A method for estimating lake water volume based on geospatial data

Abstract

This invention discloses a method for estimating lake water volume based on geospatial data, belonging to the field of lake water volume estimation technology. The steps are as follows: Step S1: Based on digital elevation model (DEM) data, calculate the slope value of each raster cell on the lake boundary and smooth the slope value; Step S2: Construct a lake polygon buffer and extract the lake boundary point set; Step S3: Match the nearest boundary point for each raster cell inside the lake; This invention uses the "31-point moving average method" to smooth the boundary slope data derived from the DEM, eliminating subsequent calculation errors caused by single-point elevation deviations and ensuring the stability of the basic data; and by incorporating watershed elements into the calculation of lakebed sediment thickness, it accurately corrects the theoretical maximum water depth, conforming to the actual topographic formation logic of the lake; Finally, through field measurement verification, the water volume estimation RE < 3%, R 2 >0.99, area estimation RE <4%, R 2 >0.97, the verification error of the Selin error is <2%, which effectively improves the estimation accuracy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of lake water volume estimation, and particularly relates to a lake water volume estimation method based on geographic spatial data. BACKGROUND

[0002] As the core carrier of global hydrological cycle and biogeochemical cycle, lakes play an irreplaceable role in climate regulation, groundwater recharge, freshwater ecosystem maintenance, and water supply for human production and life, and are the key water resource library for maintaining regional ecological security and sustainable development. In recent years, affected by factors such as accelerated glacier melting and water cycle disorder caused by global warming, the spatiotemporal variation of global lake water volume has become more and more significant, and some lakes have appeared shrinkage, salinization or expansion, which directly threatens the safety of freshwater resources and the stability of the ecological system.

[0003] However, there are many proven lakes in the world, and most of them are distributed in remote mountainous areas, plateaus and other areas with poor transportation. The existing lake water volume estimation technology still has some deficiencies, and it is difficult to meet the monitoring needs of large scale and high precision, which is embodied in the following two aspects:

[0004] 1. Limitations of field measurement method

[0005] Traditional lake water volume estimation relies on field measurement to obtain underwater topography (bathymetric map), and the mainstream technologies include laying in-situ monitoring stations and using unmanned aerial vehicles / unmanned ships to carry sonar or laser radar systems for detection. Although such methods can obtain high-precision data in local areas, they have inherent defects: on the one hand, due to the limitations of bad weather, complex terrain (such as lake bottom reefs and marshes) and equipment cost, field measurement is time-consuming and labor-intensive, and the economic investment is extremely high, making it difficult to cover large lakes (such as large lakes on the Qinghai-Tibet Plateau) or achieve batch monitoring of global lakes; on the other hand, field measurement is easily disturbed by external interference (such as wind waves and water turbidity), and it is difficult to reach some areas (such as deep water areas and remote lake areas), which may lead to insufficient data integrity and affect the overall accuracy of water volume estimation.

[0006] 2. Deficiencies of remote sensing and model estimation methods

[0007] In order to break through the limitations of field measurement, existing technologies have gradually developed lake water volume estimation technologies based on remote sensing data and mathematical models, which can be divided into "relative water volume estimation" and "absolute water volume estimation", but both have obvious deficiencies:

[0008] Relative water volume estimation techniques: These techniques aim to monitor the trend of lake water volume changes, but cannot obtain the total water volume (absolute water volume) and underwater topographic maps of lakes. For example, Siyu Zhu et al. established a volume-area-height curve database by integrating global water body bathymetry maps to achieve monthly-scale monitoring of lake water volume changes; Fangfang Yao et al. combined satellite observations and climate and hydrological data to reveal the declining trend of water volume in large global lakes. However, these techniques can only reflect the "change in water volume" and cannot provide key information such as the actual total water volume and water depth distribution of lakes. Moreover, they have insufficient coverage of small lakes and are difficult to support refined water resource management.

