CN111709147A - Hydrologic crash mechanism-based flood area composition calculation method - Google Patents
Hydrologic crash mechanism-based flood area composition calculation method Download PDFInfo
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Abstract
The invention discloses a method for calculating composition of a designed flood area based on a hydrologic failure mechanism. The invention considers the interaction between the flood volume of the upstream reservoir section and the interval and the reservoir flood regulation and the river flood evolution process, defines the flood control safety standard by the frequency that the peak flow of the flood of the design section influenced by the upstream reservoir regulation exceeds a certain specified flow, can represent the hydrologic failure mechanism, and provides a more scientific and steady method for the composition calculation of the design flood area.
Description
Technical Field
The invention belongs to the field of flood control safety design of hydraulic engineering, and particularly relates to a flood area composition calculation method based on a hydrologic crash-failure mechanism.
Background
The method is an important content for engineering design flood calculation of the watershed step reservoir group and the flood control system. Usually, a flood area design composition method is adopted, namely, the flood volume of the design section is distributed to the section and the interval of the upstream reservoir so as to research the flood regulation influence of the upstream reservoir. The scholars put forward flood distribution rules such as typical annual method, co-frequency method, JC method and Copula function method. However, there are several design flood distribution schemes with the same frequency, and the peak design values of the design cross section which is obtained by the distribution schemes and affected by the regulation of the upstream reservoir are different, so that the frequency meaning of the flood of the design cross section after the regulation of the reservoir becomes vague, and the rationality is questioned.
In fact, the most important factor in terms of designing flood area composition analysis calculations is the design cross-sectional flood peak flow affected by upstream reservoir regulation. The dangerous event and flood control risk concerned in engineering practice should be that the design section peak flow exceeds a certain specified flow. Therefore, the interaction between hydrologic load (the section and interval flood volume of the upstream reservoir) and reservoir flood regulation and river flood evolution should be emphasized more, and the flood control safety standard is defined by the frequency that the peak flow of the designed section flood influenced by the regulation and storage of the upstream reservoir exceeds a certain specified flow, so that the hydrologic crash-proof mechanism is more met, and the problem that the frequency meaning of the designed section flood after the regulation and storage of the reservoir is unclear is solved. At present, no literature researches the calculation method for designing the composition of the flood area based on the hydrologic crash mechanism.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a flood area composition calculation method based on a hydrologic crash-loss mechanism.
In order to solve the technical problems, the invention adopts the following technical scheme:
a flood area composition calculation method based on a hydrologic crash-loss mechanism comprises the following steps:
step 2, selecting a proper edge probability distribution function line type according to the upstream reservoir section and interval flood volume series data in the step 1, and estimating parameters of the edge probability distribution function line type;
step 3, selecting a proper Copula function to construct a joint probability distribution function of the section of the upstream reservoir and the interval flood according to the serial data of the section of the upstream reservoir and the interval flood in the step 1, and estimating parameters of the joint probability distribution function;
step 4, solving a conditional probability distribution function of the flood volume in the time interval of the given upstream reservoir section flood volume according to the edge probability distribution function obtained in the step 2 and the combined probability distribution function constructed in the step 3, and obtaining a design section flood peak flow probability distribution function influenced by the upstream reservoir regulation and storage by adopting a random simulation method;
and 5, calculating the designed section flood peak flow of the designated design frequency according to the probability distribution function of the designed section flood peak flow in the step 4, and calculating the designed flood area composition based on the hydrologic crash-loss mechanism.
In the step 2, P-III type distribution is adopted as an edge probability distribution function line type of the upstream reservoir section and the interval flood, and parameters of the edge probability distribution function line type of the upstream reservoir section and the interval flood are estimated by adopting a linear moment method.
In the step 3, a Gumbel-Hougaard Copula function is adopted to construct a joint probability distribution function of the cross section of the upstream reservoir and the regional flood volume, and a Kendall rank correlation coefficient method is adopted to estimate parameters of the Gumbel-Hougaard Copula function.
The invention collects and arranges flood data of the sections and intervals of the upstream reservoir, determines the edge probability distribution function of the sections and the intervals of the upstream reservoir, constructs a joint probability distribution function of the sections and the intervals of the upstream reservoir, and calculates the peak flow probability distribution function of the design sections influenced by the regulation and storage of the upstream reservoir, thereby calculating the composition of the design flood area based on the hydrologic failure mechanism.
