Uncertainty in Projection of Climate Extremes: A Comparison of CMIP5 and CMIP6

CMIP5与CMIP6极端气候预测不确定性对比分析

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  • Corresponding author: Jie CHEN, jiechen@whu.edu.cn
  • Funds:

    Supported by the National Key Research and Development Program of China (2017YFA0603704), National Natural Science Foundation of China (51779176), and China 111 Project (B18037)

  • doi: 10.1007/s13351-021-1012-3

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  • Climate projections by global climate models (GCMs) are subject to considerable and multi-source uncertainties. This study aims to compare the uncertainty in projection of precipitation and temperature extremes between Coupled Model Intercomparison Project (CMIP) phase 5 (CMIP5) and phase 6 (CMIP6), using 24 GCMs forced by 3 emission scenarios in each phase of CMIP. In this study, the total uncertainty (T) of climate projections is decomposed into the greenhouse gas emission scenario uncertainty (S, mean inter-scenario variance of the signals over all the models), GCM uncertainty (M, mean inter-model variance of signals over all emission scenarios), and internal climate variability uncertainty (V, variance in noises over all models, emission scenarios, and projection lead times); namely, T = S + M + V. The results of analysis demonstrate that the magnitudes of S, M, and T present similarly increasing trends over the 21st century. The magnitudes of S, M, V, and T in CMIP6 are 0.94–0.96, 1.38–2.07, 1.04–1.69, and 1.20–1.93 times as high as those in CMIP5. Both CMIP5 and CMIP6 exhibit similar spatial variation patterns of uncertainties and similar ranks of contributions from different sources of uncertainties. The uncertainty for precipitation is lower in midlatitudes and parts of the equatorial region, but higher in low latitudes and the polar region. The uncertainty for temperature is higher over land areas than oceans, and higher in the Northern Hemisphere than the Southern Hemisphere. For precipitation, T is mainly determined by M and V in the early 21st century, by M and S at the end of the 21st century; and the turning point will appear in the 2070s. For temperature, T is dominated by M in the early 21st century, and by S at the end of the 21st century, with the turning point occuring in the 2060s. The relative contributions of S to T in CMIP6 (12.5%–14.3% for precipitation and 31.6%–36.2% for temperature) are lower than those in CMIP5 (15.1%–17.5% for precipitation and 38.6%–43.8% for temperature). By contrast, the relative contributions of M in CMIP6 (50.6%–59.8% for precipitation and 59.4%–60.3% for temperature) are higher than those in CMIP5 (47.5%–57.9% for precipitation and 51.7%–53.6% for temperature). The higher magnitude and relative contributions of M in CMIP6 indicate larger difference among projections of various GCMs. Therefore, more GCMs are needed to ensure the robustness of climate projections.
    全球气候模式(GCM)提供的气候预测存在相当大的、多源的不确定性。本研究基于24个GCMs在三种温室气体排放情景下的极端降雨与极端气温预测,对比了CMIP5与CMIP6极端气候预测的不确定性。气候预测的总不确定性(T)被分解为排放情景不确定性(S,不同排放情景下同一模式预测的不同)、GCM不确定性(M,相同排放情景下不同模式预测之间的不同)和气候内部变率不确定性(V,不同模式、排放情景和预测时段造成的预测信号噪音的不同),即T = S + M + V。分析结果表明,SMT的大小在21世纪表现出了相似的上升趋势;CMIP6中SMVT分别是CMIP5中的0.94–0.96, 1.38–2.07, 1.04–1.69, 及1.20–1.93倍;CMIP6表现出与CMIP5类似的不确定性空间分布特征,以及类似的不确定性贡献排序。降雨的不确定性通常在中纬度和赤道部分地区较低,而在低纬度与极地地区较高;气温的不确定性通常在陆地高于海洋、北半球高于南半球。对降雨而言,T在21世纪初期主要由MV决定,而在21世纪末期由MS决定,转折点出现在2075年左右。对气温而言,T在21世纪初期由M决定,而在21世纪末期由S决定,转折点出现在2065年左右。CMIP6中S贡献(降雨:12.5%–14.3%;气温:31.6%–36.2%)低于CMIP5(降雨:15.1%–17.5%;气温:38.6%–43.8%),但是CMIP6中M贡献(降雨:50.6%–59.8%;气温:59.4%–60.3%)高于CMIP5(降雨:47.5%–57.9%;气温:51.7%–53.6%)。CMIP6的M数值更大,相对贡献也更大,说明CMIP6中不同GCM预测的差异更大,因而需要使用更多的GCM以保证预测的可靠性。
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  • Fig. 1.  Global mean values of the extreme and mean precipitation indices of each GCM under each emission scenario (individual GCM), their multimodel and multiscenario ensemble mean (ensemble mean), and their upper and lower confidence limits (upper and lower confidence limits, which are the 95% and 5% quantiles of the global mean and annual mean values, respectively).

    Fig. 2.  As in Fig. 1, but for temperature.

    Fig. 3.  Global mean trends of uncertainty magnitudes for the extreme and mean precipitation indices simulated by GCMs in the CMIP5 and CMIP6 archives.

    Fig. 4.  As in Fig. 3, but for temperature.

    Fig. 5.  Global mean trends of uncertainty contributions for the extreme and mean precipitation indices simulated by GCMs in the CMIP5 and CMIP6 archives.

    Fig. 6.  As in Fig. 5, but for temperature.

    Fig. 7.  Spatial variability patterns of the mean greenhouse gas (GHG) and aerosol emission scenario uncertainty (S), global climate model (GCM) response uncertainty (M), internal climate variability uncertainty (V), and total uncertainty (T) magnitudes (%2) over the near and far future periods for the maximum 1-day precipitation amount (Rx1day), simulated by GCMs in the CMIP5 and CMIP6 archives.

    Fig. 8.  As in Fig. 7, but for the mean value of daily precipitation (Pm).

