System and method for calculating lateral mixing coefficient of pollutants in vegetated ecological rivers

Abstract

The system and method for calculating the lateral mixing coefficient of pollutants in vegetated ecological rivers, by selecting three different types of vegetation, carried out pollutant concentration tests in flumes with vegetation on beach, and calculated the measured TMC values ​​by linear graphical method. Through dimensional analysis, the parameters affecting TMC were studied, and the characteristics of vegetation were innovatively taken into account, and the adjustment length scale was introduced and dimensionless with the vegetation inundation height, so as to construct a new TMC influencing factor. Based on the flume test results and dimensional analysis, the flume was divided into the slope-main flume area and the slope-beach area in the horizontal direction, and the empirical formula for TMC prediction was constructed for each area. Error analysis shows that the formula can predict TMC well. The system and method for calculating the lateral mixing coefficient of pollutants in vegetated ecological rivers of the present invention are of great significance for evaluating the diffusion of pollutants, predicting the response and stability of ecosystems, and guiding related environmental management and protection work.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulics and river dynamics, and more specifically, to a system and method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river. Background Art

[0002] River mixing is an extremely complex process, which is of great significance to river ecological environment protection, pollution control and treatment, and scientific management of water resources. The transverse mixing coefficient (TMC) is a parameter that describes the degree of transverse mixing in a river. It indicates the rate and degree of material transfer and mixing between different parts of the river. Most scholars are keen to establish a relationship between the sinuosity of natural rivers and TMC. However, in natural rivers, the presence of vegetation also plays an important role in TMC.

[0003] In the process of modernization, when pollutants enter rivers and mix with water, the water is polluted. Due to irregularities such as flow velocity, bed structure, secondary flow development, and dead zones, the mixing process of pollutants in rivers is very complex. Studies have shown that pollutants entering rivers will experience three stages: vertical mixing, lateral mixing, and longitudinal mixing. At present, research on mixed transport of pollutants mainly focuses on lateral and longitudinal mixing.

[0004] In the study of lateral mixing, scholars usually focus on the study of lateral mixing coefficients in straight river channels (Azamathulla & Ahmad, 2012; Chau, 2000) and natural meandering river channels (Baek & Seo, 2013; Yotsukura & Sayre, 1976), while the study of lateral mixing coefficients in compound river channels is relatively rare. Since natural rivers usually appear as compound river channels with side beaches, and vegetation is widely present in the side beaches, the flow characteristics and vegetation characteristics of compound river channels will affect the lateral mixing coefficient, making the lateral mixing process more complicated. For example, vegetation will reduce the flow rate, making the water flow between vegetation relatively uniform, and around each plant, a large number of vortices and vortex streets will be generated, which changes the lateral mixing process of pollutants. At the junction of vegetated and non-vegetated areas, the turbulence of water flow accelerates the lateral exchange of materials, making the lateral mixing process more complicated.

[0005] Therefore, the problems existing in the prior art need to be further improved and developed. Summary of the invention

[0006] (I) Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a system and method for calculating the lateral mixing coefficient of pollutants in vegetated ecological rivers.

[0007] (II) Technical solution: In order to solve the above technical problems, this technical solution provides a method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river, which is applied to a system for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river. The system includes a region determination unit, a measurement unit, a prediction unit, and an error unit, specifically including:

[0008] Step 1. The area determination unit divides the compound river channel into different test areas in the horizontal direction, monitors the pollutant concentration of each monitoring point on the measuring point section, and determines the measured data of the monitoring points under different working conditions;

[0009] Step 2: The measurement unit determines the TMC relationship by solving the basic equation of the two-dimensional stable water quality model, and obtains the TMC of different test areas based on the measured data. 实测 value;

[0010] Step 3. The prediction unit considers vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs TMC empirical formulas of different test areas, and calculates the TMC of different test areas. 预测 value;

[0011] Step 4. The error unit is passed through TMC 实测 With TMC 预测 The error between them verifies the accuracy of the empirical formula.

[0012] Furthermore, the compound river channel includes a main channel area, a slope area and a beach area in the transverse direction, that is, along the river width; the test area includes two areas: the slope-main channel area and the slope-beach area.

[0013] The slope area is between the main trough area and the beach area. The main trough area is a flat area without vegetation, forming a first boundary with the slope area; the beach area is a flat area with vegetation, forming a second boundary with the slope area; the first boundary and the second boundary form the slope area, and the slope area is an area without vegetation and has a slope, and the depth gradually decreases on the side close to the beach area.

