Non-consistent flood frequency analysis method based on historical flood and reservoir regulation and storage

Abstract

The invention belongs to the technical field of hydraulic engineering and hydrology, and discloses a non-consistent flood frequency analysis method based on historical flood and reservoir regulation and storage, which comprises the following steps: acquiring actually measured flood data and reservoir observation data in a preset time period of a to-be-researched drainage basin, and respectively constructing an actually measured flood sequence and a reservoir flood regulation index sequence; constructing a joint distribution model according to the reservoir flood regulation index sequence and the actually measured flood sequence, determining a source function of tracing reconstruction based on the joint distribution model, and reconstructing the actually measured flood sequence into a flood reconstruction sequence which is not influenced by reservoir regulation and storage according to the source function; determining a first flood frequency curve according to the historical flood data of the to-be-studied area and the flood reconstruction sequence; and converting the first flood frequency curve into a second flood frequency curve under a non-consistency condition according to the source function so as to carry out flood frequency analysis. According to the method, the problem of flood sequence inconsistency caused by reservoir regulation and storage is solved, and the accuracy of inconsistent flood frequency analysis is improved by introducing historical flood data.

Description

Technical Field

[0001] The invention discloses an inconsistent flood frequency analysis method based on historical floods and reservoir storage, and belongs to the technical fields of water conservancy engineering and hydrology. Background Art

[0002] Flood frequency analysis, a crucial component of river basin flood control and water resources planning and management, is a widely accepted theoretical framework for design flood calculations, and its results directly determine the accuracy of design flood calculations. However, since the 1990s, large-scale reservoir regulation has significantly altered the natural hydrological regime of river basins. Through regulation activities such as water storage and peak shaving, the spatiotemporal distribution of runoff has been reshaped, and the statistical characteristics of flood peak sequences (such as mean and variance) have varied. Consequently, traditional flood frequency analysis methods face challenges in practical applications, such as inconsistency in flood sequences and insufficient measured data. This problem severely restricts the accuracy and reliability of design flood calculations.

[0003] The current standard (NB / T 35046-2014) stipulates that when conducting flood frequency analysis in basins with existing water conservancy projects, the flood sequence after the project construction should be restored to the natural conditions before the reservoir was built. However, existing technologies for dynamically quantifying the regulation and storage effects of reservoirs have significant shortcomings. For example, traditional water balance methods restore flood peaks by simplifying the inflow and outflow process. However, their linear assumptions ignore the nonlinear characteristics of hydrological processes and rely on high-precision precipitation and evaporation data, leading to cumulative error propagation and insufficient reliability of the restored results. Another approach quantifies the impact of reservoirs by constructing static reservoir regulation indicators based on fixed parameters such as the designed regulation capacity. However, the actual regulation and storage capacity varies dynamically with the reservoir's real-time storage capacity and scheduling rules. Static indicators cannot reflect the true impact, resulting in significant model bias.

[0004] Furthermore, measured flood data typically spans less than a century, and directly deriving design values ​​for millennia or even ten-thousand-year floods will result in significant extrapolation errors due to insufficient sample representativeness. While the inclusion of historical floods (including paleofloods) can extend the data time span, existing methods are only applicable under consistent conditions. Traditional non-sequential flood frequency analysis methods assume sequence consistency and fail to address the issues of historical flood weight assignment and distribution parameter correction under inconsistent conditions. While the fuzzy historical flood fusion method based on the L-moment method can handle discontinuous data, its parameter estimation still relies on the consistency assumption and cannot account for distribution parameter variations caused by reservoir regulation. This fragmented nature results in low utilization of historical flood information, making it difficult to overcome the statistical limitations of short sequences. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing inconsistent flood frequencies based on historical floods and reservoir storage, in order to address the technical issues in the prior art of difficulty in restoring the inconsistent flood sequences affected by reservoir storage, and to address the technical issues of considering the impact of historical floods under inconsistent conditions. To achieve the above objectives, the present invention proposes a method for analyzing inconsistent flood frequencies based on historical floods and reservoir storage, the specific scheme of which is as follows:

[0006] The inconsistent flood frequency analysis method based on historical floods and reservoir storage includes the following steps:

[0007] Step 1: Obtain measured flood data and reservoir observation data within a preset period of time in the basin to be studied, and construct a measured flood sequence based on the measured flood data, and construct a reservoir flood control index sequence based on the reservoir observation data;

[0008] Step 2: constructing a joint distribution model based on the reservoir flood regulation index sequence and the measured flood sequence, and determining a source function for source tracing reconstruction based on the joint distribution model; reconstructing the measured flood sequence into a flood reconstruction sequence unaffected by reservoir regulation according to the source function;

[0009] Step 3: determining a first flood frequency curve based on the historical flood data of the area to be studied and the flood reconstruction sequence;

[0010] Step 4: Convert the first flood frequency curve into a second flood frequency curve under inconsistency conditions according to the source function, and perform flood frequency analysis according to the second flood frequency curve.

[0011] Preferably, a reservoir flood control index sequence is constructed based on reservoir observation data, including:

[0012] Determining the real-time available flood control storage capacity and the actual flood control storage capacity based on the reservoir observation data;

[0013] Determining a reservoir flood control index according to a ratio of the real-time available flood control storage capacity to the actual flood control storage capacity;

[0014] A reservoir flood control index sequence is determined based on the plurality of reservoir flood control indexes.

[0015] Preferably, determining the real-time available flood control storage capacity and the actual flood control storage capacity based on the reservoir observation data includes:

[0016] Determining flood sequences and corresponding flood time series within the basin based on the measured flood data;

[0017] According to the reservoir observation data and based on the flood time series, the real-time available flood control storage capacity and the actual flood control storage capacity of the reservoir before the preset window period corresponding to each flood time are extracted.

[0018] Preferably, constructing a joint distribution model based on the reservoir flood control index sequence and the measured flood sequence includes:

[0019] respectively constructing a first marginal distribution function of the measured flood sequence and a second marginal distribution function of the reservoir flood control index sequence;

[0020] A joint distribution model of the first marginal distribution function and the second marginal distribution function is constructed by using a copula function.

[0021] Preferably, before respectively constructing the first marginal distribution function of the measured flood sequence and the second marginal distribution function of the reservoir flood control index sequence, the method further includes:

[0022] Determining whether the correlation between the measured flood sequence and the reservoir flood control index sequence meets the preset requirements;

[0023] If not, the preset window period is adjusted until the correlation between the measured flood sequence and the reservoir flood control index sequence meets the preset requirements.

[0024] Preferably, after step 2 and before step 3, the following steps are further included:

[0025] Determining whether a consistency check and / or a historical review check of the flood reconstruction sequence meets a first requirement;

[0026] If not, the source function is re-determined until the consistency check and / or the historical review check of the flood reconstruction sequence meets the first requirement.

[0027] Preferably, the flood reconstruction sequence is subjected to a historical review test, including:

[0028] Calculating statistical parameters of the flood reconstruction sequence using a line fitting method, and performing flood frequency analysis under consistency conditions based on the statistical parameters;

[0029] The flood frequency analysis results are checked to see if they meet the preset range based on the design standards before reservoir construction.

[0030] Preferably, the statistical parameters of the flood reconstruction sequence are calculated using a line fitting method, including:

[0031] Constructing a historical flood sequence based on historical flood data of the area to be studied;

[0032] Using a unified processing method to calculate the empirical frequencies of the historical flood sequence and the flood reconstruction sequence;

[0033] Based on the empirical frequency, the statistical parameters of the flood reconstruction sequence are calculated using a line fitting method.

[0034] Preferably, the step 3 is specifically:

[0035] Constructing a source-tracing reconstructed flood sequence containing historical floods based on the historical flood data of the area to be studied and the flood reconstruction sequence;

[0036] The first flood frequency curve of the source-tracing and reconstructed flood sequence under consistency conditions is calculated according to the linear moment method.

