Bayesian time-varying model and expected annual loss based flood risk analysis method for coastal cities

Abstract

The application discloses a coastal city flood risk analysis method based on a Bayesian time-varying model and an expected annual loss, and comprises the following steps: (1) fusing a time-varying parameter model and a Bayesian model average method to obtain a non-stationary distribution of rainfall and tide level; (2) using a Copula function to analyze the change of joint and co-occurrence probability under a non-stationary state; (3) generating a flood loss grid of different rainfall and tide level combination events under different working conditions through a city flood inundation model simulation; and (4) based on the flood occurrence probability and the loss caused by the flood, using an expected annual loss method to quantize the flood risk change and uncertainty under a changing environment. The coastal city flood risk analysis method based on the Bayesian time-varying model and the expected annual loss can reasonably generate the non-stationary distribution of rainfall and tide level, and comprehensively consider the flood risk possibility and loss to analyze the flood risk change and uncertainty under a changing environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of flood risk analysis, and particularly relates to a coastal city flood risk analysis method based on a Bayesian time-varying model and an expected annual loss. BACKGROUND

[0002] Due to the unique geographical location, coastal cities are faced with multiple driving factors of floods, such as heavy rainfall, high tide level, etc. When different driving factors act together, the harm degree of urban floods is significantly increased, which can cause serious social and economic losses. In addition, the population is concentrated and the social economy is developed in coastal cities, and once a flood disaster occurs, the loss is serious. Therefore, the quantitative evaluation method of joint flood risk of rainfall and tide level under changing environment is of great importance to the flood management of coastal cities.

[0003] The time-varying distribution model can well describe the non-stationarity of hydrological series, and this method has been widely used in the analysis of hydrological events under changing environment. When constructing the time-varying distribution model, it is crucial to select the distribution parameters that change with time. In the past research, it is directly assumed that a certain distribution parameter changes with time, and the uncertainty caused by the selection of changing parameters is ignored. When the distribution function has multiple parameters (such as the location, scale and shape parameters in GEV distribution), it is an important problem to select which parameter and how to describe its trend of change (such as linear change or exponential change). At present, few studies focus on this problem, and unreasonable parameter selection will increase the uncertainty of hydrological frequency analysis under non-stationary state.

[0004] The Bayesian model averaging (BMA) method plays an important role in the fusion of multiple models, which maximizes the advantages of each model structure, and then provides more accurate simulation values, and evaluates the uncertainty of the simulation of multiple model fusion. However, the current research on time-varying analysis and Bayesian model averaging is mainly for single variable non-stationary analysis, and it is known that the flood in coastal area is jointly affected by rainfall and tide level.

[0005] Copula function has the advantage of not requiring single variable to have the same marginal distribution, and is widely used in solving the problem of bivariate joint distribution. In recent years, hydrodynamic model has also been used in flood risk assessment of coastal cities. However, there are still some deficiencies in the use of Copula function and hydrodynamic model in flood risk assessment. Copula function can only reflect the possibility of flood occurrence, and does not consider the flood loss. Hydrodynamic model can only intuitively represent the consequences of flood, and ignores the probability of flood occurrence. So far, the future flood risk and uncertainty, especially considering the probability of flood and flood loss, is still rare in coastal cities. Therefore, the present application provides a flood risk measurement standard, i.e. expected annual loss, to quantify the flood risk caused by the joint action of rainfall and tide level and to evaluate the influence of changing environment on the uncertainty of flood risk. SUMMARY

[0006] In order to solve the above problems, the present application provides a coastal city flood risk analysis method based on Bayesian time-varying model and expected annual loss. The present application analyzes the non-stationary distribution of rainfall and tide level by combining time-varying distribution model and Bayesian model average method, and reduces the influence of uncertainty; a flood risk measurement standard, i.e. expected annual loss, is used to quantify the flood risk caused by the joint action of rainfall and tide level and to evaluate the influence of changing environment on the uncertainty of flood risk.

