Global climate change and rapid urbanization increase the risk of urban flooding, especially in China. Climate change and the ‘heat island effect’ have increased the frequency of extreme precipitation. Affected by the backwardness of drainage facilities and the lack of drainage capacity, many cities have experienced large-scale waterlogging in low-lying areas, and ocean-like phenomena appear in cities. The public infrastructure was damaged and caused a lot of economic losses. Therefore, it is important to investigate the adaptability of drainage systems to the future in a changing environment. The Sixth International Coupled Model Intercomparison Project (CMIP6) and Storm Water Management Model (SWMM) were used to quantify the impact of climate change on Beijing's waterlogging under different rainstorm scenarios for the future 40 years. The quantile delta mapping method of daily precipitation based on frequency (DFQDM) is proposed to correct the daily precipitation of the climate model and which is proved to be feasible. After the annual precipitation and extreme precipitation index are corrected, percent bias (PBIAS) is significantly reduced. The PBIAS of the extreme precipitation index of the corrected model is all controlled within 6%. The corrected accuracy of CanESM5 is the best. The total flood volume (TFV) of the node increases with the aggravation of climate change. The TFV of SSP5-8.5 and SSP2-4.5 increased by 45.43 and 20.8% in the 100-year return period, respectively, and more than 94% of the conduits reached the maximum drainage capacity in different return periods. After the low impact development (LID) was installed, the improvement effect on the outflow with a smaller return period was significant, decreasing by about 50%. The LID can effectively reduce the overflow of the drainage system. The results of this study can provide suggestions for the reconstruction of the drainage system and the management of flood risk for Beijing in the future.

  • The DFQDM method for daily precipitation correction of the climate model is proposed.

  • The TFV of SSP5-8.5 and SSP2-4.5 increased by 45.43 and 20.8% in the 100-year return period, respectively.

  • The LID can effectively reduce the overflow of the drainage system.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Urban flooding is one of the major challenges facing the world in the 21st century. Future flood risk is exacerbated by climate change, urbanization and ageing infrastructure (O'Donnell & Thorne 2020). Climate change has added heavier rainstorms, as well as severe and frequent floods that are hard to predict (Tingsanchali 2012). Affected by intensified urbanization, population growth and ageing of urban drainage systems, the risk of urban flooding is increasingly affected by climate change (Zeng et al. 2021). The design of a drainage system is usually based on the statistical data of historical precipitation in a certain period, without considering the potential change of extreme precipitation value in the design return period (Zhou et al. 2018). Arnbjerg-Nielsen (2012) indicated that the design storm intensity in Denmark is expected to increase by 10–50% over a return period of 2–100 years. The recent Intergovernmental Panel on Climate Change (IPCC) special report on the impact of 1.5 °C of global warming estimated that global warming could reach 1.5 °C between 2030 and 2052. The final reflection of the climate system will be in the form of an increase in the intensity and frequency of extreme precipitation. In China, flood disasters have occurred in many cities and caused huge economic losses. For example, the rainstorm in Beijing in July 2012 caused 79 deaths and a loss of $1.86 billion. The rainstorm in Shanghai on September 13th, 2013 caused huge direct impact and indirect losses. The rainstorm in Wuhan on July 23, 2015 caused many places in the city to be flooded, and its maximum rainfall exceeded 100 mm. During the ‘7.20’ extreme rainstorm in Zhengzhou, serious mountain torrents and waterlogging disasters occurred in the city, resulting in road damage, traffic disruption and dam break of a large number of reservoirs. Therefore, it is very important to understand the future climate change for urban flood disaster management and the design of flood control facilities.

The research on the drainage capacity of the urban drainage system adopts the historical precipitation process and rarely considers the impact of climate change on the intensity of short-duration rainstorms. For example, Hou et al. (2020) adopted the designed storm intensity formula of the Xixian New Area to study the effects of different return periods, peak coefficients and durations on flood inundation. Palla & Gnecco (2015) studied the effects of low impact development (LID) as source control measures on hydrological processes in urban catchments under different precipitation return periods. Wang et al. (2019) studied the changes of urban flood resilience under different return periods. The rainstorm intensity formula is an important basis for reflecting the rainfall pattern, guiding the design of urban drainage and waterlogging prevention projects and the construction of related facilities. If the impact of climate change on the intensity–duration–frequency (IDF) curve can be considered in the design of the drainage system, the drainage system will be able to accommodate greater extreme precipitation, and that will increase its reliability and stability (Kourtis & Tsihrintzis 2022; Kourtis et al. 2022).

The current way to quantify climate change is to use the future precipitation predicted by global climate models (GCMs) (Shen et al. 2018). Climate data published by the Coupled Model Intercomparison Project (CMIP) is widely adopted (Touzé Peiffer et al. 2020). The most recent CMIP6 has 55 GCMs (Iqbal et al. 2021). Although CMIP6 can reflect the changes in the precipitation in the future, these data also have great uncertainty. Numerous studies indicated that CMIP6 overestimates or underestimates future precipitation. For example, Iqbal et al. (2021) indicated that some models of CMIP6 have large deviations of 25–75% for annual precipitation in northern Mainland South-East Asia and show an underestimation of −25 to −50% in coastal areas. CMIP6 can be used to assess the impact of climate change after bias correction. Therefore, CMIP6 needs to be bias corrected before use. Most of the researches are about the correction of the monthly precipitation. The monthly precipitation cannot meet the requirements of the drainage model for the resolution of the precipitation. The resolution of the precipitation must be daily or less.

In order to solve the problems mentioned in the above analysis, the objectives of this study are as follows: (1) evaluating the simulation accuracy of CMIP6 on daily precipitation; (2) proposing a new statistical downscaling method for correction of daily precipitation; (3) the response of this urban drainage system to different design storm scenarios in the future is analyzed; (4) the effect of LID on rainfall runoff was analyzed under different precipitation conditions to provide guidance for flood risk management in small-scale urban developments.

Study area

A residential area in Beijing is used as a study area, the area of which is 4.24 km2 (Figure 1(a)). The drainage system contains 907 conduits, 902 junctions and the total length of the conduit is 29.687 km (Yang et al. 2012). The DEM shows a decreasing trend from upstream to downstream. The range of the elevation is from 35.5212 to 43.5275 (Figure 1(a)). Seven types of landuse are shown in Figure 1(b) for the study area, which are roadway (17.71%), build-up (24.87%), river (0.03%), bare soil (7.37%), others (3.33%), hard pavement (32.82%) and green land (13.87%), respectively. The area of the subcatchments ranges from 43.19 to 175,553 m2.
Figure 1

Distribution map of study area. (a) Distribution of drainage conduits and nodes; (b) Distribution map of landuse.

Figure 1

Distribution map of study area. (a) Distribution of drainage conduits and nodes; (b) Distribution map of landuse.

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Data series

In this study, the daily precipitation from 1951 to 2012 for observation are from China meteorological forcing dataset (1979–2018) (Yang et al. 2010; Kun & Jie 2019; He et al. 2020) (http://data.tpdc.ac.cn/). The name and code of the weather station are ‘Beijing’ and ‘54,511’. The distance between the weather station and the study area is 6.5 km. The daily precipitation data of CMIP6 in the historical period from 1951 to 2012 is used to evaluate the simulation accuracy. The model with the best accuracy will be used for bias correction. Daily precipitation for the future period of CMIP6 is adopted to assess climate change from 2023 to 2062 (https://esgf-node.llnl.gov/search/cmip6/). Compared with CMIP5, CMIP6 has made great improvements in the parameterization scheme of dynamics and resolution of the model, and most of the models adopt the bidirectional coupling of atmosphere and chemistry (Eyring et al. 2016). In the design of future scenarios, compared with CMIP5, CMIP6 adopts Scenario Model Intercomparison Project (ScenarioMIP), which is produced with integrated assessment models (IAMs) based on new future pathways of societal development, the Shared Socioeconomic Pathways (SSPs) and related to the RCPs (O'Neill et al. 2016). CMIP6 applies a new combined scenario (SSP-RCP) and increases three new emissions paths (RCP1.9, RCP3.4, RCP7.0). These scenarios take into account changes in the global economy and population, as well as emissions of greenhouse gas. Two scenarios for SSP Tier 1 are adopted in this study, which are, respectively, SSP2-4.5 and SSP5-8.5. SSP2-4.5 represents the medium part of the range of future forcing pathways and updates the RCP4.5 pathway. SSP5-8.5 represents the high end of the range of future pathways and updates the RCP8.5 pathway. Nominal Resolution of CMIP6 is 100 and 250 km, Variant Label of which is ‘r1i1p1f1’. The spatial resolution and land model of each GCMs are presented in Table 1.

