A tidal river water level discharge relation analysis method based on tidal level harmonic analysis

Abstract

The application discloses a kind of tidal river reach water level discharge relation analysis method based on tidal harmonic analysis, including collecting the measured water level data of research tidal river reach hydrological site, river basin river terrain and digital elevation data;Based on tidal harmonic analysis, the characteristic parameters of each tidal component of tidal river reach tidal level and the variation characteristics of water surface elevation are obtained, and then the independent tidal flow and river runoff flow are obtained;Establish one-dimensional hydrodynamic model of tidal river reach, analyze the flow variation process and water level discharge variation relation under different water level variation scenarios;The contribution degree of tidal flow and river runoff to actual flow size and variation process is analyzed using multiple regression analysis and path analysis method, and the variation characteristics of water level discharge relation of tidal river reach are obtained.The advantage is: the water level discharge relation of tidal river reach can be quickly analyzed, without complex estuary hydrodynamic process simulation, and it is also applicable when lacking measured flow data.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydrological calculation and hydrological data compilation, and particularly relates to a tidal river water level flow relationship analysis method based on tidal level harmonic analysis. BACKGROUND

[0002] River water level flow relationship is one of the key elements of hydrological data compilation work, and the accuracy and rationality of the water level flow relationship will directly affect the reliability and timeliness of the hydrological data compilation work, and further affect the subsequent work such as hydrological forecasting, flood warning, river regulation and reservoir scheduling. The water level flow relationship can provide scientific decision-making basis for the comprehensive management of river basins, the development and sustainable utilization of water resources, and the flood control and drought resistance work. Therefore, obtaining accurate river water level flow relationship has practical significance for improving the quality of hydrological data compilation, optimizing the development and comprehensive utilization of river basin water resources, etc.

[0003] For the monitoring and acquisition process of river water level flow data, due to the complex terrain of natural river channels, the flow velocity and shape of different sections of the river are difficult to monitor in real time, and long-term continuous monitoring of river flow data requires a lot of manpower, material resources and economic resources. The continuous monitoring of river water level data is relatively easy to achieve, so most hydrological sites usually only continuously monitor river water level data, and the continuous river flow data is obtained by recursive water level flow relationship. Under the influence of factors such as river bed scouring and silting, flood rise and fall, backwater change, and tidal action, the water level flow relationship of natural river channels mostly shows a single or complex rope sleeve curve relationship, which is difficult to directly and accurately determine the mathematical function relationship, and needs to be processed by single value to build a stable single water level flow relationship curve. At present, the relatively mature river water level flow relationship calculation methods include correction factor method, fall index method, data-driven optimization method, etc. These methods are widely used in river flood process water level flow relationship calculation and checking, and have good calculation accuracy and applicability.

[0004] At present, a relatively complete hydrological data compilation system has been established for large rivers in China, and a relatively complete hydrological data database has been formed. However, for some small and medium-sized river basins, the hydrological data collection and compilation is not perfect, the river water level flow relationship acquisition and calibration work has not been carried out in the basin area, and the hydrological station can only obtain continuous water level data and lacks long time series flow data. In addition, the hydrological station in the tidal reach is mainly a tidal station, which mainly obtains continuous tidal water level data. Under the background of global climate warming, extreme weather events such as typhoon and storm surge occur frequently, and the tidal flow upwelling and erosion process in the estuarine area is intensified. When numerically simulating and analyzing the hydrodynamic process of the tidal reach, the flow data of the tidal reach is needed to calibrate and verify the model. Due to the limitation of the acquisition process of the measured data, the flow data of the tidal reach calculated by the hydrodynamic model is mainly relied on, so as to analyze the water level flow relationship of the tidal reach.

