CN110287605A - A kind of Tongjiang lake level analogy method based on Copula function - Google Patents
A kind of Tongjiang lake level analogy method based on Copula function Download PDFInfo
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Abstract
The Tongjiang lake level analogy method based on Copula function that the invention discloses a kind of, by collecting, outer river position, basin becomes a mandarin and lake level data, on the basis of determining marginal probability distribution function, utilize the joint probability distribution function that Copula function constructs outer river position, basin becomes a mandarin with lake level, and then inquire into given outer river position, when basin becomes a mandarin lake level conditional probability distribution function, to carry out lake level simulation and analysis of uncertainty.The present invention can not only describe outer river position, basin becomes a mandarin with the abnormal feature of lake level and effectively capture non-linear, Singular variance correlation structure, statistical theory basis is stronger, applied widely, but also the uncertainty that can be simulated with quantitative assessment lake level.
Description
Technical field
The invention belongs to lake hydrology field, in particular to a kind of Tongjiang lake level simulation based on Copula function
Method.
Background technique
Water level is that characterization Lake Water end of loveization most directly manages lake with most important index, accurate simulation lake level
Reason is of great significance with protection.The double influence that Tongjiang lake level is become a mandarin by outer river position and basin, lake level and
Reciprocation between its influence factor is extremely complex.
Currently used water-level simulation method is divided into two class of hydrodynamic model and statistical model.Although hydrodynamic model is simulated
Precision is high, but this method needs detailed topographic(al) data, data boundary and parameter information, and these data are often difficult to obtain,
In addition hydrodynamic model needs to spend a large amount of runing time, these factors all limit hydrodynamic model in reality to a certain extent
Application in border.Statistical model mainly linear regression model, gradually linear regression model, BP neural network model and support to
Measure regression model etc..Wherein, linear regression model (LRM) and gradually linear regression model are difficult to reflect lake level and its influence factor
Between non-linear relation；The network structure of BP neural network model determines there is no unified and complete theoretical direction so far, and one
As can only be selected by experience；When support vector regression model will expend a large amount of machine memory and operation when number of samples is very big
Between, cause to be difficult to carry out large-scale training sample.In addition, existing Tongjiang lake level method can only simulate to obtain one really
Qualitative Lake Water place value, can not assess the uncertainty of this analogue value.
Copula function can construct the Joint Distribution for multiple stochastic variables that edge distribution is Arbitrary distribution, and then solve
The analytical expression of condition distribution, can preferably capture non-linear, the abnormal, Singular variance feature between stochastic variable, in the hydrology
Field of water resources is widely used.It is ground currently, Copula function is introduced the simulation of Tongjiang lake level without document
In studying carefully.
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of Tongjiang lake level mould based on Copula function
Quasi- method.
In order to solve the above technical problems, the present invention adopts the following technical scheme that: a kind of Tongjiang based on Copula function
Lake level analogy method, comprising steps of
Step 1, collect that outer river position, basin becomes a mandarin and lake level data；
Step 2, it is become a mandarin according to outer river position, the basin in step 1 and lake level data, chooses marginal probability appropriate
Distribution function line style, and estimate the parameter of marginal probability distribution function；
Step 3, according to the series of samples in step 1, using river position outside Copula construction of function, basin becomes a mandarin and lake
The joint probability distribution function of water level, and estimate the parameter of Copula function；
Step 4, the joint probability distribution function that the marginal probability distribution function and step 3 estimated according to step 2 construct pushes away
The conditional probability distribution function of lake level when given outer river position, basin being asked to become a mandarin；
Step 5, according to the resulting conditional probability distribution function of step 4, lake level simulation and analysis of uncertainty are carried out.
In the step 2, Gamma is distributed to the marginal probability distribution to become a mandarin as outer river position, basin with lake level
Function line style.
In the step 2, using the parameter of linear Moment method estimators marginal probability distribution function.
