A method for lake underwater terrain modeling based on a small amount of measured water depth data

Abstract

The present invention discloses a method for modeling the underwater terrain of a lake based on a small amount of measured water depth data. The elevation profile collected along the central axis of the lake is regarded as the terrain skeleton of the lake. On the basis of determining the range of the lakeshore buffer zone, a series of lake cross-sections connecting the lakeshore and the central axis are constructed. Furthermore, the known elevation of the lakeshore is utilized, and the elevation values of the underwater area of the cross-section are inferred under the constraint of the measured elevation values on the central axis. Finally, based on the elevation of each cross-section and the central axis, spatial interpolation is used to construct the complete underwater terrain of the lake. This method does not require a full-lake survey, greatly reducing the time and economic costs of the field investigation work of the lake. The invention is applicable to the survey work of large lakes in areas with scarce data, and the constructed underwater terrain data of the lake will provide technical support for monitoring the dynamic changes of lake water resources and revealing the response characteristics of lake water resources to global changes, etc.

Description

Technical Field

[0001] The present invention belongs to the field of lake hydrology, and particularly relates to a method for modeling the underwater topography of a lake based on a small amount of measured water depth data. Background Technique

[0002] Lakes store approximately 87% of the world's surface fresh water and are an important source of water for human production and life (Downing et al., 2006). At the same time, lakes are also a key link in the terrestrial water cycle and are of great significance for maintaining the stability of regional ecosystems (Woolway et al., 2020). The underwater topography of a lake is a basic property of the lake, which determines the size of the lake water storage. Mastering the underwater topography information of a lake is an important basis for evaluating and monitoring lake water resources, and also provides important background data for conducting research on lake sedimentation, lake hydro-ecological environment, lake biology, etc.

[0003] Field investigations are the most direct means of obtaining the underwater topography of a lake, and underwater topography mapping can be achieved through shipborne sonar. However, the time and economic costs of conducting a full-lake survey are very high. Especially in remote areas or harsh environments with high cold and high altitude, it is extremely difficult and challenging to obtain underwater topography through field measurements (Qiao et al., 2017). Although some scholars have tried to use remote sensing data such as optical images and lidar to invert the water depth of lakes, existing methods are mainly applicable to waters with relatively shallow depths and high transparency, such as coastal waters or waters around reefs, and are not an effective means for lakes (Ma et al., 2020; Pereira et al., 2019). In the absence of measured data, spatial inference is an efficient alternative strategy. The basic assumption of the spatial inference method is that the topography around the lake and the underwater topography have spatial continuity. Therefore, the underwater topography can be inferred or a statistical model of water depth can be constructed using the topographic features around the lake. Existing studies have used the measured underwater topography or water depth data globally to construct lake depth estimation models for different lake regions, achieving the estimation of lake water storage at the global scale (Cael et al., 2017; Messager et al., 2016). Although the spatial inference method has achieved the estimation of lake water depth and water volume at a large regional scale, affected by the sample quantity, distribution, and representativeness, there are still large uncertainties in the estimation results of individual lakes and lakes in some regions.

[0004] In summary, existing field measurement and spatial inference methods both have their respective drawbacks and cannot balance accuracy and efficiency. The present invention proposes a fusion solution. The basic idea of this solution is that a certain amount of field-measured water depth data is necessary for lake underwater terrain modeling. However, by using the spatial inference method to fully utilize the known elevation information in the lakeshore zone, the elevation inference of some areas can be realized, thereby reducing the dependence on field measurement and avoiding the high cost brought by full-lake measurement. The present invention provides a method support for lake surveys, lake water resource management, lake science-related research, etc. by designing a lake underwater terrain modeling method based on a small amount of measured water depth data.

[0005] References:

[0006] [1] Downing, J.A., Prairie, Y.T., Cole, J.J., Duarte, C.M., Tranvik, L.J., Striegl, R.G., et al. (2006). The global abundance and size distribution of lakes, ponds, and impoundments. Limnology and Oceanography, 51(5), 2388 - 2397.