[0037] Preferably, calculating the first flood frequency curve of the source-tracing and reconstructed flood sequence under consistency conditions according to the linear moment method specifically includes:

[0038] Determine multiple distribution parameter groups of various distribution models by linear moment method;

[0039] Performing a goodness of fit test on the source-tracing and reconstructed flood sequence based on the multiple distribution parameter groups, and determining an optimal distribution model of the source-tracing and reconstructed flood sequence as an optimal probability distribution model;

[0040] A first flood frequency curve under consistency conditions is drawn according to the optimal probability distribution model and the distribution parameters.

[0041] Beneficial effects: The present invention fully considers the actual regulation and storage function of the reservoir, distinguishes and quantifies the impact of the reservoir regulation and storage function on the downstream flood situation. At the same time, the invention avoids over-reliance on a large amount of measured data, realizes the restoration of inconsistent hydrological sequences under the influence of the actual regulation and storage of the reservoir, and reduces the difficulty and uncertainty of the restoration calculation of inconsistent flood sequences. The present invention introduces historical flood data to enhance the representativeness of flood data. Taking historical floods into account solves the problem of introducing historical floods into inconsistent flood data, and further improves the accuracy and reliability of inconsistent flood frequency analysis. The present invention can be widely used in the analysis of inconsistent flood frequencies under the influence of reservoir regulation, and provides scientific and technical support for the safety assessment of water conservancy projects themselves and downstream flood control under the influence of human activities, flood data restoration calculation, and historical design results review. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the process of the present invention;

[0043] Figure 2 The results of the Pettitt mutation test in Example 2 of the present invention are shown, where (a) is the Tangnaihai hydrological station and (b) is the Guide hydrological station;

[0044] Figure 3 This is a diagram of the flood process measured at Guide Station and Tangnaihai Station in 1964 and 1967 in Example 2 of the present invention;

[0045] Figure 4 The reservoir flood control index one day before the flood peak in the second embodiment of the present invention;

[0046] Figure 5 ACRI source function fitting in Example 2 of the present invention;

[0047] Figure 6 The peak reconstruction sequence RS in the second embodiment of the present invention ACRI, t ;

[0048] Figure 7 The peak reconstruction sequence RS in the second embodiment of the present invention ACRI, t Pettitt mutation test results;

[0049] Figure 8 This is the frequency analysis of the P-III curve using the fitting method in Example 2 of the present invention;

[0050] Figure 9 is the designed peak flow under the corresponding recurrence period in the second embodiment of the present invention, where (a) is the peak flow sequence RS reconstructed by tracing back to the source under the consistency condition. ACRI, t Designed flood peak flow; (b) Source-tracing reconstruction of flood peak sequence RS ACRI, t Restore to the corresponding design peak flow under non-consistent conditions. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0052] As mentioned above, flood frequency analysis, as an important guarantee for basin flood control safety and water resources planning and management, is a generally accepted theoretical framework for design flood calculations. However, the calculation accuracy of design floods is affected by the length limit of measured data and the inconsistency of flood sequences. For the inconsistency problem of flood sequences, the causal mechanism is the key to solving the inconsistency flood frequency analysis. However, existing technologies all use complex mathematical models and statistical techniques, ignoring the physical reality of the inconsistency of flood sequences. At the same time, accurate quantification of the impact of reservoir regulation is the key to realizing the inconsistency flood frequency analysis under the influence of reservoir regulation. For the problem of the length of measured data, existing technologies usually introduce historical flood data or even ancient flood data into the measured flood data to form discontinuous samples, but they are only applicable under consistent conditions and do not consider flood frequency analysis under inconsistent conditions.

[0053] In response to the above problems, the idea of ​​this application is to propose a non-consistent flood frequency analysis method based on historical floods and reservoir regulation, by restoring the non-consistent flood sequence affected by reservoir regulation, to solve the flood frequency analysis considering the impact of historical floods under non-consistent conditions.

[0054] Example 1:

[0055] A method for analyzing inconsistent flood frequency based on historical floods and reservoir storage includes the following steps:

[0056] The present invention proposes a method for analyzing the frequency of non-consistent floods taking into account historical floods and reservoir regulation. The method covers the frequency analysis of both flood peaks and flood volumes. In order to specifically illustrate this method, this embodiment will take the flood peak frequency analysis as an example for detailed description. Accordingly, those skilled in the art can flexibly apply this method to the frequency analysis of flood volumes based on the content of this embodiment. It is hereby stated that the purpose of the present invention is to provide a comprehensive analysis framework that is suitable for the analysis of flood peak frequencies and can also be easily extended to the analysis of flood volume frequencies. Therefore, in the context of this embodiment, the "flood peak" mentioned specifically refers to the object for flood peak frequency analysis.

[0057] Step 1: Obtain measured flood data and reservoir observation data within a preset period of time in the basin to be studied, and construct a measured flood peak sequence based on the measured flood data, and construct a reservoir flood control index sequence based on the reservoir observation data;

[0058] Step 1.1: Obtain measured flood data and reservoir observation data for the study basin within a predetermined time period. Specifically, the measured flood data here refers to the annual maximum peak flow rate, selected from the measured runoff data for the study basin within a predetermined time period using the Annual Maximum Method (AM). The measured flood peak sequence is a chronological arrangement of the selected annual maximum peak flows.

[0059] It should be noted that, in another embodiment, a flood volume sequence within a preset period of time in the basin to be studied is constructed. Specifically, the annual maximum method (AM) is used to select the flood volume of the corresponding time scale from the measured runoff data within the preset period of time in the basin to be studied, and the maximum 15-day flood volume (W 15 ) as an example. Then, these maximum 15-day flood values ​​are sorted in chronological order to form a flood sequence (W 15 sequence).

[0060] Due to the combined effects of reservoir regulation and other natural and human factors, measured flood peak sequences often exhibit inconsistent variations. To further explore this variation and verify whether reservoir regulation is the primary cause, this application conducted an inconsistency test on the measured flood peak sequences. This test process consists of two key steps: trend testing and mutation testing. First, trend testing, using methods such as the Mann-Kendall (MK) test, Pearson correlation coefficient analysis, and Breusch-Pagan (BP) variance test, aims to capture possible long-term, stable trends in the flood peak sequence. These tests reveal the temporal evolution of flood peak flows from different perspectives, providing important statistical evidence for subsequent analysis. Next, mutation testing focuses on potential sudden changes or turning points in the flood peak sequence. Methods such as the Mann-Kendall (MK) mutation test and the Pettitt test were used. These tests can accurately identify mutation points in the sequence, revealing significant changes in flood peak flows over a short period of time. Based on these tests, attribution analysis was further conducted. By comparing the historical records of reservoir storage and the inconsistent variation characteristics of flood peak sequences, this study aims to clarify whether reservoir storage is the primary influencing factor and to further explore its influencing mechanism. This will help to better understand the inconsistent variation of flood peak sequences and provide a basis for the subsequent construction of reservoir flood regulation indicators.

[0061] Having determined that reservoir regulation is the primary cause of the non-uniform changes in measured flood peak sequences, this application further develops a reservoir flood regulation index. This index aims to quantify the specific impact of reservoir regulation on the non-uniform changes in flood peak sequences, providing a more accurate and scientific basis for reservoir flood control, water resources management, and risk assessment.

[0062] Step 1.2: Construct a reservoir flood control index sequence based on reservoir observation data.

[0063] In this embodiment of the present invention, reservoir observation data includes the reservoir water level line and storage capacity curve, the measured reservoir water level, and the reservoir's historical implementation standards. The Available Flood Control Reservoir Index (ACRI) is the ratio of the real-time available flood control storage capacity determined based on the reservoir observation data to the actual flood control storage capacity.

[0064] Specifically, the real-time available flood control storage capacity refers to the storage capacity between the reservoir's verified flood level and the real-time water level; the actual flood control storage capacity refers to the storage capacity corresponding to the reservoir's verified flood level to the reservoir's actual flood control restriction water level implemented in previous years.