[0005] In view of the above problems, the present application provides a technical scheme based on tidal level harmonic analysis method and combined with hydrodynamic model numerical simulation analysis, which is used to solve the problem of lack of measured flow data in the tidal reach water level flow relationship analysis. The method of the present application effectively makes up for the shortcomings of the prior art, and can provide more reliable data and technical support for hydrological analysis and hydrodynamic model research in the tidal reach. SUMMARY

[0006] The purpose of the present application is to provide a tidal reach water level flow relationship analysis method based on tidal level harmonic analysis, so as to solve the aforementioned problems in the prior art.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0008] A tidal reach water level flow relationship analysis method based on tidal level harmonic analysis, comprising the following steps,

[0009] S1, tidal level harmonic analysis:

[0010] Based on the tidal level harmonic analysis, the characteristic parameters and water surface elevation variation characteristics of each tidal level segment in the tidal reach are obtained, and then the independent tidal flow and river runoff flow are obtained;

[0011] S2, one-dimensional hydrodynamic model real-time flow calculation:

[0012] The Saint-Venant equation set describing the hydrodynamic process of the tidal reach is discretized and solved to obtain the water level and flow information of each calculation section; the one-dimensional hydrodynamic equation of the tidal reach is established, and the flow variation process and water level flow variation relationship of the tidal reach under different water level variation scenarios are analyzed;

[0013] S3, multiple regression analysis and path analysis:

[0014] The tidal flow and runoff flow are set as independent variables, the actual flow is set as dependent variable, the partial regression coefficient obtained by using multiple regression analysis and the path coefficient obtained by using path analysis reflect the contribution degree of the independent variable to the value and change process of the dependent variable respectively, and the variation characteristics of the water level-flow relationship of the tidal reach are obtained.

[0015] Preferably, the step S1 specifically comprises the following contents,

[0016] S11, the classical tidal level harmonic analysis method assumes that the amplitude and phase angle of each component are constant, the tidal level time series function is represented by linear superposition of a series of cosine functions, and each cosine function used for superposition represents a component;

[0017]

[0018] Wherein, Z(t) is the observed tidal level data at t time; σ j , H j , g j are the angular frequency, amplitude and phase angle of the jth component respectively; j = 1, 2, …, J, J is the total number of components; S0 is the current sea level height;

[0019] S12, according to the amplitude and phase angle of the component, new variables a j and b j are obtained, and the tidal level time series function is linearized by using the new variables a j and b j ;

[0020]

[0021] a j = H j cosg j

[0022] b j = H j sing j

[0023] Wherein, Z(t)' is the observed tidal level data at t time linearized by using the new variables a j and b j ;

[0024] S13, when there are N time observed tidal level data, N tidal level equations can be constructed, and the least square method of multivariate function extremum is used to solve the variables a j and b j ;

[0025] S14, after the variables a j and b j are obtained, the amplitude and phase angle of each component are

[0026]

[0027] g j = arctan(b j / a j )

[0028] wherein the value range of the lag angle g j is (0, 360°); the result range of the arctangent function arctan is (-90°, 90°); the lag angle g j is corrected according to the parameters a j and b j .

[0029] S15, obtaining the fitted prediction tidal level time series and the sea level elevation change time series of the research period through the tidal level harmonic analysis and the tidal fitting prediction.

[0030] Preferably, the step S13 specifically comprises solving the following equation by using the matrix operation,

[0031] Z = KU

[0032] wherein Z is the observation tidal level data matrix; K is the known coefficient matrix; U is the unknown parameter matrix to be solved;

[0033] The specific form of the above matrix is,

[0034]

[0035] According to the least square method, the optimal solution of U is,

[0036] U = (K T K) -1 K T Z

[0037] wherein T is the transpose of the matrix.

[0038] Preferably, the steps S14 and S15 further comprise,

[0039] S15, determining the shortest observation tidal level time series length required for distinguishing each tidal component by using the Rayleigh criterion,

[0040]

[0041] wherein N0 is the observation sequence length; t0 is the observation interval; T1 and T2 are the periods of any two tidal components.

[0042] Preferably, the step S2 specifically comprises the following contents,

[0043] S21, the Saint-Venant equation set describing the shallow one-dimensional unsteady gradually varied flow movement law is used to describe the water dynamic process of the tidal river section;

[0044] S22, the four-point eccentric Preissmann implicit difference format is used to discretize and solve the Saint-Venant equation set, so as to obtain the water level and flow information of each calculation section;

[0045] S23, a one-dimensional water dynamic model of the tidal river section is established, and the water level-flow relationship change process under the action of different influencing factors of the river section is analyzed and studied;

[0046] S24, different calculation scenarios are set to analyze the water level-flow relationship of the tidal river section under the action of tides, river runoff and actual conditions.

