CN107066425A - Overdetermination amount flood nonuniformity analysis method under a kind of changing environment - Google Patents

Abstract

The invention discloses a method for analyzing the inconsistency of over-quantitative floods in a changing environment, which comprises the following steps: sample selection: adopting an over-quantitative sampling method to screen sample sequences; sequence inconsistency diagnosis: judging whether the sequence has a jump variation of a catastrophic flood and trend variation, using different methods for over-quantitative flood frequency analysis for two different situations of jump and trend; over-quantitative frequency calculation under changing environment: over-quantitative flood frequency analysis considering historical floods, according to the selected continuous POT samples Combine with historical floods to form discontinuous POT samples, and analyze the flood frequency of each sample segment sequence; conduct frequency analysis based on the POT sequence, and consider the sequence inconsistency, and reflect the change of flood over time from the aspects of flood magnitude and flood occurrence process It proposes a new method for studying non-uniform floods, promotes the study of hydrological evolution laws in changing environments, and provides a powerful reference for water conservancy project construction.

Description

A non-consistency analysis method for superquantitative floods under changing environment

technical field

The invention relates to the technical field of flood frequency analysis, and more specifically, relates to a non-consistency analysis method for over-quantitative floods under changing environments.

Background technique

Under the influence of climate change and human activities, the hydrological regimes of many rivers have undergone significant changes, and extreme hydrological events of floods and droughts have occurred frequently, and the "consistency" of the environmental background formed by the flood sequences of many rivers in the world no longer exists. The traditional The "extreme value theory" of extreme value flow analysis needs to be modified to accommodate sequence non-stationarity. Watershed development and utilization projects, flood control and drought relief projects and their operation scheduling designed by existing engineering hydrological analysis methods will face the risk of design frequency distortion caused by changing environments.

The flood frequency analysis method adopts the general distribution to fit the observed extreme value, so as to obtain the design flood with a specified or average return period, which provides a unified basis for the planning and operation of water conservancy projects, and its application has a history of nearly a hundred years. The biggest problem in estimating project design flood through flood frequency analysis is that the observation data is too short and the available flood information is insufficient. The traditional method of obtaining flood information is the Annual Maximum Series (AMS), but using AMS sampling will ignore the second and third largest flood peaks in the year after the environment is changed, although they are generally larger than the flood magnitude before the environment change much. The over-quantity (Peak-over-Threshold, POT) model considers both the over-quantity annual occurrence frequency distribution model and the over-quantity distribution model, which can describe the flood and its generation process more completely and flexibly than the AMS method. Therefore, the POT model can be used as a frequency analysis method suitable for changing environments. POT sampling selects all flood peaks that exceed the threshold in the measured data as samples, which can obtain more flood information than the traditional annual maximum (AMS) sequence, and effectively improve the calculation accuracy of design floods. Statistical experiments show that the longer the historical flood return period added to the calculation, the more beneficial it is to improve the accuracy and stability of frequency analysis. Considering the POT flood frequency analysis of historical floods, it can maximize the utilization of flood information from the two aspects of actual measurement and research data, improve the accuracy of design floods, and has great research value. At present, there have been some studies on considering historical floods in the POT method, but they only consider adding historical floods in a research period to continuous samples, and do not consider the existence of grouped historical floods; the data used are mostly obtained through statistical experiments rather than specific sites. Experimental and research data. Few studies have analyzed the impact of historical floods on POT flood frequency analysis for specific watersheds. In practical applications, the verified historical floods may have multiple research periods, and the processing of grouped historical floods needs to be considered. Therefore, it is of great significance to study the influence of grouping historical floods on the POT method to improve the applicability of POT flood frequency analysis. The frequency calculation of non-consistent (non-stationary) hydrological series is an emerging research topic, and the relevant research results are quite few. The more commonly used methods in China are based on the reduction/rediscovery approach, which mainly includes: the relationship analysis method between the series before and after the variation point and a certain parameter, the decomposition and synthesis method of the time series, and the hydrological model. However, the above-mentioned methods have shortcomings. For example, when the time series decomposition and synthesis method has a long prediction period, the existing deterministic component prediction method is difficult to be convincing and has a large extension risk; By separating the deterministic components of the hydrological sequence, the calibration of many parameters of the model is limited to the physical conditions of the watershed in a certain period of history. With the in-depth research on the influence of global changes on hydrological processes, the study of hydrological frequency under non-stationary conditions caused by changing environments has received special attention in recent years. Aiming at the non-stationary of hydrological series, non-stationary series based on time-varying statistical parameters can be established for estimation. At present, the commonly used methods of non-stationary flood frequency analysis in foreign countries mainly include: Time Variation Moment (TVM), regional pooled flood frequency analysis, local likelihood method, quantile regression and mixed distribution model, etc. Since the statistical parameters (such as mean and standard deviation) and the distribution line shape of the non-stationary flood sequence change from time to time, the uncertainty of the corresponding design flow will also change. In this regard, Strupczewski et al. proposed a TVM model for dealing with non-stationary extreme value sequences. This model considers the trend of statistical parameter mean and variance, and can obtain the relationship between design values and time changes. Strupczewski et al. took the Poisson-exponential distribution as an example to propose a TVM frequency analysis model based on the POT sequence, considering the first-order moment of the POT annual occurrence sequence and the trend of the first and second-order moments of the POT sequence, and using the moment of the sequence to describe the model distribution parameters. And according to the corresponding relationship between POT model and AMS model, the distribution parameters of AMS model are described by the number of annual occurrences and the first and second order time-varying moments of POT flood peak sequence, so as to obtain the relationship of design values with time. The non-uniform frequency analysis model based on the POT sequence can not only reflect the change trend of flood peak discharge over time, but also reflect the change trend of flood occurrence times, and can better reflect the change characteristics of flood over time from two aspects of magnitude and process. The TVM model based on the POT sequence proposed by Strupczewski et al. uses a fixed threshold value. Kysely et al. proposed a time-varying threshold value based on quantile regression technology when analyzing temperature inconsistency with time-varying moments. The annual occurrence frequency of POT sequence satisfies the consistency assumption. Since then, the TVM method has been successfully applied to other regions by scholars, and it has also been obtained that under a certain standard P, the flood design value XP has a significant change relationship with time.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the lack of available flood information and the inconsistency assumption of the flood extreme value sequence, provide a kind of flood frequency analysis based on the POT sequence using the TVM model, and consider the sequence inconsistency, from the flood The magnitude and process of floods reflect the characteristics of flood changes over time, and a new method for analyzing the frequency of non-uniform floods is proposed. For the case where there are extreme flood jump points in the over-quantitative flood peak sequence, the influence of historical floods on the frequency analysis results of over-quantitative floods is discussed; for the case where there is a time-varying trend in the over-quantitative flood sequence, the non-uniform flood frequency analysis based on time-varying moments The method is applied to the analysis of ultra-quantitative samples, and realizes the application of the sampling method with time-varying threshold value in the analysis of flood frequency.

