A hydrological design method for flood control and drainage of urban lakes along the river plain under land use change

Abstract

The present invention discloses a hydrological design method for flood control and drainage of urban lakes along the river plain under land use change. By constructing a simulation model of the flood process of urban lakes along the river plain considering land use change, a joint distribution of two variables of rainstorm and outer river water level based on Copula function is constructed. On this basis, the frequency distribution curve of the highest flood level of urban lakes along the river plain under land use change is obtained, and then the joint design value of rainstorm and outer river water level based on risk rate is derived, and the uncertainty of the joint design value of rainstorm and outer river water level is quantitatively evaluated. The advantages of the present invention are: the present invention can quantitatively evaluate the uncertainty of the hydrological design results of flood control and drainage of urban lakes along the river plain under land use change, and provide scientific support for reasonably determining the scale of flood control and drainage projects of urban lakes along the river plain.

Description

Technical Field

[0001] The invention belongs to the field of flood control and drainage, and in particular relates to a hydrological design method for flood control and drainage of urban lakes in plain areas along rivers under land use changes. Background Art

[0002] Reasonable determination of the scale of urban lake flood control and drainage projects is crucial for safe and economic operation and the realization of project benefits. Whether the rainstorm water in urban lakes along the river plain can be successfully discharged is greatly restricted by the water level of the outer river in the discharge area. The rainstorm and the corresponding outer river water level are the two most important disaster factors for flood disasters in urban lakes along the river plain. The risk of flood control and drainage is the result of the combined effect of hydrological loads such as rainstorm and outer river water level. Therefore, the key to the hydrological design of flood control and drainage projects in urban lakes along the river plain is to select a combination of rainstorm and outer river water level that meets the flood control and drainage standards.

[0003] In existing engineering practice, the combination of the maximum rainstorm design in the flood-prone area and the multi-year average highest water level of the outer river is usually used as the design basis. However, this method is only a subjective assumption, and the concept of frequency is vague, which makes it questionable whether the designed flood control and drainage project can meet the specified flood control and drainage standards. In recent years, more and more scholars have devoted themselves to using Copula functions to quantitatively analyze the encounter rules of rainstorms and outer river water levels, assuming that the recurrence period of two variables (such as "OR", "AND" and "Kendall") is equal to the flood control and drainage standard, and derive the combination of rainstorms and outer river water levels. However, this method actually only reflects the probability of encountering the combination of hydrological load rainstorms and outer river water levels, not the real flood control and drainage risk rate of urban lakes along the river plain under the joint action of rainstorms and outer river water levels. It has limitations in the determination of flood control and drainage safety and dangerous events and the risk assessment of flood disasters. In addition, with the rapid development of economy, society and urban construction, the change of land use in the basin has changed the characteristics of runoff generation and convergence, and also affected the storm flood storage capacity of the lake itself. The current research has not considered the impact of land use change on the flood control and drainage risk and engineering hydrological design of urban lakes along the river plain. It is urgent to develop a hydrological design method for flood control and drainage of urban lakes along the river plain under land use change to improve the accuracy and reliability of the design results. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a hydrological design method for flood control and drainage of urban lakes in riverside plains under land use changes.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a hydrological design method for flood control and drainage of urban lakes along the river plain under land use change, comprising the steps of:

[0006] Step 1: construct a simulation model of the flood process of urban lakes along the river plain taking into account land use changes;

[0007] Step 2, construct the joint distribution of two variables, heavy rain and outer river water level, based on the Copula function;

[0008] Step 3, based on the simulation model of the flood process of urban lakes in the riverside plain considering land use change constructed in step 1 and the joint distribution of the two variables of heavy rain and outer river water level based on the Copula function constructed in step 2, obtain the frequency distribution curve of the highest flood level for flood control and drainage of urban lakes in the riverside plain under land use change;

[0009] Step 4, according to the frequency distribution curve of the highest flood level of flood control and drainage of urban lakes in the plain along the river under the land use change obtained in step 3, derive the joint design value of heavy rain and outer river water level based on risk rate;

[0010] Step 5, quantitatively evaluate the uncertainty of the combined design values ​​of heavy rain and outer river water level in step 4.

[0011] Furthermore, the construction of a simulation model for the flood process of urban lakes in the riverside plain taking into account land use changes includes the following steps:

[0012] (1) Analysis of dynamic changes in land use in urban lake basins along the river plain;

[0013] Based on the remote sensing monitoring data of land use in the urban lake basin along the river plain at different periods, ArcGIS software was used to calculate the area and proportion of each land use type in the basin at different periods, and the land use structure was analyzed;

[0014] The dynamic degree of land use is used as an indicator to quantitatively describe the rate of land use change, and the quantitative changes and regional differentiation characteristics of each land use type during the study period are analyzed; the mutual transformation between different land use types is analyzed by calculating the land use transfer matrix;

[0015] The land use types are divided into five categories: cultivated land, forest land, grassland, water area and urban and rural construction;

[0016] (2) Construction of a simulation model for flooding into lakes in urban plains along the river under land use change;

[0017] The HEC-HMS model is used to construct a simulation model of the flood process of urban lakes along the river plain taking into account land use changes; the urban lake basin along the river plain is divided into several grid units or natural sub-basins according to the DEM, and the flow generation of each unit is calculated. The confluence includes slope confluence and river confluence, and finally the flow is calculated to the outlet section of the basin; the SCS curve method is used to calculate the hydrological loss, the SCS unit line method is used to calculate the direct runoff, the Muskingum method is used to carry out the evolution of river floods, and the base flow index retreat method is used to simulate the basin base flow;

[0018] The inverse distance weighted method is used to calculate the unit area rainfall; the HEC-HMS model parameters are calibrated and the model effect is verified based on the measured precipitation, lake flow, land use, soil type and other data in the basin.