Table 1

List of the CMIP6 GCMs used in this study

NoModelInstitutionCountryLand modelResolution
CESM2-WACCM US National Center for Atmospheric Research (NCAR) USA CLM5 288 × 192 
CMCC-CM2-SR5 Euro-Mediterranean Center on Climate Change (CMCC) Italy CLM4.5 288 × 192 
CMCC-ESM2 Italy CLM4.5 288 × 192 
MPI-ESM1-2-HR Max Planck Institute for Meteorology (MPI-M) Germany JSBACH3.20 288 × 192 
MRI-ESM2-0 Meteorological Research Institute (MRI) Japan HAL 1.0 320 × 160 
NorESM2-MM NorESM Climate modeling Consortium consisting of CICERO (NCC) Norway CAM-OSLO 288 × 192 
FGOALS-g3 Chinese Academy of Sciences (CAS), China China GAMIL2 180 × 90 
TaiESM1 Research Center for Environmental Changes (AS-RCEC) China CLM4.0 288 × 192 
ACCESS-CM2 Commonwealth Scientific and Industrial Research Organisation (CSIRO) Australia CABLE2.3.5 192 × 144 
10 ACCESS-ESM1-5 CABLE2.2.3  192 × 145 
11 CanESM5 Canadian Centre for Climate Modelling and Analysis (CCCma) Canada CLASS3.6/CTEM1.2 128 × 64 
12 MIROC6 Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute, National Institute for Environmental Studies, and RIKEN Center for Computational Science (MIROC) Japan MATSIRO6.0 256 × 128 
NoModelInstitutionCountryLand modelResolution
CESM2-WACCM US National Center for Atmospheric Research (NCAR) USA CLM5 288 × 192 
CMCC-CM2-SR5 Euro-Mediterranean Center on Climate Change (CMCC) Italy CLM4.5 288 × 192 
CMCC-ESM2 Italy CLM4.5 288 × 192 
MPI-ESM1-2-HR Max Planck Institute for Meteorology (MPI-M) Germany JSBACH3.20 288 × 192 
MRI-ESM2-0 Meteorological Research Institute (MRI) Japan HAL 1.0 320 × 160 
NorESM2-MM NorESM Climate modeling Consortium consisting of CICERO (NCC) Norway CAM-OSLO 288 × 192 
FGOALS-g3 Chinese Academy of Sciences (CAS), China China GAMIL2 180 × 90 
TaiESM1 Research Center for Environmental Changes (AS-RCEC) China CLM4.0 288 × 192 
ACCESS-CM2 Commonwealth Scientific and Industrial Research Organisation (CSIRO) Australia CABLE2.3.5 192 × 144 
10 ACCESS-ESM1-5 CABLE2.2.3  192 × 145 
11 CanESM5 Canadian Centre for Climate Modelling and Analysis (CCCma) Canada CLASS3.6/CTEM1.2 128 × 64 
12 MIROC6 Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute, National Institute for Environmental Studies, and RIKEN Center for Computational Science (MIROC) Japan MATSIRO6.0 256 × 128 

Research framework

Research framework of the study is illustrated in Figure 2. Firstly, the observation data and CMIP6 are processed, which includes extraction of data, interpolation of missing values and leap years. Secondly, multiple error indicators are used for the accuracy evaluation and selection of climate models on annual and monthly scales. Thirdly, the climate model with better accuracy was corrected by DFQDM. The design storm intensity is calculated in the future period. Finally, the impact of climate change on urban flooding is analyzed under SSP2-4.5 and SSP5-8.5 scenarios. For the shortage of drainage capacity in the study area, this method of controlling flood risk is analyzed.
Figure 2

Research framework of the study.

Figure 2

Research framework of the study.

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Metrics of the evaluation for GCMs

Due to uncertainties of the simulation for CMIP6 in different regions, it is necessary to evaluate the applicability of the data before use. The evaluation methods used in this study include correlation coefficient (CC) (Ding et al. 2019), percent bias (PBIAS), root mean square error (RMSE), coefficient of variation (CV), Mann–Kendall Trend Test (MK) (Ding et al. 2019), Sen's slope estimator (SSE), Taylor diagram (Taylor 2005) and extreme precipitation index (ETCCDI) (Ding et al. 2019). The ETCCDI indices used in this study are shown in Table 2. In Table 2, RR denotes daily precipitation and PRCP denotes precipitation.

Table 2

List of nine extreme precipitation indices used in this study

Index nameDescriptionDefinitionUnit
RX1day Max 1-day precipitation amount Annual maximum 1-day precipitation mm 
RX5day Max 5-day precipitation amount Annual maximum consecutive 5-day precipitation mm 
SDII Simple daily intensity index Annual total precipitation divided by the number of wet days in the year mm/day 
R10 Number of precipitation ≥10 mm days Annual count of days when RR ≥ 10 mm days 
R20 Number of precipitation ≥20 mm days Annual count of days when RR ≥ 20 mm days 
CDD Consecutive dry days Maximum number of consecutive days with RR < 1 mm days 
CWD Consecutive wet days Maximum number of consecutive days with RR ≥ 1 mm days 
R95PTOT Precipitation in very wet days Annual total PRCP when RR > 95th percentile in wet days mm 
PRCPTOT Annual total wet-day precipitation Annual total PRCP in wet days mm 
Index nameDescriptionDefinitionUnit
RX1day Max 1-day precipitation amount Annual maximum 1-day precipitation mm 
RX5day Max 5-day precipitation amount Annual maximum consecutive 5-day precipitation mm 
SDII Simple daily intensity index Annual total precipitation divided by the number of wet days in the year mm/day 
R10 Number of precipitation ≥10 mm days Annual count of days when RR ≥ 10 mm days 
R20 Number of precipitation ≥20 mm days Annual count of days when RR ≥ 20 mm days 
CDD Consecutive dry days Maximum number of consecutive days with RR < 1 mm days 
CWD Consecutive wet days Maximum number of consecutive days with RR ≥ 1 mm days 
R95PTOT Precipitation in very wet days Annual total PRCP when RR > 95th percentile in wet days mm 
PRCPTOT Annual total wet-day precipitation Annual total PRCP in wet days mm 

Estimates of the accuracy for GCMs are calculated in the historical period. For the change in traditional climate tendency, it is obtained by using the least squares method to estimate the slope of the linear regression equation. The Theil–Sen estimation method is used in this study to calculate the slope, which is less affected by outliers in the sample data. The calculated accuracy of the slope is better than the least squares method (Wilcox 2001). Taylor diagrams are used in this study, which display the CC, the central root mean square error (CRMSE) and the standard deviation (SD) on a polar plot. It provides a graphical way to compare how well simulation and observation match when more models are evaluated (Taylor 2001). The SD is normalized in the Taylor diagram, which is obtained by calculating the ratio of the SD of the model and the observation. After processing, the coordinate of the observation on the polar x-axis is always (1,0). Compared with the original Taylor diagram, the method can compare the accuracy of different models on the same grid and can also compare the performance of different models on different grids. The comprehensive performance of the climate models for Taylor diagram is quantitatively evaluated using the Taylor Skill Score (TSS) (Ngoma et al. 2021), which is calculated as follows:
formula
(1)
where Rm is CC between model and observation; R0 is the attainable maximum CC which is set to 0.999; is the SD of the model; is the SD of the observation.
Comprehensive rating index (CRI) (Zhang et al. 2018) is a sorting model. It comprehensively considers different evaluation indicators of the model. This study ranks the simulation capabilities of CMIP6 based on PBIAS, RMSE and CC. The formula is as follows:
formula
(2)
where n is the number of evaluation indicators; m is the number of models; ranki is the ranking of the ith indicator of the model.

The range of CC is [−1,1]. The closer CC is to 1, the closer PBIAS and RMSE values are to 0 and the closer TSS and CRI values are to 1, indicating that the model performs better.