In order to solve the above-mentioned technical problems, the technical solution of the present invention is as follows: a non-consistency analysis method for over-quantitative floods under a changing environment, comprising the following steps:

Sample selection: consider historical floods for flood frequency analysis, determine threshold values, and use super-quantitative sampling methods to screen sample sequences;

Sequence inconsistency diagnosis: judging whether there is jump variation and trend variation of catastrophic floods in the sequence, using different methods for super-quantitative flood frequency analysis for the two different situations of jump and trend;

Calculation of over-quantitative frequency under changing environment: considering the over-quantitative flood frequency analysis of historical floods, according to the selected continuous POT samples, combined with historical floods to form discontinuous POT samples, the flood frequency analysis is performed on each sample segment sequence; The likelihood method is used to estimate the GP distribution parameters, and the goodness of fit of each sequence and the calculation results of the design flood in the return period are obtained. Non-consistent super-quantitative flood frequency analysis, using the TVM model to analyze the non-consistent annual maximum daily flow series, and using the Mann-Kendall (M-K) method and CSDMC method to diagnose the trend and stage change characteristics of the series can be used as a basis to select TVM The time base point of the method, and finally deduce the distribution of the corresponding AMS model, fit the AMS sequence and conduct the non-consistent flood frequency analysis. Fitting AMS series and performing non-uniform flood frequency analysis.

In a preferred solution, the threshold value is determined according to an independence criterion and an over-quantity threshold value selection criterion. The threshold value is jointly determined based on the occurrence frequency distribution of the over-quantity series, the frequency distribution of over-quantity floods and the assumption of independent and identical distribution, and the value of the threshold value is determined by using the over-quantity sample mean method, the dispersion index method, and the annual average number of over-quantity occurrence times μ method scope.

In a preferred solution, the sequence inconsistency diagnosis is analyzed by using the M-K trend test method to determine the trend and jump of the flood sequence.

In a preferred solution, different flood frequency analysis methods are used for different flood sequences. The frequency analysis method of the time-varying threshold value refers to: considering the time-varying characteristics of the threshold value, using the time-varying threshold value to extract super-quantitative samples, and obtaining the annual occurrence frequency sequence of POT that satisfies the consistency assumption. After using the time-varying threshold to obtain POT samples, considering the trend of the first and second order moments of the POT sequence, using the Poisson-GP distribution, using the time-varying moment to describe the model distribution parameters, the threshold value and the time-varying moment of the POT sample are time-varying. Quantitative Flood Frequency Analysis.

In a preferred solution, the flood frequency analysis method includes a time-varying moment method with a fixed threshold value and a time-varying moment method with a time-varying threshold value.

In a preferred solution, the time-varying moment method for the fixed threshold value is to determine a unique fixed threshold value, select different probability distributions in the flood frequency analysis, and construct different TVM models considering the different trends of the first two moments of the sequence inconsistency handling method. The TVM model considers the trend components of the first and second moments (mean m and standard deviation σ) of the flood time series, expresses the original parameters of the distribution as time-varying moments, and estimates the parameters of the probability density function. Applying the maximum likelihood method to the flood sequence that meets the independence requirement, assuming that the sequence does not meet the independence requirement is only due to the sequence's trend, and this trend is taken into account in the model. Finally, the AIC criterion is used as the criterion of the optimal model.

In a preferred scheme, the time-varying threshold time-varying moment method is to apply the time-varying threshold value of the inconsistency research of temperature to the extraction of flood over-quantitative samples, and use the regression quantile to calculate the time-varying Threshold value, and determine the sub-threshold value according to the regulation and storage of reservoirs in the river basin, and consider the inconsistency of the number of flood occurrences when sampling.

Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

(1) Apply historical floods to super-quantitative frequency analysis, and analyze the influence of grouped historical floods on POT flood frequency analysis results when there are severe floods in the measured data.

