CN107093013A - A kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution - Google Patents
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Abstract
The invention discloses a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution, comprise the following steps：IHA is chosen as the index system for evaluating the variation of River Hydrology situation；The probability density function for meeting hydrology function is chosen using principle of maximum entropy and minimal information entropy；The intensity of variation of index is represented by the difference of the Shannon entropy of IHA each component indexs in two periods；The weight that power calculates the diversity change for meeting hydrology index is assigned using multiple attribute decision making (MADM)；Calculating is obtained after each index weights, by the intensity of variation of each index be multiplied with corresponding index weights and sum obtain all indexs overall change degree obtain consider the hydrology distribution hydrologic regime degree of change.Hydrology degree of variation is targetedly evaluated, more rational support is provided for local water resources management department.
Description
Technical field
The present invention relates to hydrologic regime analysis technical field, more particularly to a kind of water for considering the hydrology index regularity of distribution
Literary situation evaluation method.
Background technology
Hydrologic regime is as the key factor of river channel ecology is influenceed, and the research of its index system and evaluation method is more next
More it is valued by people.
In terms of hydrologic regime index system establishment, Richard B.D. etc. propose IHA index systems in 1996
(Indicators of Hydrologic Alteration, IHA), the index system from the flow of current, frequency, last, send out
Raw 5 aspects such as time and rate of change characterize ecologic structure information, are analyzed by the Eco-hydrological Characteristics to Roanoke river,
It was found that building the river before and after dam there occurs larger Eco-hydrological Characteristics change；Growsn etc. is extended for 2000 to IHA, is carried
A set of index system being made up of 7 class, 333 indexs is gone out, has been added compared to IHA in the year of flow, Annual variations and flood refer to
The indexs such as number, and Australian 107 rivers in the southeast are analyzed；Olden]171 hydrology are summarized within 2003 to refer to
Mark, and statistical analysis is carried out to the hydrological data of 420, America river website, it is proposed that one has statistical significance and ecological table
Levy the Eco-hydrological evaluation index framework of ability；Suen etc. applies fish Ecological Matrices, binding area special climate in 2004
Environment, it is proposed that north Taiwan river ecological hydrology index system (TEIS), includes general changes in flow rate, high-low flow, flow
60 characteristic indexs such as rate of change, time of occurrence；Vogel etc. proposes ecological footpath in 2007 based on flow duration curve (FDC)
Index (Eco-flow) is flowed, is represented with ecological remaining (ecosurpluse) and ecological-deficit (ecodeficit) by artificial shadow
Departure degree of the discharge of river with respect to nature after sound.At home, Xu Tianbao etc. establishes a set of for 2007 in the Yangtze river basin
Hydrology index system, and be applied in influence evaluation of the Gezhouba Dam to Yangtze middle reaches Eco-hydrological Characteristics；Zhang Hongbo
The Yellow River Eco-hydrological feature was combined Deng 2012, the Huanghe valley Eco-hydrological index body comprising 7 major class, 50 indexs is established
It is (Yellow River Eco-hydrological Index system, YEHIS).
In terms of evaluation method, Richard B.D. etc. pass through the further analysis to IHA indexs in 1997, it is proposed that mesh
The preceding wide variety of excursion method (Range of Variability Approach, RVA) for quantifying hydrological variation degree；
Black A.R. etc. propose the broader hydrology for 2005 and change analysis method DHRAM (Dundee Hydrological
Regime Alteration Method), the degree of risk that the river ecological hydrology changes is divided into 5 grades, bigger grade,
Regime of river change degree is bigger, and the risk that the ecosystem wrecks is bigger；Shiau J.T. etc. 2008 are by RVA methods
Comparative analysis in varied situations, it is believed that RVA methods have certain limitation, to changing for the hydrologic parameter in target zone
Variation has preferable estimation, and to falling the parameter outside target zone, its intensity of variation then can not preferably consider, this may
Cause hydrologic regime falseness assessment, Shiau J.T. propose the method for Histogram Matching to evaluate hydrologic regime on this basis
Change；Zooho Kim etc. 2014 preferably provide support to simplify the evaluation index of RVA indexs for policymaker, by based on
The OWA operators of principle of maximum entropy are by the degree of variation synthesis of 33 indexs for an index, i.e. ecological index (Eco-
index)；Li Yunyun etc. is improved RVA methods for 2015, it is proposed that subjective weight is calculated with analytic hierarchy process (AHP), with entropy weight
Method calculates objective weight, and both are combined to the method to evaluate degree of variation.
