CN107066425B - Method for analyzing non-uniformity of ultra-quantitative flood in changing environment - Google Patents
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Abstract
The invention discloses a method for analyzing the non-uniformity of ultra-quantitative flood in a changing environment, which comprises the following steps: selecting a sample: screening the sample sequence by adopting an over-quantitative sampling method; sequence non-identity diagnosis: judging whether the sequence has jump variation and trend variation of the extra flood, and carrying out ultra-quantitative flood frequency analysis on two different conditions of the jump and the trend by using different methods; calculating the ultra-quantitative frequency under the changing environment: considering the over-quantitative flood frequency analysis of the historical flood, combining the selected continuous POT samples with the historical flood to form discontinuous POT samples, and carrying out the flood frequency analysis on each sample segment sequence; frequency analysis is carried out based on the POT sequence, sequence non-uniformity is considered, the change characteristics of flood along with time are reflected from two aspects of flood magnitude and flood generation process, a novel method for researching non-uniform flood is provided, the research of hydrological evolution rules under the change environment is promoted, and powerful reference is provided for hydraulic engineering construction.
Description
Technical Field
The invention relates to the technical field of flood frequency analysis, in particular to a method for analyzing the non-uniformity of ultra-quantitative flood in a changing environment.
Background
Under the influence of climate change and human activities, a plurality of river hydrological conditions have changed remarkably, hydrographic extreme value events of flood and drought occur frequently, the consistency of environmental backgrounds formed by a plurality of river flood sequences in the world is not existed, and the extreme value theory of the traditional extreme value flow analysis needs to be corrected to adapt to the non-stationarity of the sequences. The watershed development and utilization engineering, flood control and drought control engineering, operation scheduling and the like designed by adopting the existing engineering hydrological analysis method face the risk of design frequency distortion caused by the changing environment.
The flood frequency analysis method adopts a generalized distribution fitting observation extreme value so as to obtain the design flood in a designated or average recurrence period, provides a systematic basis for the planning and operation of hydraulic engineering, and has almost a century history in application. The biggest problem of estimating engineering flood setting through flood frequency analysis is that observation data is too short, and available flood information is insufficient. The traditional method for acquiring flood information is Annual Maximum Series (AMS), but with AMS sampling, the second and third major flood peaks in the year after the changing environment are ignored, although they are generally much larger than the magnitude of the flood before the changing environment. A Peak-over-Threshold (POT) model considers a super-quantitative annual occurrence frequency distribution model and a super-quantitative distribution model at the same time, and can describe flood and the production process thereof more completely and flexibly compared with an AMS method. Therefore, the POT model can be used as a frequency analysis method suitable for a changing environment. POT samples and selects all flood peaks exceeding a threshold value in measured data as samples, so that more flood information amount than a traditional annual maximum value (AMS) sequence can be obtained, and the calculation accuracy of design flood is effectively improved. Statistical tests show that the longer the historical flood recurrence period added with calculation is, the more beneficial the frequency analysis precision and stability are to be improved. By considering POT flood frequency analysis of historical flood, flood information utilization can be maximized from two aspects of actual measurement and evidence examination data, the flood design precision is improved, and the method has great research value. At present, some researches on considering historical flood in a POT method are carried out, but only the historical flood in an examination period is considered to be added into a continuous sample, and the condition that the historical flood is grouped is not considered; the data is obtained through statistical tests instead of actual measurement and examination data of specific sites. There are fewer studies on the impact of analyzing historical floods on POT flood frequency analysis for specific watersheds. In practical application, there may be multiple examination periods in the examined historical flood, and the treatment of grouping the historical flood needs to be considered. Therefore, the influence of the grouping historical flood on the POT method is researched, and the method has important significance for improving the applicability of POT flood frequency analysis. Frequency calculation of non-uniform (non-stationary) hydrological sequences is an emerging research topic, and related research results are quite few. The more common domestic method is based on a reduction/reduction approach, and mainly comprises the following steps: a relational analysis method of a series before and after a variation point and a certain parameter, a decomposition and synthesis method of a time series and a hydrological model 3. However, the methods have disadvantages, such as that under the condition that the prediction period of the time series decomposition and synthesis method is long, the existing deterministic component prediction method is difficult to convince and has large extension risk; by establishing a hydrological model and separating the deterministic components of a hydrological sequence from a causal path, the rate determination of many parameters of the model is limited to the historical drainage basin physical conditions in a certain period. With the deep research on influence of global changes on hydrological processes, hydrological frequency research under non-stationary conditions caused by changing environments has received much attention in recent years. And aiming at the non-stationarity of the hydrological sequence, a non-stationary sequence based on time-varying statistical parameters can be established for estimation. At present, the common method for analyzing the frequency of the non-stationary flood abroad mainly comprises the following steps: time Variation Moment (TVM), regional collection flood frequency analysis, local likelihood method, quantile regression, mixed distribution model and the like. Since the statistical parameters (such as mean and standard deviation) of the non-stationary flood sequence and the distribution line type change at any moment, the uncertainty of the corresponding design flow will also change. In contrast, Strupczewski et al propose a TVM model for processing a non-stationary extremum sequence, which considers the trends of the mean and variance of statistical parameters and can obtain the time-varying relationship of the design values. Strupczewski and the like propose TVM frequency analysis models based on POT sequences by taking Poisson-index distribution as an example, consider the trends of first moment of POT annual occurrence frequency sequences and first and second moments of POT sequences, describe model distribution parameters by using the moments of the sequences, and describe AMS model distribution parameters by using annual occurrence frequency and first and second order time-varying moments of POT flood peak sequences respectively according to the corresponding relation between the POT models and AMS models, thereby obtaining the variation relation of design values along with time. The non-uniform frequency analysis model based on the POT sequence not only can reflect the trend of the peak flow changing along with time, but also can reflect the change trend of the occurrence times of flood, and can well reflect the change characteristics of the flood along with time from two aspects of magnitude and process. The TVM model based on the POT sequence, which is proposed by Strupczewski and the like, adopts a fixed threshold value, Kysely and the like propose a quantile regression technology to realize time variation of the threshold value when time variation is used for analyzing temperature inconsistency, and the annual occurrence times of the POT sequence obtained by adopting the method meet the consistency assumption. Afterwards, the TVM method is successfully applied to other areas by scholars, and the flood design value XP has a significant change relation with time under a certain standard P.