[0014] The measuring point section is located in the fully developed water flow area, and the measuring point section position is: X B =min{3.5B,7h v ′}, where B is the width of the water tank, h v ′ is the height of submerged vegetation.

[0015] Furthermore, the step 2 comprises:

[0016] Step 201. The measuring unit draws a Ct curve showing the change of pollutant concentration over time under different working conditions according to the measured data;

[0017] Step 202. Determine the solution equation of the basic equation of the two-dimensional stable water quality model including the transverse mixing coefficient TMC;

[0018] Step 203: Construct a linear equation to determine the TMC relationship, and calculate the TMC of each test area based on the measured data. 实测 value.

[0019] Furthermore, the solution equation is: Where C′ is the tracer concentration at the point (x, y) downstream of the injection point; Q is the flow rate; L q is the tracer solution concentration; x, y are spatial coordinate variables; k1 is the first-order reaction rate constant of the tracer, when the tracer is inert, k1 = 0;

[0020] The linear equation of one variable: Y=A0+A1X,

[0021] The TMC relationship is:

[0022] Furthermore, the step 3 comprises:

[0023] Step 301: The prediction unit determines the functional relationship between the TMC of the slope-main groove area and related parameters;

[0024] Step 302: Introduce the characteristic length scale of the influencing factor to non-dimensionalize the vegetation characteristic parameters, and determine the TMC function relationship of the slope-beach area;

[0025] Step 303. Perform correlation analysis between dependent variables and independent variables on the TMC function relationship between the slope-main trough area and the slope-beach area, and construct TMC empirical formulas for the slope-main trough and slope-beach, respectively, and then calculate the TMC of the slope-main trough area and slope-beach area respectively. 预测 value.

[0026] Furthermore, the related parameters include three aspects: fluid properties, hydraulic parameters, and geometric properties. The functional relationship between the related parameters and TMC is: y =f1(u,u * ,B,H,ρ,μ,S,S n ,g), where u is the flow velocity, u * is the shear velocity, B is the river width, H is the water depth, ρ is the water flow density, μ is the water flow kinematic viscosity, S is the riverbed slope, S n is the sinuosity and g is the acceleration due to gravity.

[0027] Furthermore, ignoring the parameter S and Reynolds number, the functional relationship between TMC and related parameters in the slope-main channel area is:

[0028] Furthermore, the vegetation characteristic parameters include vegetation height, vegetation diameter, and density parameters.

[0029] The characteristic length scale: l c =(C d a) -1 , where Cd is the vegetation drag coefficient, Cd is equal to 1.0, and a = mD is the vegetation volume retaining area;

[0030] The characteristic length scale is dimensionless with the vegetation submergence height: h v ′ / l c ;

[0031] The TMC function relationship of the slope-beach area is:

[0032] The empirical formula for TMC in the slope-main channel area is:

[0033]

[0034] The empirical formula for TMC in the slope-beach area is:

[0035]

[0036] Furthermore, TMC is calculated 实测 With TMC 预测 The absolute error AE, relative error RE, and root mean square error RMSE are between them; the smaller the absolute error AE, the smaller the error, the smaller the relative error RE, the higher the accuracy, the smaller the root mean square error, and the TMC 实测 With TMC 预测 The higher the fit, the higher the accuracy.

[0037] The lateral mixing coefficient calculation system of pollutants in vegetation ecological rivers includes a region determination unit, a measurement unit, a prediction unit, and an error unit. The region determination unit monitors the pollutant concentration of each monitoring point on the measurement point section to obtain the measured data of each monitoring point under different working conditions in each test area; the measurement unit determines the TMC relationship by solving the basic equation of the two-dimensional stable water quality model, and obtains the TMC of different test areas based on the measured data. 实测 The prediction unit considers the vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs the TMC empirical formula of different test areas, and obtains the TMC of different test areas.预测 value; the error unit will be obtained by the system TMC 实测 Value and TMC 预测 The values ​​were compared to verify the accuracy of the TMC empirical formula.