[0007] The coastal city flood risk analysis method based on Bayesian time-varying model and expected annual loss of the present application comprises the following steps:

[0008] (1) obtaining the non-stationary distribution and uncertainty interval of rainfall and tide level by combining time-varying parameter model and Bayesian model average method;

[0009] (2) analyzing the change of joint and co-occurrence probability under non-stationary state by using Copula function, so as to represent the influence of changing environment on the combination event of rainfall and tide level;

[0010] (3) generating flood loss grid of different rainfall and tide level combination events under different working conditions by using city flood inundation model;

[0011] (4) quantifying the change of flood risk and uncertainty under changing environment by using expected annual loss method based on the probability of flood occurrence and the loss caused by flood.

[0012] The coastal city flood risk analysis method based on Bayesian time-varying model and expected annual loss of the present application can reasonably generate the non-stationary distribution of rainfall and tide level, and comprehensively consider the possibility and loss of flood risk, analyze the change and uncertainty of flood risk under changing environment. The research method and result can help decision makers to evaluate the future flood risk of coastal cities, and provide support for sustainable flood management to adapt to climate change.

[0013] The final rainfall and tidal level frequency distribution, i.e., a non-stationary marginal distribution, is obtained by weighting the set of time-varying distribution models in step (1).

[0014] The weights of the Bayesian model averaging in step (1) are solved by an expectation-maximization algorithm, and a Monte Carlo sampling method is used to generate simulated values at each hydrological value, and then the uncertainty interval of the simulated sequence is derived.

[0015] The uncertainty interval is a range between 5% and 95% quantiles.

[0016] In step (2), the Copula function adopts two Archimedean family Copula functions and two elliptical Copula functions to construct a bivariate joint distribution model, and according to AIC, OLS and KS test, the optimal Copula function is selected.

[0017] The two Archimedean family Copula functions are Gumbel Copula and Frank Copula, and the two elliptical Copula functions are Gaussian Copula and Student's t-Copula.

[0018] In step (3), the urban flood inundation model adopts the PCSWMM model, and the coupling mode of the one-dimensional and two-dimensional hydrodynamic models is an orifice connection mode.

[0019] The expected annual loss method in step (4) is based on the flood event probability in a non-stationary state in step (2) and the corresponding flood loss in step (3), and the flood risk change of the corresponding region is quantitatively obtained. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is a flowchart of the coastal city flood risk analysis method based on the Bayesian time-varying model and the expected annual loss of the application.

[0021] Figure 2 It is a time-varying distribution model schematic diagram of the application.

[0022] Figure 3 It is a rainfall (left) and tidal level (right) empirical distribution and candidate marginal distribution fitting comparison of the embodiment of the application.

[0023] Figure 4 It is a one-dimensional and two-dimensional model coupling mode in the urban flood inundation model of the embodiment of the application.

[0024] Figure 5 It is a comparison of the observed inundation water depth and the simulated water depth of the observation point of the embodiment of the application.

[0025] Figure 6 are the trends of the rainfall and tide level marginal distribution parameters over time for embodiments of the invention. In the figures, the black dots represent the time series of the distribution parameters, the grey dashed lines represent the fitted parameter change model, and the grey bands represent the 5 to 95% prediction intervals. (a) rainfall location parameter (b) tide level location parameter (c) rainfall scale parameter (d) tide level scale parameter (e) rainfall shape parameter (f) tide level shape parameter.

[0026] Figure 7 are the non-stationary distributions of rainfall and tide level and the 5 to 95% prediction intervals for embodiments of the invention.

[0027] Figure 8 are the exceedance probability distributions and growth rate distributions of rainfall and tide level for embodiments of the invention.

[0028] Figure 9 are the theoretical and empirical distribution correlation plots for preferred Frank Copula functions for embodiments of the invention.

[0029] Figure 10 are the non-stationary state joint probability changes of rainfall and tide level combined events for embodiments of the invention. In the figures, (a) increase value (b) increase rate (i) represents the median value (ii) and (iii) represent the 5 and 95% prediction boundaries.

[0030] Figure 11 are the non-stationary state concurrence probability changes of rainfall and tide level combined events for embodiments of the invention. In the figures, (a) increase value (b) increase rate (i) represents the median value (ii) and (iii) represent the 5 and 95% prediction boundaries.

[0031] Figure 12 are the flood losses for different rainfall and tide level combinations for embodiments of the invention. In the figures, (a) flood loss grid (b) flood loss as a function of rainfall for a typical tide level (c) flood loss as a function of tide level for a typical rainfall.

