CN109408989B - Method for calculating flood process line - Google Patents
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Abstract
The invention provides a method for calculating a design flood process line, which comprises the following steps: selecting a flood peak and a flood volume sequence in a plurality of time periods by adopting a maximum value method; performing trend analysis on the flood peak and the flood volume sequence in multiple periods by adopting a Mann-Kendall method, and fitting by adopting a GALSS model according to the trend analysis result; calculating time-varying Kendall coefficients of a flood peak and the flood volume in each period, fitting a Kendall coefficient sequence by adopting an ARIMA model, and converting the Kendall coefficients into Copula parameters according to a correlation coefficient method; calculating condition distribution of each time period based on a flood peak univariate recurrence period; amplifying the typical flood process line. The method fully considers the time-varying property of the extreme value sequences of the flood and the time-varying property of the correlation between the extreme value sequences, better accords with the actual condition and has higher reliability.
Description
Technical Field
The invention relates to the field of engineering hydrology, in particular to a method for calculating a flood process line.
Background
The premise of the application of the calculation method for designing the flood process line at present is that a flood extreme value sequence meets the assumption of stationarity. The process comprises the following steps: firstly, calculating a flood design value, and fitting by adopting a Pearson distribution function under a consistency condition; in the second step of flood process line amplification, the traditional same frequency amplification method is adopted to take the flood peak and the flood volume as two independent variables for respective amplification, and the correlation between the two variables is not considered. In essence, due to human activities and climate changes, the phenomenon of non-uniformity of hydrologic sequences is increasingly prominent, a traditional pearson distribution function cannot depict the changes, and in consideration of the inherent hydrologic law, a certain correlation exists between flood peaks and flood volume sequences, the correlation also has time-varying property due to climate changes, and the flood peaks and the flood volumes do not always occur at the same frequency in general. Therefore, if the conventional method is still adopted, the two time-varying characteristics are often neglected, the reliability of the result is questioned, and the flood risk is often overestimated or underestimated.
At present, researchers also consider the influence of environmental changes on the flood extremum events and study the inconsistency of the distribution function of the extremum sequences, but fail to consider that the correlation between the extremum sequences also changes along with the change of the climate environment.
Disclosure of Invention
In order to solve the defects and shortcomings in the prior art, the invention provides a method for designing a flood process line, which fully considers the time-varying property of the extreme value sequences of the flood and the time-varying property of the correlation among the extreme value sequences.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for calculating a flood process line comprises the following steps:
selecting a flood peak and a plurality of period flood volume sequences according to the existing flood sequence;
performing trend analysis on the selected flood peak and the flood quantity sequences in multiple time periods, and fitting the flood peak with trend change and the flood quantity sequences in multiple time periods by adopting a GALSS model according to the trend analysis result;
calculating Kendall correlation coefficients between the flood peak and the flood volume in each period, and fitting the Kendall correlation coefficients;
predicting Kendall correlation coefficients between a flood peak of a certain year and the flood volume of each period according to the fitting result, and obtaining a Copula function and parameters thereof between two variables according to a correlation coefficient method;
establishing joint distribution according to the GALSS model, the Copula function and parameters thereof, and calculating the most possible design value of the flood volume in each time period under the condition distribution based on the flood peak frequency by adopting a flood peak single variable design value as a control condition;
and amplifying the typical flood process line according to the obtained design value.
Further, when GALSS model fitting is adopted, fitting is carried out by taking the annual maximum rainfall as a covariate, a proper extreme value distribution function is selected, and model time-varying parameters are estimated.
Further, parameters in the GAMLSS model are fitted by a maximum likelihood method, preference is given according to the minimum criterion of AIC, and fitting evaluation is carried out by using a Worm graph and a QQ graph.