Disclosure of Invention
The invention aims to solve the technical problems that the flood information is insufficient and the flood extreme value sequence does not meet the consistency assumption, provides a novel method for analyzing the non-consistency flood frequency by utilizing a TVM model based on a POT sequence, takes the sequence non-consistency into consideration, and reflects the change characteristics of the flood along with time from two aspects of the flood magnitude and the flood generation process. For the condition that the over-quantitative flood peak sequence has extra-large flood jumping points, the influence of historical flood on the over-quantitative flood frequency analysis result is discussed; and for the condition that the trend of the overdetermined sequence is time-varying, applying a time-varying-based non-uniform flood frequency analysis method to the analysis of the overdetermined sample, and realizing the application of a threshold time-varying sampling method to the flood frequency analysis.
In order to solve the technical problems, the technical scheme of the invention is as follows: a method for analyzing the non-uniformity of ultra-quantitative flood in a changing environment comprises the following steps:
selecting a sample: carrying out flood frequency analysis by considering historical flood, determining a threshold value, and screening a sample sequence by adopting an over-quantitative sampling method;
sequence non-identity diagnosis: judging whether the sequence has jump variation and trend variation of the extra flood, and carrying out ultra-quantitative flood frequency analysis on two different conditions of the jump and the trend by using different methods;
calculating the ultra-quantitative frequency under the changing environment: considering the over-quantitative flood frequency analysis of the historical flood, combining the selected continuous POT samples with the historical flood to form discontinuous POT samples, and performing the flood frequency analysis on each sample segment sequence; and estimating GP distribution parameters by adopting a maximum likelihood method to obtain the goodness of fit of each sequence and a flood calculation result designed in a recurrence period. Analyzing the non-consistency over-quantitative flood frequency, analyzing the non-consistency annual maximum daily flow sequence by adopting a TVM (transient response) model, diagnosing the trend change and the stage change characteristics of the sequence by using a Mann-Kendall (M-K) method and a CSDMC (transient stability dynamic response matrix) method, selecting a time base point of the TVM method, finally deducing the distribution of a corresponding AMS (automatic system simulator) model, fitting the AMS sequence and performing non-consistency flood frequency analysis. Fitting AMS sequences and performing non-uniform flood frequency analysis.
In a preferred embodiment, the threshold is determined according to an independence criterion and an over-quantification threshold selection criterion. The threshold value is determined according to the distribution of the occurrence times of the overdetermined series, the frequency distribution of the overdetermined flood and the independent equal distribution hypothesis, and the value range of the threshold value is determined by utilizing an overdetermined sample average method, a dispersion index method and an annual average overdetermined occurrence time mu method.
In a preferred embodiment, the sequence non-uniformity diagnosis is performed by analyzing the trend and jump of flood sequences by using M-K trend test.
In a preferred embodiment, different flood frequency analysis methods are used for different flood sequences. The frequency analysis method of the time-varying threshold value comprises the following steps: and (4) taking the time change characteristic of the threshold value into consideration, and extracting an over-quantitative sample by adopting the time change threshold value to obtain a POT annual occurrence frequency sequence meeting the consistency assumption. After the POT sample is obtained by adopting the time-varying threshold value, the trend of the first moment and the second moment of the POT sequence is considered, Poisson-GP distribution is adopted, the time-varying moment is used for describing model distribution parameters, and the time-varying over-quantitative flood frequency analysis of the threshold value and the POT sample moment is carried out.
In a preferred embodiment, the flood frequency analysis method includes a fixed threshold time-varying moment method and a time-varying threshold time-varying moment method.
In a preferred scheme, the fixed threshold value-time-varying moment method is a non-consistency processing method for determining a unique fixed threshold value, selecting different probability distributions in flood frequency analysis, and constructing different TVM models by considering different trends of two moments before a sequence. The TVM model considers trend components of first and second moments (mean m and standard deviation sigma) of a flood time sequence, expresses original parameters of distribution by time-varying moments, and estimates parameters of a probability density function. The maximum likelihood method is applied to flood sequences that satisfy independence requirements, and the trend is considered in the model assuming that the sequences do not satisfy independence only because the sequences have a trend. And finally, using the AIC criterion as a criterion of the optimal model.
In a preferred scheme, the time-varying threshold value time-varying moment method is that the time-varying threshold value of temperature inconsistency research is applied to extraction of a flood over-quantitative sample, a regression quantile is adopted to calculate the time-varying threshold value, a segmented threshold value is determined according to the regulation and storage conditions of the reservoir in the watershed, and the inconsistency of flood occurrence times is considered during sampling.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
(1) and applying the historical flood to ultra-quantitative frequency analysis, and analyzing the influence of grouping the historical flood to the POT flood frequency analysis result when the ultra-large flood exists in the actually measured data.
