Cross-sectional velocity distribution inversion method based on river surface flow velocity

Abstract

The application discloses a cross-section flow velocity distribution inversion method based on river surface flow velocity, which comprises the following steps: grid segmentation is performed on the river cross-section, and each grid point is divided into an inner region and an outer region; the eddy viscosity of the outer region is calculated, and the flow velocity at the boundary point between the inner region and the outer region is obtained according to the calculated eddy viscosity of the outer region and the radar measured surface flow velocity distribution; the flow velocity of each inner region grid point is calculated according to the flow velocity at the boundary point between the inner region and the outer region; the flow velocity of each outer region grid point is calculated according to the radar measured surface flow velocity distribution and the flow velocity at the boundary point between the inner region and the outer region; and the inverted flow velocity of each inner region grid point, the flow velocity at the boundary point between the inner region and the outer region, the flow velocity of each outer region grid point and the radar measured surface flow velocity are combined to obtain the cross-section flow velocity distribution. The application analyzes the difference and connection between the inner region flow velocity distribution and the outer region flow velocity distribution, and inverses the inner region flow velocity distribution and the outer region flow velocity distribution by using the logarithmic deficit law and the RANS equation respectively, so that the cross-section flow velocity distribution of the river is obtained.

Description

Technical Field

[0001] This invention belongs to the technical field of microwave radar river remote sensing, specifically relating to a method for inverting cross-sectional velocity distribution based on river surface velocity. Background Technology

[0002] River cross-sectional velocity distribution is crucial hydrological information, significantly impacting flow estimation, channel evolution, and sediment transport. Traditional velocity distribution measurement tools, such as flow meters and acoustic Doppler current profilers, only provide locally effective velocity data. These instruments require immersion in water, leading to high installation and maintenance costs. Furthermore, their operation is cumbersome, the workload for a single cross-sectional velocity distribution measurement is substantial, and their real-time performance is poor. With the rapid development of electronic technology, non-contact flow measurement technologies, such as microwave radar, are increasingly being applied to river hydrological monitoring. Microwave radar can obtain real-time, accurate, and high-resolution surface velocity distribution without contacting the water body. However, microwave radar can only detect surface velocity in rivers and cannot directly measure the velocity below the water surface. Therefore, how to invert cross-sectional velocity distribution based on surface velocity is a pressing problem to be solved in microwave river remote sensing. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for inverting the cross-sectional velocity distribution based on the surface velocity of a river. This method obtains the cross-sectional velocity distribution of a river by analyzing the differences and relationships between the velocity distribution in the inner and outer regions of the cross-section, thus solving the problem that microwave radar cannot measure the velocity below the water surface.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A method for inverting cross-sectional velocity distribution based on river surface velocity, characterized by comprising the following steps:

[0006] Step 1: Divide the river cross section into grids, and divide each grid point into an inner zone and an outer zone;

[0007] Step 2: Calculate the eddy viscosity in the outer region and obtain the flow velocity at the boundary between the inner and outer regions based on the calculated eddy viscosity and the surface velocity distribution measured by radar.

[0008] Step 3: Calculate the flow velocity at each grid point in the inner zone based on the flow velocity at the boundary point between the inner and outer zones obtained in Step 2;

[0009] Step 4: Calculate the flow velocity at each grid point in the outer zone based on the surface velocity distribution measured by radar and the flow velocity at the boundary between the inner and outer zones;

[0010] Step 5: Combine the inverted flow velocities at each inner grid point, the flow velocities at the boundary between the inner and outer regions, the flow velocities at the outer grid points, and the surface flow velocities measured by radar to obtain the cross-sectional flow velocity distribution.

[0011] Furthermore, the gridding of the river cross-section specifically includes:

[0012] Based on the surface velocity distribution measured by microwave radar, N vertical lines are set up, where N is the number of surface velocity points measured by microwave radar. Combined with the set vertical distance resolution, each vertical line is vertically divided into multiple discrete grid points, so that the river cross section is divided into multiple discrete grid points. The grid points are divided into inner and outer zones according to the vertical distance of each grid point from the riverbed. The grid points closer to the riverbed are divided into the inner zone, and the grid points farther away from the riverbed are divided into the outer zone.

