A method for simulating the underwater topography of natural lakes based on shoreline topography features

Abstract

This invention discloses a method for simulating the underwater topography of natural lakes based on shoreline topographic features, belonging to the field of earth science technology. This invention focuses on "simulating the natural process of lake level drop," fully utilizing the lakeside topographic information and morphological parameters extracted from DEM data to achieve reliable estimation of water depth and water storage in natural lakes without actual measured data. The main advantages are as follows: 1) This method can automatically adjust the calculation formula for underwater topography based on lake morphological parameters, thereby achieving autonomous adjustment for water depth prediction of different types of lakes, effectively improving the accuracy and reliability of the simulation results; 2) In the underwater topography simulation process, the reshaping effect of lake sediments on the underwater topography is considered, and a correction formula is introduced into the slope calculation module, making the slope calculation results closer to the actual lakebed morphology, further improving the accuracy of the simulation process.

Description

Technical Field

[0001] This invention relates to the field of Earth science technology, specifically to a method for simulating the underwater topography of natural lakes based on the characteristics of lake shore topography. Background Technology

[0002] Currently, the most accurate method for measuring lake water storage is to conduct on-site measurements using sonar equipment mounted on ships or lidar carried by drones to obtain sounding point data of the lake being measured. Then, a sounding map in triangular mesh or raster image format is generated from these sounding points to estimate the lake's water storage. However, these on-site sounding methods are costly and difficult to widely apply in large-scale lake water resource surveys. To address these challenges, some scholars have proposed and developed a series of methods for estimating lake depth and water storage. Based on their theoretical mechanisms, these methods are mainly divided into two categories: one integrates optical imagery and satellite altimetry data to construct a lake area-elevation relationship, and further estimates the lake's water storage based on this; the other reconstructs underwater topography based on the geomorphological features surrounding the lake or reservoir to generate a sounding map, from which the lake's water storage is derived.

[0003] The first type of method combines optical imagery and satellite altimetry data. First, it extracts changes in lake surface area based on optical imagery from different periods and generates an area sequence. Second, it processes and corrects the satellite altimetry data, extracting altimetry data passing over the lake to calculate the lake's water level elevation. Then, it matches temporally adjacent area sequences with the extracted water level elevations to obtain the area-elevation correspondence. Finally, it uses the most suitable geometric volume calculation formula for a specific lake to approximately estimate the lake's water storage. This method can estimate lake water storage relatively accurately, but only if the lake has distinct dry and flood seasons, such as seasonal or intermittent lakes. For most permanent lakes, this method cannot obtain a complete area-elevation correspondence. Li et al. combined altimetry data from multiple satellites and Landsat satellite imagery data to derive the area-elevation relationship of a reservoir. They applied the obtained relationship to surface water occurrence data to obtain the water depth values ​​of the dynamic area of ​​the reservoir, and finally used an extrapolation method to obtain a complete water depth dataset. [1] Although Li can obtain a complete bathymetric map after introducing the extrapolation method, the accuracy of the water depth values ​​in the extrapolation area largely depends on the extrapolation method, and the maximum water depth needs to be introduced as a constraint condition.

[0004] The second type of method typically relies on Digital Elevation Model (DEM) data to extract topographic features around lakes, used to infer underwater topography and estimate water depth and storage capacity. Since complete underwater topographic information is unavailable for the water surface area in DEM data, it is generally set to a fixed value—the elevation of the water surface area. Therefore, DEM data cannot directly reflect the underwater topography of a lake area. Some scholars have used geostatistical models to statistically analyze lakes and reservoirs with a large amount of known water depth information, constructing nonlinear models based on surrounding topographic information to reveal the relationship between lake area and average or maximum water depth. Subsequently, water storage capacity is estimated based on average water depth and lake area. The geostatistical model developed by Messer et al. estimates the volume of lakes with a global surface area of ​​10 hectares or more based on surrounding topography. [2] Due to the offsetting effect of underestimation and overestimation, the water storage estimates are acceptable for large-scale studies. However, uncertainties and potential biases at specific lake or local scales cannot be ignored. In water storage estimation studies of specific lakes, some scholars believe that the underwater topography of a lake can be regarded as an extension of the surrounding topography and can be inferred using extrapolation or interpolation methods. For example, Tseng et al. used DEM data to reconstruct the underwater topography of Lake Mead by linearly extrapolating the shore elevation. [3] Liu et al. combined the skeleton method to divide the lake into multiple lake profiles along its long axis, and then performed interpolation calculations on the profiles using depth sounding data as a constraint to obtain the lake profile elevations. They further used these elevation data to generate lake depth sounding maps and extracted the lake's water storage from the depth sounding maps. [4] These methods, based on extrapolation or interpolation, can reconstruct underwater topographic changes and estimate water storage to some extent, but they usually rely on prior measured data such as the maximum water depth of the lake or reservoir to constrain the interpolation results; otherwise, they may lead to a serious overestimation of the lake's water storage. Furthermore, due to the gradual accumulation of historical sediments in lakes, most modern lakes typically have relatively flat bottoms. However, current DEM-based water storage estimation methods generally truncate the predicted water depth when it is greater than the measured depth. The resulting depth maps still show a flat lake bottom area, but they are not directly related to the lake's sedimentary processes, ignoring the reshaping of underwater topography by these processes.