[0065] This paper considers reservoir storage as a key factor affecting flood inconsistency. Therefore, the reservoir's storage capacity for each flood event is quantified based on the remaining storage capacity before the flood peak. This is done by constructing a reservoir flood control index to quantify the reservoir's storage capacity for floods.

[0066] Furthermore, a reservoir flood control index sequence is constructed based on reservoir observation data, including:

[0067] Step 1.2.1: Based on the measured flood data, determine the flood peak sequence and the corresponding peak time series in the basin;

[0068] Specifically, in this embodiment, the peak occurrence time series is a sequence composed of the time points at which each flood peak in the flood peak sequence occurs.

[0069] It should be noted that, in another embodiment, based on the flood sequence (W 15 sequence), determine the flood sequence and the corresponding flood time series. The flood time series here is for the flood sequence (W 15 Each flood magnitude value in the time series is composed of the set of 15 consecutive flood event time points that constitute the flood magnitude value.

[0070] After obtaining the peak time series, to calculate the reservoir flood control index corresponding to each flood peak, we first set a preset window period. Next, for each flood peak, we extract the reservoir's real-time available flood control capacity and actual flood control capacity during the preset window period before that time. This extracted data will be used to subsequently calculate the reservoir flood control index corresponding to each flood peak. The specific steps are as follows:

[0071] Step 1.2.2: According to the reservoir observation data and based on the peak time series, the real-time available flood control storage capacity and the actual flood control storage capacity of the reservoir before each flood peak preset window period are extracted.

[0072] Specifically, the actual flood control storage capacity here differs from the conventional flood control storage capacity used in existing technologies. This is because, to ensure project safety, reservoir managers typically do not immediately adopt the designed flood control water level as the flood control limit water level during the initial operation of the reservoir. Instead, they gradually adjust the actual flood control water level based on the actual operating conditions of the reservoir to avoid the risks that may arise from directly using the designed flood control water level.

[0073] Therefore, the actual flood control storage capacity of this application represents: the storage capacity corresponding to the reservoir's verified flood level to the reservoir's actual flood control limit water level implemented over the years.

[0074] Furthermore, in this application, the preset window period is determined based on an analysis of typical flood hydrographs at reservoir inlet and outlet hydrological stations. Specifically, the flood evolution duration is first determined—that is, the time it takes for floodwater to enter the reservoir and exit the reservoir or reach a specific hydrological station. Then, based on this evolution duration, a preset window period is set.

[0075] Specifically, in this embodiment, the real-time available flood control storage capacity and the actual flood control storage capacity before each flood peak preset window period are extracted.

[0076] Step 1.2.3: After obtaining the real-time available flood control storage capacity and the actual flood control storage capacity before each flood peak preset window period, the reservoir flood control index corresponding to each flood peak is determined by the ratio of the two. The expression of the reservoir flood control index is shown in the following formula (1):

[0077] (1)

[0078] Where: ARC is the real-time available flood control storage capacity of the reservoir, that is, the storage capacity corresponding to the reservoir's verified flood level and real-time water level;

[0079] RC is the actual flood control storage capacity of the reservoir, that is, the storage capacity corresponding to the reservoir's verified flood level to the reservoir's actual flood control limit water level over the years.

[0080] After obtaining the reservoir flood control index corresponding to each flood peak, the multiple reservoir flood control indexes corresponding to the flood peak sequence are arranged in sequence to form a reservoir flood control index sequence.

[0081] It should be noted that, in another embodiment, based on the flood volume time series, the reservoir flood control indexes corresponding to 15 flood events are obtained, and the 15 reservoir flood control indexes are further summed to obtain W 15 The reservoir flood control index sequence corresponding to the sequence.

[0082] Step 2: constructing a joint distribution model based on the reservoir flood regulation index sequence and the measured flood peak sequence, and determining a source tracing and reconstruction source function based on the joint distribution model; reconstructing the measured flood peak sequence into a flood peak reconstruction sequence not affected by reservoir storage according to the source tracing and reconstruction source function; specifically comprising:

[0083] Step 2.1, constructing a joint distribution model based on the reservoir flood control index sequence and the measured flood peak sequence;

[0084] Step 2.1.1: In order to verify the effectiveness and rationality of the reservoir flood control index of the preset window period constructed in this application in quantifying the reservoir's flood storage capacity, three methods are also used, namely, the Pearson correlation coefficient test, the Spearman correlation coefficient test, and the Kendall correlation coefficient test. In this embodiment, it is specifically determined whether the correlation between the measured flood peak sequence and the reservoir flood control index sequence meets the preset requirements; specifically, when the significance level of these tests is less than 0.05 (i.e. ), it is determined that the reservoir flood control index during the preset window period is significantly correlated with the flood peak situation downstream, that is, the correlation between the measured flood peak sequence and the reservoir flood control index sequence meets the preset requirements.

[0085] If, after inspection, the correlation between the measured flood peak sequence and the reservoir flood control index sequence does not meet the preset requirements, it is necessary to adjust the preset window period and re-perform the correlation inspection until the correlation between the measured flood peak sequence and the reservoir flood control index sequence meets the preset requirements.

[0086] Step 2.1.2, constructing the first marginal distribution function of the measured flood peak sequence and the second marginal distribution function of the reservoir flood control index sequence respectively;

[0087] Specifically, when constructing the first marginal distribution function of the measured flood peak sequence and the second marginal distribution function of the reservoir flood control index sequence, in order to reduce the uncertainty caused by over-reliance on a single distribution linearity, multiple alternative distributions are used for comparison. The alternative distributions include but are not limited to: Gamma distribution, Normal distribution, Lognormal distribution, Peaarson-III distribution and Gumbel distribution. The distribution line types of the alternative distributions and their corresponding probability density functions are shown in Table 1.

[0088] Table 1: Alternative distribution line types and corresponding probability density distribution functions

[0089] Note: μ, σ and are the location, scale, and shape parameters of the sequence distribution, respectively.

[0090] Subsequently, according to a goodness of fit test, optimal marginal distribution functions of the first marginal distribution function and the second marginal distribution function are respectively selected from the alternative distribution line types to construct them.

[0091] Specifically, when selecting the optimal marginal distribution function based on the goodness of fit test, in order to reduce human subjectivity, the fitting accuracy of each distribution is evaluated through a variety of goodness of fit evaluation criteria. These criteria include the Kolmogorov-Smirnov test, the Nash efficiency coefficient of the theoretical frequency (quantile) and the empirical frequency (quantile). ( , root mean square error RMSE, etc.

[0092] Step 2.1.3: Construct a joint distribution model of the first marginal distribution function and the second marginal distribution function using a copula function. The joint distribution model is used to describe the dependency relationship between the reservoir flood control index sequence and the measured flood peak sequence.

[0093] Specifically, based on the first marginal distribution function and the second marginal distribution function, a probability integral transform is performed on the sample to obtain its marginal distribution value on (0, 1). Based on the first marginal distribution function and the second marginal distribution function, a copula function is constructed. Copula functions include but are not limited to Gaussian copula, t copula, Clayton copula, Gumbel copula, and Frank copula.

[0094] According to Sklar's theorem, the joint distribution of random variables X and Y can be represented by a two-dimensional Copula function C. Therefore, the reservoir flood control index series (ACRI series) and the measured flood peak series ( ) , decomposed into two marginal distributions and , and a Copula function , where u and v are respectively distributed by the edge and The original variable and The marginal probability value converted to is as shown in formula (2):

[0095] (2)

[0096] Where: Copula parameters.

[0097] In order to determine the optimal copula function, the maximum likelihood method is used for parameter estimation. Based on the log-likelihood value loglik, the AIC criterion (Akaike Information Criterion) and the BIC criterion (Bayesian Information Criterion) are used for model screening. Specifically, the optimal copula model can be selected by comparing the AIC and BIC values ​​of different copula functions. The AIC criterion is shown in formula (3), and the BIC criterion is shown in formula (4):

[0098] (3)

[0099] (4)

[0100] Where: is the sample size; is the number of Copula model parameters.