[0013] Furthermore, the division between the inner and outer zones satisfies the following relationship:

[0014] ;

[0015] In the formula, z is the vertical distance from the grid point to the riverbed. denoted by , where is the vertical distance from the grid point at the boundary between the inner and outer zones to the riverbed, and h is the water depth along the vertical line where the grid point is located.

[0016] Furthermore, step 2 specifically includes:

[0017] The RANS equations in the flow direction are expressed as follows:

[0018] ;

[0019] In the formula, Let be the kinematic viscosity coefficient of the liquid. The flow velocity is in the direction of flow. and These represent the lateral and vertical directions, respectively. Eeddy current viscosity, It is the acceleration due to gravity. Indicates the riverbed slope;

[0020] The above RANS equation can be simplified to:

[0021] ;

[0022] In the formula, The viscosity of the outer eddy current is... Indicates the flow velocity in the outer zone. This represents the vertical distance from the grid point to the riverbed.

[0023] The RANS equations are applied vertically from the lower boundary of the outer region. z 1 point to the upper boundary of the outer areaz 2. Results:

[0024] ;

[0025] In the formula, Shear velocity, and These are the upper boundary velocity and the lower boundary velocity, respectively.

[0026] According to Prandtl's mixing length theory, the viscosity of the inner eddy current... for:

[0027] ;

[0028] In the formula, Karman's constant, This represents the vertical distance from the grid points in the inner area to the riverbed.

[0029] and The same applies at the lower boundary, which is the dividing point between the inner and outer zones:

[0030] ,

[0031] The viscosity of the outer eddy current is thus obtained as: ;

[0032] Substituting the outer region eddy viscosity into the above RANS equation, we obtain the flow velocity at the boundary between the inner and outer regions:

[0033] ;

[0034] In the formula, Karman's constant, h The water depth is the perpendicular line to the grid point. Shear velocity, Represents gravitational acceleration. Indicates the riverbed slope. This indicates the flow velocity at the boundary between the inner and outer zones. The velocity at the upper boundary of the outer region is the surface velocity at that grid point, obtained from the surface velocity distribution measured by radar.

[0035] Furthermore, in step 3, the flow velocity at the boundary point between the inner and outer zones obtained in step 2 is calculated using the logarithmic deficit law. The formula for calculating the flow velocity at the inner zone grid points is as follows:

[0036]

[0037] In the formula, Indicates the vertical distance from the riverbed as The inner zone grid point velocity, z1 is the vertical distance from the grid point at the boundary between the inner and outer zones to the riverbed. This indicates the flow velocity at the boundary between the inner and outer zones.

[0038] Furthermore, step 4 specifically includes the following sub-steps:

[0039] Step 4.1: Establish the RANS equations in the flow direction of the outer zone, and discretize them into linear equations corresponding to the flow velocities of each grid point in the outer zone on each vertical line using the finite difference method.

[0040] Step 4.2: Convert the flow velocity at each grid point in the outer zone into the linear equations from Step 4-1. All linear equations form a system of linear equations. For the system of linear equations, use a matrix... , , , These respectively represent the coefficients, the flow velocity at the outer grid points, the outer boundary flow velocity term in each linear equation, and the right-hand side term. The linear equation system is expressed as:

[0041] ;

[0042] Step 4-3: Calculate the values ​​of each element in matrix C based on the surface velocity along each vertical line and the velocity at the boundary points between the inner and outer zones. Then, solve the linear equations to obtain the velocity at all grid points in the outer zone. The formula for calculating the velocity at the grid points in the outer zone is as follows:

[0043] .

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] 1. By analyzing the differences and relationships between the velocity distribution in the inner and outer regions of the cross section, the velocity distribution in the inner and outer regions is inverted using the logarithmic deficit law and the RANS equation, respectively, thereby obtaining the velocity distribution of the river cross section. This solves the problem that microwave radar cannot directly measure the velocity below the river surface, laying a good foundation for subsequent flow monitoring and having important application value for river hydrological monitoring and environmental protection.

[0046] 2. This invention utilizes surface velocity measured by microwave radar to invert the cross-sectional velocity distribution without contacting the water body, significantly reducing the workload required for velocity distribution measurement and playing an important role in advancing the modernization of hydrological surveying.