[0019] Furthermore, the construction of the joint distribution of two variables, namely, heavy rain and outer river water level, based on the Copula function comprises the following steps:

[0020] (1) Alternative line types and parameter estimation of marginal distributions; Normal distribution, lognormal distribution, Gumbel distribution, Gamma distribution and Pearson type III distribution were selected as alternative marginal distribution line types; Linear moment method was used to estimate the parameters of marginal distributions of rainstorm and outer river water level;

[0021] (2) Alternative types of copula functions and parameter estimation; Gumbel-Hougaard, Clayton, Frank and Gaussian copula are selected as alternative copula function types; the maximum likelihood method is used to estimate the parameters of the copula function;

[0022] (3) The joint distribution of the two variables of heavy rain and external river water level is determined;

[0023] It is necessary to test the fitting and optimization of the marginal distribution and Copula function to determine the joint distribution of the two variables of heavy rain and outer river water level based on the Copula function;

[0024] The Kolmogorov-Smirnov test method is used to test the fitting of marginal distribution and Copula function. The root mean square error (RMSE) criterion is used to evaluate the fitting of theoretical frequency and empirical frequency of marginal distribution and joint distribution respectively for marginal distribution and Copula function that pass the test, and the marginal distribution and Copula function with the minimum RMSE value are selected.

[0025] Assume that R and H represent the rainstorm and the water level of the outer river respectively, and the corresponding values ​​are r and h respectively, and their marginal distributions are F R (r), F H (h); According to Sklar's theorem, the joint distribution function of R and H can be expressed by a two-dimensional Copula function:

[0026] F(r,h)=C θ (F R (r),F H (h))=C θ (u,v) (1)

[0027] Among them, F(r,h) is the joint distribution function of R and H, and θ is the parameter of the Copula function.

[0028] Furthermore, the frequency distribution curve of the highest flood level for flood control and drainage of urban lakes in the plain along the river under land use change is obtained; the specific steps are:

[0029] (1) Conditional probability calculation: According to the joint distribution C of the two variables of heavy rain and outer river water level based on the Copula function constructed in step 2, θ (u, v), solve the analytical expression of the conditional distribution of the corresponding outer river water level H when the rainstorm R is the specified value r:

[0030]

[0031] (2) Determine the frequency distribution curve of the maximum flood level for flood control and drainage in urban lakes along the river plain under land use change; perform numerical solution based on the Monte Carlo method of Copula function.

[0032] Furthermore, the Monte Carlo method based on the Copula function is used for numerical solution. The specific steps are as follows:

[0033] (1) Generate two independent random numbers r1 and r2 that obey the uniform distribution between [0,1];

[0034] (2) Let u=r1,S U (v|U=u)=r2;

[0035] (3) Solve for S U (v|U=u)=r2, so v=S U -1 (r2|U=u);

[0036] (4) Calculate r = F R -1 (u), h = F H -1 (v), we get a pair of heavy rain and outer river water level combinations (r, h);

[0037] (5) Select representative synchronous typical rainstorm processes and corresponding outer river water level processes, and obtain the design rainstorm process and corresponding design outer river water level process by amplifying the random simulated rainstorm and outer river water level combination (r, h) at the same ratio;

[0038] (6) Input the designed rainstorm process into the HEC-HMS model of the flood process of urban lakes along the river plain considering land use change constructed in step 1, and simulate the corresponding flood process of the lake;

[0039] (7) The flood process entering the lake and the corresponding design outer river water level process are calculated according to the flood regulation calculation rules of urban lakes along the river plain to obtain the highest flood level z value of the lake;

[0040] (8) Repeat steps (1) to (7) N times to simulate N z values, sort them from large to small, and use the mathematical expectation formula to calculate the empirical frequency to obtain the frequency distribution curve of the highest flood level Z of urban lakes along the river plain.