    Fig. 9.  Spatial variability patterns of the mean S, M, V, and T magnitudes (°C2) over the near and far future periods for the maximum value of daily maximum temperature (TXx) simulated by GCMs in the CMIP5 and CMIP6 archives.

    Fig. 10.  As in Fig. 9, but for the mean value of daily maximum temperature (TXm).

    Fig. 11.  Global mean trends of the signal-to-noise ratio (S/N) for extreme and mean precipitation and temperature indices simulated by GCMs in the CMIP5 and CMIP6 archives.

    Table 1.  Basic information regarding the 24 global climate models (GCMs) in the Coupled Model Intercomparison Project phase 5 (CMIP5; https://esgf-node.llnl.gov/projects/cmip5/) and phase 6 (CMIP6; https://esgf-node.llnl.gov/projects/cmip6/) archives

    InstitutionCMIP5 CMIP6
    Model nameMemberModel nameMember
    BCCBCC-CSM1.1r1i1p1BCC-CSM2-MRr1i1p1f1
    BNUBNU-ESMr1i1p1
    CASFGOALS-g3r1i1p1f1
    CCCMACESM1-CAM5r1i1p1
    CCCMACanESM2r1i1p1CanESM5r1i1p1f1
    CMCCCMCC-CM2-SR5r1i1p1f1
    CNRM-CERFACSCNRM-CM5r1i1p1CNRM-CM6-1r1i1p1f1
    CNRM-CERFACSCNRM-ESM2-1r1i1p1f1
    CSIROACCESS-ESM1-5r1i1p1f1
    CSIRO-ARCCSSACCESS-CM2r1i1p1f1
    CSIRO-QCCCECSIRO-Mk3.6.0r1i1p1
    ICHECEC-EARTHr8i1p1
    EC-Earth-ConsortiumEC-Earth3r1i1p1f1
    EC-Earth-ConsortiumEC-Earth3-Vegr1i1p1f1
    INMINM-CM4-8r1i1p1f1
    INMINM-CM5-0r1i1p1f1
    IPSLIPSL-CM5A-LRr1i1p1IPSL-CM6A-LRr1i1p1f1
    IPSLIPSL-CM5A-MRr1i1p1
    LASG-CESSFGOALS-g2r1i1p1
    MIROCMIROC5r1i1p1MIROC6r1i1p1f1
    MIROCMIROC-ESMr1i1p1MIROC-ES2Lr1i1p1f2
    MIROCMIROC-ESM-CHEMr1i1p1
    MOHCHadGEM2-ESr1i1p1HadGEM3-GC31-LLr1i1p1f3
    MOHCUKESM1-0-LLr1i1p1f2
    MPI-MMPI-ESM-LRr1i1p1MPI-ESM1-2-HRr1i1p1f1
    MPI-MMPI-ESM-MRr1i1p1MPI-ESM1-2-LRr1i1p1f1
    MRIMRI-CGCM3r1i1p1MRI-ESM2-0r1i1p1f1
    NCARCCSM4r1i1p1
    NCCNorESM1-Mr1i1p1NorESM2-LMr1i1p1f1
    NCCNorESM2-MMr1i1p1f1
    NIMR-KMAHadGEM2-AOr1i1p1
    NOAA-GFDLGFDL-CM3r1i1p1GFDL-ESM4r1i1p1f1
    NOAA-GFDLGFDL-ESM2Gr1i1p1
    NOAA-GFDLGFDL-ESM2Mr1i1p1
    NSF-DOE-NCARCESM1-CAM5r1i1p1
    NUISTNESM3r1i1p1f1
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Uncertainty in Projection of Climate Extremes: A Comparison of CMIP5 and CMIP6

    Corresponding author: Jie CHEN, jiechen@whu.edu.cn
  • 1. State Key Laboratory of Water Resources & Hydropower Engineering Science, Wuhan University, 299 Bayi Road, Wuchang District, Wuhan 430072
  • 2. Hubei Provincial Key Lab of Water System Science for Sponge City Construction, Wuhan University, Wuhan 430072
Funds: Supported by the National Key Research and Development Program of China (2017YFA0603704), National Natural Science Foundation of China (51779176), and China 111 Project (B18037)

Abstract: Climate projections by global climate models (GCMs) are subject to considerable and multi-source uncertainties. This study aims to compare the uncertainty in projection of precipitation and temperature extremes between Coupled Model Intercomparison Project (CMIP) phase 5 (CMIP5) and phase 6 (CMIP6), using 24 GCMs forced by 3 emission scenarios in each phase of CMIP. In this study, the total uncertainty (T) of climate projections is decomposed into the greenhouse gas emission scenario uncertainty (S, mean inter-scenario variance of the signals over all the models), GCM uncertainty (M, mean inter-model variance of signals over all emission scenarios), and internal climate variability uncertainty (V, variance in noises over all models, emission scenarios, and projection lead times); namely, T = S + M + V. The results of analysis demonstrate that the magnitudes of S, M, and T present similarly increasing trends over the 21st century. The magnitudes of S, M, V, and T in CMIP6 are 0.94–0.96, 1.38–2.07, 1.04–1.69, and 1.20–1.93 times as high as those in CMIP5. Both CMIP5 and CMIP6 exhibit similar spatial variation patterns of uncertainties and similar ranks of contributions from different sources of uncertainties. The uncertainty for precipitation is lower in midlatitudes and parts of the equatorial region, but higher in low latitudes and the polar region. The uncertainty for temperature is higher over land areas than oceans, and higher in the Northern Hemisphere than the Southern Hemisphere. For precipitation, T is mainly determined by M and V in the early 21st century, by M and S at the end of the 21st century; and the turning point will appear in the 2070s. For temperature, T is dominated by M in the early 21st century, and by S at the end of the 21st century, with the turning point occuring in the 2060s. The relative contributions of S to T in CMIP6 (12.5%–14.3% for precipitation and 31.6%–36.2% for temperature) are lower than those in CMIP5 (15.1%–17.5% for precipitation and 38.6%–43.8% for temperature). By contrast, the relative contributions of M in CMIP6 (50.6%–59.8% for precipitation and 59.4%–60.3% for temperature) are higher than those in CMIP5 (47.5%–57.9% for precipitation and 51.7%–53.6% for temperature). The higher magnitude and relative contributions of M in CMIP6 indicate larger difference among projections of various GCMs. Therefore, more GCMs are needed to ensure the robustness of climate projections.

