth) suggests that the vertical development of beach capes is gradually decoupled from the control of planar patterns and is becoming dominated by local hydrodynamic processes. Therefore, regardless of whether from... Figure 6 The results of the DSM topographic change map and the temporal decay of the correlation of beach corner morphological parameters indicate that the beach corner system is transitioning from a heterogeneous non-equilibrium state to a self-organized critical steady state, and that the beach corner is in different stages in the early and late stages: the early stage is in the early development stage, the late stage is in the near-mature development stage, and the monitoring period is the rapid development period of the beach corner.

[0074] Waves are one of the key factors shaping the shape of beach headlands. Figure 6 The morphology of mid-slope promontory exhibits partial asymmetry and partial symmetry in both horizontal and vertical directions. At some locations on the promontory, the incident direction and energy distribution of waves are relatively uniform, resulting in similar erosion and deposition processes on adjacent promontory promontory sections, thus leading to high symmetry. For example, when waves propagate perpendicular to the coastline, the impact forces on adjacent promontory promontory sections are similar, and over time, their height and length may tend towards symmetry. At other locations, waves may impact the coastline at a certain angle or be influenced by coastal currents. In this case, one side of the promontory promontory will experience stronger erosion, resulting in a decrease in height and a shortening in length; the other side may experience an increase in height and a length increase due to sediment deposition, leading to asymmetry in height and length. Due to the influence of topography, waves undergo refraction and diffraction during propagation, causing significant differences in wave forces on adjacent promontory promontory sections, further resulting in asymmetry.

[0075] This study was conducted during the winter period (November 2024 to January 2025), during which wind speed and wave characteristics were studied. Figure 3This provided a specific dynamic background for the evolution of the beach head. During the monitoring period, southerly winds prevailed in the study area, with consistently high wind speeds (mostly greater than 4 m / s), providing a stable energy source for wave generation. Wave characteristics exhibited moderate intensity and relative stability: significant wave heights mainly ranged from 0.6 to 0.9 m, wave periods were concentrated between 4 and 6 s, and wave directions remained stable in the southeast-east direction (80°–95°). These continuous, stable, and moderate-energy wind and wave conditions were the key external factors driving the significant homogenization evolution of the beach head system during the monitoring period. The stable wave direction ensured that the waves acted in a relatively consistent direction on the beach surface, promoting the orderly development of rhythmic landforms; while the moderate wave height and wave period provided continuous but non-destructive dynamics, sufficient to initiate and maintain the lateral transport and redistribution of sediments, creating an ideal dynamic environment for the beach head to evolve from a heterogeneous non-equilibrium state to a critical steady state through self-organization mechanisms.

[0076] Within the study area, through observation Figure 11 The orthophoto from the UAV in (a) shows that the waterline also exhibits rhythmic characteristics, highly similar to those of the beach promontory. Simultaneously, the waterline reflects wave energy and dynamic characteristics. As can be seen from the waterline in the image, the waterline in the concave area of ​​the beach promontory is higher than that in the convex area. This indicates that when waves act on the concave and convex parts of the beach promontory, the difference in their morphology leads to a difference in wave energy between the two areas, and this energy difference is key to the development of the beach promontory morphology. Figure 11 (b) The concave section of the beach promontory has a gentler slope and lower overall topography, resulting in lower wave energy consumption and the potential for wave energy concentration, making it more susceptible to erosion. Conversely, the convex section of the beach promontory has a steeper slope and higher topography, leading to greater wave energy consumption. When wave energy weakens to a certain extent at the convex section, its ability to carry sediment decreases, making sediment accumulation more likely. This is also related to the circulation of the upwelling current. The upwelling current is divided into two streams by the convex section of the beach promontory, which then flow towards the coast. These two streams converge at the concave section of the beach promontory to form a strong backflow that flows towards the sea. Because the convex section has coarser, more permeable sediment, it is less susceptible to erosion compared to the concave section, which is more prone to erosion due to the strong backflow. This demonstrates the positive feedback effect of the circulation on the development of the beach promontory. Figure 11 As shown in the side view photograph (c), a large number of shells are accumulated in the top area of ​​the concave part of the tidal flat. These shells are only transported to the upper part of the tidal flat by the current under the action of waves of a certain intensity, indicating that the waves have a large wave energy in this area. This is also the main controlling factor leading to the continuous erosion and deepening of the concave part. Therefore, wave action is crucial to the formation, evolution and morphological development of the tidal flat.