[0041] Furthermore, the specific steps of deriving the joint design value of rainstorm and outer river water level based on risk rate are as follows:

[0042] (1) Derivation of the design value of the highest flood level of urban lakes along the river plain given the flood control and drainage standards;

[0043] Given the flood control and drainage standard T, the corresponding flood control and drainage risk rate is P = 1 / T; according to the frequency distribution curve of the highest flood level Z of the lake in step 3, the highest flood level design value z of the urban lake along the river plain corresponding to the flood control and drainage risk rate 1 / T is obtained. T ;

[0044] (2) Establishment of the maximum flood level function for flood control and drainage of lakes in the plain cities along the river;

[0045] Based on the risk rate of the combined design value of the rainstorm and the outer river water level, it is necessary to obtain the highest flood level function z of the urban lakes along the river plain T =g(r,h);

[0046] Combined with the characteristics of the edge probability distribution of heavy rain R and the water level H of the outer river, the values ​​of heavy rain R and the water level H of the outer river are discretized at equal intervals of 0.1 mm and 0.01 m within the upper and lower limits. R and n H values, get n R ·n H A combination of rainstorm and outer river water level is formed, and the corresponding maximum flood level z of the lake is obtained according to steps (5) to (7) of the flood control and drainage risk rate calculation model of urban lakes along the river plain under the combined effect of rainstorm and outer river water level in step 3; R ·n H Select the water level z from the highest flood level series of the lakes T The corresponding combination of heavy rain R and external river water level H forms a contour line of the highest flood level of the lake z T =g(r,h), all combinations of rainstorm and external river water level on the contour line are equivalent, and the corresponding highest flood level of the lake is z T ;

[0047] The highest flood level design value z of a given urban lake along the river plain is obtained by fitting regression. T The functional relationship between the rainstorm R and the water level of the outer river H under the condition h=f T (r);

[0048] (3) Derivation of the joint design values ​​of rainstorm and external river water level;

[0049] The most likely combination method is used to derive the joint design value of rainstorm and outer river water level based on risk rate; the most likely joint design value (r m ,h m ) refers to the design value of the highest flood level of a given riverside plain urban lake. T Under these conditions, the joint design value corresponding to the maximum joint probability density of heavy rain R and outer river water level H can be solved by the following formula:

[0050]

[0051] Among them, c θ (u,v) is the density function of the Copula function.

[0052] Furthermore, the quantitative assessment of the uncertainty of the combined design value of the rainstorm and the outer river water level specifically includes the following steps:

[0053] (1) Quantification of uncertainty in the joint distribution of two variables: heavy rain and external river water level;

[0054] The Bootstrap method is used to study the sampling uncertainty of samples. The Bayesian statistical method based on the MCMC algorithm is used to evaluate the uncertainty of line type selection and parameter estimation. The influence of different marginal distribution line types and Copula function types is analyzed. On this basis, the uncertainty of the joint distribution of the two variables of heavy rain and outer river water level is quantitatively evaluated.

[0055] (2) Quantification of uncertainty in the simulation model of flood inflow into lakes in urban plains along the Yangtze River;

[0056] The uncertainty of the simulation model of flood flow into the urban lakes in the plain along the river is quantified by using the comprehensive uncertainty analysis method of the hydrological model based on the Copula function, which can simultaneously consider the uncertainty of the model parameters and the model structure; the joint probability distribution function of the actual flow and the simulated flow is constructed by using the Copula function, and the conditional probability distribution function of the actual flow is solved when the simulated flow is given, and the uncertainty of the simulation model of flood flow into the urban lakes in the plain along the river is quantitatively evaluated based on this;

[0057] (3) Quantitative assessment of uncertainty in the combined design values ​​of rainstorm and outer river water levels;

[0058] Based on the uncertainty evaluation results of the joint distribution of the two variables of heavy rain and external river water level, the uncertainty of the combination of heavy rain and external river water level (r, h) obtained by random simulation is evaluated, and then the uncertainty of the simulation model of the flood process of urban lakes in the plain along the river is coupled to obtain the probability distribution of the flood control and drainage risk rate of urban lakes in the plain along the river, and the expected value and 95% confidence interval of the flood control and drainage risk rate of urban lakes in the plain along the river are obtained;

[0059] On this basis, combined with the method and process of deriving the joint design values ​​of heavy rain and outer river water level based on risk rate in step 4, the uncertainty of the joint design values ​​of heavy rain and outer river water level is quantitatively evaluated through 95% binary confidence interval.

[0060] The present invention constructs a simulation model of the flood process entering the urban lakes in the riverside plain taking into account the change of land use, and constructs the joint distribution of the two variables of heavy rain and outer river water level based on the Copula function. On this basis, the frequency distribution curve of the maximum flood level of flood control and drainage of urban lakes in the riverside plain under the change of land use is obtained, and then the joint design value of heavy rain and outer river water level based on the risk rate is derived, and the uncertainty of the joint design value of heavy rain and outer river water level is quantitatively evaluated.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention adopts the flood control and drainage standards for urban lakes along the river plain based on the risk rate, takes into account the interaction between the hydrological load and the flood control and drainage calculation, and characterizes the hydrological disaster mechanism that is more in line with reality. The designed flood control and drainage project can meet the specified flood control and drainage standards. In addition, the present invention can quantitatively evaluate the uncertainty of the hydrological design results of flood control and drainage for urban lakes along the river plain under land use changes, and provide scientific support for the reasonable determination of the scale of flood control and drainage projects for urban lakes along the river plain. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0063] The present invention will be further described below by way of embodiments and in conjunction with the accompanying drawings.