Compared with the prior art, the invention has the beneficial effects that:
the invention considers the interaction between the flood volume of the upstream reservoir section and the interval and the reservoir flood regulation and the river flood evolution process, defines the flood control safety standard by the frequency that the peak flow of the flood of the design section influenced by the upstream reservoir regulation exceeds a certain specified flow, can represent the hydrologic crash-failure mechanism, and provides a more scientific and steady method for the composition calculation of the design flood area.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a probability distribution function of flood peak flow of a design section influenced by regulation and storage of an upstream reservoir.
Fig. 3 is a schematic diagram of a flood area composition based on a hydrologic crash mechanism.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings.
As shown in fig. 1 to 3, a method for calculating a composition of a designed flood area based on a hydrologic crash mechanism collects and collates flood data of sections and intervals of an upstream reservoir, determines an edge probability distribution function of the floods of the sections and the intervals of the upstream reservoir, constructs a joint probability distribution function of the sections and the intervals of the upstream reservoir, and calculates a peak flow probability distribution function of the designed sections influenced by regulation and storage of the upstream reservoir, thereby calculating the composition of the designed flood area based on the hydrologic crash mechanism. Fig. 1 is a calculation flowchart of the present embodiment, which is performed according to the following steps:
1. collecting and arranging flood data of the section and the interval of the upstream reservoir.
According to the implementation, flood process lines of the upstream reservoir section and the designed section over the years are collected and sorted, and the time interval is delta t (generally 1 hour, 3 hours and the like). The flood process line in the interval of the past year is obtained by subtracting the flood process line from the corresponding flood process line of the design section to the design section through river calculation of the upstream reservoir by the Masjing's method. And (4) counting the sections and the interval flood process lines of the upstream reservoirs in the past year and the sections and the interval flood process lines of the upstream reservoirs in the typical year based on the collected and sorted sections and interval flood process lines of the upstream reservoirs.
In the specific implementation, the flood control period is determined according to the characteristics of the flood in the drainage basin and the regulation characteristics of the upstream reservoir to the flood, and the typical year with large peak amount and capable of reflecting the composition characteristics of the flood area is selected in the typical year.
2. And determining the edge probability distribution function of the section and interval flood volume of the upstream reservoir.
Selecting a proper edge probability distribution function line type according to the flood volume series data of the section and the interval of the upstream reservoir in the step 1, and estimating parameters of the edge probability distribution function line type, wherein the step comprises two substeps:
2.1 Selective edge probability distribution function profiles
As the overall distribution frequency line type of the flood volume of the section and the interval of the upstream reservoir is unknown, the hydrologists in China find that the P-III type distribution has good fitting effect on most river flood data in China through years of analysis and comparative research, and the P-III type distribution is recommended to be adopted in engineering practice.
In the specific implementation, P-III type distribution is adopted as an edge probability distribution function line type of the flood volume of the section and the interval of the upstream reservoir.
2.2 estimating parameters of the edge probability distribution function linetype
The existing commonly used linear parameter estimation methods for the edge probability distribution function mainly include a moment method, a maximum likelihood method, a probability weight moment method, a weight function method, a linear moment method (L-moment method), and the like. The L-moment method is most characterized in that the method is sensitive to the maximum value and the minimum value of a sequence without the conventional moment, the obtained parameter estimation value is more stable, and the method is an effective parameter estimation method acknowledged at home and abroad at present.
In the specific implementation, parameters of the upstream reservoir section and interval flood edge probability distribution function line type are respectively estimated by adopting an L-moment method.
3. And constructing a joint probability distribution function of the section and interval flood volume of the upstream reservoir.
According to the series data of the section and the interval flood of the upstream reservoir in the step 1, selecting a proper Copula function to construct a combined probability distribution function of the section and the interval flood of the upstream reservoir and estimating parameters of the combined probability distribution function, wherein the step comprises two substeps:
3.1 selecting Copula function
Suppose X, Y denotes the upstream reservoir section andand the interval flood volume x and y are corresponding implementation values respectively. FX(x)、FY(Y) edge probability distribution function respectively representing upstream reservoir section flood X and interval flood Y, fX(x)、fY(y) are the corresponding edge probability density functions, respectively. The joint probability distribution function of X, Y can be represented by a two-dimensional Copula function C:
FX,Y(x,y)＝Cθ(FX(x),FY(y))＝Cθ(u,v) (1)
wherein, θ is a parameter of the Copula function; u ═ FX(x),v＝FY(y) is the edge distribution function.