(2) The time-varying moment-based inconsistent flood frequency analysis is applied to an over-quantification method, and compared with the annual maximum value method, the inconsistent over-quantification flood frequency analysis can reflect the change characteristics of the flood generation process and the flood magnitude at the same time.
(3) The frequency analysis of the non-uniform over-quantitative flood mostly adopts a fixed threshold value to extract samples, the time-varying threshold value is researched by using the non-uniformity of the air temperature and is applied to the extraction of the flood over-quantitative samples, the time-varying threshold value is calculated by adopting a regression quantile, the segmented threshold value is determined according to the storage regulation condition of the reservoir in the watershed, and the non-uniformity of the flood occurrence times is considered during sampling.
Drawings
FIG. 1 is a diagram of a model framework of the present invention.
Fig. 2 is a schematic diagram of selection of POT samples according to embodiment 1 of the present invention.
FIG. 3 is a schematic diagram of sequence non-uniformity diagnosis in example 1 of the present invention.
Fig. 4 is a system block diagram of embodiment 1 of the present invention.
Fig. 5 shows the time-varying threshold values and peak flows of the three stations in east river according to embodiment 2 of the present invention.
Fig. 6 shows the segmented threshold values and peak flows of the three stations in east river according to embodiment 2 of the present invention.
Fig. 7 shows the POT flood frequency curve change based on the time reference point of the east jiang three stations in embodiment 2 of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, a method for analyzing the non-uniformity of ultra-quantitative flood under a changing environment includes the following steps:
selecting a sample: carrying out flood frequency analysis by considering historical flood, determining a threshold value, and screening a sample sequence by adopting an over-quantitative sampling method;
sequence non-identity diagnosis: judging whether the sequence has jump variation and trend variation of the extra flood, and carrying out ultra-quantitative flood frequency analysis on two different conditions of the jump and the trend by using different methods;
calculating the ultra-quantitative frequency under the changing environment: considering the over-quantitative flood frequency analysis of the historical flood, combining the selected continuous POT samples with the historical flood to form discontinuous POT samples, and performing the flood frequency analysis on each sample segment sequence; and estimating GP distribution parameters by adopting a maximum likelihood method to obtain the goodness of fit of each sequence and a flood calculation result designed in a recurrence period. Analyzing the inconsistent over-quantitative flood frequency, analyzing the inconsistent annual maximum daily flow sequence by adopting a TVM (transient dynamic model), selecting a time base point of the TVM by using trend change and stage change characteristics of a diagnosis sequence of an M-K (transient-dynamic-matrix-mass-transfer) method and a CSDMC (transient-dynamic-matrix-dynamic-mass-transfer) method as a basis, finally deducing the distribution of a corresponding AMS (automatic system simulator) model, fitting the AMS (automatic system simulator) sequence and performing inconsistent flood frequency analysis. Fitting AMS sequences and performing non-uniform flood frequency analysis.
In a specific implementation process, the threshold value is determined according to an independence criterion and an over-quantification threshold value selection criterion. The threshold value is determined according to the distribution of the occurrence times of the overdetermined series, the frequency distribution of the overdetermined flood and the independent equal distribution hypothesis, and the value range of the threshold value is determined by utilizing an overdetermined sample average method, a dispersion index method and an annual average overdetermined occurrence time mu method.
In the specific implementation process, the sequence non-uniformity diagnosis is to analyze by using an M-K trend test method to judge the trend and the jump of the flood sequence.
In the specific implementation process, different flood frequency analysis methods are adopted for different flood sequences. The frequency analysis method of the time-varying threshold value comprises the following steps: and (4) taking the time change characteristic of the threshold value into consideration, and extracting an over-quantitative sample by adopting the time change threshold value to obtain a POT annual occurrence frequency sequence meeting the consistency assumption. After the POT sample is obtained by adopting the time-varying threshold value, the trend of the first moment and the second moment of the POT sequence is considered, Poisson-GP distribution is adopted, the time-varying moment is used for describing model distribution parameters, and the time-varying over-quantitative flood frequency analysis of the threshold value and the POT sample moment is carried out.
In a specific implementation process, the flood frequency analysis method includes a fixed threshold time-varying moment method and a time-varying threshold time-varying moment method.
In a specific implementation process, the fixed threshold value-time-varying moment method is a non-consistency processing method which determines a unique fixed threshold value, selects different probability distributions in flood frequency analysis, and constructs different TVM models by considering different trends of the first two moments of a sequence. The TVM model considers trend components of first and second moments (mean m and standard deviation sigma) of a flood time sequence, expresses original parameters of distribution by time-varying moments, and estimates parameters of a probability density function. The maximum likelihood method is applied to flood sequences that satisfy independence requirements, and the trend is considered in the model assuming that the sequences do not satisfy independence only because the sequences have a trend. And finally, using the AIC criterion as a criterion of the optimal model.
In the specific implementation process, the time-varying threshold value and time-varying moment method is characterized in that the time-varying threshold value for temperature inconsistency research is applied to extraction of a flood over-quantitative sample, a regression quantile is adopted to calculate the time-varying threshold value, a segmented threshold value is determined according to the storage regulation condition of a reservoir in a drainage basin, and the inconsistency of flood occurrence times is considered during sampling.