[0007] [2] Woolway, R.I., Kraemer, B.M., Lenters, J.D., Merchant, C.J., O’Reilly, C.M., & Sharma, S. (2020). Global lake responses to climate change. Nature Reviews Earth & Environment, 1(8), 388–403.

[0008] [3] Qiao, B., Zhu, L., Wang, J., Ju, J., Ma, Q., & Liu, C. (2017). Estimation of lakes water storage and their changes on the northwestern Tibetan Plateau based on bathymetric and Landsat data and driving force analyses. Quaternary International, 454, 56–67.

[0009] [4]Pereira, P., Baptista, P., Cunha, T., Silva, P. A., S., & Lafon, V. (2019). Estimation of the 546nearshore bathymetry from high temporalresolution Sentinel-1A C-band SAR data - A case 547study. Remote SensingofEnvironment, 223(1), 166–178.

[0010] [5]Ma, Y., Xu, N., Liu, Z., Yang, B., Yang, F., Wang, X. H., & Li, S. (2020). Satellite-derived bathymetry 540using the ICESat-2lidar and Sentinel-2imagery datasets. Remote Sensing of Environment, 541250(7), 112047.

[0011] [6]Messager, M. L., Lehner, B., Grill, G., Nedeva, I., & Schmitt, O. (2016). Estimating the volume and age of water stored in global lakes using a geo-statistical approach. Nature Communications, 7, 1–11.

[0012] [7]Cael, B. B., Heathcote, A. J., & Seekell, D. A. (2017). The volume and meandepth of Earth’s lakes. Geophysical Research Letters, 44(1), 209–218. Summary of the Invention

[0013] Lake underwater terrain modeling is a bottleneck problem in the current field of lake science. Traditional full-lake measurement methods are time-consuming and labor-intensive, and it is difficult to promote them in large-scale lake surveys. This application proposes a lake underwater terrain modeling method based on a small amount of measured water depth data, which greatly simplifies the field measurement workload. At the same time, it makes full use of the known terrain in the lakeshore zone to infer the terrain of some areas, avoiding a significant loss of modeling accuracy due to the small number of measured points.

[0014] To achieve the above technical objectives, the present invention adopts the following technical solutions:

[0015] A lake underwater terrain modeling method based on a small amount of measured water depth data, comprising the steps of:

[0016] Step 1: According to the lake morphology, determine the long axis of the lake and select the starting points for measurement at both ends of the long axis;

[0017] Step 2: According to the starting points, determine the central axis of the lake and measure the underwater elevation values along the central axis;

[0018] Step 3: Generate a number of sampling points along the lake shoreline, connect each sampling point to the point on the central axis closest to it and extend it to the lakeshore buffer zone to generate a lake cross-section;

[0019] Step 4: Based on the known elevation in the lakeshore buffer zone and the measured points on the central axis, use the elevation values of the measured points on the central axis as constraint values to infer the elevation values of each grid in the underwater area of the lake cross-section;

[0020] Step 5: Based on the measured points on the central axis and the inferred elevation values of each grid in the underwater area, generate a complete lake underwater terrain through spatial interpolation.

[0021] As a preferred implementation manner, the basic principle for determining the long axis of the lake is: generate the circumscribed rectangle of the lake, and use the group of intersections between the lake and its circumscribed rectangle with the longest distance as the two endpoints of the long axis of the lake.

[0022] As a preferred implementation manner, when selecting the measurement start and end points, it is necessary to select areas that are convenient for vehicles to reach in combination with the actual field situation, avoiding wetlands and shoals.

[0023] As a preferred implementation manner, the determination method of the central axis is: based on the start and end points, divide the closed lake shoreline into two sections of shoreline on the left and right. Determine the lake shoreline to which each grid in the lake water area belongs based on the principle of proximity (using the Euclidean distance function to calculate), so as to divide the lake interior into two areas, and extract the boundary between the two areas as the central axis of the lake.