Further, the Kendall correlation coefficient is calculated by adopting a sliding window method, and the two variables of the flood peak and the flood amount in a certain control period are respectively set as X ═ X (X) 1 ,x 2 …x N )、Y＝(y 1 ,y 2 …y N ) Wherein N represents the total length of the flood peak or the flood sequence in the period, and the calculation formula is as follows:
in the formula, τ t Is the t-th Kendall correlation coefficient, t is more than or equal to 1 and less than or equal to N-N, N is the length of the sliding window, x i 、y i Respectively represents the ith value of two random variables, t is not less than i and not more than t + n-1, x j 、y j J is more than or equal to t +1 and less than or equal to t + n; sgn is the indicator function:
the Kendall correlation coefficients are considered as a time series.
Further, an ARIMA (p, d, q) autoregressive model is adopted to fit the Kendall correlation coefficient, wherein p is an autoregressive term, q is the number of moving average terms, and d is the difference times when the time sequence becomes stable, and the method comprises the following steps:
the method comprises the following steps: carrying out stability inspection on the Kendall correlation coefficient sequence, and entering the next step if the Kendall correlation coefficient sequence passes the stability inspection; if not, continuously differentiating the sequence until the differentiated sequence meets the stationarity test and using the unit root ADF for testing;
step two: obtaining difference times d of the model through the step I; and (p, q) traversing the combination by taking the AIC information criterion as a criterion and combining the ACF and the PACF graph to define the range of the autoregressive term p and the moving average term number q, and finding out the (p, q) combination model with the minimum AIC value.
Further, the Copula function and the parameters thereof between the two variables are obtained according to a correlation coefficient method, and the Copula function and the parameters thereof comprise: and (3) fitting by using Gumbel-Houggard Copula in hydrologic sequence analysis only by considering the variable parameters Copula and not considering the variable structure Copula, namely the corresponding Copula parameter calculation formula is as follows:
in the formula, theta t Is a parameter of Copula at time t;
the corresponding Copula function is expressed in the form:
wherein u is F X (x) Denotes the edge distribution of the flood peak, v ═ F Y (y) represents the edge distribution of the period flood.
Further, the flood peak one-hundred-year-round is taken as a condition, and the most possible design value of the flood volume in each period under the condition distribution is calculated.
And further dividing the typical flood process line into three sections according to the calculated design value.
Further, the method further comprises: and (5) smoothing a typical flood process line.
Compared with the prior art, the time-varying characteristics of the flood peak and the flood volume in each period and the time-varying characteristics of the correlation between the flood peak and the flood volume in each period are fully considered, a more scientific and reasonable calculation method which is more in line with the actual situation is provided for the calculation of the design of the flood process line, and the reliability of the flood risk estimated by using the method is higher.
Drawings
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 shows the Kendall coefficients fitted and the prediction and confidence intervals over 10 years;
wherein the solid line is a Kendall coefficient measured value, the dot-dash line is a model fitting value, the dotted line is a predicted value within 10 years, and the gray filling part is a 95% confidence interval;
FIG. 3 shows a comparative graph of a one hundred year flood process line for 2016 calculated using the method of the present invention;
fig. 4 shows a comparison graph of the hundred year flood process lines in 2017, which are calculated by the method.
Detailed Description
The invention is further described with reference to specific examples. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1, which is a flowchart of a method for planning a flood process line according to an embodiment of the present invention, a flood sequence in 65 years in 1951 and 2015 at a kindergarten station is taken as an example:
step (1): and selecting a maximum flood extreme value sample sequence (including a flood peak, a maximum flood amount of 30d and a maximum flood amount of 60 d) in the year by adopting a maximum-value-in-year method.
Step (2): and (2) performing trend analysis on the extreme value sequences in the step (1) by adopting a Mann-Kendall method, wherein the result shows that the extreme value sequences have non-uniformity of different degrees.
