CN109543147A - A kind of method of the non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons - Google Patents
A kind of method of the non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons Download PDFInfo
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Abstract
The invention discloses a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship and the methods of classification, Reasons, it is first determined research basin, the annual rainfall data of collection research watershed control hydrometric station annual runoff and valley rainfall station；Obtain optimal theoretical probability-distribution function；The optimal two-dimentional joint distribution function of theory for establishing annual rainfall and annual runoff rainfall runoff relation using Archimedes family Copula function；The likelihood ratio statistics of theoretical optimal two-dimentional Joint Distribution are obtained, the likelihood ratio statistical value of sample is calculated, determines catastrophe point；Assuming that being nature period before the mutation time, and using nature period as base period, the mutation time is the period of the effect of human activity later；Rainfall Runoff Model is established, annual runoff data is reconstructed；Annual runoff data and field data are compared, analysis obtains the contribution rate that climate change and human activity influence streamflow change, and the present invention improves the efficiency and accuracy for quickly carrying out the diagnosis of Basin Rainfall runoff relationship.
Description
Technical field
The invention belongs to hydrographic features variation diagnostic method technical fields, and in particular to a kind of Basin Rainfall runoff relationship is non-
The method of linear quick diagnosis and classification, Reasons.
Background technique
In the world, river flow be human survival, life, production water resource important sources, in recent years,
Since especially reforming and opening up to the outside world, with the fast development of industrialization and urbanization, the construction of Chinese society doctrine and economic level
It is continuously improved, influence of the mankind's activity to natural environment obviously aggravates, and water resources problems also constantly highlight, while global gas
Variation is waited also to play an important role to hydrologic cycle.Therefore, science accurately evaluates mankind's activity and climate change to rivers and creeks diameter
The influence of stream is particularly significant.
For a long time, the influence of climate change and mankind's activity to river flow is the one of hydrographic water resource researcher concern
A important directions, researcher proposes trend analysis and the various single argument catastrophe point methods of inspection, but these methods are all deposited
In the serious problems that can not analyze non-linear variation between bivariate.Therefore propose that a kind of Basin Rainfall runoff relationship is non-thread
Property quick diagnosis and the method for classification, Reasons are highly important.
Summary of the invention
The object of the present invention is to provide a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship and the method for classification, Reasons,
Improve the efficiency and accuracy for quickly carrying out the diagnosis of Basin Rainfall runoff relationship.
The technical scheme adopted by the invention is that a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons
Method, be specifically implemented according to the following steps:
Step 1 determines research basin, the annual rainfall of collection research watershed control hydrometric station annual runoff and valley rainfall station
Measure data；
Step 2, according to hydrological statistics principle, determine the optimal theoretical probability distribution letter of basin annual rainfall and annual runoff
Number；
Step 3 establishes annual rainfall and annual runoff rainfall runoff relation using Archimedes family Copula function
Theoretical optimal two-dimentional joint distribution function；
The likelihood ratio statistics of step 4, the optimal two-dimentional Joint Distribution of the theory of building rainfall runoff relation, according to foundation
Likelihood ratio statistics calculate the likelihood ratio statistical value of sample, and determine catastrophe point according to the boundary threshold of likelihood ratio statistics；
Step 5, according to step 4 determine catastrophe point, it is assumed that mutation the time before be nature period, it is described nature period be
Period without the effect of human activity, and using nature period as base period, the mutation time is the period of the effect of human activity later；
The natural period of step 6, the annual rainfall and the variation of annual runoff rainfall runoff relation that are obtained according to step 5 analysis
Data establish Rainfall Runoff Model, reconstruct annual flow using the Rainfall Runoff Model established further according to the annual rainfall data of all the period of time
Amount data；
Step 7 is compared using the obtained annual runoff data of reconstruct and field data, analysis obtain climate change and
The contribution rate that human activity influences streamflow change.
The features of the present invention also characterized in that
Step 1 is specifically implemented according to the following steps:
Step 1.1 first determines that the website continuous several years for research website, are then collected in the control hydrometric station in some basin
Daily flow data, and annual annual runoff is calculated；
Step 1.2, selection basin and its near zone several rainfall website continuous several years daily precipitation datas, root
The annual face rainfall in basin is calculated according to arithmetic mean method.
Step 2 are as follows:
According to hydrological statistics principle, is examined by nonparametric Andrei Kolmogorov-Si meter Nuo Fu, use the hydrology common four
Kind probability distribution exponential distribution EXP, Geng Beier distribution GUM, gamma distribution GAM, three type of Pearson came distribution PE3 are to the step 1
In annual rainfall and annual runoff carry out probability-distribution function inspection, basin annual rainfall and Nian Jing are determined by AIC criterion
The theoretical optimum probability distribution function of flow.