[0064] like Figure 1 As shown in the figure, a hydrological design method for flood control and drainage of urban lakes in the river plain under land use change is proposed. A simulation model of the flood process of urban lakes in the river plain considering land use change is constructed, and the joint distribution of two variables, heavy rain and outer river water level, based on the Copula function is constructed. On this basis, the frequency distribution curve of the maximum flood level of flood control and drainage of urban lakes in the river plain under land use change is obtained, and then the joint design value of heavy rain and outer river water level based on risk rate is derived, and the uncertainty of the joint design value of heavy rain and outer river water level is quantitatively evaluated. Figure 1 : is the calculation flow chart of this embodiment, and is performed according to the following steps:

[0065] 1. Construct a simulation model for the flood process into urban lakes in the riverside plain taking into account land use changes.

[0066] This step consists of two sub-steps:

[0067] 1.1 Analysis of dynamic changes in land use in urban lake basins along the river plain

[0068] Based on the remote sensing monitoring data of land use in the urban lake basins along the river plains at different periods, ArcGIS software was used to calculate the area and proportion of each land use type in the basin at different periods, and the land use structure was analyzed.

[0069] The dynamic degree of land use is used as an indicator to quantitatively describe the rate of land use change, and the quantitative changes and regional differentiation characteristics of each land use type during the study period are analyzed. By calculating the land use transfer matrix, the mutual transformation between different land use types is analyzed.

[0070] In this specific implementation, land use types are divided into five categories: cultivated land, forest land, grassland, water area and urban and rural construction.

[0071] 1.2 Construction of a simulation model for flooding into urban lakes along the river plain under land use change

[0072] The HEC-HMS model is a rainfall-runoff model developed by the Water Resources Research Center of the United States Army Corps of Engineers (USACE) in the 1990s. It is a semi-distributed hydrological model with physical concepts that takes into account the spatiotemporal variability of the underlying surface. It has been widely used in flood response studies of land use changes and has good applicability and effectiveness.

[0073] In this specific implementation, the HEC-HMS model is used to construct a simulation model of the flood process of urban lakes along the river plain taking into account land use changes. According to the DEM, the urban lake basin along the river plain is divided into several grid units or natural sub-basins, and the flow generation of each unit (sub-basin) is calculated. The confluence includes slope confluence and river confluence, and finally it is calculated to the outlet section of the basin. The SCS curve method (Curve Number, CN) is used to calculate hydrological losses, the SCS unit line method is used to calculate direct runoff, the Muskingum method is used to carry out river flood evolution, and the base flow index retreat method is used to simulate the basin base flow.

[0074] In this specific implementation, the inverse distance weighted method is used to calculate the unit (sub-basin) surface rainfall.

[0075] In this specific implementation, the HEC-HMS model parameters were calibrated and the model effect was verified based on the measured precipitation, lake flow, land use, soil type and other data in the basin. The Nash efficiency coefficient (NSE), total water error (RE), mean absolute error (MAE), peak-to-peak time difference (ΔT) were selected as evaluation indicators of model simulation accuracy.

[0076] 2. Construct the joint distribution of two variables, heavy rain and outer river water level, based on the Copula function.

[0077] This step consists of three sub-steps:

[0078] 2.1 Alternative Line Shapes and Parameter Estimation of Marginal Distributions

[0079] Since the line shape of the marginal distribution frequency curve of heavy rain and outer river water level is unknown, the line shape that can better fit the majority of sample data series is usually selected.

[0080] In this specific implementation, normal distribution, lognormal distribution, Gumbel distribution, Gamma distribution and Pearson III distribution are selected as alternative marginal distribution line types.

[0081] In this specific implementation, the linear moment method is used to estimate the parameters of the marginal distribution of the rainstorm and the outer river water level.

[0082] 2.2 Alternative types of copula functions and parameter estimation

[0083] Since the type of the frequency curve of the two variables of heavy rain and outer river water level is unknown, the Copula function type that can better fit most sample data series is usually selected.

[0084] In this specific implementation, Gumbel-Hougaard, Clayton, Frank and Gaussian Copula are selected as alternative Copula function types.

[0085] In this specific implementation, the maximum likelihood method is used to estimate the parameters of the Copula function.

[0086] 2.3 Determination of the joint distribution of two variables: heavy rain and outer river water level

[0087] It is necessary to test the fitting and optimization of marginal distribution and Copula function to determine the joint distribution of heavy rain and outer river water level based on Copula function.

[0088] In this specific implementation, the Kolmogorov-Smirnov test method is used to perform a fitting test on the marginal distribution and the Copula function. The marginal distribution and the Copula function that pass the test are then evaluated using the root mean square error (RMSE) criterion to evaluate the fitting of the theoretical frequency and the empirical frequency of the marginal distribution and the joint distribution, and the marginal distribution and the Copula function with the minimum RMSE value are selected.

[0089] Assume that R and H represent the rainstorm and the water level of the outer river respectively, and the corresponding values ​​are r and h respectively, and their marginal distributions are F R (r), F H (h). According to Sklar's theorem, the joint distribution function of R and H can be expressed by a two-dimensional Copula function:

[0090] F(r,h)=C θ (F R (r),FH (h))=C θ (u,v) (1)

[0091] Among them, F(r,h) is the joint distribution function of R and H, and θ is the parameter of the Copula function.