And (3): and (3) fitting the extreme value sequence with trend change by adopting a GAMLSS model according to the analysis result in the step (2):
g k (θ k )＝X k β k
wherein, theta k Representing k statistical parameters of the distribution, the mean value theta is mainly considered in the embodiment 1 And variance θ 2 Two parameters, i.e. theta k ＝(θ 1 ,θ 2 )，β k Is of length J k Regression coefficient vector (J) k Is equal to the number of additive terms in the covariate function), X) k Is n × J k The interpretation variable matrix of (1) is the maximum rainfall, and a linear equation is adopted as a parameter function form (a cubic linear equation is selected here), so that the interpretation variable matrix and the regression coefficient vector are respectively:
wherein P represents the maximum rainfall, and a parameter theta in a distribution function is established k The relation with covariate factor (selecting the maximum rainfall P of Xinyang station year), fitting the parameters in the model by using maximum likelihood method, optimizing the model according to the minimum criterion of AIC, and performing fitting evaluation by using word graph and QQ graph, wherein the result shows thatBoth the two selected optimal distribution functions are Gamma distribution, the function form of the parameter adopts a linear function, and a cubic linear equation (namely J) is selected k Is 3).
And (4): kendall correlation coefficient description is adopted for the correlation relationship between the flood peak and the flood volume in each period, Kendall coefficients for 65 years are calculated by adopting a sliding window method, and the two variables of the flood peak and the maximum flood volume in 30 days (or the maximum flood volume in 60 days) are respectively set as X ═ X (X ═ X) 1 ,x 2 …x N )、Y＝(y 1 ,y 2 …y N ) Where N represents the total length of the flood peak or the maximum flood volume of 30 days (or the maximum flood volume of 60 days), N is 65 in this embodiment, the length of the sliding window is selected to be 35 years, and the sliding step is set to be 1 year, i.e. τ 1 The correlation coefficient, τ, in 1951- 2 The correlation coefficients in 1952-1986 are shown, and by analogy, 30 Kendall coefficients are calculated, and each Kendall coefficient is calculated by the following formula:
in the formula, τ t Is the t (t is more than or equal to 1 and less than or equal to N-N) Kendall coefficient, N is the sample length (i.e. the length of the sliding window), N is 35 in the embodiment, and x is x when the flood peak and the maximum flood volume of 30 days are researched i 、y i Respectively representing the ith (i is more than or equal to t and less than or equal to t + n-1) value, x, of the flood peak and the maximum flood amount of 30 days j 、y j J (t +1 is not more than j not more than t + n) values respectively representing the peak and the maximum flood amount of 30 days, and the same is also applied when the peak and the maximum flood amount of 60 days are researched. sgn is an indicator function, the corresponding form is:
and (5): considering the Kendall coefficient as a time sequence, fitting the Kendall coefficient by adopting an ARIMA (p, d, q) autoregressive model for the Kendall coefficient, wherein p is an autoregressive term, q is the number of moving average terms, and d is the difference times when the time sequence becomes stable, and the method comprises the following steps:
the method comprises the following steps: carrying out stationarity test on the hydrological time sequence, if the hydrological time sequence passes through the stationarity test, entering the next step, if the hydrological time sequence does not pass through the stationarity test, continuously differentiating the sequence until the differentiated sequence meets the stationarity test, and testing by using a unit root ADF;
step two: obtaining difference times d of the model through the step I; and (p, q) traversing the combination by taking the AIC information criterion as a criterion and combining the ACF and the PACF graph to define the range of the autoregressive term p and the moving average term number q, and finding out the (p, q) combination model with the minimum AIC value. The fitting results are shown in fig. 2, where fig. 2 (left) shows the correlation coefficient between the flood peak and the maximum 30d flood, the ARIMA (7,3,0) model is better for the fitting, fig. 2 (right) shows the correlation coefficient between the flood peak and the maximum 60d flood, the ARIMA (3,2,0) model is better for the fitting, the Kendall coefficient within 10 years is predicted according to the ARIMA model, and a 95% confidence interval is given.
And (6): calculating the parameter theta according to the conversion relation (namely a correlation coefficient method) between the Kendall coefficient and the Copula parameter t In this embodiment, only the variable parameters Copula are considered, and the variable structure Copula is not considered, fitting is performed by using Gumbel-Houggard Copula commonly used in the hydrological sequence analysis, that is, the corresponding parameters are calculated as:
in the formula, theta t For the parameters of Copula at time t,
the corresponding Copula expression form is:
wherein u is F X (x) Denotes the edge distribution of the flood peak, v ═ F Y (y) represents the edge distribution of maximum 30-day floods (or maximum 60-day floods).