(2) Applying the non-uniform flood frequency analysis based on time-varying moments to the super-quantitative method, compared with the annual maximum method, the non-uniform super-quantitative flood frequency analysis can reflect the change characteristics of the flood occurrence process and flood magnitude at the same time.

(3) The frequency analysis of non-uniform and over-quantitative floods usually uses a fixed threshold value to extract samples. In this paper, the time-varying threshold value of the non-uniform study of temperature is applied to the extraction of over-quantitative flood samples, and the regression quantile is used to calculate The time-varying threshold value is determined according to the regulation and storage of reservoirs in the basin, and the non-uniformity of flood occurrence times is taken into account when sampling.

Description of drawings

Fig. 1 is a frame diagram of the model of the present invention.

FIG. 2 is a schematic diagram of POT sample selection in Embodiment 1 of the present invention.

Fig. 3 is a schematic diagram of sequence inconsistency diagnosis in Example 1 of the present invention.

FIG. 4 is a system block diagram of Embodiment 1 of the present invention.

Fig. 5 is the time-varying threshold value and flood peak flow of the three Dongjiang stations in Embodiment 2 of the present invention.

Fig. 6 shows the subsection thresholds and flood peak flows of the three Dongjiang stations in Embodiment 2 of the present invention.

Fig. 7 is the change of the POT flood frequency curve based on the time reference point of the three Dongjiang stations according to the second embodiment of the present invention.

detailed description

The accompanying drawings are for illustrative purposes only and cannot be construed as limiting the patent;

In order to better illustrate this embodiment, some parts in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product;

For those skilled in the art, it is understandable that some well-known structures and descriptions thereof may be omitted in the drawings.

The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Example 1

As shown in Figure 1, a non-consistency analysis method for over-quantitative floods in a changing environment includes the following steps:

Sample selection: consider historical floods for flood frequency analysis, determine threshold values, and use super-quantitative sampling methods to screen sample sequences;

Sequence inconsistency diagnosis: judging whether there is jump variation and trend variation of catastrophic floods in the sequence, using different methods for super-quantitative flood frequency analysis for the two different situations of jump and trend;

Calculation of over-quantitative frequency under changing environment: considering the over-quantitative flood frequency analysis of historical floods, according to the selected continuous POT samples, combined with historical floods to form discontinuous POT samples, the flood frequency analysis is performed on each sample segment sequence; The likelihood method is used to estimate the GP distribution parameters, and the goodness of fit of each sequence and the calculation results of the design flood in the return period are obtained. Non-consistent super-quantitative flood frequency analysis, using the TVM model to analyze the non-consistent annual maximum daily flow series, and using the M-K method and CSDMC method to diagnose the trend and phase change characteristics of the series can be used as a basis to select the time base point of the TVM method. Finally, the distribution of the corresponding AMS model is deduced, the AMS sequence is fitted, and the non-uniform flood frequency analysis is performed. Fitting AMS series and performing non-uniform flood frequency analysis.

In a specific implementation process, the threshold value is determined according to the independence criterion and the selection criterion of the over-quantity threshold value. The threshold value is jointly determined based on the occurrence frequency distribution of the over-quantity series, the frequency distribution of over-quantity floods and the assumption of independent and identical distribution, and the value of the threshold value is determined by using the over-quantity sample mean method, the dispersion index method, and the annual average number of over-quantity occurrence times μ method scope.

In the specific implementation process, the sequence inconsistency diagnosis is analyzed by using the M-K trend test method to judge the trend and jump of the flood sequence.

In the specific implementation process, different flood frequency analysis methods are used for different flood sequences. The frequency analysis method of the time-varying threshold value refers to: considering the time-varying characteristics of the threshold value, using the time-varying threshold value to extract super-quantitative samples, and obtaining the annual occurrence frequency sequence of POT that satisfies the consistency assumption. After using the time-varying threshold to obtain POT samples, considering the trend of the first and second order moments of the POT sequence, using the Poisson-GP distribution, using the time-varying moment to describe the model distribution parameters, the threshold value and the time-varying moment of the POT sample are time-varying. Quantitative Flood Frequency Analysis.

In a specific implementation process, the flood frequency analysis method includes a time-varying moment method with a fixed threshold value and a time-varying moment method with a time-varying threshold value.

In the specific implementation process, the time-varying moment method of the fixed threshold value is to determine the only fixed threshold value, select different probability distributions in the flood frequency analysis, and consider the different trends of the first two order moments of the sequence to construct different TVM models. consistent approach. The TVM model considers the trend components of the first and second moments (mean m and standard deviation σ) of the flood time series, expresses the original parameters of the distribution as time-varying moments, and estimates the parameters of the probability density function. Applying the maximum likelihood method to the flood sequence that meets the independence requirement, assuming that the sequence does not meet the independence requirement is only due to the sequence's trend, and this trend is taken into account in the model. Finally, the AIC criterion is used as the criterion of the optimal model.

In the specific implementation process, the time-varying threshold time-varying moment method is to apply the time-varying threshold value of the inconsistency research of temperature to the extraction of flood over-quantitative samples, and use the regression quantile to calculate the time-varying threshold value, and determine the segmentation threshold value according to the adjustment and storage of the basin reservoir, and consider the inconsistency of the number of flood occurrences when sampling.

