The capabilities of 23 global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 were evaluated for six extreme precipitation indices from 1961 to 2010 using interannual variability and Taylor skill scores in the Yellow River Basin and its eight subregions. The temporal variations and spatial distributions of extreme precipitation indices were projected from 2021 to 2050 under the shared socioeconomic pathway scenarios (SSP2–4.5 and SSP5–8.5). The results show that most GCMs perform well in simulating extreme values (1-day maximum precipitation (RX1day) and 5-day maximum precipitation (RX5day)), duration (consecutive dry days), and intensity index (simple daily intensity index (SDII)), and perform poor in simulating the threshold indices (precipitation on very wet days (R95p) and number of heavy precipitation days (R10mm)). The projected changes in extreme precipitation indicate that under the SSP2-4.5 scenario, future extreme precipitation will increase by 15.7% (RX1day), 15.8% (RX5day), 30.3% (R95p), 1d (R10mm), and 6.6% (SDII), respectively, decrease by 2.1d (CDD). The aforementioned changes are further enhanced under the SSP5-8.5 scenario. Extreme precipitation changes widely in Hekou Town to Longmen, in the northeastern part of the region from Longmen to Sanmenxia, below Huayuankou, and in the interflow basin.

  • The study evaluated the biases of 23 global climate models (GCMs) from observations and the spatial distribution of the biases.

  • Interannual variability score, Taylor diagram, and Taylor skill score were used to evaluate CMIP6 GCMs.

  • The future changes of the Yellow River Basin and its subregions extreme precipitation under SSP2-4.5 and SSP5-8.5 scenarios were projected by using six ETCCDI indices.

Extreme precipitation events are greatly impacted by climate warming (Tabari 2020), and observations indicate that each 1 °C rise in global temperature could cause a 7% increase in extreme daily precipitation events (IPCC 2021). The influence of extreme precipitation on human life, economy, and society is severe, as it can lead to disasters such as floods, mudslides, and landslides (Konapala et al. 2020; Liu et al. 2020). It is widely recognized that extreme precipitation will become more frequent and intense under climate warming (O'Gorman 2015; Yu et al. 2023), and therefore, accurate projection of future extreme precipitation is crucial.

The global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6) are the major tools for projecting future climate (Li et al. 2022a; Feng et al. 2023). Many studies have been found to project extreme precipitation using CMIP6 GCMs. Li et al. (2021) projected the future trends and spatiotemporal distributions in extreme precipitation globally. Wang et al. (2023) analyzed changes of extreme precipitation in China and the sensitivity of extreme precipitation to climate change across various regions. Furthermore, Zhang et al. (2023) projected the future trends and cycle characteristics in extreme precipitation for the Jialing River Basin under the four shared socioeconomic pathway (SSP) scenarios. Current studies found that extreme precipitation exhibited spatial heterogeneity across regions, making it imperative to research the future changes in extreme precipitation on subregional and regional scales (Jin et al. 2023).

The capability of GCMs to simulate the climate of historical periods is an important aspect of the credibility of their future projections (Wang et al. 2023). Therefore, the simulation capability of GCMs needs to be evaluated before using their outputs for projecting future extreme precipitation. Previously, various studies have evaluated the capability of GCMs to simulate extreme precipitation. Ali et al. (2023) used the Kling Gupta efficiency metric to evaluate the capability of GCMs to replicate the extreme precipitation indices during the historical period over Pakistan. Lei et al. (2023) evaluated the capability of 33 CMIP6 GCMs to simulate extreme precipitation indices across Central Asia using interannual variability scores (IVS), Taylor diagrams, and comprehensive evaluation indices. The study found that GCMs performed differently in regions with different topographic and climatic characteristics. Liu et al. (2022) found that GCMs had different performances in capturing spatial patterns of extreme precipitation in different seasons. Consequently, the historical simulated performances of GCMs need to be evaluated before projecting in the future.

The Yellow River Basin (YRB) is of vital importance to the economic, social, and environmental well-being of China (Wang et al. 2022). Nevertheless, the YRB is being severely impacted by extreme precipitation events. For example, in September 2021, the average precipitation (179.0 mm) was 1.7 times higher than that of the same period of the normal year in the YRB, which was the highest in the same period of history since 1961, resulting in 4,986 km2 of crop damage and a direct economic loss of 15.34 billion RMB. According to Zhang et al. (2014) and Li et al. (2022a), precipitation in the upstream of the YRB is increasing at a rate of 8.1 mm/a, and the number and index of heavy precipitation processes are also increasing. The midstream and downstream of the YRB are situated in the eastern monsoon region, where evident seasonal changes are notable in the extreme precipitation. The extreme precipitation indices exhibited a low spatial pattern in the northwest and a high pattern in the southeast, with significant spatial variability in the YRB (Niu et al. 2020). However, there are fewer studies projecting the spatial and temporal distribution of subregional extreme precipitation under different SSP scenarios. Therefore, it is imperative to project and analyze potential variations in extreme precipitation in the YRB and subregions and implement measures to reduce the associated hazards.

In this study, 23 CMIP6 GCMs were evaluated for their capabilities to simulate extreme precipitation indices in the YRB and its eight level-II water resource regions during the historical period (from 1961 to 2010). The SSP2-4.5 and SSP5-8.5 scenarios were selected to project the temporal variability and spatial distribution of extreme precipitation for the future period (from 2021 to 2050). The study could provide a reference for future impact evaluation of extreme precipitation.