[0101] Finally, based on the selected optimal Copula model, sampling is generated Marginal probability pairs , and based on the marginal distribution and The inverse transformation of the above The marginal probability pairs are mapped to the original variable space, and we get Sample points These sample points represent ACRI and The possible values ​​in the joint distribution are shown in formula (5):

[0102] (5)

[0103] Step 2.2: Based on the joint distribution model, the measured flood peak sequence is reconstructed into a flood peak reconstructed sequence not affected by reservoir storage through a source tracing reconstruction method.

[0104] Step 2.2.1, based on the reservoir flood control index sequence (ACRI sequence) and the measured flood peak sequence ( ), we can get the mechanism of reservoir regulation affecting flood peak situation, which is recorded as , which is the ACRI source function.

[0105] Construct a product model to express the impact factor (including ACRI and other known impact factors) ) and the measured flood peak sequence The model also includes a natural random variable representing an unknown influencing factor , the model expression is shown in formula (6):

[0106] (6)

[0107] Where: It is the source function of reservoir flood regulation index, reflecting the impact of the reservoir's actual regulation and storage function on the flood peak; Refers to the number of other factors known to humans that affect flood peak conditions;

[0108] Impact Factor The source function is usually consistent or not a key influencing factor; It represents the effect of unknown human factors on flood peaks and is usually considered to be a natural random variable.

[0109] Step 2.2.2: Based on the above mechanism and product model, construct the traceability reconstruction function , this function achieves consistent reconstruction of inconsistent flood peak sequences by removing the influence of the actual storage function of the reservoir. As shown in formula (7):

[0110] (7)

[0111] Reconstruction sequence Has the same dimension as the flood peak sequence ( ), unit is m 3 / s, reconstruct sequence It represents the flood peak situation in the basin that is not affected by reservoir regulation, namely the flood peak reconstruction sequence.

[0112] Step 2.3: Determine whether the consistency check and / or historical review check of the flood peak reconstruction sequence meets the first requirement; if not, re-determine the source function until the consistency check and / or historical review check of the flood peak reconstruction sequence meets the first requirement.

[0113] Specifically, in the process of tracing back to the source and reconstructing the flood peak sequence, due to the influence of various potential factors, the reconstructed sequence may not fully meet the consistency requirements, or there may be certain deviations from the actual original sequence. Therefore, in order to ensure that the flood peak reconstructed sequence can meet the expected consistency characteristics, it needs to be tested. The consistency test refers to the inconsistency test method in step 2.1.1 of this embodiment. This method is common knowledge among those skilled in the art and is therefore not described in detail in this embodiment of the present application. The historical review test is a review test conducted by those skilled in the art on the historical design results of the reservoir to verify the flood peak reconstructed sequence. Specifically, the historical design results represent the hydrological data and analysis results used in the planning, design and operation of the reservoir, including but not limited to key parameters such as historical flood process lines, design flood peaks, and design flood volumes. These historical design results are an important basis for the safe and efficient operation of the reservoir and are also an important reference for verifying the accuracy of the reconstructed sequence. The first requirement refers to the statistical consistency standards that the flood peak reconstructed sequence needs to meet, the degree of consistency with historical flood data, and the feasibility in practical applications. This requirement is determined by those skilled in the art based on the actual project. Specifically, the first requirement is that the statistical characteristics of the reconstructed flood peak sequence, such as the coefficient of variation, trend, and periodicity, must be consistent with the original sequence or historical data. Furthermore, the reconstructed flood peak sequence must be able to reasonably interpret historical flood events and provide a reliable reference for reservoir design and operation. If the reconstructed flood peak sequence fails to meet the first requirement in consistency checks and / or historical verification tests, the source function must be redefined and the reconstruction method and parameters adjusted accordingly until the reconstructed sequence meets all pre-set requirements. This iterative process aims to continuously optimize the reconstructed sequence to improve its accuracy and reliability, providing a strong guarantee for the safe and efficient operation of the reservoir.

[0114] In this embodiment, the historical review and verification of the flood peak reconstruction sequence includes:

[0115] The statistical parameters of the flood peak reconstruction sequence are calculated using the fitting method, and the design flood peak flow with different recurrence periods under consistency conditions is calculated based on the statistical parameters; and the design flood peak flow is checked to see whether it meets the preset range based on the design standards before reservoir construction.

[0116] Specifically, the historical verification method includes: according to the relevant specifications such as "Code for Flood Calculation of Water Conservancy and Hydropower Engineering Design" (SL44-2006), based on the reconstruction sequence RS ACRI, t The design peak flow was calculated using the P-III curve fitting method. The calculated statistical parameters and design peak flow were compared with historical design results before reservoir construction.

[0117] Furthermore, the statistical parameters of the flood peak reconstruction sequence are calculated using the line fitting method, including:

[0118] Constructing a historical flood sequence based on historical flood data of the area to be studied;

[0119] A unified processing method is used to calculate the empirical frequencies of the historical flood sequence and the flood peak reconstruction sequence.

[0120] It should be noted that the historical design results before reservoir construction may or may not include historical flood data. If the historical design results do not include historical flood data, then the present invention will rely solely on the data from the peak reconstruction sequence when calculating the design peak flow. Conversely, if historical flood data has been included in the historical design results, then the present invention will combine this historical flood data with the peak reconstruction sequence when calculating the design peak flow. The purpose of this approach is to ensure that a unified and consistent flood data base is used during the historical verification process.

[0121] When historical flood data is introduced, historical flood data within N years of the study area are first obtained to construct a historical flood sequence. The empirical frequencies of the historical flood sequence and the flood peak reconstruction sequence are then calculated. However, during this process, there may be "overlap" in the empirical frequencies of historical floods and measured floods, that is, the empirical frequencies of some extremely large floods are greater than those of measured floods. This paper uses a unified processing method to calculate the sample empirical frequencies. The details are as follows:

[0122] ① The empirical frequency of a major flood is:

[0123] (8)

[0124] Where:

[0125] For the The empirical frequency of major floods;

[0126] is the number of extremely large floods; is the rank of the major flood in year N;

[0127] This is the period of historical investigation and verification.

[0128] ② The measured flood data corresponding to the measured period within the preset period within The empirical frequency of consecutive floods is:

[0129] (9)

[0130] Where:

[0131] For the Item flood experience frequency;

[0132] For The extreme floods extracted from the reconstructed annual flood peak sequence.

[0133] Based on the above-mentioned empirical frequency, the statistical parameters of the flood peak reconstruction sequence are calculated using the fitting method, and the flood frequency analysis under consistency conditions is calculated based on the statistical parameters; the flood frequency analysis results are checked to see if they meet the preset range based on the design standards before reservoir construction.

[0134] The embodiments of the present invention specifically describe the derivation of design peak flood flows for different return periods (e.g., 10-year, 50-year, and 100-year floods) under consistent conditions based on statistical parameters. However, it should be noted that this embodiment uses the design peak flood flow as an example to illustrate the verification process for evaluating flood frequency analysis results. In reality, flood frequency analysis is not limited to the calculation of design peak flood flows but also includes analysis of other important hydrological elements such as flood volume and flood processes. Therefore, it is more accurate to describe a comprehensive flood frequency analysis under consistent conditions based on statistical parameters.

[0135] The design peak flows for these different return periods are then compared with the design standards before reservoir construction to determine whether they meet the expected range, for example, whether the deviation from the design standards before reservoir construction is less than a certain set value; and whether the parameter changes in the frequency analysis results are reasonable. If so, the peak reconstruction sequence is determined to reflect the flood conditions before reservoir construction. If not, it is necessary to readjust the preset window period and reselect the optimal marginal distribution or Copula function until the deviation of the calculated design peak flows for different return periods from the design standards before reservoir construction is less than a set value.