To sum up, the research to hydrologic regime index system is more, the characteristics of especially for different basins, constructs corresponding
Index system, and evaluation method then the less point index regularity of distribution for the hydrology the characteristics of, the change to hydrologic regime is ground
Study carefully.
The content of the invention
In order to solve the deficiencies in the prior art, the invention provides a kind of hydrologic regime for considering the hydrology index regularity of distribution
Evaluation method, the present invention passes through the parameter Estimation and minimum of principle of maximum entropy according to the regularity of distribution of a certain regional hydrology index
The comentropy test of fitness of fot, obtains the best probability density function of each hydrology index fitting degree, using Shannon entropy to artificial
The diversity of each hydrology index is compared before and after influence, is assigned and weighed by multiple attribute decision making (MADM), targetedly evaluates hydrology variation
Degree, more rational support is provided for local water resources management department.
A kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution, comprises the following steps：
Choose hydrology indicator evaluation system；
The probability density function for meeting hydrology index rule is chosen using principle of maximum entropy and minimal information entropy；
The intensity of variation of each index is represented by the difference of the Shannon entropy of each hydrology index in two periods；
The weight that power method calculates the diversity change for meeting hydrology index is assigned using multiple attribute decision making (MADM)；
Calculating is obtained after each index weights, and the intensity of variation of each index, which is multiplied and summed with corresponding index weights, to be obtained
The overall change degree of all indexs is the hydrologic regime degree of change for obtaining considering hydrology distribution.
Further, when each index of selection meets the probability density function of hydrology function, specifically include：
It is assumed that each hydrology index is stochastic variable, according to conventional hydrology distribution pattern, normal distribution, lognormal are chosen
Distribution, gamma distribution and the distribution of the types of P- III are calculated as each index probability density function to be fitted by principle of maximum entropy
To the estimates of parameters of probability density function；
Goodness is fitted using minimal information entropy method to the distribution of four classes to examine, the minimum distribution of comentropy is the index
Optimum probability density function.
Further, the parameter Estimation equation of maximum entropy is shown in formula：
In formula, μnIt is x n-th order moment of the orign, is determined by sample sequence；
By introducing Lagrange multiplier, the probability that can go out maximum entropy distribution by the parameter Estimation equation inference of maximum entropy is close
Function analytic expression is spent, formula is seen：
In formula, λ0λ1···λnFor Lagrange multiplier.
Further, the multifarious intensity of variation calculation formula of each hydrology index：
ΔHi=| Hpre-Hpost|i
In formula, Δ HiFor the change degree of i-th of index, i=1,2,3...n；HpreAnd HpostRepresent respectively by man's activity
The Shannon entropy of front and rear i-th of IHA indexs, calculation formula sees below formula：
In formula, p (xi) for the probability of occurrence of i-th parameter value, it can be determined by probability density function；
The diversity difference for obtaining two periods, i.e. intensity of variation are calculated by above formula, is reflected by after the effect of human activity
River Hydrology situation deviate nature degree.
Further, when calculating the weight for the diversity change for meeting hydrology index, the OWA operators power based on normal distribution
Expanded on the basis of method of reruning, it is considered to which data distribution rule determines many attribute weights, i.e., true based on logarithm normal distribution
Determine weight, determine that weight calculation formula is based on logarithm normal distribution：
In formula, wiFor the weighted value of i-th of index；xiFor the actual value of i-th of index；U and σ are respectively data sequence phase
Should be in the average and standard deviation that are each distributed.
Compared with prior art, the beneficial effects of the invention are as follows：
The present invention passes through the parameter Estimation and minimum letter of principle of maximum entropy according to the regularity of distribution of a certain regional hydrology index
The entropy test of fitness of fot is ceased, the best probability density function of each hydrology index fitting degree is obtained, using Shannon entropy to artificial shadow
The diversity of each hydrology index is compared before and after ringing, and is assigned and weighed by multiple attribute decision making (MADM), targetedly evaluates hydrology degree of variation,
More rational support is provided for local water resources management department.
Brief description of the drawings
The Figure of description for constituting the part of the application is used for providing further understanding of the present application, and the application's shows
Meaning property embodiment and its illustrate be used for explain the application, do not constitute the improper restriction to the application.