In the specific implementation process, the working process of over-quantitative flood frequency analysis considering historical floods is as follows:

1. Super-quantitative flood frequency analysis. Assuming that the annual occurrence frequency of POT obeys the Poisson distribution, the probability of the annual occurrence frequency m is: In the formula, m is the number of occurrences per year, λ is the parameter of Poisson distribution, and the mathematical expectation of Poisson distribution is E(m)=λ. The frequency distribution of over-quantity floods obeys the GP distribution, and under the condition that the number of over-quantity occurrences obeys the Poisson distribution, the return period T(x) of the flood peak flow x is: In the formula, μ is the average annual number of over-quantity occurrences, and F(x) is the probability that x does not exceed.

2. Flood peak independence and threshold value selection. The premise of super-quantitative flood frequency analysis is that the flood peak samples are independent. This model adopts the independent flood peak criterion proposed by the United States Water Resources Council (USWRC). The conditions for selecting two consecutive flood peaks at the same time are θ>5+ln(A) and X _min <0.75min[Q1, Q2], where θ is the interval time (days) between two peaks; A is the watershed area, Mile ² ; Qi is the maximum daily discharge of the i-th flood. Among the continuous flood peaks that do not meet the above conditions, only the largest flood peak is taken. The threshold value is jointly determined based on the occurrence frequency distribution of over-quantity series, the frequency distribution of over-quantity floods and the assumption of independent and identical distribution. The value range of the threshold value was determined by using the over-quantity sample mean method, the dispersion index method, and the annual average over-quantity occurrence times μ method.

3. Parameter estimation. This model adopts maximum likelihood estimation, under the condition of including a historical flood in a research period, assuming that the research period is N years, there are k historical floods in the year (N-S) without actual measurement data, and the minimum historical flood is X0, for The data of unknown flood discharge during the research period, but known that its discharge is less than the minimum flood in the known historical floods during the research period, is expressed by the probability of not exceeding, and the historical flood with known discharge is expressed by the probability density function, then the logarithmic likelihood The function is:

In the formula, h=μ*(N-S), which is the number of floods exceeding the threshold value in (N-S) years without actual measurement data; xi is the measured flood, yj is the historical flood, and the meanings of other parameters are the same as before.

4. Goodness of fit test. The criterion-based minimum sum of squares (OLS) and the probability point data correlation coefficient (PPCC) were used to evaluate the goodness of fit of the model. PPCC test statistic:

In the formula, x _(i) and x _m represent the sorted measured value and the mean value of the measured sample, respectively; y _(i) and y _m are the theoretical value and mean value of the hypothetical distribution relative to x _(i) , respectively. In theory, y _(i) = E(x _(i) ), y _m = x _m .

OLS test:

In the formula, P _i is the empirical frequency corresponding to x _(i) , f(P _i , θ) is the ordinate of the frequency curve, and the meanings of other parameters are the same as before.

5. Trend test. The sample trend was tested by the Spearman rank correlation coefficient method. The statistic Z _SP converges to the standard normal distribution with the increase of n. If the data xi are sorted in ascending order, then Z _SP > 0, indicating that the sequence has an upward trend; Z _SP < 0, indicating that the sequence has a downward trend; if sorted in descending order, the opposite is true. |Z _SP |≤Z _α/2 , the null hypothesis is accepted, that is, the trend is not significant; otherwise, the trend is significant. α is the significance level Z _0.05/2 = 1.96.

In the specific implementation process, the working process of non-uniform over-quantitative flood frequency analysis based on time-varying moments is as follows:

1. Flood sequence inconsistency diagnosis. The Cumulative Sum of Departures of Modulus Coefficient (CSDMC) is used to detect the stage characteristics of the flood peak flow change, which can reflect the detailed information of the sequence time change. The M-K trend test method was used to analyze the trend characteristics of the flood time series.

2. Conversion between POT model and AMS model. The Poisson distribution is used to fit the over-quantity flood annual occurrence sequence, the GP distribution is used to fit the over-quantity sequence, and the Pareto-Poisson distribution is used to describe the POT model, then the corresponding AMS sequence obeys the GEV distribution. Convert the parameters of the POT model and the AMS model. For xx0, the parameters k*, α*, ξ* of the GEV distribution of the AMS sequence and the Pareto-Poisson distribution of the POT sequence The conversion relationship of parameters λ, α, k, is: ξ ^* ＝ ξ+αln(λ) α ^* ＝ αk ^* ＝k≠0

α is the scale parameter of GP distribution, k is the shape parameter; k* is the shape parameter of AMS, α* is the scale parameter of AMS, and ξ* is the location parameter of AMS.

3. Time-varying moment method. In the flood frequency analysis, the trend components of the first and second moments of the flood time series are considered to deal with the inconsistency of the series.

The specific implementation method of the time-varying moment method is as follows:

3.1. Time-varying moment model. Suppose the probability density function of the distribution is f=f(x;p), where p is the distribution parameter, and the relationship with the first two moments is p=p(m,σ), then the probability density function is f=f(x ; m,σ). Among them, m and σ are the sample moments considering the trend component, related to time, there are m=m(t; θ ^(m) ) and σ=(t; θ ^(σ) ), use θ ^(m) and θ ^(σ) represent the parameter vectors of m and σ respectively, then the parameter p is p=p(t; θ), and θ is a parameter matrix composed of θ ^(m) and θ ^(σ) . Transform the distribution parameter vector p into the parameter vectors θ ^(m) and θ ^(σ) of m and σ by the time-varying moment method, that is, f=f(x,t; θ).