[0136] Step 3: Determine a first flood frequency curve based on the historical flood data of the area to be studied and the flood peak reconstruction sequence.

[0137] Step 3.1: construct a source-tracing and reconstructed flood peak sequence containing historical floods based on the historical flood data of the area to be studied and the flood peak reconstruction sequence.

[0138] Among them, the historical flood data of the area to be studied are obtained through various channels, mainly including field investigations, literature records, flood trace surveys, etc.; during the acquisition process, it is necessary to focus on investigating the reliability, occurrence time, peak flow and recurrence period of the flood, and clarify the time sequence of occurrence of each historical flood during the historical investigation and verification period. It should be noted that in the embodiment of the present invention, if historical flood data has been introduced into the historical design results during the historical review and inspection, then when the present invention calculates the design peak flow, this part of the historical flood data will be combined with the peak reconstruction sequence and calculated together. In this case, the historical flood data used in the historical review and inspection are consistent with the historical flood data obtained in this step, and these data can be sorted and obtained in the preparation stage of flood frequency analysis.

[0139] According to the historical flood data and the flood peak reconstruction sequence, they are arranged in chronological order as a discontinuous source-tracing reconstructed flood peak sequence.

[0140] Step 3.2: Calculate the first flood frequency curve of the source-tracing and reconstructed flood peak sequence under consistency conditions according to a frequency analysis method.

[0141] Specifically, the traditional frequency analysis method is used to calculate the design peak flow of the source-tracing reconstructed peak sequence under non-uniform conditions. The process mainly includes estimating the distribution parameters and determining the distribution line shape.

[0142] Step 3.2.1. First, determine multiple distribution parameter groups of multiple distribution models using the linear moment method (L-moment).

[0143] Specifically, define the linear moment ( ) is shown in formula (10):

[0144] (10)

[0145] in is a probability polynomial, defined as shown in formula (11):

[0146] (11)

[0147] Subsequently, the study expressed the linear moment as a linear combination of probability weight moments. The probability weight moments are shown in Equation (12) or Equation (13):

[0148] (12)

[0149] (13)

[0150] Where:

[0151] for Order exceeds the probability weight moment;

[0152] for The order is less than the probability weight moment.

[0153] Linear Moment The relationship with the probability weight moment is shown in formula (14):

[0154] (14)

[0155] The above relationship reflects how to use the probability weight moment and To calculate the linear moment .

[0156] In addition, in order to reflect the shape (skewness) characteristics of the probability distribution, the linear moment coefficient is introduced , also known as L-skewness, is calculated as shown in formula (15):

[0157] (15)

[0158] When historical flood data are introduced, the flood peak sequence constructed by tracing back to the source is specifically a sequence with The discontinuous flood peak sequence during the historical investigation and verification period. In this sequence, there are Extreme flood values, including The extreme flood values ​​come from the measured period (i.e., the preset period for obtaining measured flood data), and the length of the measured flood series is For the convenience of analysis, The flood peaks are uniformly sorted within a time span of one year.

[0159] In order to ensure the accuracy of the calculation of discontinuous source tracing and reconstruction of flood peak sequence, the probability weight moment is calculated. When the probability weight moment is adjusted Calculation method.

[0160] Specifically, the probability weight moment The calculation formula is as follows:

[0161] (16)

[0162] (17)

[0163] (18)

[0164] when 、 、 After determination, equations (14) and (15) can be used to obtain 、 、 and , and then determine the distribution parameters of the flood peak sequence reconstructed by tracing back the historical floods.

[0165] Step 3.2.2. Subsequently, a goodness of fit test is performed on the source-tracing and reconstructed flood peak sequence based on the multiple distribution parameter groups, and the optimal distribution model of the source-tracing and reconstructed flood peak sequence is determined as the optimal probability distribution model; specifically, a goodness of fit test is performed on the multiple distribution models with determined distribution parameters to screen out the optimal probability distribution model. The goodness of fit test refers to the method in step 2.1.3 of this embodiment. This method is common knowledge to those skilled in the art, and therefore, the embodiments of this application will not be repeated here.

[0166] Step 3.2.3: Draw the first flood frequency curve under consistency conditions based on the optimal probability distribution model and its corresponding distribution parameters.

[0167] After determining the distribution parameters and selecting the distribution line type, the first flood frequency curve under the consistency condition is drawn according to the distribution line type and its corresponding distribution parameters. The first flood frequency curve represents the relationship between the flood frequency and the design value without the influence of reservoir regulation and taking into account the historical floods. In this embodiment, the reconstructed sequence design value can also be determined according to the first flood frequency curve. .

[0168] Step 4: Convert the first flood frequency curve into a second flood frequency curve under inconsistency conditions according to the source function, and analyze the flood frequency according to the second flood frequency curve.

[0169] Specifically, in this embodiment, the source function is determined by the joint distribution model based on the mechanism of the reservoir flood control index sequence (ACRI sequence) on the measured flood peak sequence. , to quantify the impact of reservoir regulation on flood peak situation. It should be noted that due to the small number of sample points of the measured flood peak sequence that can be obtained within a limited preset time, in order to obtain a more accurate source function, this application generates more joint distribution sample points through the joint distribution model, thereby making the obtained source function more accurate. This application returns the impact of reservoir regulation on flood peak situation to the previously calculated reconstructed sequence design value, and thus obtains the flood peak design value under the actual reservoir regulation effect. , as shown in formula (19):

[0170] (19)

[0171] Where:

[0172] It refers to the value of the reservoir flood control index during the design stage (a historical, current or future stage).

[0173] It should be noted that in this embodiment, the reconstruction sequence design value is determined according to the first flood frequency curve. Then, the reconstructed sequence design value is determined according to the source function determined by the joint distribution model. Converted into flood peak design value under the actual storage function of reservoir In another embodiment, the design flood volume of the reconstruction sequence is determined based on the first flood frequency curve. The design flood volume is then converted into the design flood volume under the actual storage function of the reservoir based on the source function determined by the joint distribution model.

[0174] Next, if Figure 1 As shown, taking the Longyangxia Reservoir in the upper reaches of the Yellow River as an example, the application of the present invention in actual engineering is described in detail.

[0175] Example 2:

[0176] The upper reaches of the Yellow River are a key national hydropower development base. As of 2024, 24 hydropower stations have been built along the upper reaches of the Yellow River. Among them, the Longyangxia Reservoir, the "leading" reservoir in the cascade development plan for the Longyangxia-Qingtongxia section of the Yellow River mainstream, controls 65% of the water flow in the upper reaches. The Longyangxia Reservoir's storage and regulation function has significantly altered the physical conditions of the water cycle and runoff formation in the basin, reshaping the spatiotemporal distribution of runoff and directly affecting flood characteristics such as river flow size, duration, occurrence time, frequency, and rate of change. This has led to significant non-uniform variations in flood peak patterns across the basin.

[0177] Under inconsistent conditions, inconsistency issues such as flood data restoration calculation, flood frequency analysis, and quantification of reservoir storage impacts remain unresolved major scientific issues and key technical difficulties. In particular, most hydrological stations in the upper reaches of the Yellow River were built in the 1950s, and the length of measured hydrological data available to date is only about 70 years. Shorter hydrological data are less representative and it is difficult to accurately reflect the statistical characteristics of basin floods. Therefore, it is crucial to consider historical floods and extend flood information. In combination with historical flood data, a frequency analysis of inconsistent floods under the influence of Longyangxia Reservoir storage will be conducted. Through this embodiment and the accompanying drawings, the technical solution of the present invention will be further specifically explained.

[0178] S1: Tangnaihai and Guide Hydrological Stations, serving as inflow and outflow control stations for the Longyangxia Reservoir, have recorded in detail the changing characteristics of the basin's hydrological regime before and after the reservoir's operation. Furthermore, Tangnaihai and Guide Hydrological Stations, as important control stations on the upper Yellow River, have observed a long series of data and achieved high precision. The following data were collected and organized:

[0179] (1) Measured flood peak data

[0180] Based on the historical flood data of Tangnaihai and Guide hydrological stations from 1960 to 2020, the peak flow rate was calculated using the annual maximum method to construct a measured peak flow sequence. The measured peak flow sequence in this embodiment specifically includes the Tangnaihai peak flow sequence and the Guide peak flow sequence.