[0047] 3. This invention uses microwave radar as a detection tool, which is unaffected by rain and fog, and can achieve all-weather monitoring of flow velocity. It is suitable for working under high flow velocity and large flow conditions. In addition, this invention is not only applicable to shore-based microwave radar, but can also be extended to other non-contact flow measurement methods, such as large particle image velocimetry and space-time image velocimetry.

[0048] 4. The present invention is simple and quick to calculate, which can meet the requirements of radar real-time operation and help to grasp real-time and accurate cross-sectional velocity distribution information. Attached Figure Description

[0049] Figure 1 This is a flowchart of the inversion method for cross-sectional velocity distribution according to an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of the finite difference method according to an embodiment of the present invention;

[0051] Figure 3 The cross-sectional velocity distribution inverted in an embodiment of the present invention;

[0052] Figure 4 This is the absolute error distribution between the cross-sectional velocity distribution retrieved in an embodiment of the present invention and the acoustic instrument measurement results;

[0053] Figure 5 This is a scatter plot of the cross-sectional velocity distribution and acoustic instrument measurement results obtained from the inversion of an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0055] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0056] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0057] like Figure 1 As shown in the figure, this invention provides a method for inverting cross-sectional velocity distribution based on river surface velocity, characterized by the following steps:

[0058] Step 1: Divide the river cross section into grids, and divide each grid point into inner and outer zones;

[0059] Based on the surface velocity distribution measured by microwave radar, N vertical lines are set, where N is the number of surface velocity points measured by the microwave radar. In this embodiment, each vertical line is vertically divided equally, taking into account the set vertical distance resolution of 0.02m, so that the river cross section is divided into multiple discrete grid points. The river is further divided into inner and outer zones according to the vertical distance of each grid point from the riverbed. The division of the inner and outer zones satisfies the following relationship:

[0060] ;

[0061] In the formula, The vertical distance from the grid point to the riverbed. The water depth along the perpendicular line to the grid point;

[0062] All grid points are divided into inner and outer zones using the method described above. Alternatively, in other embodiments, other vertical distances such as 0.15h can be chosen as the boundary between the inner and outer zones.

[0063] Step 2: Calculate the eddy viscosity in the outer region and obtain the flow velocity at the boundary between the inner and outer regions based on the calculated eddy viscosity and the surface velocity distribution measured by radar.

[0064] Based on the Boussinesq hypothesis, for a steady, uniform, and fully grown river, the RANS equation in the flow direction is expressed as follows:

[0065] ;

[0066] In the formula, Let be the kinematic viscosity coefficient of the liquid. The flow velocity is in the direction of flow. and These represent the lateral and vertical directions, respectively. Eeddy current viscosity, It is the acceleration due to gravity. Indicates the riverbed slope;

[0067] In the central part of the river cross-section, exist The change in direction is much greater than Changes in direction and It can be ignored that in the outer region, turbulent stress dominates, while viscous stress term is negligible. and It can be ignored; RANS can be simplified to:

[0068] ;

[0069] In the formula, The viscosity of the outer eddy current is... Indicates the flow velocity in the outer zone;

[0070] The RANS equations are transferred along the vertical direction from... Integrating to water depth We can obtain:

[0071]

[0072] On the surface of the river, The RANS equation can be expressed as:

[0073]

[0074] The RANS equations are applied vertically from the lower boundary of the outer region. z 1 =0.2h Integrate to the upper boundary of the outer region z 2 =h We can obtain:

[0075] ;

[0076] In the formula, Shear velocity, For surface flow rate, The flow velocity at the boundary between the inner and outer zones;

[0077] According to Prandtl's mixing length theory, the viscosity of the inner eddy current... for:

[0078] ;

[0079] In the formula, Karman's constant, This represents the vertical distance from the grid points in the inner area to the riverbed.

[0080] because and At the boundary between the inner and outer zones The same in place, therefore ;

[0081] Therefore, at any vertical line, substituting the inner eddy viscosity into the above formula yields the outer eddy viscosity of the single vertical line and the flow velocity at the boundary between the inner and outer regions:

[0082]

[0083]

[0084] In the formula, For the first The viscosity of the eddy current in the outer region of the root perpendicular line, Karman's constant, For the first The water depth at the root perpendicular line, For the first Shear velocity along the root vertical line, Represents gravitational acceleration. Indicates the riverbed slope. Indicates the first The flow velocity at the boundary between the inner and outer regions of the root perpendicular. For the first Surface velocity along the root perpendicular line.