[0009] Absolute water volume estimation techniques: These techniques focus on reconstructing the total water volume and underwater topography of lakes, but they generally suffer from low accuracy, reliance on single data sources, or neglect of key natural processes. For example, Zhu, S et al. developed the progressive recession method (WRM) based on a digital elevation model (DEM) to construct a digital lake bathymetry model (DLBM). Although it does not require field data, it relies entirely on the accuracy of the DEM data. The elevation errors inherent in the DEM itself (such as deviations caused by snow cover in high-altitude areas) directly affect the water volume estimation results, limiting accuracy. Messer, M et al. combined the HydroLAKES database with... While statistical models for estimating global lake volume perform well on a global scale, they have significant estimation errors for individual lakes (especially those heavily influenced by sediments). Furthermore, they fail to consider the effects of watershed soil erosion and sedimentation on lakebed topography, which does not reflect the actual formation process of lakes. In addition, existing auxiliary methods based on elevation-area relationships, machine learning, or regression analysis often rely on a single data source (such as lake area or slope alone) and fail to integrate watershed-scale natural elements (such as precipitation, soil properties, and watershed slope). This results in poor model adaptability to lakes under different climatic zones and topographic conditions, leading to insufficient stability of the estimation results.

[0010] In summary, existing lake water volume estimation technologies are either too costly and have limited coverage to be applied on a large scale, or they lack accuracy because they ignore key processes such as watershed sedimentation and rely on single data. Moreover, most technologies cannot simultaneously obtain absolute water volume and underwater topographic maps, making it difficult to meet the needs of refined management of global lake resources. Summary of the Invention

[0011] The problem to be solved

[0012] In view of the problems mentioned in the prior art, the present invention provides a method for estimating lake water volume based on geospatial data.

[0013] Technical solution

[0014] To solve the above problems, the present invention adopts the following technical solution.

[0015] This application provides a method for estimating lake water volume based on geospatial data, the steps of which are as follows:

[0016] Step S1: Based on the digital elevation model data, calculate the slope value of each raster cell on the lake boundary, and smooth the slope value.

[0017] Step S2: Construct a polygonal buffer zone for the lake and extract the set of lake boundary points;

[0018] Step S3: Match the nearest boundary point for each raster cell inside the lake;

[0019] Step S4: Based on the lake area and the average slope of the boundary points, calculate the theoretical maximum water depth D of the lake. Tmax By combining the watershed area, average watershed slope, multi-year average precipitation, and soil silt content, the lakebed sediment thickness ST is calculated, thus obtaining the actual maximum water depth D of the lake. max ;

[0020] Step S5: Based on the distance between each internal raster cell and its matching boundary point, the boundary point slope value, the theoretical maximum water depth, and the actual maximum water depth, calculate the depth value of each raster cell and generate an underwater topographic map of the lake.

[0021] Step S6: Calculate the total water volume of the lake based on the depth value and grid area of ​​each grid cell;

[0022] The actual maximum water depth D of the lake max The calculation formula is: D max =D Tmax -ST.

[0023] Furthermore, the formula for calculating the slope value in step S1 includes:

[0024]

[0025] Δz x It is the rate of change of elevation in the x-direction, Δz y It is the rate of change of elevation in the y-direction;

[0026]

[0027] Δx and Δy are the size of the grid cell, z0 is the elevation of the central grid cell, and z1, z2, ..., z8 are the elevations of the eight adjacent grid cells surrounding the central grid cell.

[0028] Furthermore, the formula for calculating the theoretical maximum water depth of the lake in step S4 is:

[0029]

[0030] Where slope is the average slope value at the lake boundary point, A is the area of ​​the lake, and a and b are water depth parameters.

[0031] Furthermore, the formula for calculating the lakebed sediment thickness in step S4 is as follows:

[0032] ST=D Tmax -D max =α·D A β ·P·SILT·Slope

[0033] Where Slope is the average slope value of the watershed where the lake is located, D A α is the area of ​​the watershed where the lake is located, P is the average annual precipitation of the watershed where the lake is located, SILT is the soil silt content, and α and β are sedimentary parameters.

[0034] Furthermore, in step S5, when calculating the depth value of each raster cell, the calculation formula is as follows:

[0035]

[0036] Where L is the distance from the lake boundary point to the lake center point, and D... i It is the depth of that pixel, D max α is the maximum depth of the lake, l is the shortest distance from the raster cell to the lake shore, α is the slope value of the lake boundary point corresponding to the raster cell, and D is the maximum depth of the lake. Tmax It is the theoretical maximum depth of a lake.

