Urban rainfall regional idf curve establishment constraint method and system

Abstract

The application provides a kind of urban rainfall area IDF curve establishment constraint method and system, comprising: collecting measured rainfall data, GCM simulation rainfall data;Establish spatial downscaling model, carry out spatial downscaling to the grid monthly rainfall of future period estimated by GCM;Calculate the conditional transition probability of each calendar month rainfall occurrence in future period;Generate the parameter set of driving random rainfall generator, input it into random rainfall generator to obtain future period daily rainfall sequence;Carry out time discretization of daily scale to hour scale to future period daily rainfall sequence;Extract annual maximum value sequence from future period hourly rainfall sequence to carry out regional frequency analysis, and construct urban rainfall regional IDF curve;Construct random forest model, and deduce the alternative factor of IDF curve migration change;Emergent constraint model is constructed, and the uncertainty of urban rainfall risk prediction under future climate change is reduced.The application improves the accuracy of rainfall frequency analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of water conservancy projects, and in particular relates to a method and system for establishing constraints on an IDF curve in an urban rainfall area. Background Art

[0002] When designing and assessing the risk of urban water conservancy project infrastructure, it is necessary to estimate the extreme rainfall intensity of different durations and recurrence periods. The rainfall intensity-duration-frequency (IDF) curve can meet this requirement and is one of the important design bases for urban basic drainage facilities.

[0003] The traditional method for establishing an IDF curve is to extract the annual maximum rainfall values ​​of different durations from the hourly-scale measured rainfall data at a single site and use an appropriate probability distribution function to perform rainfall frequency analysis. The IDF curve derived from historical measured rainfall data is based on the consistent extreme value assumption, which assumes that the exceedance probability of extreme rainfall events will not change significantly over time during the service life of urban infrastructure drainage facilities. However, in the context of global climate change, the intensity and frequency of extreme rainfall events in most parts of the world are increasing. The resulting extreme flood events will increase the flood control pressure of urban infrastructure drainage facilities. The IDF curve based on the consistency assumption may not be able to meet the design requirements of urban infrastructure drainage facilities under future climate change. On the other hand, the IDF curve established based on rainfall data from a single site is difficult to guarantee the accuracy of rainfall frequency analysis due to problems such as data shortage or lack of representativeness.

[0004] Currently, how to construct IDF curves that account for future climate change has become a new research hotspot. To address this issue, scholars at home and abroad primarily employ two approaches: 1) constructing inconsistent IDF curves based on covariates; and 2) constructing IDF curves based on future rainfall data simulated by global climate models (GCMs). The former modeling extreme rainfall trends observed in the field and incorporating the trends in the simulated rainfall data into consistent IDF curves using covariates to construct inconsistent curves. However, constructing inconsistent IDF curves based on covariates is complex, and its accuracy depends on the selection of optimal covariates, a difficult task. Consequently, this approach has been less widely used. GCMs, on the other hand, provide rainfall series under different future climate change scenarios, providing valuable information on future climate change for IDF curve construction.

[0005] However, GCM-simulated rainfall data has a low spatiotemporal resolution. Specifically, the spatial resolution of GCM output data is generally greater than 1° × 1°, making it difficult to accurately reflect the spatial heterogeneity of urban rainfall and flooding events. Furthermore, GCMs often only provide data at daily or monthly scales. Even if some GCMs provide data at 3-hour or 6-hour scales, their accuracy is low. Furthermore, GCM-projected rainfall data often exhibit large systematic biases, which are particularly pronounced under complex urban convective conditions. Therefore, it is not possible to directly construct IDF curves using GCM-output rainfall data. Before constructing IDF curves using GCM-projected future rainfall data, they must be spatiotemporally downscaled to obtain high-resolution and high-precision rainfall data series. Statistical downscaling methods have been widely used due to their simplicity, low computational complexity, and high accuracy. However, existing statistical downscaling methods primarily focus on spatial downscaling. Currently, there is a lack of statistical methods that directly downscale coarse-grid GCM monthly rainfall data to hourly station data, making them inadequate for constructing IDF curves for urban areas. Summary of the Invention

[0006] The purpose of the present invention is to address the shortcomings of the existing technology and provide a method for establishing constraints on the IDF curve of urban rainfall areas. The method compensates for the low spatiotemporal resolution of rainfall data simulated by GCM through a spatiotemporal cascade statistical downscaling method, and comprehensively considers the rainfall information of multiple stations in the consistent area, thereby improving the accuracy of rainfall frequency analysis.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A method for establishing a constraint for an IDF curve in an urban rainfall area includes the following steps:

[0009] Step 1: Collect rainfall data in the study area and GCM-estimated gridded monthly rainfall for future periods;

[0010] Step 2: Based on the data collected in step 1, a relationship is established between the measured monthly rainfall at the site and the grid monthly rainfall in the historical period simulated by the GCM. Based on the relationship and the grid monthly rainfall data for the future period predicted by the GCM, a data series of station-scale monthly rainfall predictions for the future period is obtained.

[0011] Step 3: Based on the measured daily rainfall data, the relationship between the conditional transition probability of rainfall and the average monthly rainfall is obtained. The monthly rainfall data for the future period obtained in step 2 is then used to calculate the conditional transition probability of rainfall occurring in each calendar month in the future period.

[0012] Step 4: Based on the monthly rainfall in the future period obtained in step 2 and the rainfall transition probability obtained in step 3, a parameter set for driving the random rainfall generator is generated, and the parameter set is input into the random rainfall generator to obtain a data sequence of daily rainfall forecasts in the future period;

[0013] Step 5: based on the daily rainfall forecast data sequence for the future period, discretize the daily rainfall forecast data for the future period from the daily scale to the hourly scale;

[0014] Step 6: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for future periods obtained in Step 5, perform regional frequency analysis on them, and calculate the design rainfall values ​​of different return periods to construct the urban rainfall regional IDF curve considering future climate change;

[0015] Step 7: Based on the IDF curve established in step 6, deduce the changes in urban rainfall risk under each climate model, and build a random forest model with the daily meteorological factors output by the climate model to deduce the candidate factors for the migration change of the IDF curve;

[0016] Step 8: Based on the candidate factors selected in step 7, an emergence constraint model is constructed to reduce the uncertainty of urban rainfall risk prediction under future climate change.