The parameter Estimation of 4 kinds of theoretical probability distribution functions of basin annual rainfall and annual runoff uses linear in step 2
Moments method is estimated that calculation formula is as follows respectively:
If X is that real value is overall, distribution function is F (x)=P (X≤x), and there are inverse function x=G (F), and G (F) is also known as
Kernel smooth, for sample x1..., xn, remember order statistic: x1:n≤x2:n,....,≤xn:n,
The linear moment estimator of r rank of Hosking is as follows:
Wherein:
In formula: r is linear moment order, and n is number of samples.
The optimal theoretical probability-distribution function of basin annual rainfall and annual runoff uses nonparametric Ke Ermoge in step 2
Love-Si meter Nuo Fu is examined and AIC criterion, calculation formula are as follows:
If Sn (x) is the cumulative distribution function of random sample observed value, i.e. empirical distribution function, sample size n；Fo
(x) it is a specific cumulative distribution function, i.e. theoretic distribution function, defines D=| Sn (x)-Fo (x) |, if for
Each x value, Sn (x) and Fo (x) are close, then show that the fitting degree of empirical distribution function and theoretic distribution function is very high, reasonable
By thinking sample data from the totality for obeying the theoretical distribution；
K-S examine be absolute value D=| Sn (x)-Fo (x) | in maximum deviation, i.e., examined using following statistic
It tests:
Dmax=max | Sn (x)-Fo (x) |；
AIC information criterion calculation formula is as follows:
AIC=2k-2ln (L).
Step 4 calculation method is as follows:
Copula function likelihood ratio test method, it detects multivariable series of hydrological phase by measurement Copula Parameters variation
The change point of structure is closed, the logarithmic form of this method likelihood ratio statistics is as follows:
It is converted under conditions of height λ is unknown are as follows:
In formula, n is number of samples, ΛλIt examines as Copula function likelihood ratio statistics, λ is catastrophe point in data sequence
Position, η1For before catastrophe point sample subsequence establish Copula joint distribution function parameter, wherein comprising mutation
Point itself,For η1Estimated value, η2For the ginseng for the Copula joint distribution function that the sample subsequence after catastrophe point is established
Number,For η2Estimated value, η0For sample sequence establish Copula joint distribution function parameter,For η0Estimated value,
The boundary value of statistic Zn is taken under 5% significance, i.e., refuses null hypothesis, Joint Distribution when statistic is greater than boundary value
There are catastrophe points for dependency structure.
The boundary value of Zn is 3.69.
The invention has the advantages that the side of a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons
Method, checkout result is reliable, calculation method is simple, can be diagnosed to be drop by obtaining research annual rainfall data and annual flow data
Rain runoff relationship changes time and climate change and mankind's activity to the contribution rate of runoff.
Detailed description of the invention
Fig. 1 is Wudinghe River in a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship of the present invention and the method for classification, Reasons
Basin Rainfall runoff is mutated time diagnostic result schematic diagram；
Fig. 2 is Wudinghe River in a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship of the present invention and the method for classification, Reasons
Watershed Runoff changes classification, Reasons contribution rate schematic diagram of calculation result.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The method of a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship of the present invention and classification, Reasons, specifically according to following
Step is implemented:
Step 1 determines research basin, the annual rainfall of collection research watershed control hydrometric station annual runoff and valley rainfall station
Data are measured, are specifically implemented according to the following steps:
Step 1.1 first determines that the website continuous several years for research website, are then collected in the control hydrometric station in some basin
Daily flow data, and annual annual runoff is calculated；
Step 1.2, selection basin and its near zone several rainfall website continuous several years daily precipitation datas, root
The annual face rainfall in basin is calculated according to arithmetic mean method；
Step 2, according to hydrological statistics principle, examined by nonparametric Andrei Kolmogorov-Si meter Nuo Fu, it is normal using the hydrology
Four kinds of probability distribution exponential distribution EXP, Geng Beier distribution GUM, gamma distribution GAM, three type of Pearson came distribution PE3 are to described
Annual rainfall in step 1 and annual runoff carry out probability-distribution function inspection, by AIC criterion determine basin annual rainfall and
