A stochastic simulation method for multi-station flood processes considering historical extreme flood characteristics

Abstract

The present invention relates to the technical field of flood prevention and disaster reduction in river basins, and specifically to a random simulation method for multi-station flood processes that takes into account the characteristics of historical extreme floods. A multi-station flood simulation model that takes into account high-order autocorrelations is constructed to generate a multi-station flood simulation sample library; a flood feature sequence set that takes into account historical extreme floods is generated in combination with the characteristics of historical extreme floods; and a matching search is performed in the multi-station flood simulation sample library based on the flood feature sequence of the master station to obtain a multi-station simulated flood sequence that takes into account the characteristics of historical floods. This can solve the problem that the existing random simulation technology is limited in the process of multi-station flood simulation due to model complexity and other reasons. Most of them only consider the low-order correlation characteristics of the flood process at each station, and it is difficult to characterize the high-order autocorrelation and cross-correlation structure between the super-standard flood processes at each station in the basin.

Description

Technical Field

[0001] The present invention relates to the technical field of flood prevention and disaster reduction in river basins, and in particular to a multi-station flood process stochastic simulation method that takes into account the characteristics of historical extreme floods. Background Art

[0002] At present, and due to factors such as the limited length of measured data sequences, existing technical means are difficult to accurately simulate the hydrological characteristics of super-standard floods in the basin under extreme climatic conditions, further increasing the difficulty of compiling super-standard flood defense plans in the basin. Under the background of existing data, most of them adopt the "historical measured sequence method" or "typical year method", select a typical large flood or amplify the design flood process through the "same multiple ratio" and "same frequency" methods to plan and design the water conservancy project application plan under extreme flood conditions. However, with the completion of the flood control system of water conservancy projects in the basin, the flood control standards of each district are different, and the overall flood control safety of the region is difficult to coordinate. It is difficult to comprehensively consider the flood control safety of local and overall, upstream and downstream, left and right banks, and main and tributary areas by using traditional floods with a certain frequency or recurrence period or typical large floods for flood control planning and design. Therefore, the random simulation method, as a reasonable and effective method of data augmentation, is widely used to solve the problem of insufficient diversity of flood sequence samples. This method can simulate a large number of possible water inflow conditions based on the statistical characteristics of historical measured data without dealing with complex flood combination encounter problems, which can meet various application requirements such as conventional operation of reservoir groups and super-standard operation.

[0003] However, the existing random flood simulation models are limited by the complexity of the model, and most of them can only guarantee the low-order statistical characteristics of the sequence, and it is difficult to guarantee the high-order autocorrelation and cross-correlation characteristics of the simulated multi-station hydrological time series. At the same time, the flood control standards of each area (station) in the basin are different. Most of the existing multi-station random simulation methods are modeled only based on the historical continuous measured flood data of each station. The modeling process rarely considers the historical super-standard hydrological extreme values ​​that appear at each station in the flood control area. Therefore, the simulated characteristic values ​​of the flood peak, flood volume, etc. of the flood sequence under extreme conditions deviate greatly from the actual design flood characteristic values, and the correlation between the flood characteristic values ​​of each station in the simulation sequence is difficult to maintain. The reliability of the simulated super-standard flood sequence in the basin is low, which will bring data deviation to the preparation of super-standard flood defense plans.

[0004] Therefore, how to utilize limited and discontinuous hydrological data, comprehensively consider the high-order autocorrelation characteristics of multiple sites in the basin and the historical extreme hydrological characteristics of the basin to upgrade the existing random simulation technology, and then simulate a reasonable and reliable super-standard flood process in the basin under extreme climate scenarios, is a scientific and technological problem that needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to address the defects of the prior art and provide a multi-station flood process random simulation method taking into account the characteristics of historical extreme floods. The method can solve the limitations of the existing random simulation technology in the multi-station flood simulation process due to model complexity and other reasons. Most of the methods only consider the low-order correlation characteristics of the flood processes at each station, and it is difficult to characterize the high-order autocorrelation and mutual correlation structure between the super-standard flood processes at each station in the basin. The method also solves the problems that the existing random simulation technology is difficult to use to characterize the high-order autocorrelation and mutual correlation structure between the flood processes at each station in the basin, and because the historical extreme flood characteristics of the station cannot be considered, the reliability of the simulated extreme flood sequence is low, and the uncertainty of the super-standard flood in the flood protection zone cannot be accurately characterized.