In the step 3, using river position outside Gumbel-Hougaard Copula construction of function, basin becomes a mandarin and lake
The joint probability distribution function of water level estimates the asymmetric Gumbel-Hougaard of two and three dimensions using maximum-likelihood method
The parameter of Copula function.
Outer river position, basin becomes a mandarin and lake level data by collecting by the present invention, is determining marginal probability distribution function
On the basis of, using the joint probability distribution function that Copula function constructs outer river position, basin becomes a mandarin with lake level, in turn
Inquire into given outer river position, when basin becomes a mandarin lake level conditional probability distribution function, carry out lake level on this basis
Simulation and analysis of uncertainty.
Compared with prior art, the beneficial effects of the present invention are:
The present invention can not only describe outer river position, basin becomes a mandarin with the abnormal feature of lake level and effectively capture it is non-thread
Property, Singular variance correlation structure, statistical theory basis is stronger, applied widely, but also can be with quantitative assessment lake level
The uncertainty of simulation.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is Lakes schematic diagram in Tongjiang of the present invention.
Fig. 3 is that the present invention is based on the Tongjiang lake levels of Copula function to simulate schematic diagram.
Specific embodiment
The invention will be further described below by way of examples and with reference to the accompanying drawings.
As shown in Figure 1-Figure 3, a kind of Tongjiang lake level analogy method based on Copula function, the outer river position of collection,
Basin becomes a mandarin and lake level data, on the basis of determining marginal probability distribution function, constructs outer river using Copula function
The joint probability distribution function that water level, basin become a mandarin with lake level, and then inquire into given outer river position, lake when basin becomes a mandarin
The conditional probability distribution function of water level, to carry out lake level simulation and analysis of uncertainty.Fig. 1 is the calculating of the present embodiment
Flow chart follows the steps below:
1. collecting, outer river position, basin becomes a mandarin and lake level data.
As shown in Fig. 2, giving Tongjiang Lakes schematic diagram.It suppose there is 3 rivers in this specific implementation and import lake.
Wherein, outer river position, stream gauging station B are represented using the water level of gaging station A1、B2And B3Flow summation becomes a mandarin as basin in the same time,
The water level of gaging station C indicates lake level, and three stochastic variables are indicated with W, Q and H respectively.This specific implementation China and foreign countries river position,
Basin becomes a mandarin and the time scale of lake level is day.This specific implementation is by the way of accordingly sampling, i.e., with lake level H
For reference standard, outer river position W is obtained and basin enters according to the become a mandarin average transmission time in Q to lake of outer river position W and basin
Flow the corresponding series of samples of Q.
2. determining that outer river position, basin becomes a mandarin and the marginal probability distribution function of lake level.
Outer river position W, basin according to obtained in step 1 become a mandarin Q and lake level H series of samples, choose side appropriate
Edge probability-distribution function line style, and estimate its parameter, this step includes two sub-steps:
2.1 selection marginal probability distribution function line styles
Due to outer river position W, basin become a mandarin Q and lake level H overall distribution frequency curves be it is unknown, usually select
The line style of energy good fit majority sample data series.Correlative study and practice have shown that, Gamma distribution can preferably be fitted day
The water level of scale, flow series.
It is become a mandarin the marginal probability of Q and lake level H using Gamma distribution as outer river position W, basin in this specific implementation
Distribution function line style.
The parameter of 2.2 estimation marginal probability distribution function line styles
After curve type of frequency distribution is selected, following step is to estimate the parameter of Gamma frequency distribution.It is currently used
Method mainly includes moments method, maximum-likelihood method, probability-weighted moment, weight-function method and linear moments method etc..Wherein, linear moments method is
The parameter value of the effective ways that domestic and foreign scholars generally acknowledge at present, estimation is more steady.
The parameter of linear Moment method estimators marginal probability distribution function line style is used in this specific implementation.
3. being constructed using Copula function, outer river position, basin becomes a mandarin and the joint probability distribution function of lake level.