3.2. Trend model. Using a simple continuous function to describe the trend of the first second moment of the sample, considering the existence of linear and parabolic trends, a total of six time-trend types are analyzed: ①The mean has a linear trend (AL); ②The standard deviation has a linear trend (BL); ③The mean value and standard deviation have a linear trend, and a fixed value (coefficient of variation Cv) is proportionally related (CL); ④The mean value and standard deviation have a linear trend, and are not correlated (DL); ⑤ The mean has a parabolic trend (AP); ⑥The mean and standard deviation have a parabolic trend, and a fixed value (coefficient of variation Cv) is proportionally related (CP). In the flood frequency analysis, the trend components of the first and second moments of the flood time series are considered to deal with the inconsistency of the series. There is also a steady-state situation (S), which assumes that there is no trend change in the sample moments, that is, the parameters of the distribution are stable. There are two sequences that need to be considered in the POT model, one is the overquantitative annual occurrence sequence fitted by the Poisson distribution, and the other is the overquantified flood sequence fitted by the GP distribution. If any of the two sequences has a trend, it will be Calculated results of parameters affecting the GEV distribution of the AMS model. Since the parameter λ of the Poisson distribution is the mathematical expectation of the sample of overquantitative annual occurrences, only the trend of the first-order moment is considered for the overquantitative annual occurrence sequence; the trend of the first second-order moment is considered for the POT sequence. Considering the two series together, a variety of trend models can be derived. This model considers 15 types in total. The model name "ALS" indicates that the sample mean of the over-quantitative annual occurrence times has a linear trend, and the first second-order moments of the over-quantitative flood series do not have a trend. "SAL" indicates that the sample mean of over-quantitative annual occurrences does not have a trend, and the mean of over-quantitative flood series has a linear trend, and the rest of the models are the same. For the expression of the first second-order moment of each trend model sample and the number of parameters added to the model, see Table 1 for the expression of the second-order moment of each trend model.

3.3. Parameter estimation. Using the maximum likelihood method to estimate the parameters, the parameter estimation results are the parameter matrices g and h when the logarithmic likelihood function lnL takes the maximum value, thus calculating the parameters of the POT model at each time reference point t, and then according to the POT model and AMS Model correlations calculate the corresponding GEV distribution parameters.

3.4. Optimal trend model selection. This model uses the AIC criterion based on the principle of maximum entropy as the selection criterion for the optimal trend model. This criterion considers two parts, one is the fitting effect of the model to the sample, which is reflected by the likelihood function value; the other is the model stability, which is realized by punishing the number of parameters of the model. Finally, the model that fits the data well and has as few parameters as possible is selected as the optimal model. Increasing the model parameters can improve the fitting effect of the sample, but the extension of the curve may be reduced due to overemphasis on the fitting effect of the sample. Since the flood frequency analysis is more concerned with the extension part of the curve, the parameters should be simplified as much as possible in the model selection . The AIC criterion can test the significance of the difference between different models, and comprehensively weigh the relationship between the applicability of the model and the number of parameters, and the calculation is simple and objective. Calculation formula: AIC=-2lnML+2k, where ML is the maximum value of the likelihood function, which is the value of the likelihood function corresponding to the maximum likelihood parameter estimation result; k is the number of model parameters. The trend model with the smallest AIC value is the optimal model.

3.5. Sequence reconstruction. After using the maximum likelihood method to estimate the time-varying moment parameters of the POT model GP-Poisson distribution, any year (t ₀ ) can be taken as the reference year, and the measured sequence can be converted into a sequence under stable conditions by exceeding the probability.

Table 1 The expressions of the second-order moments of each trend model.

In the specific implementation process, the working process of the over-quantitative flood frequency analysis considering the time-varying threshold value is as follows:

1. Time-varying threshold estimation.

1.1 The time-varying threshold value is estimated by the quantile regression method, and the high quantile of the variable distribution is naturally and intuitively taken as the time-varying threshold value for super-quantitative analysis. Quantile regression is estimated by Complete the minimum linear program. In the formula, θ is the quantile value to be estimated, representing the percentage of the data below the regression line or the regression surface in the whole data, θ∈(0,1); β is the coefficient vector that changes with θ, called β( θ) is the θth regression quantile; y _i is the dependent variable vector, and _xi is the independent variable vector. Taking the year corresponding to the flood peak flow as the independent variable and the peak flow as the dependent variable, quantile regression estimation is performed to determine the time-varying threshold. Firstly, the over-quantity flood peak is initially extracted as the dependent variable based on the relatively large annual average number of over-quantity occurrences μ, and then the quantile is determined according to the required annual average occurrence number, and finally the quantile regression estimation is performed. The flood peak flow on the regression line is based POT flood peak sequence obtained by time-varying threshold.

1.2 Determine the segmentation threshold value according to the change characteristics of the watershed environment. The measured flow data is divided into different time intervals, and over-quantitative samples are extracted separately through a given annual average occurrence number in each time stage, so as to determine the threshold value of the corresponding stage. The division of time stages can be determined according to the human activities in the watershed controlled by each hydrological station, such as land use, impact of water conservancy projects, and climate change characteristics. The threshold value thus determined can reflect the characteristics of the watershed environment change. In addition, a fixed threshold value can also be used to extract POT samples first, and then determine by analyzing the phase change characteristics of the over-quantitative annual occurrence sequence.

