Before we analyze the global mean or zonal mean of the variables, the monthly variables are regridded to 1∘ lat–long grids with the first-order conservative remapping method through NetCDF Operators (NCO) version 4.8.1. CMIP6 models project an overall higher warming with a larger intermodel spread for different forcing levels, particularly for the high-emission SSP5-8.5 scenario, compared to the corresponding CMIP5 future climate projections e.g.,. These changes are likely due to the different experimental designs between CMIP5 and CMIP6 experiments and the higher climate sensitivities in a subset of the CMIP6 models . To adopt the CMIP6 models as the reference, this study analyzes these CMIP6 model runs of which both the historical simulation and SSP5-8.5 simulation are available at the time of writing. Only one ensemble member (r1i1p1f1) of the CMIP6 model runs is included in this study.

Figure  presents the time evolution of annual global mean near-surface air temperature (Tair) anomalies and surface precipitation rate anomalies with respect to 1850–1869 from E3SMv1.0 along with the other CMIP6 models. As shown in , E3SMv1.0 simulated global mean Tair anomalies during the historical period demonstrate a prolonged cooling after 1950 and then a rapid warming around 2000. E3SMv1.0 is at the lower end of the model range during the prolonged cooling period (Fig. a). However, the Tair anomalies in E3SMv1.0 catch up and reach the middle range of the CMIP6 model spread by the end of the historical run (year 2014) due to the rapid warming. This rapid warming in E3SMv1.0 continues in the SSP5-8.5 experiment at a speed faster than that of most of CMIP6 models. Near the end of the 21st century, E3SMv1.0 projects one of the warmest Tair anomalies at ∼8 K, consistent with the overly strong TCR and ECS. The global mean precipitation rate is driven by the energy balance between the radiative cooling and the latent heating ; the global mean change in precipitation is mainly set by the Clausius–Clapeyron relation as an approximately 7 % K−1 increase in atmospheric water vapor content e.g.,. As a result, the time evolution of the global mean surface precipitation rate (Fig. b) is strongly correlated with the Tair trend with larger interannual fluctuations. The median and mean values of the Pearson correlation coefficients for Tair and precipitation anomalies from the CMIP6 models and the E3SMv1.0 simulations are higher than 0.96. The global mean precipitation in E3SMv1.0 increases by >0.3 mm d-1 from the end of the historical period (year 2014) to the end of the future projection (year 2099). The spread of the E3SMv1.0 ensemble members is much smaller than the CMIP6 intermodel spread throughout the historical and future climate projection periods for both Tair and surface precipitation rate anomalies. Treating the available CMIP6 models as a reference, we sort the global mean Tair changes between the years 2070–2099 and 1850–1869 in the SSP5-8.5 simulations from the available CMIP6 models (blue bars) and E3SMv1.0 ensemble members (red bars) from the lowest warming to the highest warming (Fig. c). The global mean Tair changes in the E3SMv1.0 ensemble members are comparable to the CMIP6 models with the highest warming.

The global distribution of the Tair and surface precipitation change in E3SMv1.0 resembles the ensemble average pattern from the ScenarioMIP participant models for the SSP5-8.5 scenario based on the global maps of Tair (Fig. e) and surface precipitation rate (Fig. e) for the years 2070–2099 from the SSP5-8.5 simulations and those for the years 1985–2014 from the historical simulations. The global pattern of Tair change between 2070–2099 and 1985–2014 reveals a polar amplification of surface warming and interhemispheric asymmetric warming. Along the same latitude bands, the surface warming over the continents is generally higher than that of the ocean. The strongest surface warming occurs over the Arctic with a magnitude >15 ∘C.