In the specific implementation, a Gumbel-Hougaard Copula function is adopted to construct a combined probability distribution function of the section flood X and the interval flood Y of the upstream reservoir, and the expression is as follows:
3.2 estimating the parameters of the Copula function
In the specific implementation, a Kendall rank correlation coefficient method is adopted to estimate parameters of a Gumbel-Hougaard Copula function. The Kendall correlation coefficient tau is related to the parameter theta by:
let { (x)1,y1),…,(xn,yn) Denotes random samples of n observations taken from successive random variables (X, Y), among which are samples
Different combinations of observations (x)i,yi) And (x)j,yj). The Kendall rank correlation coefficient tau of the sample is calculated by the following formula
Where sign (·) is a sign function.
4. And (5) calculating a design section flood peak flow probability distribution function influenced by the regulation and storage of the upstream reservoir.
Solving a conditional probability distribution function of the flood volume of the interval when the section flood volume of the upstream reservoir is given according to the edge probability distribution function obtained by the step 2 and the combined probability distribution function constructed by the step 3, and obtaining a design section flood peak flow probability distribution function influenced by the regulation and storage of the upstream reservoir by adopting a random simulation method, wherein the step comprises two substeps:
4.1 solving conditional probability distribution function
When the value X of the section flood volume X of the upstream reservoir is given, the value of the interval flood volume Y is not unique, and a conditional probability distribution function exists
FY|X(y)＝P(Y≤y|X＝x) (5)
By means of Copula function, conditional probability distribution function FY|X(y) may be expressed as:
substituting formula (2) into:
4.2 calculating probability distribution function of flood peak flow of designed section
In the specific implementation, a random simulation method is adopted to calculate a probability distribution function of the flood peak flow of the design section influenced by the regulation and storage of the upstream reservoir, and the basic steps are as follows:
(1) generating compliance [0,1 ]]Two independent random numbers r uniformly distributed1And r2；
(2) Let u be r1，SV|U(v)＝r2；
(3) Solving for SV|U(v)＝r2Obtaining v ═ SV|U -1(r2) In which S isV|U -1(. represents S)V|U(v) The inverse function of (c);
(4) calculating x ═ FX -1(u)，y＝FY -1(v) Obtaining a pair of upstream reservoir section and interval flood combinations (x, y), wherein FX -1(·)、FY -1(. represents respectively FX(x)、FY(y) the inverse function of (y);
(5) based on the section and the interval flood process line of the upstream reservoir in the typical year, obtaining the section and the interval design flood process line of the upstream reservoir by adopting a same-multiple-ratio amplification method;
(6) inputting the designed flood process line of the section of the upstream reservoir into the reservoir to carry out flood regulation calculation according to flood regulation rules, carrying out river course calculation on the lower flood process line to the designed section by adopting a Mass Jing root method, overlapping the lower flood process line with the section designed flood process line to obtain the designed section flood process line influenced by the regulation and storage of the upstream reservoir, and carrying out statistics to obtain a design section flood peak flow z value;
(7) repeating the steps (2) to (6) for m times, simulating m designed section flood peak flow Z values, and calculating empirical frequency by adopting a mathematical expectation formula to obtain a probability distribution function F of the designed section flood peak flow ZZ(z)。
As shown in fig. 2, a schematic diagram of a probability distribution function of flood peak flow of a design section influenced by regulation and storage of an upstream reservoir is provided. Wherein, the abscissa is the peak flow Z of the designed section, and the ordinate is the corresponding function value F of the probability distributionZ(z)。
5. Calculating the composition of the designed flood area based on the hydrologic crash mechanism.
According to the probability distribution function F of the design section flood peak flow Z in the step 4Z(z) calculating a design cross-section flood peak flow z of a specified design frequencypAnd calculating the composition of a designed flood area based on a hydrologic crash mechanism, wherein the step comprises two substeps:
5.1 calculating the design section flood peak flow of the designated design frequency
For a given design frequency p, the corresponding design profile flood peak flow zpComprises the following steps:
zp＝FZ -1(1-p) (8)
wherein, FZ -1(. represents a probability distribution function FZ(z), 1-p is the probability distribution function value for a given design frequency p.
FIG. 2 is a schematic diagram of a probability distribution function of flood peak flow of a design section affected by regulation of an upstream reservoir, where 1-p is a probability distribution function value corresponding to a design frequency p, and z ispAnd inquiring the probability distribution function value 1-p on a probability distribution function curve of the flood peak flow of the design section influenced by the regulation and storage of the upstream reservoir to obtain the corresponding flood peak flow of the design section.