[0006] The present invention provides a multi-station flood process stochastic simulation method considering the characteristics of historical extreme floods, and its technical solution is:

[0007] Construct a multi-station flood simulation model considering high-order autocorrelation and generate a multi-station simulated flood sample library;

[0008] Combined with the characteristics of historical extreme floods, a flood characteristic sequence set considering historical extreme floods is generated;

[0009] According to the flood characteristic sequence of the main station, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account the historical flood characteristics.

[0010] Preferably, the constructing of a multi-station flood simulation model taking into account high-order autocorrelation and generating a multi-station simulated flood sample library comprises:

[0011] The multi-station measured flood series are cointegrated into a multi-station measured flood series matrix, and the distribution characteristics of different column variables of the multi-station measured flood series matrix and the correlation between column variables are analyzed;

[0012] The joint distribution of multiple variables is constructed based on the correlation between the variables in the matrix of flood series measured at multiple stations;

[0013] The joint distribution is randomly sampled to generate a multi-station simulated flood sample library.

[0014] Preferably, combining the characteristics of historical extreme floods, the flood characteristic sequence set considering historical extreme floods is generated, including:

[0015] According to the flood control characteristics of the basin, the main control stations in the flood control system of the reservoir group are selected, and the flood characteristics of the main stations that need to be simulated are selected in combination with the completeness of historical flood data;

[0016] Fitting marginal distribution and joint distribution of flood characteristics of discontinuous main stations;

[0017] Correlation sampling is performed on the joint distribution of the flood characteristics of the master station, and the inverse function of the marginal distribution of the flood characteristics of the master station is combined to simulate and generate a sequence set of the flood characteristics of the master station.

[0018] Preferably, the method of matching and searching in the multi-station simulated flood sample library according to the master station flood feature sequence to obtain the multi-station simulated flood sequence considering historical flood characteristics comprises:

[0019] Based on the multi-station simulated flood sample library, characteristic values ​​of the main station flood characteristics that need to be simulated in the multi-station simulated flood sample library are calculated to generate a flood characteristic sequence of the multi-station simulated flood sample library;

[0020] According to the master station flood feature sequence set generated by simulation and in accordance with the set sampling target, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account the historical flood characteristics.

[0021] Preferably, the set sampling target is:

[0022] The sampling error of flood characteristics is minimal, and the continuity characteristics of the simulated flood sequence from year to year are consistent with the measured sequence.

[0023] Preferably, after generating the multi-station simulated flood sample library, the method further includes testing the rationality of the multi-station simulated flood sample library generated by sampling, and the testing process includes:

[0024] Calculate the correlation coefficient matrix ρ of the multi-station simulated flood sequence matrix based on the multi-station simulated flood sequence sim ;

[0025] Based on ρ sim and the correlation coefficient matrix ρ of the measured flood series obs Calculate the matrix error index Eor;

[0026] If the matrix error index Eor is less than the preset value, the multi-station simulated flood sample library generated by sampling is reasonable.

[0027] Preferably, the main control stations in the flood control system of the reservoir group are selected according to the flood control characteristics of the river basin, and the flood characteristics of the main stations to be simulated are selected in combination with the completeness of historical flood data, including:

[0028] According to the geographical location of each station in the study area, the downstream stations of each sub-basin are selected as the master stations, and according to the flood characteristics of the master stations, the flood characteristics of the master stations that need to be simulated are selected;

[0029] The main station flood characteristics that need to be simulated include annual peak flow, annual average flow, annual maximum one-day flood volume, annual maximum three-day flood volume, and annual maximum seven-day flood volume.