Study area

The Yellow River originates from the Bayan Kara Mountains on the Qinghai–Tibet Plateau, with a total length of 5,464 km. It flows from west to east through nine provinces (autonomous regions) of China and finally flows into the Bohai Sea. The Yellow River has a basin area of 795,000 km2 and an average annual precipitation of 446 mm. The precipitation generally decreases from southeast to northwest. The midstream and upstream of the Yellow River are dominated by mountains, whereas the midstream and downstream are dominated by plains and hills. The YRB is mainly characterized by a continental monsoon climate.

The main tributaries of the Yellow River are Huangshui, Tao River, Zuli River, Wei River, Qingshui River, Dahei River, Wuding River, Yiluo River, Fen River, Qin River, and so on. The YRB was analyzed by dividing the basin into eight subregions according to the standard of the national level-II water resource regions classified by the Ministry of Water Resources of the People's Republic of China (Figure 1).
Figure 1

Location of the study area and locations of the meteorological station.

Figure 1

Location of the study area and locations of the meteorological station.

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Data

Observations

The observations are the daily precipitation of 126 meteorological stations from 1961 to 2010, which are obtained from the China Meteorological Sharing Network (http://data.cma.cn). The precipitation series were relatively complete and of good quality (Wang et al. 2020; Guan et al. 2022), and the missing values were interpolated linearly to complete the series. The inverse distance interpolation method (Chen & Liu 2012) was used to interpolate into 431 grids with a resolution of 50 km × 50 km in the YRB.

CMIP6 GCMs outputs

The climate projection scenarios of the Scenario Model Intercomparison Project (ScenarioMIP) are rectangular combinations of different SSPs and radiative forcing. Among them, SSP2-4.5 represents the medium development and the radiative forcing stabilizes at 4.5 W/m2 in 2100, and SSP5-8.5 represents the general development and the radiative forcing stabilizes at 8.5 W/m2 in 2100.

Because SSP2-4.5 scenario has the highest likelihood of occurring in the future compared to the other emission scenarios (Ning et al. 2022), SSP5-8.5 scenario represents the most pessimistic scenario in 2100. We collected the available outputs of 23 CMIP6 GCMs under the SSP2-4.5 scenario and 21 CMIP6 GCMs under the SSP5-8.5 scenario (Table 1) for the historical (from 1961 to 2010) and future (from 2021 to 2050) (https://esgf–node.llnl.gov/projects/esgf–llnl) to project future extreme precipitation. Considering the different spatial resolutions of the models, a bilinear interpolation method (Mastyło 2013) was used to standardize all models to a 50 km × 50 km grid resolution.

Table 1

Basic information of the 23 CMIP6 models

NoModel nameInstituteAtmospheric resolution (Lat × Lon)SSP2-4.5SSP5-8.5
ACCESS–CM2 CSIRO 144 × 192 √ √ 
ACCESS–ESM1–5 CSIRO 145 × 192 √ √ 
BCC–CSM2–MR BCC 160 × 320 √ √ 
CanESM5 CCCMA 64 × 128 √ √ 
CMCC–ESM2 CMCC 192 × 288 √ √ 
CNRM–CM6–1 CNRM 128 × 256 √ √ 
CNRM–ESM2–1 CNRM 128 × 256 √ √ 
EC–Earth3 EC–Earth–Consortium 256 × 512 √ √ 
EC–Earth3–Veg EC–Earth–Consortium 256 × 512 √ √ 
10 EC–Earth3–Veg–LR EC–Earth–Consortium 160 × 320 √ √ 
11 FGOALS–g3 CAS 80 × 180 √  
12 HadGEM3–GC31–LL MOHC 144 × 192 √ √ 
13 INM–CM4–8 INM 120 × 180 √ √ 
14 INM–CM5–0 INM 120 × 180 √ √ 
15 IPSL–CM6A–LR IPSL 143 × 144 √ √ 
16 MIROC6 MIROC 128 × 256 √ √ 
17 MIROC–ES2L MIROC 64 × 128 √ √ 
18 MPI–ESM1–2–HR MPI 192 × 384 √ √ 
19 MPI–ESM1–2–LR MPI 96 × 192 √  
20 MRI–ESM2–0 MRI 160 × 320 √ √ 
21 NorESM2–LM NCC 96 × 144 √ √ 
22 NorESM2–MM NCC 192 × 288 √ √ 
23 UKESM1–0–LL MOHC 144 × 192 √ √ 
NoModel nameInstituteAtmospheric resolution (Lat × Lon)SSP2-4.5SSP5-8.5
ACCESS–CM2 CSIRO 144 × 192 √ √ 
ACCESS–ESM1–5 CSIRO 145 × 192 √ √ 
BCC–CSM2–MR BCC 160 × 320 √ √ 
CanESM5 CCCMA 64 × 128 √ √ 
CMCC–ESM2 CMCC 192 × 288 √ √ 
CNRM–CM6–1 CNRM 128 × 256 √ √ 
CNRM–ESM2–1 CNRM 128 × 256 √ √ 
EC–Earth3 EC–Earth–Consortium 256 × 512 √ √ 
EC–Earth3–Veg EC–Earth–Consortium 256 × 512 √ √ 
10 EC–Earth3–Veg–LR EC–Earth–Consortium 160 × 320 √ √ 
11 FGOALS–g3 CAS 80 × 180 √  
12 HadGEM3–GC31–LL MOHC 144 × 192 √ √ 
13 INM–CM4–8 INM 120 × 180 √ √ 
14 INM–CM5–0 INM 120 × 180 √ √ 
15 IPSL–CM6A–LR IPSL 143 × 144 √ √ 
16 MIROC6 MIROC 128 × 256 √ √ 
17 MIROC–ES2L MIROC 64 × 128 √ √ 
18 MPI–ESM1–2–HR MPI 192 × 384 √ √ 
19 MPI–ESM1–2–LR MPI 96 × 192 √  
20 MRI–ESM2–0 MRI 160 × 320 √ √ 
21 NorESM2–LM NCC 96 × 144 √ √ 
22 NorESM2–MM NCC 192 × 288 √ √ 
23 UKESM1–0–LL MOHC 144 × 192 √ √ 

