CN110673230A - Entropy decision method based dynamic critical rainfall calculation method - Google Patents

Entropy decision method based dynamic critical rainfall calculation method Download PDF

Info

Publication number
CN110673230A
CN110673230A CN201910630957.7A CN201910630957A CN110673230A CN 110673230 A CN110673230 A CN 110673230A CN 201910630957 A CN201910630957 A CN 201910630957A CN 110673230 A CN110673230 A CN 110673230A
Authority
CN
China
Prior art keywords
distribution
rainfall
function
entropy
critical
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201910630957.7A
Other languages
Chinese (zh)
Inventor
林凯荣
梁汝豪
兰甜
陈海燕
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sun Yat Sen University
National Sun Yat Sen University
Original Assignee
National Sun Yat Sen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by National Sun Yat Sen University filed Critical National Sun Yat Sen University
Priority to CN201910630957.7A priority Critical patent/CN110673230A/en
Publication of CN110673230A publication Critical patent/CN110673230A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01W—METEOROLOGY
    • G01W1/00—Meteorology
    • G01W1/14—Rainfall or precipitation gauges
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
    • Y02A10/40—Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A50/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE in human health protection, e.g. against extreme weather

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Data Mining & Analysis (AREA)
  • General Physics & Mathematics (AREA)
  • Environmental & Geological Engineering (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Algebra (AREA)
  • Evolutionary Biology (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Operations Research (AREA)
  • Hydrology & Water Resources (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Atmospheric Sciences (AREA)
  • Biodiversity & Conservation Biology (AREA)
  • Ecology (AREA)
  • Environmental Sciences (AREA)
  • Alarm Systems (AREA)

Abstract

The invention relates to a dynamic critical rainfall calculation method based on an entropy decision method; s1, collecting and settling actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of a previous period; s2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection; s3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions; and S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions. The invention solves the problem of determining the mountain torrent disaster early warning index by using a risk decision method.