[0030] Preferably, fitting the marginal distribution and joint distribution of the discontinuous master station flood characteristics includes:

[0031] Based on the selected measured flood data of the main station, the flood characteristic values ​​of the historical major floods at the main station are considered, and the distribution of flood characteristics of the main station is fitted;

[0032] The correlation coefficients between flood characteristics at different master stations are calculated, and the joint distribution between multiple flood characteristics is established.

[0033] Preferably, based on the multi-station simulated flood sample library, calculating the characteristic value of the main station flood characteristic to be simulated in the multi-station simulated flood sample library, and generating the flood characteristic sequence of the multi-station simulated flood sample library includes:

[0034] Counting the flood characteristics of each row in the multi-station simulated flood sample library;

[0035] The flood characteristics of the main station that needs to be simulated are screened to generate a flood characteristic sequence of the multi-station simulated flood sample library.

[0036] Preferably, according to the master station flood feature sequence set generated by simulation, a matching search is performed in the multi-station simulated flood sample library according to the set sampling target to obtain a multi-station simulated flood sequence considering historical flood characteristics:

[0037] According to the master station flood feature sequence set CM generated by simulation, n1 samplings are performed without replacement according to the set sampling target, and the matching n1-year flood features are found in the flood feature sequence CS of the multi-station simulated flood sample library, and the matrix row number of the extracted flood feature in the matrix CS is recorded;

[0038] According to the n1 matrix row numbers, the multi-station measured flood sequence matrix S obs Take out the flood sequence of each station in the corresponding row and get the multi-station simulated flood sequence of n1 years;

[0039] Among them, when conducting n1 sampling without replacement according to the set sampling target, the first sampling only needs to meet some conditions in the sampling target, and the remaining n1-1 samplings need to meet all conditions in the sampling target.

[0040] The beneficial effects of the present invention are:

[0041] 1. The problem that the existing random simulation technology is limited in the process of multi-site flood simulation due to model complexity and other reasons, and most of them only consider the low-order correlation characteristics of the flood process at each site, and it is difficult to characterize the high-order autocorrelation and cross-correlation structure between the super-standard flood processes at various sites in the basin; The problem that the existing random simulation technology is difficult to use to characterize the high-order autocorrelation and cross-correlation structure between the flood processes at various sites in the basin, and because it is impossible to consider the historical extreme flood characteristics of the site, the reliability of the simulated extreme flood sequence is low, and it is impossible to accurately characterize the uncertainty of floods exceeding the standard in the flood protection area.

[0042] 2. This method can simulate multi-station flood processes on different time scales of year, month and day. The simulated flood process can not only meet the low-order statistical characteristics such as the mean, skewness coefficient, and coefficient of variation of each cutoff, but also characterize the high-order auto- and cross-correlation characteristics of the flood process at each station.

[0043] 3. This method overcomes the difficulty of stochastic simulation modeling of discontinuous flood sequences considering historical floods. The simulation sequence can effectively maintain the marginal distribution of different flood characteristics at the downstream key control stations, making the simulated extreme flood conditions more reliable.

[0044] 4. The final sampling simulation sequence can further maintain the inter-annual correlation of floods on the basis of ensuring the intra-annual correlation structure of floods at each station, and the different flood characteristics of simulated floods at the main downstream control stations. The research results can generate multi-station flood processes considering extreme hydrological characteristics according to actual engineering needs, and can further provide data support for the planning and design of flood control scheduling schemes and risk assessment of water engineering groups. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the process of the present invention;

[0046] Figures 2 to 5 This is a schematic diagram of the distribution fitting results of different flood characteristics at Yichang Station in the present invention. DETAILED DESCRIPTION

[0047] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. 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.