The model is interpolated to the weather station by bilinear interpolation. Since most models adopt the calendar as ‘noleap’, leap years are not considered, the study averaged the precipitation on February 28 and March 1 in leap years to interpolate the data on February 29, so that the daily data of model are equal to the number of observations. Many studies have pointed out that the performance of Multiple Model Ensembles (MMEs) is better than that of a single model, which can reduce the PBIAS. Therefore, this paper adopts the Equal Weight Ensemble Mean (EWEM) (Cos et al. 2022) in MMEs to obtain EWEM data. The purpose of the processing is to compare with a single model, evaluate the simulation effect of the ensemble model on precipitation and obtain models with higher precision.

Statistical downscaling

PBIAS of the climate model can be corrected by dynamic or statistical downscaling. Dynamic downscaling adopts regional climate models (RCMs), which have a clear physical meaning and can reflect the ground characteristics of regional climate elements, but the output variables of RCMs still have large uncertainties and amount of calculation (Baghanam et al. 2020). Statistical downscaling has low computational complexity and high accuracy, which has been widely used in the correction of the model. Therefore, this paper adopts the statistical downscaling method to correct the model. The most commonly used methods of statistical downscaling mainly include QM (quantile mapping) (Gupta et al. 2020), EDCDF (equidistant cumulative distribution function) (Li et al. 2010), DQM (detrended quantile mapping), QDM (quantile delta mapping) (Cannon et al. 2015), DBC (daily bias correction) (Luo et al. 2018). QM assumes that the cumulative probability distribution (CDF) of climate variables is unchanged in the future, and it establishes a transfer function between the CDF curve of the model and the observation to obtain the corresponding relationship of variation at different quantiles. The CDF curve of the model is corrected, but it ignores the change of precipitation in the future period relative to the historical period and is not suitable for correcting the precipitation beyond the range of observation. In Figures 3 and 4, represents the quantile distance, and represent the original and corrected precipitation for the future period of the model, respectively. Figure 3 illustrates the specific principle of QM. The correction of EDCDF and QDM is the same as QM for the historical period, changes in precipitation are taken into account for the future period. EDCDF assumes that the difference between observation and model in historical period is applicable to the future period. The QDM calculates the ratio of the observed value to the modeled historical precipitation at different quantiles and uses the ratio coefficient to correct the modeled future precipitation. Figure 4 illustrates the specific principle of EDCDF. The DBC method is similar to the QDM method, but it modifies the frequency of wet days for daily precipitation.
Figure 3

Illustration of the methodology of the QM.

Figure 3

Illustration of the methodology of the QM.

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Figure 4

Illustration of the methodology of the EDCDF.

Figure 4

Illustration of the methodology of the EDCDF.

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The correction effect of the above methods on monthly precipitation is better than that of daily precipitation. Most areas in China have less precipitation from November to March of the following year, especially from December to February, the daily precipitation of most sites is zero. For the QDM method, when the daily precipitation of the model in the historical period is zero, the proportional coefficient is inf or NaN. When the corrected value of EDCDF is less than zero, if the absolute value of which is greater than the precipitation of the future period, the corrected value will be negative. If the empirical CDF is used for QM, frequent interpolation and extrapolation are required, which is not satisfactory (Li et al. 2010). The parametric distribution function is used to fit the empirical CDF of daily precipitation. It is different from the fitting of extreme values. After fitting with different distribution functions, it is found that the accuracy of the Gamma distribution fitting is the best, but the Gamma distribution requires that the sample is greater than zero. A large number of zeros are included in the daily precipitation, so that the parameters of the theoretical distribution cannot be calculated, and only the moment method can be used, but the fitting accuracy of which is lower. Many studies firstly correct the monthly precipitation and then correct the daily precipitation proportionally according to the ratio of the monthly precipitation before and after the correction. This method will cause the time and position of the extreme value of the daily precipitation to be changed, which increases the error. Therefore, in order to solve the correction problem of modeled daily precipitation, this paper proposes a QDM method of daily precipitation based on frequency (DFQDM). Firstly, the frequency of wet days with daily precipitation from January to December is corrected. Secondly, the 95th percentile of daily precipitation in each month is calculated, and the daily precipitation is divided into two sections according to the percentile value. Based on the mixed Gamma distribution, the cumulative distribution of each segment is calculated. Then the quantile delta map is adopted to correct the daily precipitation. Finally, the corrected precipitation is synthesized into a complete time series. The specific steps of DFQDM method are as follows:

Step 1: is the daily precipitation in mth month of the observation. and are the daily precipitation of the model. The subscript his and fut represent the historical and future periods of the model, respectively. Firstly, the thresholds of the frequency of wet days for the model in different months are determined, which can ensure that the frequency of daily precipitation of the model in different months is equal to the observed value, and the thresholds of the historical period of the model are assumed to be suitable for future periods:
formula
(3)
formula
(4)
formula
(5)
formula
(6)
formula
(7)
where is the proportion of wet days for observation; is the number of data; is the threshold for no precipitation, the study adopts 0.1 mm; is to sort the data in ascending order; , is the modified threshold of wet precipitation in the modeled historical and future period, respectively.
Step 2: The extreme precipitation for the CDF affects the accuracy of the correction. This study calculates the 95th percentile of the monthly daily precipitation. The precipitation is divided into two series to be corrected separately:
formula
(8)
formula
(9)
formula
(10)
where , , are the precipitation within the 95th percentile; , , are the precipitation above the 95th percentile.
Step 3: The CDF of the monthly daily precipitation is calculated. Since the monthly precipitation from December to February may be 0, when the precipitation is zero, the Gamma distribution cannot be fitted by the maximum likelihood method or the optimization algorithm. The study refers to the method of Yang et al. (2018) and Li et al. (2010). The mixed Gamma distribution is used, which assigns a fixed proportion to the months without precipitation, and superimposes the Gamma distribution of the precipitation part on this proportion. It is calculated by the following formula:
formula
(11)
formula
(12)
where is the mixed Gamma distribution function; is the percentage of days with daily precipitation in mth month.
Step 4: The QDM is used to correct the daily precipitation of the modeled history and future periods.
formula
(13)
formula
(14)
If α ≠ NaN or Inf:
formula
(15)
If α = NaN or Inf:
formula
(16)
where , is the corrected daily precipitation for the model in different months; is the ratio of delta. Precipitation less than zero in will be assigned the value zero.

Hydraulic model

In this study, the Storm Water Management Model (SWMM), the newest ver. 5.2, was selected as a tool for simulating current and future flooding. The runoff portion of SWMM is calculated over a subcatchment that receives rainfall to generate runoff and pollutant loads. The routing portion of the SWMM transmits runoff to structures, such as conduits, channels, storage tanks, pumps, and so on. It can completely simulate the hydrological and hydrodynamic process from the occurrence of rainfall to the outflow of runoff from the outfall. The routing portion of SWMM is solved by dynamic wave method. In this study, the design precipitation scenario is used to represent historical precipitation events. The average rainstorm intensity in different return periods and durations adopts the design rainstorm intensity formula (DRIF) of Beijing. This formula is quoted from the Chinese design standard ‘DB11/685-2021’, which is expressed in Equation (17). The range of duration and return period for the formula is [5 min, 1440 min] and [2-year, 100-year], respectively:
formula
(17)
where i is the storm intensity, mm/min; P is the return period, year; T is the rainstorm duration, min.
The rainfall process is calculated using the Chicago Rainfall Pattern with the same parameters as the storm intensity formulas (Keifer & Chu 1957). The ratio of the peak time of the precipitation is 0.4. The calculation method of the Chicago Rainfall Pattern refers to InfoWorks ICM, as follows:
formula
(18)
when 0 ≤ trT:
formula
(19)
when rT < tT:
formula
(20)
where r is the ratio of pre-peak duration to total duration; T is the storm duration, min; b and n are constants of storm intensity formula; t is the time in minutes from start of storm, min; R is the total precipitation, mm.