[0017] Furthermore, step 2 includes the following sub-steps:

[0018] Step 2.1 For different calendar months, rank the observed monthly rainfall at the observation site and the GCM simulated monthly rainfall for the historical period, and use a polynomial to fit the nonlinear relationship between the two, R obs,his,m =f1(R GCM,his,m ), as a spatial downscaling model, where R GCM,his,m is the grid monthly rainfall data for the historical period, R obs,his,m The monthly rainfall data of the observation site;

[0019] Step 2.2: Substitute the gridded monthly rainfall data for the future period predicted by GCM into the spatial downscaling model established in step 2.1 to obtain the station monthly rainfall forecast data R for the future period. fut,m =f1(R GCM,fut,m ), R GCM,fut,m Gridded monthly rainfall data for future periods projected by GCM.

[0020] Furthermore, step 3 includes the following sub-steps:

[0021] Step 3.1: Divide the measured daily rainfall data into multiple rainfall subsets of equal length. For each rainfall subset, calculate the conditional transition probability of rainfall in each calendar month: P 11 = P{rainfall on day t|rainfall on day t-1}, P01 = P{rainfall on day t | no rainfall on day t-1};

[0022] Step 3.2 For different rainfall subsets, calculate the monthly average rainfall of the measured rainfall data for each calendar month, denoted as μ m , then fit the conditional transition probability and the average monthly rainfall μ m The linear relationship between 11 =f2(μ m ), P 01 =f3(μ m );

[0023] Step 3.3 Based on the linear relationship fitted in step 3.2 and combined with the spatially downscaled monthly rainfall data in step 2, calculate the conditional transition probability P of rainfall in each calendar month in the future period. 11,fut =f2{e[f1(R GCM,fut,m )]},P 01,fut =f3{E[f1(R GCM,fut,m )]}, where E[f1(R gCM,fut,m )] is the mean monthly rainfall in the future period after spatial downscaling in step 2, R GCM,fut,m Gridded monthly rainfall data for future periods projected by GCM.

[0024] Furthermore, step 4 includes the following sub-steps:

[0025] Step 4.1 Calculate the mean and variance of daily rainfall in the future period based on the monthly rainfall in the future period obtained in step 2, where the mean of daily rainfall in the future period is:

[0026] Where, E[f1(R gCM,fut,m )] is the mean monthly rainfall in the future period after spatial downscaling, N d is the number of days in the calendar month, is the probability of rainfall in each calendar month in the future period, is the average number of rainy days in that calendar month;

[0027] Variance of daily rainfall in future time periods:

[0028]

[0029] Where, D[f1(R GCM,fut,m )] is the variance of the monthly rainfall in the future period after spatial downscaling for the calendar month, P 01,fut -P 11,fut Autocorrelation coefficient of the unconditional probability of rainfall;

[0030] Step 4.2: The conditional transition probability of rainfall in each calendar month of the future period calculated in step 3 and the variance of daily rainfall in the future period calculated in step 4.1 are organized into a rainfall parameter set par{P 11,fut ,P 01,fut ,μ d,fut ,σ 2 d,fut}, and input the parameter set into the random rainfall generator to obtain the daily rainfall data sequence for the future period, denoted as R fut,d .

[0031] Furthermore, step 5 includes the following sub-steps:

[0032] Step 5.1 Use the K-nearest neighbor resampling algorithm to select the K nearest neighbors of the target day’s rainfall, calculate the corresponding weights, and select the parent individuals required by the genetic algorithm from them, denoted as x p , and the parent individual, denoted as x o* ;

[0033] Step 5.2, for x o and x p* Perform crossover and mutation processing to obtain offspring individuals, denoted as Based on the K nearest neighbors obtained in step 5.1, select a nearest neighbor x δ,h right Each chromosome of the gene is mutated to obtain the mutated offspring individuals. Finally, based on the obtained offspring individuals, the hourly rainfall distribution ratio α is calculated. t,h , and as a time discrete model on the scale of day to hour;

[0034] Step 5.3 Set the target day rainfall R fut,d(t) Substitute into the time discrete model established in step 5.2 to obtain the rainfall from 1 to 24 hours on day t: R t,h＝ α t,h R fut,d(t) , where t is the tth day and h is 1-24 hours;

[0035] Step 5.4 Repeat the above steps n times, where n is the daily rainfall sequence R fut,d The number of days until the hourly rainfall data sequence R of the future period after spatiotemporal downscaling is obtained fut,h .

[0036] Furthermore, step 6 includes the following sub-steps:

[0037] Step 6.1: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for the future period obtained in step 5;

[0038] Step 6.2: Use the partitioned linear moment method to perform regional frequency analysis on the annual maximum rainfall series extracted in step 6.1;

[0039] Step 6.3: Based on the design rainfall values ​​of different return periods at each station obtained by regional frequency analysis, construct the urban rainfall regional IDF curve considering climate change information.

[0040] Furthermore, the specific implementation of step 6.2 is as follows:

[0041] 1) The initial hydrological consistency area is divided according to the annual maximum rainfall sequence. The inharmony test and uniformity test are performed based on the linear moment coefficient of each station in the initial hydrological consistency area, and outliers are eliminated to obtain the final hydrological consistency area;

[0042] 2) Perform dimensionless processing on the sample series of each station within the determined hydrologically consistent area to generate a dimensionless sample series reflecting the commonality of regional rainfall and a scaling factor reflecting the rainfall characteristics of the station;

[0043] 3) Calculate the regional linear moment coefficient based on the dimensionless sample sequence of each station;

[0044] 4) Calculate the parameters of the alternative probability distribution line type based on the regional linear moment coefficient, and use the Monte Carlo simulation test method to perform a goodness of fit test to determine the optimal distribution line type and obtain the regional growth curve;

[0045] 5) Based on the scale factor of each station and the regional growth curve, the index flood method is used to calculate the design rainfall value under different recurrence periods for each station.

[0046] Furthermore, step 7 includes the following sub-steps:

[0047] Step 7.1: Collect multiple observational meteorological factor data and interpolate them to each rainfall station;

[0048] Step 7.2: After calibration with multiple climate models for the historical period, a random forest model is established using the maximum annual rainfall intensity values ​​obtained from the IDF curve and the candidate meteorological factor sequence for the same period of maximum rainfall intensity, and the prediction effect of the random forest model is verified;

[0049] Step 7.3: Based on the prediction results of the verified random forest model, the out-of-bag error index is used to obtain the degree of explanation of each meteorological factor on rainfall intensity, and the meteorological factors with the greatest importance in predicting rainfall intensity series are selected as candidate factors for constructing the emergence constraint model.