CMIP5与CMIP6极端气候预测不确定性对比分析

全球气候模式(GCM)提供的气候预测存在相当大的、多源的不确定性。本研究基于24个GCMs在三种温室气体排放情景下的极端降雨与极端气温预测,对比了CMIP5与CMIP6极端气候预测的不确定性。气候预测的总不确定性(T)被分解为排放情景不确定性(S,不同排放情景下同一模式预测的不同)、GCM不确定性(M,相同排放情景下不同模式预测之间的不同)和气候内部变率不确定性(V,不同模式、排放情景和预测时段造成的预测信号噪音的不同),即T = S + M + V。分析结果表明,SMT的大小在21世纪表现出了相似的上升趋势;CMIP6中SMVT分别是CMIP5中的0.94–0.96, 1.38–2.07, 1.04–1.69, 及1.20–1.93倍;CMIP6表现出与CMIP5类似的不确定性空间分布特征,以及类似的不确定性贡献排序。降雨的不确定性通常在中纬度和赤道部分地区较低,而在低纬度与极地地区较高;气温的不确定性通常在陆地高于海洋、北半球高于南半球。对降雨而言,T在21世纪初期主要由MV决定,而在21世纪末期由MS决定,转折点出现在2075年左右。对气温而言,T在21世纪初期由M决定,而在21世纪末期由S决定,转折点出现在2065年左右。CMIP6中S贡献(降雨:12.5%–14.3%;气温:31.6%–36.2%)低于CMIP5(降雨:15.1%–17.5%;气温:38.6%–43.8%),但是CMIP6中M贡献(降雨:50.6%–59.8%;气温:59.4%–60.3%)高于CMIP5(降雨:47.5%–57.9%;气温:51.7%–53.6%)。CMIP6的M数值更大,相对贡献也更大,说明CMIP6中不同GCM预测的差异更大,因而需要使用更多的GCM以保证预测的可靠性。
1.   Introduction
2.   Data and methods
  • Since precipitation and temperature are the most highly scrutinized climate variables in climate change studies (IPCC, 2007, 2013), the uncertainties of precipitation and temperature projections were investigated in this study. In order to obtain a robust comparison, similar GCMs and emission scenarios in two CMIP archives were selected. Specifically, 24 GCMs were selected from each CMIP archive. The basic information for these GCMs is presented in Table 1. Even though the models selected from CMIP6 are not exactly the same as those selected from CMIP5, the use of 24 simulations can adequately represent the uncertainty related to climate models (Chen et al., 2016; Wang et al., 2018, 2020). GCMs in the CMIP5 archive were carried out based on the historical forcing for the period of 1850–2005, and on three GHG and aerosol emission scenarios (i.e., RCP2.6, RCP4.5, and RCP8.5) for the period of 2006–2100. GCMs in the CMIP6 archive were carried out based on the historical forcing for the period of 1850–2014, and on three GHG and aerosol emission scenarios (i.e., SSP1-2.6, SSP2-4.5, and SSP5-8.5) for the period of 2015–2100. The three emission scenarios in the CMIP6 archive are similar to those in the CMIP5 archive in terms of radiative forcing (Moss et al., 2010; Meinshausen et al., 2011; O’Neill et al., 2017). In particular, the RCP2.6/SSP1-2.6, RCP4.5/SSP2-4.5, and RCP8.5/SSP5-8.5 emission scenarios represent the low, middle, and high concentration scenarios over the projection lead times, respectively. Although some of the models have several realizations of these simulations, only one realization was used for all GCMs.

    InstitutionCMIP5 CMIP6
    Model nameMemberModel nameMember
    BCCBCC-CSM1.1r1i1p1BCC-CSM2-MRr1i1p1f1
    BNUBNU-ESMr1i1p1
    CASFGOALS-g3r1i1p1f1
    CCCMACESM1-CAM5r1i1p1
    CCCMACanESM2r1i1p1CanESM5r1i1p1f1
    CMCCCMCC-CM2-SR5r1i1p1f1
    CNRM-CERFACSCNRM-CM5r1i1p1CNRM-CM6-1r1i1p1f1
    CNRM-CERFACSCNRM-ESM2-1r1i1p1f1
    CSIROACCESS-ESM1-5r1i1p1f1
    CSIRO-ARCCSSACCESS-CM2r1i1p1f1
    CSIRO-QCCCECSIRO-Mk3.6.0r1i1p1
    ICHECEC-EARTHr8i1p1
    EC-Earth-ConsortiumEC-Earth3r1i1p1f1
    EC-Earth-ConsortiumEC-Earth3-Vegr1i1p1f1
    INMINM-CM4-8r1i1p1f1
    INMINM-CM5-0r1i1p1f1
    IPSLIPSL-CM5A-LRr1i1p1IPSL-CM6A-LRr1i1p1f1
    IPSLIPSL-CM5A-MRr1i1p1
    LASG-CESSFGOALS-g2r1i1p1
    MIROCMIROC5r1i1p1MIROC6r1i1p1f1
    MIROCMIROC-ESMr1i1p1MIROC-ES2Lr1i1p1f2
    MIROCMIROC-ESM-CHEMr1i1p1
    MOHCHadGEM2-ESr1i1p1HadGEM3-GC31-LLr1i1p1f3
    MOHCUKESM1-0-LLr1i1p1f2
    MPI-MMPI-ESM-LRr1i1p1MPI-ESM1-2-HRr1i1p1f1
    MPI-MMPI-ESM-MRr1i1p1MPI-ESM1-2-LRr1i1p1f1
    MRIMRI-CGCM3r1i1p1MRI-ESM2-0r1i1p1f1
    NCARCCSM4r1i1p1
    NCCNorESM1-Mr1i1p1NorESM2-LMr1i1p1f1
    NCCNorESM2-MMr1i1p1f1
    NIMR-KMAHadGEM2-AOr1i1p1
    NOAA-GFDLGFDL-CM3r1i1p1GFDL-ESM4r1i1p1f1
    NOAA-GFDLGFDL-ESM2Gr1i1p1
    NOAA-GFDLGFDL-ESM2Mr1i1p1
    NSF-DOE-NCARCESM1-CAM5r1i1p1
    NUISTNESM3r1i1p1f1