[0032] Figure 13 are simulated rainfall and tide level combined events for embodiments of the invention. In the figures, (a) simulated rainfall and tide level combined distribution and flood loss contours, with lines representing flood loss contours in units of 100 million yuan; (b) flood loss and relative probability product results, with all small squares summed to EAD under non-stationary state.

[0033] Figure 14 are the characteristic values and increase rates of expected annual losses for different design years. In the figures, (a) EAD box plot for different design years, with black lines in the box representing the median value; (b) increase rates of each quantile of EAD for different design years. DETAILED DESCRIPTION

[0034] Embodiments of the present application are described below in detail with reference to examples shown in the accompanying drawings. The embodiments described below by reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0035] As Figure 1 shown, a coastal city flood risk analysis method based on Bayesian time-varying model and expected annual loss includes the following steps:

[0036] (1) Fusion of time-varying parameter model and Bayesian model average method to obtain non-stationary distribution and uncertainty interval of rainfall and tidal level;

[0037] (2) Use Copula function to analyze the change of joint and co-occurrence probability under non-stationary state, to represent the influence of changing environment on rainfall and tidal level combination event;

[0038] (3) Generate flood loss grid of different rainfall and tidal level combination events under different working conditions by urban flood inundation model simulation;

[0039] (4) Based on the probability of flood occurrence and the loss caused by flood, use the expected annual loss method to quantify the change and uncertainty of flood risk under changing environment.

[0040] The time-varying distribution model has good effect in describing the hydrological characteristics under changing environment. The distribution parameters change with time, and then reflect the influence of factors such as climate change on the variable (such as Figure 2 ). The calculation formula of time-varying GEV distribution is as follows:

[0041]

[0042] In the formula, respectively indicate the time-varying position, scale and shape parameters.

[0043] Different change parameter selection corresponds to different time-varying distribution model. Bayesian model average (BMA) is a method of obtaining a comprehensive value by weighting the calculated values of different models. Bayesian model average can maximize the weight of the optimal model when the model is weighted, and then reduce the uncertainty when multiple models are fused. After weighting the set different time-varying models, the comprehensive frequency distribution, i.e. the non-stationary marginal distribution, is obtained.

[0044] Suppose y is the simulation variable of multiple models, D=[ , ] is the measured data, f=[ , , …, is the set of K model simulations. The BMA simulates the probability density function of variable y as:

[0045] (2)

[0046] where: is a non-stationary distribution. is the posterior probability of the kth model, which is actually the weight of the BMA distribution , and the higher the precision of the model, the greater the corresponding weight value, and the total weight of all is 1. is the probability distribution of different models given and the measured data.

[0047] The expectation maximization algorithm (EM) can be used to derive the weight value in Bayesian average . The EM algorithm assumes that the simulation sequence of each model satisfies the normal distribution, so before using the EM algorithm, the Box-Cox function in MATLAB is used to perform normal transformation on the measured sequence and the simulation sequence of each model. The EM algorithm mainly solves the weight value by setting a hidden variable. By using the two steps of expectation and maximization to iterate repeatedly until the interpolation of the likelihood function of the previous two operations meets the error requirement, the maximum likelihood value is obtained. After obtaining the BMA weight and model error , the Monte Carlo sampling method is used to generate simulation values at each hydrological value, and then the uncertainty interval of the simulation sequence is derived.

[0048] The advantage of the Copula function is that it does not require variables to have the same marginal distribution during construction. According to the binary Sklar theory, H (r, t) is a binary joint distribution with marginal distribution F1(x1), F2(x2), then there exists a Copula function C (u, v), such that:

[0049]

[0050] This application uses two Archimedean family Copula functions (Gumbel Copula, Frank Copula) and two elliptical Copula functions (Gaussian Copula, Student's t-Copula) to construct a binary joint distribution model. According to AIC, OLS and KS test, the optimal Copula function is selected. The form of the binary Copula function is as follows:

[0051] Table 1 Form of candidate Copula functions

[0052]

[0053] Note: u and v are marginal distributions;

[0054] The joint probability of rainfall and tide level is represented by the joint probability and the co-occurrence probability in this application. The probability of one variable exceeding a certain magnitude is called the joint probability, denoted as .

[0055]

[0056] The probability of both rainfall R and tide level T exceeding a certain magnitude is called the co-occurrence probability, denoted as .