[0005] Therefore, a new solution is needed to address the above problems. Summary of the Invention

[0006] The purpose of this invention is to provide a method for simulating the underwater topography of natural lakes based on the topographic features of the lake shore, so as to solve the technical problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for simulating the underwater topography of natural lakes based on lake shore topographic features, comprising at least the following steps:

[0008] S1: Collect 30m resolution DEM data of the area surrounding the lake as input variables;

[0009] S2: Construct an underwater terrain simulation algorithm based on the principle of terrain continuity. The underwater terrain simulation algorithm consists of a parameter initialization module and an underwater elevation calculation module.

[0010] S3: Obtain DEM data containing the underwater topographic elevation of the lake area through underwater topographic simulation algorithm. Combined with the given lake surface elevation or lake surface boundary, the corresponding water depth and water storage of the lake can be estimated.

[0011] Furthermore, the parameter initialization module in S2 is used to initialize the parameters. The parameters that need to be initialized include the water mask matrix and the lake shore slope. Before initializing the parameters, the parameter initialization module needs to calculate intermediate parameters, which at least include the lake boundary, the buffer zone, and the slope map.

[0012] Furthermore, the calculation of the lake boundary and water mask matrix includes at least the following steps:

[0013] Since the water cell values ​​in the DEM data used are reassigned to water surface elevation, the DEM values ​​of the water surface area need to be uniformly set to water surface elevation, and a water-land binary classification is generated by filtering the swb band values ​​in the DEM to distinguish between water bodies and land areas.

[0014] in:

[0015] 255: Land. In the results of the land-water classification, a pixel value of 255 indicates that the location is a "land" area.

[0016] 0: Water body, meaning a pixel value of 0 indicates that the location is a "water body" area;

[0017] The results of the water-land binary classification usually contain small water body patches, so a connected component detection algorithm is needed to retain the largest connected component as the main body of the lake.

[0018] After determining the main body of the lake, lake boundary pixels are identified based on an edge detection function.

[0019] The lake boundary cells are assigned a value of 2, and the main lake cells are assigned a value of 1. These cells are stored in a new matrix with the same spatial coordinate system as the original data. This matrix serves as a water mask matrix that includes the lake boundary. The remaining cells in this matrix are assigned a value of 0. In other words, in the water mask matrix, a cell value of 2 represents the lake boundary, a cell value of 1 represents the water body, and a cell value of 0 represents the land.

[0020] Furthermore, the calculation buffer range includes at least the following steps:

[0021] The buffer zone is determined by a combination of multiple buffer levels, with the first step being to define a maximum buffer zone of 21 pixels.

[0022] Secondly, within this range, multiple buffer zones are defined at intervals of 3 pixels, and the average elevation within each buffer zone is calculated.

[0023] Thus, each level of buffer is matched with an elevation value. The turning point of the elevation value of the multi-level buffer is searched from the inside of the lake boundary outward, that is, the point where the elevation value changes from rising to falling. The area from the outside of the buffer to the lake shore boundary corresponding to this turning elevation value is the final buffer range.

[0024] The elevation values ​​within this buffer range will be used in subsequent calculations. If there is no inflection point, 21 pixels will be used as the buffer range.

[0025] Furthermore, the calculation of the lake shore slope involves three sets of data: the elevation band in the DEM, the lake boundary array, and the water mask matrix. In the water mask matrix, for each lake boundary pixel (i.e., the pixel value is 2), the eight-neighbor detection method is used to identify the land area in its domain (i.e., the adjacent pixel value is 0).

[0026] Elevation values ​​within the buffer zone are extracted for the elevation band in the direction identified as land, and the slope in that direction is calculated based on linear or polynomial fitting.

[0027] After all land-direction calculations are completed, the average of all fitted slope calculations is taken as the starting value for underwater topographic slope calculations.

[0028] Repeat the above steps for all lake shore boundary cells to map the lake shore boundary cell value domain to the slope value domain within the buffer zone, thereby mitigating the impact of local extreme topography on the calculation results.

[0029] Furthermore, the calculation of the slope map and the initial slope stretching includes at least the following steps:

[0030] Using the elevation band within the buffer zone, the slope map of the buffer zone is output based on the ArcGIS slope calculation method. That is, the slope calculated using a 3×3 window is more representative of the slope situation in the entire buffer zone.

[0031] By combining the characteristics of slope map calculation with those of lake shore slope calculation, the average value of the lake shore slope is selected as the criterion to determine whether to perform a stretching operation on the entire lake shore slope.