[0047] Preferably, the one-dimensional water dynamic model of the tidal river section in step S23 is established, and specifically includes the following contents,

[0048] S231, an engineering file is established;

[0049] S232, the river system is drawn and the river terrain data is imported;

[0050] S233, the boundary conditions and initial conditions are set;

[0051] S234, the operation parameters are set;

[0052] S235, model operation and post-processing.

[0053] Preferably, the scenario setting in step S24 specifically includes,

[0054] (1) all flow boundaries are closed, and the downstream water level boundary is set to the tidal level data without the influence of river runoff; used to simulate and analyze the water level-flow relationship under the action of tides;

[0055] (2) the flow boundary is not changed, and the downstream water level boundary is set to the river water level data after removing the tidal effect; used to simulate and analyze the river runoff action;

[0056] (3) the flow boundary and the water level boundary are set to the measured data; used to simulate the actual situation and the combined action of tides and runoff.

[0057] Preferably, step S3 specifically includes the following contents,

[0058] S31, multiple regression analysis: let y be an observable random variable, affected by n factors x1, x2, …, xn, if there is a linear relationship between them, the expression is, n

[0059]

[0060] ​Wherein, a is the intercept; x i is the i-th factor, i = 1, 2, …, n; β i is the partial regression coefficient; ε is the random error, which is subject to normal distribution; is the regression variance;

[0061] The expression of the multiple regression fitting model is,

[0062]

[0063] The calculation formula of the regression sum of squares Q is,

[0064]

[0065] Let SS i = ∑X i 2 , SP ij = ∑X i Y i , SP iy = ∑X i Y; Let the coefficient matrix be A, the partial regression coefficient matrix be b, and the constant matrix be K. According to the least squares method, the relationship between the three matrices is expressed as,

[0066] Ab = K

[0067] Wherein,

[0068]

[0069] The optimal solution of the partial regression coefficient matrix b is,

[0070] b = (A T A) -1 A T K

[0071] After calculating the optimal solution of the partial regression coefficient matrix b, the intercept a is,

[0072]

[0073] S32, path analysis: calculate the path coefficient p i ,

[0074]

[0075] Wherein, SS y is the total sum of squares of the dependent variable y; the path coefficient p i The value range of the path coefficient is (-1, 1), and the greater the absolute value of the path coefficient, the greater the degree of influence of the independent variable on the dependent variable.

[0076] Preferably, step S1 further comprises,

[0077] S0, data collection:

[0078] Collect the measured water level data of the hydrological station in the tidal river section, the river terrain of the basin and the digital elevation data, and process these data.

[0079] Preferably, S0 specifically comprises the following contents,

[0080] S01, obtaining the high-resolution digital elevation data of the basin area corresponding to the tidal river section from the open source data set, and performing splicing, cutting, geographic and projection coordinate setting on the high-resolution digital elevation data;

[0081] S02, obtaining the river terrain data of the tidal river section by means of sailing surveying and mapping or historical hydrological data of mobile phones, and integrating the river terrain data into the above-mentioned digital elevation data;

[0082] S03, collecting and arranging the long-period measured water level data of the hydrological station in the tidal river section, and performing time averaging processing on the measured water level data.

[0083] The beneficial effects of the present application are: 1. The method of the present application utilizes tidal level harmonic analysis and tidal component processing to explore the tidal level change rule and tidal component contribution of the tidal river section, and can obtain real-time tidal level change data without river runoff influence and river water level change data without tidal influence. 2. The method of the present application solves the problem of lack of long-period continuous measured flow data of the hydrological station in the tidal river section by calculating real-time flow by using a one-dimensional hydrodynamic model, and can calculate the real-time flow change process of the tidal river section under the action of tides and river runoff. 3. The method of the present application utilizes multiple regression analysis and path analysis to analyze the contribution degree of tidal flow and runoff to the size and change process of real-time flow, and realizes rapid analysis of the water level-flow relationship of the tidal river section lacking measured flow data. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 is a flowchart of the analysis method in the embodiment of the present application;

[0085] Figure 2 is a schematic diagram of the Preissmann implicit difference format in the embodiment of the present application;

[0086] Figure 3 is a schematic diagram of the water system in the research area in the embodiment of the present application;

[0087] Figure 4 is a schematic diagram of the results of tidal level harmonic analysis in the embodiment of the present application;

[0088] Figure 5 is a schematic diagram of the predicted tidal level and river runoff water level in the embodiment of the present application;