[0038] (III) Beneficial effects: The present invention provides a system and method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river channel, and uses a linear graphical method to calculate the TMC 实测 The calculations were carried out. Through dimensional analysis, the parameters affecting TMC were determined, and considering the characteristics of vegetation, the length scale was adjusted and dimensionless was made with the vegetation inundation height, and a new TMC influencing factor was constructed. Based on the measured data and dimensional analysis, the TMC empirical formulas for different test areas were constructed respectively. Finally, the accuracy of the empirical formulas was verified through error analysis, which is of great significance for evaluating the diffusion of pollutants, predicting the response and stability of ecosystems, and guiding related environmental management and protection work. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of the structure of the test water tank of the present invention;

[0040] Figure 2 It is a schematic diagram of the division of the test area;

[0041] Figure 3 It is a schematic diagram of the dimensions of the simulated vegetation;

[0042] Figure 4 It is a schematic diagram of the arrangement of monitoring points in the present invention;

[0043] Figure 5 It is a schematic diagram of the Ct curve of the change of pollutant concentration over time under different working conditions in the present invention;

[0044] Figure 6 It is a schematic diagram of the results of correlation analysis of different test areas in the present invention;

[0045] Figure 7 TMC in the present invention 实测 With TMC 预测 A comparison chart between

[0046] Figure 8 It is a flow chart of the steps of the system and method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river channel of the present invention. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below in conjunction with preferred embodiments. More details are elaborated in the following description to facilitate a full understanding of the present invention. However, the present invention can obviously be implemented in a variety of other ways different from the description. Those skilled in the art can make similar generalizations and deductions based on actual application situations without violating the connotation of the present invention. Therefore, the protection scope of the present invention should not be limited by the content of this specific embodiment.

[0048] The accompanying drawings are schematic diagrams of embodiments of the present invention. It should be noted that the drawings are only examples and are not drawn to scale, and should not be used to limit the actual protection scope of the present invention.

[0049] The method for calculating the lateral mixing coefficient of pollutants in vegetated ecological rivers is applied to the lateral mixing coefficient calculation system of pollutants in vegetated ecological rivers. The system includes a region determination unit, a measurement unit, a prediction unit, and an error unit. The region determination unit monitors the pollutant concentration of each monitoring point on the measurement point section and obtains the measured data of each monitoring point under different working conditions in each test area. The measurement unit determines the TMC relationship by solving the basic equation of the two-dimensional stable water quality model, and obtains the TMC of different test areas based on the measured data. 实测 The prediction unit considers the vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs TMC empirical formulas of different test areas, and obtains TMC of different test areas. 预测 The error unit will be obtained by the system TMC 实测 Value and TMC 预测 The values ​​were compared to verify the accuracy of the TMC empirical formula.

[0050] The calculation method of the lateral mixing coefficient of pollutants in vegetated ecological rivers specifically includes the following steps:

[0051] Step 1. The area determination unit divides the compound river channel into different test areas in the horizontal direction, monitors the pollutant concentration of each monitoring point on the measuring point section, and determines the measured data of the monitoring points under different working conditions;

[0052] Step 2: The measuring unit establishes a linear equation based on the measured data to calculate the TMC of different test areas. 实测 value;

[0053] Step 3. The prediction unit considers vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs TMC empirical formulas of different test areas, and calculates the TMC of different test areas. 预测 value;

[0054] Step 4. The error unit is passed through TMC 实测 With TMC 预测 The error between them verifies the accuracy of the empirical formula.

[0055] Specifically, the step 1 includes the following steps:

[0056] Step 101. The area determination unit divides the test area of ​​the retest river channel in the horizontal direction;

[0057] In the present invention, the compound river channel includes a main trough area, a slope area and a beach area in the transverse direction, that is, along the river width. The slope area is between the main trough area and the beach area. The main trough area is a flat area without vegetation, forming a first boundary with the slope area; the beach area is a flat area with vegetation, forming a second boundary with the slope area; the first boundary and the second boundary form the slope area, and the slope area is a slope area, and the depth gradually decreases on the side close to the beach area. The test area includes two areas: the slope-main trough area and the slope-beach area.

[0058] Step 102: Determine the measuring point section of the monitoring point;

[0059] The measuring point section should be located in the fully developed area of ​​water flow: after the tracer is injected, it will be evenly mixed in the fully developed area of ​​water flow to determine the fully developed area of ​​water flow: X B =min{3.5B,7h v ′},

[0060] Where B is the width of the water tank, h v ′ is the height of submerged vegetation.

[0061] Step 103. Setting monitoring points on the measuring point section according to different working conditions, and monitoring the pollutant concentration at each monitoring point by monitoring equipment to obtain measured data of each monitoring point under different working conditions.