In the specific implementation process, the working process of the overdetermined flood frequency analysis considering the historical flood is as follows:
1. and (5) carrying out overdetermined flood frequency analysis. The annual occurrence frequency of POT is subject to Poisson distribution, and the probability of the annual occurrence frequency m is as follows:
where m is the number of annual occurrences, λ is a Poisson distribution parameter, and the mathematical expectation of the Poisson distribution is e (m) ═ λ. The over-quantitative flood frequency distribution obeys GP distribution, and under the condition that the over-quantitative occurrence times obey Poisson distribution, the recurrence period T (x) of the flood peak flow x is as follows:
wherein mu is the average number of the over-quantification occurrences per year, and F (x) is the probability that x does not exceed.
2. And selecting flood peak independence and threshold values. The precondition of the over-quantitative flood frequency analysis is that the flood peak samples have independence. The model adopts the independent flood peak judging standard provided by the American Water resource Association (USWRC). Selecting two continuous flood peaks at the same time under the conditions that theta is more than 5+ ln (A) and Xmin＜0.75min[Q1，Q2]Where θ is the interval between two peaks (days); a is the basin area, Mile2(ii) a Qi is the maximum daily flow of the ith flood. And only taking the maximum one-time flood peak from the continuous flood peaks which do not meet the conditions. The threshold value is determined according to the occurrence frequency distribution of the over-quantitative series, the over-quantitative flood frequency distribution and the independent same distribution hypothesis. By using an overdetermined sample averaging method, a dispersion index method and an annual average overdetermined hairThe generation number mu method determines the value range of the threshold value.
3. And (6) parameter estimation. The model adopts maximum likelihood estimation, under the condition of containing one examination period historical flood, the examination period is set to be N years, k fields of historical flood exist in the years (N-S) without actual measurement data, wherein the minimum historical flood is X0, for the data of unknown flood flow in the examination period, the known flow is smaller than the minimum flood in the known historical flood in the examination period, the minimum flood is represented by no more than probability, the historical flood with the known flow is represented by a probability density function, and then the log-likelihood function is as follows:
wherein, h is mu (N-S) and is the flood quantity exceeding the threshold value in the (N-S) year without measured data; xi is actually measured flood, yj is historical flood, and the meanings of the other parameters are the same as the above.
4. And (5) testing the goodness of fit. The goodness of fit of the model is evaluated using a criterion-based least-squares-sum-of-deviation (residual) criterion (OLS) and a probability point data correlation coefficient (PPCC). PPCC test statistics:
in the formula, x(i)And xmRespectively representing the mean values of the sequenced measured values and the sequenced measured samples; y is(i)And ymRespectively, assuming the distribution with respect to x(i)Theoretical values and mean values of (a), theoretically, y(i)＝E(x(i))，ym＝xm。
OLS test:
in the formula, PiTo correspond to x(i)Empirical frequency of f (P)iAnd theta) is the ordinate of the frequency curve, and other parameters have the same meanings as above.
5. And (5) checking the trend. The Spearman rank correlation coefficient method was used to test sample trends. StatisticsZSPConverges to a standard normal distribution with increasing n. If data xi are sorted in ascending order, then ZSP>0, indicating that the sequence has an ascending trend; zSP<0, indicating that the sequence has a downward trend; if sorted in descending order, the reverse is true. I ZSP|≤Zα/2Then the null hypothesis is accepted, i.e. the trend is not significant, otherwise the trend is significant α is the significance level Z0.05/2＝1.96。
In the specific implementation process, the working process of the non-uniformity over-quantification flood frequency analysis based on the time-varying moment is as follows:
1. flood sequence non-uniformity diagnosis. The method can reflect the detailed information of the time change of the sequence by using the current Sum of the department of the Module Coefficient (CSDMC) to detect the characteristics of the peak flow change stage. And analyzing the trend characteristics of the flood time series by adopting an M-K trend inspection method.
And 2, converting parameters of the POT model and the AMS model, namely xx0, parameters k, α and ξ of GEV distribution of the AMS sequence and parameter of the POT sequence Pareto-Poisson distribution of the POT model
The conversion relation of the parameters lambda, α, k is ξ*＝ξ+αln(λ)α*＝αk*＝k≠0
Alpha is a scale parameter of GP distribution, and k is a shape parameter; k is the AMS shape parameter, α is the AMS dimension parameter, ξ is the AMS position parameter.
3. Time-varying moment method. And in the flood frequency analysis, the trend components of the first moment and the second moment of the flood time sequence are considered to carry out non-uniformity processing on the sequence.
The specific implementation method of the time variation moment method comprises the following steps:
3.1. a time-varying moment model. Assuming that 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), the probability density functionThe number f is f (x; m, σ). Where m, σ is the sample moment of the trend component considered, is time dependent, with m ═ m (t; θ)(m)) And σ ═ t; theta(σ)) By theta(m)And theta(σ)If the parameter vectors represent m and σ, the parameter p is p ═ p (t; θ), and θ is represented by θ(m)、θ(σ)And (4) forming a parameter matrix. Converting the distribution parameter vector p into the parameter vector theta of m and sigma by the time-varying moment method(m)、θ(σ)I.e., f ═ f (x, t; θ).