[0057]

[0058] PCSWMM is a hydrodynamic model developed based on SWMM. In this application, a one-dimensional river, pipe network, and two-dimensional surface flood coupling simulation model is constructed by selecting orifice connection mode. The dynamic wave equation is used for hydrodynamic calculation, and its calculation formula is as follows:

[0059]

[0060]

[0061] In the formula: is the cross-sectional area of the water passage, m 2 ; is the water depth, m; is the distance, m; is the flow rate, m 3 / s; is the time, s; is the friction slope; is the gravitational acceleration, m / s 2 .

[0062] The expected annual loss (EAD) method can simultaneously use Copula functions and hydrodynamic models to comprehensively reflect the probability of flood occurrence and flood loss, and better quantify the changes in flood risk. The general calculation formula is:

[0063] #(8)

[0064] EAD is the expected annual loss, is the flood loss caused by the flood event with a probability of occurrence. In this application, the compound flood risk caused by the joint action of rainfall and tide level is evaluated, so the binary integral method is used to estimate the flood loss (see formula 9). In order to simplify the integral operation, we choose a sufficient number of rainfall and tide level joint events by random simulation. Multiply the flood event probability of each event by the corresponding flood loss, and finally sum up to get the expected annual loss.

[0065] (9)

[0066] wherein: is the loss caused by a specific rainfall and tide level; is the probability density function corresponding to a specific rainfall and tide level.

[0067] Reference is made below Figures 3-14 Taking Haixiandao as an example, the specific situation of Haixiandao is analyzed by using the coastal city flood risk analysis method based on the Bayesian time-varying model and the expected annual loss of the present application.

[0068] The data involved in the present embodiment has three parts. The first part is the historical rainfall and tide level data for constructing the binary joint distribution. The second part is the basic data for constructing the urban flood inundation model, including digital elevation data, drainage pipe network data and river data. The third part is the historical rainfall tide level process and the measured inundation data. The sources and main uses of the above data are as follows: the historical daily rainfall and tide level data from 1974 to 2012 are provided by the Water Affairs Bureau of Haikou City, Hainan Province, China. The annual maximum rainfall and the highest tide level corresponding to the day are selected to establish the marginal distribution and the joint distribution. The digital elevation data is used to construct the two-dimensional model in the urban flood inundation model, which is provided by the Data Center of Resource and Environment Science of the Chinese Academy of Sciences. The drainage pipe network and river data are used to build the one-dimensional model in the urban flood inundation model, which is provided by the Water Affairs Bureau of Haikou City, Hainan Province, China. The historical inundation data is the basic data for parameter calibration of the urban flood inundation model, including the rainfall tide level process of Typhoon Wima in July 2014 and the measured inundation depth of the observation point.

[0069] Marginal distribution selection: four commonly used functions (i.e. GEV, Lognorm, Norm and Gamma) are selected to determine the marginal distribution of rainfall and tide level. The maximum likelihood estimation is used to fit the parameters in the distribution function. The Kolmogorov-Simirnov (KS) test method is selected for fitting test, and the Nash efficiency coefficient (NSE), relative error (RE), least principle of sum of squared deviations (OLS) and Akaike information criterion (AIC) are used to evaluate the goodness of fit of the distribution function. Figure 3 The fitting effects of the candidate marginal distribution function and the empirical distribution function are compared, and Table 2 gives the test and evaluation results of the candidate marginal distribution function.

[0070] The KS test significance level is selected as 0.05 = 0.05, the critical value corresponding to the sample size n = 39 is approximately 0.2178, and all the candidate marginal distributions pass the KS test as shown in Table 2. For the goodness-of-fit evaluation, the NSE index of GEV distribution is greater than that of the other three distribution functions, and the calculated values of RE, OLS and AIC are less than those of the other three distribution functions, indicating that the generalized extreme value (GEV) distribution is the optimal fitting distribution of rainfall and tidal level.