Description

Entropy decision method based dynamic critical rainfall calculation method
Technical Field
The invention relates to the field of mountain torrent disaster early warning and forecasting, in particular to a dynamic critical rainfall calculation method based on an entropy decision method.
Background
The mountain torrent disaster refers to the sudden strong and destructive mountain area flood caused by short-time rainstorm. In recent years, with the rapid development of economy and society and the aggravation of extreme weather in China, mountain torrent disasters become one of the most serious natural disasters in China. According to statistics, the direct economic loss caused by mountain torrent disasters in China accounts for about 70% of the national flood disaster loss, and the casualties account for about 80%. Most areas of China belong to monsoon climate, rainfall periods are concentrated, and in addition, mountainous areas of China are wide, water loss and soil erosion are serious, so that mountain torrent disasters are frequent, serious casualties and property loss are caused, and the economic and social development of the mountainous areas is also hindered.
The mountain torrent disaster has the characteristics of strong burst and large destructive power, and the problems of few monitoring sites, shortage of hydrological and meteorological data and the like in a mountain area make the mountain torrent disaster difficult to effectively early warn and prevent. The problem can be effectively solved by a method for determining the mountain torrent disaster early warning index. The method is an important link for preventing and controlling the mountain torrent disasters, and whether the mountain torrent disasters occur can be determined only by comparing the early warning indexes with the forecast data before the mountain torrent arrives. The current commonly used early warning index is critical rainfall. The critical rainfall refers to the occurrence of mountain torrents disasters in a drainage basin when the rainfall reaches a certain magnitude, and is the critical rainfall. When the rainfall reaches the critical rainfall, runoff is formed on the ground surface, so that the flow of a certain section of the river exceeds the critical flow, and the flood submerges the farmlands on two sides of the river, thereby causing certain social and economic losses. For medium and small watershed, torrential flood is strong in outburst, and accurate critical rainfall can enable people to predict arrival of torrential flood, so that flood alarm is issued in advance, evacuation transfer work is carried out, and loss caused by torrential flood is reduced to the maximum extent. If the critical rainfall is too small, the personnel can be transferred prematurely, which results in increased transfer cost and confusion of social order. If the critical rainfall is too large, the mountain torrent disaster occurs and the materials of the masses are not transferred, which causes serious loss. Therefore, the accurate and feasible dynamic critical rainfall is calculated by a scientific method, the personnel property loss in the mountain area can be reduced to the maximum extent, the technical support is provided for the evaluation, early warning, prevention and control and decision deployment work of the mountain torrent disasters, and the method has great significance for the early warning and forecast of the mountain torrent disasters and the work of disaster prevention and reduction.
Disclosure of Invention
The invention aims to overcome the defect that the critical rainfall calculation is inaccurate in the prior art, and provides a dynamic critical rainfall calculation method based on an entropy decision-making method.
In order to solve the technical problems, the invention adopts the technical scheme that: a dynamic critical rainfall calculation method based on an entropy decision method comprises the following steps:
s1, collecting and arranging actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of the former period.
The rainfall runoff data of the multi-field actual measurement flood in the drainage basin is collected and sorted, and the correlation between the critical rainfall and the soil moistening degree in the early stage is considered, the conventional method is to divide the rainfall runoff data according to the soil moistening degrees (AMCI, AMCI II and AMCI III) in the early stage, and then subdivide the rainfall runoff data according to different durations (3h, 6h, 12h and 24h) under the condition of each early stage soil moistening degree. If the collected rainfall runoff data is less, the data is divided according to the soil moisture degree in the early stage to generate a very short data sequence, and accurate edge distribution is difficult to select. Therefore, rainfall data of each flood needs to be input into a hydrological model, flow series under different early soil wetting degree conditions are simulated, and then are subdivided according to different durations to obtain a plurality of groups of sample series of accumulated rainfall v and corresponding flood peak flow q.
And S2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection.
Further, the invention selects exponential distribution, lognormal distribution and Weibull distribution to fit the cumulative rainfall v and the corresponding flood peak flow q sample series, and selects the distribution with the best fitting effect by K-S test, and the specific calculation steps are as follows:
s21, selecting exponential distribution, lognormal distribution and Weibull distribution to perform edge distribution fitting on the accumulated rainfall v and the corresponding flood peak flow q sample series under different early-stage soil wetting degrees and different duration conditions, and meanwhile, solving parameters corresponding to all distributions. The function expressions of the exponential distribution, the lognormal distribution and the Weibull distribution are respectively as follows:
Figure BDA0002128679150000021
in the formula, x is a random variable, and lambda is a proportional parameter of exponential distribution;
Figure BDA0002128679150000031
wherein x is a random variable, and μ and σ are the mean and standard deviation, respectively, of y ═ ln (x);
Figure BDA0002128679150000032
in the formula, x is a random variable, alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter;
the fitting of the three edge distributions can be achieved with the functions expfit, logfit and wblfit, respectively, in MATLAB software.
S22, judging whether the sample obeys a certain distribution by using a K-S test method, and comparing P values of the three distributions, wherein the P value is a statistic used for measuring significance level in the K-S test method. In the present invention it is assumed that the sample obeys the theoretical distribution function f (x), and if at the significance level (α ═ 0.05) the P value is less than 0.05, the original assumption is rejected, the sample does not obey the given distribution function f (x). Otherwise, the original assumption is accepted, and the larger the P value is, the better the fitting effect is. And finally, selecting the distribution with the best fitting effect as the optimal edge distribution of the sample series. The K-S test can be implemented using the function kstest in MATLAB software.
And S3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions.
Further, step S3 specifically includes the following steps:
s31, selecting a Frank Copula function to construct joint distribution, wherein the joint distribution is defined as follows:
Figure BDA0002128679150000033
in the formula, F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), C is a Copula function, θ is a parameter of the Copula function, and can be calculated by a Kendall correlation coefficient τ, and the calculation formula of τ is as follows:
Figure BDA0002128679150000035
the joint cumulative distribution function F (x, y) of the random variables v and q may be defined as:
F(x,y)＝C(F(x),G(y))＝C(u,v)
wherein F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), and C is a Copula function; the joint density function is shown below:
f(x,y)＝c[F(x),G(y)]f(x)g(y)
wherein C is the density function of C, f (X) and g (Y) are the probability density functions of random variables X and Y, respectively;
kendall correlation coefficient tau is obtained through a sample series, a parameter theta can be obtained through the formula in a reverse mode, and then the joint distribution can be obtained through combining the edge distribution of two random variables v and q.
In MATLAB software, Kendall correlation coefficient tau can be calculated by a function corr, parameters of a Copula function can be calculated by a function Copula param, and joint probability distribution of the Copula function can be calculated by a function Copula and df.
And S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions.
Further, the step S4 specifically includes:
s41, the utility-entropy decision model is expected to combine the objective risk of performing an action with the subjective preference of the decision maker. The function expression is as follows:
Figure BDA0002128679150000041
in the formula, meana∈A{|E[(u(X(a,θ))]| } ≠ 0, Ha (θ) represents the entropy of action a corresponding to state θ; x (a, θ) represents the result for state θ when action a is taken, and consists of four parts: x11(accurately give an alarm, Q is greater than or equal to Q and V is greater than or equal to V)T)、X12(missing report, Q is more than or equal to Q and V is less than VT)、X21(false alarm, Q is less than Q and V is more than or equal to V)T) And X22(No alarm is issued accurately, Q < Q and V < V)T)；λ∈[0,1]The "trade-off coefficient" reflects the trade-off between the subjective expected utility and the objective uncertainty of the decision maker's behavior. When λ is 0, only the subjective preference of the decision maker is considered, and it is expected that the utility will have a greater impact; when λ is 1, then the desired utility of the decision maker is not considered, only the entropy, i.e. the influence of the objective uncertainty, is considered. However, in actual decision making, both subjective expectation and objective risk of a decision maker need to be considered, so that a case where λ is 0.5 is assumed as both factors is considered. When action a is taken to make the function obtain the minimum value, namely the risk is minimum, action a is the optimal action scheme, and V is at the momentTThe optimal critical rainfall is obtained;
s42, calculating the critical rainfall only considering the subjective preference of the decision maker by using a Bayesian utility function, wherein the critical rainfall is defined as follows:
Figure BDA0002128679150000051
wherein q is a flow rate value, m3S; q is the critical flow value of the river critical section, m3S; v is the cumulative rain value, mm; vTCritical rain value, mm; t is duration of heavy rain (3h, 6h, 12h, 24 h); parameter a is 10 × 106，b＝200，c＝0.025，C0＝10×103，a’＝5×106，b’＝800，c’＝0.03；
Critical rainfall V for different soil wetting degrees in the early stages (AMCI, AMCII) and different rainfall durations (3, 6, 12, 24 hours)TCan be determined by minimizing the expected utility loss function, i.e. finding the V that minimizes the expected utility loss functionTValue VTThis value is the evaluated value; the specific formula is as follows:
Figure BDA0002128679150000052
where f (q, V | T) is the joint probability density of the cumulative rainfall and corresponding peak flows, U (q, V | V)TT) is the utility function value;
s43, only considering the critical rainfall when objective uncertainty is calculated by utilizing entropy, and if two continuous random variables X and Y exist, the joint entropy and the conditional entropy can be respectively shown as the following formulas:
Figure BDA0002128679150000053
wherein f (X, Y) is the joint probability density of random variables X and Y;
Figure BDA0002128679150000054
in the formula, f (X | Y) is a conditional probability density, namely the probability density of the value of X when Y takes any fixed value; the properties according to the conditional probability density can be given as:
the conditional entropy in the calculation of the critical rainfall can be expressed as the following form, wherein v is the accumulated rainfall, and q is the peak flow corresponding to the accumulated rainfall:
Figure BDA0002128679150000061
entropy decision methods are classical methods in the field of investment decision making, and can combine objective risk of performing an action with subjective preferences of the decision maker. When a mountain flood arrives, it is a risk action for a decision maker whether to issue a flood alarm. When taking action, the subjective judgment of a decision maker and the uncertainty of an objective event jointly determine the risk of the action, the smaller the risk is, the better the risk is, the critical rainfall at the minimum risk can be obtained by adopting the method, and the decision maker can make the minimum risk by comparing the actual rainfall with the critical rainfall when facing the coming mountain torrents. Therefore, the method for determining the critical rainfall has strong rationality and accuracy, and has a great prospect in the future research of mountain torrent disaster early warning and forecasting. The method solves the problem of determining the mountain torrent disaster early warning index by using a risk decision method, not only considers the influence of subjective preference of a decision maker, but also considers the uncertainty of objective state, fully embodies the characteristics of risk action, and has the advantages of lower calculation complexity, clear and definite structure and reasonable and accurate calculation result, thereby being widely applied to mountain torrent disaster early warning and forecasting work.
Compared with the prior art, the beneficial effects are: according to the dynamic critical rainfall calculation method based on the entropy decision method, dynamic critical rainfall under different early soil humidity conditions is calculated by introducing the entropy decision method in the risk decision field, so that personnel and property losses caused by torrential mountain torrents can be reduced to the maximum extent, scientific basis is provided for evaluation, early warning, prevention and control and decision deployment of the mountain torrents, and the method has great significance for early warning and forecast of the mountain torrents and disaster prevention and reduction.
Drawings
FIG. 1 is an overall flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of three time periods (points) for calculating the accumulated rainfall v and the corresponding peak flow q according to the present invention.
Fig. 3 is a scatter diagram of a series of samples of accumulated rainfall v and corresponding flood peak flow q at different early soil wetting degrees and different durations.
Fig. 4 is a comparison graph of the fitting effect of the edge distribution of the cumulative rainfall v and the corresponding flood peak flow q sample series according to the present invention.
FIG. 5 is a graph of combined probability density over different durations under early soil wetting conditions in accordance with the present invention.
FIG. 6 is a graph showing the joint probability distribution of different durations under the soil wetting condition at the early stage of the present invention.
Fig. 7 is a diagram of a result of a critical rainfall calculation obtained by an entropy decision method according to the present invention.
Fig. 8 is a diagram illustrating evaluation of critical rainfall application effect by the entropy decision method of the present invention.
Detailed Description
The drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.
Example 1:
as shown in fig. 1, a dynamic critical rainfall calculation method based on an entropy decision method includes the following steps:
step 1: the invention selects river upstream basin of Fugang county in Guangdong province as an experimental area. The Guangdong province is in subtropical monsoon climate areas in the same period of rain and heat, is positioned on movement paths of tropical storms, is easily attacked by rainstorm extreme weather, and is easily subjected to mountain areas and hills in Guangdong province, and rivers are dense, so that mountain flood disasters are easily caused. The intensive population in the mountainous area leads to excessive development of land, and the water and soil loss is aggravated due to cutting and excessive cutting, and the influence of mountain torrent disasters in Guangdong province is also aggravated. The Fugang county in Qingyuan province of Guangdong province is located in the middle of the Guangdong province and is one of three heavy rainstorm centers of the Guangdong province, terrain topography inclines from the northeast to the southwest, low mountains in the country, hills and plains are staggered, rivers are numerous, and mountain flood disasters are easy to occur. Therefore, in order to further make the work of early warning, forecasting, preventing and controlling the mountain torrent disasters in the area, the invention provides a dynamic critical rainfall calculation method, which provides technical support for the work of early warning, forecasting, preventing and reducing the mountain torrent disasters in the area.