[0062] Different working conditions are determined according to different planted vegetation and water depths. Monitoring points are set in the main channel area, slope area, and beach area in the horizontal direction on the measuring point section. Under the same working condition, two monitoring devices are used to monitor the tracer concentration change process of the main channel-slope and slope-beach at the measuring point section, so as to study the transport of pollutants.

[0063] Specifically, step 2 includes the following steps:

[0064] Step 201. The measuring unit draws a Ct curve showing the change of pollutant concentration over time under different working conditions based on the measured data.

[0065] Before drawing the Ct curve, it is necessary to dimensionlessly convert the tracer concentration values ​​of the main trough-slope and slope-beach at the measuring point section into the peak value of the pollutant concentration at each monitoring point according to the measured data.

[0066] Step 202. Determine the equation for the solution of the basic equation of the two-dimensional stable water quality model containing the transverse mixing coefficient TMC.

[0067] The water flow direction is the longitudinal x, the river width direction is the transverse y, and the discharge point is the origin of the coordinate system.

[0068] According to the law of conservation of mass, the pollutant concentration distribution can be represented by a two-dimensional model:

[0069]

[0070] Where C is the average pollutant concentration at depth (kg / m3); x and y are the longitudinal and transverse directions, respectively; H is the depth of the water flow (m); U x and U y are the flow velocities in the x and y directions (m / s), M y is TMC(m 2 / s).

[0071] If the river flow is uniform and the longitudinal dispersion of the tracer in the river is ignored, that is, U y = 0, the basic equation of the two-dimensional stable water quality model of the river is:

[0072]

[0073] The solution to this equation is:

[0074]

[0075] Where C′ is the tracer concentration at the point (x, y) downstream of the injection point; Q is the flow rate; L q is the concentration of the tracer solution; x, y are spatial coordinate variables; k1 is the first-order reaction rate constant of the tracer. When the tracer is inert, k1=0.

[0076] Step 203: Construct a linear equation to determine the TMC relationship, and calculate the TMC of each test area based on the measured data. 实测 value.

[0077] Taking the logarithm of both ends of equation (3) yields:

[0078]

[0079] Let: Y = lnC′ (5)

[0080] X=y2 (6)

[0081] That is:

[0082]

[0083] Then formula (4) can be written as:

[0084] Y=A0+A1X (9)

[0085] From equations (5-8), we can know that Y is a function of the test data C', X is a function of y, and A0 and A1 contain parameters to be determined. According to the linear regression method, the values ​​of A0 and A1 are calculated. q , H and k1 are known, M can be derived as follows y Relational formula:

[0086]

[0087] According to the measured data, the TMC of each test area is calculated. 实测 value.

[0088] Specifically, step 3 includes the following steps:

[0089] Step 301: The prediction unit determines the functional relationship between the TMC of the slope-main groove area and related parameters.

[0090] In rivers, the relevant parameters that affect pollutant transport include: fluid properties, hydraulic parameters, and geometric properties. Among them, water flow density and viscosity are selected from the fluid properties, river width, water depth, cross-sectional average flow velocity and friction flow velocity are selected from the hydraulic parameters, and riverbed slope and sinuosity are selected from the geometric properties.

[0091] A functional relationship with TMC is established according to the relevant parameters:

[0092] M y =f1(u,u * ,B,H,ρ,μ,S,S n ,g)(11)

[0093] Where, u is the water flow velocity, u * is the shear velocity, B is the river width, H is the water depth, ρ is the water flow density, μ is the water flow kinematic viscosity, S is the riverbed slope, S n is the sinuosity and g is the acceleration due to gravity.

[0094] Take S n =1, then: M y =f1(u,u * ,B,H,ρ,μ,S,g)(12)

[0095] Considering the influence of transverse shear velocity on the transverse mixing process, the functional relationship between the normalized parameters is obtained according to Buckingham's Pi-theorem:

[0096]

[0097] in, is the Reynolds number.

[0098] Since the effect of vertical irregularities is included in the friction term, the parameter S can be ignored (Jeon et al., 2007). For fully turbulent flow in a rough open channel, the effect of the Reynolds number can also be ignored (Seo & Cheong, 1998). Therefore, equation (13) can be written as

[0099]

[0100] Step 302: Introduce the characteristic length scale of the influencing factor to non-dimensionalize the vegetation characteristic parameters and determine the TMC function relationship of the slope-beach area.