Fig. 1 is overall flow figure of the invention；
The optimum density function statistics of IHA5 component in Fig. 2 (a) good ecological environment phases；
The optimum density function statistics of IHA5 component in Fig. 2 (b) good ecological environment phases.
Embodiment
It is noted that described further below is all exemplary, it is intended to provide further instruction to the application.Unless another
Indicate, all technologies used herein and scientific terminology are with usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singulative
It is also intended to include plural form, additionally, it should be understood that, when in this manual using term "comprising" and/or " bag
Include " when, it indicates existing characteristics, step, operation, device, component and/or combinations thereof.
As background technology is introduced, there is the deficiency evaluated hydrologic regime in the prior art, in order to solve such as
On technical problem, present applicant proposes it is a kind of consider the hydrology index regularity of distribution hydrologic regime evaluation method.
In a kind of typical embodiment of the application, the hydrology index regularity of distribution is considered there is provided one kind as shown in Figure 1
Hydrologic regime evaluation method, including：
The determination of 1 hydrology index and optimal probability density function：
The selection of 1.1 hydrology indexs
IHA index systems include 33 hydrology indexs related to river ecological, day footpath of these indexs based on long series
Stream data, River Hydrology situation is described in terms of uninterrupted, occurrence frequency, time of origin, duration, fluctuation speed
Situation of change.IHA index systems (Richard B.D., 1996) since the proposition, are at home and abroad widely used, 33
Individual hydrology index also more comprehensively reflects the change of River Hydrology.Therefore, the present invention chooses IHA as evaluation River Hydrology feelings
The index system of gesture variation, each indexs of IHA are shown in Table 1.
The IHA indexs of table 1
1.2 selection on probability density function
It is assumed that IHA each hydrology index is stochastic variable, optimal probability density function is carried out respectively to five classes, 33 indexs
Fitting.With reference to the hydrology distribution curve that China is conventional, the present invention choose normal distribution, logarithm normal distribution, gamma distribution and
The distribution of the types of P- III is calculated by principle of maximum entropy as each index probability density function to be fitted and obtains probability density function
Estimates of parameters.The parameter Estimation equation of maximum entropy is shown in formula (1).
In formula, μnIt is x n-th order moment of the orign, is determined by sample sequence.
By introducing Lagrange multiplier, the probability density function analytic expression of maximum entropy distribution can be derived by formula (1), is seen
Formula (2).
In formula, λ0λ1···λnFor Lagrange multiplier.
By deriving between each probability density function parameter and Lagrange multiplier, between Lagrange multiplier and constraints
Relation, finally give the relation between the parameter of probability density function and constraints, i.e. parameter Estimation equation group, thus may be used
Inquire into the Lagrange multiplier expression formula for four class probability density functions.Choose the yellow gram of minimal information entropy proposed for medium 1996
Method is fitted goodness to the distribution of four classes and examined, and the minimum distribution of comentropy is optimal type.Four class probability density functions
Lagrange multiplier expression formula and minimum entropy calculation formula are shown in Table 2.
The Lagrange multiplier and minimum entropy calculation formula of the class of table 2 four distribution
The calculating of 2 index diversity intensity of variations
The intensity of variation of index represented by the difference of the Shannon entropy of IHA each component indexs in two periods, calculation formula
See formula (3).Shannon entropy illustrates the uncertainty of variable, namely variable diversity, Shannon entropy is bigger, the uncertainty of variable
Also bigger, the diversity of variable is better.
ΔHi=| Hpre-Hpost|i (3)
In formula, Δ HiFor the change degree of i-th of index, i=1,2,3...n；HpreAnd HpostRepresent respectively by man's activity
The Shannon entropy of front and rear i-th of IHA indexs, calculation formula is shown in formula (4).
In formula, p (xi) for the probability of occurrence of i-th parameter value, it can be determined by probability density function, see formula (2).
The diversity difference for obtaining two periods, i.e. intensity of variation are calculated by formula (3) and formula (4), reflects and is lived by the mankind
River Hydrology situation after dynamic influence deviates the degree of nature.
