Method for determining designed flood level of Dongting lake area

Abstract

The invention relates to the technical field of flood control planning of water conservancy projects, and discloses a method for determining the designed flood level of a Dongting lake district, which comprises the following steps of: a) constructing a flood peak quantity joint distribution model: acquiring historical flood peak flow of a research area and flood quantity data in corresponding time periods, edge distribution fitting is carried out on the flood peak flow data and the time period flood volume data, and a Copula function is adopted to construct a joint distribution model of the flood peak flow data and the time period flood volume data; b) determining a combined recurrence period and a reasonable peak quantity combination boundary: defining and calculating the combined recurrence period of a design event based on the combined distribution model constructed in the step a), and determining a reasonable region boundary of the combination of the flood peak flow and the time period flood quantity in the combined recurrence period in combination with a preset confidence level; and c) deducing the designed flood level: selecting at least one design peak quantity combination in the reasonable area determined in the step b), obtaining the corresponding flood level through flood regulation calculation, and determining the final designed flood level in combination with the flood control guarantee rate. According to the method, by constructing the flood peak quantity joint distribution model and introducing confidence level screening reasonable combination, the scientificity and reliability of determining the design flood level of the Dongting lake area are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of flood control planning technology for water conservancy projects, specifically a method for determining the design flood level in the Dongting Lake area. Background Technology

[0002] As a typical polder-type river network and lake complex system, the Dongting Lake area has a two-way interactive characteristic of "flood peaks being supported by the Yangtze River main stream and flood volume being regulated by the polders in the lake area". Its flood peak volume relationship is significantly affected by the exchange of water and sediment between rivers and lakes (such as the three flood diversion points and siltation) and the layout of dike and polder engineering (such as the flood diversion and retention functions of more than 1,200 polders).

[0003] Existing methods for determining design flood levels are mainly based on univariate flood frequency analysis, considering only the flood peak or flood volume alone, without fully taking into account the correlation between the two. This makes it difficult to accurately depict the complex coupling relationship between "flood peak-flood volume-water level." In extreme cases of combined flood peak and flood volume (such as a small flood peak with an exceptionally large flood volume), this method cannot accurately assess the risk, potentially leading to an overestimation of risk and wasted resources, or an underestimation of risk and the creation of flood control hazards. With the increasing complexity of water inflow conditions due to climate change and human activities, there is an urgent need for a method for determining design flood levels that comprehensively considers the correlation between flood peak and flood volume. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for determining the design flood level in the Dongting Lake area, which solves the problem of insufficient assessment of extreme peak volume combinations in "multi-source coupled watersheds" in existing technologies.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for determining the design flood level in the Dongting Lake area, comprising the following steps:

[0006] a) Construct a joint distribution model of flood peak volume: Collect historical flood peak flow and corresponding time period flood volume data of the study area, perform marginal distribution fitting on the flood peak flow and time period flood volume data respectively, and use the Copula function to construct a joint distribution model of the flood peak flow and time period flood volume;

[0007] b) Determine the joint return period and reasonable peak volume combination boundary: Based on the joint distribution model constructed in step a), define and calculate the joint return period of the design event, and combine it with the preset confidence level to determine the reasonable regional boundary of the combination of peak flow and time-period flood volume under the joint return period;

[0008] c) Determine the design flood level: Within the reasonable area determined in step b), select at least one combination of design peak volumes, obtain the corresponding flood level through flood regulation calculation, and determine the final design flood level in combination with the flood control guarantee rate.

[0009] Preferably, the marginal distribution fitting of the peak flow and time-period flood volume data in step a) includes fitting the data using a Pearson Type III distribution or a generalized extreme value distribution and estimating its distribution parameters.

[0010] Preferably, the construction of the joint distribution model using Copula functions in step a) includes: selecting at least two different types of Copula functions as candidates, and selecting the optimal Copula function from the candidate Copula functions through statistical testing methods to construct the joint distribution model.

[0011] Preferably, the statistical test methods include the Kolmogorov-Smirnov test, the Akaike information criterion, or the Bayesian information criterion.