[0032] If the average value of the pixels at the lake shore boundary is greater than This indicates that the lake shore is relatively steep, and directly using the lake shore slope to calculate the water depth may result in a serious overestimation. In this case, the lake shore slope will be stretched and transformed, and its value will be reassigned according to the value range in the slope map.

[0033] Furthermore, the underwater elevation calculation module in S2 includes at least the following steps:

[0034] The formula for calculating the pixel elevation of underwater areas is as follows:

[0035]

[0036] In the formula, The elevation values ​​of adjacent land pixels. The distance between two pixels. The slope of the current calculated pixel;

[0037] Due to the The calculation of each pixel's elevation involves the elevation values ​​of neighboring pixels, i.e. Therefore, the calculation order and calculation mode of underwater area pixels are particularly important;

[0038] Based on the natural law that the lake surface elevation remains basically the same when the lake level drops, a cyclic model is used to simulate and calculate the underwater topographic elevation.

[0039] Slope calculation, in the formula, These are the key input parameters, in the first... On the vertical profile where each pixel is located, the underwater topography is approximated as a quadratic function:

[0040]

[0041] In the formula, Represents the elevation value. The independent variable represents the distance between the pixel and the lake shore.

[0042] To simplify the calculation, a lowest point needs to be assumed on the profile as the lake bottom point. A coordinate system is established on the profile. According to the actual topographic change law, on the vertical profile of the lake, the lake bottom point is usually closer to the steeper shore. Therefore, the slope of the lake shore on both sides of the profile is extracted, and the assumed lake bottom point in the slope calculation process is determined based on the slope values ​​of both sides. The horizontal distance between the lake bottom point and the left bank is calculated using the following formula (3):

[0043]

[0044] In the formula, This represents the distance between the two shores of the lake on the current cross-section. and These represent the slopes of the lake shore on the left and right banks, respectively.

[0045] After determining the horizontal position of the hypothetical lake bottom point, and assuming that the slope of the lake bottom point approaches 0 infinitely, the slope of the target pixel is the derivative of the formula at that point, calculated as follows:

[0046]

[0047] In the formula, The distance between the target pixel and the left bank;

[0048] Because sedimentation processes in lakes reshape and flatten the lakebed topography, the calculation results in the formula need to be corrected to make the simulation results closer to the actual underwater topography. The specific correction formula is as follows:

[0049]

[0050] In the formula, The corrected current calculated cell slope, The current cell slope is uncorrected. Let this be the distance between the target pixel and the opposite shore within the current land boundary. The power exponent, determined based on the characteristics of the lake, has the following value range:

[0051]

[0052] In the formula, The average value of the slope map within the buffer range in the parameter initialization module.

[0053] Furthermore, the specific process for calculating the pixel elevation of the underwater area includes at least the following steps:

[0054] The process is repeated multiple times, mimicking the process of the lake level dropping. Starting from the lake boundary, the lake level gradually drops, and underwater pixels will be exposed gradually along the shore towards the lake bottom as the lake level drops. There are fewer underwater pixels exposed in steep areas and more underwater pixels exposed in gentle areas. The elevation value is calculated for each pixel according to the exposure order.

[0055] In the first loop, starting from the current lake boundary, the elevation of all cells adjacent to the boundary is calculated, and then the minimum elevation value among them is used as the stopping threshold for the first lake level drop process.

[0056] It should be noted that once the elevation value of the underwater pixel is calculated, the pixel value at the corresponding position in the water mask matrix will change from 1 to 0, that is, from water to land.

[0057] For the current land boundary, continue to extract its inner boundary and calculate the elevation value of the inner boundary. Filter out the cells that are not less than the stopping threshold and repeat the above operation until the elevation value of all cells in a certain round of calculation is not greater than the stopping threshold. At this time, the loop ends and the next round of loop begins.

[0058] At the end of each cycle, the elevation of the lake boundary pixels tends to be consistent, and the simulation results are consistent with the process of lake surface drop. When there are no water pixels in the water mask matrix, that is, when all values ​​are 0, the elevation calculation ends.

[0059] Furthermore, the specific formula for estimating the water storage in S3 is as follows:

[0060]

[0061] in The volume of the lake water. For the first The volume of a water cell For the first The area of ​​a water cell is numerically equal to the product of the cell's length and width. For the first Simulated water depth for each water cell.

[0062] Compared with the prior art, the beneficial effects of the present invention are:

[0063] 1. This invention focuses on "simulating the natural process of lake level drop," fully utilizing the topographic information and morphological parameters of the lake's surrounding area extracted from DEM data. It achieves reliable estimation of natural lake depth and water storage without actual measured data. The main advantages are as follows: 1) This method can automatically adjust the underwater topography calculation formula based on lake morphological parameters, thereby enabling autonomous adjustment of water depth prediction for different types of lakes and effectively improving the accuracy and reliability of the simulation results; 2) During the underwater topography simulation process, the reshaping effect of lake sediments on the underwater topography is considered, and a correction formula is introduced into the slope calculation module, making the slope calculation results closer to the actual lakebed morphology, further improving the accuracy of the simulation process.