[0048] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0049] It should be understood that the orientation or position relationship indicated by terms such as "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0050] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0051] like Figure 1 As shown in the figure, a multi-station flood process stochastic simulation method considering the characteristics of historical extreme floods is implemented as follows:

[0052] Step 1: Construct a multi-station flood simulation model considering high-order autocorrelation and generate a multi-station simulated flood sample library. This step mainly calculates the correlation of each station, analyzes the correlation between the flow processes of different cutoffs at each station, constructs the joint distribution of flood flow at each station, and performs joint sampling. The obtained simulated flood sample library can not only meet the marginal distribution of each flood variable, but also effectively characterize the high-order autocorrelation structure of the historical multi-station measured flood series.

[0053] Step 2: Combine the characteristics of historical extreme floods to generate a flood feature sequence set that takes into account historical extreme floods. This step selects the main control sites and key flood features, combines the historical flood feature data to perform distribution fitting on the selected flood features, and uses the correlation sampling method described in step 1 to jointly sample the flood features to generate a flood feature sequence set.

[0054] Step 3: According to the flood characteristic sequence of the master station, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account historical flood characteristics. This step is used to match the flood process sample library S generated in step 1 according to the flood characteristic sequence CM. sim By matching search in the middle, a multi-station super-standard flood sequence considering the historical flood characteristics is obtained.

[0055] Step 1 includes steps 101 to 103, and steps 101 to 103 are specifically as follows:

[0056] Step 101, cointegrating multi-station measured flood series into a multi-station measured flood series matrix, and analyzing the distribution characteristics of different column variables of the multi-station measured flood series matrix and the correlation between the column variables;

[0057] Step 102, constructing a joint distribution of multiple variables based on the correlation between the column variables of the multi-station measured flood sequence matrix;

[0058] Step 103, randomly sampling the joint distribution to generate a multi-station simulated flood sample library.

[0059] The implementation process of step 101 is as follows:

[0060] ①: Cointegrate the measured flood sequences of k stations into a flood sequence matrix. If the simulation time scale is days, the measured flood sequence matrix S obs As shown below:

[0061]

[0062] Where n is the total number of simulated variables. If the total number of simulated sites is k, then n = k × 365. Each column represents the simulation time scale.

[0063] ②: Select a suitable distribution function to fit each column of flood flow and calculate the matrix S obs The Pearson correlation coefficient between the columns is ρ obs .

[0064] The implementation process of step 102 is as follows:

[0065] ③: Select a suitable Copula function and construct a joint distribution based on the correlation between the variables of the multi-station flood series. The parameters of the joint distribution function can be expressed as Pearson correlation coefficient ρ obs Make an estimate:

[0066] F(Q1,Q2,...,Q n )=C(F1(x),F2(x),...,F n (x)) (2)

[0067] In the formula, Q n is the flood vector of the nth cut; C(x) is the joint distribution function of floods at different cuts; F(x) is the joint distribution function of n flood variables, F n (x) is the marginal distribution of the nth flood variable.

[0068] The implementation process of step 103 is as follows:

[0069] ④: Randomly generate vectors (ε1,ε2,…,ε n), the flow value at the station at time t can be obtained by the inverse function of the marginal distribution; then let u1 = ε1. Since u1 and ε2 are known, u2 can be calculated by the conditional distribution C(u2|u1) = ε2. Similarly, i |u1,…,u i-1 )=ε i The unique value u can be obtained i Finally, we get the simulation vector (u1,u2,…,u n ); Repeat M times to obtain the M-year multi-station flood process.

[0070] ⑤: Through the inverse function of the marginal distribution of each sampled variable i=1,…,n, the simulated flood sequence matrix S can be obtained sim .

[0071]

[0072] In the formula, S sim is the simulation sequence matrix; its structure is similar to S obs Similar, except that the number of rows is the total number of simulated years M.

[0073] ⑥: Calculate the correlation coefficient matrix ρ of the simulated sequence matrix sim , combined with the measured flood series correlation coefficient matrix ρ obs The following matrix error index Eor is used to judge the degree to which the correlation structure of the simulation sequence is maintained.

[0074]

[0075] In the formula, Eor represents the RMSE of the correlation coefficient matrix between the measured sequence and the simulated sequence. The smaller its value is, the better the correlation structure of the simulated sequence is maintained.