[0012] Preferably, the determination of the reasonable area boundary for the combination of peak flow and time-period flood volume under the joint return period in step b) includes: drawing contour lines of the joint return period, and determining the boundary points for dividing the reasonable area and the unreasonable area on the contour lines by integrating the joint probability density function of the joint distribution model.

[0013] Preferably, the selection of at least one design peak quantity combination in c) includes selecting a combination of the same frequency and / or a conditionally desired combination.

[0014] Preferably, the same frequency combination refers to a combination in which the peak flow and the flood volume in a given time period have the same marginal exceedance probability; the conditional expectation combination refers to a combination formed by calculating the flood volume given the design peak flow, or calculating the peak flow given the design flood volume, under the premise of satisfying the design joint return period.

[0015] Preferably, the process of obtaining the corresponding flood level through flood control calculation in c) includes: using the lake basin volume-water level relationship curve and the polder flood control model, and considering the impact of siltation on the lake area's storage capacity.

[0016] Preferably, the determination of the final design flood level by combining the flood control guarantee rate in step c) includes: comparing multiple flood levels calculated by different combinations of design peak volumes, and selecting the higher or more unfavorable flood level as the final design flood level.

[0017] Preferably, the historical flood data includes the inflow of the Yangtze River into the lake at its three outlets, the flood volume at the four water control stations in Hunan, and the water level data at representative stations in the lake area.

[0018] This invention provides a method for determining the design flood level in the Dongting Lake area. It has the following beneficial effects:

[0019] 1. This invention introduces a Copula function to construct a joint distribution model of flood peak and flood volume, which can more scientifically reveal the complex correlation between these two factors in the Dongting Lake area. Compared with traditional univariate flood frequency analysis methods, this invention fully considers the actual occurrence mechanism of the combination of flood peak and flood volume, so that the determination of the design flood level is no longer limited to isolated extreme events, thereby significantly improving the scientific nature of flood risk assessment and the depth of understanding of the unique flood patterns in the Dongting Lake area.

[0020] 2. This invention innovatively introduces the concept of confidence level to define the boundary of reasonable peak volume combinations when determining the design flood level. This method effectively eliminates extreme and unreasonable peak volume combinations that, while statistically likely to occur on specific joint return period isohyets, actually have extremely low probabilities of occurrence or even contradict hydrophysical laws. This technical feature ensures that the selection of the design flood level is based on more realistic flood scenarios, avoiding design deviations caused by adopting extremely low-probability events and enhancing the reliability of flood control planning.

[0021] 3. This invention not only innovates in statistical modeling but also fully incorporates the specific hydrological and hydraulic characteristics of the Dongting Lake area in the process of determining the design flood level. By selecting typical design combinations within a reasonable range of peak flow combinations and conducting flood regulation calculations that take into account practical factors such as lake basin siltation and the regulation and storage effects of polder areas, the final determined design flood level can more realistically reflect the evolution pattern and disaster potential of floods within the lake area, thus improving the applicability and accuracy of the design results in complex lake systems.

[0022] 4. The method for determining design flood levels provided by this invention forms a logically rigorous and clearly defined technical system, encompassing data processing, joint distribution modeling, rational combination and screening, and flood regulation calculation. This system can provide more refined and systematic technical support for flood control planning and engineering design in the complex Dongting Lake area, helping to optimize flood control project layout and investment decisions, and has significant practical guiding significance for improving regional flood control and disaster reduction capabilities. Attached Figure Description

[0023] Figure 1 This is a diagram illustrating the method steps of the present invention.

[0024] Figure 2 This is a model surface diagram of the present invention.

[0025] Figure 3 This is a two-dimensional contour map of the present invention. Detailed Implementation

[0026] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please see the appendix Figure 1 This invention provides a method for determining the design flood level in the Dongting Lake area, comprising the following steps:

[0028] a) Construct a joint distribution model of flood peak volume: Collect historical flood peak flow and corresponding time period flood volume data of the study area, perform marginal distribution fitting on the flood peak flow and time period flood volume data respectively, and use the Copula function to construct a joint distribution model of the flood peak flow and time period flood volume;

[0029] In this embodiment, the construction of the joint distribution model of flood peak volume includes three technical steps: data acquisition, marginal distribution fitting, and joint distribution modeling. Specifically, firstly, historical flood data of the Dongting Lake area is collected systematically. The data covers the inflow of the Yangtze River into the lake from the three outlets (Songzi, Taiping, and Ouchi), the flood volume of the four rivers in Hunan (Xiangjiang, Zishui, Yuanjiang, and Lishui), and the water level data of representative stations in the lake area. The time span of the data needs to meet the requirements of hydrological frequency analysis, and a complete hydrological sequence since 1950 is preferred. The collected data needs to be consistent and interpolated to eliminate systematic deviations caused by station relocation and changes in measurement methods, ensuring the spatiotemporal consistency of the data sequence.