[0037] Furthermore, the formula for calculating the distance from the lake boundary point to the lake center point is as follows:

[0038]

[0039] The formula for calculating the shortest distance from the raster cell to the lake shore is:

[0040]

[0041] Where x I y I The x-coordinates are the planar coordinates of the grid point (I) inside the lake. B y B It is the planar coordinate of the nearest lake boundary point (B) that matches the interior point (I).

[0042] Furthermore, the formula for calculating the total water volume of the lake in step S6 is as follows:

[0043]

[0044] Where V is the total water volume of the lake, and D iIt is the depth corresponding to the i-th pixel, Δx 2 It is the area size of a single grid cell.

[0045] Furthermore, the method also includes generating underwater topographic maps of the lake using geographic information system software.

[0046] Furthermore, the smoothing process employs a 31-point moving average method.

[0047] Furthermore, the watershed data includes watershed area, average slope, multi-year average precipitation, and soil silt content, which are used to improve the calculation accuracy of lake sediment thickness and actual maximum water depth.

[0048] Beneficial effects

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] (1) This invention uses the "31-point moving average method" to smooth the boundary slope data derived from the DEM, eliminating subsequent calculation errors caused by single-point elevation deviations and ensuring the stability of basic data; and by incorporating watershed elements (area, average slope, multi-year precipitation, and soil silt content) into the calculation of lakebed sediment thickness, it accurately corrects the theoretical maximum water depth, conforming to the actual topographic formation logic of the lake; finally, through field measurement verification, the water volume estimation RE < 3%, R 2 >0.99, area estimation RE <4%, R 2 >0.97, the Selin error verification error is <2%, the accuracy far exceeds that of existing single data-dependent models, and the estimation accuracy is effectively improved.

[0051] Figure 1 This is a flowchart illustrating the lake water volume estimation method based on geospatial data according to the present invention.

[0052] Figure 2 The geographical information of the three lakes used in the implementation of this invention;

[0053] Figure 3 A comparative evaluation chart of the area and water volume estimation results of three lakes at different depths during the implementation of this invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments. Generally, the components of the embodiments of this application described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0055] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0056] Example:

[0057] In the specific implementation, three typical lakes in western China (Qinghai Lake, Namtso Lake, and Ebinur Lake) were selected as research subjects. These three lakes differ significantly in geographical location, area, and watershed characteristics (as shown in Table 1), which can fully cover lake types under different climatic zones and topographic conditions, and effectively verify the universality of the method.

[0058] This embodiment uses the measured data (lake area, water depth, and total water volume) from the water conservancy census as a benchmark. By comparing the deviation between the estimated results of this invention and the measured data, the accuracy of the method is evaluated.

[0059]

[0060] Table 1

[0061] Before conducting the specific experiment, it is necessary to prepare the data required for the experiment, and all data must be preprocessed (such as noise reduction, cropping, and coordinate unification) to ensure spatial consistency (the coordinate system used is WGS84).

[0062] In practice, the experimental data sources are as follows:

[0063] Digital Elevation Model (DEM) data: SRTM1Arc-SecondDEM (resolution 30m×30m) was used, sourced from the U.S. Geological Survey, to calculate the grid slope of the lake boundary;

[0064] Lake boundary vector data: derived from the 2024 National Water Resources Census dataset, and obtained by vector clipping using ArcGIS 10.8, with precise polygonal boundaries for the three lakes.

[0065] Watershed data:

[0066] Watershed boundaries: extracted from DEM data using ArcGIS hydrological analysis tools;

[0067] Average slope of the watershed: The average value of the slopes of all grid cells within the watershed calculated using the DEM.

[0068] Multi-year average precipitation P (1980-2024): derived from the CRU global meteorological reanalysis dataset, with a spatial resolution of 0.5°×0.5°, and matched to each watershed after interpolation;

[0069] Soil Silt Content SILT: The average soil silt content within the watershed was extracted from the HWSD Global Soil Database.

[0070] Actual measurement verification data: derived from the 2024 National Water Resources Census, including the water surface area, total water volume and maximum water depth corresponding to different water depths of lakes.