Methods

Extreme precipitation indices

Six extreme precipitation indices, as defined by the Expert Team on Climate Change Detection and Indicators (PL et al. 2002), were selected taking into account the climatic characteristics of the region and the statistics of extreme precipitation events (Table 2). Since the statistics show an increase in the frequency of short-duration heavy precipitation events in the YRB, RX1day and 5-day maximum precipitation (RX5day) were selected to capture these types of precipitation events. Meanwhile, considering that YRB is located in arid and semi-arid areas where droughts are common, CDD represents exactly the conditions of very low precipitation. In addition, R95p, as an indicator of the intensity of extreme precipitation, is essential for understanding and predicting the impacts of climate change related to extreme precipitation. Simultaneously, R10mm is a common indicator of the frequency of extreme precipitation, which is directly relevant to agricultural planning and the development of flood control measures. A simple daily intensity index (SDII) shows changes in the distribution of precipitation, which is very helpful in assessing overall changes in precipitation patterns. These indices have the characteristics of weak extremity, small noise, and large significance, and are widely used in the study of extreme precipitation (Dong & Dong 2021; Zhu et al. 2023).

Table 2

Information of extreme precipitation indicators

CategoryIndicatorDefinitionUnits
Extreme values RX1day Monthly maximum 1-day precipitation mm 
RX5day Monthly maximum consecutive 5-day precipitation mm 
Threshold values R95p Annual total precipitation from days > 95th percentile mm 
R10mm Annual count when precipitation ≥ 10 mm 
Duration CDD Maximum number of consecutive days when precipitation < 1 mm 
Intensity SDII The ratio of annual total precipitation to the number of wet days (≥1 mm) mm/d 
CategoryIndicatorDefinitionUnits
Extreme values RX1day Monthly maximum 1-day precipitation mm 
RX5day Monthly maximum consecutive 5-day precipitation mm 
Threshold values R95p Annual total precipitation from days > 95th percentile mm 
R10mm Annual count when precipitation ≥ 10 mm 
Duration CDD Maximum number of consecutive days when precipitation < 1 mm 
Intensity SDII The ratio of annual total precipitation to the number of wet days (≥1 mm) mm/d 

Biases between CMIP6 models and observations

Bias was an important indicator of GCM performance, which is defined as follows:
formula
(1)
formula
(2)
where Sim and Obs are the GCMs outputs and observations, respectively. Equation (1) is used when calculating relative biases for RX1day, RX5day, R95p, and SDII, and Equation (2) is used when calculating absolute biases for R10mm and CDD.

The spatial biases of YRB and its subregions are the average of the absolute values of all grid biases within the YRB or subregions.

Interannual variability score

We used the IVS to explore the temporal simulation performance of GCMs to observations (Chen et al. 2011). The IVS was calculated using the equation:
formula
(3)
where Stdm represents the standard deviation of each grid GCM outputs over the time series and Stdo represents the standard deviation of each grid observation over the time series. A value of the IVS closer to 0 indicates better temporal simulation performance of GCMs.

Taylor diagrams and Taylor skill score

The capability to quantify the spatial simulation between GCM outputs and observations was determined using Taylor diagrams (Taylor 2001). The Taylor skill score (TSS) was applied to evaluate the overall spatial simulation performance of the GCMs (Ullah et al. 2021). The TSS depended on both the correlation and the variance of the GCMs outputs and observations, which were defined as follows:
formula
(4)
where R represents the spatial correlation coefficient between the GCMs outputs and the observations, Rmax is the maximum value of R, and σm and σo represent the standard deviations of the GCMs outputs and the observations, respectively. TSS equal to 1 indicates that GCMs match the observations perfectly.

Bias correction

Bias correction is necessary to eliminate the systematic biases in GCMs. The quantile map method (Li et al. 2010) of revising precipitation elements at the same frequency has a good application in the evaluation of the impacts of extreme precipitation (Li et al. 2022b). The bias correction method is shown in Equation (5):
formula
(5)
where xm-p and are the precipitation outputs of the GCMs before and after correction for bias, respectively. Fo-c and Fm-c are the cumulative probability density functions of the observations and GCMs outputs, respectively.

