Time-varying unit line method for river channel flat beach flow simulation

Abstract

The invention discloses a time-varying unit line method for river channel flat beach flow simulation. Comprising the following steps: S1, on the basis of measured data of daily flow and sand content in different hydrological years of a river channel calculation section, determining annual effective sand transport flow and sand content; s2, determining the flat beach flow based on the actual measurement water level-flow relation data of the cross section in the flood season of the riverway; s3, constructing an instantaneous unit line equation for river channel calculation section flat beach flow simulation; s4, constructing a time period unit line equation for river channel calculation section flat beach flow simulation; s5, constructing a time-varying unit line model for calculating the flat beach flow of the cross section of the riverway; and S6, model parameter time-varying analysis and simulation application. According to the method, the influence of water and sediment conditions in different time periods on the flat beach flow can be decomposed and reflected, the time-varying rule of model parameters under the water and sediment conditions in different time periods is considered, the calculation method is relatively simple, and a more scientific and reasonable method can be provided for simulation of the change process of the river channel flat beach flow.

Description

Technical Field

[0001] The present invention relates to a method for simulating river flat flow, which is mainly based on a riverbed lag response model and takes the flat flow as a characteristic variable. A time-varying unit line method for simulating river flat flow is proposed, thereby providing a more scientific and reasonable method for simulating the change process of river flat flow. Background Art

[0002] Flat-shoal flow refers to the flow corresponding to the height of the floodplain (or the beach edge of the side beach) in a complex river channel with a beach-channel structure. It is an important indicator reflecting the flow capacity of the river. In recent years, affected by climate change, human activities and other factors, the water and sediment conditions of many rivers have changed significantly, causing obvious adjustments in flat-shoal flow. Therefore, how to simulate the change process of flat-shoal flow under different water and sediment conditions has become an important issue of concern in river planning and management.

[0003] In the past, the determination of flat beach flow was mainly based on the measured cross-section data of the hydrological station to determine the beach lip elevation, and the measured water level-flow relationship was used to find the flow corresponding to the beach lip elevation, which is the flat beach flow. However, due to the frequent swing of the mainstream of natural rivers, the large amplitude of changes in river channel scouring and silting, and the influence of beaches and production embankments, the elevation of the river beach lip is not easy to determine, and it is difficult to find the flat beach flow corresponding to the beach lip elevation through the measured water level-flow relationship, and this method is difficult to simulate and predict the change process of the flat beach flow. Therefore, in actual work, many scholars have tried to calculate by establishing the relationship between the river flat beach flow and different influencing factors, including: basin area and gradient, average flow and sediment content during the flood season, annual water volume and sediment volume, etc. In the process of simulating the change of flat beach flow, some scholars found that the flat beach flow has a lag effect on the change of water and sediment conditions, and the previous water and sediment conditions have a cumulative effect on the flat beach flow. For this reason, it is proposed to use the sliding average or geometric average method for water and sediment conditions in different periods. Later, a lag response model of river flat beach flow was developed, and finally it was upgraded to a riverbed lag response model. It is widely used in the simulation of the change process of flat beach flow in the Inner Mongolia section of the upper reaches of the Yellow River, the lower reaches of the Yellow River, and the lower reaches of the Wei River, and achieved good results. For the lag response model of river flat beach flow, there are two calculation modes: single-step analysis and multi-step recursion. The former has a short forecast period and is not conducive to long-term prediction; the latter is described as the superposition of the influence of water and sediment conditions in different periods. The decomposition form of the influence of water and sediment conditions in different periods on flat beach flow has not yet been established, so it is impossible to fully and deeply reflect the difference in the influence of water and sediment conditions in different periods on flat beach flow.

[0004] Therefore, on the basis of the riverbed hysteresis response model, taking the flat beach flow as the characteristic variable and drawing on the unit line model in hydrology that describes the "memory lag" effect of basin confluence, whether it is possible to derive and establish a time-varying unit line method for simulating river flat beach flow in order to decompose and reflect the impact of water and sand conditions in different periods on the flat beach flow has become a problem to be studied. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to provide a more scientific and reasonable method for simulating the flow changes in river flats. It is mainly based on the riverbed lag response model, takes the flat flow as the characteristic variable, and proposes a time-varying unit line method for simulating river flat flow through deduction.