[0076] Step 2 includes steps 201 to 203, and steps 201 to 203 are specifically as follows:

[0077] Step 201, according to the flood control characteristics of the river basin, select the main control stations in the flood control system of the reservoir group, and select the main station flood characteristics that need to be simulated in combination with the completeness of historical flood data;

[0078] Step 202, fitting the marginal distribution and joint distribution of the discontinuous master station flood characteristics;

[0079] Step 203, performing correlation sampling on the joint distribution of the master station flood characteristics, combining the inverse function of the master station flood characteristic marginal distribution, simulating and generating the master station flood characteristic sequence set, and verifying the rationality of the multi-station simulated flood sample library generated by sampling.

[0080] The implementation process of step 201 is as follows:

[0081] ①: According to the geographical location of each station in the study area, select the downstream stations of each sub-basin as the main station, and select the flood characteristics of the main station to be simulated according to the flood characteristics of the main station. The flood characteristics of the main station may include: annual peak flow, annual average flow, annual maximum one-day flood volume, annual maximum three-day flood volume, annual maximum seven-day flood volume, etc.

[0082] The implementation process of step 202 is as follows:

[0083] ②: Based on the measured flood data of the selected main station, the flood characteristic values ​​of the historical floods of the main station are considered to fit the distribution of flood characteristics of the main station. For hydrological stations in most parts of China, the Pearson III distribution (P-III) is often used to fit the distribution of hydrological characteristics, and the parameters of the distribution are estimated by the discontinuous moment method in combination with the historical flood data.

[0084] ③: Calculate the Pearson correlation coefficient between flood characteristics of different master stations, and use the Copula function to establish the joint distribution between N flood characteristics:

[0085] F'(CH1,CH2,...,CH N )=C'(F1(x),F'2(x),...,F' N (x)

[0086] In the formula, CH n is the flood characteristic vector measured at the Nth master station, which is obtained by statistics of the continuous flood data measured at the selected master station; C'(x) is the joint distribution function between different flood characteristics; F'(x) is the joint distribution function of N flood characteristics, F' N (x) is the marginal distribution of the Nth flood characteristic variable, and its parameters are estimated by step (2).

[0087] The implementation process of step 203 is as follows:

[0088] Calculate the correlation coefficient matrix ρ of the multi-station simulated flood sequence matrix based on the multi-station simulated flood sequence sim ;

[0089] Based on ρ sim and the correlation coefficient matrix ρ of the measured flood series obs Calculate the matrix error index Eor;

[0090] If the matrix error index Eor is less than the preset value, the multi-station simulated flood sample library generated by sampling is reasonable.

[0091] It can be verified specifically in the following ways.

[0092] ④: Based on the (4) to (5) described in step 1, the joint distribution F'(x) of N flood characteristics is sampled, wherein the conditional distribution C(u2|u1) between runoff variables in step 1 (4) is replaced by the conditional distribution C'(u2|u1) between flood characteristics, and the inverse function of the marginal distribution of the sampling variables in step 1 (5) is replaced by the inverse function F' of the marginal distribution of flood characteristics. -1 N (x). Perform correlation sampling on the flood characteristics of the main station and generate the simulation sequence matrix CM of the flood characteristics of the main station.

[0093]

[0094] Where n1 is the total number of years of simulated flood characteristic sequences; each row in the matrix represents the flood characteristics considered by each main station in each simulated year, and the total number is l. If k main stations and r flood characteristics are selected, then l = k × r; Cm i,j is the jth simulated flood feature in the ith simulated year, i = 1, 2…n1, j = 1, 2,…l. The matrix CM can be used as a flood feature sequence, in which the historical extreme flood feature values ​​are considered in the marginal distribution calculation process of each flood feature. At the same time, the correlation structure between the flood features in the sample library is also consistent with the correlation structure between the actual flood features.