[0050] Furthermore, step 8 includes the following sub-steps:

[0051] Step 8.1 Collect the measured data of the candidate factors inferred in step 7, denoted as X O, the rainfall intensity in the future period is recorded as Y, and the correlation coefficient ρ between the historical alternative factor simulated by GCM and the rainfall intensity in the future period estimated by GCM is calculated, where the historical alternative factor simulated by GCM is recorded as X GCM , the rainfall intensity in the future period predicted by GCM is recorded as Y GCM ;

[0052] Step 8.2: Standard deviation of the historical candidate factor simulated by GCM and the standard deviation σ of the observation data n Calculate the observation signal-to-noise ratio:

[0053]

[0054] Among them, σ represents the standard deviation of each variable, and the observation error is recorded as n;

[0055] Step 8.3: Based on the data obtained in steps 8.1 and 8.2, the emergence constraint relationship is established using the Bayesian hierarchical emergence constraint method:

[0056]

[0057] in, is the mean precipitation intensity in the future period after the emergence constraint forecast, is the regression coefficient;

[0058] The selected main controlling meteorological factors are used to constrain the extreme rainfall intensity at different durations in the future, so as to reduce the uncertainty in estimating urban rainstorm risks.

[0059] Another object of the present invention is to provide a system for implementing the above-mentioned method for establishing constraints on the IDF curve of urban rainfall areas, comprising:

[0060] The data acquisition module collects rainfall data in the study area and the gridded monthly rainfall in the future period estimated by GCM;

[0061] The monthly rainfall prediction module is used to establish the relationship between the measured monthly rainfall at the site and the grid monthly rainfall of the historical period simulated by the GCM based on the collected data. Based on the established relationship and the grid monthly rainfall data of the future period estimated by the GCM, a data series of station-scale monthly rainfall estimates for the future period is obtained;

[0062] The conditional transition probability calculation module is used to obtain the relationship between the conditional transition probability of rainfall and the average monthly rainfall based on the measured daily rainfall data, and then calculate the conditional transition probability of rainfall in each calendar month in the future period using the obtained monthly rainfall data;

[0063] The daily rainfall prediction module is used to generate a parameter set for driving the random rainfall generator based on the obtained monthly rainfall in the future period and the obtained rainfall transition probability, and input the parameter set into the random rainfall generator to obtain a data sequence of daily rainfall prediction in the future period;

[0064] The rainfall discretization module is used to discretize the daily rainfall forecast data of the future period from the daily scale to the hourly scale based on the daily rainfall forecast data sequence of the future period;

[0065] The module for constructing an IDF curve for urban rainfall regions is used to extract annual maximum rainfall series of different durations from the hourly rainfall forecast data obtained for future periods using a sliding time window, perform regional frequency analysis on these series, and calculate design rainfall values ​​for different return periods to construct an IDF curve for urban rainfall regions that takes into account future climate change.

[0066] The candidate factor derivation module is used to deduce the changes in urban rainfall risk under various climate models based on the established IDF curve, and to construct a random forest model with the daily meteorological factors output by the climate model to deduce the candidate factors for the migration changes of the IDF curve;

[0067] The urban rainfall risk prediction module is used to construct an emergence constraint model based on the preferred alternative factors to reduce the uncertainty of urban rainfall risk prediction under future climate change.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention first obtains a sequence of estimated rainfall extremes with high spatiotemporal resolution for future periods. Subsequently, the partitioned linear moment method is further used to divide the study area into several hydrologically consistent zones, and the rainfall extreme sequence of each station in the consistent zone is subjected to regional frequency analysis to obtain rainfall design values ​​under different recurrence periods, and thereby constructs an IDF curve of urban rainfall areas that considers future climate change information, and finally adopts an emergence constraint method to reduce the uncertainty of extreme rainfall risk prediction results. The present invention compensates for the low spatiotemporal resolution and large deviation of rainfall data simulated by GCM through the proposed spatiotemporal cascade statistical downscaling method, and adopts a regional frequency analysis method based on the partitioned linear moment method to comprehensively consider the rainfall information of multiple stations in the consistent zone, thereby improving the accuracy of rainfall frequency analysis, and reduces the uncertainty of the prediction results by adopting the emergence constraint method, thereby improving the reliability of the prediction results. Therefore, the present invention can scientifically and rationally establish an IDF curve of urban rainfall areas that considers future climate change information. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A specific flow chart of a method for establishing constraints on an IDF curve for an urban rainfall area according to an embodiment of the invention;

[0070] Figure 2The schematic diagram of QQ plot of monthly rainfall before and after the spatial downscaling of the invention embodiment conversion function method;

[0071] Figure 3 The schematic diagram of the relationship between the monthly average rainfall of each calendar month and the conditional transition probability of rainfall occurrence of the invention embodiment;

[0072] Figure 4 The schematic diagram of the comparison between the multi-year average of the hourly rainfall of the historical period of the invention embodiment and the simulation;

[0073] Figure 5 The schematic diagram of the regional IDF curve of the future period under different return periods of the invention embodiment. DETAILED DESCRIPTION

[0074] The technical solutions in the embodiments of the present application will be clearly and completely described in combination with the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work belong to the scope of protection of the present application.

[0075] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0076] The present application will be further described in combination with specific embodiments, but not as a limitation of the present application.

