River channel water depth inversion method based on water depth-water surface area mathematical model and remote sensing

Abstract

The present invention is applied to the technical field of river channel water depth inversion. Disclosed is a river channel water depth inversion method based on a water depth-water surface area mathematical model and remote sensing, comprising constructing a first water depth-water surface area mathematical model of a river channel; on the basis of the type of the river channel, calculating a relationship function among the discharge section area, the water depth and the flow path of the river channel, and a relationship function among the area of triangles on two sides, the water depth and the flow path of the river channel, and substituting the relationship functions into the first water depth-water surface area mathematical model to obtain a second water depth-water surface area mathematical model; on the basis of the relationship between a water level and the water depth, converting the second water depth-water surface area mathematical model into a water level-water surface area mathematical model, in view of a water level-water surface area relationship obtained by remote sensing, solving an unknown number in the mathematical model, and substituting the solved number into the second water depth-water surface area mathematical model to obtain a third water depth-water surface area mathematical model; and substituting a water surface area extracted by remote sensing into the third water depth-water surface area mathematical model to obtain the water depth of the river channel. The present invention improves the representativeness of a water depth value, and also overcomes the difficulty of using bands to invert the water depth of water having high sediment content.

Description

River channel depth inversion method based on water depth-water surface area mathematical model and remote sensing Technical Field

[0001] The present invention relates to the technical field of river depth inversion, and in particular to a river depth inversion method based on a water depth-water surface area mathematical model and remote sensing. Background Art

[0002] The conventional method for measuring the water depth of rivers is to use a sounding rod, a sounding hammer and an echo sounder. The sounding rod and the sounding hammer are two tools used simultaneously in the actual sounding process, but they will be affected by factors such as water depth, flow rate and weather conditions, resulting in large errors; while the echo sounder's measurement results are more reliable in still water and clear water, but the measurement accuracy is significantly reduced in rivers with high sand content.

[0003] With the continuous enrichment of satellite remote sensing data, the use of remote sensing to invert water depth has attracted more and more attention. Scholars have inverted water depth by establishing a relationship between one or more bands and water depth. However, compared with the ocean, inland water bodies will be disturbed by suspended sediment in the water body when performing water depth remote sensing inversion, which makes it more difficult to invert using the relationship between bands and water depth. In addition, the measured water depth is accidental. Due to the complex underwater terrain, the water depth at the measured point is less representative.

[0004] Therefore, how to provide a river depth inversion method based on the water depth-water surface area mathematical model and remote sensing that can overcome the difficulties of using band inversion to invert the water depth of water bodies with high sediment content and improve the representativeness of water depth values ​​is an urgent problem that technicians in this field need to solve.

[0005] Summary of the Invention

[0006] In view of this, the present invention proposes a river depth inversion method based on a water depth-water surface area mathematical model and remote sensing.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] River channel depth inversion methods based on the water depth-water surface area mathematical model and remote sensing include:

[0009] Step (1): Construct the first water depth-water surface area mathematical model of the river;

[0010] Step (2): Based on the river channel type, the relationship function between the cross-sectional area of ​​the river channel and the water depth and flow rate, and the relationship function between the area of ​​the two triangles and the water depth and flow rate are calculated, and the relationship functions are substituted into the first water depth-water surface area mathematical model to obtain the second water depth-water surface area mathematical model;

[0011] Step (3): Based on the relationship between water level and water depth, the second water depth-water surface area mathematical model is converted into a water level-water surface area mathematical model, and combined with the water level-water surface area relationship obtained by remote sensing, the unknowns in the water level-water surface area mathematical model are solved and substituted into the second water depth-water surface area mathematical model to obtain a third water depth-water surface area mathematical model;

[0012] Step (4): Substitute the water surface area extracted by remote sensing into the third water depth-water surface area mathematical model to obtain the river depth.

[0013] Optionally, in step (1), the first water depth-water surface area mathematical model is as follows:

[0014] Among them, H is the water depth; L is the length of the river; A1(H,x) is the cross-sectional area of ​​the water flow; x is the flow rate; A2(H,x) and A3(H,x) are the areas of the two sides of the triangle; A is the water surface area.

[0015] Optionally, in step (2), the river channel types include: trapezoidal cross-section river channels and triangular cross-section river channels.

[0016] Optionally, the relationship function between the cross-sectional area of ​​the trapezoidal cross-section river channel and the water depth and flow rate is as follows: A1(H,x)=(w+mH)*H;

[0017] Among them, A1(H,x) is the cross-sectional area of ​​the water flow; w is the river bottom width; m is the river slope coefficient; H is the water depth;

[0018] The relationship function between the area of ​​the two triangles on the trapezoidal cross-section river channel and the water depth and flow rate is as follows:

[0019] Where A2(H,x) and A3(H,x) are the areas of the two triangles.