[0024] As a preferred implementation manner, in step 2, a shipborne sonar device is used to measure the underwater elevation values along the central axis.

[0025] As a preferred embodiment, the lake cross-section includes a known elevation area in the lakeside buffer zone, an unknown underwater elevation area, and a measured elevation area of the central axis.

[0026] As a preferred embodiment, the method for inferring the elevation value of each grid in the underwater area of the lake cross-section is as follows:

[0027] Calculate the average slope of the known elevation area in the lakeside buffer zone, and extrapolate the elevation value of the grid in the flooded area based on the average slope until the inferred elevation value drops to the measured elevation value of the central axis point. The remaining grids are uniformly assigned the measured elevation value of the central axis point.

[0028] Furthermore, if the elevation value still does not reach the measured elevation value of the central axis point when extrapolating to the central axis measurement point, then change the inference method, and based on the known elevation value in the lakeside buffer zone and the measured elevation value of the central axis point, use a linear fitting function to infer the elevation value of each grid in the underwater area.

[0029] As a preferred embodiment, in step 5, based on the measured points of the central axis and the inferred elevation values of each grid in the underwater area, an underwater terrain is constructed by first constructing an irregular triangular network (TIN) and then generating a grid digital elevation model (DEM).

[0030] The theoretical basis of the method of the present invention is that there is geomorphic continuity between the underwater terrain of the lake and the lakeside terrain. Therefore, the known elevation in the lakeside area can be used to realize the spatial inference of the elevation in the underwater area of the lake. However, considering that large lakes are generally affected by lake sedimentation, the natural extension of the lakeside elevation will be interrupted by the relatively flat terrain at the bottom of the lake. Therefore, it is necessary to collect elevation constraint points along the central axis of the lake in the present invention, which is of great significance for reducing the uncertainty of the lakeside elevation extrapolation.

[0031] The present invention has the following two advantages:

[0032] (1) The method for modeling the underwater terrain of the lake proposed by the present invention greatly simplifies the field measurement workload and is especially suitable for alpine and high-altitude regions;

[0033] (2) The algorithm of the present invention is simple to implement, can quickly reconstruct the underwater terrain of the lake, and has good applicability to lakes with different shapes, sizes, and geomorphic environments. The invention can be extended to large-scale and even global-scale research, providing method support for large-scale lake hydrology and water resources research and lake water storage change monitoring under the background of global change. Description of the Drawings

[0034] Figure 1Lake samples selected in the embodiments of the present invention: (a) Spatial distribution of lake samples, (b) Longmu Co, (c) Guozha Co, (d) Aksaiqin Lake, (e) Bangda Lake, (f) Kusai Lake, (g) Donggei Co, (h) Eling Lake, (i) Chibuzhang Co, (j) Dangreyong Co, (k) Zhari Namco, (l) Taroco Lake, (m) Mapam Yumco.

[0035] Figure 2 It is a schematic diagram of the central axis and cross-section of the lake.

[0036] Figure 3 It is a schematic diagram for inferring the elevation of the lake cross-section: (a) Typical lake cross-section, (b) Method for inferring the unknown elevation on the cross-section.

[0037] Figure 4 They are the underwater terrain modeling results of twelve typical lakes in the embodiments of the present invention.

[0038] Figure 5 They are the correlations between the underwater terrain modeling results and the measured elevations of twelve typical lakes in the embodiments of the present invention. Detailed implementation manners

[0039] The following further describes in detail the specific implementation manners of the present invention in conjunction with the drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0040] The embodiments of the present application are twelve lakes with measured underwater terrain data in the Qinghai-Tibet Plateau. When selecting the lakes, the differences in lake morphology, size, spatial distribution, depth, etc. are fully considered, and the representativeness of the sample data is sought to be reflected. Since these lakes have shown an expanding trend since 2000, the SRTM DEM data collected in 2000 corresponds to the period when the lake water area was relatively small. In the embodiments, the lake water area in 2000 is used as the benchmark, which can make full use of the existing DEM data and reduce the uncertainty of underwater terrain modeling.