[0077] The constraint method for establishing the regional IDF curve of urban rainfall of the embodiments of the present application is based on the constructed spatio-temporal cascade statistical downscaling model. First, the conversion function method is used to perform spatial downscaling on the grid scale monthly rainfall data estimated by the GCM to obtain the station scale monthly rainfall estimation data. Then, the spatially downscaled monthly rainfall estimation data is disassembled into daily rainfall series by using the random rainfall generator. In the process of temporal downscaling, on the one hand, the rainfall occurrence state is down-scaled, and on the other hand, the rainfall amount is down-scaled. Finally, the daily rainfall estimation data generated by the random rainfall generator is input into the time discrete model coupled with the K-nearest neighbor resampling and genetic algorithm to obtain the hourly scale rainfall estimation data and extract the rainfall extreme value sequence of different durations therefrom. Further, the study area is divided into a plurality of hydrologically consistent regions by using the partition linear moment method, and the rainfall extreme value sequences of the stations in the consistent regions are subjected to regional frequency analysis to obtain the design rainfall values under different return periods. Finally, the regional IDF curve of urban rainfall is established according to the design rainfall values, and the specific process is shown in Figure 1 :

[0078] Step 1, collect the rainfall data in the study area and the grid monthly rainfall estimated by the GCM in the future period; this step includes:

[0079] Step 1.1 Collect the hourly rainfall data series (denoted as R) measured at the stations in the study area. his,h ), and accumulate to obtain the corresponding daily rainfall data series (denoted as R his,d ) and the monthly rainfall data series (denoted as R his,m ); The hourly rainfall data sequence measured at the station collected in this embodiment is from January 1, 1981 to December 31, 2010, a total of 30 years of hourly rainfall data at the station;

[0080] Step 1.2 Collect the historical grid monthly rainfall data (denoted as R) simulated by GCM in the study area. GCM,his,m ), and the gridded monthly rainfall data for the future period predicted by GCM (denoted as R GCM,fut,m The simulated rainfall data collected in this embodiment include gridded monthly rainfall data for the historical period from January 1, 1981 to December 31, 2010, a total of 30 years, and gridded monthly rainfall data for the future period from January 1, 2011 to December 31, 2040, a total of 30 years, simulated by GCM.

[0081] Step 2: Based on the data collected in step 1, establish a relationship between the measured monthly rainfall at the site and the grid monthly rainfall for the historical period simulated by the GCM. Then, based on this relationship and the grid monthly rainfall data for the future period predicted by the GCM, obtain a data series of station-scale monthly rainfall predictions for the future period. This step includes the following sub-steps:

[0082] Step 2.1 For different calendar months, arrange the observed monthly rainfall at the site and the GCM simulated monthly rainfall for the historical period in ascending order, and use a polynomial to fit the nonlinear relationship between the two: R obs,his,m =f1(R GCM,his,m ) and use it as a spatial downscaling model;

[0083] Step 2.2: Substitute the gridded monthly rainfall data for the future period predicted by GCM into the spatial downscaling model established in step 2.1 to obtain the monthly rainfall forecast data for the future period:

[0084] R fut,m =f1(R GCM,fut,m );

[0085] Figure 2 The QQ plots of GCM simulated monthly rainfall and measured monthly rainfall before and after spatial downscaling using the transfer function method are shown, which can reflect the performance of the transfer function method in downscaling grid data to station data.

[0086] Step 3: Based on the measured daily rainfall data, the relationship between the conditional transition probability of rainfall and the average monthly rainfall is obtained. The monthly rainfall data for the future period obtained in step 2 is then used to calculate the conditional transition probability of rainfall occurring in each calendar month in the future period. Specifically:

[0087] Step 3.1: Divide the measured daily rainfall data into four rainfall subsets of equal length and calculate the conditional transition probability of rainfall occurrence in different subsets.

[0088] First, the observed daily rainfall data were divided into four rainfall subsets of equal length. These included two rainfall subsets divided equally by year (e.g., 50 years of data were divided equally into two 25-year periods), and two rainfall subsets divided by monthly rainfall: the driest group and the wettest group (e.g., 50 years of data were divided into 25 years with more precipitation and 25 years with less precipitation). Then, for each rainfall subset, the conditional transition probability of rainfall occurring in each calendar month was calculated:

[0089] P 11 = P{Rainfall on day t|Rainfall on day t-1}

[0090] P 01 = P{rainfall on day t|no rainfall on day t-1}

[0091] Among them, P 11 P is the conditional transition probability that there is rainfall on the tth day of the calendar month and there is rainfall on the t-1th day, 01 is the conditional transition probability that there is rainfall on the tth day of the calendar month and no rainfall on the t-1th day;

[0092] In this embodiment, the rainfall threshold is 0.1 mm; if the rainfall on a day is greater than 0.1 mm, it is a rainy day, otherwise it is a no-rainy day. Based on the above steps, for each calendar month, a set of conditional transition probabilities of rainfall occurrence containing four subsets will be derived, namely P 11 Set and P 01 Collection to characterize the rainfall occurrence status under different climatic conditions;

[0093] Step 3.2 For different rainfall subsets, calculate the monthly average rainfall (denoted as μ m ), and fitted P 11 、P 01 and μ m The linear relationship between:

[0094] P 11 =f2(μ m )

[0095] P 01 =f3(μ m )

[0096] Figure 3 A linear relationship graph of the average monthly rainfall for each calendar month and the conditional transition probability of rainfall occurrence is shown;

[0097] Step 3.3: Combine the linear relationship fitted in step 3.2 with the spatially downscaled monthly rainfall data for the future period in step 2 to calculate the conditional transition probability of rainfall for each calendar month in the future period:

[0098] P 11,fut =f2{E[f1(R GCM,fut,m )]}

[0099] P 01,fut =f3{E[f1(R GCM,fut,m )]}

[0100] Among them, E[f1(R GCM,fut,m )] is the mean monthly rainfall in the future period after spatial downscaling in step 2. Through the above two formulas, the monthly rainfall after spatial downscaling is effectively cascaded with the conditional transition probability of rainfall in temporal downscaling.