[0089] Figure 6 is a schematic diagram of the calculation results of tidal flow and river runoff in the embodiment of the present application;

[0090] Figure 7 is a verification result graph of multiple regression analysis in the embodiment of the present application. DETAILED DESCRIPTION

[0091] In order to make the objects, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the drawings. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0092] Embodiment one

[0093] As shown in the figure, in the embodiment, a tidal river section water level flow relationship analysis method based on tidal level harmonic analysis is provided, which includes the following four parts, Figure 1

[0094] I. Data collection

[0095] The measured water level data of the hydrological station of the tidal river section (research river section), the river terrain of the basin and the digital elevation data are collected and processed. Specifically, the following contents are included,

[0096] 1.1, the high-resolution digital elevation data of the basin area corresponding to the research river section is obtained from the open source data set, and operations such as splicing, cutting, geographic and projection coordinate setting, etc. are performed.

[0097] 1.2, the river terrain data of the research river section is obtained by using the sailing surveying and mapping or collecting historical hydrological data, and is integrated into the above digital elevation data.

[0098] 1.3, the long-term measured water level data of the hydrological station of the research river section is collected and sorted, and the measured data is processed by time averaging.

[0099] II. Tidal level harmonic analysis:

[0100] The characteristic parameters and water surface elevation variation characteristics of each tidal level segment of the tidal river section are obtained based on tidal level harmonic analysis, and then independent tidal flow and river runoff flow are obtained. Specifically, the following contents are included,

[0101] 2.1, the classic tidal level harmonic analysis method assumes that the amplitude and phase angle of each tidal segment are constant, and the tidal level time series function is represented by a linear superposition of a series of cosine functions, each cosine function used for superposition represents a tidal segment;

[0102]

[0103] ​where Z(t) is the observed tide level data at time t; σ j , H j , g j are the angular frequency, amplitude and phase angle of the jth constituent, respectively; j = 1, 2, …, J, J is the total number of constituents; S0is the current sea level elevation.

[0104] 2.2, According to the amplitude and phase angle of the constituent, new variables a j and b j are obtained, and the tide level time series function is linearized using the new variables a j and b j ;

[0105]

[0106] where,

[0107] a j = H j cos g j , b j = H j sin g j

[0108] where Z(t)' is the observed tide level data at time t linearized using the new variables a j and b j .

[0109] 2.3, When there are N observed tide level data at different times, N tide level equations can be formed, and the least squares method of multivariate function extremum is used to solve the variables a j and b j ; Specifically, in order to facilitate programming and calculation, matrix operations are used to solve,

[0110] Z = KU (3)

[0111] where Z is the observed tide level data matrix; K is the known coefficient matrix; U is the unknown parameter matrix to be solved; and the specific forms of the above matrices are,

[0112]

[0113]

[0114] According to the least squares method, the optimal solution of U is,

[0115] U = (K T K) -1 K T Z

[0116] where T is the transpose of the matrix.

[0117] 2.4, after obtaining the variables a j and b j , the amplitude and the lag angle of each constituent are,

[0118]

[0119] wherein the value range of the lag angle g j is (0, 360°); the result range of the arctangent function arctan is (-90°, 90°); the lag angle g j needs to be corrected according to the parameters a j and b j .

[0120] 2.5, in order to improve the resolution accuracy of the constituents, the Rayleigh criterion is used to determine the shortest observation tidal level time series length required for resolving each constituent,

[0121]

[0122] wherein N0 is the observation sequence length; t0 is the observation interval; T1, T2 are the periods of any two constituents;

[0123] 2.6, through the tidal level harmonic analysis and the tidal fitting prediction, the fitting prediction tidal level time series of the research period is obtained, that is, the tidal level time series without the influence of river runoff, and the sea level elevation change time series of the research period. For the tidal river section, it can be regarded as the river water level sequence reflecting the influence of river runoff after removing the influence of tidal effect.