[0041] This embodiment includes the following steps:

[0042] Step 1: Determine the starting and ending points of the measured underwater terrain at both ends of the long axis of the lake. First, generate the circumscribed rectangle of the lake, and take the two points with the farthest distance among all the intersection points of the lake and the circumscribed rectangle as the two ends of the long axis of the lake. In addition, when determining the measurement points, the actual field situation also needs to be considered, especially paying attention to vehicle accessibility, water depth, etc., and avoiding areas that are difficult to reach such as wetlands and shoals.

[0043] Step 2: Based on the measured points at both ends of the determined major axis, divide the lake shoreline into left and right segments. Use the Euclidean distance function to calculate the nearest shoreline for each grid inside the lake and assign values, thereby realizing the spatial division of the area inside the lake. The shared boundary of the divided left and right regions is the central axis of the lake. Along the determined central axis of the lake, use a shipborne sonar to measure the underwater terrain along the line.

[0044] Step 3: Determine sampling points along the lake shoreline at a certain distance. For each sampling point, first determine the measured point on the central axis that is closest to it. After connecting the two points, extend it towards the lakeshore zone until reaching the boundary of the lakeshore zone buffer. Figure 2 A typical example is shown. At this time, the buffer of the lakeshore zone is 1500 meters, and the interval of the sampling points is 1500 meters along the length of the lake shoreline. In actual applications, we recommend using relatively smaller buffers for the lakeshore zone and shoreline intervals. In this embodiment, the buffer range used is 900 meters, and the sampling point interval is 500 meters.

[0045] Step 4: For each cross-section of the lake, the speculation of the unknown elevation part underwater consists of two parts. First, calculate the average slope of the known elevation area in the lakeshore zone buffer, and use this slope as a reference to speculate the elevation value of the underwater point to be speculated ( Figure 3 a), and the specific calculation formula is shown in Formulas (1) and (2). Second, when the calculated H P corresponds to the elevation value of the central axis, stop extrapolation and assign all the remaining grid elevation values to the measured elevation of the central axis. There may also be a special situation in Step 4, that is, when using the elevation extrapolation in Step 1 until the central axis, the elevation is still higher than the central axis point, indicating that the slope of the underwater area of the lake shows an increasing trend. In this case, directly use the elevation points in the lakeshore zone buffer and the measured points on the central axis, and through linear fitting, realize the speculation of the unknown elevation.

[0046] θ = arctan(ΔH / ΔL) (1)

[0047] H P = H A – θ * D AP (2)

[0048] In the formula, ΔH and ΔL are the elevation difference and horizontal distance of the lakeshore zone buffer respectively, θ is the elevation slope in the buffer, H A is the elevation value of the lake shoreline, D AP is the distance of the point to be speculated from the lake shoreline, and H P is the speculated elevation value.

[0049] Step 5: Based on the speculated elevation points, first construct a TIN, and then convert it into a grid DEM.