[0101] Step 4: Based on the monthly rainfall for the future period obtained in step 2 and the rainfall transition probability obtained in step 3, a parameter set for driving the random rainfall generator is generated, and the parameter set is input into the random rainfall generator to obtain a data sequence of daily rainfall forecasts for the future period. Specifically, step 4 includes:

[0102] Step 4.1 Calculate the mean and variance of daily rainfall in the future period based on the monthly rainfall in the future period obtained in step 2. First, for each calendar month, construct an analytical expression to calculate the mean of daily rainfall in the future period:

[0103]

[0104] Where, E[f1(R GCM,fut,m )] is the mean monthly rainfall in the future period after spatial downscaling, N d is the number of days in the calendar month, is the probability of rainfall in each calendar month in the future period, is the average number of rainy days in that calendar month;

[0105] Then construct an analytical expression to calculate the variance of daily rainfall in the future period:

[0106]

[0107] Where, D[f1(R GCM,fut,m )] is the variance of the monthly rainfall in the future period after spatial downscaling for the calendar month, P 01,fut -P 11,fut Autocorrelation coefficient of the unconditional probability of rainfall;

[0108] Through the above two formulas, an effective cascade of spatial downscaling and daily temporal downscaling is achieved;

[0109] Step 4.2 For each calendar month, generate a set of rainfall parameter sets containing 4 parameters, par{P 11,fut ,P 01,fut ,μ d,fut ,σ 2 d,fut}, this parameter set is the input parameters required by the common random rainfall generator to simulate the daily rainfall sequence in the future period;

[0110] This embodiment assumes that the skewness coefficient of daily rainfall in the future period does not change, and calculates the skewness coefficient g of daily rainfall based on the measured daily rainfall data.

[0111] Step 4.3 Input the parameter set generated in step 4.2 into the random rainfall generator to obtain the daily rainfall data sequence for the future period (denoted as R fut,d This embodiment uses the rainfall module in the random rainfall generator CLIGEN to simulate a series of daily rainfall data for a future period. This step is conventional in the art. To facilitate understanding, the principles of the random rainfall generator CLIGEN involved in this step are briefly described below.

[0112] When simulating daily rainfall, CLIGEN uses a first-order two-state Markov chain to simulate the conditional transition probability P of rainfall occurrence. 11 and P 01 The basic idea is that the probability of rainfall on a certain day is only related to the dry and wet conditions of the previous day. When simulating the rainfall state of a certain day, first give the rainfall state of the previous day (rainy day or no rain day) arbitrarily, then generate a random number in the interval [0,1], and compare the random number with the conditional transition probability P 11 or P 01 For comparison, if the generated random number is less than the conditional transition probability, then the day is a rainy day. For rainy days, this embodiment uses the skew normal distribution function to simulate daily rainfall, and the calculation formula is:

[0113]

[0114] Where P is the daily rainfall, μ, σ and g are the mean, standard deviation and skewness coefficient of the daily rainfall in the calendar month respectively, and x is the standard normal deviation of the daily rainfall in the calendar month, which is generated by two uniformly distributed random numbers in the range [0,1].

[0115] On the contrary, the day is a rainless day and the rainfall is 0. Then, the dry and wet state of this day is used as the initial value to determine the rainfall state of the next day and calculate the rainfall of the next day. Similarly, the daily rainfall data series of the required period can be obtained.

[0116] Step 5: based on the daily rainfall forecast data sequence for the future period, discretize the daily rainfall forecast data for the future period from the daily scale to the hourly scale;

[0117] Based on the daily rainfall forecast data for the future period, the K-nearest neighbor algorithm is used to select the K nearest neighbors with the highest similarity from the measured hourly rainfall data sequence and calculate the corresponding weights. The father and mother individuals are then selected from the nearest neighbors based on the calculated weights. The two individuals are then subjected to crossover and mutation processing using a genetic algorithm to obtain offspring individuals. A time discrete model is then established based on the hourly rainfall distribution ratio within the day to discretize the daily rainfall forecast data for the future period from the daily scale to the hourly scale. The specific sub-steps include:

[0118] Step 5.1 Use the K-nearest neighbor resampling algorithm to select the K nearest neighbors of the target day rainfall, calculate the corresponding weights, and select the parent individuals required by the genetic algorithm (denoted as x p ) and the mother individual (denoted as x p* ); For each calendar month, first take the t-day rainfall in the future period daily rainfall sequence obtained in step 4 as the target daily rainfall (denoted as R fut,d(t) ), calculate its difference with the measured daily rainfall data series daily rainfall R on the i-th day obs,his,d(i) The Euclidean distance of :

[0119] (R fut,d(t) -R obs,his,d(i) ) 2

[0120] The smaller the Euclidean distance is, the higher the similarity between the two.

[0121] Then, D i Arrange in ascending order, and according to the time index i of the first K distances, select the corresponding K days of hourly rainfall in the measured hourly rainfall data sequence as the K nearest neighbors, and calculate the corresponding weights:

[0122]

[0123] The number of nearest neighbors set in this embodiment is K=20;

[0124] Then, based on the calculated weights, two are selected from the K nearest neighbors as the parent individuals x required to run the genetic algorithm. p =[x p,h ] h∈{1,24} and parent individual x p* =[xp*,h ] h∈{1,24} ,The rainfall amounts from 1 to 24 hours corresponding to the two correspond to the 24 chromosomes of the genetic algorithm;

[0125] Step 5.2 for x p and x p* Perform crossover and mutation to obtain offspring individuals (denoted as ); For each calendar month, first, the x obtained in step 5.1 p and x p* Perform crossover on each chromosome to obtain the offspring individuals after crossover:

[0126]

[0127] Among them, ε is a random number uniformly distributed between the interval [0,1], P c is the crossover probability;

[0128] The crossover probability P used in this embodiment is c =0.1;

[0129] Then, based on the K nearest neighbors obtained in step 5.1, another nearest neighbor x is selected δ,h right Each chromosome of is mutated to obtain the mutated offspring individuals:

[0130]

[0131] Among them, ε is a random number uniformly distributed between the interval [0,1], P m is the crossover probability;

[0132] The mutation probability P used in this embodiment is m =0.01.

[0133] Finally, based on the obtained offspring individuals, calculate their hourly rainfall distribution ratio within the day:

[0134]

[0135] α h As a time discrete model on the daily to hourly scale;

[0136] Through steps 5.1 and 5.2, the coupling of the nearest neighbor resampling algorithm and the genetic algorithm is achieved.

[0137] Step 5.3 Set the target day rainfall R fut,d(t) Substituting this into the time discrete model established in step 5.2, we can obtain the hourly rainfall:

[0138] R t,h =α t,hR fut,d(t)

[0139] Where, t is the tth day, h is 1-24 hours;

[0140] Step 5.4 Repeat the above steps n times (n is the daily rainfall sequence R fut,d until the hourly rainfall data sequence R for the future period after time and space downscaling is obtained. fut,h .

[0141] The above steps achieve an effective cascade of daily and hourly downscaling. The time discrete model used in this embodiment is a stochastic model. To eliminate the uncertainty of random simulation, this embodiment generates 300 30-year random rainfall sequences each time to capture the overall trend of hourly rainfall.