[0085] Step 3: Calculate the flow velocity at the grid points in the inner zone based on the flow velocity at the boundary point between the inner and outer zones obtained in Step 2;

[0086] In this step, the flow velocity at the boundary point between the inner and outer zones obtained in step 2 is calculated using the logarithmic deficit law for each vertical line; the formula for calculating the flow velocity at the inner zone grid point of a single vertical line is as follows:

[0087]

[0088] In the formula, The perpendicular line number. Indicates the vertical distance from the riverbed as Flow velocity at the inner grid points;

[0089] Repeat this step for N perpendicular lines until the velocity calculation of the inner grid points of all perpendicular lines is completed.

[0090] Step 4: Calculate the flow velocity at each grid point in the outer zone based on the surface velocity distribution measured by radar and the flow velocity at the boundary between the inner and outer zones;

[0091] Step 4.1, establishing the RANS equations in the flow direction of the outer region, can be expressed as:

[0092]

[0093] The symbols in the above formula that are the same as those in step 2 also have the same meaning; according to Figure 2 Discretization is performed using the finite difference method shown. , ,in, The perpendicular line number. For the first Grid point numbers in the inner and outer zones of the root perpendicular line. The distance between two adjacent perpendicular lines. This is the set vertical distance resolution. The first perpendicular line inside the root The RANS equations corresponding to the flow velocities at each outer grid point can be transformed into linear equations as follows:

[0094]

[0095] ;

[0096] Step 4-2: Convert the flow velocity at each grid point in the outer zone into the linear equations obtained in Step 4-1. All linear equations form a system of linear equations. Assuming the cross section contains M grid points in the outer zone, set a linear equation obtained from Step 4-1 for each grid point in the outer zone. The system of linear equations consisting of M linear equations can be expressed as:

[0097] ;

[0098] In the formula, For the first In the linear equations coefficient, Indicates the first Flow velocity at grid points in the outer region It is the first The outer boundary velocity term included in the linear equations is the right-hand side term of the linear equation;

[0099] Using matrices , , , Let the coefficients, outer zone grid point velocities, outer zone boundary velocity terms, and right-hand side terms in each linear equation be represented respectively, to obtain:

[0100] , , ,

[0101] The system of linear equations can be represented as:

[0102] ;

[0103] Step 4-3: Calculate the values ​​of each element in matrix C based on the surface velocity along each vertical line and the velocity at the boundary points between the inner and outer zones. Then, solve the linear equations to obtain the velocity at all grid points in the outer zone. The formula for calculating the velocity at the grid points in the outer zone is as follows:

[0104] .

[0105] Step 5: Combine the inverted inner region velocity distribution, the velocity at the boundary between the inner and outer regions, the outer region velocity distribution, and the surface velocity measured by radar to obtain the cross-sectional velocity distribution. Figure 3 The result shows the cross-sectional velocity distribution obtained by applying the method of this embodiment. From... Figure 3As can be seen, the larger flow velocities are mainly concentrated in the central area of ​​the river and near the river surface, while the smaller flow velocities are concentrated in the sidewall area and near the riverbed.

[0106] To illustrate the beneficial effects of this invention, the applicant will compare the cross-sectional velocity distribution inverted in this embodiment with the measurement results of acoustic instruments, see [link to relevant documentation]. Figure 4 and Figure 5 ,from Figure 4 As can be seen from the data, the flow velocity inversion error of the entire river cross section inverted using the method of this embodiment is less than 0.1 m / s for 80% of the time. Figure 5 The scatter plot of the cross-sectional velocity distribution inverted in this embodiment and the acoustic instrument measurement results shows a correlation coefficient of 0.9, indicating that the cross-sectional velocity distribution inverted in this invention has high accuracy.