[0077] This invention attempts to explain the formation of beach angle morphology using edge wave theory, but the actual value of the beach angle spacing during the monitoring period in this study area differs significantly from the theoretical value under edge wave theory. Figure 10 (See Table 4). Although edge wave theory provides an important theoretical framework for predicting beach angle distances, significant differences often exist between actual observations and theoretical predictions. These differences may stem from simplifications in the theoretical model, the complexity of actual beach dynamics, and the multi-factor coupling of beach angle formation mechanisms. Edge wave theory is based on the linear wave assumption and typically ignores nonlinear wave effects (such as wave breaking and nonlinear wave-wave interactions) and the complex dynamics of nearshore currents. In natural beach environments, waves often exhibit strong nonlinear characteristics, especially near the break zone, where wave energy dissipation and reflection can significantly alter the propagation characteristics of edge waves. Furthermore, self-organizing mechanisms suggest that beach angle formation originates from a positive feedback process of sediment transport, rather than simple wave interference. Under this mechanism, beach angle distances may depend more on the nearshore current scouring range or sediment grain size. If the self-organizing effect in the study area is strong, the predictive power of edge wave theory will be limited. However, as discussed earlier in the analysis of the reasons for the temporal decay of the correlation of beach corner morphological parameters, it was mentioned that the beach corner system transforms from a heterogeneous non-equilibrium state to a self-organized critical steady state during its development, indicating a strong self-organizing effect in this study area. Therefore, this explains the significant difference between the actual and theoretical values ​​of beach corner spacing, making it impossible to directly explain the formation of beach corner morphological features using edge wave theory. Furthermore, existing research has shown that simulations using cellular automata models reveal that beach corner formation is a result of feedback from sediment, hydrodynamics (waves, currents), and topography, exhibiting self-organizing characteristics. In addition, the responses of geomorphology, sediment, and other factors to wave action vary. Therefore, further in-depth discussions on the combined effects of multiple factors, including beach corner geomorphology and sediment, are needed in future research.

[0078] Meanwhile, the wave data used in calculating the beach angle distance using edge wave theory comes from the ERA5 hourly reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). This data has certain limitations, including low spatial resolution, lack of temporal sensitivity, difficulty in parameter matching, and unsuitability for specific scenarios. These limitations may restrict the explanation of beach angle morphology by edge wave theory. ERA5 data is essentially a wave climate background field in open sea areas, and its resolution and physical mechanisms are insufficient to drive accurate predictions by edge wave theory at the nearshore micro-topographic scale.

[0079] This invention utilizes a combination of UAV aerial surveying technology and RTK-GNSS ground-based measurements to conduct high-precision dynamic monitoring and analysis of the morphological characteristics of sandy beaches. The main conclusions are as follows: (1) Through verification point accuracy analysis (RMSE=0.1087m, R2 =0.9956), confirming that UAV aerial surveys can achieve centimeter-level topographic resolution (minimum absolute error 2.75cm) on exposed sandy beaches, significantly outperforming traditional monitoring methods. This technology can accurately capture the dynamics of micro-topography erosion and deposition at beach corners, providing reliable technical support for high-precision and high-frequency monitoring of coastal landforms.

[0080] (2) During the monitoring period, the beach cape system showed a significant trend towards homogenization: the number of beach capes increased (25 → 48) and the spatial distribution became more regular, the spacing remained stable (26.52 ± 7.22 m → 26.47 ± 5.00 m), and the mean values ​​of depth (12.73 ± 4.39 m → 9.94 ± 1.33 m) and height (1.32 ± 0.41 m → 1.13 ± 0.12 m) decreased. The dispersion of spacing, depth, and height parameters generally decreased, reflecting the evolution of the system from heterogeneity to equilibrium. The correlation of morphological parameters showed a systematic decline, the correlation between spacing and depth, and depth and height weakened significantly, and spacing and height were completely decoupled, marking the gradual shift of beach cape development from an early non-equilibrium state to a mature stage dominated by morphological dynamic self-regulation.

[0081] (3) The predicted value (12.94 m) of the beach angle distance by the edge wave theory deviates significantly from the measured value (26.47 m), indicating that the formation of the beach angle in this area is mainly regulated by a self-organizing mechanism, including the combined effects of positive feedback of sediment transport, circulation in the rip current zone, and spatial differentiation of wave energy. The limitations of the theoretical model highlight the importance of nonlinear wave effects and complex nearshore dynamic processes in the actual beach environment. In addition, this study reveals that the continuous and stable medium-energy wind and wave conditions in winter are an ideal external dynamic environment for promoting the evolution of the beach angle system towards homogenization and steady-state through self-organizing mechanisms. Future research needs to increase the monitoring frequency, couple hydrodynamic and sediment multi-source data, and develop numerical models that integrate self-organizing mechanisms and nonlinear feedback to deepen the understanding of the evolution law of beach angle geomorphology.

[0082] The results of this study can provide data support for the geomorphological evolution mechanism of sandy coastlines and provide a scientific basis for coastal zone protection and management decisions. It also highlights the importance of UAV technology in dynamic monitoring of coastal zones.