[0006] The technical solution adopted by the present invention is as follows: a time-varying unit line method for simulating river flat beach flow, which is mainly based on the riverbed lag response model, takes the flat beach flow as the characteristic variable, derives and establishes the instantaneous unit line equation of the flat beach flow, and further converts it into a discrete time period unit line equation through S integral transformation, taking into account the water and sand conditions and model parameter changes in different time periods, and considering non-zero initial conditions, and finally constructing a time-varying unit line model of river flat beach flow.

[0007] The following steps are involved:

[0008] S1, based on the measured data of daily flow and sediment content in different hydrological years at the river calculation section, determine the annual effective sediment transport flow and sediment content;

[0009] The calculation of annual effective sediment transport flow and sediment content is mainly based on the concept of geomorphic work and adopts the water-sediment two-dimensional vector frequency statistical method. The specific steps include:

[0010] S11, according to the measured data of daily flow and sediment content in different hydrological years of the river calculation section, is divided into several magnitude combinations;

[0011] S12, count the time frequency of different magnitude flow and sediment content interval combinations, and draw a frequency statistics table;

[0012] S13, respectively calculate the geomorphic work corresponding to the combination of different magnitude flow and sediment content intervals, that is, the product of sediment transport rate and duration frequency. Among them, the flow and sediment content are taken as the median of the interval;

[0013] S14, using flow rate and sediment content as coordinate axes, draw the corresponding geomorphic work surface or express it in a table, and take the combination of flow rate and sediment content corresponding to the maximum value of geomorphic work as the effective sediment transport flow rate and sediment content combination.

[0014] S2, based on the measured water level-discharge relationship data of the river calculation section during the flood season, determine the flat beach flow;

[0015] The measured water level-flow relationship data of the river calculation section during the flood season can be obtained by consulting the relevant hydrological data yearbook. If there is no high water level data in the current year, the relationship extension of the adjacent years can be referred to, and the flow value corresponding to the elevation measured after the flood season can be interpolated to obtain the flow value corresponding to the elevation, which is the flow of the flat beach.

[0016] S3, construct the instantaneous unit line equation for flat-shoal flow simulation in the river calculation section;

[0017] Based on the delayed response model of riverbed evolution, taking the flat beach flow as the characteristic variable, the differential equation of the flat beach flow changing with time can be expressed as:

[0018]

[0019] Where: Q b is the flat beach flow, m 3 / s;Q be is the flow balance value on the flat beach, m 3 / s; t is time, s; β is the change rate parameter, 1 / s.

[0020] According to formula (1), let Q be With β as constants, under zero initial conditions, the instantaneous unit line equation of the flat beach flow in the river calculation section can be derived:

[0021] u(0,t)=βe -βt (2)

[0022] Where: u(0,t) is the instantaneous unit line.

[0023] S4, construct the time period unit line equation for flat beach flow simulation of river calculation section;

[0024] The main steps for constructing the unit line of the flat beach flow period of the river calculation section include:

[0025] S41, based on the instantaneous unit line equation (2) of the flat flow of the river calculation section, construct the S curve of the instantaneous unit line by integration:

[0026]

[0027] Where: S(t) is the instantaneous unit line S curve.

[0028] S42, based on the instantaneous unit line S curve of the flat beach flow of the river calculation section, by shifting it backward for a period of time, another S curve S(t-Δt) can be obtained. By calculating the difference between the ordinates of the two S curves, the discrete form of the unit line equation of the flat beach flow of the river calculation section is obtained:

[0029] q(Δt,n)=S(t)-S(t-Δt)=(e-βΔt ) n-1 (1-e -βΔt ) (4)

[0030] In the formula: q(Δt,n) is the unit line of the time period; Δt is the unit line time period; n is the time period number.