5.2 calculating the composition of the flood area based on the mechanism of hydrologic crash
Screening out all the values equal to z from the values of the flood peak flow z of the m design sections simulated in the step 4pThe combination of the section of the upstream reservoir and the flood volume in the interval is provided with K pairs of (x)1,y1)，…，(xk,yk)，…， (xK,yK)。
By using (x)k,yk) Is given by a joint probability density fX,Y(xk,yk) To measure the probability of occurrence of the region composition, the calculation formula is as follows:
fX,Y(xk,yk)＝cθ(uk,vk)fX(xk)fY(yk) k＝1，2，...，K (9)
wherein, cθ(uk,vk) Probability density function which is Copula function; u. ofk＝FX(xk),vk＝FY(yk) As a function of the edge probability distribution, fX(xk)、fY(yk) Respectively, corresponding edge probability density functions.
From calculated fX,Y(x1,y1)，…，fX,Y(xk,yk)，…，fX,Y(xK,yK) Find out the combination with the maximum joint probability density
Namely the flood area design based on the hydrologic crash mechanism.
As shown in fig. 3, a schematic diagram of the composition of a designed flood area based on a hydrologic crash mechanism is given. Wherein, the abscissa is the section flood X of the upstream reservoir, and the ordinate is the interval flood Y. (x)1,y1)，…，(xk,yk)，…， (xK,yK) For K pairs to satisfy the design that the peak flow of the section is equal to zpThe section and the interval flood volume of the upstream reservoir are combined,
and (4) designing the flood area composition for the combination with the maximum joint probability density, namely the calculated hydrologic crash mechanism-based design flood area composition.
In conclusion, the invention collects and arranges flood data of the sections and intervals of the upstream reservoir, determines the edge probability distribution function of the sections and the intervals of the upstream reservoir, constructs a combined probability distribution function of the sections and the intervals of the upstream reservoir, and calculates the design section flood peak flow probability distribution function influenced by the regulation and storage of the upstream reservoir, thereby calculating the composition of the design flood area based on the hydrologic failure mechanism. The invention considers the interaction between the flood volume of the upstream reservoir section and the interval and the reservoir flood regulation and the river flood evolution process, defines the flood control safety standard by the frequency that the peak flow of the flood of the design section influenced by the upstream reservoir regulation exceeds a certain specified flow, can represent the hydrologic failure mechanism, and provides a more scientific and steady method for the composition calculation of the design flood area.
Claims (3)
1. A flood area composition calculation method based on a hydrologic crash-loss mechanism is characterized by comprising the following steps:
step 1, collecting and arranging flood data of the section and the interval of an upstream reservoir;
step 2, selecting a proper edge probability distribution function line type according to the upstream reservoir section and interval flood volume series data in the step 1, and estimating parameters of the edge probability distribution function line type;
step 3, selecting a proper Copula function to construct a joint probability distribution function of the section of the upstream reservoir and the interval flood according to the serial data of the section of the upstream reservoir and the interval flood in the step 1, and estimating parameters of the joint probability distribution function;
step 4, solving a conditional probability distribution function of the flood volume in the time interval of the given upstream reservoir section flood volume according to the edge probability distribution function obtained in the step 2 and the combined probability distribution function constructed in the step 3, and obtaining a design section flood peak flow probability distribution function influenced by the upstream reservoir regulation and storage by adopting a random simulation method;
and 5, calculating the designed section flood peak flow of the designated design frequency according to the probability distribution function of the designed section flood peak flow in the step 4, and calculating the designed flood area composition based on the hydrologic crash-loss mechanism.
2. The flood area composition calculation method based on the hydrologic crash mechanism as claimed in claim 1, wherein: in the step 2, P-III type distribution is adopted as the edge probability distribution function linear type of the flood volume of the upstream reservoir section and the interval, and parameters of the edge probability distribution function linear type of the flood volume of the upstream reservoir section and the interval are estimated by adopting a linear moment method.
3. The flood area composition calculation method based on the hydrologic crash mechanism as claimed in claim 1, wherein: in the step 3, a Gumbel-Hougaard Copula function is adopted to construct a joint probability distribution function of the section and the interval flood of the upstream reservoir, and a Kendall rank correlation coefficient method is adopted to estimate parameters of the Gumbel-Hougaard Copula function.
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