[0142] Figure 4 This is a comparison chart of the multi-year average of the hourly rainfall data series for the historical period simulated by the time discrete model and the multi-year average of the measured hourly rainfall data series. The simulated values ​​are presented through box plots of 300 random rainfall sequences.

[0143] Step 6: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for future periods obtained in Step 5, perform regional frequency analysis on them, and calculate the design rainfall values ​​for different return periods to construct the regional IDF curve of urban rainfall considering future climate change. This step includes the following sub-steps:

[0144] Step 6.1: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for future periods obtained in step 5;

[0145] When this embodiment uses a sliding time window to extract the annual maximum rainfall sequence, the window length is set to 1 hour, 3 hours, 6 hours, 12 hours and 24 hours (corresponding to different rainfall durations), and the step size of each sliding is 1 hour.

[0146] Step 6.2 uses the partitioned linear moment method to perform regional frequency analysis on the annual maximum rainfall series extracted in step 6.1 to obtain the design rainfall values ​​for different return periods at each station. The partitioned linear moment method is a conventional technique in this field and has been widely used. The following is a brief introduction and includes the following five steps:

[0147] 1) The initial hydrological consistency area is divided according to the annual maximum rainfall sequence. The inharmony test and uniformity test are performed based on the linear moment coefficient of each station in the initial hydrological consistency area, and outliers are eliminated to obtain the final hydrological consistency area;

[0148] 2) Perform dimensionless processing on the sample series of each station within the determined hydrologically consistent area to generate a dimensionless sample series reflecting the commonality of regional rainfall and a scaling factor reflecting the rainfall characteristics of the station;

[0149] 3) Calculate the regional linear moment coefficient based on the dimensionless sample sequence of each station;

[0150] 4) Based on the regional linear moment coefficient, the parameters of the alternative probability distribution line type are calculated, and the Monte Carlo simulation test method is used to perform a goodness of fit test to determine the optimal distribution line type and obtain the regional growth curve.

[0151] 5) Based on the scale factor of each station and the regional growth curve, the index flood method is used to calculate the design rainfall value under different return periods for each station;

[0152] Step 6.3: Connect the design rainfall values ​​of different return periods of each station obtained by regional frequency analysis to obtain the urban rainfall regional IDF curve considering future climate change. Figure 5 Shown is a schematic diagram of regional IDF curves under different return periods.

[0153] Step 7: Based on the IDF curve established in step 6, the changes in urban rainfall risk under each climate model are deduced. A random forest model is constructed with the daily meteorological factors output by the climate model to derive candidate factors for the migration changes of the IDF curve. Step 7 further includes the following sub-steps:

[0154] Step 7.1 collects multiple observed meteorological factor data and interpolates them to each rainfall station using the inverse distance weighted interpolation method. The meteorological factors considered in this embodiment include daily average temperature, relative humidity, shortwave radiation, leaf area index (LAI), specific humidity, soil moisture, and annual temperature variability, relative humidity variability, shortwave radiation variability, LAI variability, specific humidity variability, and soil moisture variability;

[0155] Step 7.2: After calibration using multiple climate models with a historical duration of d (d = 1h, 2h, 4h, ...), the maximum annual rainfall intensity value obtained from the IDF curve is used to establish a random forest model with the candidate meteorological factor sequence of the same period of maximum rainfall intensity, and the root mean square error of the rainfall intensity prediction result and the original result is calculated. and the correlation coefficient Verify the prediction effect of the random forest model, y pre,i Represents the rainfall intensity result predicted by the random forest model, y ori,i represents the original result of rainfall intensity, and m represents the total number of prediction samples;

[0156] Step 7.3 Based on the prediction results of the verified random forest model, use the out-of-bag error index to measure the importance of each meteorological factor to the rainfall intensity during duration d.d , screen out the meteorological factors with the greatest importance in predicting the rainfall intensity series of duration d as candidate factors for constructing the emergence constraint model; the method of selecting important factors based on the out-of-bag error index is a conventional technology in this field.

[0157] Step 8: Based on the candidate factors obtained in step 7, an emergence constraint model is constructed to reduce the uncertainty of urban rainfall risk prediction under future climate change;

[0158] The meteorological factors with the greatest importance for rainfall intensity prediction are selected as candidate factors for constructing emergent constraints in this step. Taking into account the uncertainty of observational data, a Bayesian hierarchical emergent framework is used to further constrain rainfall intensity under different future scenarios. This step specifically includes the following substeps:

[0159] Step 8.1 Collect the measured data of the candidate factors derived in step 7 (denoted as X O ) and the rainfall intensity in the future period (denoted as Y), and calculate the historical alternative factor (denoted as X) simulated by GCM GCM ) and the rainfall intensity in the future period predicted by GCM (denoted as Y GCM )’s correlation coefficient ρ;

[0160] Step 8.2 Due to the uncertainty in observational data, use the standard deviation of the historical candidate factor simulated by GCM and the standard deviation σ of the observation data n , calculate the signal-to-noise ratio of the observed data:

[0161]

[0162] Step 8.3 Calculate the regression coefficient using the model's historical candidate factors (predictors) and the model's future rainfall intensity (predicted values):

[0163]

[0164] Where ρ is the correlation coefficient between the current prediction factor and the future prediction value, and The standard deviation of the two respectively;

[0165] On this basis, the Bayesian hierarchical emergence constraint method is used to construct the emergence constraint model. Specifically, the Bayesian hierarchical emergence constraint relationship with observation uncertainty is:

[0166]

[0167] That is, through the above formula, the selected alternative meteorological factors are used to constrain the rainfall intensity of different durations in the future, so as to reduce the uncertainty of estimating urban rainfall risks.

