Flood area composition calculation method and system based on MCMC

Abstract

The invention provides an MCMC-based flood area composition calculation method and system, and the method comprises the steps: determining a design section and branch and interval incoming water according to the water system composition of a research drainage basin, and collecting and sorting the flow data of related sites; determining a design flood duration, and determining a flood sample according to the sorted site flow data; performing frequency analysis on the selected flood sample, and determining the designed flood volume according to the recurrence period; mCMC iteration is carried out on flow data of different branch incoming water and interval incoming water, and the composition proportion of each part of flood is calculated; calculating the flood volume of each subarea according to the calculated design flood volume and the calculated area composition proportion; and setting a confidence interval, performing uncertainty calculation on the calculated region composition parameters, and analyzing the uncertainty of the flood region composition.

Description

Technical Field

[0001] The invention relates to the field of hydrological and water conservancy calculation, and in particular to a flood area composition calculation method and system based on MCMC. Background Art

[0002] Since the mid-to-late 1950s, my country has begun to develop water conservancy and hydropower projects on a large scale. Since the 1970s, my country has formed a relatively standardized and complete system for design flood calculation. In the construction of new water conservancy projects, the construction of river basin flood control systems, the safety appraisal of existing water conservancy projects and the review of flood control standards, and the operation and dispatch management of river basin cascade reservoirs, how to adapt the design flood analysis and calculation to the changes in the underlying surface and river confluence conditions, and take the impact of reservoir dispatch into consideration, is a major issue that needs to be improved in the planning and design of water conservancy and hydropower projects and the operation and management of river basin cascade reservoirs.

[0003] The flood area composition method analyzes the statistical laws of the flood sources of the design section from the perspective of climate causes and combines statistical methods. After formulating the representative flood area composition of the design section, the design flood of the downstream section affected by regulation and storage can be deduced based on the joint dispatching rules, so it is widely used in engineering practice.

[0004] When data is insufficient, the analysis results are more accidental. The same frequency method is simple to calculate, but its design results are not clear for flood control; and for high-dimensional cascade reservoirs, there are many options, and there is great uncertainty in which option to choose.

[0005] In order to make up for the shortcomings of the existing flood area composition calculation method, and comprehensively consider the new requirements for design floods and flood area composition in the planning and design of water conservancy and hydropower projects and the operation of cascade reservoirs in the changing environment, the present invention proposes a flood area composition calculation method and system based on MCMC, which implements multiple iterations of MCMC through a computer system to obtain the probability distribution of flood area composition under a specific return period in the study area. The method is simple to calculate and flexible to use. While obtaining the flood area composition, it also gives the probability distribution and confidence interval of the regional composition, which can assist flood control calculations and their uncertainty analysis; under the background of climate change and frequent human activities, the regional composition can be flexibly recalculated and adjusted, and has good temporal and spatial portability, and is particularly suitable for cascade reservoirs with more partitions and more complex regional composition. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a method and system for calculating the composition of flood areas based on MCMC to solve the problem of analyzing the composition of flood areas under a changing environment.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] The present invention provides a method for calculating flood area composition based on MCMC, comprising the following steps:

[0009] S1. According to the water system composition of the study basin, determine the design section and the water inflow of tributaries and intervals, and collect and organize the flow data of relevant stations;

[0010] S2. Determine the design flood duration and determine the flood sample based on the site flow data compiled in S1;

[0011] S3. Conduct frequency analysis on selected flood samples and determine the design flood volume based on the recurrence period;

[0012] S4, perform MCMC iteration on the flow data of different tributaries and intervals to calculate the proportion of flood components in each part;

[0013] S5. Calculate the flood volume of each subarea according to the design flood volume calculated by S3 and the regional composition ratio calculated by S4;

[0014] S6. Set a confidence interval, perform uncertainty calculation on the regional composition parameters calculated in S4, and analyze the uncertainty of the flood area composition.