The distribution function for precipitation used a hybrid function consisting of a step function and a two-parameter gamma distribution function due to the interpolated diffusion problem associated with corrections using empirical functions.

The hybrid function T(x) is expressed as follows:
formula
(6)
where t is the proportion of months with precipitation in the total monthly series. L(x) takes the value of 1 for precipitation and 0 for no precipitation. F(x) is a two-parameter gamma distribution function with the probability density function as shown in Equation (7):
formula
(7)

Biases

Biases in the YRB and subregions

The overall spatial bias of R95p is greater at 47.96%, followed by RX5day (21.04%) and CDD (18.91d) (Table 3). Meanwhile, R10mm exhibits a smaller overall spatial bias at 5.66d. Compared to other subregions, Regions I and II exhibit the greatest regional spatial biases for the indices, particularly for RX5day (37.79 and 40.65%), R95p (97.27 and 83.22%), R10mm (14.49d and 9.05d), and CDD (27.76d and 32.75d). In Region VII, the regional spatial biases are especially high for RX1day and SDII, with biases of 27.91 and 28.47%, respectively.

Table 3

Overall spatial biases in the YRB and subregions

IndicesRegionsRX1day/%RX5day/%R95p/%R10mm/dCDD/dSDII/%
The whole basin 15.30 21.04 47.96 5.66 18.91 16.55 
Ⅰ 18.20 37.79 97.27 14.49 27.76 15.70 
Ⅱ 11.11 40.65 83.22 9.05 32.75 9.04 
Ⅲ 14.81 17.56 34.53 2.49 19.27 17.21 
Ⅳ 15.23 7.32 18.59 1.68 11.91 18.16 
Ⅴ 12.02 15.65 41.58 4.34 14.68 14.64 
Ⅵ 12.07 9.75 32.12 4.06 10.32 17.38 
Ⅶ 27.91 16.49 10.04 2.69 7.38 28.47 
Ⅷ 13.88 9.36 19.59 1.12 14.77 17.18 
IndicesRegionsRX1day/%RX5day/%R95p/%R10mm/dCDD/dSDII/%
The whole basin 15.30 21.04 47.96 5.66 18.91 16.55 
Ⅰ 18.20 37.79 97.27 14.49 27.76 15.70 
Ⅱ 11.11 40.65 83.22 9.05 32.75 9.04 
Ⅲ 14.81 17.56 34.53 2.49 19.27 17.21 
Ⅳ 15.23 7.32 18.59 1.68 11.91 18.16 
Ⅴ 12.02 15.65 41.58 4.34 14.68 14.64 
Ⅵ 12.07 9.75 32.12 4.06 10.32 17.38 
Ⅶ 27.91 16.49 10.04 2.69 7.38 28.47 
Ⅷ 13.88 9.36 19.59 1.12 14.77 17.18 

Spatial distribution of biases

The spatial performances of RX1day (Figure 2) and SDII (Figure 7) show the predominance of negative biases. Specifically, 69.6 and 74.5% of the total number of grids in the basin exhibit negative biases for RX1day and SDII, respectively. This indicates that the GCMs are lower than the observations. Moreover, the spatial performance of CDD (Figure 6) has a negative bias in more than 99.9% of the grids. The positive biases dominate the spatial performance of RX5day (Figure 3), R95p (Figure 4), and R10mm (Figure 5). For RX5day, 71.2% of the grids in the basin have positive biases, while in R95p and R10mm simulations, more than 80% of the grids have positive biases. For the single model, the extreme precipitation indices' results differed between models. CanESM5 only shows a negative bias for CDD and positive biases for the other five indices. Meanwhile, EC–Earth3, EC–Earth3–Veg, and EC–Earth–Veg–LR predominantly exhibit negative biases for six indices. It has been determined that INM–CM4–8 and INM–CM5–0 have comparable performance in replicating the six extreme precipitation indices, while GCMs from the same institution may have similar results due to similarities in the parameterization process, among other factors.

In Regions I and II, biases generally perform similarly for the other indices, except negative biases in the simulation of CDD. However, the simulations of SDII perform slightly differently, with SDII showing significant positive biases with biases higher than 10% in Region I, while the simulations of SDII show negative biases near the Datong River Basin in Region II. Nevertheless, in Region III, changes in extreme precipitation indices are relatively complex. RX1day, CDD, and SDII show negative biases, while RX5day, R95p, and R10mm show positive biases in Region III except for the Dahei River Basin. In Region IV, only the R95p exhibits positive biases. The extreme precipitation indices perform similarly in Regions V and VI. RX1day, CDD, and SDII exhibit negative biases of over 5%, while R95p and R10mm exhibit a positive bias of more than 10% and over 3d, respectively. In Region VII, six extreme precipitation indices exhibit negative biases, particularly in the Yellow River estuary. R95p and R10mm exhibit positive biases, while the other indices have negative biases in Region VIII.

These results indicate that there are some biases between GCM outputs and observations, and these biases show a certain pattern in different subregions. In general, CDD shows negative biases in all subregions, and SDII shows positive biases only in Region I and negative biases in other subregions. On the contrary, R95p and R10mm mainly show positive biases in all subregions, while RX1day and RX5day do not show the same performances in all subregions (Figures 611).
Figure 2

The simulated biases of the RX1day from 1961 to 2010.