The determination of 3 index weights and the calculating of overall degree of change
Each index is obtaining two to the influence degree of river ecological and hydrologic regime difference in IHA index systems
After each index intensity of variations of period IHA, it can not say that its weight of the big index of intensity of variation is just high, this is accomplished by rational determination
The weight of each index.Induced ordered weighted averaging operator (ordered weighted averaging operator, OWA) is Yager
Teach and data are re-started with sequence in order in a kind of of proposition in 1988, and pass through the position where data or evidence and carry out
Weight the multiple attributive decision making method assembled again.The weight for determining OWA operators is the key for calculating OWA operators, and Yager etc. is carried
Gone out two important correlated measure functions of OWA operators, i.e., " orness measure " and " dispersion measure ", its
In " orness measure " are used for measuring the degree of " or " computing or " and " computing, and " dispersion measure " are used for
The degree that each data are utilized in value is concentrated is measured, formula (5) is shown in the calculating of the operator weight based on principle of maximum entropy.
0≤α≤1；wi∈ [0,1], i=1,2 ..., n
In formula, wiFor the operator weight of i-th of index；α is optimism degree.
The computational methods of a variety of OWA operators weights are had at present, wherein the OWA operator weight calculations based on normal distribution exist
While meeting principle of maximum entropy, the information of Data Position is not only allowed for, and considers the size of data itself, is data
Weight calculation provides relatively reasonable method.Therefore, the present invention uses the OWA operator Weight algorithms based on normal distribution first
(see formula 6) calculates the weight of each hydrology indexs of IHA, and the regularity of distribution then obeyed in view of each indexs of IHA may be different, this hair
It is bright to be expanded on the basis of the OWA operator Weight algorithms based on normal distribution, it is proposed that one kind considers data distribution rule
Many attribute weights of rule determine method, the i.e. Weight Determination based on logarithm normal distribution, see formula (7).
In formula, wiFor the weighted value of i-th of index；xiFor the actual value of i-th of index；U and σ are respectively data sequence phase
Should be in the average and standard deviation that are each distributed.
After calculating obtains each index weights, the intensity of variation of each index is multiplied and summed with corresponding index weights
To the overall change degree of 33 indexs, formula (8) is seen.
In formula, C is the overall degree of change of hydrologic regime for considering the hydrology index regularity of distribution；Other symbolic significances are the same.
In order that the technical scheme of the application can clearly be understood by obtaining those skilled in the art, below with reference to tool
The embodiment of body describes the technical scheme of the application in detail with comparative example.
Calculated examples
The determination of 1 optimum probability density function
The yellow platform bridge station diurnal courses data of 1960~2014 years of Xiaoqinghe River is chosen, 33 hydrology indexs of IHA5 groups are calculated.
According to principle of maximum entropy, programmed by Matlab, calculate the probability density function of two periods each four kinds of distribution patterns of index
Parameter value, result of calculation is shown in Table 3 and table 4.
The probability density function parameter value of 3 good ecological environment phase of table, four kinds of distributions
The probability density function parameter value of 4 Effects of Urbanization phase of table, four kinds of distributions
Minimal information entropy formula calculates the goodness of fit for obtaining each index density functions of two period IHA, IHA in table 2
The statistical conditions of the optimum density function of 33 hydrology indexs of index system 5 group are shown in Fig. 2 (a)-Fig. 2 (b).
From Fig. 2 (a)-Fig. 2 (b), monthly flow component (totally 12 indexs) more meets P- III within the good ecological environment phase
Distribution, more meets logarithm normal distribution in the Effects of Urbanization phase；Average annual extreme value component (totally 12 indexs), within the good ecological environment phase
More meet gamma distribution and the distributions of P- III, log series model and gamma distribution are then more met in the Effects of Urbanization phase；And other
Component more conforms to logarithm normal distribution.
The calculating of 2 index diversity intensity of variations
The probability density function for meeting the IHA each group index regularities of distribution is have chosen by the minimum entropy test of fitness of fot, by
Formula (3) and formula (4) calculate the diversity parameters H for obtaining each indexiAnd the diversity intensity of variation of two periods each hydrology index
ΔHi, Δ HiResult of calculation be shown in Table 5.
5 33 hydrology index intensity of variation computational charts of table
From table 5, the Effects of Urbanization phase is all higher than for preceding two groups of indexs good ecological environment phase；It is most of to latter three groups
Index then shows as the Effects of Urbanization phase more than the good ecological environment phase.This shows, the monthly stream of Xiaoqinghe River (Jinan City's section, similarly hereinafter)
Amount and the diversity of average annual extreme value substantially diminish after man's activity, and high-low flow occurrence frequency and flood fluctuation speed is more
Sample but becomes big.This causes Xiaoqinghe River under year yardstick, and same trend is presented in each moon monthly flow；And under moon yardstick, play
The time of origin and peak value of flood but discrete trend is presented.These changes destroy the original hydrologic regime of Xiaoqinghe River, point
Its reason is analysed, is mainly had：1. artificial water transfer moisturizing causes the monthly flow in low water month in year substantially to increase in the Effects of Urbanization phase
Greatly；2. Effects of Urbanization causes Xiaoqinghe River to occur flood probability and become big, and flood fluctuation speed also increases therewith.