[0015] Furthermore, in S4, the MCMC iteration is specifically:

[0016] S401, let C be the research section, A1, A2...A n-1 , A n are n cascade reservoirs upstream; B1, B2...B n-1 , B n is the interval watershed of n cascade reservoirs upstream; random variable X i , Y i and Z for A i , B i and natural flooding of C, Note x i =α i ·Z,y i =β i Z, i = 1, 2, ..., n; random variable X i , Y i The values ​​of and Z are x i ,y i and z; α i is the proportion of flood volume above the reservoir; β i is the proportion of flood volume in the uncontrolled interval;

[0017] S402, setting the number of MCMC iterations, and specifying a set of initial values ​​of parameters in the regional composition ratio space (0,1) as the MCMC iteration starting point;

[0018] S403, according to the prior distribution of the parameters, on the basis of the initial value, each parameter is randomly changed in the parameter space, and the probability density of the parameter combination after the change is calculated;

[0019] S404, judging whether to retain the changed parameter vector according to whether the ratio of the probability density of the parameter combination after the change in S303 to the initial probability density is greater than a uniformly distributed random number u~U(0,1) between 0 and 1;

[0020] If the ratio of the probability density before and after the change is greater than the random number u<P / P b , then accept the change; P b is the probability density of the parameter at time t; P is the probability density of the parameter at time t+1; the changed parameter is recorded as the new initial parameter, and then returned;

[0021] If the probability density ratio after the change is less than the random number, the changed parameters will not be retained, and the parameters before the change will be used as the starting point to return;

[0022] If a non-periodic Markov has a state transition matrix M, and any two states i′ and j′ are connected, then limM x When x approaches infinity, it has nothing to do with the time, that is:

[0023]

[0024] π is the only non-negative solution of the equation πP=π, where π=[π(1),π(2),…,π(j),], π is the stationary distribution of the Markov chain, and the regional composition ratio needs to be calculated;

[0025] Assuming that the Markov chain converges at the xth step, then α x ~π(t), α x+1 ~π(t), α x+2 ~π(t), ..., so a x 、a x+1 、a x+2 ,…π(t) are all random variables with distribution;

[0026] Receiving probability P / P b According to Markov's detailed stationary condition, the probability of the Markov chain transferring from time t to time t+1 is consistent with the probability of the state from time t+1 to time t, that is:

[0027] π(t)P(t,t+1)a(t)=π(t+1)P(t+1,t);

[0028]

[0029] Furthermore, the prior distribution is a uniform distribution without information ~U(0,1); the random change is a random walk method a t+1 =a t +ε, ε is the random walk step length; the probability density of the posterior distribution of the parameter is P = P α ×P β ×C(P α ,P β ), where C(P α ,P β ) is the Copula function of the partition flood.

[0030] Furthermore, the flow data are as follows: if the duration is 30 days or 10 days, the flow data required for the design flood is on a daily scale; if the duration is medium or short, such as 3 days or 1 day, the flow data required for the design flood is on an hourly scale.

[0031] Furthermore, in S2, the maximum value method is used for flood samples. If the flow data of the study area for 30 consecutive years cannot be obtained, the super-quantitative method is used to select flood samples.

[0032] Furthermore, in S3, a probability distribution function line type is used to perform frequency analysis.

[0033] Furthermore, in S6, the confidence interval of the parameter is selected as 95%, or 90% or 75% according to the characteristics of the watershed or actual design requirements.

[0034] Furthermore, a flood area composition calculation system based on MCMC is implemented by using a flood area composition calculation method based on MCMC, and further includes:

[0035] Data acquisition module: obtain traffic data of different sites based on the calculation area;

[0036] Sample selection module: determine the design flood duration and select flood samples based on flow data;

[0037] Design flood calculation module: conduct frequency analysis on selected flood samples, determine the design flood recurrence period, and determine the design flood volume based on the recurrence period;

[0038] MCMC iteration module: MCMC iteration is performed on flood data of different stations to obtain the composition ratio of water inflow in different tributaries and intervals;

[0039] Flood area composition calculation module: inline the design flood calculation module and MCMC iteration module to calculate the flood area composition under a specific return period;

[0040] Uncertainty Analysis Module: Calculates the uncertainty of flood area composition based on the confidence interval analysis input by the user;

[0041] Input display module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module and uncertainty analysis module, for allowing users to input operation instructions and display accordingly;

[0042] Control module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module, uncertainty analysis module and input display unit to control operation.