Figure 2

The simulated biases of the RX1day from 1961 to 2010.

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Figure 3

The simulated biases of the RX5day from 1961 to 2010.

Figure 3

The simulated biases of the RX5day from 1961 to 2010.

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Figure 4

The simulated biases of the R95p from 1961 to 2010.

Figure 4

The simulated biases of the R95p from 1961 to 2010.

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Figure 5

The simulated biases of the R10mm from 1961 to 2010.

Figure 5

The simulated biases of the R10mm from 1961 to 2010.

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Figure 6

The simulated biases of the CDD from 1961 to 2010.

Figure 6

The simulated biases of the CDD from 1961 to 2010.

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Figure 7

The simulated biases of the SDII from 1961 to 2010.

Figure 7

The simulated biases of the SDII from 1961 to 2010.

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Evaluation of model simulation capabilities

Interannual variability

GCMs perform best in capturing the interannual variability of SDII in the YRB, with the IVS equal to 0.078 (Figure 8). RX1day, RX5day, and CDD are the second-best performers, with the IVS ranging from 0.092 to 0.191. However, the simulation performance for R95p and R10mm is relatively weak, especially for R95p with the IVS equal to 0.705. It is worth noting that the IVS of all the indices are within an acceptable range (IVS is less than or equal to 1). This suggests that the GCMs perform well in capturing the interannual variability of the indices.
Figure 8

The IVS of extreme precipitation indices in the YRB and subregions from 1961 to 2010.

Figure 8

The IVS of extreme precipitation indices in the YRB and subregions from 1961 to 2010.

Close modal

GCMs perform better in Regions III and VIII, with the IVS of five extreme precipitation indices being less than 0.2. However, the GCMs perform poorly in Regions I, II, V, and VII, with the IVS of most indices being greater than 0.2 and the IVS of R95p being greater than 1.

Twenty-three GCMs perform well in capturing the interannual variability of SDII, with the IVS less than 1, followed by RX1day, and only the MIROC6 has the IVS greater than 1 (Figure 9). The GCMs have a poor capability to capture interannual variability in R95p, with eight GCMs having the IVS greater than 1. The CMCC–ESM2 and the FGOALS–g3 have better abilities to capture interannual variability of extreme precipitation indices, with the IVS equal to 0–0.151 and 0–0.119, respectively. The other models perform differently in simulating different indices, e.g., CNRM–ESM2–1 performs better for CDD with the IVS equal to 0.002, while it performs poorly for R95p with the IVS above 4.
Figure 9

The IVS of extreme precipitation indices for 23 GCMs in the YRB from 1961 to 2010.

Figure 9

The IVS of extreme precipitation indices for 23 GCMs in the YRB from 1961 to 2010.

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Spatial simulation capability analysis

All GCMs are positively correlated with the observations for the six extreme precipitation indices (Figure 10), indicating that they have better spatial performance with consistency from 1961 to 2010. For most GCMs, the R is between 0.5 and 0.95. Furthermore, over 80% of the GCMs simulate RX1day and SDII with the R greater than 0.75. Notably, the standard deviation varies based on the specific indices. The GCMs perform best in simulating the standard deviation of RX5day and CDD. Over 50% of GCMs show a standard deviation near 1, indicating that the observations closely align with the variations of the GCMs, implying their capability to capture extreme precipitation indices. Most GCMs have standard deviations greater than 1.2 in the simulations for R95p and R10mm, indicating that the GCMs are more dispersed from the observations and less likely to capture extreme precipitation variability. The centered root mean square errors (ubRMSE) for R95p and R10mm are greater than 1 mm for most GCMs, indicating a high degree of divergence from observations. In contrast, the other four indices have ubRMSE values ranging from 0.25 to 0.75 mm, indicating that the GCMs are more consistent with observations.
Figure 10

Taylor diagram of the extreme precipitation indices based on 23 GCMs in the YRB from 1961 to 2010: (a) RX1day, (b) RX5 day, (c) R95p, (d) R10mm, (e) CDD, and (f) SDII.

Figure 10

Taylor diagram of the extreme precipitation indices based on 23 GCMs in the YRB from 1961 to 2010: (a) RX1day, (b) RX5 day, (c) R95p, (d) R10mm, (e) CDD, and (f) SDII.

Close modal
The capability of GCMs to reproduce the spatial distribution of RX1day, RX5day, and CDD is the best, with the TSS greater than 0.8. In addition, GCMs display the second-best simulation performance for R95p and SDII in the YRB (Figure 11). The simulation of R10mm is relatively poor, with the TSS of only 0.581.
Figure 11

The TSS of extreme precipitation indices in the YRB and subregions from 1961 to 2010.

Figure 11

The TSS of extreme precipitation indices in the YRB and subregions from 1961 to 2010.

Close modal

The GCM simulations show the strongest spatial distribution of extreme precipitation indices in Region VIII, with the TSS greater than 0.8. In Region IV, five indices exhibit the TSS greater than 0.8, resulting in the second highest simulation capability. The simulation capacity of GCMs is inadequate in Region VII, with RX1day and SDII with the TSS less than 0.4. This implies that GCMs do not effectively replicate the spatial distribution of extreme precipitation indices in Region VII.