[0030] In this embodiment, the marginal distribution fitting is modeled using a Pearson Type III (P-III) distribution. Specifically, probability distribution functions are established for the peak flow Q and the time-period flood volume W sequences, respectively, and their probability density function expressions are as follows:

[0031]

[0032] In the formula, α is the shape parameter, β is the scale parameter, γ is the position parameter, and Γ(·) is the gamma function.

[0033] Parameter estimation uses the method of moments or the maximum likelihood method, and the expression is:

[0034]

[0035] In the formula, x is the sample mean. i Let C represent the value of the i-th sample, n be the sample size, and C be the value of the i-th sample. v C is the coefficient of variation. s This is the skewness coefficient.

[0036] In this embodiment, the joint distribution modeling is implemented using Copula functions. Preferably, four functions—Frank, Joe, Gumbel, and Clayton—are selected from the Archimedesian Copula family to construct a candidate model set, and the observed data are mapped to a uniform distribution space of [0,1] through marginal distribution transformation. For any Copula function C(u,v; θ), its joint distribution function expression is:

[0037] F Q,W (q,w)=C(F Q (q),F W (w); θ);

[0038] In the formula, F Q (q), F W (w) represents the marginal distribution function values ​​of the peak flow Q and the flood volume W during the time period, respectively, indicating the probability that the variable does not exceed a certain threshold; θ is the dependency parameter of the Copula function, reflecting the correlation between the peak flow and the flood volume.

[0039] The parameter estimation adopts a semi-parametric method, which is based on the analytical relationship between Kendall's rank correlation coefficient τ and Copula parameter θ. For example, Gumbel Copula satisfies θ = 1 / (1-τ).

[0040] In this embodiment, the optimal Copula selection is achieved through a multi-criteria joint evaluation. First, the Kolmogorov-Smirnov test is used to assess the goodness of fit between the theoretical joint distribution and the empirical distribution, and the statistic is calculated:

[0041]

[0042] In the formula, D n The Kolmogorov-Smirnov test statistic is used to assess the goodness of fit between the theoretical and empirical distributions, and is defined as the maximum absolute value of the difference between the two; F n (q,w) is the joint empirical distribution function, which describes the empirical probability in the observed data that simultaneously satisfies peak flow Q≤q and time period flood volume W≤w.

[0043] Simultaneously, the model is optimized by combining the AIC and BIC criteria, and their calculation formulas are as follows:

[0044] AIC=-2lnL+2k, BIC=-2lnL+klnn;

[0045] In the formula, L is the maximum value of the likelihood function, k is the number of model parameters, and n is the sample size. Finally, the Copula function, which simultaneously passes the KS test (p-value > 0.05) and has the smallest AIC / BIC value, is selected as the joint distribution model to fully characterize the correlation structure of flood peak and flood volume.

[0046] b) Determine the joint return period and reasonable peak volume combination boundary: Based on the joint distribution model constructed in step a), define and calculate the joint return period of the design event, and combine it with the preset confidence level to determine the reasonable regional boundary of the combination of peak flow and time-period flood volume under the joint return period;

[0047] In this embodiment, the construction of the flood return period consistency model aims to further derive the return period consistency relationship between different flood indicators (such as peak flow and total flood volume) based on the joint distribution model, and construct a joint return period model with clear statistical meaning to guide water resource scheduling and flood risk assessment in lake areas.

[0048] In this embodiment, the derivation of the joint return period is based on the joint probability distribution function and the Copula function theoretical framework. Considering random variable Q representing peak flow and W representing total flood volume, based on the established joint distribution function F... Q,W (q,w)=C(F Q (q),F W (w); θ) can further define various types of joint return periods, including joint no more than (AND), joint at least one more than (OR), and conditional return periods.