[0043] The beneficial effects of the present invention are as follows: the provided method and system for calculating flood area composition based on MCMC can obtain the flood area composition and its probability distribution under a specific return period of the study area by using a computer system to implement multiple iterations of MCMC, and can also perform uncertainty analysis on the flood area composition scheme. The present invention introduces the MCMC method into the calculation of flood area composition, and based on the randomness and ergodicity of the MCMC method, effectively solves the problems of high data demand and poor portability in traditional area composition methods. The method is simple to calculate and flexible to use. While obtaining the flood area composition, it also gives the probability distribution and confidence interval of the area composition, which can assist in flood control calculations and their uncertainty analysis; under the background of climate change and frequent human activities, the area composition can be flexibly recalculated and adjusted, which is particularly suitable for cascade reservoirs with more partitions and more complex area composition, and provides new ideas for the calculation method of flood area composition. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flowchart of a method for calculating flood area composition based on MCMC;

[0045] Figure 2 A schematic diagram of a cascade reservoir group in a flood area of ​​the present invention;

[0046] Figure 3 This is the distribution and uncertainty analysis diagram of regional composition parameters of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0048] A method for calculating flood area composition based on MCMC, comprising the following steps:

[0049] S1. According to the water system composition of the study basin, determine the design section and the water inflow of tributaries and intervals, and collect and organize the flow data of relevant stations;

[0050] Specifically, the flow data of these stations are collated assuming the simplest case where the flood area consists of one reservoir controlled and one interval incoming flow;

[0051] S2. Determine the design flood duration and determine the flood sample based on the site flow data compiled in S1;

[0052] Specifically, the design flood duration is determined to be 30 days, and flood sampling is carried out according to the annual maximum value;

[0053] S3. Conduct frequency analysis on selected flood samples and determine the design flood volume based on the recurrence period;

[0054] Specifically, the P-III curve is used to conduct frequency analysis on the selected flood volume samples, and the recurrence period of the design flood volume is determined to be once in a hundred years, and the design flood is determined based on the recurrence period;

[0055] S4, perform MCMC iteration on the flow data of different tributaries and intervals to calculate the proportion of flood components in each part;

[0056] Specifically, MCMC iterations are performed on the flow data of reservoir water and interval water to calculate the flood area composition ( Figure 3 );

[0057] S5. Calculate the flood volume of each subarea according to the design flood volume calculated by S3 and the regional composition ratio calculated by S4;

[0058] S6. Set the confidence interval to 95%, perform uncertainty calculation on the regional composition parameters calculated in S4, and analyze the uncertainty of the flood area composition.

[0059] In S4, the MCMC iteration is specifically:

[0060] S401, let C be the research section, A1, A2...A n-1 , A n are n cascade reservoirs upstream; B1, B2...B n-1 , B n is the interval watershed of n cascade reservoirs upstream; random variable X i , Y i and Z for A i , B i and natural flooding of C, Note x i =α i ·Z,y i =β i Z, i = 1, 2, ..., n; random variable X i , Y iThe values ​​of and Z are x i ,y i and z; α i is the proportion of flood volume above the reservoir; β i is the proportion of flood volume in the uncontrolled interval;

[0061] S402, setting the number of MCMC iterations to 10,000, and specifying the initial value of the proportion of flood volume above the reservoir to be 0.7 and the initial value of the proportion of flood volume in the uncontrolled interval to be 0.3 in the regional composition ratio space (0,1) as the initial value, which are used as the MCMC iteration starting point;

[0062] S403, according to the prior distribution of the parameters, on the basis of the initial value, each parameter is randomly changed in the parameter space, and the probability density of the parameter combination after the change is calculated;

[0063] S404, judging whether to retain the changed parameter vector according to whether the ratio of the probability density of the parameter combination after the change in S303 to the initial probability density is greater than a uniformly distributed random number u~U(0,1) between 0 and 1;

[0064] If the ratio of the probability density before and after the change is greater than the random number u<P / P b , then accept the change; P b is the probability density of the parameter at time t; P is the probability density of the parameter at time t+1; the changed parameter is recorded as the new initial parameter, and then returned;

[0065] If the probability density ratio after the change is less than the random number, the changed parameters will not be retained, and the parameters before the change will be used as the starting point to return;