Annual precipitation evaluation

The simulated performance of different GCMs for annual precipitation was first evaluated in 1951–2012. It can be seen from Table 3 that the MEAN of annual precipitation is overestimated and underestimated by GCMs. The absolute error (AE) between MEAN of CanESM5 and that of the observation is the smallest, which is 43.48 mm. The AE of CMCC-CM2-SR5 and TaiESM1 are larger, which are 457.37 and 430.16 mm, respectively, and CMCC-CM2-SR5 is nearly double the observation. The PBIAS and RMSE of CanESM5 are the smallest, which are −7.33% and 239.66 mm, respectively. The PBIAS of CMCC-CM2-SR5 is 77.16%, which is the largest and severely overestimated precipitation. The CC of GCMs is all close to 0, which indicates that the model has a poor simulation of the changing trend of annual precipitation. The CV of the observation is 0.35. The CV of MRI-ESM2-0 is 0.31, which is close to the observation, and the CV of TaiESM1 is far from the observation, which is 0.17. For the MK, the observation shows a downward trend, the MK and SSE of ACCESS-ESM1-5 are close to the observation, MK and SSE of which are −1.45 and −1.57, respectively. CMCC-ESM2, MPI-ESM1-2-HR, FGOALS-g3 and MIROC6 showed a large opposite trend compared with the observation. In summary, CanESM5 performs well for the simulation of annual precipitation, and its error is the lowest and the change of trend is more consistent with the observation.

Table 3

Statistical metrics of CMIP6 models in simulating annual precipitation

NoModelMEAN/mmPBIAS/%RMSE/mmCCCVMKSSE
Observation 592.79 – – – 0.35 −1.74 −2.35 
CESM2-WACCM 840.27 41.75 400.57 −0.15 0.25 0.78 1.14 
CMCC-CM2-SR5 1050.16 77.16 559.25 −0.08 0.22 0.36 0.59 
CMCC-ESM2 891.67 50.42 395.18 0.11 0.21 1.62 2.50 
MPI-ESM1-2-HR 671.92 13.35 278.34 −0.14 0.22 1.79 1.53 
MRI-ESM2-0 397.93 −32.87 317.77 −0.11 0.31 −0.89 −0.74 
NorESM2-MM 672.68 13.48 265.80 0.04 0.24 0.77 0.96 
FGOALS-g3 346.45 −41.56 331.79 −0.09 0.20 1.07 0.58 
TaiESM1 1022.95 72.57 504.28 0.02 0.17 0.77 1.28 
ACCESS-CM2 430.95 −27.30 286.27 −0.01 0.27 0.44 0.36 
10 ACCESS-ESM1-5 646.51 9.06 260.62 0.10 0.27 −1.45 −1.57 
11 CanESM5 549.31 −7.33 239.66 −0.05 0.19 −0.17 −0.15 
12 MIROC6 860.21 45.11 371.85 0.08 0.20 1.15 1.82 
NoModelMEAN/mmPBIAS/%RMSE/mmCCCVMKSSE
Observation 592.79 – – – 0.35 −1.74 −2.35 
CESM2-WACCM 840.27 41.75 400.57 −0.15 0.25 0.78 1.14 
CMCC-CM2-SR5 1050.16 77.16 559.25 −0.08 0.22 0.36 0.59 
CMCC-ESM2 891.67 50.42 395.18 0.11 0.21 1.62 2.50 
MPI-ESM1-2-HR 671.92 13.35 278.34 −0.14 0.22 1.79 1.53 
MRI-ESM2-0 397.93 −32.87 317.77 −0.11 0.31 −0.89 −0.74 
NorESM2-MM 672.68 13.48 265.80 0.04 0.24 0.77 0.96 
FGOALS-g3 346.45 −41.56 331.79 −0.09 0.20 1.07 0.58 
TaiESM1 1022.95 72.57 504.28 0.02 0.17 0.77 1.28 
ACCESS-CM2 430.95 −27.30 286.27 −0.01 0.27 0.44 0.36 
10 ACCESS-ESM1-5 646.51 9.06 260.62 0.10 0.27 −1.45 −1.57 
11 CanESM5 549.31 −7.33 239.66 −0.05 0.19 −0.17 −0.15 
12 MIROC6 860.21 45.11 371.85 0.08 0.20 1.15 1.82 

For annual precipitation, the PBIAS of GCMs is positive or negative. If overestimated and underestimated models are ensemble averaged, the PBIAS for the precipitation will become very low. To obtain a better simulation of precipitation, GCMs were processed by the EWEM in this study. In Table 3, GCMs processed by EWWM are No.1 and No.5, No.1 and No.7, No.3 and No.5, No.3 and No.7, No.4 and No.11, No.5 and No.12, No.6 and No.11, No.7 and No.12, No.10 and No.11, respectively. The ensemble GCMs is named by appending the number of model to EWEM. Table 4 shows the error of annual precipitation of EWEM. PBIAS of all models is ensembled as EWEMALL. Affected by the overestimation of precipitation in most models, the mean of EWEMALL is quite different from the observation. EWEM0107 and EWEM1011 have the lowest PBIAS, which are, respectively, 0.1 and 0.86%; For CC, CV, MK and SSE, EWEM1011 performs best, and the change trends of other ensemble models are opposite to the observation.

Table 4

Statistical metrics of EWEM in simulating annual precipitation

EWEM NameMEANPBIAS/%RMSECCCVMKSSE
EWEMALL 698.42 17.82 237.60 −0.06 0.07 2.09 0.74 
EWEM0105 619.10 4.44 255.60 −0.20 0.19 0.44 0.38 
EWEM0107 593.36 0.10 249.34 −0.17 0.19 1.19 0.89 
EWEM0305 644.80 8.77 235.80 0.03 0.17 1.49 1.14 
EWEM0307 619.06 4.43 224.04 0.07 0.17 1.77 1.51 
EWEM0411 610.61 3.01 235.82 −0.15 0.15 0.92 0.56 
EWEM0512 629.07 6.12 234.91 0.00 0.17 0.67 0.60 
EWEM0611 610.99 3.07 223.97 0.00 0.15 0.49 0.35 
EWEM0712 603.33 1.78 224.32 0.04 0.17 1.41 1.00 
EWEM1011 597.91 0.86 220.38 0.06 0.16 −1.14 −0.98 
EWEM NameMEANPBIAS/%RMSECCCVMKSSE
EWEMALL 698.42 17.82 237.60 −0.06 0.07 2.09 0.74 
EWEM0105 619.10 4.44 255.60 −0.20 0.19 0.44 0.38 
EWEM0107 593.36 0.10 249.34 −0.17 0.19 1.19 0.89 
EWEM0305 644.80 8.77 235.80 0.03 0.17 1.49 1.14 
EWEM0307 619.06 4.43 224.04 0.07 0.17 1.77 1.51 
EWEM0411 610.61 3.01 235.82 −0.15 0.15 0.92 0.56 
EWEM0512 629.07 6.12 234.91 0.00 0.17 0.67 0.60 
EWEM0611 610.99 3.07 223.97 0.00 0.15 0.49 0.35 
EWEM0712 603.33 1.78 224.32 0.04 0.17 1.41 1.00 
EWEM1011 597.91 0.86 220.38 0.06 0.16 −1.14 −0.98 

Figure 5 shows the boxplot of precipitation of observation and GCMs. The medians of CanESM5, EWEM0107 and EWEM1011 are the closest to the observation, which are, respectively, 549.31, 593.36 and 597.91 mm. The median of observation is 550.85 mm. The medians of CMCC-CM2-SR5 and TaiESM1 are larger, which are 1032.22 and 1022.73 mm, respectively. For the interquartile range (IQR) of the box, the observation is 256 mm. CMCC-CM2-SR5 and NorESM2-MM are closer to the observed value, which are 253.4 and 250.5 mm, respectively. CanESM5 and EWEM1011 are 152.11 and 137.52 mm, respectively, and the distribution of which is concentrated around the median. The outliers of the observations are 1115.7 and 1406 mm. The outliers of CMCC-CM2-SR5 are 1731.02 mm which is the largest, and CanESM5 and EWEM1011 have no outliers.
Figure 5

Boxplot of annual precipitation. (‘A’ represents observation on the x-axis).

Figure 5

Boxplot of annual precipitation. (‘A’ represents observation on the x-axis).

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Monthly precipitation evaluation

Table 5 shows the evaluation results of monthly precipitation. The AE between ACCESS-ESM1-5, CanESM5, EWEM0105, EWEM0107, EWEM0305, EWEM0307, EWEM0411, EWEM0512, EWEM0611, EWEM0712, EWEM1011 and the mean of the observation are the smallest, which are, respectively, 4.48, −3.62, 2.19, 0.05, 4.33, 2.19, 1.49, 3.02, 1.52, 0.88, and 0.43 mm. The AE of EWEM0107 is the smallest, and the PBIAS of the above models are also the smallest. The RMSE of EWEMALL is the smallest, which is 53.51 mm. The RMSE of CMCC-CM2-SR5 is the largest, which is 90.37 mm. The CC of EWEMALL is the largest, which is 0.74, and that of CanESM5 is 0.59. The CC of the model is around 0.65. The variation of the model for monthly precipitation is consistent with the observation. For the CV, the variation of MRI-ESM2-0 relative to the overall mean is the closest to the observed value; the SSE of all models is 0, which indicates that the monthly precipitation does not have a significant trend of change.