[0064] 2. Compared with existing lake water storage prediction methods, this invention can actively adjust the calculation method based on extracted lake morphology parameters. The simulation results of this method are excellent for lakes of different areas and geometries. Without any prior measured data, the model can achieve low-cost and high-efficiency estimation of water depth and storage capacity solely based on DEM data of the lake's perimeter. Furthermore, the simulation results show high consistency with field measurements such as those from radar depth sounders, providing reliable data support for regional water resource management. Attached Figure Description

[0065] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a technical roadmap of the present invention;

[0067] Figure 2 This is a composite schematic diagram of the present invention, wherein... Figure 2 (a) is a diagram showing the determination of the buffer in the parameter initialization module, where Figure 2 (b) and (c) show the calculation process for the lake shore slope;

[0068] Figure 3 This is a schematic diagram of the simulated lake surface drop process in the underwater elevation calculation process of the present invention;

[0069] Figure 4 This is a schematic diagram showing the differences between the parameters of the slope calculation process of this invention and the underwater terrain simulation before and after slope correction;

[0070] Figure 5 For the slope calculation of this invention and A schematic diagram;

[0071] Figure 6 This invention provides a simulated three-dimensional water depth map of a lake.

[0072] Figure 7 This is a three-dimensional water depth map of a lake generated based on measured data according to the present invention;

[0073] Figure 8 This is a scatter plot of the measured water depth map and the simulated water depth map of the present invention. Detailed Implementation

[0074] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0075] Please see Figure 1 - Figure 8 A method for simulating the underwater topography of natural lakes based on shoreline topographic features includes at least the following steps:

[0076] Step 1: Collect 30m resolution DEM data of the area surrounding the lake as input variables. See the table below for details:

[0077]

[0078] Step 2: Construct an underwater terrain simulation algorithm based on the principle of terrain continuity. This algorithm consists of a parameter initialization module and an underwater elevation calculation module, detailed below:

[0079] (1) Parameter initialization module

[0080] The parameters that need to be initialized include the water mask matrix and the lake shore slope. In initializing these parameters, intermediate parameters such as the lake boundary, buffer zone, and slope map must first be calculated.

[0081] Lake Boundary and Water Mask Matrix: Since the water cell values ​​in the DEM data used in this study have been reassigned to water surface elevation, the DEM values ​​of the water surface area need to be uniformly set to water surface elevation. A land-water binary classification is generated by filtering the SWB band values ​​(255: land; 0: water) in the DEM to distinguish between water and land areas. The results of the land-water binary classification often contain small water patches, requiring a connected component detection algorithm to retain the largest connected component as the main body of the lake. After determining the main body of the lake, lake boundary cells are identified based on an edge detection function. Lake boundary cells are assigned a value of 2, and main lake cells are assigned a value of 1, stored in a new matrix with the same spatial coordinate system as the original data. This new matrix serves as the water mask matrix containing the lake boundary, with the remaining cells assigned a value of 0. That is, in the water mask matrix, a cell value of 2 represents the lake boundary, a cell value of 1 represents water, and a cell value of 0 represents land.

[0082] Buffer Range: The buffer range is determined by combining multiple buffer levels. First, a maximum buffer range of 21 pixels is defined. Then, multiple buffer levels are defined within this range at intervals of 3 pixels. For each buffer level, the average elevation value within its range is calculated, thus each buffer level is matched with an elevation value. The inflection point of the elevation values ​​of the multiple buffer levels (i.e., the point where the elevation value changes from rising to falling) is searched from the inside of the lake boundary outwards. The area from the outer edge of the buffer zone to the lake shore boundary corresponding to this inflection elevation value is the final buffer range. The elevation values ​​within this buffer range will be used in subsequent calculations. If no inflection point exists, 21 pixels are used as the buffer range.

[0083] Lake shore slope: This step involves three sets of data: the elevation bands in the DEM, the lake boundary array, and the water mask matrix. For example... Figure 2 As shown in (b), for each lake boundary cell (with a cell value of 2) in the water mask matrix, the eight-neighbor detection method is used to identify the land area in its vicinity (i.e., adjacent cells with a value of 0). Figure 2As shown in (c), elevation values ​​within the buffer zone are extracted for the elevation band in the direction identified as land, and the slope in that direction is calculated based on linear or polynomial fitting. After calculations are completed for all land directions, the average of all fitted slope calculations is taken as the starting value for underwater topographic slope calculation. The above steps are repeated for all lake shore boundary pixels, mapping their value range to the slope value range within the buffer zone to mitigate the influence of local extreme topography on the calculation results.