Outer river position W, basin according to obtained in step 1, which become a mandarin, to be estimated in Q and lake level H series of samples and step 2
The marginal probability distribution function of meter chooses joint probability distribution of the Copula function appropriate as contiguous function construction W, Q and H
Function, and estimate its parameter, this step includes two sub-steps:
3.1 selection Copula functions
The marginal distribution function for enabling W, Q and H is respectively u1=FW(w)、u2=FQ(q) and u3=FH(h), corresponding probability is close
Spending function is respectively fW(w)、fQ(q) and fH(h)。
By Copula function, the joint probability distribution function of W and Q can be indicated are as follows:
F (w, q)=Cθ(FW(w),FQ(q))=Cθ(u1,u2) (1)
In this specific implementation, using the joint probability distribution letter of Gumbel-Hougaard Copula construction of function W and Q
Number, expression formula are as follows:
Wherein, θ is the parameter of dimensional Co pula function, and meets θ >=1.
Similarly, by Copula function, the joint probability distribution function of W, Q and H can be written as:
F (w, q, h)=Cθ(FW(w),FQ(q),FH(h))=Cθ(u1,u2,u3) (3)
In this specific implementation, using the joint of three-dimensional asymmetric Gumbel-Hougaard Copula construction of function W, Q and H
Probability-distribution function, expression formula are as follows:
Wherein, parameter θ={ θ2,θ1It is the parameter of three-dimensional Copula function, and meet θ2≥θ1≥1。
The parameter of 3.2 estimation Copula functions
The common method of the parameter of estimation Copula function has Kendall correlation coefficient process, maximum-likelihood method, limit at present
Deduction method and kernel density estimation method etc..Wherein, the thought of maximum-likelihood method is to maximize likelihood function about parameter θ, is obtained
The estimated value of parameter vector θ is widely used in the parameter Estimation of Copula function.
In this specific implementation, the asymmetric Gumbel-Hougaard Copula of two and three dimensions is estimated using maximum-likelihood method
The parameter of function.
4. given outer river position, basin become a mandarin, the conditional probability distribution function of lake level is solved.
Given outer river position W, basin become a mandarin Q value when, there is a conditional probability distribution functions by correspondence lake level H
F (h | w, q)=Pr(H≤h | W=w, Q=q) (5)
Wherein, PrRepresent the probability value of event generation.
By Copula function, conditional probability distribution function F (h | w, q) it can indicate are as follows:
Wherein,For the density function of dimensional Co pula function.
5. carrying out lake level simulation and analysis of uncertainty.
After obtaining the conditional probability distribution function F (h | w, q) of lake level H, median can be calculated as lake
The point estimate of water level H, while the interval estimation obtained under given confidence level carries out analysis of uncertainty.
The median h of lake level HmIt is solved by following formula:
F(hm| w, q)=0.5 (7)
Formula (7) are solved using dichotomy tentative calculation in this specific implementation and obtain numerical solution.
Certain confidence level (1- ξ) is selected, enabling lake level H value appear in the probability at distribution both ends is ξ, so that it may
The interval estimation of H is defined, the upper and lower limit of confidence is provided by following two formula respectively:
F(hl| w, q)=ξ1 (8)
F(hu| w, q)=1- ξ2 (9)
Wherein, ξ1+ξ2=ξ indicates significance；ξ is taken in this specific implementation1=ξ2=ξ/2.
Formula (8) are solved using dichotomy tentative calculation in this specific implementation, (9) obtain numerical solution.Therefore
P(hl≤H≤hu)=1- ξ (10)
That is [hl,hu] be lake level H confidence level (1- ξ) interval estimation, can be to Lake Water according to confidence interval
The uncertainty of position H estimated value is quantitatively evaluated.
As shown in figure 3, give actual measurement lake level, the median analog result that is calculated according to the method for the present invention and
90% uncertain simulation section comparative situation schematic diagram.Wherein, median analog result is point of conditional probability distribution 50%
Digit；Given significance ξ=0.1, ξ1=ξ2=0.05, the quantile of conditional probability distribution 5% and 95% is calculated,
The confidence lower limit and upper limit value in 90% uncertain simulation section is set forth in they.