Table 5

Statistical metrics of models in simulating monthly precipitation

ModelMEAN/mmPBIAS/%RMSE/mmCCCVMKSSE
Observation 49.40 – – – 1.59 0.00 0.00 
CESM2-WACCM 70.02 41.75 80.85 0.59 1.31 −0.02 0.00 
CMCC-CM2-SR5 87.51 77.16 90.37 0.62 1.18 0.26 0.00 
CMCC-ESM2 74.31 50.42 71.49 0.67 1.15 0.21 0.00 
MPI-ESM1-2-HR 55.99 13.35 69.21 0.56 1.19 0.45 0.00 
MRI-ESM2-0 33.16 −32.87 66.29 0.58 1.43 −0.99 0.00 
NorESM2-MM 56.06 13.48 65.95 0.63 1.31 0.67 0.00 
FGOALS-g3 28.87 −41.56 69.49 0.56 1.06 0.63 0.00 
TaiESM1 85.25 72.57 84.24 0.67 1.19 0.42 0.00 
ACCESS-CM2 35.91 −27.30 66.71 0.56 1.18 −0.24 0.00 
ACCESS-ESM1-5 53.88 9.06 67.03 0.62 1.37 −1.20 0.00 
CanESM5 45.78 −7.33 64.14 0.59 1.21 0.67 0.00 
MIROC6 71.68 45.11 76.30 0.59 1.16 0.52 0.00 
EWEMALL 58.20 17.82 53.31 0.74 1.01 0.34 0.00 
EWEM0105 51.59 4.44 61.19 0.65 1.22 −0.32 0.00 
EWEM0107 49.45 0.10 60.83 0.64 1.13 0.21 0.00 
EWEM0305 53.73 8.77 56.98 0.70 1.13 −0.15 0.00 
EWEM0307 51.59 4.43 56.70 0.69 1.04 0.36 0.00 
EWEM0411 50.88 3.01 60.57 0.64 1.08 0.41 0.00 
EWEM0512 52.42 6.12 60.26 0.65 1.12 0.20 0.00 
EWEM0611 50.92 3.07 58.03 0.68 1.14 0.72 0.00 
EWEM0712 50.28 1.78 61.18 0.63 1.05 0.73 0.00 
EWEM1011 49.83 0.86 57.96 0.68 1.16 −0.26 0.00 
ModelMEAN/mmPBIAS/%RMSE/mmCCCVMKSSE
Observation 49.40 – – – 1.59 0.00 0.00 
CESM2-WACCM 70.02 41.75 80.85 0.59 1.31 −0.02 0.00 
CMCC-CM2-SR5 87.51 77.16 90.37 0.62 1.18 0.26 0.00 
CMCC-ESM2 74.31 50.42 71.49 0.67 1.15 0.21 0.00 
MPI-ESM1-2-HR 55.99 13.35 69.21 0.56 1.19 0.45 0.00 
MRI-ESM2-0 33.16 −32.87 66.29 0.58 1.43 −0.99 0.00 
NorESM2-MM 56.06 13.48 65.95 0.63 1.31 0.67 0.00 
FGOALS-g3 28.87 −41.56 69.49 0.56 1.06 0.63 0.00 
TaiESM1 85.25 72.57 84.24 0.67 1.19 0.42 0.00 
ACCESS-CM2 35.91 −27.30 66.71 0.56 1.18 −0.24 0.00 
ACCESS-ESM1-5 53.88 9.06 67.03 0.62 1.37 −1.20 0.00 
CanESM5 45.78 −7.33 64.14 0.59 1.21 0.67 0.00 
MIROC6 71.68 45.11 76.30 0.59 1.16 0.52 0.00 
EWEMALL 58.20 17.82 53.31 0.74 1.01 0.34 0.00 
EWEM0105 51.59 4.44 61.19 0.65 1.22 −0.32 0.00 
EWEM0107 49.45 0.10 60.83 0.64 1.13 0.21 0.00 
EWEM0305 53.73 8.77 56.98 0.70 1.13 −0.15 0.00 
EWEM0307 51.59 4.43 56.70 0.69 1.04 0.36 0.00 
EWEM0411 50.88 3.01 60.57 0.64 1.08 0.41 0.00 
EWEM0512 52.42 6.12 60.26 0.65 1.12 0.20 0.00 
EWEM0611 50.92 3.07 58.03 0.68 1.14 0.72 0.00 
EWEM0712 50.28 1.78 61.18 0.63 1.05 0.73 0.00 
EWEM1011 49.83 0.86 57.96 0.68 1.16 −0.26 0.00 

The Taylor plot can visually compare the difference between the simulation and the observation. The ‘REF’ on the X-axis in Figure 6 is the position of the observed value, the length of the polar diameter represents SD, the polar angle represents CC and the distance from the point to REF represents CRMSE, so the points closer to the REF and the red line represent better accuracy for the model. CC has already been analyzed in Table 5, so this part mainly analyses SD, CRMSE and TSS. The actual value of SD before normalization in the figure will be analyzed. The SDs of CMCC-ESM2, NorESM2-MM, ACCESS-ESM1-5 and MIROC6 are the closest to the observation, which are 85.63, 73.39, 73.88 and 82.85, respectively. The SD of CanESM5 is 55.45. The first six models with higher TSS values of monthly data are EWEM, CMCC-ESM2, EWEM0305, NorESM2-MM, TaiESM1, ACCESS-ESM1-5 and TSS of which are, respectively, 0.70, 0.69, 0.67, 0.66, 0.65, and 0.65.
Figure 6

Taylor diagrams for monthly precipitation between models and observation.

Figure 6

Taylor diagrams for monthly precipitation between models and observation.

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The simulation accuracy of monthly precipitation from January to December was evaluated. The number of points closest to ‘REF’ and the red line of the models shows that the three indicators without models in different months are better than others in Figure 7. The SD of the model with better CC and CRMSE is smaller. The CC of all models is poor. The models with lower CRMSE are FGOALS-g3 for January, March, July and September. The models with lower CRMSE are EWEM for February, April to June, August and December.
Figure 7

Taylor diagram of monthly precipitation from January to December.

Figure 7

Taylor diagram of monthly precipitation from January to December.

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The models with lower CRMSE are, respectively, EWEM0105 and EWEM0512 for October and November.

The models that perform better for SD are ACCESS-CM2, EWEM0305, MRI-ESM2-0, EWEM0512, EWEM0712, MPI-ESM1-2-HR, ACCESS-ESM1-5, CESM2-WACCM, CMCC-ESM2, MPI-ESM1-2-HR, EWEM0611 and NorESM2-MM. The models with larger TSS are ACCESS-ESM1-5, EWEM0105, EWEM0107, TaiESM1, TaiESM1, CMCC-ESM2, TaiESM1, CMCC-ESM2, CMCC-ESM2, CESM2-WACCM, MIROC6 and NorESM2-MM.

Model selection

CRI represents the overall performance of the model after they have been evaluated. The ranking of the different models can be seen from Figure 8. For annual precipitation, the CRIs of EWEM1011 and EWEM0307 are higher in the MMEs, which are 0.88 and 0.8, respectively. The CRIs of ACCESS-ESM1-5, CanESM5 and NorESM2-MM in the GCMs are higher, which are, respectively, 0.62, 0.53 and 0.52. CRI of CMCC-CM2-SR5 is the lowest, which is 0.11. For monthly precipitation, the CRIs of EWEM1011 and EWEM0307 in the MMEs are higher, which is, respectively, 0.85 and 0.83, and the CRIs of NorESM2-MM, CanESM5 and ACCESS-ESM1-5 in the GCMs are higher, which are 0.44, 0.44 and 0.38, respectively. The CRI of CMCC-CM2-SR5 is the lowest, which is 0.12. In summary, NorESM2-MM, CanESM5, ACCESS-ESM1-5 and MMEs have better simulation results. The simulation of CMCC-CM2-SR5 has the worst performance. By comparing the accuracy of the models on different time scales, NorESM2-MM, CanESM5, ACCESS-ESM1-5, EWEM0307 and EWEM1011 were selected for bias correction in this study. The model with the highest accuracy after correction was adopted as the basic data for the analysis of future climate change.
Figure 8

CRI of annual and monthly precipitation for the models.