[0020] Optionally, the relationship function between the cross-sectional area of ​​the triangular river channel and the water depth and flow rate is as follows: A1(H,x)=(mH)*H;

[0021] Among them, A1(H,x) is the cross-sectional area of ​​the water flow; m is the slope coefficient of the river channel; H is the water depth;

[0022] The relationship function between the area of ​​the two triangles on the triangular river channel and the water depth and flow rate is as follows:

[0023] Among them, A2(H,x) and A3(H,x) are the areas of the two sides of the triangle.

[0024] Optional, the second water depth-water surface area mathematical model for the trapezoidal cross-section river is as follows:

[0025] Among them, H is the water depth; A is the water surface area; w is the river bottom width; L is the river length; m is the river slope coefficient.

[0026] Optional, the second water depth-water surface area mathematical model of the triangular river is as follows:

[0027] Among them, H is the water depth; A is the water surface area; m is the river slope coefficient; and L is the river length.

[0028] Optionally, in step (3), the relationship between water level and water depth is as follows: Z = H + Z0;

[0029] Among them, Z is the water level; H is the water depth; Z0 is the elevation of the trough bottom.

[0030] Optionally, in step (3), based on the water level-water surface area mathematical model and in combination with the water level-water surface area relationship obtained by remote sensing, the unknowns in the water level-water surface area mathematical model are solved, specifically as follows:

[0031] Assuming that the corresponding parts of the water level-water surface area mathematical model and the water level-water surface area relationship are equal, the unknowns in the water level-water surface area mathematical model are solved.

[0032] The above technical solution demonstrates that, compared to existing technologies, the present invention proposes a method for inverting river channel water depth based on a water depth-water surface area mathematical model and remote sensing. Based on the relationship between the cross-sectional area of ​​the water flow and the areas of the two triangles on either side, water depth, and flow, a water depth-water surface area mathematical model is constructed. Combined with the water level-water surface area relationship derived from remote sensing, the unknowns in the mathematical model are solved to determine the relationship between average water depth and water surface area. Substituting this relationship into the water surface area, the average water depth of the river can be inverted. This improves the representativeness of water depth values ​​while overcoming the difficulties of using wavebands to invert the water depth of water bodies with high sediment content. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0034] FIG1 is a schematic flow chart of the method of the present invention.

[0035] FIG2 is a schematic diagram of a general river channel of the present invention.

[0036] FIG3 is a schematic diagram of a river channel with a trapezoidal cross section according to the present invention.

[0037] FIG4 is a schematic diagram of a triangular river channel according to the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] Example 1:

[0040] Embodiment 1 of the present invention discloses a river depth inversion method based on a water depth-water surface area mathematical model and remote sensing, as shown in FIG1 , including:

[0041] Step (1): Construct the first water depth-water surface area mathematical model of the river.

[0042] As shown in Figure 2, the cross-sectional area of ​​a general river channel is not only related to the location, but also to the water depth. The x-axis is set along the river direction, and the cross-sectional area is A1(H,x), the river length is L, the river area is A, and the water depth is H. The water volume in the river channel is calculated based on the cross-sectional area. At the same time, the volume is calculated based on the water surface area. Let the remaining triangle areas on both sides be A2(H,x) and A3(H,x). Then the volume expression of the water body in the river is: At the same time, the volume of water is the same, so the first water depth-water surface area mathematical model is obtained as follows:

[0043] Among them, H is the water depth; L is the length of the river; A1(H,x) is the cross-sectional area of ​​the water flow; x is the flow rate; A2(H,x) and A3(H,x) are the areas of the two sides of the triangle; A is the water surface area.

[0044] Step (2): Based on the river channel type, calculate the relationship function between the cross-sectional area of ​​the river channel and the water depth and flow rate, and the relationship function between the area of ​​the two triangles and the water depth and flow rate, and substitute them into the first water depth-water surface area mathematical model to obtain the second water depth-water surface area mathematical model.

[0045] The channel types include: trapezoidal cross-section channel, as shown in Figure 3, and triangular channel, as shown in Figure 4.

[0046] Assuming the channel bottom width is w and the channel slope coefficient is m, the relationship function between the cross-sectional area of ​​the trapezoidal cross-section channel and the water depth and flow rate is as follows: A1(H,x)=(w+mH)*H;

[0047] Among them, A1(H,x) is the cross-sectional area of ​​the water flow; w is the river bottom width; m is the river slope coefficient; H is the water depth;

[0048] The relationship function between the area of ​​the two triangles on the trapezoidal cross-section river channel and the water depth and flow rate is as follows:

[0049] Among them, A2(H,x) and A3(H,x) are the areas of the two sides of the triangle.