The global mean precipitation increases by ∼10% due to the warmer climate. In the tropics, the rain bands over the Intertropical Convergence Zone (ITCZ) are all strengthened, while the precipitation in the Amazon and Central America is reduced (Fig. e). Furthermore, the ITCZ over the central and eastern Pacific Ocean becomes narrower, whereas it shifts northward over the Indian and Atlantic oceans with more precipitation over the monsoon regions. In the midlatitudes and high latitudes, the precipitation over both the North American and the Eurasian continents increases in the SSP5-8.5 simulations except that in the Mediterranean region. The major drying regions include the Mediterranean region, Central America, the Amazon region, southern Africa, and western Australia. The drying regions experience more severe precipitation reduction during boreal summer (JJA, Fig. e) than boreal winter (DJF, Fig. e). As shown in Fig. c, E3SMv1.0 has a double-ITCZ bias that is persistent in generations of CMIP models . The double-ITCZ bias is found to have a large impact on the projection of precipitation and tropical climate change. Specifically, the projected precipitation change tends to be proportional to the precipitation bias in the double-ITCZ regions . Furthermore, the drying regions projected by E3SMv1.0 also show dry biases in the historical runs based on the Global Precipitation Climatology Project v2.2 observational estimate for the years 1979–2014 . The magnitudes of the midlatitude continental summer warm biases in the present climate in CMIP5 models were found to be closely linked to the projected climate change amplification in the local warming . Due to the strong land–atmosphere coupling, we speculate that the magnitude of the precipitation bias in the current climate simulation also links to the projected climate change amplification in the drying signal, which needs further multi-model investigation in order to be confirmed in a future study.

As for the response of the atmospheric circulation, the pattern change in the annual zonal wind at 250 hPa between the years 2070–2099 and 1985–2014 (Fig. a, c, e) indicates that the subtropical edges of the Hadley cell in both hemispheres shift poleward in the warmer climate. The poleward shift is larger in the Southern Hemisphere, which is also seen in CMIP5 and CMIP6 models e.g.,and references therein. Meanwhile, the boreal winter (DJF) precipitation change (Fig. e) shows a sign of the poleward shift of the storm tracks especially in the North Pacific Ocean and the North Atlantic Ocean, which is projected by most general circulation models (GCMs) .

Besides the global mean Tair anomaly and surface precipitation rate, we analyze the time evolution of zonal mean Tair and shortwave cloud radiative effect (SWCRE) to characterize the regional temperature changes and cloud responses simulated by E3SMv1.0 in the historical and future climate simulations. We also analyze the CMIP6 models with low (0–20th percentiles) and median warming (40–60th percentiles) from Fig. c to better illustrate the model intercomparison of these regional patterns. Figure a shows the time evolution of the zonal mean Tair from all E3SMv1.0 ensemble members, revealing a rapid warming in the Arctic and a clear warming asymmetry between the Northern Hemisphere and the Southern Hemisphere in the SSP5-8.5 simulations. To better detect the regional pattern in Tair changes from the historical simulations and the future climate simulations, we calculated the local Tair anomalies (Fig. b) by subtracting the zonal mean Tair for the years 1850–1869 from the time evolution of the zonal mean Tair (i.e., Fig. a). The local Tair anomalies reveal a continuous enhanced cooling in the Northern Hemisphere (10–60∘ N) lasting from 1870 to 2000 in E3SMv1.0 (Fig. b), which is the main contributor to the prolonged cooling shown in the global mean Tair anomaly (Fig. a). The time evolution of SWCRE (Fig. a and b) indicates that this continuous enhanced cooling in the Northern Hemisphere before 2000 corresponds clearly to an enhanced negative SWCRE over the same region. The local changes in Tair and SWCRE from CMIP6 models with low and median warming have no signal of such a continuous cooling in the Northern Hemisphere in the historical simulations (Fig. c and d).