And (7): establishing combined distribution according to the Copula and GALLSS models of 2016 and 2017, calculating conditional distribution, calculating maximum value of conditional probability density, and taking flood peak one hundred years as condition, that is
The corresponding most likely combination value is:
in the formula (f) 1 、f 2 Respectively represents the maximum value of the conditional probability corresponding to the maximum flood volume of 30 days and the maximum value of the conditional probability corresponding to the maximum flood volume of 60 days,
respectively representing maximum 30-day designed flood volume and maximum 60-day designed flood volume when the conditional probability density value is maximum, W 30 、W 60 Respectively representing two variables of maximum 30-day flood volume and maximum 60-day flood volume;
representing design flood peak, Q 1％ Representing a design flood peak for a century.
Determining the maximum possible values of 30 days and 60 days according to the numerical method
And
in conclusion, the design values of the flood peak and each time interval can be obtained, and the calculated design values are divided into three sections to amplify a typical flood process line of the flood reduction process in 1954:
wherein, Q, w 30 、w 60 Respectively representing the peak flood, 30-day flood and 60-day flood in 1954, wherein the amplification ratio of the peak flood is K 1 The maximum amplification factor of the peak removal part in 30 days is K 2 The amplification ratio of the part excluding the maximum 30 days in the maximum 60 days is K 3 And then, the process line at the amplification ratio junction is properly corrected, so that the designed flood process line in one hundred years of 2016 (figure 3) and 2017 (figure 4) can be obtained, and from the result, the flood peak design values are consistent under the condition of the single variable recurrence period of the flood peak, but the flood quantity difference in each period is obvious, and the influence of environmental change on the designed flood process line is reflected. Therefore, the annual design flood process line can be rechecked by combining the time-varying model under the varying environment and rainfall data.
The present invention has been disclosed in terms of the preferred embodiment, but is not intended to be limited to the embodiment, and all technical solutions obtained by substituting or converting equivalents thereof fall within the scope of the present invention.
Claims (9)
1. A method for calculating a flood process line, comprising the steps of:
selecting a flood peak and a plurality of period flood volume sequences according to the existing flood sequence;
performing trend analysis on the selected flood peak and the flood quantity sequences in multiple time periods, and fitting the flood peak with trend change and the flood quantity sequences in multiple time periods by adopting a GALSS model according to the trend analysis result;
calculating Kendall correlation coefficients between the flood peak and the flood volume in each period, and fitting the Kendall correlation coefficients;
predicting Kendall correlation coefficients between a flood peak of a certain year and the flood volume of each period according to the fitting result, and solving a Copula function and parameters between two variables according to a correlation coefficient method;
establishing joint distribution according to the GALSS model, the Copula function and parameters thereof, and calculating the most possible design value of the flood volume in each time period under the condition distribution based on the flood peak frequency by adopting a flood peak single variable design value as a control condition;
amplifying a typical flood process line according to the obtained design value;
wherein the GAMLSS model is:
g k (θ k )＝X k β k
wherein, theta k Representing k statistical parameters of the distribution, taking into account the mean value theta 1 And variance θ 2 Two parameters, theta k ＝(θ 1 ,θ 2 )；β k Is of length J k A regression coefficient vector; j. the design is a square k The value of (a) is equal to the number of additive terms in the covariate function; x k Is n × J k The interpretation variable matrix of (2); n is the sample length;
selecting an explanation variable as the maximum rainfall, adopting a linear equation as a parameter function form, and respectively expressing an explanation variable matrix and a regression coefficient vector as follows:
where P represents the maximum rainfall.
2. The method of claim 1, wherein the fitting is performed using a GALSS model fitting, wherein a maximum rainfall per year is used as a covariate, and an extreme distribution function is selected and model time-varying parameters are estimated.