[0031] S5, construct a time-varying unit line model for the flow of the flat beach in the river calculation section;

[0032] Based on the time unit line equation (4) of the flat beach flow of the river calculation section, the calculation period is year, the water and sediment conditions and model parameter changes in different years are considered, and the non-zero initial conditions are considered. Finally, the time-varying unit line model of the flat beach flow of the river calculation section can be constructed:

[0033]

[0034] Where: Q b (n) is the flat beach flow in the nth year, m 3 / s;Q be (i) is the flat beach flow balance value in the i-th year, m 3 / s;Q b0 is the initial value of flat beach flow, m 3 / s; Δt is the calculation period, generally taken as 1 year, y; β i is the change rate parameter of the i-th year, 1 / y; β0 is the change rate parameter of the initial value of flat beach flow, 1 / y; n, i are the calculation year numbers.

[0035] S6, time-varying analysis and simulation applications of model parameters.

[0036] Based on the time-varying unit line model of the flat-shoal flow in the river calculation section, the time-varying law of the model parameters is analyzed and simulation applications are carried out:

[0037] The balance value of flat beach flow in different years can be expressed as the power law empirical relationship between annual effective sediment transport flow and sediment content:

[0038]

[0039] Where: Q f,i is the effective sediment transport flow in the i-th year, m 3 / s;S f,i is the sediment content corresponding to the effective sediment transport flow in the i-th year, kg / m 3 ξ f,i is the effective sediment coefficient in the i-th year, kg·s / m 6 ; K is the unknown coefficient; a and b are unknown exponents.

[0040] For the model change rate parameters in different years, it can be expressed as the following empirical relationship:

[0041]

[0042] In the formula: c is the coefficient to be determined; d is the index to be determined.

[0043] The parameters β0, coefficients K, c and exponents a, b, d in equations (5), (6) and (7) can be calibrated in combination with the annual effective sediment transport flow, sediment content and post-flood flat flow data of the river calculation section, and the change process of the flat flow of the river calculation section can be simulated.

[0044] Compared with the existing river flat flow simulation technology, the advantages of the present invention are mainly reflected in the following aspects:

[0045] (1) Based on the riverbed hysteresis response model, the present invention proposes a time-varying unit line method for simulating river flat flow, which can decompose and reflect the influence of water and sediment conditions at different time periods on flat flow;

[0046] (2) The time-varying unit line model of river flat flow constructed by the present invention takes into account the time-varying laws of model parameters under water and sediment conditions in different time periods, and the model method is more reasonable;

[0047] (3) The calculation method of the present invention is relatively simple and is convenient for simulating the flow change process of river flats. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a technical roadmap of the method of the present invention;

[0049] Figure 2 A schematic diagram of a river section to which the method of the present invention is applied;

[0050] Figure 3 The diagram of the change process of annual effective sediment transport flow, sediment content and flat beach flow in the embodiment of the method of the present invention;

[0051] Figure 4 1 is an example diagram of time-varying unit lines in different years of the embodiment of the method of the present invention, (a) is 1968, (b) is 1987, and (c) is 2001;

[0052] Figure 5 This is a diagram of the simulation results of flat beach flow in an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0053] The specific implementation of the present invention will be described in detail below in conjunction with the embodiments of the present invention and the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] Taking the simulation of the change process of the flat beach flow at Bayangol Station in the Inner Mongolia section of the Yellow River as an example, the specific implementation method of the time-varying unit line method for simulating the flat beach flow of the present invention is further explained. The technical process is as follows: Figure 1 As shown, the following steps are included:

[0055] S1, based on the measured data of daily flow and sediment content in different hydrological years at the river calculation section, determine the annual effective sediment transport flow and sediment content;

[0056] The calculation of annual effective sediment transport flow and sediment content is mainly based on the concept of geomorphic work and adopts the water-sediment two-dimensional vector frequency statistical method. The specific steps include:

[0057] S11, according to the measured data of daily flow and sediment content in different hydrological years of river calculation sections, is divided into several magnitude combinations;

[0058] S12, count the time frequency of different magnitude flow and sediment content interval combinations, and draw a frequency statistics table;

[0059] S13, respectively calculate the geomorphic work corresponding to the combination of different magnitude flow and sediment content intervals, that is, the product of sediment transport rate and duration frequency. Among them, the flow and sediment content are taken as the median of the interval;

[0060] S14, using flow rate and sediment content as coordinate axes, draw the corresponding geomorphic work surface or express it in a table, and take the combination of flow rate and sediment content corresponding to the maximum value of geomorphic work as the effective sediment transport flow rate and sediment content combination.

[0061] In this embodiment, the river flat flow calculation section is located at the Bayangaoler hydrological station in the Inner Mongolia section of the Yellow River. Figure 2 Based on the above calculation methods and steps of annual effective sediment transport and sediment content, the annual effective sediment transport and sediment content of Bayangol Station in different years are calculated. Taking 2003 as an example, Table 1 is the frequency statistics table of the two-dimensional vector combination of daily flow and sediment content of Bayangol Station in the year. Correspondingly, it can be determined that the annual effective sediment transport flow and sediment content are 525m 3 / s、4.5kg / m 3 For the changes in the annual effective sediment discharge and sediment content at Bayangol Station in different years, please refer to Figure 3 .

[0062] Table 1 Statistical table of two-dimensional vector combination frequency of flow and sediment content at Bayangol station

[0063]

[0064] S2, based on the measured water level-discharge relationship data of the river calculation section during the flood season, determine the flat beach flow;

[0065] The measured water level-flow relationship data of the river calculation section during the flood season can be obtained by consulting the relevant hydrological data yearbook. If there is no high water level data in the current year, the relationship extension of the adjacent years can be referred to, and the flow value corresponding to the elevation measured after the flood season can be interpolated to obtain the flow value corresponding to the elevation, which is the flow of the flat beach.

[0066] In this embodiment, the relevant hydrological data yearbook of the Bayangaoler hydrological station in the Inner Mongolia section of the Yellow River is consulted, and the flat beach flow is determined based on the measured water level-flow relationship data of the Bayangaoler section in different flood seasons. The corresponding change process can be seen in Figure 3 .

[0067] S3, construct the instantaneous unit line equation for flat-shoal flow simulation in the river calculation section;

[0068] Based on the delayed response model of riverbed evolution, taking the flat beach flow as the characteristic variable, the differential equation of the flat beach flow changing with time can be expressed as:

[0069]

[0070] Where: Q b is the flat beach flow, m 3 / s;Q be is the flow balance value on the flat beach, m 3 / s; t is time, s; β is the change rate parameter, 1 / s.

[0071] According to formula (1), let Q be With β as constants, under zero initial conditions, the instantaneous unit line equation of the flat beach flow in the river calculation section can be derived:

[0072] u(0,t)=βe -βt (2)

[0073] Where: u(0,t) is the instantaneous unit line.

[0074] S4, construct the time period unit line equation for flat beach flow simulation of river calculation section;

[0075] The main steps for constructing the unit line of the flat beach flow period of the river calculation section include:

[0076] S41, based on the instantaneous unit line equation (2) of the flat flow of the river calculation section, construct the S curve of the instantaneous unit line by integration:

[0077]

[0078] Where: S(t) is the instantaneous unit line S curve.

[0079] S42, based on the instantaneous unit line S curve of the flat beach flow of the river calculation section, by shifting it backward for a period of time, another S curve S(t-Δt) can be obtained. By calculating the difference between the ordinates of the two S curves, the discrete form of the unit line equation of the flat beach flow of the river calculation section is obtained:

[0080] q(Δt,n)=S(t)-S(t-Δt)=(e -βΔt ) n-1 (1-e -βΔt ) (4)

[0081] In the formula: q(Δt,n) is the unit line of the time period; Δt is the unit line time period; n is the time period number.