[0066] If a non-periodic Markov has a state transition matrix M, and any two states i′ and j′ are connected, then limM x When x approaches infinity, it has nothing to do with the time, that is:

[0067]

[0068] π is the only non-negative solution of the equation πP=π, where π=[π(1),π(2),…,π(j),], π is the stationary distribution of the Markov chain, and the regional composition ratio needs to be calculated;

[0069] Assuming that the Markov chain converges at the xth step, then α x ~π(t), α x+1 ~π(t), α x+2 ~π(t),…, so a x 、a x+1 、a x+2 ,…π(t) are all random variables with distribution;

[0070] Receiving probability P / P b According to Markov's detailed stationary condition, the probability of the Markov chain transferring from time t to time t+1 is consistent with the probability of the state from time t+1 to time t, that is:

[0071] π(t)P(t,t+1)a(t)=π(t+1)P(t+1,t);

[0072]

[0073] The prior distribution is a uniform distribution without information ~U(0,1); the random change is a random walk method a t+1 =a t +ε, ε is the random walk step length; the probability density of the posterior distribution of the parameter is P = P α ×P β ×C(P α ,P β ), where C(P α ,P β ) is the Copula function of the partition flood.

[0074] The flow data are as follows: for a duration of 30 days or 10 days, the flow data required for the design flood is on a daily scale; for a medium or short duration of 3 days or 1 day, the flow data required for the design flood is on an hourly scale.

[0075] In S2, the maximum value method is used for flood samples. If the flow data of the study area for 30 consecutive years cannot be obtained, the super-quantitative method is used to select flood samples.

[0076] In S3, a probability distribution function line is used to perform frequency analysis.

[0077] In S6, the confidence interval of the parameter is selected as 95%, or 90% or 75% according to the characteristics of the watershed or actual design requirements.

[0078] A flood area composition calculation system based on MCMC is implemented by using the flood area composition calculation method based on MCMC, and further includes:

[0079] Data acquisition module: obtain traffic data of different sites based on the calculation area;

[0080] Sample selection module: determine the design flood duration and select flood samples based on flow data;

[0081] Design flood calculation module: conduct frequency analysis on selected flood samples, determine the design flood recurrence period, and determine the design flood volume based on the recurrence period;

[0082] MCMC iteration module: MCMC iteration is performed on flood data of different stations to obtain the composition ratio of water inflow in different tributaries and intervals;

[0083] Flood area composition calculation module: inline the design flood calculation module and MCMC iteration module to calculate the flood area composition under a specific return period;

[0084] Uncertainty Analysis Module: Calculates the uncertainty of flood area composition based on the confidence interval analysis input by the user;

[0085] Input display module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module and uncertainty analysis module, for allowing users to input operation instructions and display accordingly;

[0086] Control module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module, uncertainty analysis module and input display unit to control operation.

[0087] The above-mentioned embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be based on the attached claims.

Claims

1. A method for calculating flood area composition based on MCMC, characterized by: The following steps are involved: S1. According to the water system composition of the study basin, determine the design section and the water inflow of tributaries and intervals, and collect and organize the flow data of relevant stations; S2. Determine the design flood duration and determine the flood sample based on the site flow data compiled in S1; S3. Conduct frequency analysis on selected flood samples and determine the design flood volume based on the recurrence period; S4, perform MCMC iteration on the flow data of different tributaries and intervals to calculate the proportion of flood components in each part; S5. Calculate the flood volume of each subarea according to the design flood volume calculated by S3 and the regional composition ratio calculated by S4; S6. Set a confidence interval, perform uncertainty calculation on the regional composition parameters calculated in S4, and analyze the uncertainty of the flood area composition.