[0049] The conjunctive return period is defined as follows:

[0050]

[0051] In the formula, R d For the joint no-recurrence period, where ∧ represents the logical "AND", F(q,w)=P(Q≤q,W≤w).

[0052] This definition reflects the average recurrence interval of events where all peak values ​​exceed a threshold simultaneously within a certain time period. Its probability is given by the complement of the joint distribution function, which depends on the marginal distribution and the structure function form of the Copula.

[0053] The definition of a combined at least one disjunctive return period is:

[0054]

[0055] In the formula, R cTo combine at least one repeating period of the type where ∨ represents the logical "OR".

[0056] This return period characterizes the expected occurrence cycle when at least one indicator exceeds a set threshold, and is suitable for flood control design scenarios that are highly sensitive to risk. In this embodiment, the conditional return period model calculates the average recurrence time for another indicator to reach a specific value, given one of the indicators. If W = w is fixed, the return period for the peak flow to reach or exceed q, given the total flood volume, can be expressed as:

[0057]

[0058] In the formula, R Q|W＝w The conditional return period represents the average interval at which the flood peak Q exceeds the threshold when the given flood volume W = w. This formula uses the partial derivatives of the joint distribution with respect to a certain variable to construct the conditional probability density, thereby establishing the expected return interval on the conditional distribution, which has a clear probabilistic and statistical significance.

[0059] To construct the aforementioned return period relationship, in this embodiment, firstly, based on the marginal distribution function and Copula function already fitted in step a), the joint distribution function values ​​of different (q,w) combination points are calculated to obtain the corresponding family of joint return period curves. Then, numerical methods are used to perform equal-probability inversion on multiple sets of (q,w) points to obtain the correspondence between flood peak and flood volume, thereby constructing the joint return period consistency relationship model surface. Figure 2 In this embodiment, preferably, the return period surface can be converted into a two-dimensional contour map, with appended... Figure 3 This facilitates the visualization of peak quantity combination regions under different return period conditions, providing technical support for the compilation of flood maps for engineering design. In this embodiment, to enhance the applicability and robustness of the model, the joint return period model can be further combined with the Markov Chain Monte Carlo (MCMC) method for uncertainty analysis, estimating the impact of model parameter fluctuations within the statistical confidence interval on the joint return period results, ensuring that the constructed model has sufficient openness and completeness, and meets the general requirements of technical review.

[0060] c) Deriving the design flood level: Within the reasonable area determined in step b), select at least one combination of design peak volumes, obtain the corresponding flood level through flood regulation calculation, and determine the final design flood level in combination with the flood control guarantee rate;

[0061] In this embodiment, the determination of the design flood level is based on the joint distribution model constructed in step a) and the joint return period consistency model established in step b). Typical peak quantity combinations are screened through a multi-criteria optimization method, and the corresponding flood level is derived by combining the hydrological and hydraulic model. Specifically, the target joint return period (e.g., 100-year return period) is first determined according to the flood control design standard, and representative peak quantity combination points are selected on the corresponding contour lines, including combinations with the same frequency and combinations with conditional expectations.

[0062] In this embodiment, the same-frequency combination is defined as a combination point where the peak flow and the total flood volume have the same univariate return period. Its mathematical expression is:

[0063]

[0064] In the formula, T is the univariate return period, and the joint return period Tn is the return period. ∪ The association expression for using the Copula function is as follows: By simultaneously solving the joint distribution equation and the univariate frequency equation, the (q,w) combination point that satisfies the conditions can be determined, ensuring the consistency of the peak quantity in a statistical sense.

[0065] In this embodiment, the conditional expectation combination is constructed using conditional probability distribution theory. Given a peak flow rate q, the conditional expectation of the total flood volume is calculated as follows:

[0066]

[0067] The conditional probability density function is derived from the joint distribution:

[0068]

[0069] In the formula, c(·) is the Copula density function. Solving this integral using numerical integration or Monte Carlo sampling methods yields the conditionally expected flood quantity w corresponding to a given q. e , forming (q,w e Combination point.