    Table 1.  Basic information regarding the 24 global climate models (GCMs) in the Coupled Model Intercomparison Project phase 5 (CMIP5; https://esgf-node.llnl.gov/projects/cmip5/) and phase 6 (CMIP6; https://esgf-node.llnl.gov/projects/cmip6/) archives

  • To estimate the uncertainties with regard to precipitation and temperature projections in terms of extremes, three precipitation indices including the maximum 1-day precipitation amount (Rx1day; mm), maximum consecutive 3-day precipitation amount (Rx3day; mm), and maximum consecutive 5-day precipitation amount (Rx5day; mm), and two temperature indices including the maxi-mum value of daily maximum temperature (TXx; °C) and minimum value of daily minimum temperature (TNn; °C) were calculated. These five indices were recommended by the Expert Team on Sector-Specific Climate Indices and are commonly used in extreme climate studies (Aguilar et al., 2005; Chu et al., 2010; Lee et al., 2012; Nakaegawa et al., 2014; Yao et al., 2020). To compare the uncertainties of climate extremes and climate means, three mean indices including the mean value of daily precipitation (Pm; mm day–1), mean value of daily maximum temperature (TXm; °C), and mean value of daily minimum temperature (TNm; °C) were also calculated. In total, eight indices were used in this study to analyze uncertainty. The eight indices were first individually calculated for each year at the GCM grid scale, and then interpolated into a common 2° longitude × 2° latitude grid by using the inverse distance weighted interpolation approach. The mean change (${\Delta _{s,m,y}}$) in each index between the 10-yr time slices of the future period (2020–2096) and the reference period (1971–2000) was calculated for each grid cell via Eqs. (1), (2) following the studies of Hawkins and Sutton (2009, 2011).

    Precipitation indices:

    $$\hspace{-40pt} {\Delta _{s,m,y}} = 100 \times \left(\dfrac{\displaystyle\sum\limits_{y \;=\; y \;-\; 5}^{y \;+\; 4} {{p_{s,m,y}}} }{\dfrac{1}{{30}} \times \displaystyle\sum\limits_{y \;=\; 1971}^{2000} {{p_{s,m,y}}} } - 1 \right)\text%. $$ (1)

    Temperature indices:

    $$\hspace{-40pt} {\Delta _{s,m,y}} = \displaystyle\sum\limits_{y \;=\; y \;-\; 5}^{y \;+\; 4} {{p_{s,m,y}}} - \dfrac{1}{{30}} \times \displaystyle\sum\limits_{y \;=\; 1971}^{2000} {{p_{s,m,y}}}, $$ (2)

    where s is the number of emission scenarios ($s = 1, \ldots,s' $), m is the number of GCMs ($m = 1, \ldots,m' $), y is the number of years ($y = 2020, \ldots,2096 $), and ${p_{s,m,y}}$ is the projection of precipitation or temperature indices for the sth scenario, mth GCM, and year of y.

    With the calculated mean change in each index, the uncertainty of ${\Delta _{s,m,y}}$ was then estimated and decomposed via the typical method of Hawkins and Sutton (2009, 2011). In other words, the uncertainty was estimated for each index over each grid cell. Although various methods have been proposed to estimate and decompose the uncertainties of climate projections (Yip et al., 2011; Hingray and Saïd, 2014; Evin et al., 2019; Zhuan et al., 2019), the method of Hawkins and Sutton (2009, 2011) is the most accepted one. Although the GCMs were weighted based on their abilities to simulate the global mean warming and historical precipitation changes in Hawkins and Sutton (2009, 2011), there is some controversy concerning whether the GCMs should be unequally weighted (Stainforth et al., 2007; Brekke et al., 2008; Chen et al., 2016; Wang et al., 2018). In addition, the weights of GCMs may be largely affected by the methods used to calculate them and the precipitation and temperature datasets used. Therefore, all GCMs in this paper are equally weighted. The procedures to estimate the uncertainty are summarized as follows.

    (1) The mean change series of each GCM in response to each emission scenario was decomposed into the climate change signal series and noise series by means of first-order (for precipitation indices) or fourth-order (for temperature indices) polynomial fitting.

    $$\hspace{-52pt} {\Delta _{s,m,y}} = {i_{s,m,y}} + {\varepsilon _{s,m,y}}, $$ (3)

    where ${i_{s,m,y}}$ and ${\varepsilon _{s,m,y}}$ are respectively the climate change signal series and noise series separated from ${\Delta _{s,m,y}}$.