Comparison before and after bias correction

We have corrected the bias for 23 GCMs, and restricted to space, using EC–Earth3 as an example. Figure 12 shows the difference in simulation performance of the EC–Earth3 before and after the bias correction. Figure 12(a) shows the comparison of the effect before and after the bias correction on the grid with a centroid of 38.7244°N 108.141°E. From Figure 12(b), after the bias correction, the bias of EC–Earth3 in the indices is decreased by 8.4 mm (RX1day), 16.3 mm (RX5day), 15.8 mm (R95p), 1.4 d(R10mm), 11.4d (CDD), and 0.6 mm/d (SDII), respectively. From Figure 12(b), after bias correction, EC–Earth3 increases the simulated bias for all indices except R10mm and decreases it for all others, with CDD having the largest decrease in bias of 22.4d. There are also other GCMs whose bias correction results are consistent with EC–Earth3, so the bias correction is effective in decreasing the existence of uncertainty in the GCMs.
Figure 12

Bias correction effects of EC–Earth3: (a) a grid with the centroid at 38.7244°N 108.141°E and (b) the YRB.

Figure 12

Bias correction effects of EC–Earth3: (a) a grid with the centroid at 38.7244°N 108.141°E and (b) the YRB.

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Projections under the SSP2-4.5 and SSP5-8.5 scenarios

The temporal variation and spatial distribution of extreme precipitation indices were projected under the SSP2-4.5 and SSP5-8.5 scenarios from 2021 to 2050, with 1981 to 2010 as the base period. The median of GCMs on each grid was used as a multimodel ensemble to project future changes in extreme precipitation indices.

Time variations

All indices increase to varying degrees except for CDD, which decreases by 2.1d (Figure 13). Specifically, R95p increased by 30.3%, while RX1day and RX5day increased by 15.7 and 15.8%, respectively. SDII increased by a lesser 6.6%, and R10mm increased by 1d.
Figure 13

Changes in extreme precipitation from 2021 to 2050 under the SSP2-4.5 scenario in the YRB (the baseline period: from 1981 to 2010).

Figure 13

Changes in extreme precipitation from 2021 to 2050 under the SSP2-4.5 scenario in the YRB (the baseline period: from 1981 to 2010).

Close modal

Two GCMs display outliers: CNRM–ESM2–1 shows outliers in 49.0% (RX1day), 46.5% (RX5day), 72.8% (R95p), 3.2d (R10mm), and −6.8d (CDD). The other GCM, CMCC–ESM2, has outliers in 55.1% (RX1day) and 17.5% (SDII), which are approaching or exceeding three times the median. This may be due to the characteristics or assumptions inherent in the GCMs or to the uncertainty of the GCMs in addressing particular variables or conditions.

All extreme precipitation indices except the CDD increase to varying degrees in the projected for the subregions (Figure 14). The extreme precipitation indices have the greatest change in Region VII, especially the 42.1% increase in R95p, and the changes in Regions I and II are relatively small. In Region VIII, both RX1day and R95p increased more than neighboring regions (Regions III, IV, and V).
Figure 14

Changes in extreme precipitation from 2021 to 2050 under the SSP2-4.5 scenario in the subregions (the baseline period: from 1981 to 2010).

Figure 14

Changes in extreme precipitation from 2021 to 2050 under the SSP2-4.5 scenario in the subregions (the baseline period: from 1981 to 2010).

Close modal
Under the SSP5-8.5 scenario, only the CDD decreased by 2.2 days compared to the baseline period, while the other indices increased (Figure 15). By contrast, the other indices increased by 22.6% (RX1day), 20.1% (RX5day), 39% (R95p), 9.5% (SDII), and 1.4 d (R10mm). The CNRM–CM6–1 simulates RX1day, RX5day, and R95p showed outliers with 83.8, 76, and 116.6% outliers, respectively.
Figure 15

Changes in extreme precipitation from 2021 to 2050 under the SSP5-8.5 scenario in the YRB (the baseline period: from 1981 to 2010).

Figure 15

Changes in extreme precipitation from 2021 to 2050 under the SSP5-8.5 scenario in the YRB (the baseline period: from 1981 to 2010).

Close modal

Compared to the SSP2-4.5 scenario, the relative variability of the indices increases significantly under the SSP5-8.5 scenario, with an increase in extreme precipitation on the temporal scale.

Temporal variations in extreme precipitation indices in the subregions under the SSP5-8.5 and SSP2-4.5 scenarios are consistent. However, the largest change occurs in Region VIII under the SSP5-8.5 scenario, where R95p increases by 47.9%, followed by Region IV (Figure 16).
Figure 16

Changes in extreme precipitation from 2021 to 2050 under the SSP5-8.5 scenario in the subregions (the baseline period: from 1981 to 2010).

Figure 16

Changes in extreme precipitation from 2021 to 2050 under the SSP5-8.5 scenario in the subregions (the baseline period: from 1981 to 2010).