[0071] Table 2 Test and evaluation of candidate marginal distribution functions

[0072]

[0073] The PCSWMM model construction includes the construction of one-dimensional and two-dimensional models and the model parameter calibration. The finally constructed model includes 2071 one-dimensional inspection wells, 2038 pipes and channels, 23580 two-dimensional grids, and 13 sub- catchment areas. The one-dimensional model is constructed by processing with ArcGIS, and the pipe network, river channel and digital elevation data in the study data are imported into the PCSWMM model for connection processing to generate a one-dimensional model. When the one-dimensional model is established, the two-dimensional grid is established based on the set boundary, and the one-dimensional and two-dimensional models are coupled through the orifice (such as Figure 4 ). When the two-dimensional model is established, the hexagonal grid is adopted with a resolution of 25 m, a roughness of 0.085 and a sampling factor of 3. When simulating and calculating different rainfall and tidal level combinations, the Horton model is selected as the infiltration model, and the flood simulation calculation is performed by the dynamic wave method, and the time step of the simulation calculation is selected as 0.5 s.

[0074] The measured data of Typhoon Rammasun in July 2014 are selected for the parameter calibration of the urban flood inundation model, and the actual rainfall and tidal level process is taken as the boundary condition of the model input. The observed and simulated depths are shown in Figure 5 . Due to the accuracy of the data such as terrain, the simulated depth and the measured depth are completely consistent. However, the error value of the measured depth and the simulated depth is small in general, and the relative error is less than 15%, and the NSE value reaches 0.73, so it is considered that the model can reasonably simulate the urban flood.

[0075] Figure 6 shows the variation trend of the distribution parameters obtained by accumulating rainfall and tidal level data, and then the Levenberg-Marquardt algorithm is used to fit to generate time-varying models with different distribution parameters. From Figure 6 (d) and Figure 6(e) It is found that the shape parameter of rainfall distribution and the scale parameter of tidal level distribution have no obvious trend and the correlation coefficient is less than 0.4, so these two parameters are not considered in the construction of time-varying distribution model. For the other four distribution parameters, the correlation coefficient between the parameter value and the fitting model is more than 0.7, which indicates that these fitting models are reasonable. Linear and exponential fitting models are shown in FIG. 2. Figure 6 The location and scale parameters of rainfall distribution show an upward trend, and the location parameter of tidal level shows an upward trend, while the shape parameter shows a downward trend. At the same time, the 5% to 95% prediction interval can completely cover the time series of the parameters, reflecting all possible changes in the parameters, so it can reasonably represent the uncertainty of the time-varying distribution model.

[0076] Based on the selected four distribution parameters, different time-varying distribution models are set for rainfall and tidal level. For rainfall, model one: location parameter time-varying, scale and shape parameters unchanged; model two: location and scale parameters time-varying, shape parameter unchanged. For tidal level, model one: location parameter time-varying, scale and shape parameters unchanged; model two: location and shape parameters time-varying, scale parameter unchanged.

[0077] Table 3 gives the weight values of each time-varying distribution model after Bayesian model averaging. It can be clearly found that whether it is rainfall or tidal level, the weight of model two is higher than that of model one, which indicates that model two has a higher contribution to the final non-stationary distribution, and the distribution model considering multiple time-varying parameters has better accuracy. The Bayesian model averaging method ensures that the better time-varying distribution model has a higher weight, so that the non-stationary distribution model obtained by weighting is more reasonable.

[0078] Table 3 Weight of different models in BMA simulation

[0079]

[0080] To verify the effectiveness of the Bayesian model averaging method based on time-varying model, we use the historical rainfall and tidal level data from 1974 to 2003 to establish a non-stationary model, and derive the prediction results to 2012. Figure 7 The non-stationary distribution of rainfall and tidal level and the 5% and 95% prediction interval are shown. Overall, the non-stationary distribution of rainfall and tidal level is better fitted than the empirical distribution, which indicates that the method is reasonable. At the same time, the prediction interval can describe the uncertainty of Bayesian model averaging, and the 5% and 95% prediction interval includes all distribution models, which can reflect all results of Bayesian model averaging. Figure 7 It can also be seen that the greater the rainfall and tidal level, the greater the uncertainty.

[0081] Figure 8The Bayesian model averaging method based on time-varying distribution model is used to obtain the exceedance probability and increasing rate of rainfall and tide level in 2030 under stationary and non-stationary conditions. Overall, the exceedance probability of rainfall and tide level is significantly higher in non-stationary conditions than in stationary conditions. Among them, the probability growth rate of rainfall increases with the increase of rainfall, with an average growth rate of 61.09%. While the probability growth rate of tide is weaker than that of rainfall, with an average growth rate of 15.08%. The maximum growth rate is 31.11%, corresponding to a 2.82m tide. Therefore, it is shown that the changing environment will have a significant impact on heavy rainfall and high tide, thereby increasing the probability of flood occurrence in coastal cities.