[0095] Step 3 includes steps 301 to 302, and steps 301 to 302 are specifically as follows:

[0096] Step 301, based on the multi-station simulated flood sample library, calculate the characteristic values ​​of the main station flood characteristics that need to be simulated in the multi-station simulated flood sample library, and generate a flood characteristic sequence of the multi-station simulated flood sample library.

[0097] Step 302, based on the master station flood feature sequence set generated by simulation, according to the set sampling target, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account historical flood characteristics. The set sampling target is: the flood feature sampling error is minimized, and the continuity characteristics between years of the simulated flood sequence are consistent with the measured sequence.

[0098] The implementation process of step 301 is as follows:

[0099] ①: Flood characteristic sequence S generated by statistical step 1 sim The flood characteristics of each year (row) in the sample library are obtained, and the flood characteristics of each station selected in step 2 are screened to generate the master station flood characteristic matrix CS of the sample library.

[0100]

[0101] Where Fs has M rows and r columns, and Csi,j represents the jth flood characteristic of the master station in the i-th year in the simulation sequence, where i = 1, 2…M, j = 1, 2,…l.

[0102] The implementation process of step 302 is as follows:

[0103] ②: Based on the flood feature matrix CM generated in step 2, find the matching flood feature of year n1 in CS and record the matrix row number of the extracted flood feature in matrix CS.

[0104] The sampling objectives are divided into two parts. The first part is to minimize the sampling error of flood characteristics, and the sum of the relative error values ​​of each flood characteristic between Cs and CM is used for quantitative representation. The second part uses the difference in correlation coefficients to represent the continuity characteristics of the simulated flood series at each station between years and the consistency of the measured series.

[0105]

[0106] In the formula, Cm k With Cs k are the kth flood eigenvalues ​​of the corresponding rows of the characteristic matrices CM and CS, respectively; Ns is the total number of stations; Na is the total number of cuts in a year; and are the correlation coefficients of flood at the pth and qth cutoffs of the jth station in the simulated sequence and the measured sequence, respectively, where the time lag between cutoff p and cutoff q is L.

[0107] ③: According to the sampling target Obj, perform n1 samplings without replacement. For the first sampling, it is only necessary to meet the goal of minimizing the sum of relative errors of simulating different flood characteristics. For the remaining n1-1 samplings without replacement, sampling must be carried out strictly in accordance with the target Obj.

[0108] ④: The flood sequence matrix S obtained by simulating n1 row numbers in step 1 obs The flood sequence of each station in the corresponding row is taken out, and then the multi-station simulated flood sequence of n1 years is simulated.

[0109] The flood process obtained according to this target search can make the marginal distribution of the simulated sequence flood characteristics consistent with the marginal distribution under the condition of historical floods. The simulated extreme conditions are more reliable, and the simulated flood characteristics have the continuity unique to time series and are consistent with the continuity of the measured series.

[0110] Embodiment 1

[0111] This embodiment takes Pingshan Station in the lower reaches of Jinsha River and Cuntan Station and Yichang Station in the main stream of Yangtze River as research objects, and conducts example simulation to verify the effect of the present invention. The specific implementation steps are as follows:

[0112] Step 1. First, the flood series of the three stations are cointegrated into the measured flood series matrix, and a specific distribution is selected to fit the distribution of the daily flood process of each station, and the correlation structure of the measured flood series matrix is ​​analyzed and calculated. On this basis, the Gaussian Copula function is used to fit the joint distribution of different daily floods at each station, and correlation sampling is performed. Combined with the daily marginal distribution simulation, the daily flood process of the three stations in n1 years can effectively guarantee the high-order autocorrelation characteristics.

[0113] Step 2. Select Yichang Station, the main downstream control station, as the main control station, and select four flood characteristics, namely, annual maximum peak flow, annual maximum 7-day flood volume, annual maximum 15-day flood volume, and annual maximum 30-day flood volume, as quantitative indicators of extreme flood characteristics. Use the method described in step 1 to simulate the four flood characteristics of the main station and obtain the n2-year simulated flood characteristic sequence set of Yichang Station.