[0181] (2) Historical flood data

[0182] ①1904;

[0183] Investigations have revealed numerous major floods in the upper reaches of the Yellow River. The July 1904 flood is widely considered the largest since 1811. Based on reliable flood traces from 1904 near the Guide Hydrological Station, combined with the station's cross-section and flood gradient, the peak flow rate for July 1904 was determined to be between 5,900 and 6,300 m³ / s. This study used a flow rate of 6,100 m³ / s. Regarding the recurrence period of the 1904 flood, based on water level records from the Qingtongxia Gorge Gauge, it is considered the largest flood between 1811 and 2020, with a recurrence period of 210 years.

[0184] ②1981;

[0185] The September 1981 flood was the largest flood at stations in the upper reaches of the Yellow River since measured data became available. Its peak and volume were second only to the historical flood of 1904.

[0186] (3) Reservoir observation data

[0187] Based on the historical reservoir operation data, the water level-reservoir capacity curve, daily scale measured operating water level and flood control limit water level implementation standards of previous years were collected and sorted. According to the survey, the design flood limit water level of Longyangxia Reservoir is 2594m, and the corresponding reservoir capacity is 21.845 billion m 3 . However, since the reservoir was put into operation, in order to ensure the flood control safety of the project itself, the actual flood limit water level has been gradually increased. Since 2002, the flood limit water level has been 2588m. From 2009 to 2018, the flood limit water level in July and August was 2588m, and on September 1, it will transition to 2594m depending on the water inflow and water storage conditions. Since 2019, the flood limit water level of the reservoir in July and August has been raised to 2592m. After experiencing many high water level operation tests, the Longyangxia Reservoir operated at the designed flood limit water level of 2594m in 2020.

[0188] S2: Diagnosis of inconsistent variations in the peak sequence and attribution analysis.

[0189] The MK trend test, Pearson correlation coefficient test and BP variance test methods were used to test the trend of the measured flood peak sequences at Tangnaihai and Guide hydrological stations, and the results are shown in Table 2. It can be seen that at the significance level of 0.05, the results of the MK trend test, Pearson test and BP variance test show that the Tangnaihai flood peak sequence does not show a significant trend change. It is worth noting that the MK trend test statistic of the Guide flood peak sequence is ; Pearson test correlation coefficient , P-value=0.0003<0.05, that is, there is a significant downward trend in the Guide flood peak sequence.

[0190] Table 2: Tangnaihai and Guide hydrological stations Trend test results

[0191] Note: Black bold indicates that the corresponding trend test results have significant characteristics.

[0192] Subsequently, mutation tests were conducted on the flood peak sequences measured at the two hydrological stations, namely, mutation tests were conducted on the Tangnaihai flood peak sequence and the Guide flood peak sequence. Figure 2 The results of the Pettitt mutation test are shown. It can be seen that the Pettitt statistic value of the Tangnaihai hydrological station is the largest in 1989, U max =403 and P-value=0.0293<0.05; the statistical value of Guide Hydrological Station in 1986 was the largest, U max =761 and P-value=5.7529×10 -7 <0.05. Therefore, based on the results of the Pettitt mutation test, the flood peak sequences measured at the Tangnaihai and Guide hydrological stations from 1960 to 2020 underwent significant mutations in 1989 and 1986, respectively.

[0193] Overall, although the results of the Pettitt mutation test at the Tangnaihai hydrological station showed a significant mutation in 1989, combined with the trend test results, the flood peak sequence only showed a slight downward trend, maintaining good overall consistency and showing no significant trend change. However, the flood peak sequence measured at the Guide Hydrological Station showed a significant downward trend, and the P-value of the Pettitt mutation test in 1986 was only 5.7529×10 -7 Therefore, the measured flood peak sequence at the Tangnaihai hydrological station upstream of the Longyangxia Reservoir conforms to the consistent characteristics; however, the measured flood peak sequence at the Guide hydrological station shows a significant downward trend and a significant mutation in 1986, showing a significant inconsistency.

[0194] The Longyangxia Hydropower Project began storing water in its diversion tunnel in October 1986, and its first generating unit began generating electricity in September 1987. As the leading reservoir for long-term regulation of the upper Yellow River, the Longyangxia Reservoir's immense storage capacity has enabled it to regulate upstream water flow, directly influencing the natural runoff patterns at the downstream Guide Hydrological Station and causing significant non-uniform changes in flood patterns there.

[0195] S3: Construct the ACRI (Accumulated Reservoir Flood Control Index).

[0196] (1) Determine the preset window period. Tangnaihai and Guide hydrological stations, as the inlet and outlet stations of Longyangxia Reservoir, respectively effectively record the changes in the inflow flow of Longyangxia Reservoir and the evolution characteristics of floods in the downstream basin before and after Longyangxia storage. Figure 3 As shown in the figure, the flood process lines of the measured large floods are drawn respectively. It can be seen that whether it is a single-peak large flood ( Figure 3 (a)), or multi-peak large flood ( Figure 3 (b) Since there are relatively few tributaries between the Guide and Tangnaihai hydrological stations, the flood peaks at the two hydrological stations are basically the same. From the flood processes in 1964 and 1967, it can be seen that their evolution lasted about 1 day, so the preset window period is determined to be 1 day.

[0197] (2) Establish reservoir flood control indicators.

[0198] Based on the actual implementation of the flood control limit water level standard of Longyangxia Reservoir, the flood control capacity (RC) is calculated. In combination with the actual flood process, considering the one-day simulation duration, the peak time of Guide Hydrological Station is used to construct the reservoir flood control index (ACRI) one day before the flood peak, such as Figure 4 As shown in Figure 2, it can be seen that since the construction and operation of the Longyangxia Reservoir in 1986, the ACRI has shown irregular fluctuations, indicating that the reservoir's flood storage capacity is constantly changing with the inflow status and the reservoir's own operating status.

[0199] S4: The validity and rationality of the reservoir flood control index (ACRI) during the preset window period are verified through Pearson correlation coefficient test, Spearman correlation coefficient test and Kendall correlation coefficient test.

[0200] The results are shown in Table 3. It can be seen that the P-values ​​of the Pearson, Spearman and Kendall correlation coefficient tests for the correlation between the peak flow rate of the Guide Hydrological Station and the reservoir flood control index (ACRI) are 1.42×10 -4 , 2.63×10 -6 and 1.20×10 -5, are significantly less than 0.05, indicating that the reservoir flood regulation index (ACRI) is significantly correlated with the peak flow of the Guide Hydrological Station, indicating that the reservoir flood regulation index (ACRI) one day before the peak flow can reasonably reflect the actual storage function of the reservoir.

[0201] Table 3: ACRI and Correlation test results

[0202] Note: Black bold indicates that the two variables are significantly correlated at the significance level α=0.05.

[0203] S5: Using Copula theory, construct the reservoir flood control index sequence (ACRI sequence) and the measured flood peak sequence ( ) to generate a two-dimensional Copula joint model between them to generate a joint distribution model.

[0204] Screening the optimal marginal distribution through goodness of fit test The results are shown in Table 4. Overall, for the reservoir flood control index series (ACRI series), the Lognormal (LOGNO) distribution fits best; for the measured flood peak series ( sequence), Gumbel (GU) distribution is the optimal distribution.

[0205] Table 4: Marginal distribution goodness-of-fit test results

[0206] Based on ACRI sequence and The optimal marginal distribution of the sequence was used to screen the optimal Copula model, and the results are shown in Table 5. In particular, the Normal Copula model has the smallest AIC and BIC values ​​of -14.8601 and -13.4262, respectively, which is the optimal Copula model.