[0101] Since the characteristics of vegetation affect the movement of pollutants in water bodies, vegetation characteristic parameters are introduced in the present invention. The vegetation characteristic parameters include vegetation height, vegetation diameter, and density parameters. Then, the above formula (14) can be written as:

[0102]

[0103] Among them, h v ′ is the height of underwater vegetation, D is the diameter of vegetation, and m is the density of vegetation.

[0104] In order to make the vegetation characteristic parameters dimensionless, the characteristic length scale is introduced: l c =(C d a) -1 , unit is (m). Among them, C d is the vegetation drag coefficient. According to the research of Tanino & Nepf (2008) and Stone and Shen (2002), the vegetation drag coefficient C d It can be considered equal to 1.0; a = mD is the water retaining area of ​​vegetation volume. The characteristic length scale and the vegetation flooding height are dimensionless to obtain: h v ′ / l c Therefore, formula (15) can be written as:

[0105]

[0106] Step 303. Perform correlation analysis between dependent variables and independent variables on the TMC function relationship of the slope-main trough area and the slope-beach area, and construct TMC empirical formulas for the slope-main trough and slope-beach respectively, and then calculate the TMC prediction values ​​of the slope-main trough area and slope-beach area respectively.

[0107] For the slope-main channel area, the lateral mixing of pollutants does not involve vegetation. The lateral mixing process can be regarded as occurring in an independent open channel. At this time, the river channel width is B1, and the water depth is the corresponding cross-section average water depth H1. Formula (14) can be rewritten as:

[0108]

[0109] Where: M y1 is the TMC in the area of ​​the slope-main channel.

[0110] For the slope-beach area, the pollutants are mixed horizontally and are affected by vegetation. While considering the characteristics of vegetation, the slope-beach area is regarded as an independent open channel. At this time, the river width is B2 and the water depth is the corresponding cross-section average water depth H2. Formula (16) is rewritten as:

[0111]

[0112] Where: M y2 is the TMC in the area of ​​the slope-main channel.

[0113] Based on equations (17) and (18), we can respectively and Carry out correlation analysis; In addition, and Conduct correlation analysis.

[0114] According to the correlation analysis results, the transverse mixing coefficient TMC formula is constructed empirically:

[0115] For the slope-main channel area, the TMC calculation formula is:

[0116]

[0117] For the slope-beach area, the TMC calculation formula is:

[0118]

[0119] The specific coefficients in equations (19) and (20) can be calculated using methods such as nonlinear regression and genetic algorithms.

[0120] Finally, the TMC of the slope-main channel area and the slope-beach area is calculated according to equations (19) and (20). 预测 value.

[0121] Specifically, in step 4, the error unit calculates

[0122] TMC 实测 With TMC 预测 The absolute error AE between:

[0123]

[0124] TMC 实测 With TMC 预测 The relative error RE between:

[0125]

[0126] Root mean square error RMSE:

[0127]

[0128] Among them, TMC 预测 is the predicted value calculated by the empirical formula, TMC 实测 is the measured value calculated by the histogram solution method in the experiment, and NUM is the number of monitoring points under each working condition.

[0129] The smaller the absolute error AE, the smaller the error. The smaller the relative error RE, the higher the accuracy. The relative error is around 10%, which can be considered accurate. The root mean square error is used to indicate the degree of fit between the calculated value and the measured value. The smaller the root mean square error, the better the TMC. 实测 Value and TMC 预测 The better the fit between the values, the higher the accuracy.

[0130] In a first preferred embodiment of the present invention, a test water tank is used to simulate the compound river channel morphology. The test water tank is a variable slope circulation water tank made of glass. Figure 1 As shown, the test trough is rectangular, and the dimensions are: length × width × depth = 10m × 1.0m × 1.0m. The bottom of the test trough is paved with a PVC bottom plate. The test trough is divided into three areas on the horizontal y-axis: the main trough, the slope, and the beach. The width of the main trough area is 0.4m, the height and width of the slope area are both 0.2m, and the height and width of the beach area are 0.2m and 0.4m respectively. The test trough is divided into two test areas in the horizontal direction: I slope-main trough area and II slope-beach area. Figure 2 shown.

[0131] During the test, the upstream valve and the downstream tail gate are controlled to maintain a constant uniform flow condition under different working conditions, so that the water depth in the test water tank meets the test requirements under different working conditions.