[0050] The second water depth-water surface area mathematical model of the trapezoidal cross-section river is as follows:

[0051] Among them, H is the water depth; A is the water surface area; w is the river bottom width; L is the river length; m is the river slope coefficient.

[0052] The relationship function between the cross-sectional area of ​​a triangular river channel and the water depth and flow rate is as follows: A1(H,x)=(mH)*H;

[0053] Among them, A1(H,x) is the cross-sectional area of ​​the water flow; m is the slope coefficient of the river channel; H is the water depth;

[0054] The relationship function between the area of ​​the two triangles on the triangular river channel and the water depth and flow rate is as follows:

[0055] Among them, A2(H,x) and A3(H,x) are the areas of the two sides of the triangle.

[0056] The second water depth-water surface area mathematical model of the triangular river channel is as follows:

[0057] Among them, H is the water depth; A is the water surface area; m is the river slope coefficient; and L is the river length.

[0058] Step (3): Based on the relationship between water level and water depth, the second water depth-water surface area mathematical model is converted into a water level-water surface area mathematical model, and combined with the water level-water surface area relationship obtained by remote sensing, the unknowns in the water level-water surface area mathematical model are solved and substituted into the second water depth-water surface area mathematical model to obtain the third water depth-water surface area mathematical model.

[0059] The relationship between water level and water depth is as follows: Z=H+Z0;

[0060] Among them, Z is the water level; H is the water depth; Z0 is the elevation of the trough bottom.

[0061] The water level-water surface area mathematical model of the trapezoidal cross-section river is as follows:

[0062] Among them, Z is the water level; A is the water surface area; m is the river slope coefficient; L is the river length; w is the river bottom width; Z0 is the channel bottom elevation.

[0063] The mathematical model of water level-water surface area in a triangular river is as follows:

[0064] Among them, Z is the water level; A is the water surface area; m is the river slope coefficient; L is the river length; Z0 is the elevation of the channel bottom.

[0065] Based on the water level-water surface area mathematical model and the water level-water surface area relationship obtained by remote sensing, the unknowns in the water level-water surface area mathematical model are solved as follows:

[0066] Assuming that the corresponding parts of the water level-surface area mathematical model and the water level-surface area relationship are equal, the unknowns in the water level-surface area mathematical model are solved as follows:

[0067] The embodiment of the present invention uses 40 Sentinel-2 remote sensing images from 2019 to 2022 to extract the water surface area of ​​the study area, and combines the measured water levels of the hydrological stations during the same period as the remote sensing images to establish a water level-water surface area relationship. The water level-water surface area relationship obtained by remote sensing is as follows: Z = 7*10 -6 *A+22.472;

[0068] Among them, Z is the water level; A is the water surface area;

[0069] There are three unknown variables in the second depth-water surface area mathematical model of the trapezoidal cross-section river channel: the river channel slope coefficient m, the river channel bottom width w, and the river channel length L. Assuming that the corresponding parts of the water level-water surface area mathematical model of the trapezoidal cross-section river channel are equal to the corresponding parts of the water level-water surface area relationship, that is, The river length L is extracted from remote sensing images and is 2500 meters. The river bottom width w is approximated to be 75.16 meters by selecting remote sensing images of the dry season and using the ratio of the water surface area to the river length. The river slope coefficient m is solved to be 26.946. Substituting it into the second water depth-water surface area mathematical model of the trapezoidal cross-section river channel, the third water depth-water surface area mathematical model of the trapezoidal cross-section river channel is obtained as follows:

[0070] Among them, H is the water depth and A is the water surface area.

[0071] There are three unknown variables in the second water depth-water surface area mathematical model of the triangular river channel, namely, the river channel slope coefficient m and the river channel length L. Assuming that the corresponding parts of the water level-water surface area mathematical model of the triangular river channel are equal to the corresponding parts of the water level-water surface area relationship, that is, Z0=22.472, the river length L is extracted from remote sensing images as 2500 meters, and the river slope coefficient m is solved as 26.946. Substituting it into the second water depth-water surface area mathematical model of the triangular river channel, the third water depth-water surface area mathematical model of the triangular river channel is obtained as follows:

[0072] Among them, H is the water depth and A is the water surface area.

[0073] Step (4): Substitute the water surface area extracted by remote sensing into the third water depth-water surface area mathematical model to obtain the river depth.