The theoretical optimum probability distribution function of annual runoff, wherein 4 kinds of theoretical probabilities of basin annual rainfall and annual runoff are distributed letter
Several parameter Estimations is estimated that calculation formula is as follows using linear moments method respectively:
If X is that real value is overall, distribution function is F (x)=P (X≤x), and there are inverse function x=G (F), and G (F) is also known as
Kernel smooth, for sample x1..., xn, remember order statistic: x1:n≤x2:n,....,≤xn:n,
The linear moment estimator of r rank of Hosking is as follows:
Wherein:
In formula: r is linear moment order, and n is number of samples；
The optimal theoretical probability-distribution function of basin annual rainfall and annual runoff using nonparametric Andrei Kolmogorov-this
Minot husband examines and AIC criterion, calculation formula are as follows:
If Sn (x) is the cumulative distribution function of random sample observed value, i.e. empirical distribution function, sample size n；Fo
(x) it is a specific cumulative distribution function, i.e. theoretic distribution function, defines D=| Sn (x)-Fo (x) |, if for
Each x value, Sn (x) and Fo (x) are close, then show that the fitting degree of empirical distribution function and theoretic distribution function is very high, reasonable
By thinking sample data from the totality for obeying the theoretical distribution；
K-S examine be absolute value D=| Sn (x)-Fo (x) | in maximum deviation, i.e., examined using following statistic
It tests:
Dmax=max | Sn (x)-Fo (x) |；
AIC information criterion calculation formula is as follows:
AIC=2k-2ln (L)；
Step 3 establishes annual rainfall and annual runoff rainfall runoff relation using Archimedes family Copula function
Theoretical optimal two-dimentional joint distribution function；
The likelihood ratio statistics of step 4, the optimal two-dimentional Joint Distribution of the theory of building rainfall runoff relation, according to foundation
Likelihood ratio statistics calculate the likelihood ratio statistical value of sample, and determine catastrophe point according to the boundary threshold of likelihood ratio statistics, count
Calculation method is as follows:
Copula function likelihood ratio test method, it detects multivariable series of hydrological phase by measurement Copula Parameters variation
The change point of structure is closed, the logarithmic form of this method likelihood ratio statistics is as follows:
It is converted under conditions of height λ is unknown are as follows:
In formula, n is number of samples, ΛλIt examines as Copula function likelihood ratio statistics, λ is catastrophe point in data sequence
Position, η1For before catastrophe point sample subsequence establish Copula joint distribution function parameter, wherein comprising mutation
Point itself,For η1Estimated value, η2For the ginseng for the Copula joint distribution function that the sample subsequence after catastrophe point is established
Number,For η2Estimated value, η0For sample sequence establish Copula joint distribution function parameter,For η0Estimated value,
The boundary value of statistic Zn is taken under 5% significance, i.e., refuses null hypothesis, Joint Distribution when statistic is greater than boundary value
There are catastrophe points for dependency structure；
The boundary value of Zn is 3.69；
Step 5, according to step 4 determine catastrophe point, it is assumed that mutation the time before be nature period, it is described nature period be
Period without the effect of human activity, and using nature period as base period, the mutation time is the period of the effect of human activity later；
The natural period of step 6, the annual rainfall and the variation of annual runoff rainfall runoff relation that are obtained according to step 5 analysis
Data establish Rainfall Runoff Model, reconstruct annual flow using the Rainfall Runoff Model established further according to the annual rainfall data of all the period of time
Amount data；
Step 7 is compared using the obtained annual runoff data of reconstruct and field data, analysis obtain climate change and
The contribution rate that human activity influences streamflow change.
Wherein, data reconstruct and contribution rate calculating are realized using double mass curve method in step 6 and step 7:
Double cumulative curves have been widely used in hydrographic features consistency or long-term evolution tendency analysis, double cumulative curves
It is exactly that the relation line in the phase same time between the continuous accumulated value of two variables is being drawn in rectangular coordinate system, in step 5
Mutation the time before be used as base period, establish the rainfall runoff linear regression model (LRM) of accumulated value, with building regression model and
All the period of time year precipitation data calculates the run-off of effect of human activity phase, the i.e. reconstruct of run-off time series, with field data
Comparison in difference is carried out, contribution rate is calculated.