Close modal

Spatial distributions

The other five indices show different degrees of increase, except for CDD (Figure 21), which shows a decrease from 2010 to 2050 relative to 1981 to 2010 in most regions of the YRB. The spatial distributions of RX1day (Figure 17) and RX5day (Figure 18) show an increase from the upstream to the downstream. However, the Jing River Basin and Luo River Basin in Region V show a smaller increase, while the Wuding River Basin in Regions IV and VII show an increase exceeding 20%. The spatial distribution of R95p (Figure 19) is opposite to them, except for the upstream of the Jing River Basin and Wei River Basin in Region V, in which the increase is larger. In other subregions, the increase is generally less than 20%, and in the upstream of Region I, the Wuding River Basin in Region IV, and Region VIII, the increase is more than 30%. R10mm (Figure 20) has increased by less than 0.5d in the upstream of Region III and by more than 2d in the downstream of Regions VI and VII. Meanwhile, CDD has decreased by more than 2d, except for the Wei River Basin, Jing River Basin, and Luo River Basin in Region V, as well as a portion of Region VI. The overall increase of SDII (Figure 22) is less than 2d, with increasing from the upstream to the downstream, and the increase of most regions is less than 10%.
Figure 17

Changes in RX1day under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 17

Changes in RX1day under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 18

Changes in RX5day under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 18

Changes in RX5day under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 19

Changes in R95p under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 19

Changes in R95p under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 20

Changes in R10mm under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 20

Changes in R10mm under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 21

Changes in CDD under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 21

Changes in CDD under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 22

Changes in SDII under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 22

Changes in SDII under the SSP2-4.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal

Most GCMs produce projection results that align with the multi-model median projection results. However, some models exhibit different behaviors, for example, the projection results of INM–CM4–8 and INM–CM5–0 are opposite to other GCMs. The projections of other indices except for CDD projected by INM–CM4–8 and INM–CM5–0 show negative biases in the downstream of Region I, Huangshui River Basin of Region II, Dahei River Basin near Region III, and Fen River Basin of Region V. The results differ from the simulation results of most models.

Overall, there is an increasing trend in extreme precipitation changes from the west to the east. Extreme precipitation indices change greatly in Region IV and the downstream of Regions V, VII, and VIII. This is especially true for the Wuding River Basin in Region IV and parts of Region V. The Jing River Basin and Luo River Basin in Region V have relatively minor changes (Figures 21 and 22).

The spatial distribution changes in indices under the SSP5-8.5 scenario are generally consistent with those of the SSP2-4.5 scenario, but there are some differences (Figures 2328). Compared to the SSP2-4.5 scenario, the SSP5-8.5 scenario shows greater increases in RX1day, RX5day, and SDII. In addition, there is a slight increase in R95p and essentially similar increases in R10mm and CDD. Regarding subregions, only RX1day and R95p slightly decrease in Region VII, while RX1day and SDII remain essentially unchanged in Region I. All other subregions exhibit varying degrees of improvement in the changes in spatial distribution of indices.
Figure 23

Changes in RX1day under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 23

Changes in RX1day under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 24

Changes in RX5day under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 24

Changes in RX5day under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 25

Changes in R95p under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 25

Changes in R95p under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 26

Changes in R10mm under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 26

Changes in R10mm under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 27

Changes in CDD under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 27

Changes in CDD under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal
Figure 28

Changes in SDII under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Figure 28

Changes in SDII under the SSP5-8.5 scenario from 2021 to 2050 relative to 1981 to 2010.

Close modal

Although the increase in most indices is greater in the MED, the change in the range of a single model is different. For example, in the case of RX1day, compared to the SSP2-4.5 scenario, the CMCC–ESM2 increases less in the SSP5-8.5 scenario and the CanESM5 increases more, especially in Region I where the increase is very pronounced.

CMIP6 GCMs have differences in simulating extreme precipitation indices. Our study found that most GCMs performed poorly in the spatiotemporal simulation of R95p and R10mm, which aligns with the findings of Lei et al. (2023). Due to the complex topography of the YRB, the low resolution of GCMs makes it difficult to simulate the changes in extreme precipitation thresholds. You & Ting (2023) pointed out that improving the resolution of the models could better simulate extreme precipitation, particularly in regions with complex topography. However, it does not mean that the higher resolution, the better the GCMs simulation, as Xiao et al. (2023a) showed that some low-resolution models may have better performance in simulating extreme climate events. Therefore, the resolution of the GCMs does not entirely reflect their simulation performance but also needs to consider the model's parameterization scheme, boundary conditions, and other relevant considerations.

The different altitudes may lead to different performances of GCMs in the YRB when simulating extreme precipitation indices. Ombadi et al. (2023) found that extreme precipitation events at high altitudes were anticipated to intensify by 15% for every Celsius degree increase in temperature, and the increase in extreme precipitation at high altitudes was much greater than average. Therefore, it is probable that there will be a greater increase in extreme precipitation in the future for Region I, located in the northeastern part of the Tibetan Plateau at higher altitudes, compared to Region VI, situated in the plains. In addition, Zhang & Zhou (2019) showed that the monsoon region experiences the most severe extreme precipitation. The YRB is located in the northern part of the East Asian sea–land monsoon region, with the western portion of the midstream and upstream of the YRB also affected by the plateau monsoon. Consequently, extreme precipitation is expected to differ in various regions.

The BCC–CSM2–MR and EC–Earth3–Veg have great spatial simulation capability, while the CMCC–ESM2 and FGOALS–g3 have strong temporal simulation capability, which is consistent with the findings of Tebaldi et al. (2015). Wu et al. (2021) concluded that the BCC–CSM2–MR has improved the global temperature and precipitation climate distributions, atmospheric radiation, and oceanic heat balance, among others, and the model has greatly enhanced the simulation ability of the annual mean precipitation climate distribution in China. Shi et al. (2022) showed that FGOALS–g3 had better simulation performance, and the innovative model boasts improved atmospheric composition resolution, as well as enhanced modeling of atmospheric physical processes and more.