[0082] S5, construct a time-varying unit line model for the flow of the flat beach in the river calculation section;

[0083] Based on the time unit line equation (4) of the flat beach flow of the river calculation section, the calculation period is year, the water and sediment conditions and model parameter changes in different years are considered, and the non-zero initial conditions are considered. Finally, the time-varying unit line model of the flat beach flow of the river calculation section can be constructed:

[0084]

[0085] Where: Q b (n) is the flat beach flow in the nth year, m 3 / s;Q be (i) is the flat beach flow balance value in the i-th year, m 3 / s;Q b0 is the initial value of flat beach flow, m 3 / s; Δt is the calculation period, generally taken as 1 year, y; β i is the change rate parameter of the i-th year, 1 / y; β0 is the change rate parameter of the initial value of flat beach flow, 1 / y; n, i are the calculation year numbers.

[0086] S6, time-varying analysis and simulation applications of model parameters.

[0087] Based on the time-varying unit line model of the flat-shoal flow in the river calculation section, the time-varying laws of the model parameters are analyzed and simulation applications are carried out:

[0088] The balance value of flat beach flow in different years can be expressed as the power law empirical relationship between annual effective sediment transport flow and sediment content:

[0089]

[0090] Where: Q f,i is the effective sediment transport flow in the i-th year, m 3 / s;S f,iis the sediment content corresponding to the effective sediment transport flow in the i-th year, kg / m 3 ξ f,i is the effective sediment coefficient in the i-th year, kg·s / m 6 ; K is the unknown coefficient; a and b are unknown exponents.

[0091] For the model change rate parameters in different years, it can be expressed as the following empirical relationship:

[0092]

[0093] In the formula: c is the coefficient to be determined; d is the index to be determined.

[0094] The parameters β0, coefficients K, c and exponents a, b, d in equations (5), (6) and (7) can be calibrated in combination with the annual effective sediment transport flow, sediment content and post-flood flat flow data of the river calculation section, and the change process of the flat flow of the river calculation section can be simulated.

[0095] In this embodiment, based on the annual effective sediment transport flow, sediment content and post-flood flat flow change process data of the Bayangaoler Station of the Yellow River in Inner Mongolia in different years, the model parameters β0, coefficients K, c and exponents β0, a, b, d are calibrated. The results can be seen in Table 2; taking 1968, 1987 and 2001 as examples, examples of time-varying unit lines in different years are as follows Figure 4 As shown; the flow change process of the flat beach at Bayangaoler Station in Inner Mongolia section of the Yellow River was simulated, and the results are shown in Figure 5 .

[0096] Select the coefficient of certainty R 2 and Nash-Sutcliffe efficiency coefficient E NS As the evaluation index of model effect, the results are listed in Table 2. Among them, the coefficient of certainty R 2 It is the most basic quantitative analysis method for evaluating the model effect. Excel software can be used to perform linear regression between the flow calculation value and the measured value. 2 The closer the value is to 1, the better the fit between the simulated flow value and the measured value is;

[0097] Nash-Sutcliffe efficiency coefficient E NS It is a standardized statistical value to determine the relative amount of variance between the residual and the measured data. NS The value is generally between -∞ and 1. NS =1 indicates that the calculated flow value is completely consistent with the measured value. <E NS When NSE is less than 1, it indicates that the calculation effect is within an acceptable level. When NSE is less than 0, it indicates that there is a large deviation between the calculated flow value and the measured value. NS The efficiency coefficient calculation expression is:

[0098]

[0099] Where: E NS is the Nash-Sutcliffe efficiency coefficient; Q bo i is the measured value of flat beach flow, m 3 / s;Q bc i is the simulated value of flat beach flow, m 3 / s.

[0100] Table 2 Model parameter calibration results comprehensive Figure 5 As can be seen from Table 2, the calculated value of the flat-land flow at the Bayangaoler Station in the Inner Mongolia section of the Yellow River is consistent with the measured value, and the certainty coefficient R 2 and Nash-Sutcliffe efficiency coefficient E NS The values ​​reach 0.83 and 0.84 respectively, and the simulation effect is good.