    (2) The means of ${i_{s,m,y}}$ and ${\varepsilon _{s,m,y}}$ were calculated by using Eqs. (4)–(7).

    $$\hspace{-56pt} {{\overline i_{s,*,y}}} = \dfrac{1}{{{m^\prime }}}\displaystyle\sum\limits_{m \;=\; 1}^{{m^\prime }} {{i_{s,m,y}}} , $$ (4)
    $$\hspace{-58pt} { {{\overline i_{*,m,y}}} = \dfrac{1}{{{s^\prime }}}\displaystyle\sum\limits_{s \;=\; 1}^{{s^\prime }} {{i_{s,m,y}}} }, $$ (5)
    $$\hspace{-20pt} {{\overline i_{*,*,y}}} = \dfrac{1}{{{s^\prime } \times {m^\prime }}}\displaystyle\sum\limits_{s \;=\; 1}^{{s^\prime }} {\displaystyle\sum\limits_{m \;=\; 1}^{{m^\prime }} {{i_{s,m,y}}} }, $$ (6)
    $$\begin{split} {{\bar \varepsilon_{*,*,*}}} = & \dfrac{1}{{{s^\prime } \times {m^\prime } \times (2096 - 2020 + 1)}}\\ & \cdot \displaystyle\sum\limits_{s \;=\; 1}^{{s^\prime }} {\displaystyle\sum\limits_{m \;=\; 1}^{{m^\prime }} {\displaystyle\sum\limits_{y \;=\; 2020}^{2096} {{\varepsilon _{s,m,y}}} } } . \end{split} $$ (7)

    (3) The mean inter-scenario variance of the signals over all the models was defined as the scenario uncertainty. The mean inter-model variance of signals over all emission scenarios was defined as the model uncertainty. The variance in noise over all models, emission scenarios, and projection lead times was defined as the internal climate variability uncertainty. The sum of the three uncertainty components was defined as the total uncertainty.

    $$\hspace{-34pt} {{S_y} = \dfrac{1}{{{s^\prime }}}\displaystyle\sum\limits_{s \;=\; 1}^{{s^\prime }} {{{\left({ {{\overline i_{s,*,y}}} - {{\overline i_{*,*,y}}} } \right)}^2}} }, $$ (8)
    $$\hspace{-30pt} {{M_y} = \dfrac{1}{{{m^\prime }}}\displaystyle\sum\limits_{m \;=\; 1}^{{m^\prime }} {{{\left({{{\overline i_{*,m,y}}} - {{\overline i_{*,*,y}}} } \right)}^2}} }, $$ (9)
    $$\begin{aligned}[b] {V_y} = & \dfrac{1}{{{s^\prime } \times {m^\prime } \times (2096 - 2020 + 1)}}\\ & \cdot \displaystyle\sum\limits_{s \;=\; 1}^{{s^\prime }} {\displaystyle\sum\limits_{m \;=\; 1}^{{m^\prime }} {\displaystyle\sum\limits_{y \;=\; 2020}^{2096} {{{\left({{\varepsilon _{s,m,y}} - {{{\bar \varepsilon} _{*,*,*}}} } \right)}^2}} } } , \end{aligned} $$ (10)
    $$ \hspace{-70pt} {T_y} = {S_y} + {M_y} + {V_y}.$$ (11)

    To investigate the influence of uncertainties on climate change signals, the signal-to-noise ratio (S/N) calculated by Eq. (12) was used in this study (Hawkins and Sutton, 2009).

    $$\hspace{-60pt} (S/{N)_y} = \frac{{ {{\overline i_{*,*,y}}} }}{{1.65 \times \sqrt {{T_y}} }}. $$ (12)
3.   Results and discussion
  • Since the trends and spreads of the precipitation and temperature projections are closely related to the levels of uncertainty, they were evaluated before estimating the uncertainties. The global mean values of the extreme and mean precipitation indices (Rx1day, Rx3day, Rx5day, and Pm) of all GCMs under all emission scenarios are presented in Fig. 1. Their upper and lower confidence limits, as well as the multimodel and multiscenario ensemble mean, are also highlighted in Fig. 1. The results for extreme and mean temperature indices (TXx, TXm, TNn, and TNm) are presented in Fig. 2. The results reveal that all precipitation and temperature indices simulated by GCMs in the CMIP5 and CMIP6 archives increase along with the projection lead times, indicating that the world as a whole is likely to be warmer and wetter in the future. This finding is consistent with that of the IPCC Fifth Assessment Report (IPCC, 2013). However, the fractions of increases relative to the spreads are smaller for precipitation indices, whereas they are larger for temperature indices. For both precipitation and temperature projections, the fractions of increases relative to the spreads for extreme indices are smaller than those for mean indices. This phenomenon is particularly obvious for precipitation projections simulated by GCMs in the CMIP5 archive, but is not so obvious for temperature projections simulated by GCMs in the CMIP6 archive.

    Figure 1.  Global mean values of the extreme and mean precipitation indices of each GCM under each emission scenario (individual GCM), their multimodel and multiscenario ensemble mean (ensemble mean), and their upper and lower confidence limits (upper and lower confidence limits, which are the 95% and 5% quantiles of the global mean and annual mean values, respectively).

    Figure 2.  As in Fig. 1, but for temperature.

    In terms of the difference between the two CMIP archives, the precipitation and temperature projections simulated by GCMs in the CMIP6 archive are generally higher than those simulated by GCMs in the CMIP5 archive, which is generally consistent with previous studies (Chen et al., 2020; Tokarska et al., 2020). Specifically, the mean values of precipitation indices in the CMIP6 archive are 1.02–1.15 times as high as those in the CMIP5 archive. The mean values of temperature indices in the CMIP6 archive are higher than those in the CMIP5 archive, with the mean differences ranging between 0.16 and 0.57°C. In addition, the increasing ratios of extreme and mean precipitation and temperature indices in the CMIP6 archive are 1.12–1.18 times as high as those in the CMIP5 archive. However, situations in terms of spreads are index-dependent. More specifically, the spreads of Rx1day and Pm in the CMIP6 archive are both 1.06 times as high as those in the CMIP5 archive. However, the spreads of Rx3day and Rx5day in the CMIP6 archive are only 0.79 and 0.83 times as high as those in the CMIP5 archive, respectively. The spread of TXx in the CMIP6 archive is 0.95 times that in the CMIP5 archive, whereas the spreads of TNn, TXm, and TNm in the CMIP6 archive are 1.12–1.32 times as high as those in the CMIP5 archive.