After the year 2000, Tair in E3SMv1.0 and other CMIP6 models starts increasing, especially over the polar regions. E3SMv1.0 shows a clearly faster warming over the Arctics than CMIP6 models with low and median warming, indicating a stronger polar amplification in E3SMv1.0. The stronger polar amplification tends to be associated with lower sea-ice concentrations, the weaker poleward ocean heat transport at high latitudes, and increases in cloud cover over the polar regions . Indeed, the negative changes in SWCRE over the polar regions, an indicator of the increased polar cloud amount, in E3SMv1.0 are stronger and are enhanced faster than CMIP6 models with low and median warming after the year 2000 (Fig. ). However, the regions with a strong negative SWCRE changes in E3SMv1.0 are confined to higher latitudes in both hemispheres. Especially after the year 2050, the region with a strong negative SWCRE change in the Northern Hemisphere retreats to latitudes higher than 60∘ N in E3SMv1.0, while the weakening of the negative SWCRE (i.e., a positive change in SWCRE in Fig. ) becomes much stronger and broader in low latitudes and midlatitudes compared with the CMIP6 models with low and median warming. Overall, the clouds in E3SMv1.0 show a slightly stronger but more confined negative SW feedback in the high latitudes, while a much stronger and broader positive SW feedback in the low latitudes and midlatitudes relative to CMIP6 models with low and median warming. Compared with CMIP6 models with medium warming, while the E3SMv1.0 simulated negative SWCRE change in the Arctic is stronger than -12 W m-2 after 2050, the positive SWCRE change in both Northern Hemisphere and Southern Hemisphere low latitudes and midlatitudes increases after 2050 and the difference exceeds 8 W m-2 by 2100 (Fig. b and d). Meanwhile, the near-surface warming across the low latitudes, midlatitudes, and high latitudes after 2050 (Fig. b) indicates that the strong warming in E3SMv1.0 is primarily due to a stronger polar amplification and stronger positive cloud feedbacks from decreasing extratropical low cloud coverage and albedo . Throughout the historical period and the future climate projection period, E3SMv1.0 produces an interhemispheric asymmetric cooling between 1900 and 2000, followed by an interhemispheric asymmetric warming until the end of the 21st century, both of which are closely linked to the cloud responses, especially in the Northern Hemisphere. A recent study found that CMIP6 models with a more positive cloud feedback tend to have a stronger cooling effect from aerosol–cloud interactions. The CMIP6 models with a weak aerosol indirect effect and a low cloud feedback are more consistent with the observed warming asymmetry during the mid–late 20th century. We will discuss the impact of the strong aerosol indirect effect in E3SMv1.0 on the future climate projection in Sect. .

The time evolution of sea surface temperature (SST) anomaly reference to the mean over 1870–1899 (Fig. a) in the historical and SSP5-8.5 simulations is consistent with that of Tair in Fig. a. The simulated SST anomaly in E3SMv1.0 historical simulations shows relatively weaker warming among the CMIP6 models. It agrees with the Hadley-NOAA/OI merged data product red pretty well, except slightly cooler than the data during 1950–1990, mostly occurring in the Northern Hemisphere . In the SSP5-8.5 simulations, however, E3SMv1.0 projects a much faster warming than most of other CMIP6 models. By the end of the year 2099, SST in E3SMv1.0 increases by ∼ 5 ∘C compared to the present state, the strongest warming among the CMIP6 models. Note that the CMIP6 models used in Sect.  are slightly different from the CMIP6 models in this section due to the availability of model output varying between the atmospheric variables, ocean, and sea-ice variables.

Together with the SST anomaly, we plot the simulated annual mean Atlantic meridional overturning circulation (AMOC) in E3SMv1.0 and other CMIP6 models in Fig. b, measured by the maximum streamfunction at 26.5∘N below 500 m depth, consistent with the observation at the RAPID array . The mean AMOC simulated in the E3SMv1.0 historical ensemble (∼ 11 Sv) is weaker than the observed mean (16.9 Sv) and the ensemble mean of CMIP6 models . It is also at the lower end of the CMIP6 ensemble for the future SSP5-8.5 climate projection. Possible reasons have been discussed in , including the spurious diapycnal mixing, poor representation of the Nordic overflows, and critical passageways transporting freshwater from the Arctic, as well as excess simulated sea ice in the Labrador Sea in E3SMv1.0.

Interestingly, E3SMv1.0 also exhibits the slowest weakening of AMOC among all the CMIP6 models available in the SSP5-8.5 experiment. This is better seen in Fig. , which shows the changes in AMOC and SST between the mean states at the end of the historical and SSP5-8.5 simulations (averaged over 1985–2014 and 2070–2099, respectively). Consistent with , a weaker simulated AMOC is often associated with a weaker change in AMOC in response to the SSP5-8.5 forcing (Fig. a), and this often corresponds to a faster warming (Fig. c). In addition to the comparison of E3SMv1.0 and CESM2 explored in their study, here we show that this relation also seems to be valid for a group of other CMIP6 models. We note that the simulated mean and change of SST do not seem to show a clear linear relationship as seen in the simulated AMOC, presumably due to the fact that SST is controlled by multiple factors happening at different temporal and spatial scales (e.g., air–sea coupling, ocean mixing). But it is interesting to see a linear relation between the changes in SST and changes in AMOC even within the ensemble of a particular model (e.g., IPSL-CM6A-LR, MPI-ESM1.2-HR, and MPI-ESM1.2-LR in Fig. c).