2. Frequency distribution of over-quantitative floods with time-varying threshold. Let X*=(x ₁ *, ..., x _i *, ..., x _n *) represent the over-quantitative peak flow sequence extracted by time-varying threshold, n is the sequence length; X=(x ₁ ,..., x _i ,...,x _n ) represent the part of the flood peak flow exceeding the threshold value; S=(s ₁ ,...,s _j ,...,s _N ) is the threshold value of each year, and N is the number of years; then x _i = _xi *-s _j , j is the year where _xi is located. Denote the POT sequence as X, and the first and second moments of the sequence X are used for time-varying moment analysis. Sample X obeys GP distribution. Since X is the over-threshold part of the over-quantitative flood peak, the location parameter ζ of the GP distribution is 0. The formula for calculating the portion x(T) of the design flood peak exceeding the threshold value in the return period T is: Since the threshold value is different in each year, the actual design flood peak X*(T) corresponding to X* each year is related to the threshold value of the year, and the calculation formula is: x _j *(T)=s _j +x(T).

3. Time-varying moment method. The specific implementation method is the same as the over-quantitative flood frequency analysis considering historical floods.

Example 2

As shown in Figures 1 to 4, a non-consistency analysis system for over-quantitative floods in changing environments includes: sample analysis (POT over-quantitative sampling method), sequence inconsistency diagnosis, and over-quantitative frequency analysis under changing environments ( TVM frequency analysis model).

The working process of non-consistency analysis of overquantitative flood under changing environment is as follows:

1. Required data

As shown in Figure 5, taking Longchuan, Heyuan, and Boluo stations in the Dongjiang River Basin as an example, the overquantitative flood frequency analysis considering the time-varying threshold value is carried out. The data used by each hydrological station for flood peak flow sample extraction is a daily flow process. According to the daily flow process of each station, the independent flood peak sequence is extracted, and the over-quantity flood peak is initially extracted with the annual average number of over-quantity occurrences μ = 10 for the determination of the time-varying threshold and the extraction of POT samples. Taking μ = 2.5 as the average annual over-quantity occurrence of POT, when using the regression quantile to estimate the time-varying threshold value, the quantile is determined to be 75%, and the flood peak flow above the regression line is the final POT flood peak. When using segmented thresholds, the time stages are divided according to the time when the upstream reservoirs of each station start storing water, and the POT sequence is extracted in segments with μ = 2.5 in each time stage. Fengshuba Reservoir began to store water in October 1973, so Longchuan Station was divided into two stages: 1954-1973 and 1974-2009; Heyuan Station was affected by Fengshuba and Xinfengjiang Reservoirs, and Xinfeng The period before the impact of the Jiang reservoir from 1954 to 1959 was too short to be divided into separate sections, so the sections of Heyuan Station were the same as those of Longchuan Station; apart from the impact of Xinfeng River and Fengshu Dam on Boluo Station, there were also Xizhi River's Baipenzhu Reservoir, so it is divided into three time periods: 1954-1973, 1974-1984, 1985-2009.

2. Determination of time-varying threshold and POT sample extraction

2.1 Time-varying threshold value determined by regression quantile

Extract independent flood peaks based on the daily flow series, and initially extract the POT series with the average annual occurrence frequency of POT μ = 10, and use the 75% regression quantile of the POT series as the threshold to extract the time-varying POT flood peak samples. The average annual occurrence times of POT of the extracted flood peak sequence is μ=2.5, and Fig. 5 shows the flood peak flow extracted by each station μ=10 and the corresponding 75% percentile threshold value, and the flood peak located above the time-varying threshold value curve Traffic is the POT sequence extracted according to the time-varying threshold.

2.2 Segmentation Threshold

As shown in Figure 6, according to the start time of water storage in the upstream reservoir of each hydrological station, the daily flow sequence is segmented to extract the POT sequence, and the average annual occurrence frequency of POT in each time period is taken as 2.5, and Figure 6 shows the flood peak extracted by each station with μ=10 The flow rate and the threshold value of each period, the peak flow rate above the threshold value curve is the POT sequence extracted according to the time-varying threshold value.

2.3 Sequence inconsistency diagnosis

The M-K method is used to test the trend of the POT sequence extracted with the time-varying threshold value and the corresponding POT sequence occurrence number sequence. According to the 5% significance level of the M-K test results, the POT samples extracted using linear time-varying and segmented thresholds have no significant trend in the corresponding annual occurrence frequency series. It can be seen that the over-quantitative samples extracted based on time-varying thresholds The annual occurrence sequence of satisfies the consistency assumption. The POT series of Longchuan and Heyuan stations had a significant downward trend, and the POT series of Boluo station had a downward trend, but it did not reach the 5% significance level.

Comparing the M-K test results of the POT annual occurrence sequence obtained by the quantile regression threshold value and the segmented threshold value, it can be seen that the trend of the annual occurrence sequence of Longchuan and Heyuan stations is small when the quantile regression threshold value is used , when Boluo station adopts segmented threshold value, the trend of annual frequency series is smaller. Therefore, when analyzing the over-quantitative flood frequency considering the moment, the Longchuan and Heyuan stations use the POT sequence extracted by the digit regression threshold value, and the Boluo station uses the POT sequence extracted by the segmented threshold value.