[0124] Three, real-time flow calculation of one-dimensional hydrodynamic model:

[0125] The Saint-Venant equation set describing the hydrodynamic process of the tidal river section is discretized and solved to obtain the water level and flow information of each calculation section; the one-dimensional hydrodynamic equation of the tidal river section is established to analyze the flow change process and the water level-flow change relationship of the tidal river section under different water level change scenarios. Specifically, the following contents are included,

[0126] 3.1, the fall of the tidal river section is small, and the section depth is large, so the Saint-Venant equation set describing the motion law of one-dimensional unsteady gradually varying flow in shallow water is used to describe the hydrodynamic process of the tidal river section. The continuity equation and the momentum equation in the Saint-Venant equation set are shown in formula (6.a) and formula (6.b):

[0127]

[0128]

[0129] Where, t is time coordinate; x is space coordinate; A is cross-section area of river section; Q is flow rate; q1 is single-width flow rate of lateral inflow (inflow is positive and outflow is negative); u is average flow velocity of cross-section; z is water level of river; g is gravity acceleration; n0 is Manning coefficient; R is hydraulic radius.

[0130] 3.2, the four-point eccentric Preissmann implicit difference format (as shown in Figure 2 ) is used to discretize and solve the Saint-Venant equation set (equations (6.a) and (6.b)), the discrete equations are shown in equations (7.a)-(7.d), and the water level and flow rate information of each calculation section is obtained.

[0131]

[0132] Where, i is section number; t is time step; △t is discrete time step; x i is space step; △x is discrete space step; θ is eccentricity coefficient; n is calculation time; q is flow rate, water level and other dependent variables in the Saint-Venant equation set; indicates the discrete variable of section i at time n. Substituting the above finite difference discrete equation into the Saint-Venant equation set can obtain a number of linear equation sets, and solving the linear equation set coefficients can obtain the water level and flow rate information of each calculation section.

[0133] 3.3, a one-dimensional hydrodynamic model of the tidal river section is established to analyze the change process of the water level-flow rate relationship under the action of different influencing factors of the river section. The establishment process of the one-dimensional hydrodynamic model is,

[0134] (1), establishing engineering files.

[0135] (2), drawing river system and importing river terrain data.

[0136] (3), setting boundary conditions and initial conditions.

[0137] (4), setting operation parameters.

[0138] (5), model operation and post-processing.

[0139] 3.4, different calculation scenarios are set to analyze the water level-flow rate relationship of the tidal river section under the action of tides, river runoff and actual conditions. The specific scenario settings are as follows,

[0140] ① all flow boundaries are closed, and the downstream water level boundary is set to tidal data without the influence of river runoff; used to simulate and analyze the water level-flow rate relationship under the action of tides;

[0141] ② the flow boundary is not changed, and the downstream water level boundary is set to river water level data without the effect of tides; used to simulate and analyze the action of river runoff;

[0142] ③ The flow boundary and water level boundary are set as the measured data; used to simulate the actual situation and the combined action of tide and runoff.

[0143] Four, multiple regression analysis and path analysis:

[0144] The tidal flow and runoff flow are set as independent variables, and the actual flow is set as dependent variable. The partial regression coefficient obtained by multiple regression analysis and the path coefficient obtained by path analysis reflect the contribution degree of independent variable to the numerical value and change process of dependent variable, respectively, so as to obtain the characteristics of water level-flow relationship in the tidal reach and realize the rapid analysis of water level-flow relationship in the tidal reach. Specifically, it includes the following contents,

[0145] 4.1 Multiple regression analysis:

[0146] Let y be an observable random variable, which is affected by n factors x1, x2,…, xn. If there is a linear relationship between them, the expression is, n

[0147]

[0148] Where, α is the intercept; x i is the i-th factor, i = 1, 2,…, n; β i is the partial regression coefficient; ε is the random error, which is subject to normal distribution; is the regression variance;

[0149] The expression of multiple regression fitting model is,

[0150]

[0151] The calculation formula of regression sum of squares Q of regression equation is,

[0152]

[0153] Let SS i =∑X i 2 ,SP ij =∑X i Y i ,SP iy =∑X i Y; the coefficient matrix is A, the partial regression coefficient matrix is b, and the constant matrix is K. According to the least square method, the relationship between the three matrices is expressed as,

[0154] Ab=K (11)

[0155] Where,

[0156] ​

[0157] The optimal solution of the partial regression coefficient matrix b is

[0158] b = (A T A) -1 A T K

[0159] After calculating the optimal solution of the partial regression coefficient matrix b, the intercept a is

[0160]

[0161] 4.2, path analysis:

[0162] Calculate the path coefficient p i ,

[0163]

[0164] Where, SS y is the total sum of squares of the dependent variable y; the path coefficient p i The value range is (-1, 1), and the greater the absolute value of the path coefficient, the greater the degree of influence of the independent variable on the dependent variable. The partial regression coefficient and the path coefficient obtained by multiple regression analysis respectively reflect the influence of the independent variable on the numerical value and the change degree of the dependent variable.