Embodiment
As shown in Figure 1, being specifically implemented according to the following steps by taking the hydrometric station Wudinghe River Catchment Bai Jiachuan as an example:
Step 1, basic data is collected first:
(1), the data on flows day by day of the hydrometric station Wudinghe River Catchment control station Bai Jiachuan 1963~2005 years, and be calculated every
The annual runoff in year, data come from the Yellow River Water Year Book；
(2), basin and its near zone Ding Jiagou, Suide, Zhao Shipan, Hengshan Mountain, hall city, Zhao's stone kiln, pacify the border region, Qing Yangcha,
Ma Huyu, Korea Spro family's loess hills, the Daily rainfall amount data of rainfall website 1963~2005 years of Meng Jiawan, Li Jiahe 12, it is flat according to arithmetic
The annual face rainfall in basin is calculated in equal method；
Step 2, it according to hydrological statistics principle, is examined by nonparametric Andrei Kolmogorov-Si meter Nuo Fu, it is normal using the hydrology
Four kinds of probability distribution exponential distributions (EXP), Geng Beier distribution (GUM), gamma distribution (GAM), the distribution of three type of Pearson came
(PE3) probability distribution inspection is carried out to Wudinghe River annual rainfall and annual runoff, by AIC criterion determine basin annual rainfall and
The theoretical optimum probability distribution form of annual runoff, the theoretical optimum probability of Wudinghe River Catchment annual rainfall are distributed as Pearson came three
The theoretical optimum probability distribution of type distribution, Wudinghe River Catchment annual runoff is also distributed for three type of Pearson came；
Step 3, the theoretical cumulative distribution for calculating separately basin annual rainfall and annual runoff by R language lmom packet is general
Rate, then annual rainfall is calculated using the theoretical cumulative distribution probability of basin annual rainfall and annual runoff by R language CDVine packet
Three kinds of Copula functions such as Clayton copula, Frank copula, Gumbel copula of amount and annual runoff water sand
Theory joint cumulative distribution probability, finally calculates AIC, selects theory of the optimal Copula function as description rainfall runoff relation
Two-dimentional Optimal Distribution function；
Step 4, the construction that Copula function likelihood ratio statistics are realized by R Programming with Pascal Language, according to λ in Document system amount
From 7~(n-6), the likelihood ratio statistics time sequence that the optimal two-dimentional Joint Distribution of rainfall runoff relation is calculated in program is run
Column, such as Fig. 1, the statistic time series and more than 3.69；
Step 5, the mutation time for determining rainfall runoff relation is 1974, and 1963~1974 years are nature period, as
Base period, 1975~2005 years periods for the effect of human activity；
Step 6, the annual rainfall that 1963~1974 years are nature period is obtained according to double mass curve method and step 5 analysis
Cumulant linear regression model (LRM) is established with annual runoff rainfall runoff relation data, is reconstructed further according to the annual rainfall data of all the period of time
Annual runoff data；
Step 7, the difference of the annual flow data and field data that are obtained using reconstruct, analysis obtains climate change and people comes
The contribution rate that activity influences streamflow change, if Fig. 2 is that Wudinghe River Catchment streamflow change classification, Reasons contribution rate calculated result is shown
It is intended to, from figure 2 it can be seen that the relationship between Wudinghe River Catchment rainfall and runoff mutated in 1974, is mutated the time
Rainfall runoff relation has good consistency before, and linear fit degree is preferable, illustrates that mankind's activity changes runoff relationship
Substantially without influence, rainfall runoff relation does not have consistency after being mutated the time, and people carrys out the movable contribution to runoff relationship variation
Rate reaches 112.9%, has leading position, and climate change only has -12.9% to the contribution rate that runoff relationship changes, to sum up illustrates
The production of the current Wudinghe River Catchment mankind and the influence lived to river flow are more violent.
The method of a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship of the present invention and classification, Reasons, can be quick and precisely
It is diagnosed to be the catastrophe point of rainfall runoff and carries out classification, Reasons and calculate the contribution of climate change and mankind's activity to runoff influence
Rate provides scientific basis for basin water resources matching and ecological construction.
Claims (7)
1. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons, which is characterized in that specifically according to
Following steps are implemented:
Step 1 determines research basin, the annual rainfall number of collection research watershed control hydrometric station annual runoff and valley rainfall station
According to；
Step 2, according to hydrological statistics principle, determine the optimal theoretical probability-distribution function of basin annual rainfall and annual runoff；
Step 3, the theory that annual rainfall and annual runoff hydro-sediment relation are established using Archimedes family Copula function are optimal
Two-dimentional joint distribution function；
The likelihood ratio statistics of step 4, the optimal two-dimentional Joint Distribution of the theory of building rainfall runoff relation, according to the likelihood of foundation
Catastrophe point is determined than the likelihood ratio statistical value of normalized set sample, and according to the boundary threshold of likelihood ratio statistics；
Step 5, the catastrophe point determined according to step 4, it is assumed that be nature period before the mutation time, the nature period is for nobody
The period that class activity influences, and using nature period as base period, the mutation time is the period of the effect of human activity later；
The natural period data of step 6, the annual rainfall and the variation of annual runoff rainfall runoff relation that are obtained according to step 5 analysis
Rainfall Runoff Model is established, is provided further according to the annual rainfall data of all the period of time using the Rainfall Runoff Model reconstruct annual runoff established
Material；
Step 7 is compared using the obtained annual runoff data of reconstruct and field data, and analysis obtains climate change and artificial
The contribution rate that activity influences streamflow change.
2. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 1 and classification, Reasons,
It is characterized in that, the step 1 is specifically implemented according to the following steps:
Step 1.1 first determines that for research website, it is daily then to collect the website continuous several years for the control hydrometric station in some basin
Data on flows, and annual annual runoff is calculated；
Step 1.2, selection basin and its near zone several rainfall website continuous several years daily precipitation datas, according to calculation
The annual face rainfall in basin is calculated in the art method of average.
3. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 2 and classification, Reasons,
It is characterized in that, the step 2 are as follows:
According to hydrological statistics principle, examined by nonparametric Andrei Kolmogorov-Si meter Nuo Fu, it is general using common four kinds of the hydrology
Rate profile exponent is distributed EXP, Geng Beier distribution GUM, gamma distribution GAM, three type of Pearson came distribution PE3 in the step 1
Annual rainfall and annual runoff carry out probability-distribution function inspection, determine basin annual rainfall and annual runoff by AIC criterion
Theoretical optimum probability distribution function.
4. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 3 and classification, Reasons,
It is characterized in that, the parameter Estimation of 4 kinds of theoretical probability distribution functions of basin annual rainfall and annual runoff makes in the step 2
Estimated that calculation formula is as follows respectively with linear moments method:
If X is that real value is overall, distribution function is F (x)=P (X≤x), and there are inverse function x=G (F), G (F) to be also known as quartile
Function, for sample x1..., xn, remember order statistic: x1:n≤x2:n,....,≤xn:n,
The linear moment estimator of r rank of Hosking is as follows:
Wherein:
In formula: r is linear moment order, and n is number of samples.
5. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 3 and classification, Reasons,
It is characterized in that, the optimal theoretical probability-distribution function of basin annual rainfall and annual runoff uses nonparametric in the step 2
Andrei Kolmogorov-Si meter Nuo Fu is examined and AIC criterion, calculation formula are as follows:
If Sn (x) is the cumulative distribution function of random sample observed value, i.e. empirical distribution function, sample size n；Fo(x)
It is a specific cumulative distribution function, i.e. theoretic distribution function, defines D=| Sn (x)-Fo (x) |, if for each
X value, Sn (x) and Fo (x) are close, then show that the fitting degree of empirical distribution function and theoretic distribution function is very high, it is reasonable to recognize
It is sample data from the totality for obeying the theoretical distribution；
K-S examine be absolute value D=| Sn (x)-Fo (x) | in maximum deviation, i.e., examined using following statistic:
Dmax=max | Sn (x)-Fo (x) |；
AIC information criterion calculation formula is as follows:
AIC=2k-2ln (L).
6. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 3 and classification, Reasons,
It is characterized in that, step 4 calculation method is as follows:
Copula function likelihood ratio test method, it detects multivariable series of hydrological correlation knot by measurement Copula Parameters variation
The logarithmic form of the change point of structure, this method likelihood ratio statistics is as follows:
It is converted under conditions of height λ is unknown are as follows:
In formula, n is number of samples, ΛλIt examines as Copula function likelihood ratio statistics, λ is position of the catastrophe point in data sequence
It sets, η1For before catastrophe point sample subsequence establish Copula joint distribution function parameter, wherein include catastrophe point sheet
Body,For η1Estimated value, η2For after catastrophe point sample subsequence establish Copula joint distribution function parameter,For η2Estimated value, η0For sample sequence establish Copula joint distribution function parameter,For η0Estimated value,
The boundary value of statistic Zn is taken under 5% significance, i.e., refuses null hypothesis, Joint Distribution phase when statistic is greater than boundary value
Closing structure, there are catastrophe points.
7. the method for a kind of non-linear quick diagnosis of Basin Rainfall runoff relationship according to claim 6 and classification, Reasons,
It is characterized in that, the boundary value of the Zn is 3.69.
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| CN118626809A (en) * | 2024-08-13 | 2024-09-10 | 水利部交通运输部国家能源局南京水利科学研究院 | Runoff non-uniformity variation identification method and system based on sequence reconstruction |
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