2.4 Optimal trend model selection

According to the AIC criterion, the optimal trend model of the POT sequence mean and standard deviation obtained from the time-varying threshold value of the three stations in Dongjiang was selected, and the model with the smallest AIC value was selected as the optimal trend. Both Longchuan and Heyuan Boluo stations had the best CP trend , that is, the mean and standard deviation of the POT series have a parabolic trend and are related by a constant ratio (CV). 3. Corresponding law of line shape and design flood peak discharge change under changing environment

3.1 Response law of flood line in changing environment

Affected by reservoir regulation and storage, there is still a downward trend in the extraction of POT peak flow at Longchuan and Heyuan Boluo Stations based on time-varying thresholds. In order to study the situation of flood frequency curves in different stages and analyze the impact of water conservancy projects (mainly water storage) on the design flood peak discharge, according to the AIC criterion, the maximum value of the POT sequence mean and standard deviation obtained from the time-varying threshold value of the three stations of the Dongjiang River was selected. Optimal trend model. The POT sequence extracted according to the time-varying threshold value is reconstructed into a stable POT sequence under each characteristic time reference point, and the time reference point is selected according to the selection basis. As shown in Figure 7, the flood frequency curve is drawn according to the stable POT sequence at each time reference point, and compared with the flood frequency distribution result that does not consider the trend characteristics of the POT sequence sample moments. The three time reference points of Longchuan Station, 1962, 1989 and 2009, respectively represent the pre-construction, post-construction and current situation of Fengshuba Reservoir. Before the impact of Fengshu Dam water regulation and storage, the time reference point represented by 1962: Compared with the POT and GP flood frequency curves without considering the POT sample moment trend (S model), the reconstructed POT with this year as the time reference point The sample point data is above the measured POT sample point data, and the high end of the GP-CP frequency curve is steeper. Taking 1989 and 2009 to represent the stage after the completion of the Fengshuba Reservoir, the positions of the GP-CP curves corresponding to these two time base points are all below the GP-S curve. It can be seen that the probability of flood occurrence of the same magnitude is reduced, indicating that the Longchuan Station The over-quantitative flood peak is obviously affected by the adjustment and storage reduction of the reservoir. The GP-CP curve in 2009 is above the curve in 1989, but the corresponding threshold value in 2009 is smaller than that in 1989. Therefore, the relationship between the designated standard design flood peak magnitude at these two time points needs to be further studied. analyze.

The four time reference points of Heyuan station are 1956, 1966, 1989 and 2009. Before the construction of Xinfengjiang Reservoir, the flow at Heyuan Station was not affected by water regulation and storage. The reconstructed POT sequence and GP-CP curve at the time reference point in 1956 were at the top of the frequency at each time base point, and the occurrence of large-scale floods was likely to be relatively large. Before the Xinfengjiang Reservoir was impounded and the Fengshuba Reservoir was built, the GP-CP curve at the time base point of 1966 declined somewhat due to the impact of Xinfengjiang's regulation and storage. After the completion of the Fengshuba Reservoir, affected by the water storage of the two major reservoirs, the frequency curves in 1989 and 2009 were both below the GP-S curve, and the probability of major floods dropped significantly. The GP-CP curve in 2009 is above the curve in 1989, but the corresponding threshold value in 2009 is smaller than that in 1989. The changing law of frequency curves at different time reference points at Heyuan Station is similar to that at Longchuan Station.

The five time reference points of Boluo Station are 1956, 1966, 1978, 1994 and 2009 respectively. The high water tail of the GP-CP frequency curves in 1956, 1966 and 1978 gradually became flat, and the position of the curves moved down. The frequency curve in 1966 was similar to the GP-S curve. The frequency change characteristics of the above several time points indicate that the probability of major floods has decreased significantly. The GP-CP curve in 1994 almost coincides with that in 1978, but the corresponding threshold value in 1994 is smaller than that in 1978, so the probability of a major flood in 1994 is lower than that in 1978. The frequency curve in 2009 is above the curve in 1994. The threshold values corresponding to the two time reference points are the same, so the year curve is above the curve. The threshold values corresponding to the two time reference points are the same. The occurrence probability of major floods in one year is greater than that in 1994, and the relationship with the design values at other time points needs to be further analyzed.

3.2 Design peak discharge change characteristics

After considering the time-varying threshold value and the change trend of the mean value and standard deviation of the POT sequence, the designated standard design peak flow is a quantity that changes with time. In order to explore the influence of the changing environment on the design value of the flood peak flow, this paper bases An optimal trend model is used to analyze the change process of flood peak discharge over time from 1954 to 2009 under the guiding standard (once in 100 years).

In the stable model, that is, under the condition that the threshold value is fixed and the overquantity sample moment is not considered, the 100-year flood peak discharge at Longchuan station is 7141m ³ /s. Considering the linear time-varying threshold value and the time-varying POT sample moment with the CP trend, as time goes by, the 100-year design flood peak discharge of Longchuan Station decreases first, and the range of change gradually decreases; the flood magnitude is about 12000m ³ /s decreased to 4000m ³ /s, and after 1995, the peak discharge increased somewhat.

The once-in-100-year design flood peak calculated under stable conditions at Heyuan Station is 10748m ³ /s. After considering the linear time-varying threshold value and the time-varying CP trend of the POT sample moment, the design flood peak discharge characteristics are similar to those at Longchuan Station, but the magnitude of change is It is bigger than Longchuan Station. The magnitude of the flood in 1954 was about 15000m ³ /s, which decreased to 4100m ³ /s in 1995, increased after 1995, and exceeded 5000m ³ /s in 2009.

The 100-year design flood peak calculated under stable conditions at Boluo Station is 13032m ³ /s. The threshold value of Boluo station is time-varying in segments, and the sample moment of POT changes in CP trend. Due to the threshold values taken at different stages, the 100-year design flood peak change process of Boluo station is not a smooth curve, but the design flood peak change process of the 1-year design flood peak is an unsmooth curve, but the 1-year design flood peak change process is an unsmooth curve , but there were mutations in 1974 and 1985. During the two stages of 1954-1973 and 1974-1984, the peak flow of Boluo Station decreased with time, and the peak flow of Boluo Station increased from 1985 to 2009.