[0132] In this experiment, three types of artificial vegetation, namely, short grass, sedge and reed, were used as research objects to simulate the composite river channel with beach vegetation. Figure 3 As shown. Among them, the height of the simulated dwarf grass is 0.06m, the base diameter is 0.025m, the vegetation width varies with the vegetation height, and the maximum width is 0.07m. The height of the simulated sedge used is 0.135m, the base diameter is 0.033m, the vegetation width varies with the vegetation height, and the maximum width is 0.08m. The simulated reed used is 0.6m, the vegetation width is 0.006m, and there are 7 leaves on each reed on average. The three types of simulated vegetation are used as rigid vegetation and are all laid in parallel in the beach area. The lateral spacing between vegetation is 0.075m, the longitudinal spacing is 0.1m, and the density is 134 plants / m 2 The length of the covered riverbed is 6.5 m. According to the different vegetation and water depth, this test is divided into 4 working conditions. Under the 4 working conditions, the test parameters are shown in Table 1.

[0133] Table 1 Test conditions parameters

[0134] Run <![CDATA[Q(m 3 / s)]]> Vegetation Type <![CDATA[h w (m)]]> <![CDATA[h s (m)]]> <![CDATA[h v (m)]]> <![CDATA[m (shares / m 2 )]]> s B(m) state Run1 0.03 Short grass 0.4 0.2 0.06 134 1 1 Submerged Run2 0.03 Sedge 0.3 0.1 0.135 134 1 1 Non-flooded Run3 0.03 Sedge 0.5 0.3 0.135 134 1 1 Submerged Run4 0.03 reed 0.3 0.1 0.60 134 1 1 Non-flooded

[0135] Among them, h w is the main tank water depth; h s is the beach water depth; s is the slope gradient (1:s = horizontal distance: vertical distance).

[0136] In this test, two multi-parameter water quality monitors (YSI) were used to monitor the changes in the measurement points in different test areas, and rhodamine reagent was used as a tracer to release pollutants. The rhodamine tracer (C0 = 10g / L) was placed at a section 0.5m from the entrance of the water tank, and the syringe was placed vertically at full water depth without pressurization (atmospheric pressure) at y = 0.5B.

[0137] The measuring point section is located in the fully developed water flow area: after the tracer is injected, it will be evenly mixed in the fully developed water flow area. B =min{3.5B,7h v ′}, where B is the width of the water channel and hv′ is the height of the submerged vegetation. Through measurement, it is believed that X B =4.5 meters, the water flow can be fully developed, so in this test, the measuring point section is located 4.5m downstream of the injection section.

[0138] In this test, monitoring points YSI-a, YSI-b, and YSI-c were set at the measuring point sections in the main trough area, slope area, and beach area along the horizontal direction. The specific arrangement of the monitoring points is as follows: Figure 4 shown.

[0139] It should be noted that in each working condition of this experiment, the pollutant transport test is divided into two tests: slope-main channel and slope-beach. In addition, in order to avoid the residual rhodamine tracer in the previous working condition affecting the data collection of the next working condition, the water needs to be replaced after each test.

[0140] According to the measured data, the rhodamine concentration values ​​of the two test areas at the measuring point section were dimensionless based on the peak concentration of the pollutant concentration at each measuring point, and the Ct curves of the pollutant concentration changing with time under the four working conditions were drawn, as shown in Figure 5 shown.

[0141] Based on the measured data of this experiment, q Under the condition that H and k1 are known, the TMC of the two test areas is calculated according to formula (10): 实测 The values ​​are shown in Table 2 below:

[0142] Table 2 Transverse mixing coefficient under different working conditions

[0143]

[0144] In this experiment, the slope-main channel area and the slope-side beach area were regarded as an independent open channel, where in the slope-main channel area, the river channel width B1=0.5, and the water depth was the corresponding cross-sectional average water depth H1; in the slope-side beach area, the river channel width B2=0.5, and the water depth was the corresponding cross-sectional average water depth H2.

[0145] Based on equations (17) and (18), we can respectively and Carry out correlation analysis; In addition, and The correlation analysis was performed and the results were as follows Figure 6 shown.

[0146] It can be seen from the results that in the slope-main groove area, and Negatively correlated with In the slope-beach area, and There is a positive correlation with a high correlation coefficient. The TMC empirical formulas of different test areas were obtained through analysis.

[0147] The empirical formula for TMC in the slope-main channel is:

[0148]

[0149] The empirical formula for TMC in slope-beach is:

[0150]

[0151] The TMC of the slope-main channel area and the slope-beach area can be calculated by equations (19) and (20) respectively: 预测 value, get TMC 实测 Value and TMC 预测 A comparison chart between values, such as Figure 7 shown.