[0074] According to the third water depth-water surface area model of the trapezoidal cross-section river channel and the triangular cross-section river channel, the simulated water depth H is calculated by combining the water surface area extracted by remote sensing. 模 , the measured water depth is H 实 , the absolute value of the absolute error is δ=|H 模 -H 实 |, the mean absolute error is Where N is the number of samples, the average absolute error of the simulated water depth of the trapezoidal cross-section river is 0.03 meters, and the average absolute error of the triangular cross-section river is 0.57 meters.

[0075] The present invention discloses a method for inverting river channel water depth based on a water depth-water surface area mathematical model and remote sensing. Based on the relationship between the cross-sectional area of ​​the water flow and the areas of the two triangles on either side, water depth, and flow, a water depth-water surface area mathematical model is constructed. Combined with the water level-water surface area relationship derived from remote sensing, the unknowns in the mathematical model are solved to determine the relationship between average water depth and water surface area. Substituting this relationship into the water surface area, the average water depth of the river can be inverted. This method improves the representativeness of water depth values ​​while overcoming the difficulties of using wavebands to invert the water depth of water bodies with high sediment content.

[0076] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0077] The above description of the disclosed embodiments will enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is to be construed in the widest possible manner consistent with the principles and novel features disclosed herein.

Claims

1. A river depth inversion method based on a water depth-water surface area mathematical model and remote sensing, characterized in that: include: Step (1): constructing the first water depth-water surface area mathematical model of the river; Step (2): based on the channel type, calculating the relationship function between the cross-sectional area of ​​the channel and the water depth and flow rate, and the relationship function between the area of ​​the two side triangles and the water depth and flow rate, and substituting them into the first water depth-water surface area mathematical model to obtain a second water depth-water surface area mathematical model; Step (3): based on the relationship between water level and water depth, converting the second water depth-water surface area mathematical model into a water level-water surface area mathematical model, and combining the water level-water surface area relationship obtained by remote sensing, solving the unknowns in the water level-water surface area mathematical model, substituting them into the second water depth-water surface area mathematical model, and obtaining a third water depth-water surface area mathematical model; Step (4): Substituting the water surface area extracted by remote sensing into the third water depth-water surface area mathematical model to obtain the river depth; In step (1), the first water depth-water surface area mathematical model is as follows: Among them, H is the water depth; L is the length of the river; A1(H,x) is the cross-sectional area of ​​the water; x is the flow rate; A2(H,x) and A3(H,x) are the areas of the two triangles; A is the water surface area; In step (2), the channel types include: trapezoidal cross-section channel and triangular cross-section channel; The relationship function between the cross-sectional area of ​​the trapezoidal cross-section river channel and the water depth and flow rate is as follows: A1(H,x)=(w+mH)*H; Among them, A1(H,x) is the cross-sectional area of ​​the water flow; w is the river bottom width; m is the river slope coefficient; H is the water depth; The relationship function between the area of ​​the two triangles on the trapezoidal cross-section river channel and the water depth and flow rate is as follows: Among them, A2(H,x) and A3(H,x) are the areas of the two triangles; The second water depth-water surface area mathematical model of the trapezoidal cross-section river channel is as follows: Among them, H is the water depth; A is the water surface area; w is the river bottom width; L is the river length; m is the river slope coefficient; The second water depth-water surface area mathematical model of the triangular river channel is as follows: Among them, H is the water depth; A is the water surface area; m is the river slope coefficient; L is the river length; The water level-water surface area relationship based on remote sensing is as follows: Based on remote sensing images, the water surface area of ​​the study area is extracted, and the water level-water surface area relationship is established by combining the measured water level of the hydrological station at the same period as the remote sensing image; The unknowns in the water level-water surface area mathematical model are specifically: The unknown variables in the water level-water surface area mathematical model of the trapezoidal cross-section river channel are the river channel slope coefficient m, the river channel bottom width w and the river channel length L; The unknown variables in the water level-water surface area mathematical model of the triangular river channel are the river channel slope coefficient m and the river channel length L.

2. The method for inverting river depth based on water depth-water surface area mathematical model and remote sensing according to claim 1 is characterized in that: In step (3), the relationship between the water level and the water depth is as follows: Z = H + Z0; Among them, Z is the water level; H is the water depth; Z0 is the elevation of the trough bottom.

3. The method for inverting river depth based on water depth-water surface area mathematical model and remote sensing according to claim 1 is characterized in that: In step (3), based on the water level-water surface area mathematical model and in combination with the water level-water surface area relationship obtained by remote sensing, the unknowns in the water level-water surface area mathematical model are solved, specifically: Assuming that the water level-water surface area mathematical model and the corresponding parts of the water level-water surface area relationship are equal, the unknowns in the water level-water surface area mathematical model are solved.

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