[0207] Table 5: Alternative Copula Models

[0208] Based on the Normal Copula, 500 marginal probability pairs are sampled and generated. , and mapped to the original variable space through Lognormal and Gumbel marginal distribution to obtain 500 joint samples.

[0209] S6: Use the source tracing reconstruction method to reconstruct the inconsistent measured flood peak sequence into a flood peak reconstruction sequence that is not affected by reservoir storage, that is, reconstruct the inconsistent flood sequence.

[0210] S6.1: According to ACRI and The statistical relationship of the joint distribution model is obtained, and the mechanism of the impact of reservoir regulation on flood peak situation is obtained, that is, source function fitting. The source function is recorded as ,like Figure 5 shown.

[0211] It can be seen that the source function of the ACRI sequence is:

[0212] (20)

[0213] S6.2: Based on the source function, build the traceability reconstruction function , as shown in formula (21):

[0214] (twenty one)

[0215] Combined reconstruction function , removing the impact of Longyangxia Reservoir regulation, and obtaining the flood peak reconstruction sequence ,like Figure 6 shown.

[0216] It can be seen that before the construction of Longyangxia Reservoir, the ACRI value was 0 from 1960 to 1986, and the flood peak reconstruction sequence was The situation changes are consistent with the measured flood peak sequence. This means that in the absence of human activities, the flood peak reconstruction sequence can better preserve the evolution characteristics of the flood peak in the natural period. After 1987-2020, the source reconstruction method successfully removed the impact of the Longyangxia Reservoir's regulation and storage function on the downstream flood peak, and the flood peak reconstruction sequence The interannual fluctuation range is consistent with the natural period (1960-1986).

[0217] S7: Verify the peak reconstruction sequence in S6 Representativeness and reliability. Specifically combine inconsistency, distribution characteristics and historical results to verify the flood peak reconstruction sequence Representativeness and reliability.

[0218] S7.1: Based on the inconsistency test method in S2, check the peak reconstruction sequence The results are shown in Table 6. Figure 7 shown.

[0219] Table 6: Peak reconstruction sequence Trend Diagnosis

[0220] Note: Black bold indicates that the corresponding trend test results have significant characteristics.

[0221] S7.2: Consistency-based flood peak reconstruction sequence The design peak flow was calculated using the P-Ⅲ curve fitting method and compared with the historical design results before the reservoir construction.

[0222] (1) Historical design achievements

[0223] The "Supplementary Preliminary Design Report of the Longyangxia Hydropower Station on the Yellow River" (hereinafter referred to as the "Longyangxia Supplementary Preliminary Design") in August 1977 used measured data from 1946 to 1974 and the historical flood of 1904 to conduct a frequency analysis of natural floods at the Guide Hydrological Station using the P-III curve fitting method. After review, it was used in engineering design and the results were adopted in future flood control and scheduling (hereinafter collectively referred to as the "historical design results").

[0224] (2) Determine historical floods.

[0225] ①Flood of 1904;

[0226] The July 1904 flood was the largest flood since 1811, with a peak flow of 5900m³ / s to 6300m³ / s. The calculation in this study was based on 6100m³ / s.

[0227] ②1981 flood;

[0228] The September 1981 flood was the largest flood since measured data became available at stations on the upper Yellow River, with peak and volume second only to the 1904 flood. However, after accounting for the Longyangxia Reservoir's role in regulating floods, the 1981 flood is no longer the second largest in the 1960–2020 source sequence reconstruction. Therefore, it was not considered a maximum value in this calculation.

[0229] ③2019 floods;

[0230] During the 2019 flood season, the upper reaches of the Yellow River experienced another significant flood. The measured peak flow at Guide Station reached 3,630 m³ / s, the highest flow since the construction of the Longyangxia Reservoir. Taking into account the Longyangxia Reservoir's storage function, the reconstructed peak flow at Guide Station was 5,510 m³ / s, second only to the 1904 flood. Therefore, this study treats the 2019 reconstructed peak flow as an exceptional value, with a return period equal to the second-largest flood since 1811, second only to the 1904 flood.

[0231] (3) PⅢ curve fitting method to calculate the design peak flow.

[0232] The unified processing method is used to calculate the flood peak reconstruction sequence of historical floods The empirical frequency is calculated by the fitting method to obtain the statistical parameters and the design peak flow under different recurrence periods. The results are as follows: Figure 8 shown.

[0233] Table 7 summarizes the design peak flow of the source-reconstructed flood peak sequence considering historical flood data and the previous review results. From the perspective of changes in statistical parameters, the mean value of the source-reconstructed flood peak sequence has increased slightly, by 170m³ / s compared with the previous review results; the Cv value of the source-reconstructed flood peak sequence has decreased by 0.3 compared with the previous review results. The main reasons for the changes in statistical parameters are as follows: As of 2020, the source-reconstructed flood peak sequence includes many major floods such as 1981, 1989, 2012, 2018, and 2019. Among them, the measured peak flow in 2019 is the largest flow since the construction of the Longyangxia Reservoir. The addition of multiple floods has made the mean value of the source-reconstructed flood peak sequence larger than the previous review results, and made the data more concentrated, and the degree of discreteness of the source-reconstructed flood peak sequence has decreased. Therefore, the source-reconstructed flood peak sequence The value also decreased slightly. Looking at the changes in design peak flow, when the return period is short, the design peak flow of the flood peak sequence reconstructed by tracing back the source is slightly larger. The design peak flow for a 20-year return period is 120 m³ / s higher than the original verified result, with a deviation of 2.86%. As the return period increases, the design peak flow of the flood peak sequence reconstructed by tracing back the source shows a slightly decreasing trend. The design peak flow for a 10,000-year return period is 190 m³ / s lower than the original verified result, with a deviation of -2.20%.

[0234] Table 7 Frequency analysis of P-Ⅲ curve by line fitting method Unit: Peak flood m 3 / s

[0235] Overall, the reconstructed flood peak sequence effectively extended the peak sequence. As of 2020, the reconstructed flood peak sequence includes more major flood events, and its designed peak discharge is more representative. The statistical parameter changes derived using the P-III curve fitting method are relatively reasonable. The calculated designed peak discharges for the reconstructed sequence are within 3% of the previously verified results, recreating the natural peak conditions at the Guide Hydrological Station.

[0236] S8: Based on source tracing and reconstruction of flood peak sequences, conduct non-uniform flood frequency analysis, and specifically use traditional frequency analysis methods to calculate the design flood peak flow under non-uniform conditions.

[0237] Based on the alternative distribution line type and determined by goodness of fit test The optimal distribution of , where the goodness of fit test results are shown in Figure 8.

[0238] Table 8: Goodness-of-fit test results of alternative distributions of flood peak sequence reconstructed by tracing the source

[0239] As can be seen from Table 8, the KS test P-values ​​of all alternative distributions are much larger than 0.05, that is, all alternative distributions have passed the KS test significantly. 、 It can be found that the different distributions The GU distribution showed significant differences in Nash values, with both reaching above 0.91. NSEQQ and NSEpp were 0.9107 and 0.9796, respectively. For extreme value sequences, the GU distribution had the smallest RMSE of 252.6122, as shown by the more informative root mean square error (RMSE). Combining the results of the three goodness-of-fit tests, the study concluded that the Gumbel (GU) distribution provided the best fit for flood peak sequences reconstructed using source tracing.

[0240] After estimating the GU distribution parameters using the linear moment method, the distribution parameters are: , After determining the distribution line type and distribution parameters of the source-reconstructed flood peak sequence, the design values ​​of the source-reconstructed flood peak sequence under different return periods can be obtained according to the traditional frequency analysis method. The results are as follows: Figure 9 (a), as shown in Table 9. The flood peak sequence reconstructed by tracing back the source without the influence of reservoir storage represents the consistent data of natural flood situation at Guide Hydrological Station. The peak flow of 100-year, 1000-year, 2000-year, and 10,000-year floods calculated by traditional flood frequency analysis is 4870m 3 / s、6130m 3 / s、6510m 3 / s、7390m 3 / s.