The ocean has a larger thermal inertia than the atmosphere so there is a delay in the seasons in the ocean as compared to the atmosphere. It is conventional to use January–February–March for boreal winter and July–August–September for boreal summer to describe the seasonal variation of ocean variables. Figure a and b show the changes in the ensemble averaged SST in E3SMv1.0 between the period of 2070–2099 and 1985–2014 in the boreal winter (January, February, March) and summer (July, August, September). We see a warming in excess of 2 ∘C almost everywhere in the global ocean, especially in the high latitudes in boreal summer, when the changes in SST can reach over 10 ∘C locally. This is consistent with the strong polar amplification described in Sect. . Correspondingly, there is a strong freshening in the Arctic in both seasons as illustrated by the changes in the sea surface salinity (SSS) in Fig. a and b. This is a result of the melting sea ice in the Arctic due to the polar amplification of global warming. The overall decrease in SSS in the North Atlantic and increase in SST in the South Atlantic may be related to the weakening of the AMOC. The mixed layer generally shoals due to an overall warming throughout the global ocean. This is especially true for the winter mixed layer depth (MLD), e.g., the Kuroshio and Gulf Stream extensions in boreal winter and the Southern Ocean in boreal summer in Fig. . Figure a and b show the ensemble averaged spatial patterns of the simulated AMOC in historical simulations and the changes in SSP5-8.5 simulations. In addition to the latitude and depth of the maximum AMOC, strong weakening also occurs at high latitudes around 50∘ N. This may be linked to the melting of sea ice and weakening of deep water formation in the high-latitude North Atlantic.

The time series of total sea-ice area in March and September for E3SMv1.0 and CMIP6 models are shown in Fig. , together with the observed sea-ice area from the National Snow and Ice Data Center Sea Ice Index version 3 . The simulated sea-ice area in E3SMv1.0 historical simulations agree reasonably well with the observation in September but is significantly larger in the Northern Hemisphere and smaller in the Southern Hemisphere in March. In general, however, the simulated sea-ice area in E3SMv1.0 is within the spread of CMIP6 models in historical simulations. Under the SSP5-8.5 forcing scenario, the projected Northern Hemisphere sea-ice reduction in E3SMv1.0 is faster than most of CMIP6 models with large seasonal variability. While it is comparable with other CMIP6 models in March at the beginning of the SSP5-8.5 simulations (Fig. a), the sea ice in September is less than that in most of CMIP6 models and rapidly deceases to zero after the year 2040 (Fig. b). The Northern Hemisphere sea ice in March rapidly decreases around 2050 and reduces to near zero after 2080. The Southern Hemisphere (SH) sea-ice reduction is within the wide model spread for both March and September (Fig. c and d). Analyses conducted during the development of E3SMv2.0 have shown that an accounting error in the exchange of frazil ice mass between the ocean and the atmosphere largely contributes to this strong reduction.

Runoff is one of the most representative variables to reflect the land climatology. The spatial patterns of the mean annual runoff for the years 1985–2014 and 2070–2099 (Fig. a and b) are generally similar. The patterns are consistent with the DECK simulation results by E3SMv1.0, which had noticeable wet biases over the arid regions such as Australia and the western United States and dry biases over the northern South America . The runoff change in the SSP5-8.5 simulations (Fig. c) agrees with previous climate change studies e.g., and other CMIP6 model predictions e.g., with decreased runoff in the Mediterranean region, southern Africa, southern North America, northern South America, and Australia, and increased runoff in high latitudes of the Northern Hemisphere, central Africa, as well as southern to eastern Asia. Similar to other land surface models, annual runoff predicted by ELMv1 is highly correlated with the precipitation changes (Fig. ). The Pearson correlation coefficients between the mean annual precipitation and mean annual runoff are 0.9 and 0.89 over the historical period (1985–2014) and future projection period (2070–2099), respectively, suggesting a high similarity in terms of the spatial pattern between the two variables. The time series of annual mean precipitation and runoff anomaly for the entire historical and future projection period (1850–2099) has a correlation coefficient of 0.99, indicating a strong correlation in terms of temporal variation between precipitation and runoff. Given that the spatial distribution and variation of the runoff are highly consistent with those in precipitation for E3SMv1.0, it is fair to presume that the position of E3SMv1.0 simulated global runoff in the CMIP6 ensemble spread is also similar to the global mean precipitation in the ensemble spread (Fig. b).