[0070] In this embodiment, the hydrological and hydraulic model uses the one-dimensional unsteady flow Saint-Venant equations to calculate flood evolution, and its governing equations are:

[0071]

[0072] In the formula, A is the cross-sectional area of ​​the water passage, Q is the flow rate, h is the water level, g is the acceleration due to gravity, and S is the velocity of water. f Let q be the friction slope. lFor lateral inflow, t and x are time and space variables, respectively. By discretizing and solving the equation system using the finite difference method or the method of characteristics, and combining the lake area topographic data, initial boundary conditions, and the inflow process line corresponding to the peak volume combination selected in step c), the highest flood level of each section can be estimated.

[0073] In this embodiment, preferably, the inflow process curve adopts a triangular or trapezoidal generalized flood process curve, with its peak discharge and total flood volume corresponding to the combination point parameters selected in step c). By adjusting the process curve shape parameters (such as the fluctuation duration ratio), the temporal distribution characteristics of different flood types can be reflected.

[0074] In this embodiment, the determination of the final design flood level requires a comprehensive analysis of multiple calculation results. A comparative analysis is performed on the flood levels corresponding to combinations with the same frequency, combinations with desired conditions, and other possible combinations (such as the most likely combination). The maximum value is selected as the recommended design flood level to ensure the safety of the flood control project under different flood encounter scenarios.

[0075] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for determining the design flood level in the Dongting Lake area, characterized in that, Includes the following steps: a) Construct a joint distribution model of flood peak volume: Collect historical flood peak flow and corresponding time period flood volume data of the study area, perform marginal distribution fitting on the flood peak flow and time period flood volume data respectively, and use the Copula function to construct a joint distribution model of the flood peak flow and time period flood volume; b) Determine the joint return period and reasonable peak volume combination boundary: Based on the joint distribution model constructed in step a), define and calculate the joint return period of the design event, and combine it with the preset confidence level to determine the reasonable regional boundary of the combination of peak flow and time-period flood volume under the joint return period; c) Determine the design flood level: Within the reasonable area determined in step b), select at least one combination of design peak volumes, obtain the corresponding flood level through flood regulation calculation, and determine the final design flood level in combination with the flood control guarantee rate.

2. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The marginal distribution fitting of peak flow and time-period flood volume data mentioned in a) includes fitting with Pearson Type III distribution or generalized extreme value distribution and estimating their distribution parameters.

3. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The method described in a) for constructing a joint distribution model using a Copula function includes: selecting at least two different types of Copula functions as candidates, and using statistical testing methods to select the optimal Copula function from the candidate Copula functions to construct the joint distribution model.

4. The method for determining the design flood level in the Dongting Lake area according to claim 3, characterized in that, The statistical testing methods include the Kolmogorov-Smirnov test, the Akaike information criterion, or the Bayesian information criterion.

5. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, Determining the reasonable regional boundary for the combination of peak flow and time-period flood volume under the joint return period as described in b) includes: drawing contour lines of the joint return period, and determining the boundary points for dividing the reasonable and unreasonable areas on the contour lines by integrating the joint probability density function of the joint distribution model.

6. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The selection of at least one design peak quantity combination in c) includes selecting a combination of the same frequency and / or a conditionally desired combination.

7. The method for determining the design flood level in the Dongting Lake area according to claim 6, characterized in that, The same frequency combination refers to a combination in which the peak flow and the flood volume in a given time period have the same marginal exceedance probability; the conditional expectation combination refers to a combination formed by calculating the flood volume given the design peak flow, or calculating the peak flow given the design flood volume, under the premise of satisfying the design joint return period.

8. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The method described in c) for obtaining the corresponding flood level through flood control calculation includes: using the lake basin volume-water level relationship curve and the polder flood control model, and considering the impact of siltation on the lake area's storage capacity.

9. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The determination of the final design flood level by combining the flood control guarantee rate in c) includes: comparing multiple flood levels calculated by different combinations of design peak volumes, and selecting the higher or more unfavorable flood level as the final design flood level.

10. The method for determining the design flood level in the Dongting Lake area according to claim 1, characterized in that, The historical flood data includes the inflow of the Yangtze River into the lake at its three outlets, the flood volume at the four water control stations in Hunan, and the water level data at representative stations in the lake area.

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