[0168] The embodiment of the present application also provides a system for implementing the urban rainfall regional IDF curve establishment constraint method, comprising:

[0169] a data acquisition module which collects rainfall data in a research region and GCM predicted future period grid monthly rainfall;

[0170] a monthly rainfall prediction module which is used for establishing a relationship between site measured monthly rainfall and GCM simulated historical period grid monthly rainfall according to the collected data, and obtaining a future period site scale monthly rainfall prediction data sequence according to the established relationship and GCM predicted future period grid monthly rainfall data;

[0171] a conditional transition probability calculation module which is used for obtaining a relationship between rainfall conditional transition probability and monthly average rainfall according to measured daily rainfall data, and then calculating future period daily calendar month rainfall occurrence conditional transition probability according to the obtained future period monthly rainfall data;

[0172] a daily rainfall prediction module which is used for generating a parameter set for driving a random rainfall generator according to the obtained future period monthly rainfall and the obtained rainfall occurrence transition probability, and inputting the parameter set into the random rainfall generator to obtain a future period daily rainfall prediction data sequence;

[0173] a rainfall discretization module which is used for discretizing future period daily rainfall prediction data from a daily scale to an hourly scale according to the future period daily rainfall prediction data sequence;

[0174] an urban rainfall regional IDF curve construction module which is used for extracting different duration annual maximum rainfall sequences from the obtained future period hourly rainfall prediction data by using a sliding time window, and performing regional frequency analysis on the sequences to calculate different return period design rainfall values and construct urban rainfall regional IDF curves considering future climate change;

[0175] an alternative factor derivation module which is used for deriving urban rainfall risk changes under each climate mode according to the established IDF curves, and constructing a random forest model with daily meteorological factors output by the climate mode to derive alternative factors of IDF curve migration change;

[0176] an urban rainfall risk prediction module which is used for constructing an emergent constraint model according to the obtained alternative factors to reduce uncertainty of urban rainfall risk prediction under future climate change.

[0177] The above are only the preferred embodiments of the present application, and do not limit the implementation manners and protection scope of the present application. It should be understood by those skilled in the art that any equivalent substitutions and obvious changes made according to the content of the present application should be included in the protection scope of the present application.

Claims

1. A method for establishing constraints on IDF curves in urban rainfall areas, characterized in that: The following steps are involved: Step 1: Collect rainfall data in the study area and GCM-estimated gridded monthly rainfall for future periods; Step 2: Based on the data collected in step 1, a relationship is established between the measured monthly rainfall at the site and the grid monthly rainfall in the historical period simulated by the GCM. Based on the relationship and the grid monthly rainfall data for the future period predicted by the GCM, a data series of station-scale monthly rainfall predictions for the future period is obtained. Step 3: Based on the measured daily rainfall data, the relationship between the conditional transition probability of rainfall and the average monthly rainfall is obtained. The monthly rainfall data for the future period obtained in step 2 is then used to calculate the conditional transition probability of rainfall occurring in each calendar month in the future period. Step 4: Based on the monthly rainfall in the future period obtained in step 2 and the rainfall transition probability obtained in step 3, a parameter set for driving the random rainfall generator is generated, and the parameter set is input into the random rainfall generator to obtain a data sequence of daily rainfall forecasts in the future period; Step 5: based on the daily rainfall forecast data sequence for the future period, discretize the daily rainfall forecast data for the future period from the daily scale to the hourly scale; Step 6: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for future periods obtained in Step 5, perform regional frequency analysis on them, and calculate the design rainfall values ​​of different return periods to construct the urban rainfall regional IDF curve considering future climate change; Step 7: Based on the IDF curve established in step 6, deduce the changes in urban rainfall risk under each climate model, and build a random forest model with the daily meteorological factors output by the climate model to deduce the candidate factors for the migration change of the IDF curve; Step 8: Based on the candidate factors obtained in Step 7, an emergence constraint model is constructed to reduce the uncertainty of urban rainfall risk prediction under future climate change; Wherein, step 6 includes the following sub-steps: Step 6.1: Use a sliding time window to extract the annual maximum rainfall series of different durations from the hourly rainfall forecast data for the future period obtained in step 5; Step 6.2 uses the partitioned linear moment method to perform regional frequency analysis on the annual maximum rainfall sequence extracted in step 6.

1. The specific implementation of step 6.2 is as follows: 1) The initial hydrological consistency zone is divided according to the annual maximum rainfall sequence. The inharmony test and uniformity test are performed based on the linear moment coefficient of each station in the initial hydrological consistency zone, and outliers are eliminated to obtain the final hydrological consistency zone; 2) Perform dimensionless processing on the sample series of each station within the determined hydrologically consistent area to generate a dimensionless sample series reflecting the common characteristics of regional rainfall and a scaling factor reflecting the rainfall characteristics of the station; 3) Calculate the regional linear moment coefficient based on the dimensionless sample sequence of each station; 4) Calculate the parameters of the alternative probability distribution line type based on the regional linear moment coefficient, and use the Monte Carlo simulation method to perform a goodness of fit test to determine the optimal distribution line type and obtain the regional growth curve; 5) Based on the scale factor of each station and the regional growth curve, the index flood method is used to calculate the design rainfall value for each station under different return periods; Step 6.3: Connect the design rainfall values ​​of different return periods of each station obtained by regional frequency analysis to obtain the urban rainfall regional IDF curve considering future climate change; Step 7 includes the following sub-steps: Step 7.1: Collect multiple observational meteorological factor data and interpolate them to each rainfall station. The meteorological factors include daily mean temperature, relative humidity, shortwave radiation, leaf area index (LAI), specific humidity, soil moisture, and annual temperature variability, relative humidity variability, shortwave radiation variability, LAI variability, specific humidity variability, and soil moisture variability. Step 7.2: After calibration with multiple climate models for the historical period, a random forest model is established using the maximum annual rainfall intensity values ​​obtained from the IDF curve and the candidate meteorological factor sequence for the same period of maximum rainfall intensity, and the prediction effect of the random forest model is verified; Step 7.3: Based on the prediction results of the verified random forest model, the out-of-bag error index is used to obtain the degree of explanation of each meteorological factor on rainfall intensity, and the meteorological factors with the greatest importance in predicting rainfall intensity series are selected as candidate factors for constructing the emergence constraint model.

2. The method for establishing constraints on the IDF curve of urban rainfall areas according to claim 1 is characterized in that: Step 2 includes the following sub-steps: Step 2.1 For different calendar months, rank the observed monthly rainfall at the observation site and the GCM simulated monthly rainfall for the historical period, and use a polynomial to fit the nonlinear relationship between the two. ), as a spatial downscaling model, where This is the grid monthly rainfall data for the historical period. The monthly rainfall data of the observation site; Step 2.2: Substitute the GCM-estimated grid monthly rainfall data for the future period into the spatial downscaling model established in step 2.1 to obtain the station monthly rainfall forecast data for the future period. ), Gridded monthly rainfall data for future periods projected by GCM.