The entitled comparison of kind more than 3
The present invention chooses the weighing computation method based on normal distribution and based on logarithm normal distribution to calculate each indexs of IHA
Weighted value, and to two kinds tax power methods result of calculations be compared, result of calculation is shown in Table 6.From table 6, based on normal state
The index that the weight of distribution thinks near normal distribution average has a higher weight, and the weight difference between index is not
Greatly；Weight based on logarithm normal distribution then thinks that the index near two ends and lognormal average has higher weights,
And the weight discrimination of each index is larger.
Meanwhile, to compare whether two kinds of weights for assigning each hydrology index that the calculating of power method is obtained meet local hydrology ecology
The characteristics of change, the present invention is small to Jinan City using principal component analytical method from hydrologic regime and the angle of ecological interaction
33, Qinghe basin IHA hydrology indexs are analyzed, and have obtained 5 class principal components, therefrom filter out 6 more important indexs
As the index closely related with ecology, 6 indexs are respectively March and monthly flow in May, 7 daily minimum flows, max-flow on the 3rd
Amount, low discharge and Dryweather flow, it is rich with fish that this is also filtered out with Yi-Chen E.Yang etc. with genetic programming algorithm (GP)
Closely related 6 hydrology indexs of degree (May monthly flow, 7 daily minimum flows, maximum stream flow on the 3rd, minimum discharge time of occurrence,
Speed of rising and reverse number of times) it is basically identical.For comprehensively analysis hydrology index and the relation of hydrological-ecological law, present invention choosing
Take March, May monthly flow, 7 daily minimum flows, maximum stream flow on the 3rd, low discharge, Dryweather flow, minimum discharge time of occurrence, rise
Speed and number of times totally 9 indexs (corresponding index number is 3,5,15,19,24,25,27,31,33 respectively) is reversed, as sentencing
Disconnected two kinds are assigned the characteristic evidences for weighing method applicability.
Comparison is visible, and what the tax power method based on lognormal was calculated has greater weight (weighted value>0.45) finger
Mark, can preferably cover the hydrology index closely related with river ecological filtered out.Therefore, Jinan City's Xiaoqinghe River is being evaluated
When hydrologic regime changes, choose the power method of the tax based on lognormal and be used as weighing computation method.
6 two kinds of tax power method result of calculations of table
4 with the contrasts of RVA methods
(1) calculating of RVA methods hydrology degree of change
RVA (excursion method) is generally using 25% and the 75% of impacted preceding each index occurrence frequency as disclosure satisfy that river
The mobility scale of ecological demand is flowed, the specific hydrology degree of change of each index is quantified to obtain by formula (9), overall hydrology degree of change Do
Calculated and obtained by formula (10), work as Do<It is mild change, 33.3% when 33.3%<Do<66.7% is that moderate changes, Do>
66.7% is Level Change.
In formula：DiFor each index degree of change；DoFor overall hydrology degree of change；NiFor i-th of index it is impacted after still fall within
Actual observation year in RVA threshold ranges；NeIt is expected to fall within the year in RVA threshold ranges, N after impacted for indexe=
rNt, wherein r is that impacted rear index is expected to fall within the ratio in RVA threshold ranges, NtThe total year for being index after impacted.
(2) calculating of the hydrology degree of change of hydrology function is considered
The intensity of variation Δ H of each index obtained by calculatingiWith each index weights wi, calculated using formula (8) and obtain entirety
Hydrology degree of change C.In calculating process, because the 23rd index (zero delivery number of days) in the value of Xiaoqinghe River (Jinan City's section) is
0, therefore do not consider the intensity of variation of the index when evaluating overall variation.The result of calculation of two methods is shown in Table 7.
From table 7, the method for assigning power with diversity indices and multiple attribute decision making (MADM) to calculate hydrology index intensity of variation, than
RVA methods directly specified 25% and 75% judge that the method for hydrology degree of variation is more objective as threshold value, comprehensively reflected
The change information of Xiaoqinghe River hydrologic regime.