[0084] Slope Map and Initial Slope Stretching: First, using the elevation bands within the buffer zone, a slope map of the buffer zone is output based on ArcGIS's slope calculation method. This method, using a 3×3 window, provides a more representative slope pattern across the entire buffer zone. The lakeshore slope calculated in c) better represents the slope from land to water. To comprehensively consider the characteristics of both methods, we choose the average lakeshore slope as the criterion for determining whether to stretch the entire lakeshore slope. If the average value of the lakeshore boundary pixels is greater than... This indicates that the lake shore is relatively steep, and directly using the lake shore slope to calculate the water depth may result in a serious overestimation. In this case, the lake shore slope will be stretched and transformed, and its value will be reassigned according to the value range in the slope map.

[0085] (2) Underwater Elevation Calculation Module

[0086] Underwater pixel elevation calculation: The formula for calculating the elevation of underwater area pixels is as follows:

[0087]

[0088] In the formula, The elevation values ​​of adjacent land pixels. The distance between two pixels. Calculate the slope for the current pixel. Since the... The calculation of individual cell elevation involves the elevation values ​​of neighboring cells (i.e., Therefore, the calculation order and calculation mode of underwater region pixels are particularly important. Based on the natural law that the lake surface elevation is basically the same when the lake surface drops, a cyclic mode is used to simulate and calculate the underwater topographic elevation. The specific process is as follows: Figure 3As shown, this loop mimics the process of lake level drop. Starting from the lake boundary, the lake level gradually decreases, exposing underwater pixels along the shore towards the lake bottom. Steep areas expose fewer underwater pixels, while gentler areas expose more. The elevation value is calculated for each pixel in the order of exposure. In the first loop, starting from the current lake boundary, the elevation of all pixels adjacent to the boundary is calculated, and the minimum elevation value is used as the stopping threshold for the first lake level drop. It's important to note that once the elevation of an underwater pixel is calculated, the corresponding pixel value in the water mask matrix changes from 1 to 0, indicating a transition from water to land. For the current land boundary, its inner boundary is extracted and its elevation value is calculated. Pixels not less than the stopping threshold are selected, and this process is repeated until all pixel elevation values ​​in a given round are not greater than the stopping threshold. At this point, the loop ends, and the next loop begins. At the end of each cycle, the elevations of the lake boundary pixels tend to be consistent, and the simulation results are consistent with the lake surface drop process. The elevation calculation ends when there are no water pixels in the water mask matrix (i.e., the value is 1).

[0089] Slope calculation: In the formula, These are the key input parameters. In the... On the vertical profile where each pixel is located, the underwater topography is approximated as a quadratic function:

[0090]

[0091] In the formula, Represents the elevation value. This represents the independent variable related to the distance between the pixel and the lake shore. To simplify the calculation, we need to assume a lowest point on the profile as the lake bottom point, and establish a structure on the profile as follows: Figure 4 The coordinate system shown is based on the actual topographical variations. In a lake's vertical profile, the lakebed is typically closer to the steeper shoreline. Therefore, we extract the shoreline slopes on both sides of the profile and determine the assumed lakebed point in the slope calculation process based on these slope values. The horizontal distance between the lakebed and the left bank can be calculated using the following formula:

[0092]

[0093] In the formula, This represents the distance between the two shores of the lake on the current cross-section. and These represent the slopes of the left and right banks of the lake, respectively. After determining the horizontal position of the hypothetical lake bottom point, we assume the slope at that point approaches 0 infinitely. Therefore, the slope of the target pixel is the derivative of the formula at that point, calculated as follows:

[0094]

[0095] In the formula, The distance between the target pixel and the left bank. Indicates As in formula (2) As in formula (2) Input, then apply the formula Differentiation Formula (4) is then obtained. Since sedimentation processes in lakes reshape the lakebed topography and flatten it, the calculation results in the formula need to be corrected to make the simulation results closer to the actual underwater topography. The specific correction formula is as follows:

[0096]

[0097] In the formula, The corrected current calculated cell slope, The current cell slope is uncorrected. Let this be the distance between the target pixel and the opposite shore within the current land boundary. and Relationship such as Figure 5 As shown, The power exponent, determined based on the characteristics of the lake, has the following value range:

[0098]

[0099] In the formula, This initializes the average slope map within the buffer range of the parameter initialization module. For example... Figure 4 As shown, the red curve represents the underwater terrain simulation result without slope correction, and the blue curve represents the underwater terrain simulation result with slope correction.

[0100] Step 3: Using an underwater topographic simulation algorithm, DEM data containing the underwater topographic elevation of the lake area was obtained. Combined with a given lake surface elevation or lake boundary, the corresponding water depth and water storage of the lake can be estimated. The specific formula for estimating water storage is as follows:

[0101]

[0102] in The volume of the lake water. For the first The volume of a water cell For the first The area of ​​a water cell is numerically equal to the product of the cell's length and width. For the first Simulated water depth for each water cell.