[0152] By calculating TMC 实测 Value and TMC 预测 The error between the values, and the error in the different test areas are obtained, as shown in Table 3:

[0153] Table 3 TMC error analysis table in the test area

[0154] RMSE AE RE <![CDATA[M y1 ]]> <![CDATA[1.38×10 -4 ]]> <![CDATA[1.25×10 -4 ]]> 10.38 <![CDATA[M y2 ]]> <![CDATA[3.90×10 -5 ]]> <![CDATA[3.88×10 -5 ]]> 1.41

[0155] As shown in Table 4, in the slope-main trough area, the average absolute error of TMC is 1.38×10-4, the average relative error is 1.25×10-4, and the root mean square error is 10.38; in the slope-beach area, the average absolute error of TMC is 3.90×10-5, the average absolute error is 3.88×10-5, and the root mean square error is 1.41. The results show that the empirical formula can be used to predict TMC in the test area.

[0156] The present invention provides a system and method for calculating the lateral mixing coefficient of pollutants in a vegetation ecological river, and uses a linear graphical method to calculate the TMC. 实测 The calculations were carried out. Through dimensional analysis, the parameters affecting TMC were determined, and considering the characteristics of vegetation, the length scale was adjusted and dimensionless was made with the vegetation inundation height, and a new TMC influencing factor was constructed. Based on the measured data and dimensional analysis, the TMC empirical formulas for different test areas were constructed respectively. Finally, the accuracy of the empirical formulas was verified through error analysis, which is of great significance for evaluating the diffusion of pollutants, predicting the response and stability of ecosystems, and guiding related environmental management and protection work.

[0157] The above content is an explanation of the preferred embodiments of the present invention, which can help those skilled in the art to more fully understand the technical solution of the present invention. However, these embodiments are merely illustrative, and it cannot be determined that the specific implementation methods of the present invention are limited to the description of these embodiments. For ordinary technicians in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions and transformations can be made, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. The method for calculating the lateral mixing coefficient of pollutants in vegetated ecological rivers is characterized by: include, Step 1. The area determination unit divides the compound river channel into different test areas in the horizontal direction, monitors the pollutant concentration at each monitoring point on the measurement point section, and determines the measured data of the monitoring points under different working conditions; Step 2. The measurement unit determines the TMC relationship by solving the basic equation of the two-dimensional stable water quality model, and obtains the TMC of different test areas based on the measured data. 实测 value; Step 3. The prediction unit considers the vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs TMC empirical formulas of different test areas, and calculates the TMC of different test areas. 预测 value; Step 4. Error unit through TMC 实测 With TMC 预测 The error between and is used to verify the accuracy of the empirical formula; The step 2 comprises: Step 201. The measuring unit draws a Ct curve showing the change of pollutant concentration over time under different working conditions according to the measured data; Step 202. Determine the solution equation of the basic equation of the two-dimensional stable water quality model including the transverse mixing coefficient TMC; Step 203: Construct a linear equation to determine the TMC relationship, and calculate the TMC of each test area based on the measured data. 实测 value; The solution equation is: ,in, Downstream of the delivery point The tracer concentration at the point; For flow; is the tracer solution concentration; is the spatial coordinate variable; is the first-order reaction rate constant of the tracer. When the tracer is inert, , u is the water flow velocity, H for water depth; The one-variable linear equation: , , ; The TMC relationship is: ; The step 3 comprises: Step 301: The prediction unit determines the functional relationship between the TMC of the slope-main groove area and related parameters; Step 302: Introduce the characteristic length scale of the influencing factor to non-dimensionalize the vegetation characteristic parameters, and determine the TMC function relationship of the slope-beach area; Step 303. Perform correlation analysis between dependent variables and independent variables on the TMC function relationship between the slope-main trough area and the slope-beach area, and construct TMC empirical formulas for the slope-main trough and slope-beach, respectively, and then calculate the TMC of the slope-main trough area and slope-beach area respectively. 预测 value; The related parameters include three aspects: fluid properties, hydraulic parameters, and geometric properties. The functional relationship between the related parameters and TMC is: ,in, u is the water flow velocity, is the shear velocity, B is the width of the river, H For water depth, is the water flow density, μ is the kinematic viscosity of water flow, S is the riverbed slope, S n is the curvature, g is the acceleration due to gravity.