The comparison of 7 two kinds of degree of variation computational methods of table
The preferred embodiment of the application is the foregoing is only, the application is not limited to, for the skill of this area
For art personnel, the application can have various modifications and variations.It is all within spirit herein and principle, made any repair
Change, equivalent substitution, improvement etc., should be included within the protection domain of the application.
Claims (5)
1. a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution, it is characterized in that, comprise the following steps：
Choose hydrology indicator evaluation system；
The probability density function for meeting hydrology index rule is chosen using principle of maximum entropy and minimal information entropy；
The intensity of variation of each index is represented by the difference of the Shannon entropy of each hydrology index in two periods；
The weight that power method calculates the diversity change for meeting hydrology index is assigned using multiple attribute decision making (MADM)；
Calculating is obtained after each index weights, and the intensity of variation of each index is multiplied and summed with corresponding index weights and is owned
The overall change degree of index is the hydrologic regime degree of change for obtaining considering hydrology distribution.
2. a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution as claimed in claim 1, it is characterized in that, choosing
When taking each index to meet the probability density function of hydrology function, specifically include：
It is assumed that each hydrology index is stochastic variable, according to conventional hydrology distribution pattern, normal distribution, lognormal point are chosen
Cloth, gamma distribution and the distribution of the types of P- III are calculated by principle of maximum entropy and obtained as each index probability density function to be fitted
The estimates of parameters of probability density function；
Goodness is fitted using minimal information entropy method to the distribution of four classes to examine, the minimum distribution of comentropy is that the index is optimal
Probability density function.
3. a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution as claimed in claim 1 or 2, its feature
It is that the parameter Estimation equation of maximum entropy is shown in formula：
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<mtr>
<mtd>
<mi>max</mi>
</mtd>
<mtd>
<mrow>
<mi>I</mi>
<mo>=</mo>
<mo>-</mo>
<msub>
<mo>&Integral;</mo>
<mi>R</mi>
</msub>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mi>ln</mi>
<mi> </mi>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>x</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
<mo>.</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mo>&Integral;</mo>
<mi>R</mi>
</msub>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>x</mi>
<mo>=</mo>
<msub>
<mi>&mu;</mi>
<mi>n</mi>
</msub>
<mo>,</mo>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>N</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, μnIt is x n-th order moment of the orign, is determined by sample sequence；
By introducing Lagrange multiplier, the probability density letter of maximum entropy distribution can be gone out by the parameter Estimation equation inference of maximum entropy
Number analytic expression, is shown in formula：
<mrow>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mo>&lsqb;</mo>
<msub>
<mi>&lambda;</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>&lambda;</mi>
<mi>n</mi>
</msub>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mi>n</mi>
</msup>
<mo>&rsqb;</mo>
</mrow>
In formula, λ0 λ1…λnFor Lagrange multiplier.
4. a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution as claimed in claim 1, it is characterized in that, respectively
The multifarious intensity of variation calculation formula of hydrology index：
ΔHi=| Hpre-Hpost|i
In formula, Δ HiFor the change degree of i-th of index, i=1,2,3...n；HpreAnd HpostRepresent respectively by before and after man's activity
The Shannon entropy of i-th of IHA index, calculation formula sees below formula：
<mrow>
<mi>H</mi>
<mo>=</mo>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>log</mi>
<mi> </mi>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
In formula, p (xi) for the probability of occurrence of i-th parameter value, it can be determined by probability density function；
The diversity difference for obtaining two periods, i.e. intensity of variation are calculated by above formula, is reflected by the river after the effect of human activity
Flow the degree that hydrologic regime deviates nature.
5. a kind of hydrologic regime evaluation method for considering the hydrology index regularity of distribution as claimed in claim 1, it is characterized in that, meter
During the weight of the diversity change of operator Heshui text index, carried out on the basis of the OWA operator Weight algorithms based on normal distribution
Expand, it is considered to which data distribution rule determines many attribute weights, i.e., determine weight based on logarithm normal distribution, based on lognormal
Distribution determines that weight calculation formula is：
<mrow>
<msub>
<mi>w</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mfrac>
<mn>1</mn>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mfrac>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>ln</mi>
<mi> </mi>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mfrac>
<mn>1</mn>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mfrac>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<mi>ln</mi>
<mi> </mi>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mi>n</mi>
</mrow>
In formula, wiFor the weighted value of i-th of index；xiFor the actual value of i-th of index；U and σ are respectively that data sequence is corresponded to
The average and standard deviation being each distributed.
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