[0092] 3. Obtain the frequency distribution curve of the maximum flood level for flood control and drainage of urban lakes in the riverside plain under land use change.

[0093] According to the simulation model of the flood process of urban lakes along the river plain considering land use change constructed in step 1 and the joint distribution of the two variables of rainstorm and outer river water level based on Copula function constructed in step 2, the Monte Carlo method based on Copula function is used to numerically solve the frequency distribution curve of the highest flood level of urban lakes along the river plain under land use change. This step includes two sub-steps:

[0094] 3.1 Conditional Probability Calculation

[0095] According to the joint distribution C of the two variables of heavy rain and outer river water level based on the Copula function constructed in step 2 θ (u, v), solve the analytical expression of the conditional distribution of the corresponding outer river water level H when the rainstorm R is the specified value r:

[0096]

[0097] 3.2 Solution of the frequency distribution curve of the highest flood level for flood control and drainage in urban lakes along the river plain under land use change

[0098] For the safety of flood control and drainage of urban lakes along the river, the real risk is that the highest flood level of the lake exceeds a certain specified elevation. Therefore, the risk rate of flood control and drainage of urban lakes along the river should be defined as the probability of load effect, that is, the probability that the highest flood level of the lake exceeds a certain specified elevation. The key is to determine the frequency distribution curve of the highest flood level of flood control and drainage of urban lakes along the river plain under land use change.

[0099] In this specific implementation, the Monte Carlo method based on Copula function is used for numerical solution. The specific steps are as follows:

[0100] (1) Generate two independent random numbers r1 and r2 that obey the uniform distribution between [0,1];

[0101] (2) Let u=r1,S U (v|U=u)=r2;

[0102] (3) Solve for S U (v|U=u)=r2, so v=S U -1(r2|U=u);

[0103] (4) Calculate r = F R -1 (u), h = F H -1 (v), we get a pair of heavy rain and outer river water level combinations (r, h);

[0104] (5) Select representative synchronous typical rainstorm processes and corresponding outer river water level processes, and obtain the design rainstorm process and corresponding design outer river water level process by amplifying the random simulated rainstorm and outer river water level combination (r, h) at the same ratio;

[0105] (6) Input the designed rainstorm process into the HEC-HMS model of the flood process of urban lakes along the river plain considering land use change constructed in step 1, and simulate the corresponding flood process of the lake;

[0106] (7) The flood process entering the lake and the corresponding design outer river water level process are calculated according to the flood regulation calculation rules of urban lakes along the river plain to obtain the highest flood level z value of the lake;

[0107] (8) Repeat steps (1) to (7) N times in total to simulate N z values, sort them from large to small, calculate the empirical frequency using the mathematical expectation formula, and obtain the frequency distribution curve of the highest flood level Z of urban lakes along the river plain;

[0108] 4. Derive the joint design values ​​of heavy rain and outer river water level based on risk rate.

[0109] According to the frequency distribution curve of the highest flood level of urban lakes along the river plain under land use change obtained in step 3, the joint design value of rainstorm and outer river water level based on risk rate is derived by the most likely combination method. This step includes three sub-steps:

[0110] 4.1 Derivation of the design value of the highest flood level of urban lakes along the river plain with given flood control and drainage standards

[0111] Given a flood control and drainage standard T, the corresponding flood control and drainage risk rate is P = 1 / T. According to the frequency distribution curve of the highest flood level Z of the lake in step 3, the highest flood level design value z of the urban lake along the river plain corresponding to the flood control and drainage risk rate 1 / T is obtained. T .

[0112] 4.2 Establishment of the maximum flood level function for flood control and drainage of urban lakes along the river plain

[0113] In order to derive the joint design value of rainstorm and outer river water level based on risk rate, it is necessary to obtain the highest flood level function z of urban lakes along the river plain T =g(r,h).

[0114] In this specific implementation, combined with the characteristics of the edge probability distribution of the rainstorm R and the water level H of the outer river, the values ​​of the rainstorm R and the water level H of the outer river are discretized at equal intervals of 0.1 mm and 0.01 m within the upper and lower limits. R and n H Values ​​(n R and n H Generally large enough), we get n R ·n H The combination of rainstorm and outer river water level is used to obtain the corresponding lake maximum flood level z value according to steps (5) to (7) in the flood control and drainage risk rate calculation model of urban lakes along the river plain under the combined effect of rainstorm and outer river water level in step 3. R ·n H Select the water level z from the highest flood level series of the lakes T The corresponding combination of heavy rain R and external river water level H forms a contour line of the highest flood level of the lake z T =g(r,h), all combinations of rainstorm and external river water level on the contour line are equivalent, and the corresponding highest flood level of the lake is z T .

[0115] In this specific implementation, the highest flood level design value z of a given urban lake along the river plain is obtained by fitting regression. T The functional relationship between the rainstorm R and the water level of the outer river H under the condition h=f T (r).