[0071] Reference Figure 1 In practice, the steps are as follows:

[0072] Step S1: Calculate the grid slope of the lake boundary:

[0073] Based on the vector data and DEM data of the lake boundary, the DEM data was converted into slope data using ArcGIS software, and the values ​​were then extracted to the raster corresponding to each boundary point. Finally, the slope of the boundary points was smoothed by averaging 30 points using code to obtain the final slope value of the boundary points used for calculation.

[0074] The formula for calculating the original slope at the lake boundary point is:

[0075]

[0076] Δz x It is the rate of change of elevation in the x-direction, Δz y It is the rate of change of elevation in the y-direction;

[0077]

[0078] Δx and Δy are the size of the grid cell, z0 is the elevation of the central grid cell, and z1, z2, ..., z8 are the elevations of the eight adjacent grid cells surrounding the central grid cell.

[0079] It should be noted that the directions of z1, z2, ..., z8 are from west to east and from north to south.

[0080] Step S2: Extract the lake boundary point set:

[0081] Based on the polygonal boundaries of the lakes, a 10m buffer is constructed in ArcGIS (ensuring coverage of all grid cells along the boundary). Then, the boundary points within the buffer range are extracted using the "Feature to Point" tool to form a lake boundary point set (B). Approximately 500-800 boundary points are extracted for each lake.

[0082] Step S3: Match the internal grid of the lake with the boundary points:

[0083] The nearest neighbor analysis method was used to calculate the Euclidean distance from each raster cell (I) inside the lake to all boundary points (B) by writing a program in Python, and the nearest boundary point was matched.

[0084] Step S4: First, calculate the theoretical maximum water depth of the lake based on the average slope of the lake's boundary points and the lake area; then, calculate the thickness of the lake's sediments by combining the area of ​​the lake's watershed, average slope, multi-year average precipitation, and silt content in the soil; finally, calculate the actual maximum depth of the lake based on these two values.

[0085] Calculate the theoretical maximum water depth D of the lake Tmax The formula is:

[0086] The formula for calculating the lake sediment thickness ST is: ST = D Tmax -D max =0.5491×D A 0.208 ·P·SILT·Slope

[0087] Calculate the actual maximum water depth D of the lake max The formula is:

[0088]

[0089] Where slope is the average slope at the lake boundary, A is the area of ​​the lake, and Slope is the average slope of the watershed containing the lake. A P is the area of ​​the watershed where the lake is located, P is the average annual precipitation of the watershed where the lake is located, and SILT is the transitional particle in the soil with a particle size between sand and clay, which is the most easily eroded part of the soil.

[0090] Step S5: Using code, calculate the depth value corresponding to each grid cell based on the location information of each grid cell, the slope value of the boundary points, and the theoretical maximum depth and actual maximum depth of the lake. The formula for calculating the depth value of each grid cell is:

[0091]

[0092] D max =max(D i )

[0093] Where l is the distance from the raster cell inside the lake to the nearest boundary point on the lake shore, L is the distance from the lake boundary point (B) to the center point (O) of the lake, and D i This is the depth value of the raster, D. max α is the maximum depth of the lake, l is the shortest distance from the raster cell to the lake shore, α is the slope value of the lake boundary point (B) corresponding to the raster cell (I), and D is the maximum depth of the lake. Tmax It is the theoretical maximum depth of a lake.

[0094] Step S6: Calculate the volume of the cylinder corresponding to each grid cell based on the area and corresponding depth of each grid cell. Add up the volumes of the cylinder cells corresponding to all grid cells within the lake area to get the water volume of the lake, i.e., the total water volume of the lake.

[0095] The maximum depth of the lake can also be adjusted as needed, facilitating the calculation of the water surface area and water volume at different depths, and yielding the lake's area-water volume curve and area-depth curve. The formulas for calculating the water surface area and water volume at different depths are as follows:

[0096]

[0097] Where V W A is the volume of water in a lake below a certain depth. W D is the area of ​​the water surface at a certain depth. i Δx is the depth corresponding to the i-th pixel, ΔD is a specific depth value, and Δx is the depth corresponding to the i-th pixel. 2 It is the area size of a single grid cell.

[0098] Step S7: Based on the calculated depth value corresponding to each grid cell, use ArcGIS to draw an underwater topographic map of the lake.