3.2. And (5) a trend model. The trend of the second moment in front of the sample is expressed by a simple continuous function, and six time-trend types are analyzed in consideration of the situations of linear trend and parabolic trend: the mean value has a linear trend (AL); ② the standard deviation has a linear trend (BL); the mean value and the standard deviation have linear trends, and a fixed value (coefficient of variation Cv) is taken as proportion Correlation (CL); the mean value and the standard deviation both have linear trends and are uncorrelated (DL); the mean value has a parabolic trend (AP); sixthly, the mean value and the standard deviation have parabolic trends, and a fixed value (coefficient of variation Cv) is taken as proportion Correlation (CP). And in the flood frequency analysis, the trend components of the first moment and the second moment of the flood time sequence are considered to carry out non-uniformity processing on the sequence. There is also a steady state case (S) where there is no trend change in the sample moments, i.e. the distribution parameters are stable. The POT model needs to consider two sequences, one is an overdetermined annual occurrence frequency sequence fitted by Poisson distribution, the other is an overdetermined flood sequence fitted by GP distribution, and any one of the two sequences has a trend and affects the parameter calculation result of the GEV distribution of the AMS model. As the Poisson distribution parameter lambda is the mathematical expectation of the over-quantitative annual occurrence number sample, the over-quantitative annual occurrence number sequence only needs to consider the trend of the first moment; the POT sequence takes into account the trend of the first second moment. The two sequences are considered in a combined mode, a plurality of trend models can be derived, 15 models are considered in the model, the model name ALS represents that the average value of the ultra-quantitative annual occurrence frequency samples has a linear trend, the first second moment of the ultra-quantitative flood sequence does not have a trend, SAL represents that the average value of the ultra-quantitative annual occurrence frequency samples does not have a trend, the average value of the ultra-quantitative flood sequence has a linear trend, and the other models are the same in principle. The expression of the second moment in front of each trend model sample and the number of the model increasing parameters are shown in table 1.
3.3. And (6) parameter estimation. Parameters are estimated by using a maximum likelihood method, the parameter estimation result is parameter matrixes g and h when the log-likelihood function lnL takes the maximum value, POT model parameters at each time reference point t are calculated, and corresponding GEV distribution parameters are calculated according to the correlation relation between the POT model and the AMS model.
3.4. And selecting an optimal trend model. The model takes the AIC criterion based on the maximum entropy principle as the selection standard of the optimal trend model. The criterion considers two contents, namely, the fitting effect of a model on a sample is reflected by a likelihood function value; and secondly, the stability of the model is realized by punishing the number of parameters of the model. And finally, selecting a model which has good fitting on data and the number of parameters as few as possible as an optimal model. Increasing the model parameters may improve the fitting effect on the samples, but may reduce the curve ductility because the fitting effect on the samples is over-emphasized, and since the flood frequency analysis is more concerned about the extension of the curve, the parameters should be simplified as much as possible in the model selection. The AIC criterion can be used for detecting the difference significance among different models, comprehensively weighing the relationship between the model applicability and the parameter number, and is simple and objective in calculation. Calculating the formula: in the formula, ML is the maximum value of the likelihood function and is the likelihood function value corresponding to the maximum likelihood parameter estimation result; and k is the number of model parameters. The trend model with the smallest AIC value is the optimal model.
3.5. And (5) sequence reconstruction. After the time-varying moment parameters of the GP-Poisson distribution of the POT model are estimated by the maximum likelihood method, the time-varying moment parameters can be taken for any year (t)0) As a reference year, the measured sequence is converted into a sequence under stable conditions by exceeding the probability.
Table 1 expression of the two 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. and estimating a time-varying threshold value.
1.1, estimating the time-varying threshold value by a quantile regression method, and naturally and intuitively taking a high quantile of variable distribution as the time-varying threshold value to perform overdetermined analysis. Quantile regression estimation by
In the formula, theta is the quantile value to be estimated and represents the percentage of data below the regression line or regression surface to the whole data, theta ∈ (0,1), β is the coefficient vector which changes along with the change of theta, and is called β (theta) as the theta regression quantile, yiIs a dependent variable vector, xiIs an argument vector. And taking the corresponding year of the flood peak flow as an independent variable and the flood peak flow as a dependent variable, and performing quantile regression estimation to determine a time-varying threshold value. Firstly, preliminarily extracting the overdetermined flood peak as a dependent variable according to the larger annual average overdetermined occurrence frequency mu, then determining quantiles according to the required annual average occurrence frequency, and finally performing quantile regression estimation, wherein the flood peak flow on a regression line is a POT flood peak sequence obtained according to a time-varying threshold value.
1.2, determining a segmentation threshold value according to the environment change characteristics of the drainage basin. The measured flow data is divided into different time intervals, and an ultra-quantitative sample is independently extracted through the number of times of occurrence in a given year in each time phase, so that the threshold value of the corresponding phase is determined. The time staging can be determined according to human activities such as land utilization, hydraulic engineering influence and climate change characteristics of the controlled watershed of each hydrological station, and the threshold value determined thereby can reflect the environment change characteristics of the watershed. In addition, a POT sample can be extracted by adopting a fixed threshold value, and the POT sample is determined by analyzing the stage change characteristics of the over-quantitative annual occurrence frequency sequence.
2. And (4) distributing the over-quantitative flood frequency with the time-varying threshold value. Let X ═ X1*，…，xi*，…，xnOne) represents the overdetermined peak flow order extracted using time-varying thresholdsColumn, n is the sequence length; x ═ X1，…，xi，…，xn) A part representing that the peak flow exceeds a threshold value; s ═ S1，…，sj，…，sN) Is a threshold value of each year, and N is the number of years; x is theni＝xi*-sjJ is xiThe year it is. The POT sequence is marked as X, and the first moment and the second moment of the sequence X are used for time-varying moment analysis. Sample X obeys the GP profile. Since X is the super-threshold part of the super-quantitative flood peak, the position parameter ζ of the GP distribution is 0. The calculation formula of the designed peak over-threshold part x (T) of the recurrence period T is as follows:
because the threshold value of each year is different, the actual design flood peak value X (T) corresponding to X in each year is related to the threshold value of the current year, and the calculation formula is as follows: x is the number ofj*(T)＝sj+x(T)。
3. Time varying moment method. The specific implementation method is the same as the over-quantitative flood frequency analysis considering the historical flood.