[0116] 4.3 Derivation of the joint design value of heavy rain and external river water level

[0117] Contour lines of the highest flood levels of lakes in plain cities along the river T =g(r,h) all combinations of rainstorm R and external river water level H meet the specified flood control and drainage standard T. There are infinite combinations of rainstorm R and external river water level H that meet the design standard. How to scientifically and reasonably select the joint design value according to certain criteria is very critical. At present, the joint design value selection methods proposed by domestic and foreign scholars mainly include the most likely combination method, the maximum exceedance probability combination method, the conditional expectation combination method, etc., among which the most likely combination method is widely used.

[0118] In this specific implementation, the most likely combination method is used to derive the joint design value of rainstorm and outer river water level based on risk rate. The most likely joint design value (r m ,h m ) refers to the design value of the highest flood level of a given riverside plain urban lake z T Under these conditions, the joint design value corresponding to the maximum joint probability density of heavy rain R and outer river water level H can be solved by the following formula:

[0119]

[0120] Among them, c θ (u,v) is the density function of the Copula function.

[0121] 5. Quantitatively evaluate the uncertainty of the joint design values ​​of heavy rain and external river water levels.

[0122] This step consists of three sub-steps:

[0123] 5.1 Uncertainty quantification of the joint distribution of two variables: heavy rain and external river water level

[0124] The uncertainty of the joint distribution of heavy rain and outer river water level is quantified from the aspects of marginal distribution and Copula function, both of which involve sample sampling, line type selection and parameter estimation uncertainty.

[0125] In this specific implementation, the Bootstrap method is used to study the uncertainty of sample sampling, and the Bayesian statistical method based on the MCMC algorithm is used to evaluate the uncertainty of line type selection and parameter estimation. The influence of different marginal distribution line types and Copula function type selection is analyzed. On this basis, the uncertainty of the joint distribution of the two variables of heavy rain and outer river water level is quantitatively evaluated.

[0126] 5.2 Uncertainty Quantification of the Simulation Model for Flood Processes in Urban Lakes along the River Plain

[0127] The simulation model of flood process inflow into lakes in urban plains along the river has uncertainties in model input, model structure and model parameters, which inevitably leads to uncertainties in the simulated output of flood process inflow into lakes in urban plains along the river.

[0128] In this specific implementation, the comprehensive uncertainty analysis method of the hydrological model based on the Copula function is used to quantify the uncertainty of the simulation model of the flood process of urban lakes in the plain along the river, which can simultaneously consider the uncertainty of the model parameters and the model structure. The Copula function is used to construct the joint probability distribution function of the actual flow and the simulated flow, and the conditional probability distribution function of the actual flow is solved when the simulated flow is given. Based on this, the uncertainty of the simulation model of the flood process of urban lakes in the plain along the river is quantitatively evaluated.

[0129] 5.3 Quantitative assessment of uncertainty in the combined design values ​​of rainstorm and external river water level

[0130] Based on the uncertainty evaluation results of the joint distribution of the two variables of heavy rain and external river water level, the uncertainty of the combination of heavy rain and external river water level (r, h) obtained by random simulation is evaluated, and then the uncertainty of the simulation model of the flood process of urban lakes in the plain along the river is coupled to obtain the probability distribution of the risk rate of flood control and drainage of urban lakes in the plain along the river, and the expected value and 95% confidence interval of the risk rate of flood control and drainage of urban lakes in the plain along the river are obtained. On this basis, combined with the method and process of deducing the joint design value of heavy rain and external river water level based on risk rate in step 4, the uncertainty of the joint design value of heavy rain and external river water level is quantitatively evaluated through 95% binary confidence interval.

[0131] In summary, the present invention constructs a simulation model of the flood process of urban lakes in the river plain taking into account land use changes, constructs a joint distribution of two variables, heavy rain and outer river water level, based on the Copula function, and on this basis obtains the frequency distribution curve of the highest flood level for flood control and drainage of urban lakes in the river plain under land use changes, and then derives the joint design value of heavy rain and outer river water level based on the risk rate, and quantitatively evaluates the uncertainty of the joint design value of heavy rain and outer river water level. The present invention adopts the flood control and drainage standard of urban lakes in the river plain based on the risk rate, takes into account the interaction between hydrological load and flood control and drainage calculation, and the characterized hydrological disaster mechanism is more in line with reality. The designed flood control and drainage project can meet the specified flood control and drainage standards. In addition, the present invention can quantitatively evaluate the uncertainty of the hydrological design results of flood control and drainage of urban lakes in the river plain under land use changes, and provide scientific support for the reasonable determination of the scale of flood control and drainage projects of urban lakes in the river plain.