[0082] Four Copula functions are adopted to construct the bivariate joint distribution of rainfall and tide level. As shown in Table 4, all candidate Copula functions pass the KS test with a significance level of 0.05. The AIC and OLS index of Frank Copula are the minimum values, so Frank Copula is selected as the optimal function. In addition, combined with Figure 9 , the correlation coefficient of Frank Copula with the distribution point reaches 0.979, indicating that this function is the optimal function to represent the correlation of rainfall and tide level under non-stationary conditions.

[0083] Table 4 Test and evaluation of candidate Copula function fitting

[0084]

[0085] Figure 10 (a) and Figure 10 (b) show the increase value and increasing rate of joint probability under the combination of rainfall and tide level in non-stationary conditions. Considering the uncertainty of non-stationary distribution, subgraphs ii and iii of Figure 10 give the 5% and 95% boundary values of probability increase value and increasing rate. Overall, due to the low probability of occurrence of heavy rainfall and high tide, the probability increase value decreases with the increase of rainfall and tide level, but the increasing rate gradually increases (as shown in Figure 10 (b)). The average increase rate of probability is 33.22%, and the maximum increase rate is 74.72%. Figure 10 (b) represents the uncertainty brought by the non-stationary distribution of rainfall and tide level, and the average increase rates corresponding to 5% and 95% are 18.97% and 48.59%, respectively.

[0086] The increase value of co-occurrence probability gradually decreases with the increase of rainfall and tide level (as shown in Figure 11 (a)), which is consistent with the characteristics of joint probability change. The increase of probability increasing rate is more obvious in the case of heavy rainfall and high tide, with an average increase rate of 64.82% and a maximum increase rate of 153.05% (as shown in Figure 11(b) shows). In addition, due to the uncertainty of the rainfall-tide edge distribution, the increase rates at 5% and 95% are 27.17% and 114.53%, respectively (see Figure 11 (b) subplots ii and iii). Thus, we notice that the probabilities of both heavy rainfall and high tide level increase significantly in the non-stationary state, which means that the changing environment has a significant impact on the extreme rainfall-tide events.

[0087] Figure 12 (a) shows the flood loss for different rainfall-tide combinations, which is calculated from the flood loss cost and inundation depth. Based on our previous study, the unit flood loss cost in the study area is set to 258 yuan based on the field survey of the two flood events in October 2010 and July 2014. The inundation depth is obtained by the urban flood inundation model. The flood loss is calculated by Figure 12 (a) shows that the flood loss increases with the increase of rainfall-tide. Figure 12 (b) shows the flood loss under typical tide level as a function of rainfall. The flood loss varies slightly with rainfall, and the flood loss under different rainfall scenarios is very close. Figure 12 (c) shows the flood loss under typical rainfall as a function of tide level. Unlike Figure 12 (b), the flood loss increases significantly with the increase of tide level. For example, when the rainfall is 400 mm, the flood loss increases from 462.89 million yuan to 1479.7 million yuan as the tide level increases from 3.0 m to 4.0 m, with an increase of 223.69%. Thus, the tide level plays a dominant role in the flood loss in the study area. Meanwhile, we find that the flood loss increases sharply once the tide level exceeds 3.0 m, and more flood control measures should be taken to predict the tide level exceeding 3.0 m.

[0088] To reflect both the flood probability and the inundation loss, the expected annual loss method is used to assess the flood risk. 10,000 sets of rainfall and tide level combination events are randomly simulated, Figure 13 (a) shows the simulated rainfall and tide level combination event distribution and the flood loss contour. These flood loss contours are all from the flood loss grid (see Figure 12 (a)).

[0089] Figure 13 (b) represents the product of the simulated rainfall and tide level combination event flood loss and its relative probability distribution. Different colored small squares represent the contribution of different rainfall and tide level combination events to the expected annual loss. In Figure 13In (b), the larger the value represented by the small square, the greater the contribution of the combined event to the expected annual loss. We found that the combined events with the largest contributions are mainly concentrated in low rainfall and low tide, involving rainfall with a return period of 4 to 10 years and tide with a return period of 1 to 5 years. Therefore, although the flood loss caused by a single heavy rainfall and high tide event is much greater than that caused by a single low rainfall and low tide event, the frequent occurrence of low rainfall and low tide events makes their contribution to the expected annual flood loss greater than that of heavy rainfall and high tide events.