Figure 8

CRI of annual and monthly precipitation for the models.

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Bias correction based on DFQDM method

After the accuracy evaluation, the PBIAS of the models selected for bias correction is low. In order to compare the effect of DFQDM correction, seven models with poor performance are selected by the study to be correct. Figure 9 shows the PBIAS of the annual precipitation before and after the model is corrected. Except for EWEM1011, the corrected PBIAS is lower than that before the correction. The minimum change of PBIAS is CanESM5, which is −0.38%. CMCC-CM2-SR5 and TaiESM1 have a significant effect of being corrected. PBIAS was changed from 76.91 and 72.34% to 0.8 and 1.66%, respectively. The PBIAS of the corrected models is all around 3%, and the accuracy is better. The PBIAS of EWEM1011 has been increased. The reason is that the PBIAS before the correction is 0.47%. The accuracy is already good, so the accuracy will not be improved too much after the correction. Affected by frequency correction, the structure of its data will be changed, which may increase PBIAS. The correction effect of PBIAS of monthly precipitation is the same as that of annual precipitation, so this study will not analyze it.
Figure 9

PBIAS of annual precipitation before and after model correction.

Figure 9

PBIAS of annual precipitation before and after model correction.

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The change of MEAN after the annual precipitation is corrected is shown in Figure 10. The red line represents the MEAN of the observation and is 592.79 mm. The correction effect of DFQDM on the MEAN is obvious. The MEAN of the corrected model is around 600 mm, which is closer to the observed value. MEAN of CanESM5 is, respectively, 548.15 and 590.56 mm after being corrected. CESM2-WACCM, CMCC-CM2-SR5, CMCC-ESM2, TaiESM1 and MIROC6 have a significant effect of being corrected.
Figure 10

MEAN of annual precipitation before and after model correction.

Figure 10

MEAN of annual precipitation before and after model correction.

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To evaluate the correction effect of DFQDM on daily precipitation, this study selected nine extreme precipitation indices of ETCCDI as evaluation indicators. The changes in indices before and after the correction are shown in Tables 6 and 7. Except for RX5day, the correction effect of other indices is significant. The PBIAS of CWD is significantly reduced, which indicates that the correction of the frequency of wet and dry days by DFQDM is reasonable. After the correction, the PBIAS of the maximum continuous precipitation days and the observation are significantly reduced. It can be seen from RX1day, RX5day, SDII, R95PTOT that DFQDM has a better effect on the correction of the intensity of extreme precipitation. For RX1day, the corrected PBIAS of all models excepting NorESM2-MM and TaiESM1 are controlled within 6%. For RX5day, the PBIAS of most models is controlled at around 10%, SDII represents the intensity of mean precipitation for wet days, and is underestimated in many models. The reason may be that CDF fitted by the mixed Gamma distribution underestimates the observation at the same frequency. The study will further improve the distribution function in the future. The absolute value of PBIAS of SDII is controlled within 10%. The PRCPTOT is controlled within 5%, which indicates that DFQDM has a good correction effect on the daily precipitation and the frequency of wet days. This method can be used to correct the climate model. In summary, by comparing the accuracy of the model before and after correction, the corrected CanESM5 is selected in the study to reflect the change in urban future precipitation.

Table 6

PBIAS of extreme precipitation index before the model was corrected

ModelRX1dayRX5daySDIIR10R20CDDCWDR95PTOTPRCPTOT
CESM2-WACCM −3.6 10.6 −27.0 39.2 20.3 −29.7 131.7 52.4 38.8 
CMCC-CM2-SR5 −3.9 13.3 −24.0 95.7 37.6 −18.2 259.9 77.3 74.9 
CMCC-ESM2 −11.4 −5.1 −30.1 63.8 5.6 −17.5 216.8 47.0 47.5 
MPI-ESM1-2-HR −28.8 −18.1 −31.2 31.3 −15.8 −15.2 136.6 1.4 11.6 
MRI-ESM2-0 −44.2 −37.9 −44.6 −29.2 −57.6 −4.4 58.8 −39.2 −35.3 
NorESM2-MM −20.9 −8.8 −35.9 16.2 −12.5 −12.2 109.9 12.9 10.2 
TaiESM1 −13.8 4.1 −18.2 105.5 60.4 −24.7 180.5 51.8 71.0 
ACCESS-ESM1-5 −24.2 −3.1 −46.7 −4.8 −28.3 −23.6 179.4 21.1 3.8 
CanESM5 −38.6 −29.4 −55.8 −29.7 −55.0 −4.3 339.7 −9.3 −10.1 
MIROC6 −13.2 −2.5 −31.2 52.0 19.9 −31.6 133.2 49.4 42.7 
EWEM0307 −53.9 −47.3 −58.2 −15.6 −59.1 −16.9 248.5 −14.6 −2.3 
EWEM1011 −53.9 −36.1 −61.8 −23.1 −56.5 −20.4 432.1 −9.1 −5.3 
ModelRX1dayRX5daySDIIR10R20CDDCWDR95PTOTPRCPTOT
CESM2-WACCM −3.6 10.6 −27.0 39.2 20.3 −29.7 131.7 52.4 38.8 
CMCC-CM2-SR5 −3.9 13.3 −24.0 95.7 37.6 −18.2 259.9 77.3 74.9 
CMCC-ESM2 −11.4 −5.1 −30.1 63.8 5.6 −17.5 216.8 47.0 47.5 
MPI-ESM1-2-HR −28.8 −18.1 −31.2 31.3 −15.8 −15.2 136.6 1.4 11.6 
MRI-ESM2-0 −44.2 −37.9 −44.6 −29.2 −57.6 −4.4 58.8 −39.2 −35.3 
NorESM2-MM −20.9 −8.8 −35.9 16.2 −12.5 −12.2 109.9 12.9 10.2 
TaiESM1 −13.8 4.1 −18.2 105.5 60.4 −24.7 180.5 51.8 71.0 
ACCESS-ESM1-5 −24.2 −3.1 −46.7 −4.8 −28.3 −23.6 179.4 21.1 3.8 
CanESM5 −38.6 −29.4 −55.8 −29.7 −55.0 −4.3 339.7 −9.3 −10.1 
MIROC6 −13.2 −2.5 −31.2 52.0 19.9 −31.6 133.2 49.4 42.7 
EWEM0307 −53.9 −47.3 −58.2 −15.6 −59.1 −16.9 248.5 −14.6 −2.3 
EWEM1011 −53.9 −36.1 −61.8 −23.1 −56.5 −20.4 432.1 −9.1 −5.3 
Table 7

PBIAS of extreme precipitation index after the model was corrected

ModelRX1dayRX5daySDIIR10R20CDDCWDR95PTOTPRCPTOT
CESM2-WACCM 2.3 11.6 −0.5 5.3 −1.5 1.6 46.6 5.3 2.5 
CMCC-CM2-SR5 −0.1 9.7 −9.6 0.5 −13.8 −5.9 41.6 8.1 1.1 
CMCC-ESM2 5.0 5.9 −7.1 2.4 −11.9 2.6 39.7 10.2 1.7 
MPI-ESM1-2-HR 5.1 14.6 3.1 6.5 0.0 8.0 24.4 1.4 1.7 
MRI-ESM2-0 4.7 16.8 1.6 3.6 −2.2 4.8 28.6 0.7 0.7 
NorESM2-MM 7.3 12.9 −0.4 4.7 −2.4 2.9 38.2 6.5 2.3 
TaiESM1 11.1 6.4 −4.2 2.7 −9.7 −3.4 19.1 9.1 1.9 
ACCESS-ESM1-5 2.3 24.3 3.8 7.0 4.3 6.8 31.3 6.5 4.7 
CanESM5 2.3 24.3 −3.5 −0.8 −6.9 5.8 71.4 0.5 −0.4 
MIROC6 3.3 6.6 1.9 5.4 3.4 −6.5 20.6 2.4 3.0 
EWEM0307 5.9 3.7 −7.5 2.4 −6.7 −0.5 28.6 10.8 2.7 
EWEM1011 6.0 25.6 2.5 3.7 4.5 3.4 35.9 4.8 4.6 
ModelRX1dayRX5daySDIIR10R20CDDCWDR95PTOTPRCPTOT
CESM2-WACCM 2.3 11.6 −0.5 5.3 −1.5 1.6 46.6 5.3 2.5 
CMCC-CM2-SR5 −0.1 9.7 −9.6 0.5 −13.8 −5.9 41.6 8.1 1.1 
CMCC-ESM2 5.0 5.9 −7.1 2.4 −11.9 2.6 39.7 10.2 1.7 
MPI-ESM1-2-HR 5.1 14.6 3.1 6.5 0.0 8.0 24.4 1.4 1.7 
MRI-ESM2-0 4.7 16.8 1.6 3.6 −2.2 4.8 28.6 0.7 0.7 
NorESM2-MM 7.3 12.9 −0.4 4.7 −2.4 2.9 38.2 6.5 2.3 
TaiESM1 11.1 6.4 −4.2 2.7 −9.7 −3.4 19.1 9.1 1.9 
ACCESS-ESM1-5 2.3 24.3 3.8 7.0 4.3 6.8 31.3 6.5 4.7 
CanESM5 2.3 24.3 −3.5 −0.8 −6.9 5.8 71.4 0.5 −0.4 
MIROC6 3.3 6.6 1.9 5.4 3.4 −6.5 20.6 2.4 3.0 
EWEM0307 5.9 3.7 −7.5 2.4 −6.7 −0.5 28.6 10.8 2.7 
EWEM1011 6.0 25.6 2.5 3.7 4.5 3.4 35.9 4.8 4.6 