[0165] Example two

[0166] In this embodiment, the Shizui Station of the tidal level station in the tidal river section of the main stream of the Tanjiang River is taken as an example to specifically illustrate the specific implementation process and results of the present application. The Shizui Station of the Tanjiang River is located in the lower reaches of the main stream of the Tanjiang River, and is a national basic tide (water) level station with a long sequence of measured tide (water) level data. The main water system of the Tanjiang River is as shown in Figure 3 The steps and benefit analysis of this embodiment are as follows:

[0167] I. Data collection

[0168] Collect the measured tide (water) level data of the Shizui Station in 2023, the channel surveying and mapping topographic data of the main stream of the Tanjiang River, the digital elevation data of the Tanjiang River basin, and the discharge data of the Heshan sluice from March 25 to April 18, 2023. Use GIS tools to process and integrate the topographic data; and time-average the measured tide (water) level data of the Shizui Station in 2023 into hourly water level data.

[0169] II. Tidal level harmonic analysis

[0170] The main information of each constituent considered in this embodiment is shown in Table 1. The process of tidal level harmonic analysis is realized by the S_TIDE tool package of Matlab language. First, the "s_tide" function in S_TIDE is used to perform harmonic analysis on the tidal level observation data of Shizui Station in 2023, and the contribution of each constituent is analyzed according to the constituent amplitude size, and the constituent amplitudes and phase lags of the 11 considered constituents are calculated. The results of tidal level harmonic analysis are shown in Table 2. The "s_consturct2" function is used to predict the tidal level changes from March 26 to April 18, considering all constituents and the above-mentioned 11 constituents, and the prediction results are shown in Figure 4 The root mean square error RMSE considering all constituents is 0.067 m, and the Nash efficiency coefficient NSE is 0.98; the root mean square error RMSE considering 11 constituents is 0.122 m, and the Nash efficiency coefficient NSE is 0.93, indicating that the tidal level prediction results of the two cases are similar to the measured values. On this basis, the tidal level change results without the influence of river runoff and the river water level change results without the influence of tides are obtained (see Figure 5 ).

[0171] Table 1 Main constituent information

[0172]

[0173] Table 2 Tidal level harmonic analysis results

[0174]

[0175] Three, real-time flow calculation of one-dimensional hydrodynamic model

[0176] In this embodiment, a one-dimensional hydrodynamic model is established by using HEC-RAS software. In order to analyze the influence and contribution of tidal flow and river runoff on the flow change of Shizui section, the following three scenarios are set for analysis:

[0177] ① Close all flow boundaries, and set the downstream water level boundary to the tidal level data without the influence of river runoff;

[0178] ② The flow boundary does not change, and the downstream water level boundary is set to the river water level data without the influence of tides;

[0179] ③ The flow boundary and water level boundary are set to the measured data.

[0180] The flow calculation results of scenario ① and scenario ② are shown in Figure 6The water level-flow relationship of the calculated tidal flow of scenario 1 presents an obvious rope noose type non-stable single value corresponding relationship, and the instantaneous water level-flow presents an alternating rise and fall characteristic; the flow of the calculated river runoff of scenario 2 is relatively stable with time, and the flow water level-flow relationship presents a stable non-single value corresponding relationship, and the movement form of the water flow under the action of the river runoff is a non-movement wave. In the embodiment case, the water level-flow relationship of the Shizui station is simultaneously affected by the rope noose type non-stable non-single value relationship of the tidal flow and the stable non-single value relationship of the river runoff.