The change of design peak discharge under the specified standard (once in a hundred years) with time shows that the magnitude of the design peak discharge of the designated standards of the three stations of the Dongjiang River has generally changed from large to small, and then has a tendency to rise again. If sequence inconsistency processing is not considered, the 100-year design floods of Longchuan, Heyuan and Boluo stations calculated by traditional methods are 7141m ³ /s, 10748m ³ /s and 13032m ³ /s respectively. After considering the time-varying threshold value and the variation trend of POT sample moments, the design flood peak value calculated by the traditional method appeared in the period from 1960 to 1970. During this period, the flow process of each station was less affected by reservoir regulation and storage. Affected by reservoir regulation and storage, the design flood peaks are smaller than the traditional calculation results. If the inconsistency of flood peak samples is not considered, the flood frequency analysis results will overestimate the design flood magnitude.

3.3 Comparison of non-consistent method and traditional method return period

Taking the current situation in 2009 as the time reference point, considering the inconsistency treatment of the threshold value change, the difference between the designated standard flood peak flow and the traditional analysis results based on the consistency assumption is considered. The trend item uses SS to represent a stable state that neither considers the time-varying threshold value nor the time-varying threshold value, nor the time-varying POT sample moment; MS represents the time-varying threshold value and the stable POT sample moment; E_MS represents MS The degree of difference between the set value calculated by the model and the design value of the SS model.

Table 2 shows that the design flood peaks of Longchuan station after non-consistency treatment are all smaller than the calculation results based on the consistency assumption; The current period increases but slightly decreases; when the threshold value is considered, the POT sample moment changes with the CP trend, and the difference between the calculation result and the traditional method is greater than 30%, and the difference increases with the increase of the return period . The design flood peaks of the Heyuan station after inconsistency treatment are all smaller than the calculation results based on the consistency assumption, and the degree of difference increases with the increase of the return period. The difference degree considering the time variation of POT sample moments is greater than that without considering the time variation of POT sample moments When the return period is 100 years, the difference between MS model and SS model reaches 25%, and the difference between CP model and SS model reaches 51%. The calculated results of the MS model at Boluo Station are smaller than those of the SS model, and the difference increases with the increase of the return period, and the difference is 15% at the 100-year return period; the relationship between the CP model and the SS model is different from that of Longchuan and Heyuan stations. When the return period is less than 20, the calculation result of the CP model is slightly larger than that of the SS model. After the return period exceeds 30 years, the calculation result of the CP model is smaller than that of the SS model, and the degree of difference increases with the increase of the return period. The time difference is 5.5%.

Table 2 The time-varying processing of the threshold value (t0=2009) and the traditional method estimate the same or similar design flood peak difference. The labels correspond to the same or similar components;

The terms describing the positional relationship in the drawings are only for illustrative purposes and cannot be interpreted as limitations on this patent;

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in different forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (7)

1. A non-consistency analysis method for super-quantitative floods under a changing environment, characterized in that, comprising the following steps: Sample selection: consider historical floods for flood frequency analysis, determine threshold values, and use super-quantitative sampling methods to screen sample sequences; Sequence inconsistency diagnosis: judging whether there is jump variation and trend variation of catastrophic floods in the sequence, using different methods for super-quantitative flood frequency analysis for the two different situations of jump and trend; Calculation of over-quantitative frequency under changing environment: considering the over-quantitative flood frequency analysis of historical floods, according to the selected continuous POT samples, combined with historical floods to form discontinuous POT samples, and performing flood frequency analysis on each sample segment sequence; inconsistency For the frequency analysis of super-quantitative floods, the TVM model is used to analyze the non-consistent annual maximum daily flow series, and the AMS series is fitted to analyze the non-consistent flood frequency. 2. The non-consistency analysis method for over-quantitative floods under changing environments according to claim 1, wherein the threshold value is determined according to an independence criterion and an over-quantitative threshold value selection standard. 3. The non-consistency analysis method of over-quantitative floods under the changing environment according to claim 1, characterized in that, the sequence non-consistency diagnosis is to use M-K trend analysis to judge the trend and jump of the flood sequence. 4. The non-consistency analysis method for over-quantitative floods under changing environments according to claim 2, characterized in that different flood frequency analysis methods are used for different flood sequences. 5. the non-consistency analysis method of overquantitative flood under the changing environment according to claim 4, is characterized in that, described flood frequency analysis method comprises fixed threshold value time-varying moment method and time-varying threshold value time-varying moment method method. 6. the non-consistency analysis method of over-quantitative flood under the changing environment according to claim 5, is characterized in that, described fixed threshold value time variable moment method is to determine unique fixed threshold value, selects in the flood frequency analysis Different probability distributions, considering the different trends of the first two moments of the sequence to construct different TVM models to deal with inconsistencies. 7. the non-consistency analysis method of over-quantitative flood under the changing environment according to claim 5, is characterized in that, described time-varying threshold value time-varying moment method is the inconsistency research time-varying threshold value application of air temperature In the extraction of flood over-quantitative samples, the regression quantile is used to calculate the time-varying threshold value, and the segmented threshold value is determined according to the regulation and storage of the reservoir in the basin, and the inconsistency of the number of flood occurrences is considered when sampling.