[0083] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for analyzing morphological features of a sandy beach cusp based on unmanned aerial vehicle technology, characterized in that, Includes the following steps: S1. Use drones to collect aerial photography data, perform preprocessing, and generate DSM data; S2. Smooth the DSM data and extract the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part. S3. Determine the morphological parameters of the beach angle based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, the optimal top control point of the concave part, and the optimal bottom control point of the concave part. S2 includes the following sub-steps: S21. Use Gaussian filtering to smooth the DSM data; S22. Based on the smoothed DSM data, place several boundary control points on several contour lines; S23. Based on several boundary control points, extract the coordinate points in the discrete point sequence and calculate the curvature of each coordinate point; S24. Based on the curvature of each coordinate point, determine the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S25. Determine the optimal control point at the top of the concave section based on the curvature of each coordinate point; S26. Determine the optimal bottom control point of the concave part based on the first optimal bottom control point of the convex part, the second optimal bottom control point of the convex part, and the optimal top control point of the concave part. In S24, two local maxima of curvature on the contour line of the seaward protrusion in the beach corner unit are respectively used as the first optimal bottom control point of the protrusion and the second optimal bottom control point of the protrusion in the beach corner unit. In S25, the local maximum curvature point of each coordinate point on the contour line of the protruding part in the direction of the shore in the beach corner unit is taken as the optimal concave top control point in the beach corner unit. In S3, the horizontal distance between the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part is taken as the beach angle spacing, the horizontal distance between the optimal top control point of the concave part and the optimal bottom control point of the concave part is taken as the beach angle depth, and the elevation difference between the optimal top control point of the concave part and the optimal bottom control point of the concave part is taken as the beach angle height.

2. The method for analyzing the morphological characteristics of sandy beach angles based on UAV technology according to claim 1, characterized in that, In S23, the coordinate points curvature The expression is: ； ； ； ； ； in, Coordinates The first derivative of the x-coordinate with respect to the parameter. coordinate point The first derivative of the ordinate with respect to the parameter at the given position. Coordinates The second derivative of the x-coordinate with respect to the parameter, Coordinates The second derivative of the ordinate with respect to the parameter at the given position. To be located at the current point in the contour point sequence The x-coordinate of the previous position. To be located at the current point in the contour point sequence The y-coordinate of the previous position. To be located at the current point in the contour point sequence The x-coordinate of the next location. To be located at the current point in the contour point sequence The y-coordinate of the next position. Coordinates x-coordinate Coordinates The vertical coordinate is [value].

3. The method for analyzing the morphological characteristics of sandy beach corners based on UAV technology according to claim 1, characterized in that, The local maxima of curvature are determined by an adaptive curvature threshold; the adaptive curvature threshold The expression is: ； ； ； in, The mean curvature of the contour lines. For the standard deviation of curvature, To adjust the coefficient, This represents the number of points on the current contour line. Coordinates The curvature.

4. The method for analyzing the morphological characteristics of sandy beach angles based on UAV technology according to claim 1, characterized in that, S26 includes the following sub-steps: S261. Calculate the normal vector of the line connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part. S262. Establish the equation of a straight line that passes through the optimal concave top control point and is parallel to the normal vector, and use it as the first straight line equation. S263. Establish the equation of the line segment connecting the first optimal bottom control point of the convex part and the second optimal bottom control point of the convex part, and use it as the equation of the second line. S264. Solve for the parameters based on the equations of the first and second lines; S265. Based on the solved parameters, determine the coordinates of the optimal control point at the bottom of the concave section.

5. The method for analyzing the morphological characteristics of sandy beach angles based on UAV technology according to claim 4, characterized in that, In S262, the expression for the equation of the first straight line is: ； in, Let x be the x-coordinate of any point on the concave axis AC. Let be the ordinate value of any point on the concave axis AC. Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S263, the expression for the equation of the second straight line is: 。 6. The method for analyzing the morphological characteristics of sandy beach corners based on UAV technology according to claim 4, characterized in that, In S264, the parameters to be solved The expression is: ； in, Let x be the x-coordinate of the optimal concave top control point. The ordinate is the ordinate of the optimal concave top control point. Let x be the x-coordinate of the control point at the bottom of the first optimal convex part. Let be the ordinate of the control point at the bottom of the first optimal convex part. Let x be the x-coordinate of the control point at the bottom of the second optimal convex part. The ordinate of the control point at the bottom of the second optimal convex part; In S265, the expression for the coordinates of the optimal concave bottom control point is: ； ； in, Let x be the x-coordinate of the optimal concave bottom control point. The coordinates of the control point at the bottom of the optimal concave section are given.

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