2. The method for calculating flood area composition based on MCMC according to claim 1, characterized in that: In S4, the MCMC iteration is specifically: S401, let C be the research section, A1, A2...A n-1 , A n are n cascade reservoirs upstream; B1, B2...B n-1 , B n is the interval watershed of n cascade reservoirs upstream; random variable X i , Y i and Z for A i , B i and natural flooding of C, Note x i =α i ·Z,y i =β i Z, i = 1, 2, ..., n; random variable X i , Y i The values ​​of and Z are x i ,y i and z; α i is the proportion of flood volume above the reservoir; β i is the proportion of flood volume in the uncontrolled interval; S402, setting the number of MCMC iterations, and specifying a set of initial values ​​of parameters in the regional composition ratio space (0,1) as the MCMC iteration starting point; S403, according to the prior distribution of the parameters, on the basis of the initial value, each parameter is randomly changed in the parameter space, and the probability density of the parameter combination after the change is calculated; S404, judging whether to retain the changed parameter vector according to whether the ratio of the probability density of the parameter combination after the change in S303 to the initial probability density is greater than a uniformly distributed random number u~U(0,1) between 0 and 1; If the ratio of the probability density before and after the change is greater than the random number u<P / P b , then accept the change; P b is the probability density of the parameter at time t; P is the probability density of the parameter at time t+1; the changed parameter is recorded as the new initial parameter, and then returned; If the probability density ratio after the change is less than the random number, the changed parameters will not be retained, and the parameters before the change will be used as the starting point to return; If a non-periodic Markov has a state transition matrix M, and any two states i′ and j′ are connected, then limM x When x approaches infinity, it has nothing to do with the time, that is: π is the only non-negative solution of the equation πP=π, where π=[π(1),π(2),…,π(j),], π is the stationary distribution of the Markov chain, and the regional composition ratio needs to be calculated; Assuming that the Markov chain converges at the xth step, then α x ~π(t), α x+1 ~π(t), α x+2 ~π(t),…, so a x 、a x+1 、a x+2 ,…π(t) are all random variables with distribution; Receiving probability P / P b According to Markov's detailed stationary condition, the probability of the Markov chain transferring from time t to time t+1 is consistent with the probability of the state from time t+1 to time t, that is: π(t)P(t,t+1)a(t)=π(t+1)P(t+1,t;) 3. The method for calculating flood area composition based on MCMC according to claim 2, characterized in that: The prior distribution is a uniform distribution without information ~U(0,1); the random change is a random walk method a t+1 =a t +ε, ε is the random walk step length; the probability density of the posterior distribution of the parameter is P = P α ×P β ×C(P α ,P β ), where C(P α ,P β ) is the Copula function of the partition flood.

4. The method for calculating flood area composition based on MCMC according to claim 3, characterized in that: The flow data are as follows: for a duration of 30 days or 10 days, the flow data required for the design flood is on a daily scale; for a medium or short duration of 3 days or 1 day, the flow data required for the design flood is on an hourly scale.

5. The method for calculating flood area composition based on MCMC according to claim 4, characterized in that: In S2, the maximum value method is used for flood samples. If the flow data of the study area for 30 consecutive years cannot be obtained, the super-quantitative method is used to select flood samples.

6. The method for calculating flood area composition based on MCMC according to claim 5, characterized in that: In S3, a probability distribution function line is used to perform frequency analysis.

7. The method for calculating flood area composition based on MCMC according to claim 6, characterized in that: In S6, the confidence interval of the parameter is selected as 95%, or 90% or 75% according to the characteristics of the watershed or actual design requirements.

8. A flood area composition calculation system based on MCMC, characterized by: The method is implemented by using a flood area composition calculation method based on MCMC as claimed in any one of claims 1 to 7, further comprising: Data acquisition module: obtain traffic data of different sites based on the calculation area; Sample selection module: determine the design flood duration and select flood samples based on flow data; Design flood calculation module: conduct frequency analysis on selected flood samples, determine the design flood recurrence period, and determine the design flood volume based on the recurrence period; MCMC iteration module: MCMC iteration is performed on flood data of different stations to obtain the composition ratio of water inflow in different tributaries and intervals; Flood area composition calculation module: inline the design flood calculation module and MCMC iteration module to calculate the flood area composition under a specific return period; Uncertainty Analysis Module: Calculates the uncertainty of flood area composition based on the confidence interval analysis input by the user; Input display module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module and uncertainty analysis module, for allowing users to input operation instructions and display accordingly; Control module: connected to the data acquisition module, sample selection module, design flood calculation module, MCMC iteration module, flood area composition calculation module, uncertainty analysis module and input display unit to control operation.

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