Effect of climate change on urban flooding

Scenarios for the future development of drivers of climate change consistent with socioeconomic development play an important role in climate research (O'Neill et al. 2016). It can evaluate the system's response to future changes and propose corresponding management measures. The SSP2-4.5 and SSP5-8.5 of this ScenarioMIP are adopted as the data for analyzing the future climate change from 2023 to 2062, which represent medium and high forcing pathways, respectively. The frequency and value of precipitation for these two scenarios have been corrected by DFQDM. Based on this historical DRIF, rainstorm intensities of different return periods and duration for this future period are calculated using the proportional coefficient method (Zhou et al. 2018). This generalized extreme value (GEV) distribution was adopted to fit the cumulative frequency distribution of daily precipitation for historical and future periods of the model. The fitted distribution is used to calculate the rainstorm intensity of the model over different return periods and 1440 min duration. The ratio of rainstorm intensity in different return periods between DRIF and climate model in 1440 min is calculated. The ratio is assumed to be applicable to other durations of the future period of the model. The rainstorm intensity calculated by GEV is corrected in the future period, which is taken as the design rainstorm intensity value of the future period of the model. Short-duration rainstorms are often used in the design of urban drainage systems. In this study, a 120-min duration and eight return periods were used to calculate the rainstorm intensity for different design scenarios. The return periods are 2-, 3-, 5-, 10-, 20-, 30-, 50-, 100-year, respectively. The designed rainfall hydrographs of the climate model (future period) and DRIF (Historical period) at different return periods are shown in Figure 11. The peak of this rainstorm is gradually increasing as future climate change intensifies.
Figure 11

Design rainfall process lines with different return periods. (a) Historical period, (b) SSP2-4.5, (c) SSP5-8.5.

Figure 11

Design rainfall process lines with different return periods. (a) Historical period, (b) SSP2-4.5, (c) SSP5-8.5.

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This rainfall process is added to SWMM to simulate the changes in total flood volume (TFV) of nodes and drainage capacity of conduits. The simulation time of SWMM is 120 min. This model has been calibrated and can accurately describe the change of water level in the study area. The calibrated parameters of this model are shown in Table 8.

Table 8

The calibrated range of SWMM parameters

NameUnitsValue
Manning's coefficient (n) of closed conduits – 0.013 
Width of subcatchment 0.43–1,755.53 
Percent of impervious area 0.02–85 
decay constant 
Manning's coefficient (n) of the impervious portion – 0.024–0.03 
Manning's coefficient (n) of the previous portion – 0.15 
NameUnitsValue
Manning's coefficient (n) of closed conduits – 0.013 
Width of subcatchment 0.43–1,755.53 
Percent of impervious area 0.02–85 
decay constant 
Manning's coefficient (n) of the impervious portion – 0.024–0.03 
Manning's coefficient (n) of the previous portion – 0.15 

Figure 12 shows that the TFV increases with the increase of the return period. The order of the TFV is SSP5-8.5 > SSP2-4.5 > Historical. This TFV reflects the amount of water that overflows from the drainage system to the ground. The higher the magnitude of the TFV, the more serious the urban waterlogging will be. In 2-year return period, the TFV is, respectively, 38,503.3, 21,173.6 and 11,439.3 m3. In 100-year return period, the TFV is, respectively, 38,503.3, 21,173.6 and 11,439.3 m3. Compared with the historical period, the TFV of SSP5-8.5 and SSP2-4.5 increased by 236.59 and 85.1% in the 2-year return period, respectively. The TFV of SSP5-8.5 and SSP2-4.5 increased by 45.43 and 20.8% in the 100-year return period, respectively. The change in TFV for the 2-year return period is greater than the 100-year return period. The reason is that most of the conduits do not reach the maximum value of drainage capacity in the 2-year return period. With the increase in rainstorm intensity, most conduits are gradually filled to reach the maximum drainage capacity, and the water exceeding the maximum drainage capacity of the conduits overflow. The proportion of overflow nodes changes greatly. For the 100-year return period, most conduits have reached the maximum drainage capacity, so the proportion of changes in the future period relative to the historical period is less than 2-year return period. This study found that the relationship between TFV and return period followed a logarithmic curve. The fitted formula is shown in Figure 12. The R2 (coefficient of determination) is close to 1, and the fitting effect is accurate. This formula can be used to extrapolate the TFV with a larger return period.
Figure 12

Change of TFV in different return periods.

Figure 12

Change of TFV in different return periods.

Close modal
Figure 13 shows the maximum and average value of overflow, the maximum value of overflow time and the change of drainage capacity in different return periods. The change trend of these indicators is the same as that of TFV. MFV represents the node with the largest overflow. Compared with the historical period, the MFV of SSP5-8.5 and SSP2-4.5 increased by 197.22 and 84.42% at the 2-year return period and 32.53 and 15.54%, respectively, at the 100-year return period, respectively. The percentage change of AFV under different return periods is the same as that of TFV. PON represents the percentage of overflow nodes in the total number of nodes. With the increase of rainstorm intensity, the PON is gradually increasing. At the 100-year return period, the PON is around 45%. About half of the nodes have overflowed. The MOT of SSP5-8.5 and SSP2-4.5 at 100-year return period were 94 and 92 min, respectively. The overflow time of the node is relatively large. If the depth of the waterlogging is relatively large, it will affect the safety of the traffic and pedestrians. PFC represents the fraction of the conduits filled with flow, which ranges from 0 to 1. PFC is close to 99% in the 100-year return period. The PFC was greater than 94% at different return periods, which indicates that the drainage capacity of the system is poor and that it needs to be upgraded in the future. The transformation can be achieved by increasing the diameter of the conduits and building LID measures, which can improve the drainage capacity and reduce the runoff from the node into the conduit.
Figure 13

Variation of overflow volume and drainage capacity at different return periods. (a) The maximum flood volume of the node (MFV); (b) average flood volume of nodes (AFV); (c) percentage of overflow nodes (PON); (d) the maximum value of overflow time (MOT); (e) percentage of filled conduits (PFC).

Figure 13

Variation of overflow volume and drainage capacity at different return periods. (a) The maximum flood volume of the node (MFV); (b) average flood volume of nodes (AFV); (c) percentage of overflow nodes (PON); (d) the maximum value of overflow time (MOT); (e) percentage of filled conduits (PFC).

Close modal

Urban flooding reduction by LID practices under climate change

The drainage system in the study area was insufficient to cope with rainfall with a return period of more than 10-years in the historical period, and the PON was more than 30%. Under the SSP2-4.5 scenario, the PON has reached 32.48% during the 5-year return period. Under the SSP5-8.5 scenario, the PON has reached 31.15% during the 3-year return period. The area of hardened pavement in this study area has a high proportion, which leads to a decrease in the infiltration capacity of rainfall. A large amount of rainwater is drained into rainfall wells, which increases the load on the conduit operation. In the future, the study area should transform the conduit network with a smaller diameter in low-lying areas. However, expanding existing drainage systems has proven expensive and unsustainable, especially in changing environments (Zhu et al. 2019). LID can effectively reduce the impact of the decline of surface permeability caused by urban development and has been adopted in many countries (Yu et al. 2022). At the same time, LID measures should be constructed to increase the interception rate of rainwater at this initial stage. This overflow will be effectively mitigated. LID can reduce the pollutants produced by the scouring of the initial rainwater on the road surface and improve the natural landscape. LID also has some disadvantages, such as (1) increase in the cost of maintenance; (2) if the design is unreasonable, it will reduce the removal effect of pollutants; (3) with the increase of time, the performance of LID will decrease.