Step 2: firstly, the invention collects the rainfall runoff data of river upstream watershed when 23 floods occur in 20 years, the rainfall data of the 23 floods are input into a well-established TOPMODEL hydrological model, the flow series with different early soil wetting degrees are simulated, and the flow series are subdivided according to different durations (3h, 6h, 12h and 24h), so that 23 groups of accumulated rainfall v and corresponding flood peak flow q sample series exist for different early soil wetting degrees and different durations. The definition of the accumulated rainfall and the corresponding peak flow of the present invention is shown in fig. 2. The black solid line in the figure indicates a hypothetical flooding process, t0 is the rainstorm start time, Tr is the rainfall duration (3h, 6h, 12h, 24h), and Tc is the basin average confluence time. The cumulative rainfall v used to fit the edge distribution is therefore the cumulative rainfall from t0 to t0+ Tr, corresponding to the maximum flow value occurring in the time interval where the flood peak flow q is from t0 to t0+ Tr + Tc. The final sample series scatter diagram is shown in fig. 3, wherein in each diagram, scatter points with different shapes represent soil wetting degrees in the previous period, and from top to bottom represent AMC1 (drought), AMC2 (normal) and AMC3 (wet) in sequence; .
And step 3: fitting each group of the accumulated rainfall v and the corresponding flood peak flow q sample series respectively by using exponential distribution, lognormal distribution and Weibull distribution, and carrying out K-S test on the fitting effect, wherein the test result is shown in figure 4. The ordinate in the figure is a P value of K-S test, and the larger the P value is, the better the edge distribution fitting effect is. The optimal edge distribution and parameters of the accumulated rainfall v and the corresponding flood peak flow q at different early soil wetting degrees and different durations are detailed in table 1.
Table 1 cumulative rainfall v and optimal edge distribution parameter values of corresponding flood peak flow q sample series
Figure BDA0002128679150000081
And 4, step 4: the joint distribution was constructed in MATLAB software using the Frank Copula function. The Kendall correlation coefficients and Copula function parameters of the v-q sample series are shown in Table 2, and the obtained joint probability density and joint probability distribution results are shown in FIGS. 5 and 6, respectively (for the case of early soil wetting). Table 2 cumulative rainfall v and Kendall correlation coefficient and Copula function parameter corresponding to peak flow q
Figure BDA0002128679150000091
And 5: the expectation of the utility function can be calculated by integrating the product of the Bayes utility function and the V-q joint probability density, and the V when the minimum value is expected to be obtainedTNamely the optimal critical rainfall. The bayesian utility function only considers the subjective judgment of the decision maker, and the calculation results are shown in table 3 and fig. 7.
Step 6: as can be seen from the definition of the expected utility-entropy risk function, when action a is taken to make the function take the minimum value, i.e. the risk is minimum, action a is the optimal action scheme, and V is the optimal action scheme at this momentTNamely the optimal critical rainfall. When λ is 1, r (a) is Ha (θ), and only the uncertainty of the objective state is considered, the critical rainfall can be determined by combining the formula of entropy. In actual decision, it is often necessary to consider both subjective expectation and objective risk of a decision maker, so the present invention also assumes that λ ═ 0.5 is considered as two factors at the same time, and the calculation results are shown in table 3 and fig. 7.
Table 3 unit of critical rainfall calculation result by entropy decision method: mm is
Figure BDA0002128679150000101
Step 6: the method selects three floods with drought, normal and humid soil moisture degrees at the early stage from the historical runoff series of the experimental area to analyze the application effect. The critical rainfall result calculated by the entropy decision method is compared with the accumulated rainfall of the actual flood, and the accuracy of the critical rainfall calculation result is evaluated, wherein the result is shown in fig. 8 (a solid line with marks in the figure represents the critical rainfall obtained by the entropy decision method, a black dotted line represents the actually-measured accumulated rainfall for verifying the flood, a red vertical dotted line represents the moment when the flood flow exceeds the critical flow, and an abscissa represents the duration from the rainfall starting moment). According to the evaluation result, the critical rainfall calculated by the entropy decision method can accurately early warn the mountain torrent disasters on the whole, and can provide technical support for early warning, forecasting, disaster prevention and reduction of the mountain torrent disasters in the area.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (4)