Example 2
As shown in fig. 1 to 4, a system for analyzing the non-uniformity of ultra-quantitative flood in a changing environment includes: sample analysis (POT super-quantitative sampling method), sequence non-uniformity diagnosis, and super-quantitative frequency analysis (TVM frequency analysis model) under a changing environment.
The working process of the ultra-quantitative flood inconsistency analysis in the changing environment is as follows:
1. required data
As shown in fig. 5, taking the three stations of the east river basin, the dragon, the river source, and the bosro station as examples to perform the overdetermined flood frequency analysis considering the time variation of the threshold value, the data of each hydrological station for the extraction of the flood peak flow sample is the daily flow process. According to the daily flow process of each station, an independent flood peak sequence is extracted, and an over-quantitative flood peak is preliminarily extracted for determining a time-varying threshold value and extracting a POT sample according to the annual over-quantitative occurrence frequency mu of 10. And taking mu-2.5 as the number of times of POT annual average excess quantification occurrence, and determining that the quantile is 75% when a regression quantile estimation time-varying threshold value is adopted, wherein the peak flow rate above a regression line is the finally obtained POT peak. When a segmented threshold value is adopted, time stages are divided according to the starting water storage time of the upstream reservoir of each station, and POT sequences are extracted in a segmented mode of mu being 2.5 in each time stage. The maple dam reservoir begins to store water in 1973 in 10 months, so that the Longchuan station is divided into two stages of 1954-1973 and 1974-2009; the river source station is influenced by a maple dam and a Xinfeng river reservoir, and the time of the stage before the influence of the Xinfeng river reservoir is too short from 1954 to 1959, and the river source station is not separately segmented, so that the segmentation of the river source station is the same as that of the Longchuan station; the bosro station is influenced by the Xinfengjiang and the maple dam, and is also provided with a white basin bead reservoir of the Xizhijiang, so that three time stages are divided: 1954-1973, 1974-1984, and 1985-2009.
2. Determination of time-varying threshold value and POT sample extraction
2.1 time-varying threshold value determined by regression quantile
Extracting independent flood peaks based on the daily flow sequence, preliminarily extracting a POT sequence by taking the average POT annual occurrence frequency mu as 10, and extracting POT flood peak samples with time-varying threshold values by taking 75% regression quantiles of the POT sequence as threshold values, wherein the average POT annual occurrence frequency mu of the extracted flood peak sequence is 2.5, fig. 5 shows flood peak flow extracted by taking each station mu as 10 and corresponding 75% percentile threshold values, and flood peak flow located above a time-varying threshold value curve is the POT sequence extracted according to the time-varying threshold values.
2.2 segmentation threshold
As shown in fig. 6, a POT sequence is extracted in a segmented manner for the daily flow sequence according to the starting water storage time of the upstream reservoir of each hydrological station, the number of times of occurrence of POT year in each time period is 2.5, fig. 6 shows the peak flow extracted when each station μ is 10 and the threshold value in each time period, and the peak flow above the threshold value curve is the POT sequence extracted according to the time-varying threshold value.
2.3 sequence non-identity diagnosis
And performing trend test on the POT sequence extracted by the time-varying threshold value and the corresponding POT sequence occurrence frequency sequence by adopting an M-K method. According to the M-K test result, a 5% significance level is obtained, POT samples extracted by linear time varying and segmented threshold values are adopted, the corresponding annual occurrence frequency sequences do not have significant trends, and it can be seen that the annual occurrence frequency sequences of the overdetermined samples extracted based on the time varying threshold values meet the consistency assumption. The pott sequences of the Longchuan and river source stations have a significant decline, and the pott sequences of the Boruo station have a decline, but the significance level is not up to 5%.
Comparing the M-K test results of POT annual occurrence frequency sequences obtained by the quantile regression threshold value and the segmentation threshold value, the annual occurrence frequency sequence trend is smaller when the quantile regression threshold value is adopted by the Longchuan and river source stations, and the annual occurrence frequency sequence trend is smaller when the segmentation threshold value is adopted by the Borot station. Therefore, when the over-quantitative flood frequency analysis considering the inter-moment is carried out, POT sequences extracted by digit regression threshold values are adopted by the Longchuan and river source stations, and POT sequences extracted by segmentation threshold values are adopted by the Borro station.