  • The global mean trends of the uncertainty magnitudes for the extreme and mean precipitation indices simulated by GCMs in the CMIP5 and CMIP6 archives are presented in Fig. 3. The results for the extreme and mean temperature indices are presented in Fig. 4. The results show that the magnitudes of the scenario uncertainty (S), model uncertainty (M), and total uncertainty (T) all increase along with the projection lead times for both extreme and mean precipitation and temperature indices in the two CMIP archives. These results are generally consistent with previous studies using GCM projections from the CMIP5 archive (Hawkins and Sutton, 2009, 2011; Yip et al., 2011; Zhuan et al., 2019; Lehner et al., 2020; Zhou et al., 2020a, b). The relative increases (the ratio between the increase in the uncertainty magnitude and the initial uncertainty magnitude) in the magnitude of uncertainty are index-dependent and uncertainty-component-dependent. The relative increases in T magnitudes are lower for precipitation indices than for temperature indices. They are lower for extreme indices than for mean indices. More specifically, the relative increases in T magnitudes over the projection lead times (2020–2096) are 2.12–3.40 for extreme precipitation indices while 4.05–6.32 for mean precipitation index, and 9.69–14.20 for extreme temperature indices while 14.64–21.64 for mean temperature indices. The situations for S magnitudes are similar to those for T magnitudes. The situations for M magnitudes, however, are somewhat different. Specifically, the relative increases in M magnitudes for extreme indices of precipitation and temperature are generally lower than those for mean indices, except for TXx and TXm in the CMIP6 archive. The relative increases in M magnitudes for extreme precipitation indices are lower than those for extreme temperature indices. However, the relative increase in M magnitude for the mean precipitation index is lower than those for the mean temperature indices in the CMIP5 archive, but is higher in the CMIP6 archive. Since the internal climate variability uncertainty (V) was assumed to be constant, the relative increases in V magnitudes are not investigated.

    Figure 3.  Global mean trends of uncertainty magnitudes for the extreme and mean precipitation indices simulated by GCMs in the CMIP5 and CMIP6 archives.

    Figure 4.  As in Fig. 3, but for temperature.

    The difference in uncertainty magnitudes between the two CMIP archives is non-negligible. The uncertainty magnitudes of the extreme and mean precipitation and temperature indices in the CMIP6 archive are generally higher than those in the CMIP5 archive, except for the S magnitudes of TXm and TNm. In particular, the T, M, and V magnitudes in the CMIP6 archive are respectively 1.20–1.93, 1.38–2.07, and 1.04–1.69 times as high as those in the CMIP5 archive. The S magnitudes in the CMIP6 archive are 1.31–1.56 times for the extreme precipitation indices, 1.78 times for the mean precipitation index, 1.03–1.05 times for the extreme temperature indices, but 0.94–0.96 times for the mean temperature indices of those in the CMIP5 archive. It should be noted that the large difference in uncertainty magnitudes for the mean precipitation index (Pm) between the two CMIP archives is partly due to the fact that the change in Pm between the future period and reference period is characterized by a relative change [calculated by Eq. (1)]. In some desert regions (the Sahara for instance), however, the Pm in the reference period may be extremely small. Thus, a small increase in Pm in the future period can lead to a large relative change and furthermore to large uncertainty magnitudes. The T, S, M, and V magnitudes in the CMIP6 archive are 1.69–2.07 times as high as those in the CMIP5 archive when characterizing the difference in Pm between the future period and reference period based on relative change, whereas they are only 1.11–1.28 times when characterizing the difference based on absolute change [calculated by Eq. (2)]. In addition, the T magnitude of Pm is lower than those of extreme precipitation indices in the CMIP5 archive but is obviously higher in the CMIP6 archive. However, for both CMIP archives, the T magnitude of TXx is lower than that of TXm, and the T magnitude of TNn is higher than that of TNm. The main conclusions in terms of M magnitudes are similar to those drawn by Lehner et al. (2020). However, the magnitudes of V are not the same for these two studies. This may be because the different numbers of GCMs in the CMIP5 and CMIP6 archives were used in Lehner et al. (2020). In other words, the fewer GCMs in the CMIP6 archive result in the slightly smaller V magnitudes compared to the CMIP5 archive.

    The global mean trends of the relative contributions of uncertainty components to total uncertainty are presented in Fig. 5 for the extreme and mean precipitation indices simulated by GCMs in the two CMIP archives. The results for the extreme and mean temperature indices are presented in Fig. 6. The results show that the two CMIP archives show similar results in ranking the relative contributions of the different uncertainty sources. More specifically, T is mainly dominated by V and M in the early 21st century for precipitation indices, but it is mainly dominated by M and S at the end of the 21st century, and the turning points appear in the 2070s. Similar conclusions were also drawn from other studies using CMIP5 models (Hawkins and Sutton, 2011; Yip et al., 2011; Zhuan et al., 2019; Lehner et al., 2020; Zhou et al., 2020a, b). For temperature indices, however, T is mainly dominated by M in the early 21st century, but it is dominated by S at the end of the 21st century, with the turning points appearing in the 2060s, which is also consistent with other studies (Hawkins and Sutton, 2009; Yip et al., 2011; Zhuan et al., 2019; Lehner et al., 2020; Zhou et al., 2020b). For both precipitation and temperature indices, the relative contributions of S show consistently increasing trends, whereas the relative contributions of V show the opposite. The relative contributions of M are relatively stable for precipitation indices, but they decrease rapidly for temperature indices. The relative contributions of V are non-negligible for precipitation indices for all the projection lead times, and are non-negligible for temperature indices in the early 21st century but very small at the end of the 21st century. In addition, the relative contributions of S are lower for precipitation indices and higher for temperature indices, and the mean differences range between 17.28% and 28.71%. However, an opposite pattern can be observed for V contributions, with the mean differences ranging between 17.27% and 32.18%. The M contributions of precipitation indices are lower in the early 21st century while higher at the end of the 21st century than those of temperature indices.