3. The method of claim 2, wherein the parameters in the GALSS model are fit using maximum likelihood, are preferred according to the minimum AIC criteria, and are evaluated by fitting using a Worm graph and a QQ graph.
4. The method of claim 1, wherein the Kendall correlation coefficient is calculated by a sliding window method, and the two variables of a flood peak and a flood volume in a certain control period are X ═ X (X), respectively 1 ，x 2 …x N )、Y＝(y 1 ，y 2 …y N ) Wherein N represents the total length of the sequence of flood peaks or period floods, and the calculation formula is as follows:
in the formula, τ t Is the t-th Kendall correlation coefficient, t is more than or equal to 1 and less than or equal to N-N, N is the length of the sliding window, x i 、y i Respectively representing the ith values of two random variables, i is more than or equal to t and is less than or equal to t + n-1, x j 、y j J is more than or equal to t +1 and less than or equal to t + n; sgn is the indicator function:
the Kendall correlation coefficients are considered as a time series.
5. The method of claim 1, wherein the method of estimating a flood process line comprises fitting Kendall correlation coefficients using an ARIMA (p, d, q) autoregressive model, wherein p is an autoregressive term, q is a number of moving average terms, and d is a difference degree when a time series becomes stationary, and comprises the steps of:
the method comprises the following steps: carrying out stability inspection on the Kendall correlation coefficient sequence, and entering the next step if the Kendall correlation coefficient sequence passes the stability inspection; if not, continuously differentiating the sequence until the differentiated sequence meets the stationarity test and using the unit root ADF for testing;
step two: obtaining difference times d of the model through the step I; and (p, q) traversing the combination by taking the AIC information criterion as a criterion and combining the ACF and the PACF graph to define the range of the autoregressive term p and the moving average term number q, and finding out the (p, q) combination model with the minimum AIC value.
6. The method of claim 4, wherein the determining the Copula function and its parameters between two variables according to the correlation coefficient method comprises: and (3) fitting by using Gumbel-Houggard Copula in hydrologic sequence analysis only by considering the variable parameters Copula and not considering the variable structure Copula, namely the corresponding Copula parameter calculation formula is as follows:
in the formula, theta t Is a parameter of Copula at time t;
the corresponding Copula function is expressed in the form:
wherein u is F X (x) Denotes the edge distribution of the flood peak, v ═ F Y (y) represents the edge distribution of the period flood.
7. The method of claim 1, wherein the most probable design value of flood volume in each period under the condition of flood peak one hundred years is calculated.
8. The method of claim 1, wherein the typical flood process line is amplified in three stages according to the calculated design value.
9. The method of claim 1, wherein the method further comprises: and (5) smoothing a typical flood process line.
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| CN111984693B (en) * | 2020-07-17 | 2023-12-08 | 河海大学 | Method for pushing out design flood for large-scale river-dredging continuous lake based on Copula function |
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| CN115510631B (en) * | 2022-09-15 | 2024-03-19 | 长江水利委员会水文局 | Flood process line design method and system considering multiple flood forms |
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| CN105714729A (en) * | 2016-02-29 | 2016-06-29 | 武汉大学 | Reservoir multi-variable design flood estimating method for achieving self-adaption to weather changes |
| CN105887751A (en) * | 2016-04-28 | 2016-08-24 | 武汉大学 | Multi-variable flood recurrence period calculating method considering reservoir flood routing calculation |
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| CN104615907A (en) * | 2015-03-11 | 2015-05-13 | 武汉大学 | Method for deriving and designing flood process line based on multi-variable most possible condition combination |
| CN105714729A (en) * | 2016-02-29 | 2016-06-29 | 武汉大学 | Reservoir multi-variable design flood estimating method for achieving self-adaption to weather changes |
| CN105887751A (en) * | 2016-04-28 | 2016-08-24 | 武汉大学 | Multi-variable flood recurrence period calculating method considering reservoir flood routing calculation |
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