The multimodel ensemble can improve future projection accuracy, and the multimodel median ensemble method can reduce the influence of a few outliers, which is a commonly used ensemble method (Srivastava et al. 2020; Moradian et al. 2023). Certain models use the same parameterization process or belong to the same institution, which leads to nonindependence and correlation between models, leading to similarity problems in the simulation results of some models (Xiao et al. 2023b). Therefore, the ensemble method based on model independence is also an issue that we need to pay attention to in our future research.

The extreme precipitation indices except CDD in the YRB would like to increase from 2021 to 2050 compared with 1981 to 2010 under the SSP2-4.5 and SSP5-8.5 scenarios, and the trend of the extreme precipitation indices is consistent with the finding of Ayugi et al. (2021). In addition, it was found that the spatial trend of extreme precipitation change amplitude is generally increasing from west to east. It is projected that extreme precipitation will become more frequent in the YRB in the future, compared to its incidence in recent years. Meanwhile, Zhu et al. (2021) also showed that the temporal distribution of precipitation in the YRB will become more heterogeneous in the future, especially under the high SSP scenario.

The increase in extreme precipitation in the YRB in the future has implications for water resources, agriculture, and infrastructure. The probability of heavy rainfall and flooding disasters increased as the annual frequency of extreme precipitation events increased (Li et al. 2023). Moreover, extreme precipitation can impact agricultural production by affecting soil moisture and causing flooding on farmland (Long et al. 2022; Fu et al. 2023). In addition, extreme precipitation can lead to changes in water and sediment (Xu et al. 2021), which can affect integrated watershed management and adversely affect infrastructure (Carnacina et al. 2019) within the basin. Therefore, it is essential to improve the forecasting and early warning capabilities of extreme climate events. Simultaneously, the management and deployment of water resources should be strengthened, ensuring their effective utilization.

In this study, we evaluate the spatiotemporal simulation capability of six extreme precipitation indices in the YRB and eight subregions using observations and 23 CMIP6 GCMs, and project the changes of extreme precipitation from 2020 to 2050 relative to 1981 to 2010 under the SSP2-4.5 and SSP5-8.5 scenarios, with the following main conclusions:

  • (1)

    The overall spatial biases of the six extreme precipitation indices are 15.3% (RX1day), 21.04% (RX5day), 47.96% (R95p), 5.66d (R10mm), 18.91d (CDD), and 16.55% (SDII). RX1day, CDD, and SDII exhibit negative biases in 69.6, 99.9, and 74.5% of the total number of basin grids, respectively. Conversely, RX5day, R95p, and R10mm have positive biases in more than 70% of the total number of grids in the basin. CDD exhibits negative biases in all subregions, and SDII exhibits positive biases only in Region I, but negative biases in the other regions. In contrast, R95p and R10mm show predominantly positive biases in all subregions except Regions III and VII, while RX1day and RX5day exhibit inconsistent performance across subregions.

  • (2)

    The GCMs can capture the temporal variability and spatial distribution of extreme values (RX1day and RX5day) and durations (CDD) well (the IVS less than 0.191 and the TSS greater than 0.8), while the spatiotemporal simulation of superthreshold indices (R95p and R10mm) is relatively poor (the IVS greater than 0.2 and the TSS less than 0.8) and can capture the temporal variability of the intensity index (SDII) temporal variability but cannot simulate the spatial distribution well. CMIP6 GCMs perform better in the spatiotemporal simulation in Regions III and VII. Specifically, CMCC–ESM2 and FGOALS–g3 demonstrate superior temporal variability of indices. In addition, BCC–CSM2–MR and EC–Earth3–Veg display better spatial simulation.

  • (3)

    The extreme precipitation indices would increase in the YRB from 2021 to 2050 relative to 1981 to 2010 under the SSP2-4.5 scenario, except for the CDD, which decreases by 2.1d. R95p experiences a more significant increase of 30.3%. Under the SSP5-8.5 scenario, the temporal variation and spatial distribution of extreme precipitation indices are consistent with that of SSP2-4.5 scenario, but with more significant variations. The overall spatial trend of extreme precipitation change is gradually increasing from west to east, with RX1day, RX5day, and R95p locally exceeding 20% from Hekou Town to Longmen (Region Ⅳ) and below Huayuankou (Region Ⅶ). The risk of extreme precipitation may further increase in the future, especially in Regions III, IV, and VIII.

This work was supported by the Key Scientific and Technological Project of Henan Province, China (Grant No. 222102320286), Science and Technology Research and Development Program Joint Fund Project of Henan Province (Grant No. 232103810102), the Research Fund of Key Laboratory of Water Management and Water Security for Yellow River Basin, Ministry of Water Resources (under construction) (Grant No. 2023–SYSJJ–04), and National Key Research and Development Program project (Grant No. 2023YFC3006603).

The authors declare there is no conflict.

All relevant data are available from an online repository or repositories: http://data.cma.cn and https://esgf-node.llnl.gov/projects/esgf-llnl.

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