    Figure 5.  Global mean trends of uncertainty contributions for the extreme and mean precipitation indices simulated by GCMs in the CMIP5 and CMIP6 archives.

    Figure 6.  As in Fig. 5, but for temperature.

    The difference in uncertainty contributions between the extreme and mean indices is obvious, as well. Specifically, the relative contributions of M to extreme precipitation indices are lower than that for the mean precipitation index, with the mean differences ranging between 8.11% and 10.36%. The relative contributions of S to extreme temperature indices are lower than those for the mean temperature indices, with the mean differences ranging between 3.46% and 5.88%. The relative contributions of V to the extreme precipitation and temperature indices are lower than those for the mean precipitation and temperature indices, with the mean differences ranging between 8.34% and 9.75% for precipitation indices and between 3.56% and 5.02% for temperature indices.

    In terms of the difference in uncertainty contributions between the two CMIP archives, the relative contributions of S in the CMIP6 archive are lower than those in the CMIP5 archive for extreme and mean precipitation and temperature indices, with the mean differences ranging between 2.32% and 3.25% for precipitation indices and between 5.99% and 7.48% for temperature indices. This is mainly due to the fact that the difference in radiative forcing in the future period (2020–2096) projected in the CMIP6 archive is slightly smaller than that in the CMIP5 archive. This may be because the emission scenarios in the two CMIP archives are not exactly consistent (Moss et al., 2010; Meinshausen et al., 2011; van Vuuren et al., 2011; O’Neill et al., 2017; Hewitt et al., 2020). In addition, the beginning of the projection period is not exactly the same for the two CMIP archives. Specifically, the projection period of CMIP5 starts in 2006, whereas that of CMIP6 starts in 2015. The opposite pattern is observed for M contributions, with the mean differences ranging between 1.93% and 3.07% for precipitation indices and between 6.64% and 8.10% for temperature indices. The difference in precipitation may be caused by the fact that the projected increase in precipitation in the CMIP6 archive is stronger than that in the CMIP5 archive (Chen et al., 2020), and partly due to the reduction in model biases in the CMIP6 models (Xin et al., 2020). The difference in temperature may be because some GCMs in the CMIP6 archive project a warmer climate (Tokarska et al., 2020). More fundamentally, it may be attributed to the fact that the positive cloud feedbacks of some GCMs in the CMIP6 archive are stronger than those in the CMIP5 archive, resulting from the decreasing extratropical low cloud coverage and albedo (Zelinka et al., 2020). Similar conclusions in terms of S and M contributions were also drawn in Lehner et al. (2020). The difference in the V contributions between the CMIP5 and CMIP6 archives is very small.

  • To investigate the spatial variability patterns of uncertainties for different future periods, two future periods (i.e., 2021–2050 and 2061–2090) were selected to represent the near and far futures. The spatial variability patterns of the mean S, M, V, and T magnitudes over the two future periods are presented in Figs. 710 for Rx1day, Pm, TXx, and TXm in the two CMIP archives. The results for Rx3day, Rx5day, TNn, and TNm are presented in Figs. S1–4. The results show that the uncertainty distribution patterns of the precipitation and temperature projections are similar between the CMIP5 and CMIP6 archives as well as between the extreme indices and mean indices.

    Figure 7.  Spatial variability patterns of the mean greenhouse gas (GHG) and aerosol emission scenario uncertainty (S), global climate model (GCM) response uncertainty (M), internal climate variability uncertainty (V), and total uncertainty (T) magnitudes (%2) over the near and far future periods for the maximum 1-day precipitation amount (Rx1day), simulated by GCMs in the CMIP5 and CMIP6 archives.

    Figure 8.  As in Fig. 7, but for the mean value of daily precipitation (Pm).

    Figure 9.  Spatial variability patterns of the mean S, M, V, and T magnitudes (°C2) over the near and far future periods for the maximum value of daily maximum temperature (TXx) simulated by GCMs in the CMIP5 and CMIP6 archives.

    Figure 10.  As in Fig. 9, but for the mean value of daily maximum temperature (TXm).

    In terms of the uncertainty magnitudes of extreme and mean precipitation indices in the two CMIP archives (Figs. 7, 8; S1, 2; see online supplements), the spatial variabilities of S, M, V, and T are similar. Generally, over the near and far futures, S, M, V, and T magnitudes are lower at the midlatitudes and in parts of the equatorial band, whereas they are higher at the low latitudes and in polar regions. In addition, T is the highest for the south of the Sahara, showing the main contribution from M in the near and far future periods. For both the CMIP5 and CMIP6 archives, S increases rapidly from the near future to the far future, whereas the increases in M are relatively slow. However, the increases in uncertainty magnitudes do not alter their general spatial patterns.

    In terms of the uncertainty magnitudes of extreme and mean temperature indices in the two CMIP archives (Figs. 9, 10; S3, 4), the spatial variabilities of S, M, V, and T are also similar. S, M, V, and T are higher for land areas than for oceans, and are higher for the Northern Hemisphere than for the Southern Hemisphere. In addition, T is the highest for the Arctic, mainly dominated by M in the near future and by M and S in the far future. In the near future, V and S make a minor contribution to T, and the minor contribution comes from V in the far future. The temporal variability of S is the highest. The increases in S and M over the two future periods are prominent but do not alter the general spatial patterns.