To sum up, outer river position, basin becomes a mandarin and lake level data by collecting by the present invention, is determining marginal probability distribution
On the basis of function, the joint probability distribution function to be become a mandarin using the outer river position of Copula function building, basin with lake level,
And then inquire into given outer river position, when basin becomes a mandarin lake level conditional probability distribution function, to carry out lake level mould
Quasi- and analysis of uncertainty.The present invention can not only describe outer river position, basin becomes a mandarin and the abnormal feature of lake level and have
Effect captures non-linear, Singular variance correlation structure, and statistical theory basis is stronger, applied widely, but also can quantitatively comment
The uncertainty of valence lake level simulation.
Claims (4)
1. a kind of Tongjiang lake level analogy method based on Copula function, it is characterised in that the following steps are included:
Step 1, collect that outer river position, basin becomes a mandarin and lake level data；
Step 2, it is become a mandarin according to outer river position, the basin in step 1 and lake level data, chooses marginal probability distribution appropriate
Function line style, and estimate the parameter of marginal probability distribution function；
Step 3, according to the series of samples in step 1, using river position outside Copula construction of function, basin becomes a mandarin and lake level
Joint probability distribution function, and estimate the parameter of Copula function；
Step 4, according to step 2 estimate marginal probability distribution function and step 3 construct joint probability distribution function inquire into
The conditional probability distribution function of lake level when fixed outer river position, basin become a mandarin；
Step 5, according to the resulting conditional probability distribution function of step 4, lake level simulation and analysis of uncertainty are carried out.
2. a kind of Tongjiang lake level analogy method based on Copula function as described in claim 1, it is characterised in that:
In the step 2, Gamma is distributed to the marginal probability distribution function line style to become a mandarin as outer river position, basin with lake level.
3. a kind of Tongjiang lake level analogy method based on Copula function as described in claim 1, it is characterised in that:
In the step 2, using the parameter of linear Moment method estimators marginal probability distribution function.
4. a kind of Tongjiang lake level analogy method based on Copula function as described in claim 1, it is characterised in that:
In the step 3, using the connection that river position, basin become a mandarin with lake level outside Gumbel-Hougaard Copula construction of function
Probability-distribution function is closed, using the maximum-likelihood method estimation asymmetric Gumbel-Hougaard Copula function of two and three dimensions
Parameter.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20160110835A1 (en) * | 2014-04-04 | 2016-04-21 | Jiangsu Provincial Academy Of Environmental Science | A method for determining ecological risks of heavy metal pollution in river and lake sediments |
| CN105808868A (en) * | 2016-03-16 | 2016-07-27 | 武汉大学 | Hydrological model comprehensive uncertainty analysis method based on Copula function |
| CN107622162A (en) * | 2017-09-22 | 2018-01-23 | 江西省水利科学研究院 | A kind of rating curve calculation method based on Copula functions |
| CN109902267A (en) * | 2019-03-07 | 2019-06-18 | 江西省水利科学研究院 | A kind of river safety discharge calculation method influenced by downstream lake jacking |
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- 2019-06-27 CN CN201910568915.5A patent/CN110287605A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20160110835A1 (en) * | 2014-04-04 | 2016-04-21 | Jiangsu Provincial Academy Of Environmental Science | A method for determining ecological risks of heavy metal pollution in river and lake sediments |
| CN105808868A (en) * | 2016-03-16 | 2016-07-27 | 武汉大学 | Hydrological model comprehensive uncertainty analysis method based on Copula function |
| CN107622162A (en) * | 2017-09-22 | 2018-01-23 | 江西省水利科学研究院 | A kind of rating curve calculation method based on Copula functions |
| CN109902267A (en) * | 2019-03-07 | 2019-06-18 | 江西省水利科学研究院 | A kind of river safety discharge calculation method influenced by downstream lake jacking |
Non-Patent Citations (1)
| Title |
|---|
| 洪兴骏等: "基于Copula函数的鄱阳湖都昌站枯水多变量频率分析", 《长江科学院院报》 * |
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