[0107] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A method for inverting cross-sectional velocity distribution based on river surface velocity, characterized in that, Includes the following steps: Step 1: Divide the river cross section into grids, and divide each grid point into an inner zone and an outer zone; Step 2: Calculate the eddy viscosity in the outer region and obtain the flow velocity at the boundary between the inner and outer regions based on the calculated eddy viscosity and the surface velocity distribution measured by radar. Step 3: Calculate the flow velocity at each grid point in the inner zone based on the flow velocity at the boundary point between the inner and outer zones obtained in Step 2; Step 4: Calculate the flow velocity at each grid point in the outer zone based on the surface velocity distribution measured by radar and the flow velocity at the boundary between the inner and outer zones; Step 5: Combine the inverted flow velocities at each inner grid point, the flow velocities at the boundary between the inner and outer regions, the flow velocities at the outer grid points, and the surface flow velocities measured by radar to obtain the cross-sectional flow velocity distribution; Step 2 specifically includes: The RANS equations in the flow direction are expressed as follows: ； In the formula, Let be the kinematic viscosity coefficient of the liquid. The flow velocity is in the direction of flow. and These represent the lateral and vertical directions, respectively. Eeddy current viscosity, It is the acceleration due to gravity. Indicates the riverbed slope; The above RANS equation can be simplified to: ； In the formula, The viscosity of the outer eddy current is... Indicates the flow velocity in the outer zone. This represents the vertical distance from the grid point to the riverbed. The RANS equations are applied vertically from the lower boundary of the outer region. z 1 point to the upper boundary of the outer area z 2. Results: ； In the formula, Shear velocity, and These are the upper boundary velocity and the lower boundary velocity, respectively. According to Prandtl's mixing length theory, the viscosity of the inner eddy current... for: ； In the formula, Karman's constant, This represents the vertical distance from the grid points in the inner area to the riverbed. and The same applies at the lower boundary, which is the dividing point between the inner and outer zones: ， The viscosity of the outer eddy current is thus obtained as: ; Substituting the outer region eddy viscosity into the above RANS equation, we obtain the flow velocity at the boundary between the inner and outer regions: ； In the formula, Karman's constant, h The water depth is the perpendicular line to the grid point. Shear velocity, Represents gravitational acceleration. Indicates the riverbed slope. This indicates the flow velocity at the boundary between the inner and outer zones. The velocity at the upper boundary of the outer region is the surface velocity at that grid point, obtained from the surface velocity distribution measured by radar. In step 3, the flow velocity at the boundary point between the inner and outer zones obtained in step 2 is calculated using the logarithmic deficit law. The formula for calculating the flow velocity at the inner zone grid points is as follows: In the formula, Indicates the vertical distance from the riverbed as The inner zone grid point velocity, z1 is the vertical distance from the grid point at the boundary between the inner and outer zones to the riverbed. Indicates the flow velocity at the boundary between the inner and outer zones; Step 4 specifically includes the following sub-steps: Step 4.1: Establish the RANS equations in the flow direction of the outer region, and discretize them into linear equations corresponding to the flow velocities of each grid point in the outer region on each vertical line using the finite difference method. Step 4.2: Convert the flow velocity at each grid point in the outer zone into the linear equations from Step 4-1. All linear equations form a system of linear equations. For the system of linear equations, use a matrix... , , , These respectively represent the coefficients, the flow velocity at the outer grid points, the outer boundary flow velocity term in each linear equation, and the right-hand side term. The linear equation system is expressed as: ； Step 4-3: Calculate the values ​​of each element in matrix C based on the surface velocity along each vertical line and the velocity at the boundary points between the inner and outer zones. Then, solve the linear equations to obtain the velocity at all grid points in the outer zone. The formula for calculating the velocity at the grid points in the outer zone is as follows: 。 2. The method for inverting cross-sectional velocity distribution based on river surface velocity according to claim 1, characterized in that, Step 1, specifically the gridding of the river cross-section, includes: Based on the surface velocity distribution measured by microwave radar, N vertical lines are set up, where N is the number of surface velocity points measured by microwave radar. Combined with the set vertical distance resolution, each vertical line is vertically divided into multiple discrete grid points, so that the river cross section is divided into multiple discrete grid points. The grid points are divided into inner and outer zones according to the vertical distance of each grid point from the riverbed. The grid points closer to the riverbed are divided into the inner zone, and the grid points farther away from the riverbed are divided into the outer zone.

3. The method for inverting cross-sectional velocity distribution based on river surface velocity according to claim 2, characterized in that, The division between the inner and outer zones satisfies the following relationship: ； In the formula, z is the vertical distance from the grid point to the riverbed. denoted by , where is the vertical distance from the grid point at the boundary between the inner and outer zones to the riverbed, and h is the water depth along the vertical line where the grid point is located.

Images