[0090] Figure 14 (a) Characteristic values ​​of expected annual losses for different design years are given. The black line in the gray box represents the median of the expected annual loss, and the edges and whiskers of the box represent specific percentiles, with the edges corresponding to the 25th and 75th percentiles and the whiskers corresponding to the 5th and 95th percentiles. Compared to a stationary state, the expected annual loss values ​​increase significantly under varying conditions. For the median loss, the increase rate rises from 20.56% in 2030 to 69.84% in 2060 (e.g., ...). Figure 14 (b) shows that flood risk will be further aggravated under changing environments. Furthermore, the percentile range of expected annual losses gradually increases with the design year. For example, the difference between the quintile and 95th percentile of expected annual losses in 2030 is RMB 26.88 million, while this figure reaches RMB 91.6 million in 2060. This indicates that future changing environments will lead to greater uncertainty in flood risk.

[0091] This invention analyzes the non-stationary distribution of rainfall and tides by combining time-varying distribution models and Bayesian model averaging methods, thereby reducing the impact of uncertainty. It also uses expected annual loss to quantify the flood risk caused by the combined effects of rainfall and tides and to assess the impact of changing environment on the uncertainty of flood risk.

Claims

1. A coastal city flood risk analysis method based on Bayesian time-varying model and expected annual loss, characterized in that, The method comprises the following steps: (1) obtaining non-stationary distribution and uncertainty interval of rainfall and tide level by fusing time-varying parameter model and Bayesian model averaging method; including: obtaining distribution parameter variation trend by accumulating rainfall and tide level data, and then generating time-varying model of different distribution parameters of rainfall and time-varying model of different distribution parameters of tide level by using Levenberg-Marquardt algorithm; the calculation formula of time-varying GEV distribution is as follows: wherein, denote the time-varying position, scale and shape parameters, respectively; different variation parameter selection corresponds to different time-varying distribution model, and the non-stationary distribution of rainfall and tide level is obtained by weighting different time-varying models set by Bayesian model averaging, the weight of Bayesian model averaging is solved by expectation maximization algorithm, and Monte Carlo sampling method is used to generate simulation values at each hydrological value, and the uncertainty interval of simulation sequence is derived; (2) based on the non-stationary distribution and uncertainty interval of rainfall and tide level, the change of joint and co-occurrence probability of rainfall and tide level under non-stationary state is analyzed by using Copula function, and the flood event probability under non-stationary state is obtained to represent the influence of changing environment on rainfall and tide level combination event; (3) generating flood loss grid of different rainfall and tide level combination events by simulating different working conditions through urban flood inundation model; the urban flood inundation model adopts orifice connection mode in PCSWMM model to construct one-dimensional river, pipe network and two-dimensional surface flood coupling simulation model; the flood loss of different rainfall and tide level combination is calculated by flood loss cost and inundation depth; (4) based on flood event probability and flood loss, the change and uncertainty of flood risk under changing environment are quantified by using expectation annual loss EAD method: where: EAD is the expected annual loss; is the flood loss due to a particular rainfall and tide level; is the probability of a flood event corresponding to a particular rainfall and tide level.

2. The Bayesian time-varying model and expected annual loss based coastal city flood risk analysis method according to claim 1, characterized in that, the uncertainty interval is the range between 5% and 95% quantile.

3. The Bayesian time-varying model and expected annual loss based coastal city flood risk analysis method according to claim 1, characterized in that, In step (2), the Copula function adopts two Archimedean family Copula functions and two elliptical type Copula functions to construct a binary joint distribution model, and according to AIC, OLS and KS test, the optimal Copula function is selected to represent the correlation of non-stationary rainfall and tide level distribution.

4. The Bayesian time-varying model and expected annual loss based coastal city flood risk analysis method according to claim 3, characterized in that, The two Archimedean family Copula functions include Gumbel Copula and Frank Copula, and the two elliptical type Copula functions include Gaussian Copula and Student's t-Copula.

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