[0099] Step S8: Based on the measured results of the water conservancy census, and combined with the calculated water depth corresponding to each grid cell inside the lake, estimate the area and volume of the water body at different depths; and compare the estimated results with the measured results of the water conservancy census to obtain the accuracy results of estimating the area and volume of the lake at different depths in this example.

[0100] In the specific implementation analysis, the accuracy results for the three groups of lakes are shown in Table 2 below:

[0101]

[0102]

[0103] Table 2

[0104] Reference Figures 2-3 As shown in Table 2, the estimation results for the area and volume of water bodies at different depths in different lakes are all highly accurate (the estimated area RE for different lakes at different depths is less than 4%, and the estimated R² is greater than 0.97; the estimated volume RE for different lakes at different depths is less than 3%, and the estimated R² is greater than 0.99). In summary, this invention has high accuracy in estimating lake water volume, as well as the area and volume of water bodies at different depths, providing a more accurate calculation method for lake water volume estimation. It is of great significance for lake water resource management in practical applications.

[0105] The embodiments described above are merely preferred embodiments of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A method for estimating lake water volume based on geospatial data, characterized in that, The steps are as follows: Step S1, based on digital elevation model data, calculating the slope value of each grid cell on the lake boundary, and smoothing the slope value; Step S2, constructing a lake polygon buffer zone and extracting a lake boundary point set; Step S3, matching a nearest boundary point for each grid cell inside the lake; Step S4, calculate the theoretical maximum water depth of the lake based on the lake area and the average slope value of the boundary points ; combined with the basin area, basin average slope, average annual precipitation and soil silt content, calculate the lake bottom sediment thickness , get the actual maximum water depth of the lake ; Step S5, based on the distance between each internal grid cell and its matching boundary point, the boundary point slope value, the theoretical maximum water depth and the actual maximum water depth, calculating the depth value of each grid cell, and generating a lake underwater topographic map; Step S6, based on the depth value of each grid cell and the grid area, calculating the total water volume of the lake; The actual maximum water depth of the lake The calculation formula is: ; The formula for calculating the depth value of each grid cell in step S5 is: wherein is the distance from the lake boundary point to the lake center point, is the depth of the pixel, is the nearest distance from the raster pixel to the lake shore, is the slope value of the lake boundary point corresponding to the raster pixel point; The formula for calculating the distance of the lake boundary point to the lake center point is: The formula for calculating the nearest distance of the grid cell to the lake shore is: wherein , is the planar coordinate of the internal grid point (I), , is the planar coordinate of the nearest lake boundary point (B) matching the internal point (I); The smoothing process uses a 31-point moving average method.

2. The method for estimating lake water volume based on geospatial data according to claim 1, characterized in that: The formula for calculating the slope value in step S1 is Including: is a rate of change of elevation in the direction, is a rate of change of elevation in the direction; and is the size of the grid cell, z0is the elevation of the central grid cell, , , are the elevations of the 8 neighboring grid cells around the central grid cell.

3. The method for estimating lake water volume based on geospatial data according to claim 2, wherein: The formula for calculating the theoretical maximum water depth of the lake in step S4 is: wherein is the average slope value of the lake boundary points, is the area size of the lake, and a and b are water depth parameters.

4. The method for estimating lake water volume based on geospatial data according to claim 3, wherein: The formula for calculating the lake bottom sediment thickness in step S4 is: wherein, is the average slope value of the catchment area of the lake, is the size of the area of the catchment area of the lake, is the average annual precipitation of the catchment area of the lake, is the soil silt content, and is the deposition parameter.

5. The method for estimating lake water volume based on geospatial data according to claim 1, wherein: The formula for calculating the total water volume of the lake in step S6 is: wherein is the total water volume of the lake, is the depth corresponding to the i-th pixel, is the size of a single grid.

6. The method for estimating lake water volume based on geospatial data according to claim 1, wherein: The method further includes generating a lake underwater topographic map using geographic information system software.

7. The method for estimating lake water volume based on geospatial data according to claim 1, wherein: The watershed data includes watershed area, average slope, multi-year average precipitation and soil silt content, which is used to improve the calculation accuracy of lake sediment thickness and actual maximum water depth.

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