Claims

1. A hydrological design method for flood control and drainage of urban lakes along the river plain under land use change, characterized by The following steps are involved: Step 1: construct a simulation model of the flood process of urban lakes along the river plain taking into account land use changes; Step 2, construct the joint distribution of two variables, heavy rain and outer river water level, based on the Copula function; Step 3, based on the simulation model of the flood process of urban lakes in the riverside plain considering land use change constructed in step 1 and the joint distribution of the two variables of heavy rain and outer river water level based on the Copula function constructed in step 2, obtain the frequency distribution curve of the highest flood level for flood control and drainage of urban lakes in the riverside plain under land use change; Step 4, according to the frequency distribution curve of the highest flood level of flood control and drainage of urban lakes in the plain along the river under the land use change obtained in step 3, derive the joint design value of heavy rain and outer river water level based on risk rate; Step 5, quantitatively evaluate the uncertainty of the combined design values ​​of rainstorm and outer river water level in step 4; The construction of a simulation model for flooding process in lakes in urban plains along the river taking into account land use changes comprises the following steps: (1) Analysis of dynamic changes in land use in urban lake basins along the river plain; Based on the remote sensing monitoring data of land use in the urban lake basin along the river plain at different periods, ArcGIS software was used to calculate the area and proportion of each land use type in the basin at different periods, and the land use structure was analyzed; The dynamic degree of land use is used as an indicator to quantitatively describe the rate of land use change, and the quantitative changes and regional differentiation characteristics of each land use type during the study period are analyzed; the mutual transformation between different land use types is analyzed by calculating the land use transfer matrix; The land use types are divided into five categories: cultivated land, forest land, grassland, water area and urban and rural construction; (2) Construction of a simulation model for flooding into lakes in urban plains along the river under land use change; The HEC-HMS model is used to construct a simulation model of the flood process of urban lakes along the river plain taking into account land use changes; the urban lake basin along the river plain is divided into several grid units or natural sub-basins according to the DEM, and the flow generation of each unit is calculated. The confluence includes slope confluence and river confluence, and finally the flow is calculated to the outlet section of the basin; the SCS curve method is used to calculate the hydrological loss, the SCS unit line method is used to calculate the direct runoff, the Muskingum method is used to carry out the evolution of river floods, and the base flow index retreat method is used to simulate the basin base flow; The inverse distance weighted method is used to calculate the unit area rainfall; the HEC-HMS model parameters are calibrated and the model effect is verified based on the measured precipitation, lake flow, land use and soil type data in the basin.

2. The hydrological design method for flood control and drainage of urban lakes along the river plain under land use change according to claim 1 is characterized by: The method of constructing a joint distribution of two variables, heavy rain and outer river water level, based on a Copula function comprises the following steps: (1) Alternative line types and parameter estimation of marginal distributions; Normal distribution, lognormal distribution, Gumbel distribution, Gamma distribution and Pearson type III distribution are selected as alternative marginal distribution line types; Linear moment method is used to estimate the parameters of marginal distributions of heavy rain and outer river water level; (2) Alternative types of copula functions and parameter estimation; Gumbel-Hougaard, Clayton, Frank and Gaussian copula are selected as alternative copula function types; the maximum likelihood method is used to estimate the parameters of the copula function; (3) Determination of the joint distribution of two variables: heavy rain and external river water level; It is necessary to test the fitting and optimization of the marginal distribution and Copula function to determine the joint distribution of the two variables of heavy rain and outer river water level based on the Copula function; The Kolmogorov-Smirnov test method is used to test the fitting of marginal distribution and Copula function. The root mean square error (RMSE) criterion is used to evaluate the fitting of theoretical frequency and empirical frequency of marginal distribution and joint distribution respectively for marginal distribution and Copula function that pass the test, and the marginal distribution and Copula function with the minimum RMSE value are selected. Assumptions R , H Respectively represent heavy rain and outer river water level, and the corresponding values ​​are r , h , and their marginal distributions are F R ( r ), F H ( h ); According to Sklar's theorem, R and H The joint distribution function can be expressed by a two-dimensional Copula function: (1)； in, F ( r , h )for R and H The joint distribution function of θ It is the parameter of the Copula function.

3. The method for flood control and drainage hydrological design of urban lakes along the river plain under land use change according to claim 2 is characterized by: The specific steps of obtaining the frequency distribution curve of the highest flood level for flood control and drainage of urban lakes along the river plain under land use change are as follows: (1) Conditional probability calculation: Based on the joint distribution of the two variables of heavy rain and outer river water level constructed in step 2 based on the Copula function C ɵ ( u , v ), solve when it rains heavily R For the specified value r Corresponding external river water level H The analytical expression of the conditional distribution of is: (2)； (2) Determine the frequency distribution curve of the maximum flood level for flood control and drainage in urban lakes along the river plain under land use change; perform numerical solution based on the Monte Carlo method of Copula function.

4. The method for designing flood control and drainage hydrology for urban lakes in riverside plains under land use change according to claim 3 is characterized by: The Monte Carlo method based on the Copula function is used for numerical solution. The specific steps are as follows: (1) Generate two independent random numbers that follow a uniform distribution between [0,1] and ; (2) Order , ; (3) Solution ,get ; (4) Calculation , , we get a pair of rainstorm and outer river water level combinations ( r , h ); (5) Select representative synchronous typical rainstorm processes and corresponding external river water level processes, and use the combination of rainstorm and external river water level ( r , h ) The design rainstorm process and the corresponding design outer river water level process are obtained by magnifying the same ratio; (6) Input the designed rainstorm process into the HEC-HMS model of flood process of urban lakes along the river plain considering land use change constructed in step 1, and simulate the corresponding flood process of lakes; (7) The flood process entering the lake and the corresponding design external river water level process are calculated according to the flood regulation calculation rules for urban lakes along the river plain to obtain the maximum flood level of the lake. value; (8) Repeat steps (1) to (7) for a total of N times, it can be simulated N indivual The values ​​are sorted from large to small, and the empirical frequency is calculated using the mathematical expectation formula to obtain the highest flood level of lakes in the plain cities along the river. Z The frequency distribution curve of .