[0241] Table 9: Designed flood peak flow based on source tracing and reconstruction of flood peak sequence

[0242] Unit: Peak flood m 3 / s

[0243] As the leading reservoir in the upper reaches of the Yellow River, Longyangxia Reservoir has to shoulder more flood control tasks downstream while achieving economic benefits. With the stable operation of Longyangxia Reservoir for nearly 40 years and multiple high-water-level operations, the safety and reliability of the reservoir itself have been effectively verified, and the design flood limit water level operation criteria are currently being implemented. Therefore, the design flood limit water level of Longyangxia Reservoir will not change now and in the future, that is, the operation will be further stabilized. When calculating the current design peak flow, the reservoir storage index basically maintains the recent operating level of the reservoir. The invention uses the average ACRI value from 2018 to 2020 to represent the reservoir's flood storage capacity under the current outflow conditions. According to the source reconstruction function, the non-uniform peak flow design value of the corresponding return period is obtained.

[0244] Reconstruct the design value of the flood peak sequence by tracing the source By restoring the reservoir to its operating conditions, the non-uniform design peak flow is finally obtained, such as Figure 9 (b) As shown in Table 9. It can be seen that after the regulation and storage of the Longyangxia Reservoir, the non-uniform design flood peak flow at the Guide Hydrological Station under the current conditions has decreased significantly. Among them, the design flood peak flow values ​​for 100-year, 1000-year, 2000-year, and 10,000-year floods are 3360m3 and 3360m4, respectively. 3 / s、4230m 3 / s、4500m 3 / s、5100m 3 In particular, under the regulation and storage function of the Longyangxia Reservoir, the non-uniform design peak flows of the Guide Hydrological Station under the influence of historical floods were reconstructed and all met the river section defense standards, ensuring the flood control safety of the basin. Specifically, the design peak flows for the 10-year, 20-year, and 30-year floods were 2480m / s, respectively. 3 / s、2750m 3 / s、2900m 3 / s, all less than the defense standard of 3660m 3 / s、4200m 3 / s、4400m 3 / s.

[0245] This invention fully considers the actual regulation and storage function of reservoirs, distinguishing and quantifying the impact of reservoir regulation and storage on downstream flood peak flows. It also avoids over-reliance on large amounts of measured data, achieving the restoration of inconsistent hydrological sequences influenced by actual reservoir regulation and storage, thereby reducing the difficulty and uncertainty of the calculation of inconsistent flood peak sequences.

[0246] The present invention introduces historical flood data to enhance the representativeness of flood data. By considering historical floods, the problem of introducing historical floods into inconsistent flood data is solved, further improving the accuracy and reliability of inconsistent flood frequency analysis.

[0247] The present invention can be widely used in the analysis of inconsistent flood frequency under the influence of reservoir regulation, and provide scientific technical support for the safety assessment of water conservancy projects themselves and downstream flood control under the influence of human activities, the review of historical design results, etc.

[0248] The above descriptions are only several embodiments of the present invention and do not limit the present invention in any form. Although the present invention is disclosed as above with preferred embodiments, they are not intended to limit the present invention. Any technician familiar with this profession, without departing from the scope of the technical solution of the present invention, makes slight changes or modifications using the technical content disclosed above, which are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. The inconsistent flood frequency analysis method based on historical floods and reservoir storage is characterized by: The following steps are involved: Step 1: Obtain measured flood data and reservoir observation data within a preset period of time in the basin to be studied, and construct a measured flood sequence based on the measured flood data, and construct a reservoir flood control index sequence based on the reservoir observation data; Step 2: constructing a joint distribution model based on the reservoir flood regulation index sequence and the measured flood sequence, and determining a source function for source tracing reconstruction based on the joint distribution model; reconstructing the measured flood sequence into a flood reconstruction sequence unaffected by reservoir regulation according to the source function; Step 3: determining a first flood frequency curve based on the historical flood data of the area to be studied and the flood reconstruction sequence; Step 4: Convert the first flood frequency curve into a second flood frequency curve under inconsistency conditions according to the source function, and perform flood frequency analysis according to the second flood frequency curve.

2. The inconsistent flood frequency analysis method according to claim 1, characterized in that: The reservoir flood control index sequence is constructed based on reservoir observation data, including: Determining the real-time available flood control storage capacity and the actual flood control storage capacity based on the reservoir observation data; Determining a reservoir flood control index according to a ratio of the real-time available flood control storage capacity to the actual flood control storage capacity; A reservoir flood control index sequence is determined based on the plurality of reservoir flood control indexes.

3. The method for analyzing inconsistent flood frequency according to claim 2, characterized in that: Determining the real-time available flood control storage capacity and the actual flood control storage capacity based on the reservoir observation data includes: Determining flood sequences and corresponding flood time series within the basin based on the measured flood data; According to the reservoir observation data and based on the flood time series, the real-time available flood control storage capacity and the actual flood control storage capacity of the reservoir before the preset window period corresponding to each flood time are extracted.

4. The method for analyzing inconsistent flood frequency according to claim 3, characterized in that: Constructing a joint distribution model based on the reservoir flood control index sequence and the measured flood sequence, including: respectively constructing a first marginal distribution function of the measured flood sequence and a second marginal distribution function of the reservoir flood control index sequence; A joint distribution model of the first marginal distribution function and the second marginal distribution function is constructed by using a copula function.

5. The method for analyzing inconsistent flood frequency according to claim 4, characterized in that: Before respectively constructing the first marginal distribution function of the measured flood sequence and the second marginal distribution function of the reservoir flood control index sequence, the method further includes: Determining whether the correlation between the measured flood sequence and the reservoir flood control index sequence meets the preset requirements; If not, the preset window period is adjusted until the correlation between the measured flood sequence and the reservoir flood control index sequence meets the preset requirements.

6. The method for analyzing inconsistent flood frequency according to claim 1, characterized in that: After step 2 and before step 3, the following steps are further included: Determining whether a consistency check and / or a historical review check of the flood reconstruction sequence meets a first requirement; If not, the source function is re-determined until the consistency check and / or the historical review check of the flood reconstruction sequence meets the first requirement.

7. The method for analyzing inconsistent flood frequency according to claim 1, characterized in that: The flood reconstruction sequence is subjected to historical verification, including: Calculating statistical parameters of the flood reconstruction sequence using a line fitting method, and performing flood frequency analysis under consistency conditions based on the statistical parameters; The flood frequency analysis results are checked to see if they meet the preset range based on the design standards before reservoir construction.

8. The method for analyzing inconsistent flood frequency according to claim 7, characterized in that: The statistical parameters of the flood reconstruction sequence are calculated using the line fitting method, including: Constructing a historical flood sequence based on historical flood data of the area to be studied; Using a unified processing method to calculate the empirical frequencies of the historical flood sequence and the flood reconstruction sequence; Based on the empirical frequency, the statistical parameters of the flood reconstruction sequence are calculated using a line fitting method.

9. The method for analyzing inconsistent flood frequency according to claim 1, characterized in that: The step 3 is specifically as follows: Constructing a source-tracing reconstructed flood sequence containing historical floods based on the historical flood data of the area to be studied and the flood reconstruction sequence; The first flood frequency curve of the source-tracing and reconstructed flood sequence under consistency conditions is calculated according to the linear moment method.

10. The method for analyzing inconsistent flood frequency according to claim 9, characterized in that: Calculating the first flood frequency curve of the source-tracing and reconstructed flood sequence under consistency conditions according to the linear moment method specifically includes: Determine multiple distribution parameter groups of various distribution models by linear moment method; Performing a goodness of fit test on the source-tracing and reconstructed flood sequence based on the multiple distribution parameter groups, and determining an optimal distribution model of the source-tracing and reconstructed flood sequence as an optimal probability distribution model; A first flood frequency curve under consistency conditions is drawn according to the optimal probability distribution model and the distribution parameters.

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