1. A dynamic critical rainfall calculation method based on an entropy decision method is characterized by comprising the following steps:
s1, collecting and settling actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of a previous period;
s2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection;
s3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions;
and S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions.
2. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 1, wherein the step S2 specifically comprises:
s21, selecting exponential distribution, lognormal distribution and Weibull distribution to perform edge distribution fitting on the accumulated rainfall v and the corresponding flood peak flow q sample series under different early-stage soil wetting degrees and different duration conditions, wherein the function expressions of the exponential distribution, the lognormal distribution and the Weibull distribution are respectively as follows:
Figure FDA0002128679140000011
in the formula, x is a random variable, and lambda is a proportional parameter of exponential distribution;
Figure FDA0002128679140000012
wherein x is a random variable, and μ and σ are the mean and standard deviation, respectively, of y ═ ln (x);
Figure FDA0002128679140000013
in the formula, x is a random variable, alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter;
s22, judging whether the sample obeys a certain distribution by using a K-S inspection method, comparing P values of the three distributions, wherein the larger the P value is, the better the fitting effect is, and finally selecting the distribution with the best fitting effect as the optimal edge distribution of the sample series.
3. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 2, wherein the step S3 specifically comprises:
s31, selecting Frank Copula function to construct joint distribution; it is defined as follows:
Figure FDA0002128679140000021
Figure FDA0002128679140000022
in the formula, F (X, Y) is a joint distribution function of random variables (X, Y) at (X, Y), C is a Copula function, and theta is a parameter of the Copula function and can be obtained by calculating a Kendall correlation coefficient tau; the formula for τ is as follows:
Figure FDA0002128679140000023
the joint cumulative distribution function F (x, y) of the random variables v and q may be defined as:
F(x,y)＝C(F(x),G(y))＝C(u,v)
wherein F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), and C is a Copula function; the joint density function is shown below:
f(x,y)＝c[F(x),G(y)]f(x)g(y)
wherein C is the density function of C, f (X) and g (Y) are the probability density functions of random variables X and Y, respectively;
s32, obtaining a Kendall correlation coefficient tau through the sample series, obtaining a parameter theta through the formula in a reverse mode, and obtaining combined distribution by combining edge distribution of two random variables v and q.
4. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 3, wherein the step S4 specifically comprises:
s41, the expectation utility-entropy decision model can combine the objective risk of implementing the action with the subjective preference of a decision maker, and the expression is as follows:
in the formula, meana∈A{|E[(u(X(a,θ))]| } ≠ 0, Ha (θ) represents the entropy of action a corresponding to state θ; x (a, θ) represents the result for state θ when action a is taken, and consists of four parts: x11-accurately issuing an alarm, Q ≧ Q and V ≧ VT；X12Missing report, Q ≧ Q and V < VT)；X21-false positive, Q < Q and V ≧ VTAnd X22-no alarm is issued, Q < Q and V < VT；λ∈[0,1]The 'weighing coefficient' reflects the balance between the subjective expected utility and the objective uncertainty of the behavior of the decision maker; when λ is 0, only the subjective preference of the decision maker is considered, and it is expected that the utility will have a greater impact; when λ is 1, then the desired utility of the decision maker is not considered, only entropy, i.e. the influence of objective uncertainty, is considered; however, in actual decision making, both subjective expectation and objective risk of a decision maker need to be considered, and it is assumed that λ is 0.5 and is considered as two factors; when action a is taken to make the function obtain the minimum value, namely the risk is minimum, action a is the optimal action scheme, and V is at the momentTThe optimal critical rainfall is obtained;
s42, calculating the critical rainfall only considering the subjective preference of the decision maker by using a Bayesian utility function, wherein the critical rainfall is defined as follows:
wherein q is a flow rate value, m3S; q is the critical flow value of the river critical section, m3S; v is the cumulative rain value, mm; vTCritical rain value, mm; t is the duration of the storm; a. b, C, C0A ', b ', c ' are defined parameters;
critical rainfall V for different soil moisture degrees in earlier stage and different rainfall durationTCan be determined by minimizing the expected utility loss function, i.e. finding the V that minimizes the expected utility loss functionTValue VTThe value is the evaluated value, and the specific formula is shown as follows：
Figure FDA0002128679140000032
Where f (q, V | T) is the joint probability density of the cumulative rainfall and corresponding peak flows, U (q, V | V)TT) is the utility function value;
s43, only considering the critical rainfall when objective uncertainty is calculated by utilizing entropy, and if two continuous random variables X and Y exist, the joint entropy and the conditional entropy can be respectively shown as the following formulas:
Figure FDA0002128679140000033
wherein f (X, Y) is the joint probability density of random variables X and Y;
Figure FDA0002128679140000041
in the formula, f (X | Y) is a conditional probability density, namely the probability density of the value of X when Y takes any fixed value; the properties according to the conditional probability density can be given as:
Figure FDA0002128679140000042
the conditional entropy in the calculation of the critical rainfall can be expressed as the following form, wherein v is the accumulated rainfall, and q is the peak flow corresponding to the accumulated rainfall:
Figure FDA0002128679140000043
CN201910630957.7A 2019-07-12 2019-07-12 Entropy decision method based dynamic critical rainfall calculation method Pending CN110673230A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910630957.7A CN110673230A (en) 2019-07-12 2019-07-12 Entropy decision method based dynamic critical rainfall calculation method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910630957.7A CN110673230A (en) 2019-07-12 2019-07-12 Entropy decision method based dynamic critical rainfall calculation method