3. The method for establishing constraints on the IDF curve of urban rainfall areas according to claim 1 is characterized in that: Step 3 includes the following sub-steps: Step 3.1: Divide the measured daily rainfall data into multiple rainfall subsets of equal length. For each rainfall subset, calculate the conditional transition probability of rainfall in each calendar month: , ; Step 3.2: For different rainfall subsets, calculate the monthly average rainfall of the measured rainfall data for each calendar month, which is recorded as , then fit the conditional transition probability and the average monthly rainfall The linear relationship between ), ); Step 3.3: Based on the linear relationship fitted in step 3.2 and the monthly rainfall data of the future period that has been spatially downscaled in step 2, calculate the conditional transition probability of rainfall in each calendar month in the future period. { [ )]}, { [ )]},in, is the mean monthly rainfall in the future period after spatial downscaling in step 2, Gridded monthly rainfall data for future periods projected by GCM.

4. The method for establishing constraints on the IDF curve of urban rainfall areas according to claim 3 is characterized in that: Step 4 includes the following sub-steps: Step 4.1 Calculate the mean and variance of daily rainfall in the future period based on the monthly rainfall in the future period obtained in step 2, where the mean of daily rainfall in the future period is: ; Where, is the number of days in the calendar month, is the probability of rainfall in each calendar month in the future period, is the average number of rainy days in that calendar month; Variance of daily rainfall in future time periods: ； Where, ] is the variance of the monthly rainfall in the future period after spatial downscaling for the calendar month, Autocorrelation coefficient of the unconditional probability of rainfall; Step 4.2: The conditional transition probability of rainfall in each calendar month in the future period calculated in step 3 and the variance of daily rainfall in the future period calculated in step 4.1 are organized into a rainfall parameter set , and input the parameter set into the random rainfall generator to obtain the daily rainfall data sequence for the future period, recorded as .

5. The method for establishing constraints on the IDF curve of urban rainfall areas according to claim 3 is characterized in that: Step 5 includes the following sub-steps: Step 5.1 Use the K-nearest neighbor resampling algorithm to select the K nearest neighbors of the target day’s rainfall, calculate the corresponding weights, and select the parent individuals required by the genetic algorithm from them, denoted as , and the mother individual, denoted as ; Step 5.2, and Perform crossover and mutation processing to obtain offspring individuals, denoted as , then based on the K nearest neighbors obtained in step 5.1, select a nearest neighbor right Each chromosome of the gene is mutated to obtain the mutated offspring individuals. Finally, the hourly rainfall distribution ratio of the offspring individuals is calculated based on the obtained offspring individuals. , and as a time discrete model on the scale of day to hour; Step 5.3 Set the target day rainfall Substituting this into the time discrete model established in step 5.2, we can obtain the rainfall for the first 24 hours on day t: , where t For the t sky, h 1-24 hours; Step 5.4 Repeat the above steps n times, among which, n Daily rainfall series until the hourly rainfall data series for the future period after spatiotemporal downscaling is obtained. .

6. The method for establishing constraints on the IDF curve of urban rainfall areas according to claim 1 is characterized in that: Step 8 includes the following sub-steps: Step 8.1 Collect the measured data of the candidate factors derived in step 7, denoted as , the rainfall intensity in the future period is recorded as Calculate the correlation coefficient between the historical alternative factors simulated by GCM and the rainfall intensity in the future period predicted by GCM , where the historical alternative factor simulated by GCM is , the rainfall intensity in the future period predicted by GCM is recorded as ; Step 8.2: Standard deviation of the historical candidate factor simulated by GCM and the standard deviation of the observation data Calculate the observation signal-to-noise ratio: ； in, represents the standard deviation of each variable, and the observation error is recorded as ; Step 8.3: Based on the data obtained in steps 8.1 and 8.2, the emergence constraint relationship is established using the Bayesian hierarchical emergence constraint method: ； in, is the mean precipitation intensity in the future period after the emergence constraint forecast, , is the regression coefficient; The selected main controlling meteorological factors are used to constrain the extreme rainfall intensity at different durations in the future, so as to reduce the uncertainty in estimating urban rainstorm risks.

7. A system for implementing the method for establishing constraints on the IDF curve of an urban rainfall area according to any one of claims 1 to 6, characterized in that: include: The data acquisition module collects rainfall data in the study area and the gridded monthly rainfall in the future period estimated by GCM; The monthly rainfall prediction module is used to establish the relationship between the measured monthly rainfall at the site and the grid monthly rainfall of the historical period simulated by the GCM based on the collected data. Based on the established relationship and the grid monthly rainfall data of the future period estimated by the GCM, a data series of station-scale monthly rainfall estimates for the future period is obtained; The conditional transition probability calculation module is used to obtain the relationship between the conditional transition probability of rainfall and the average monthly rainfall based on the measured daily rainfall data, and then calculate the conditional transition probability of rainfall in each calendar month in the future period using the obtained monthly rainfall data; The daily rainfall prediction module is used to generate a parameter set for driving the random rainfall generator based on the obtained monthly rainfall in the future period and the obtained rainfall transition probability, and input the parameter set into the random rainfall generator to obtain a data sequence of daily rainfall prediction in the future period; The rainfall discretization module is used to discretize the daily rainfall forecast data of the future period from the daily scale to the hourly scale based on the daily rainfall forecast data sequence of the future period; The module for constructing an IDF curve for urban rainfall regions is used to extract annual maximum rainfall series of different durations from the hourly rainfall forecast data obtained for future periods using a sliding time window, perform regional frequency analysis on these series, and calculate design rainfall values ​​for different return periods to construct an IDF curve for urban rainfall regions that takes into account future climate change. The candidate factor derivation module is used to deduce the changes in urban rainfall risk under various climate models based on the established IDF curve, and to construct a random forest model with the daily meteorological factors output by the climate model to deduce the candidate factors for the migration changes of the IDF curve; The urban rainfall risk prediction module is used to construct an emergence constraint model based on the obtained alternative factors to reduce the uncertainty of urban rainfall risk prediction under future climate change.

Images