[0114] Step 3. According to the n1-year flood sequence of Yichang Station obtained in step 1, the annual maximum flood peak flow, annual maximum 7-day flood volume, annual maximum 15-day flood volume, and annual maximum 30-day flood volume of Yichang Station are counted, and the n2-year simulated flood feature sequence set of Yichang Station is obtained according to step 2. With the goal of minimizing the errors between the flood characteristics of Yichang Station and ensuring the inter-annual continuity of the sampled floods at each station, sampling is carried out in the n1-year three-station simulated flood sequence obtained in step 1 to obtain the n2-year three-station synchronous flood process that meets the conditions.

[0115] According to step 1, the simulated daily flood process of three stations in 10,000 years is obtained, and the simulation results are compared with the simulation results of the multi-station seasonal autoregressive model. According to formula (4), the error Eor of the flood series correlation coefficient matrix obtained by the proposed method is 0.0146, while the Eor value obtained by the MSAR method is 0.149, which is much larger than the Eor value calculated by the proposed method. It can be concluded that the flood series simulated by the proposed method can accurately characterize the high-order autocorrelation and cross-correlation characteristics of the measured flood series.

[0116] At the same time, according to the historical design data of Yichang Station and the measured flood data, a 1000-year flood characteristic sequence set was simulated to meet the goal of minimizing the error of the main station flood characteristics and the continuity of the flood sequence. The 10000-year three-station simulation sequence was sampled to obtain the 1000-year three-station simulated flood sequence. The edge distribution of different flood characteristics at Yichang Station is as follows: Figures 2 to 4 As shown in the figure, it can be seen that the distribution of the flood peak, the annual maximum 7-day flood volume, the annual maximum 15-day flood volume and the annual maximum 30-day flood volume in the simulation sequence is slightly different from the theoretical distribution of flood characteristics obtained by considering the characteristics of extreme floods. The simulated flood sequence obtained by the proposed method can characterize the overall distribution characteristics of flood characteristics.

[0117] Table 1 shows the simulated values ​​and measured values ​​at different design frequencies of the Yichang station. It can be seen from the table that the difference between the two is very small, which proves that the design values ​​of flood characteristics simulated by this method do not deviate much from the actual design values. The extreme super-standard flood scenarios simulated by the proposed method are more reliable.

[0118] Table 1 Comparison results of design flood values ​​at Yichang Station

[0119]

[0120] In addition, the correlation coefficient matrix of the first and second days of each year and the last two days of the previous year between the measured series and the simulated series at each station was statistically analyzed, and the absolute error values ​​of the measured correlation coefficient matrix and the simulated correlation coefficient matrix were statistically analyzed, as shown in Table 2. As can be seen from the table, the maximum absolute error value of the interannual correlation coefficient is only 0.0289, which is almost negligible. In general, the simulated flood series generated by the model can better maintain the interannual correlation characteristics of the measured floods.

[0121] Table 2 Absolute error of the interannual correlation coefficient matrix of floods at each station

[0122]

[0123] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A multi-station flood process stochastic simulation method considering the characteristics of historical extreme floods, characterized by: Construct a multi-station flood simulation model considering high-order autocorrelation and generate a multi-station simulated flood sample library; Combined with the characteristics of historical extreme floods, a flood characteristic sequence set considering historical extreme floods is generated; According to the flood characteristic sequence of the main station, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account the historical flood characteristics; The construction of a multi-station flood simulation model considering high-order autocorrelation and the generation of a multi-station simulated flood sample library include: The multi-station measured flood series are cointegrated into a multi-station measured flood series matrix, and the distribution characteristics of different column variables of the multi-station measured flood series matrix and the correlation between column variables are analyzed; The joint distribution of multiple variables is constructed based on the correlation between the variables in the matrix of flood series measured at multiple stations; Randomly sampling the joint distribution to generate a multi-station simulated flood sample library; Combining the characteristics of historical extreme floods, the flood characteristic sequence set considering historical extreme floods is generated, including: According to the flood control characteristics of the basin, the main control stations in the flood control system of the reservoir group are selected, and the flood characteristics of the main stations that need to be simulated are selected in combination with the completeness of historical flood data; Fitting marginal distribution and joint distribution of flood characteristics of discontinuous main stations; Perform correlation sampling on the joint distribution of the flood characteristics of the master station, combine the inverse function of the marginal distribution of the flood characteristics of the master station, and simulate and generate a master station flood characteristic sequence set; The method of matching and searching in the multi-station simulated flood sample library according to the master station flood feature sequence to obtain a multi-station simulated flood sequence considering historical flood characteristics comprises: Based on the multi-station simulated flood sample library, characteristic values ​​of the main station flood characteristics that need to be simulated in the multi-station simulated flood sample library are calculated to generate a flood characteristic sequence of the multi-station simulated flood sample library; According to the master station flood feature sequence set generated by simulation and in accordance with the set sampling target, a matching search is performed in the multi-station simulated flood sample library to obtain a multi-station simulated flood sequence that takes into account the historical flood characteristics.

2. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: The sampling objectives set are: The sampling error of flood characteristics is minimal, and the continuity characteristics of the simulated flood sequence from year to year are consistent with the measured sequence.

3. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: After the multi-station simulated flood sample library is generated, the rationality of the multi-station simulated flood sample library generated by sampling is tested, and the testing process includes: Calculate the correlation coefficient matrix ρ of the multi-station simulated flood sequence matrix based on the multi-station simulated flood sequence sim ; Based on ρ sim and the correlation coefficient matrix ρ of the measured flood series obs Calculate the matrix error index Eor; If the matrix error index Eor is less than the preset value, the multi-station simulated flood sample library generated by sampling is reasonable.

4. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: According to the flood control characteristics of the basin, the main control stations in the reservoir group flood control system are selected, and combined with the completeness of historical flood data, the main station flood characteristics that need to be simulated are selected, including: According to the geographical location of each station in the study area, the downstream stations of each sub-basin are selected as the master stations, and according to the flood characteristics of the master stations, the flood characteristics of the master stations that need to be simulated are selected; The main station flood characteristics that need to be simulated include annual peak flow, annual average flow, annual maximum one-day flood volume, annual maximum three-day flood volume, and annual maximum seven-day flood volume.

5. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: Fitting the marginal distribution and joint distribution of the discontinuous main station flood characteristics includes: Based on the measured flood data of the selected main station, the flood characteristic values ​​of the historical major floods at the main station are considered to fit the distribution of flood characteristics of the main station; The correlation coefficients between flood characteristics at different master stations are calculated, and the joint distribution between multiple flood characteristics is established.

6. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: Based on the multi-station simulated flood sample library, calculating the characteristic value of the main station flood characteristic that needs to be simulated in the multi-station simulated flood sample library, and generating the flood characteristic sequence of the multi-station simulated flood sample library includes: Counting the flood characteristics of each row in the multi-station simulated flood sample library; The flood characteristics of the main station that needs to be simulated are screened to generate a flood characteristic sequence of the multi-station simulated flood sample library.

7. The multi-station flood process stochastic simulation method considering historical extreme flood characteristics according to claim 1 is characterized in that: According to the master station flood feature sequence set generated by simulation, a matching search is performed in the multi-station simulated flood sample library according to the set sampling target to obtain the multi-station simulated flood sequence considering the historical flood characteristics: According to the master station flood feature sequence set CM generated by simulation, n1 samplings are performed without replacement according to the set sampling target, and the matching n1-year flood features are found in the flood feature sequence CS of the multi-station simulated flood sample library, and the matrix row number of the extracted flood feature in the matrix CS is recorded; According to the n1 matrix row numbers, the multi-station measured flood sequence matrix S obs Take out the flood sequence of each station in the corresponding row and get the multi-station simulated flood sequence of n1 years; Among them, when conducting n1 sampling without replacement according to the set sampling target, the first sampling only needs to meet some conditions in the sampling target, and the remaining n1-1 samplings need to meet all conditions in the sampling target.

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