2.4 optimal Trend model selection
And selecting an optimal trend model of POT sequence mean values and standard deviations obtained by time-varying threshold values of the three stations in the east river according to an AIC criterion, selecting the model with the minimum AIC value as an optimal trend, and selecting the POT sequence mean values and standard deviations as parabolic trends for the Longchuan and river-sourced Boro stations which are optimal in CP trend, wherein the POT sequence mean values and standard deviations are related in a fixed ratio (CV). 3. Line type corresponding law and design flood peak flow change under variable environment
3.1 flood line type response law in variable environment
Under the influence of reservoir regulation, POT flood peak flow extracted by Longchuan and river-source Boro stations according to time-varying threshold values still has a descending trend. In order to research the situation of flood frequency curves in different change stages, the influence of hydraulic engineering (mainly water storage) on the design flood peak flow is analyzed, and an optimal trend model of POT sequence mean values and standard deviations obtained by time-varying threshold values of the three stations in the east river is selected according to the AIC criterion. And reconstructing the POT sequence extracted according to the time-varying threshold value into a stable POT sequence under each characteristic time reference point, and selecting the time reference point according to a selection basis. As shown in fig. 7, a flood frequency curve is drawn according to the stable POT sequences of each time reference point, and compared with the flood frequency wiring result without considering the moment trend characteristics of the POT sequence samples. The 3 time reference points of the Longchuan station represent the conditions before, after and under the current situation of the maple dam reservoir in 1962, 1989 and 2009, respectively. Before the influence of the water regulation of the maple dam, 1962 is taken as a representative time reference point: compared with POT and GP flood frequency curves when POT sample moment trend (S model) is not considered, POT sample point data reconstructed by taking the year as a time reference point is above actual measurement POT sample point data, and the high water tail end of the GP-CP frequency curve is steeper. In the stage after the maple dam reservoir is built in 1989 and 2009, the positions of GP-CP curves corresponding to the two time base points are both below GP-S curves, and it can be seen that the probability of the same-quantity flood is reduced, which shows that the influence of the over-quantitative flood peak of the Longchuan station on the regulation and storage of the reservoir is obviously caused by the GP-CP curve in 1989, but the corresponding threshold value in 2009 is smaller than 1989, so the relationship of the two time points on the designated standard design flood peak magnitude is to be further analyzed.
The 4 temporal reference points for the river source station were 1956, 1966, 1989 and 2009. Before the reservoir of the Xinfeng river reservoir is built, the flow of the river source station is not influenced by water regulation and storage, the POT sequence reconstructed at the time reference point in 1956 and the GP-CP curve are positioned at the top of the frequency of each time base point, and the occurrence probability of a large amount of levels of flood is large. The water storage of the Xinfeng river reservoir and the influence of the adjustment and storage of the Xinfeng river before the construction of the maple dam reservoir are influenced, and the GP-CP curve at the time base point of 1966 years is reduced. After the maple dam reservoir is built, the maple dam reservoir is influenced by water storage of two large reservoirs, frequency curves in 1989 and 2009 are both below GP-S curves, and occurrence probability of flood is remarkably reduced. The GP-CP curve in 2009 was above the curve in 1989, but the corresponding threshold in 2009 was less than 1989. The change rule of the frequency curves of the different time reference points of the river source station is similar to that of the Longchuan station.
The 5 temporal reference points for bosro station were 1956, 1966, 1978, 1994 and 2009, respectively. The GP-CP frequency curves in 1956, 1966 and 1978 have gradually flattened high water tails and shifted down the curve position where the frequency curve in 1966 is more similar to the GP-S curve. The frequency change characteristics of the above time points show that the occurrence probability of the flood is remarkably reduced. The GP-CP curve in 1994 is almost coincident with that in 1978, but the corresponding threshold value in 1994 is less than 1978, so the probability of occurrence of flood in 1994 is less than 1978. The frequency curve in 2009 is located above the curve in 1994, the corresponding threshold values of the two time reference points are the same as those of the accident curve, and the corresponding threshold values of the two time reference points are the same as those of the accident curve, so that the probability of occurrence of flood in 2009 is greater than that in 1994, and the relationship with the design values of other time points is to be further analyzed.
3.2 design features of peak flow variation
After considering the time variation of the threshold value and the variation trends of the mean value and the standard deviation of the POT sequence, the design flood peak flow of the standard is designated as the amount which varies along with the time, and in order to discuss the influence of the variation environment on the design flood peak flow, the variation process of the flood peak flow in 1954-2009 under the pointing standard (one meeting in 100 years) is analyzed on the basis of the previously selected optimal trend model of each station.
A stable model, namely that the peak flow rate is 7141m when the Longchuan station meets the peak in 100 years under the condition that the threshold value is fixed and the moment time variation of the super-quantitative sample is not considered3And s. Considering the linear time change of the threshold value and the time change of the POT sample moment in the CP trend, the flow of the design flood peak is firstly reduced and the change amplitude is gradually reduced in 100 years in the Longchuan station along with the time; flood level is about 12000m in 19543The/s is reduced to 4000m3Per s, peak flow increased after 1995.
The design flood peak is 10748m calculated in 100 years under the stable condition of the river source station3And/s, after linear time variation of the threshold value is considered and the POT sample moment is time-varied according to the CP trend, designing the peak flow variation characteristic to be similar to that of the Longchuan station but the variation amplitude is larger than that of the Longchuan station. About 15000m flood level in 19543S, reduced to 4100m by 19953S, increased after 1995, greater than 5000m in 20093/s。
The calculated 100-year-one-meeting design flood peak under the stable condition of the Boruostation is 13032m3And s. The threshold value of the Borot station is time-varying in segments, and the POT sample moment is changed according to the CP trend. Because the threshold values are taken at different stages, the Polo station 100 encounters a non-smooth curve of the designed flood peak change process every year, but has mutations in 1974 and 1985. In two stages of 1973 of 1954-.
The time-varying situation of the design flood peak flow under the specified standard (one hundred years) shows that the design flood peak flow magnitude of the specified standard of the three stations in east China river generally has a trend of decreasing from large to small and increasing back to the high. If the non-uniformity processing of the sequence is not considered, the traditional method is adopted to calculate the design flood of Longchuan, river source and Boruostation for one hundred years to be 7141m3/s、10748m3S and 13032m3And s. After considering the time variation of the threshold value and the variation trend of the POT sample moment, the design flood peak value calculated by the traditional method appears in the period of 1960-.