[0181] Four, multiple regression analysis and path analysis

[0182] In the embodiment case, the flow calculation results of scenario 1 and scenario 2 are set as independent variables, and the flow calculation result of scenario 3 is set as a dependent variable, so as to perform multiple regression analysis and path analysis. The multiple regression analysis result is shown in Table 3, and the verification result is shown in Table 4. Figure 7 For the verification result, the square residual coefficient R2 is 0.9095, the root mean square error RMSE is 139.9 m / s, the relative standard deviation RSD is 21.0%, and the Nash efficiency coefficient NSE is 0.92. 3 The partial regression coefficients obtained by the multiple regression analysis can better reflect the influence of the river runoff and the tidal flow on the actual flow size. For the path analysis, the path coefficient of the tidal flow is 0.9446, and the path coefficient of the river runoff is 0.0710, which indicates that the direct influence degree of the tidal flow on the actual flow in the embodiment case is much larger than that of the river runoff, and the change process of the real-time flow in the tidal river section is mainly controlled by the change process of the tidal flow.

[0183] Table 3 Parameter analysis of multiple regression analysis result

[0184]

[0185] Variance analysis

[0186]

[0187]

[0188] In summary, the water level-flow relationship analysis method of the tidal river section based on the tidal level harmonic analysis can quickly and conveniently analyze the water level-flow relationship of the tidal river section, without going through complex river mouth hydrodynamic process simulation, and is also applicable to the water level station of the tidal river section lacking long-term measured flow data, and is helpful to improve the hydrological data collection and compilation work of the small and medium river basins and the tidal river section region.

[0189] By adopting the above technical scheme disclosed in the present application, the following beneficial effects are obtained:

[0190] The application provides a tidal river reach water level-flow relationship analysis method based on tidal level harmonic analysis. The application solves the problem of lacking long-term continuous measured flow data of the hydrological station in the tidal river reach by using a one-dimensional hydrodynamic model to calculate the real-time flow, and can calculate the real-time flow change process of the tidal river reach under the action of tides and river runoff. The application uses multiple regression analysis and path analysis to analyze the contribution degree of tidal flow and runoff to the real-time flow value and change process, and realizes the rapid analysis of the water level-flow relationship of the tidal river reach lacking measured flow data.

[0191] The above only describes the preferred embodiments of the application, and it should be noted that those skilled in the art can make several improvements and refinements without departing from the principles of the application, and these improvements and refinements should be considered as the protection scope of the application.

Claims

1. A method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis, characterized by: The following steps are included: S1. Tidal harmonization analysis: Based on tidal harmonic analysis, characteristic parameters of each tidal level segment and water surface elevation change characteristics of tidal river sections are obtained, and then independent tidal flow and river runoff flow are obtained; S2. Real-time flow calculation of one-dimensional hydrodynamic model: Discretize and solve the Saint-Venant equations that describe the hydrodynamic processes in tidal river sections to obtain water level and flow information for each calculation section. Establish a one-dimensional hydrodynamic equation for tidal river sections and analyze the flow variation process and the relationship between water level and flow variation in tidal river sections under different water level change scenarios. S3. Multiple regression analysis and path analysis: Tidal flow and runoff flow are set as independent variables, and actual flow is set as dependent variable. The partial regression coefficient obtained by multiple regression analysis and the path coefficient obtained by path analysis reflect the contribution of the independent variables to the value and change process of the dependent variable, respectively, to obtain the changing characteristics of the water level and flow relationship in tidal river sections. Step S3 specifically includes the following contents: S31. Multiple regression analysis: Let y be an observable random variable, affected by n factors x1, x2, L, x n If there is a linear relationship between the two, the expression is: Among them, α is the intercept; x i is the i-th factor, i=1,2,L,n; β i is the partial regression coefficient; ε is the random error, which obeys Normal distribution; is the regression variance; The multiple regression fitting model expression is: The calculation formula of the regression equation's regression square sum Q is, make SS i =∑X i 2 ,SP ij =∑X i Y i ,SP iy =∑X i Y; let the coefficient matrix be A, the partial regression coefficient matrix be b, and the constant matrix be K. According to the least squares method, the relationship between the three matrices is expressed as, Ab=K in, The optimal solution of the partial regression coefficient matrix b is, b=(A T A) -1 A T K After calculating the optimal solution of the partial regression coefficient matrix b, the intercept a is, S32, Path analysis: Calculate the path coefficient p i , Among them, SS y is the total sum of squares of the dependent variable y; the path coefficient p i The value range is (-1,1). The larger the absolute value of the path coefficient, the greater the influence of the independent variable on the dependent variable.

2. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 1 is characterized by: Step S1 specifically includes the following contents: S11. The classical tidal harmonic analysis method assumes that the amplitude and lag angle of each tidal component are constant. The tidal time series function is represented by the linear superposition of a series of cosine functions, with each cosine function used for superposition representing a tidal component. Where Z(t) is the tide level data observed at time t; σ j 、H j 、g j are the angular frequency, amplitude and lag angle corresponding to the jth partial tide respectively; j = 1, 2, L, J, J is the total number of partial tides; S0 is the sea level elevation at the current moment; S12. Obtain a new variable a based on the amplitude and lag angle of the tide j and b j , using the new variable a j and b j Linearized tide level time series function; a j =H j cost j b j =H j sing j Among them, Z(t)' is the new variable a j and b j The tide level data observed at time t after linearization; S13. When there are N tide level data observed at each moment, N tide level equations can be constructed. The least square method of multivariate function to find the extreme value is used to solve the variable a. j and b j ; S14. Get variable a j and b j After that, the amplitude and delay angle of each tide are, g j =arctan(b j / a j ) Among them, the delay angle g j The value range of the arctan function is (-90°, 90°); according to the parameter a j and b j To correct the lag angle g j ; S15. Through tidal harmonic analysis and tidal fitting forecasting, the fitting forecast tidal level time series and the sea level elevation change time series for the study period are obtained.

3. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 2 is characterized by: Step S13 specifically involves using matrix operations to solve: Z=KU Among them, Z is the observed tide data matrix; K is the known coefficient matrix; U is the unknown parameter matrix to be solved; The specific form of the above matrix is: According to the least squares method, the optimal solution of U is, U=(K T K) -1 K T Z Where T is the transpose of the matrix.

4. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 2 is characterized by: Also included between steps S14 and S15, S15. Use the Rayleigh criterion to determine the shortest time series length of the observed tide level required to distinguish each tide component. Where N0 is the length of the observation sequence; t0 is the observation interval; T1 and T2 are the periods of any two tidal components.

5. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 1 is characterized by: Step S2 specifically includes the following contents: S21. The Saint-Venant equations describing the motion of shallow one-dimensional non-steady, gradually varying flows are used to describe the hydrodynamic processes in tidal river sections. S22. Using the four-point eccentric Preissmann implicit difference scheme, the Saint-Venant equations are discretized and solved to obtain the water level and flow information of each calculation section; S23. Establish a one-dimensional hydrodynamic model for tidal river sections and analyze the changing relationship between water level and flow under the influence of different influencing factors in the river section. S24. Set up different calculation scenarios to analyze the relationship between tides, river runoff, and the water level and flow in tidal river sections in actual conditions.

6. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 5, characterized in that: In step S23, a one-dimensional hydrodynamic model of the tidal river section is established, which specifically includes the following contents: S231. Establish engineering documents; S232, draw river systems and import river terrain data; S233, setting boundary conditions and initial conditions; S234, setting operation parameters; S235, model calculation and post-processing.

7. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 5, characterized in that: The scenario setting in step S24 specifically includes: (1) All flow boundaries are closed, and the downstream water level boundary is set to the tidal data without the influence of river runoff; this is used to simulate and analyze the relationship between water level and flow under the action of tides; (2) The flow boundary remains unchanged, and the downstream water level boundary is set to the river water level data after removing the tidal effect; this is used to simulate and analyze the river runoff effect; (3) The flow boundary and water level boundary are set as measured data; they are used to simulate the actual situation and the combined effects of tides and runoff.

8. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to any one of claims 1 to 7, characterized in that: Before step S1, the method further includes: S0. Data collection: Collect measured water level data from hydrological stations in tidal river sections, river topography and digital elevation data in the basin, and process these data.

9. The method for analyzing the relationship between water level and flow in a tidal river section based on tidal harmonic analysis according to claim 8, characterized in that: S0 specifically includes the following contents: S01. Obtain high-resolution digital elevation data of the watershed area corresponding to the tidal river section from open source datasets, and perform stitching, cropping, and geographic and projection coordinate settings on it. S02. Obtain river channel topography data of tidal river sections by using underway surveying or mobile phone historical hydrological data, and integrate it into the above-mentioned digital elevation data; S03. Collect and organize the long-term measured water level data of hydrological stations in tidal river sections, and perform time-averaging processing on the measured water level data.

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