2. According to the method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river according to claim 1, it is characterized in that: The compound river channel includes a main channel area, a side slope area and a side beach area in the transverse direction, i.e., along the river width; the test area includes two areas: a side slope-main channel area and a side slope-side beach area; The side slope area is between the main trough area and the side beach area. The main trough area is a flat area without vegetation, and forms a first boundary with the side slope area. The side beach area is a flat area with vegetation, and forms a second boundary with the side slope area. The first boundary and the second boundary form the side slope area, and the side slope area is an area without vegetation and has a slope, and the depth gradually decreases on the side close to the side beach area. The measuring point section is located in the fully developed water flow area, and the measuring point section position is: , where B is the width of the river, is the vegetation flooding height.

3. According to the method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river according to claim 2, it is characterized in that: Ignore Parameters S and Reynolds number, the functional relationship between TMC in the slope-main channel area and related parameters: .

4. According to the method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river according to claim 3, it is characterized in that: Vegetation characteristic parameters include vegetation height, vegetation diameter, and density parameters. Characteristic length scale: ,in, is the vegetation drag coefficient, is equal to 1.0, is the water retaining area of ​​vegetation volume, , where D is the diameter of vegetation and m is the density of vegetation; The vegetation inundation height and characteristic length scale are dimensionless: ; The TMC function relationship of the slope-beach area is: ; The empirical formula for TMC in the slope-main channel area is: ； The empirical formula for TMC in the slope-beach area is: ， Among them, M y1 is the TMC in the area of ​​slope-main channel, B1 is the river channel width in the area of ​​slope-main channel, H1 is the average water depth of the corresponding section in the area of ​​slope-main channel, M y2 is the TMC in the slope-beach area, B2 is the river channel width in the slope-beach area, and H2 is the average water depth of the section corresponding to the slope-beach area.

5. According to the method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river according to claim 1, it is characterized in that: Calculation of TMC 实测 With TMC 预测 The absolute error AE, relative error RE, and root mean square error RMSE are between them; the smaller the absolute error AE, the smaller the error, the smaller the relative error RE, the higher the accuracy, the smaller the root mean square error, and the TMC 实测 With TMC 预测 The higher the fit, the higher the accuracy.

6. A system for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river, used to implement the method for calculating the lateral mixing coefficient of pollutants in a vegetated ecological river as described in any one of claims 1 to 5, characterized in that , including an area determination unit, a measurement unit, a prediction unit, and an error unit. The area determination unit monitors the pollutant concentration of each monitoring point on the measurement point section to obtain the measured data of each monitoring point under different working conditions in each test area; the measurement unit determines the TMC relationship by solving the basic equation of the two-dimensional stable water quality model, and obtains the TMC of different test areas based on the measured data. 实测 The prediction unit considers the vegetation characteristics, introduces new influencing factors, determines the TMC functional relationship of different test areas, performs correlation analysis and constructs the TMC empirical formula of different test areas, and obtains the TMC of different test areas. 预测 value; the error unit will be obtained by the system TMC 实测 Value and TMC 预测 The values ​​were compared to verify the accuracy of the TMC empirical formula; The measuring unit draws a Ct curve of pollutant concentration changing with time under different working conditions based on the measured data; determines the solution equation of the basic equation of the two-dimensional stable water quality model containing the lateral mixing coefficient TMC; constructs a univariate linear equation, determines the TMC relationship, and calculates the TMC of each test area based on the measured data. 实测 value; The solution equation is: ,in, Downstream of the delivery point The tracer concentration at the point; For flow; is the tracer solution concentration; is the spatial coordinate variable; is the first-order reaction rate constant of the tracer. When the tracer is inert, ; The one-variable linear equation: , , ; The TMC relationship is: ; The prediction unit determines the functional relationship between the TMC of the slope-main trough area and related parameters; introduces the dimensionless vegetation characteristic parameters of the characteristic length scale of the influencing factor to determine the TMC functional relationship of the slope-beach area; performs correlation analysis between the dependent variable and the independent variable on the TMC functional relationship of the slope-main trough area and the slope-beach area, and constructs the TMC empirical formulas of the slope-main trough and the slope-beach respectively, and then calculates the TMC of the slope-main trough area and the slope-beach area respectively. 预测 value; The related parameters include three aspects: fluid properties, hydraulic parameters, and geometric properties. The functional relationship between the related parameters and TMC is: ,in, u is the water flow velocity, is the shear velocity, B is the width of the river, H For water depth, is the water flow density, μ is the kinematic viscosity of water flow, S is the riverbed slope, S n is the curvature, g is the acceleration due to gravity.

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