[0050] The modeling results of the twelve lake samples selected in this embodiment are as follows Figure 4 shown. To evaluate the terrain modeling error, two commonly used indicators, the mean absolute error (MAE) and the root mean square error (RMSE), were used in the embodiment. The results show that the MAEs of Lake Aksai Chin, Bangdag Co, and Lake Ngoring are all less than 5 meters, while the elevation errors of Guozhacuo and Dangreyong Co are relatively high, reaching 21.01 meters and 19.90 meters respectively. It should be noted that the absolute elevation error of underwater terrain modeling is closely related to the underwater depth. For example, the maximum water depth of Lake Aksai Chin, with the smallest error, is about 21 meters, while the maximum water depth of Guozhacuo reaches 142 meters. To better evaluate the accuracy and applicability of underwater terrain modeling, we further adopted two indicators, the relative elevation error (Bias_D) and the relative water volume estimation error (Bias_V). Taking Bias_V as an example, when estimating the water volume based on the underwater terrain constructed according to the present invention, compared with the estimation result of the measured data, the relative error is basically within 20%, and only the water volume estimation deviation of Guozhacuo exceeds 30%. This indicates that the underwater terrain constructed based on the method of the present invention can meet the accuracy requirements for water volume estimation. Further, we analyzed the elevation correlation between the estimated value and the measured value. As shown in Figure 5 shown, the fitting coefficients R 2 of Kusse Lake, Longmu Co, and Dangreyong Co are all greater than 0.80. Combining the morphological analysis of these three lakes, we can conclude that the present invention has higher accuracy in underwater terrain modeling for lakes with a relatively long and narrow shape. In summary, on the premise of greatly reducing the workload of field measured data, the present invention can ensure that the constructed underwater terrain and its water volume estimation result have good accuracy, and can provide an optimized solution for large-scale lake surveys.

Claims

1. A method for lake underwater terrain modeling based on a small amount of measured water depth data, characterized in that, it includes the following steps: Step 1: According to the lake morphology, determine the long axis of the lake and select the starting points for measurement at both ends of the long axis; Step 2: According to the starting points, determine the central axis of the lake. Based on the starting and ending points, divide the closed lake shoreline into two sections of shoreline on the left and right. Determine the lake shoreline to which each grid within the lake waters belongs based on the principle of proximity, so as to divide the lake interior into two regions, and extract the boundary of the two regions as the central axis of the lake; Measure the underwater elevation values along the central axis; Step 3: Generate several sampling points along the lake shoreline, connect each sampling point to the point on the central axis closest to it and extend to the lakeshore buffer zone to generate lake cross-sections; Step 4: Based on the known elevations in the lakeshore buffer zone and the measured points on the central axis, use the elevation values of the measured points on the central axis as constraint values to infer the elevation values of each grid in the underwater area of the lake cross-section. The method is as follows: Calculate the average slope of the known elevation area in the lakeshore buffer zone, and extrapolate the elevation values of each grid in the flooded area based on the average slope until the inferred elevation value drops to the elevation value of the measured point on the central axis, and uniformly assign the remaining grids the elevation value of the measured point on the central axis; Step 5: Based on the measured points on the central axis and the inferred elevation values of each grid in the underwater area, generate a complete lake underwater terrain through spatial interpolation.

2. The method according to claim 1, characterized in that, the basic principle for determining the long axis of the lake is: Generate the circumscribed rectangle of the lake, and take the group with the longest distance among the intersection points of the lake and its circumscribed rectangle as the two endpoints of the long axis of the lake.

3. The method according to claim 1, characterized in that, when selecting the starting and ending points for measurement, select areas where vehicles can easily reach in combination with the actual field situation, and avoid wetlands and shoals.

4. The method according to claim 1, characterized in that, Use shipborne sonar equipment to measure the underwater elevation values along the central axis.

5. The method according to claim 1, characterized in that, the lake cross-section includes areas with known elevations in the lakeshore buffer zone, unknown underwater elevations, and measured elevations on the central axis.

6. The method according to claim 1, characterized in that, if the elevation value still has not reached the elevation value of the measured point on the central axis when extrapolating to the measured point on the central axis, then change the inference method, and based on the known elevation values in the lakeshore buffer zone and the elevation values of the measured points on the central axis, use a linear fitting function to infer the elevation values of each grid in the underwater area.

7. The method according to claim 1, characterized in that, in step 5, based on the measured points on the central axis and the inferred elevation values of each grid in the underwater area, construct the underwater terrain by first constructing an irregular triangular network TIN and then generating a grid digital elevation model DEM.

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