[0103] To demonstrate the advantages of this case compared to existing technologies, the following comparison is made:

[0104] Existing underwater topography reconstruction methods based on DEM lack a holistic consideration of shoreline slope calculations or oversimplify the underwater elevation calculation process. For example, in the literature... [5] The method involves acquiring the original DEM (Depth Image Model) of the lake / reservoir basin and then obtaining a new DEM based on hydrological analysis rules. Subsequent interpolation of the underwater region within the DEM is performed using simple linear interpolation, assuming the underwater topographic slope matches the onshore slope and the underwater elevation decreases linearly with a fixed slope. The interpolated region is then merged with the surface region to obtain the final DEM. Although this method does not rely on measured water depth data, linear interpolation clearly ignores the actual underwater topographic variations, resulting in a significant deviation between the interpolated results and the actual situation.

[0105] For example, literature [6] This method obtains the lake / reservoir water body boundary from the lake / reservoir binary matrix. Based on the slope of pixels within a preset range in the reverse slope direction of the lake / reservoir water body boundary pixels, polynomial fitting is performed to determine the slope of the lake / reservoir water body boundary pixels, resulting in a slope matrix. Based on the surrounding slope matrix and the current water surface elevation, by assuming a continuous decrease in water surface height, the simulated elevation of pixels exposed above the water surface is iteratively calculated until all water body pixels are calculated, resulting in a simulated underwater topographic matrix of the lake / reservoir. The simulated underwater topographic matrix is ​​then corrected using the above-water portion to obtain the final underwater topographic matrix of the lake / reservoir. However, this method only uses polynomial fitting to calculate the slope matrix, neglecting the influence of local topographic anomalies. Furthermore, although the underwater topographic calculation follows a water surface decline pattern, the calculation formula is simplistic and does not consider the reshaping of the topography by lake sediments, resulting in relatively fixed simulation results. To highlight the advantages of this method, this section compares it with the literature... [6] The method, in the literature [7] The lake water storage and maximum water depth simulation results were compared, and the comparison results are shown in Table 2. The average percentage error of the water storage estimation results of the method in this application is about 8% lower than that of the comparative method, and the accuracy of the maximum water depth estimation results is also higher. Because the water level varies in different years, that is, the water storage value is not exactly the same in different years, the comparison results in Table 2 are the absolute percentage error between the estimated water storage and the measured water storage.

[0106] Table 1 shows the water storage results derived from the simulated lake underwater topography.

[0107]

[0108] Table 2 lists the literature related to this invention and its applications. [2] Comparison results of papers

[0109]

[0110] Furthermore, this application presents scatter plots of simulated and measured depth maps, such as... Figure 8 As shown, 2500 scatter points were randomly and uniformly selected from the lake area, covering the entire lake. The correlation coefficient was also calculated. Root mean square error Mean absolute error The calculation formula is as follows:

[0111] In the formula, Indicates the first The true value of each data point, that is, the actual measured or observed value. Indicates the first The predicted value for each data point, i.e., the prediction result generated by the model or algorithm based on the input data. The mean of the true values, i.e., the arithmetic mean of all true values, is used to measure the central tendency of the data. This indicates the total number of data points, meaning the number of actual values ​​and predicted values ​​are the same. In the formula above, It measures the model's ability to explain data variation, i.e., how well the model predicts; the closer it is to 1, the better the model's predictive performance. The impact of larger errors is emphasized by averaging and taking the square root of the squared errors. It measures the average absolute difference between predicted and actual values, reflecting the average level of model error. From Figure 8 Based on the results, the average It is 0.61, with an average of It is 9.26m, with an average of The value is 8.07m. Considering that the maximum water depth of the lake in this example varies from 18 to 130m, it can be considered that the simulation results in this example are good and can reflect the trend of underwater topographic changes more realistically.

[0112] References:

[0113] LI, Y., GAO, H., JASINSKI, M. F., et al. Deriving high-resolutionreservoir bathymetry from ICESat-2 prototype photon-counting lidar andLandsat imagery[J]. IEEE Transactions on Geoscience and Remote Sensing, 2019,57(10): 7883-7893. DOI: 10.1109 / TGRS.2019.2917012.

[0114] MESSAGER M L, LEHNER B, GRILL G, et al. Estimating the volume andage of water stored in global lakes using a geo-statistical approach[J].Nature Communications, 2016, 7(1): 13603. DOI:10.1038 / ncomms13603.

[0115] TSENG, K. H., SHUM, C. K., KIM, J. W., et al. Integrating Landsatimageries and digital elevation models to infer water level change in HooverDam[J]. IEEE Journal of Selected Topics in Applied Earth Observations andRemote Sensing, 2016, 9(4): 1696-1709. DOI: 10.1109 / JSTARS.2015.2500599.

[0116] LIU, K., SONG, C., ZHAN, P., et al. A low-cost approach for lakevolume estimation on the Tibetan Plateau: coupling the lake hypsometric curve and bottom elevation[J]. Frontiers in Earth Science, 2022, 10: 925944. DOI:10.3389 / feart.2022.925944.