In order to reduce the risk of flooding in the study area, the LID was applied and its effect on the control of precipitation at the source was evaluated without considering the reduction of performance. Based on the topographic features and future planning of this study area, five LIDs were adopted in the study area. The LIDs are, respectively, Permeable Pavement (PP), Bio-retention Cells (BRC), Green Roofs (GR), Rain Gardens (RG), Vegetative Swales (VS). In SWMM, LID is represented its coverage by setting the number and area in the subcatchment. The proportion of LID-controlled area for different land uses in the subcatchment is shown in Table 9.

Table 9

Configuration scheme of LID under different landuse

LanduseTypes of LID practicesRatioNumber of subcatchments renovatedTotal area of renovation (ha)
Roadway PP 0.70 776 62.54 
BRC 0.20 
Build-up GR 0.70 650 68.15 
Bare soil PP 0.20 103 22.57 
RG 0.60 
Hard pavement PP 0.70 778 91.07 
Green land VS 0.20 661 10.97 
LanduseTypes of LID practicesRatioNumber of subcatchments renovatedTotal area of renovation (ha)
Roadway PP 0.70 776 62.54 
BRC 0.20 
Build-up GR 0.70 650 68.15 
Bare soil PP 0.20 103 22.57 
RG 0.60 
Hard pavement PP 0.70 778 91.07 
Green land VS 0.20 661 10.97 

The layout scheme of mixed LID is adopted in the subcatchment area. In SWMM, the parameters of LID are represented by the four processing layers of surface, soil and storage drain. The configuration of the parameters of this sponge facility refers to Kim & Kim (2021), Liang et al. (2019), Men et al. (2020), Wu et al. (2018), Yu et al. (2022), and Zhang & Guo (2015). In order to compare the effect of LID facilities on the runoff of the outfall after the rain stopped, the simulation time of SWMM in this part was set to 240 min. The simulation results of this outflow before and after the installation of the LID under short-duration rainfall of 120 min are shown in Figure 14. The precipitation process under the return period of 2-, 20- and 100-year was selected to analyze the change of runoff. It can be seen that the time of the peak of the runoff is delayed when the return period is relatively small. The magnitude of the peak of the flow is reduced. The effect of this change decreases as the return period increases. Table 10 shows the peak values of the outflow at different return periods before and after the installation of the LID. During the historical period, the change in the percentage of this peak reduction was most significant due to the smaller intensity of the storm. As climate change intensifies, the percentage of this peak is diminished. For SSP2-4.5 and SSP5-8.5, the reduction ratio of this peak in the return period of 2a–20a is more than 20%. In the 100-year return period, this proportion is greater than 10%. Overall, the effect of this LID on the storage and infiltration of rainfall is obvious.
Table 10

Variation of the peak value of outflow in different return periods (m3/s)

Return period (year)Historical
SSP2-4.5
SSP5-8.5
Pre-LIDPost-LIDPercentPre-LIDPost-LIDPercentPre-LIDPost-LIDPercent
38.34 18.37 52.10 41.75 20.51 50.87 45.92 23.73 48.33 
42.88 21.41 50.07 45.92 23.73 48.32 49.64 28.16 43.26 
46.40 25.08 45.96 49.69 29.16 41.32 52.40 34.83 33.53 
10 50.63 32.04 36.71 53.49 36.37 32.01 56.42 42.06 25.45 
20 54.48 39.77 27.01 57.30 43.89 23.40 60.17 46.98 21.93 
30 56.52 41.88 25.89 59.30 47.50 19.89 61.74 50.99 17.42 
50 58.95 46.09 21.81 61.50 49.66 19.26 62.86 53.58 14.76 
100 61.58 49.80 19.14 62.89 53.64 14.71 64.38 57.37 10.89 
Return period (year)Historical
SSP2-4.5
SSP5-8.5
Pre-LIDPost-LIDPercentPre-LIDPost-LIDPercentPre-LIDPost-LIDPercent
38.34 18.37 52.10 41.75 20.51 50.87 45.92 23.73 48.33 
42.88 21.41 50.07 45.92 23.73 48.32 49.64 28.16 43.26 
46.40 25.08 45.96 49.69 29.16 41.32 52.40 34.83 33.53 
10 50.63 32.04 36.71 53.49 36.37 32.01 56.42 42.06 25.45 
20 54.48 39.77 27.01 57.30 43.89 23.40 60.17 46.98 21.93 
30 56.52 41.88 25.89 59.30 47.50 19.89 61.74 50.99 17.42 
50 58.95 46.09 21.81 61.50 49.66 19.26 62.86 53.58 14.76 
100 61.58 49.80 19.14 62.89 53.64 14.71 64.38 57.37 10.89 
Figure 14

Changes in outflow before and after LID installation. (1) (a)–(c) are historical periods; (2) (d)–(f) are SSP2-4.5; (3) (g)–(i) are SSP5-8.5.

Figure 14

Changes in outflow before and after LID installation. (1) (a)–(c) are historical periods; (2) (d)–(f) are SSP2-4.5; (3) (g)–(i) are SSP5-8.5.

Close modal
Figure 15 shows the change in this overflow volume and the drainage capacity of the conduit before and after LID installation. The reduction effect of this LID on TFV is significant. It can significantly reduce the runoff of land surface and the overflow of the node. Different LIDs significantly improved the infiltration capacity of the soil. As the intensity of the rainstorm increases, this effect is gradually weakened. The reason is that the LID facility quickly reaches its maximum capacity for a period of time after a heavy rainstorm occurs. The storage volume of this BRC and GR may be filled, and soils of other LIDs have reached their maximum infiltration capacity. In Figure 15, the reduction effect of LID on TFV is over 60%. When the rainstorm intensity is high, many nodes still overflow and a large number of conduits are filled.
Figure 15

Percentage of decrease in evaluation index of the waterlogging before and after LID installation.

Figure 15

Percentage of decrease in evaluation index of the waterlogging before and after LID installation.

Close modal

The simulation of an urban drainage system requires high resolution of precipitation for the climate model, the correction of daily precipitation is a problem to be solved. Considering the correction of frequency and bias of daily precipitation, a new statistical downscaling method called DFQDM is proposed. CMIP6 is used to calculate the rainstorm intensity under different return periods in the future. The impact of climate change and LID construction on urban flooding is analyzed. The main conclusions of this study are as follows:

  • (1)

    For the annual precipitation, CanESM5 has better accuracy for the prediction of precipitation, and the minimum absolute error between CanESM5 and the mean value of observation value is 43.48 mm. The PBIAS and RMSE of CanESM5 are also the smallest, which are −7.33% and 239.66 mm, respectively, and the change trend is more consistent with the observed value. CMCC-CM2-SR5 seriously overestimates the annual precipitation. This ensemble model performs well except for EWEMALL. For the monthly precipitation, the CC of the climate model is about 0.65, which is close to the variation trend of the observation.

  • (2)

    The correction effect of DFQDM on daily precipitation is significant. The PBIAS for annual precipitation was significantly reduced. The PBIAS of this daily extreme precipitation index are all controlled within 6%, and the PBIAS of RX5day for most climate models are controlled around 10%. SDII of many climate models is underestimated, and the correction of the average precipitation intensity on this wet day will be improved in the future research. Finally, CanESM5 is selected as the precipitation data for future climate change analysis.

  • (3)

    The simulation results of this SWMM show that the relationship between TFV and return period follows a logarithmic curve. The TFV of SSP5-8.5 and SSP2-4.5 increased by 236.59 and 85.1% in the 2-year return period and 45.43 and 20.8% in the 100-year return period, respectively. In different return periods, this LID reduces the runoff of this drainage system by more than 60%, and its control effect on waterlogging risk is significant.

This study was supported by the National Natural Science Foundation of China (No. 52179027).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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