Publications (1)

Publication Number Publication Date
CN110673230A true CN110673230A (en) 2020-01-10

Family

ID=69068629

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910630957.7A Pending CN110673230A (en) 2019-07-12 2019-07-12 Entropy decision method based dynamic critical rainfall calculation method

Country Status (1)

Country Link
CN (1) CN110673230A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116611333A (en) * 2023-05-23 2023-08-18 中国水利水电科学研究院 Urban flood risk point prediction method

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106202788A (en) * 2016-07-20 2016-12-07 中国水利水电科学研究院 A kind of tide flood combined probability analysis method based on Copula function and application thereof
CN107808237A (en) * 2017-09-30 2018-03-16 河海大学 A kind of parallel reservoir group Real time Flood risk Analytic Calculation Method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106202788A (en) * 2016-07-20 2016-12-07 中国水利水电科学研究院 A kind of tide flood combined probability analysis method based on Copula function and application thereof
CN107808237A (en) * 2017-09-30 2018-03-16 河海大学 A kind of parallel reservoir group Real time Flood risk Analytic Calculation Method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
V. MONTESARCHIO 等: "Rainfall threshold definition using an entropy decision approach and radar data", 《NATURAL HAZARDS AND EARTH SYSTEM SCIENCES》 *
李鹏 等: "基于我国洪涝灾害的多事件触发巨灾债券设计与定价", 《2017中国保险与风险管理国际年会论文集》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116611333A (en) * 2023-05-23 2023-08-18 中国水利水电科学研究院 Urban flood risk point prediction method
CN116611333B (en) * 2023-05-23 2023-11-14 中国水利水电科学研究院 Urban flood risk point prediction method

Similar Documents

Publication Publication Date Title
CN110428586B (en) Early warning method for rural basal flood based on early rainfall and upstream and downstream topological relation
CN108597189B (en) distributed medium and small watershed geological disaster and flood early warning method based on critical rainfall
Crisci et al. Extreme rainfall in a changing climate: regional analysis and hydrological implications in Tuscany
CN112329257B (en) Hydrological model segmented screening method suitable for forecasting and early warning of torrential rain, torrential flood and flood in small watershed of mountainous area
CN111639810B (en) Rainfall forecast precision assessment method based on flood prevention requirements
CN108269016B (en) Small watershed torrential flood disaster risk analysis method based on information diffusion
CN112686426B (en) Incoming water quantity early warning method and system based on hydropower station basin key points
CN111242404A (en) Extreme evaluation method and system for heavy rainfall induced flood incident
CN109887241A (en) A kind of mountain flood weather warning calculation method and system
CN112288151B (en) Disaster chain construction and disaster analysis method for disaster emergency
CN114896785A (en) Point rainstorm rainfall sorting method and point rainstorm reappearance period estimation method
CN110673230A (en) Entropy decision method based dynamic critical rainfall calculation method
Amengual et al. Hydrometeorological ensemble simulations of flood events over a small basin of Majorca Island, Spain
CN113269376B (en) River flood peak flow range calculation method
CN109671248A (en) Mountain flood method for early warning based on object of taking precautions against natural calamities
CN114692432A (en) Forecasting system and method for simulating real-time evidence booking of urban rainstorm ponding
Langat et al. A comparative flood frequency analysis of high-flow between annual maximum and partial duration series at Sungai Langat Basin
CN111047213B (en) Medium-long term water resource quantity critical early warning index method based on multi-element joint discrimination
CN112530137A (en) Distributed medium and small watershed geological disaster and flood early warning method based on critical rainfall
Kim Framework of extreme flood risk management in the typhoon country region
Huang et al. Study of risk and early warning index of rainstorm waterlogging in Wuhan City
Kang et al. Applying the dynamic critical precipitation method for flash flood early warning
CN112381285B (en) Flood inundation prediction method based on remote sensing
CN117831231B (en) Method for carrying out flooding early warning on easily flooded and easily waterlogged areas
Yucel et al. Assessment of flash flood events using remote sensing and atmospheric model-derived precipitation in a hydrological model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20200110