[0117] Ma Xiaoqi, Jing Haoxin, Zhu Bin. A method, equipment, device and medium for underwater topography reconstruction of lakes and reservoirs based on DEM [P]. Shandong Province: CN202310777707.2, 2024-03-26.

[0118] Lu Shanlong, Fang Chun, Li Mingyang, et al. Method and apparatus for underwater three-dimensional topography simulation of lakes and reservoirs based on digital elevation model [P]. Beijing: CN202110702775.3, 2021-10-19.

[0119] FANG C, LU S, LI M, et al. Lake water storage estimation methodbased on similar characteristics of above-water and underwater topography[J]. Journal of Hydrology, 2023, 618: 129146. DOI:10.1016 / j.jhydrol.2023.129146.

[0120] In summary:

[0121] This invention addresses the problems of water depth uncertainty and overly simplistic interpolation methods in lake and reservoir water storage prediction. It is the first to design an underwater topographic prediction approach that considers the sedimentary influences of different lakes. This approach fully utilizes the geometric features of lakes extracted from DEMs to achieve underwater topographic trend prediction and water storage calculation. First, initial parameters such as buffer zone range, slope, current lake boundary, and water mask matrix are initialized based on the original DEM data. Second, considering the reshaping effect of sediments on underwater topography, slope calculation and correction formulas are used to simulate the underwater topographic slope. Then, based on the principle of elevation consistency when the lake surface decreases, the changes in underwater topographic elevation are calculated iteratively. Finally, lake water depth and water storage are extracted from the simulated underwater topographic results. This method fully utilizes DEM topographic information and considers sedimentary influences, thereby achieving fully automated estimation of lake water depth and water storage. It significantly improves the accuracy of lake and reservoir water storage prediction in areas without measured data and is applicable to fields such as hydrological and meteorological research and water resource management.

[0122] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for simulating the underwater topography of natural lakes based on shoreline topographic features, characterized in that: At least the following steps are included: S1: Collect 30m resolution DEM data of the area surrounding the lake as input variables; S2: Construct an underwater terrain simulation algorithm based on the principle of terrain continuity. The underwater terrain simulation algorithm consists of a parameter initialization module and an underwater elevation calculation module. The parameter initialization module in S2 is used to initialize the parameters. The parameters that need to be initialized include the water mask matrix and the lake shore slope. Before initializing the parameters, the parameter initialization module needs to calculate intermediate parameters, which at least include the lake boundary, buffer zone, and slope map. The underwater elevation calculation module in S2 includes at least the following steps: The formula for calculating the pixel elevation of underwater areas is as follows: In the formula, The elevation values ​​of adjacent land pixels. The distance between two pixels. The slope of the current calculated pixel; Due to the The calculation of each pixel's elevation involves the elevation values ​​of neighboring pixels, i.e. Therefore, the calculation order and calculation mode of underwater area pixels are particularly important; Based on the natural law that the lake surface elevation remains basically the same when the lake level drops, a cyclic model is used to simulate and calculate the underwater topographic elevation. Slope calculation, in the formula middle, These are the key input parameters, in the first... On the vertical profile where each pixel is located, the underwater topography is approximated as a quadratic function: In the formula, The elevation values ​​of adjacent land pixels. The independent variable represents the distance between the pixel and the lake shore. To simplify the calculation, a lowest point needs to be assumed on the profile as the lake bottom point. A coordinate system is established on the profile. According to the actual topographic change law, on the vertical profile of the lake, the lake bottom point is usually closer to the steeper shore. Therefore, the slope of the lake shore on both sides of the profile is extracted, and the assumed lake bottom point in the slope calculation process is determined based on the slope values ​​of both sides. The horizontal distance between the lake bottom point and the left bank is calculated using the following formula (3): In the formula, This represents the distance between the two shores of the lake on the current cross-section. and These represent the slopes of the lake shore on the left and right banks, respectively. After determining the horizontal position of the hypothetical lake bottom point, and assuming that the slope of the lake bottom point approaches 0 infinitely, the slope of the target pixel is the derivative of the formula at that point, calculated as follows: （4） In the formula, The distance between the target pixel and the left bank; Because sedimentation processes in lakes reshape the lakebed topography and flatten it, it is necessary to modify the formula. The calculation results are corrected to make the simulation results closer to the real underwater terrain. The specific correction formula is as follows: In the formula, The corrected current calculated cell slope, The current cell slope is uncorrected. Let this be the distance between the target pixel and the opposite shore within the current land boundary. The power exponent, determined based on the characteristics of the lake, has the following value range: In the formula, The average value of the slope map within the buffer range in the parameter initialization module; S3: Obtain DEM data containing the underwater topographic elevation of the lake area through underwater topographic simulation algorithm, and estimate the corresponding water depth and water storage of the lake by combining the given lake surface elevation or lake surface boundary.

2. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 1, characterized in that: The calculation of the lake boundary and water mask matrix includes at least the following steps: Since the water cell values ​​in the DEM data used are reassigned to water surface elevation, the DEM values ​​of the water surface area need to be uniformly set to water surface elevation, and a water-land binary classification is generated by filtering the swb band values ​​in the DEM to distinguish between water bodies and land areas. in: 255: Land. In the results of the land-water classification, a pixel value of 255 indicates that the location is a "land" area. 0: Water body, meaning a pixel value of 0 indicates that the location is a "water body" area; The results of the water-land binary classification usually contain small water body patches, so a connected component detection algorithm is needed to retain the largest connected component as the main body of the lake. After determining the main body of the lake, lake boundary pixels are identified based on an edge detection function. The lake boundary cells are assigned a value of 2, and the main lake cells are assigned a value of 1. These cells are stored in a new matrix with the same spatial coordinate system as the original data. This matrix serves as a water mask matrix that includes the lake boundary. The remaining cells in this matrix are assigned a value of 0. In other words, in the water mask matrix, a cell value of 2 represents the lake boundary, a cell value of 1 represents the water body, and a cell value of 0 represents the land.

3. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 2, characterized in that: The calculation buffer range includes at least the following steps: The buffer zone is determined by a combination of multiple buffer levels, with the first step being to define a maximum buffer zone of 21 pixels. Secondly, within this range, multiple buffer zones are defined at intervals of 3 pixels, and the average elevation within each buffer zone is calculated. Thus, each level of buffer is matched with an elevation value. The turning point of the elevation value of the multi-level buffer is searched from the inside of the lake boundary outward, that is, the point where the elevation value changes from rising to falling. The area from the outside of the buffer to the lake shore boundary corresponding to this turning elevation value is the final buffer range. The elevation values ​​within this buffer range will be used in subsequent calculations. If there is no inflection point, 21 pixels will be used as the buffer range.

4. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 3, characterized in that: The calculation of lake shore slope involves three sets of data: elevation band in DEM, lake boundary array, and water mask matrix. In the water mask matrix, for each lake boundary cell (i.e., cell value 2), the eight-neighbor detection method is used to identify the land area in its domain (i.e., adjacent cell value 0). Elevation values ​​within the buffer zone are extracted for the elevation band in the direction identified as land, and the slope in that direction is calculated based on linear or polynomial fitting. After all land-direction calculations are completed, the average of all fitted slope calculations is taken as the starting value for underwater topographic slope calculations. Repeat the above steps for all lake shore boundary cells to map the lake shore boundary cell value domain to the slope value domain within the buffer zone, thereby mitigating the impact of local extreme topography on the calculation results.

5. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 4, characterized in that: The calculation of the slope map and the initial slope stretching include at least the following steps: Using the elevation band within the buffer zone, the slope map of the buffer zone is output based on the ArcGIS slope calculation method. That is, the slope calculated using a 3×3 window is more representative of the slope situation in the entire buffer zone. By combining the characteristics of slope map calculation with those of lake shore slope calculation, the average value of the lake shore slope is selected as the criterion to determine whether to perform a stretching operation on the entire lake shore slope. If the average value of the pixels at the lake shore boundary is greater than This indicates that the lake shore is relatively steep, and directly using the lake shore slope to calculate the water depth would result in a serious overestimation. In this case, the lake shore slope will be stretched and transformed, and its value will be reassigned according to the value range in the slope map.

6. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 1, characterized in that: The specific process for calculating the pixel elevation of the underwater area includes at least the following steps: The process is repeated multiple times, mimicking the process of the lake level dropping. Starting from the lake boundary, the lake level gradually drops, and underwater pixels will be exposed gradually along the shore towards the lake bottom as the lake level drops. There are fewer underwater pixels exposed in steep areas and more underwater pixels exposed in gentle areas. The elevation value is calculated for each pixel according to the exposure order. In the first loop, starting from the current lake boundary, the elevation of all cells adjacent to the boundary is calculated, and then the minimum elevation value among them is used as the stopping threshold for the first lake level drop process. It should be noted that once the elevation value of the underwater pixel is calculated, the pixel value at the corresponding position in the water mask matrix will change from 1 to 0, that is, from water to land. For the current land boundary, continue to extract its inner boundary and calculate the elevation value of the inner boundary. Filter out the cells that are not less than the stopping threshold and repeat the above operation until the elevation value of all cells in a certain round of calculation is not greater than the stopping threshold. At this time, the loop ends and the next round of loop begins. At the end of each cycle, the elevation of the lake boundary pixels tends to be consistent, and the simulation results are consistent with the process of lake surface drop. When there are no water pixels in the water mask matrix, that is, when all values ​​are 0, the elevation calculation ends.

7. The method for simulating the underwater topography of a natural lake based on shoreline topography features according to claim 1, characterized in that: The specific formula for estimating the water storage in S3 is as follows: in The volume of the lake water. For the first The volume of a water cell For the first The area of ​​a water cell is numerically equal to the product of the cell's length and width. For the first Simulated water depth for each water cell.

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