Claims

1. A time-varying unit line method for simulating river flat flow, characterized in that: The following steps are involved: S1, based on the measured data of daily flow and sediment content in different hydrological years at the river calculation section, determine the annual effective sediment transport flow and sediment content; S2, based on the measured water level-discharge relationship data of the river calculation section during the flood season, determine the flat beach flow; S3, construct the instantaneous unit line equation for flat-shoal flow simulation in the river calculation section; S4, construct the time period unit line equation for flat beach flow simulation of river calculation section; S5, construct a time-varying unit line model for the flow of the flat beach in the river calculation section; S6, time-varying analysis and simulation applications of model parameters.

2. The time-varying unit line method for simulating river flat flow according to claim 1 is characterized in that: The specific methods of S3 are as follows: Based on the delayed response model of riverbed evolution, with flat beach flow as the characteristic variable, the differential equation of flat beach flow changing with time is expressed as: Where: Q b is the flat beach flow, m 3 / s;Q be is the flow balance value on the flat beach, m 3 / s; t is time, s; β is the change rate parameter, 1 / s; According to formula (1), let Q be With β as constants, under zero initial conditions, the instantaneous unit line equation of the flat beach flow in the river calculation section is derived: u(0,t)=βe -βt (2) Where: u(0,t) is the instantaneous unit line.

3. The time-varying unit line method for simulating river flat flow according to claim 2 is characterized in that: S4 includes the following sub-steps: S41, based on the instantaneous unit line equation (2) of the flat flow of the river calculation section, construct the S curve of the instantaneous unit line by integration: Where: S(t) is the instantaneous unit line S curve; S42, based on the instantaneous unit line S curve of the flat beach flow of the river calculation section, it is shifted backward for one period to obtain another S curve S(t-Δt). By calculating the difference between the ordinates of the two S curves, the discrete form of the unit line equation of the flat beach flow of the river calculation section is obtained: q(Δt,n)=S(t)-S(t-Δt)=(e -βΔt ) n-1 (1-e -βΔt ) (4) In the formula: q(Δt,n) is the unit line of the time period; Δt is the unit line time period; n is the time period number.

4. The time-varying unit line method for simulating river flat flow according to claim 3 is characterized in that: S5 specific methods are as follows: Based on the time-varying unit line equation (4) of the change of the flat beach flow in the river calculation section, the calculation period is taken as the year, the water and sediment conditions and model parameter changes in different years are considered, and the non-zero initial conditions are considered. Finally, the time-varying unit line model of the flat beach flow in the river calculation section is constructed: Where: Q b (n) is the flat beach flow in the nth year, m 3 / s;Q be (i) is the flat beach flow balance value in the i-th year, m 3 / s;Q b0 is the initial value of flat beach flow, m 3 / s; Δt is the calculation period, y; β i is the change rate parameter of the i-th year, 1 / y; β0 is the change rate parameter of the initial value of flat beach flow, 1 / y; n, i are the calculation year numbers.

5. The time-varying unit line model of river flat flow according to claim 4 is characterized in that: The specific method of S6 is: The balance value of flat beach flow in different years is expressed as the power law empirical relationship between annual effective sediment transport flow and sediment content: Where: Q f,i is the effective sediment transport flow in the i-th year, m 3 / s;S f,i is the sediment content corresponding to the effective sediment transport flow in the i-th year, kg / m 3 ; ξ f,i is the effective sediment coefficient in the i-th year, kg·s / m 6 ; K is the coefficient to be determined; a and b are the exponents to be determined; The model change rate parameters for different years are expressed as the following empirical relationship: In the formula: c is the coefficient to be determined; d is the index to be determined; The parameters β0, coefficients K, c and exponents a, b, d in equations (5), (6) and (7) are calibrated based on the annual effective sediment transport flow, sediment content and post-flood flat flow data of the river calculation section.

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