3.3 comparison of non-uniformity methods with conventional methods for the recurrence period
And taking the current 2009 as a time reference point, and specifying the difference degree between the standard flood peak flow and the traditional analysis result based on the consistency assumption after considering the inconsistent processing of threshold value change. The trend term is represented by SS, and does not consider the time variation of a threshold value, or consider the time variation of the threshold value, or the time variation of the POT sample moment in a stable state; MS represents the time variation of the threshold value, and the POT sample moment is stable; e _ MS represents the difference degree between the set value calculated by the MS model and the SS model design value.
Table 2 shows that: after the consistency of the Longchuan stations is processed, the designed flood peaks are all smaller than the calculation result based on the consistency assumption; only considering the calculation of time varying threshold value and the hypothesis of flood peak difference degree based on consistency is about 10%, and the difference degree is slightly reduced along with the increase of the recurrence period; when the POT sample moment changes with the CP trend in consideration of the threshold value, the difference degree of the calculation result with the traditional method is more than 30%, and the difference degree increases along with the increase of the recurrence period. After the inconsistency processing of the river source station, the design flood peaks are smaller than the calculation result based on the consistency assumption, the difference degree is increased along with the increase of the recurrence period, and the situation that the difference degree of the time variation of the POT sample moment is larger than the situation that the time variation of the POT sample moment is not considered is considered; when the recurrence period is 100 years, the difference degree between the MS model and the SS model reaches 25 percent, and the difference degree between the CP model and the SS model reaches 51 percent. The calculation result of the Brookfield MS model is smaller than that of the SS model, the difference degree is increased along with the increase of the recurrence period, and the difference degree is 15% in the 100-year recurrence period; the relation between the CP model and the SS model is different from that of a Longchuan and a river source station, when the reproduction period is less than 20, the calculation result of the CP model is slightly larger than that of the SS model, after the reproduction period exceeds 30 years, the calculation result of the CP model is smaller than that of the SS model, the difference degree increases along with the increase of the reproduction period, and the difference degree is 5.5% when the reproduction period is 100 years.
Table 2 the same or similar reference numerals as those used in the conventional method for estimating the degree of difference between the design peaks correspond to the same or similar components in the time-varying threshold processing (t0 ═ 2009);
the terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (2)
1. A method for analyzing the non-uniformity of ultra-quantitative flood in a changing environment is characterized by comprising the following steps:
selecting a sample: carrying out flood frequency analysis by considering historical flood, determining a threshold value, and screening a sample sequence by adopting an over-quantitative sampling method;
sequence non-identity diagnosis: judging whether the sequence has jump variation and trend variation of the extra flood, and carrying out ultra-quantitative flood frequency analysis on two different conditions of the jump and the trend by using different methods; for jump variation, performing overdetermined flood frequency analysis considering historical flood, combining the selected continuous POT samples with the historical flood to form discontinuous POT samples, and performing flood frequency analysis on each sample segment sequence; analyzing the trend variation by using a non-uniform over-quantitative flood frequency, analyzing a non-uniform annual maximum daily flow sequence by using a TVM (transient voltage model), fitting an AMS (automatic maintenance machine) sequence and analyzing the non-uniform flood frequency;
the sequence non-consistency diagnosis utilizes M-K trend analysis to judge the trend and the jump of the flood sequence; different flood frequency analysis methods are adopted for different flood sequences; the non-consistency over-quantitative flood frequency analysis method comprises a fixed threshold value time-varying moment method and a time-varying threshold value time-varying moment method;
the fixed threshold value time-varying moment method is a non-consistency processing method which determines a unique fixed threshold value, selects different probability distributions in flood frequency analysis and constructs different TVM models by considering different trends of the first two moments of a sequence;
the time-varying threshold value and time-varying moment method is characterized in that the time-varying threshold value of temperature inconsistency research is applied to extraction of a flood over-quantitative sample, a regression quantile is adopted to calculate the time-varying threshold value, a segmented threshold value is determined according to the regulation and storage conditions of a reservoir in a watershed, and the inconsistency of flood occurrence times is considered during sampling; the method comprises the following specific steps of determining a segmentation threshold value according to the regulation and storage condition of the reservoir in the drainage basin: the measured flow data is divided into different time intervals, and an ultra-quantitative sample is independently extracted through the number of times of occurrence in a given year in each time phase, so that the threshold value of the corresponding phase is determined.
2. The method of analyzing the non-uniformity of ultra-quantitative floods under varying environments of claim 1, wherein all thresholds are determined according to an independence criterion and an ultra-quantitative threshold selection criterion.
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Application publication date: 20170818 Assignee: Guangzhou Kangpusi Network Technology Co.,Ltd. Assignor: SUN YAT-SEN University Contract record no.: X2023980054174 Denomination of invention: A method for analyzing non consistency of ultra quantitative floods in changing environments Granted publication date: 20200814 License type: Common License Record date: 20231227 Application publication date: 20170818 Assignee: Huanyi (Guangdong) emergency safety Technology Group Co.,Ltd. Assignor: SUN YAT-SEN University Contract record no.: X2023980053955 Denomination of invention: A method for analyzing non consistency of ultra quantitative floods in changing environments Granted publication date: 20200814 License type: Common License Record date: 20231225 |