5. The method for flood control and drainage hydrological design of urban lakes along the river plain under land use change according to claim 4, characterized in that: The specific steps of deriving the joint design value of rainstorm and outer river water level based on risk rate are as follows: (1) Derivation of the design value of the highest flood level of urban lakes along the river plain with given flood control and drainage standards; Given flood control and drainage standards T , the corresponding flood control and drainage risk rate is P= 1 / T ; Based on the highest flood level of the lake in step 3 Z The frequency distribution curve is queried to obtain the flood control and drainage risk rate 1 / T Corresponding design values ​​of the highest flood levels of urban lakes along the river plain z T ; (2) Establishment of the maximum flood level function for flood control and drainage of urban lakes in the plain along the river; Based on the risk rate of the combined design value of the rainstorm and the outer river water level, it is necessary to obtain the highest flood level function of the urban lakes along the river plain z T =g( r , h ); Combined with heavy rain R , Outer River Water Level H Characteristics of marginal probability distribution for heavy rain R , Outer River Water Level H The values ​​are discretized at equal intervals of 0.1 mm and 0.01 m within the upper and lower limits. n R and n H value, get n R · n H Combine the rainstorm and the outer river water level, and obtain the corresponding maximum flood level of the lake according to the steps (5) to (7) in the flood control and drainage risk rate calculation model of urban lakes along the river plain under the combined effect of rainstorm and outer river water level in step 3. Value; from n R · n H The water level is selected from the series of the highest flood levels of the lakes z T The corresponding rainstorm R , Outer River Water Level H These combinations form a contour line of the highest flood level of the lake. z T =g( r , h ), all combinations of rainstorm and outer river water level on the contour line are equivalent, and the corresponding maximum flood levels of the lake are z T ; The highest flood level design value of a given urban lake along the river plain is obtained by fitting regression. z T Heavy rain conditions R , Outer River Water Level H Functional relationship h = f T ( r ); (3) Derivation of the joint design values ​​of rainstorm and external river water level; The most likely combination method is used to derive the joint design value of rainstorm and outer river water level based on risk rate; the most likely joint design value ( ) refers to the design value of the highest flood level of a given riverside plain urban lake z T Conditions, heavy rain R , Outer River Water Level H The joint design value corresponding to the maximum joint probability density can be solved by the following formula: (3)； in, is the density function of the Copula function.

6. The method for designing flood control and drainage hydrology for urban lakes in riverside plains under land use change according to claim 5, characterized in that: The quantitative assessment of the uncertainty of the combined design values ​​of rainstorm and external river water level; The specific steps include: (1) Quantification of uncertainty in the joint distribution of two variables: heavy rain and external river water level; The Bootstrap method is used to study the sampling uncertainty of samples. The Bayesian statistical method based on the MCMC algorithm is used to evaluate the uncertainty of line type selection and parameter estimation. The influence of different marginal distribution line types and Copula function types is analyzed. On this basis, the uncertainty of the joint distribution of the two variables of heavy rain and outer river water level is quantitatively evaluated. (2) Quantification of uncertainty in the simulation model of flood inflow into lakes in urban plains along the Yangtze River; The uncertainty of the simulation model of flood flow into lakes in urban plains along the Yangtze River is quantified by using the comprehensive uncertainty analysis method of the hydrological model based on the Copula function, which can simultaneously consider the uncertainty of the model parameters and the model structure; the joint probability distribution function of the actual flow and the simulated flow is constructed by using the Copula function, and the conditional probability distribution function of the actual flow is solved when the simulated flow is given, and the uncertainty of the simulation model of flood flow into lakes in urban plains along the Yangtze River is quantitatively evaluated based on this; (3) Quantitative assessment of uncertainty in the combined design values ​​of rainstorm and external river water levels; Based on the uncertainty evaluation results of the joint distribution of the two variables of heavy rain and outer river water level, the combination of heavy rain and outer river water level obtained by random simulation is evaluated ( r , h ) uncertainty, and then coupled with the uncertainty of the simulation model of the flood process of urban lakes in the river plain, the probability distribution of the flood control and drainage risk rate of urban lakes in the river plain is obtained, and the expected value and 95% confidence interval of the flood control and drainage risk rate of urban lakes in the river plain are obtained; On this basis, combined with the method and process of deriving the joint design values ​​of heavy rain and outer river water level based on risk rate in step 4, the uncertainty of the joint design values ​​of heavy rain and outer river water level is quantitatively evaluated through 95% binary confidence interval.

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