  • The influence of uncertainties on climate change signals is quantized by S/N. The global mean trends of S/N for the extreme and mean precipitation and temperature indices simulated by GCMs in the CMIP5 and CMIP6 archives are presented in Fig. 11. The results show that the S/N values initially increase and finally decrease along with the projection lead times for all the indices and both CMIP archives. The turning points appear in the 2050s−2070s for precipitation indices, and in the 2030s−2040s for temperature indices. In addition, the S/N values in the two CMIP archives are lower for the precipitation indices and higher for the temperature indices, with a mean difference of 0.78, indicating that the influence of uncertainties on precipitation signals is larger than that on temperature signals. The S/N values in the CMIP6 archive are initially lower and finally higher than those in the CMIP5 archive, indicating that this influence in the CMIP6 archive is initially larger while finally smaller than that in the CMIP5 archive. The intersection points of the S/N curves in the two CMIP archives appear in the 2040s−2050s for precipitation indices, and in the 2040s for temperature indices. The mean differences in S/N between the two CMIP archives are 0.01 before the intersection points and 0.02 after the intersection points for precipitation indices, and 0.11 before the intersection points and 0.07 after the intersection points for temperature indices, indicating that the difference in terms of the influence between the two CMIP archives is smaller for precipitation projections than for temperature projections. In addition, the S/N values of extreme precipitation indices are generally higher than that for the mean precipitation index in the two CMIP archives, and the mean difference is 0.08. However, the S/N values of the extreme temperature indices are lower than those for the mean temperature indices, with a mean difference of 0.10. In other words, the influence on extreme precipitation indices is smaller than mean precipitation index, whereas the opposite pattern is observed for temperature indices.

    Figure 11.  Global mean trends of the signal-to-noise ratio (S/N) for extreme and mean precipitation and temperature indices simulated by GCMs in the CMIP5 and CMIP6 archives.

  • A few methods have been proposed to estimate and decompose the uncertainties of climate projections. The method proposed by Hawkins and Sutton (2009, 2011) was used in this study due to its wide acceptance. In this study, the scenario uncertainty and model uncertainty were individually estimated, without taking into account the effect of their interaction. The interaction uncertainty between two or more components was taken into account in some studies [e.g., Yip et al. (2011)]. However, this method requires each climate model to have a number of ensemble members when estimating the internal climate variability, which is not usually available.

    A few methods have also been proposed to estimate the uncertainty of the internal climate variability. The method of Hawkins and Sutton (2009, 2011) was used in this study, assuming that the internal climate variability uncertainty is constant over time, which has been proven in some studies (Yip et al., 2011; Lehner et al., 2020; Lu et al., 2020). Some other studies (Schneider and Kinter III, 1994; Knutson et al., 2013; Olonscheck and Notz, 2017) estimated the internal climate variability by using preindustrial control simulations with constant external forcing. Single-model initial-condition large ensembles were also used to estimate the internal climate variability (Zhuan et al., 2019; Lehner et al., 2020; Zhou et al., 2020a). Even though various methods have been used, the overall trends and contributions of V are generally consistent (Yip et al., 2011; Lehner et al., 2020; Lu et al., 2020). In particular, the main conclusions of this study are generally consistent with other studies (Lehner et al., 2020). Therefore, the climate projection uncertainties calculated in this study can be considered robust, even though the values of uncertainty magnitudes and contributions may be slightly different from those of other studies.

4.   Conclusions
  • In this study, the uncertainties of extreme climate projections provided by the CMIP5 and CMIP6 archives were compared. Three extreme precipitation indices (Rx1day, Rx3day, and Rx5day), one mean precipitation index (Pm), two extreme temperature indices (TXx and TNn), and two mean temperature indices (TXm and TNm) were selected to represent the extreme and mean climate projections. The uncertainty was decomposed by using the typical method of Hawkins and Sutton (2009, 2011). The following conclusions can be drawn.

    (1) The S, M, and T magnitudes exhibit similar increasing trends during the 21st century for both the extreme and mean precipitation and temperature indices in the two CMIP archives, whereas the relative increases in these uncertainty magnitudes for extreme indices are generally 0.58 (0.36−1.09) times those for the mean indices. The uncertainty magnitudes (S, M, V, and T) in the CMIP6 archive are generally 1.41 (0.94−2.07) times as high as those in the CMIP5 archive.

    (2) Both the CMIP archives show similar results in terms of ranking the contributions of different sources of uncertainty. To be specific, T is mainly dominated by V and M in the early 21st century for precipitation indices, but by M and S at the end of the 21st century, with the turning points appearing in the 2070s. For temperature indices, however, T is mainly dominated by M in the early 21st century, but by S at the end of the 21st century, with the turning points appearing in the 2060s. The relative contributions of M to extreme precipitation indices are lower than that to the mean precipitation index, with the mean differences ranging between 8.11% and 10.36%. The relative contributions of S to extreme temperature indices are lower than those to mean temperature indices, with the mean differences ranging between 3.46% and 5.88%. The relative contributions of V to extreme indices are lower than those to mean indices, and the mean differences are 9.10% (8.34%−9.75%) for precipitation indices and 4.24% (3.56%−5.02%) for temperature indices. The relative contributions of S in the CMIP6 archive are lower than those in the CMIP5 archive, and the mean differences are 2.73% (2.32%−3.25%) for precipitation indices and 7.03% (5.99%−7.64%) for temperature indices. The opposite pattern is observed for the relative contributions of M, with the mean differences being 2.61% (1.93%−3.07%) for precipitation indices and 7.45% (6.64%−8.10%) for temperature indices.

    (3) The spatial patterns of uncertainties are similar between the CMIP5 and CMIP6 archives, as well as between the extreme indices and mean indices. For precipitation indices, the uncertainty magnitudes are lower at the midlatitudes and parts of the equatorial band, and higher at the low latitudes and polar regions. For temperature indices, the uncertainty magnitudes are higher for land areas than for oceans, and higher for the Northern Hemisphere than for the Southern Hemisphere.

    (4) The influence of uncertainties on climate change signals in the CMIP6 archive is initially larger and finally smaller than that in the CMIP5 archive with the turning points appearing in the 2040s–2050s for precipitation indices and in the 2040s for temperature indices. This influence on extreme precipitation indices is smaller than that on mean precipitation indices, whereas the opposite pattern is observed for temperature indices.

    Acknowledgments. The authors would like to acknowledge the contribution of the World Climate Research Program Working Group on Coupled Modeling and that of climate modeling groups for making available their respective climate model outputs.

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