In the absence of all other external forcing, the global mean Tair increases monotonically in the GHG-only historical experiment (Fig. ). Unlike in the all-forcing historical experiment, the Tair and SWCRE changes show no signal of cooling and enhanced cooling effect in the Northern Hemisphere (Fig. a and b) over the regions with a clearly higher aerosol load in the all-forcing historical experiment, a significant portion of which is sulfate aerosol (Fig. e and f). The net cloud radiative effect (CRE) shows an extra strong cooling effect up to -5 W m-2 over the previously mentioned region and period in the all-forcing historical experiment (Fig. d). This further confirms that the overly strong ERFaero, including the strong aerosol–cloud interactions, causes the prolonged cooling between 1960 and 2000 and the delayed warming after 2000 in the E3SMv1.0 historical experiment. Near the end of the historical simulations, Tair is warmer almost everywhere in the GHG-only historical experiment, especially over the Arctic (Fig. c vs. d, Fig. b vs. Fig. a).

In the SSP5-8.5 GHG-only experiment, although Tair increases with a spatial pattern similar to the SSP5-8.5 all-forcing experiment, the warming slows down after 2000 compared to the SSP5-8.5 all-forcing experiment based on the zonal mean Tair trend, suggesting that the decline of aerosol load in the future climate projection period leads to a transient faster warming in the 21st century (Fig. e and f). Also, the polar amplification is weaker in the GHG-only experiment (Fig. c). Note that the delayed warming between 1970 and 2000 in the all-forcing experiment relative to the GHG-only experiment is statistically significant based on a two-sided t test, while the faster warming after 2000 is not statistically significant in many regions. The global distribution of the warming between 2070–2099 and 1985–2014 from the GHG-only experiment also shows weaker warming in the Northern Hemisphere than the all-forcing experiment with a poleward increased difference (Fig. e–f). The difference in the net CRE between the all-forcing experiment and the GHG-only experiment during the future climate project period (Fig. d) may contribute to the weaker polar amplification in the GHG-only experiment. Previous studies detected rapid near-term warming through the 21st century driven by decrease in aerosols in CMIP5 models e.g.,, whereas aerosol emission reduction caused gradual warming in other CMIP5 studies e.g.,. Further simulations and analyses will be needed to fully understand the mechanism underlining the accelerated warming in the Northern Hemisphere, which is beyond the GHG-induced warming.

During the historical period, the global precipitation in the GHG-only simulations is larger than that in the all-forcing simulations by 0.13 mm d-1 (∼4%) at the end of the historical period (Fig. b). The global maps (Fig. c and d) indicate that the GHG-only experiment is overall similar to the all-forcing experiment at the end of the historical period with changes resembling the SSP5-8.5 experiment except for the smaller magnitude, i.e., slightly increased precipitation in the tropics and the midlatitude oceans. The changes in precipitation rate between the future climate projection and the historical period from the all-forcing experiment and GHG-only experiment (Fig. e and f) suggest that the magnitude of the precipitation change is larger in the all-forcing experiment especially for the drying regions, e.g., the central and eastern south Pacific, the south Indian Ocean, Australia, and the Amazon region. Meanwhile, the changes over regions with increased precipitation in the future climate projection are generally larger in the all-forcing experiment than that in the GHG-only experiment, e.g., the northern Indian Ocean, the Indian peninsula, and the Tibetan Plateau, midlatitude Eurasia, and the coastal regions of the northern Pacific. One exception is that the drying signal along the tropical eastern Pacific to Central America is stronger in the GHG-only experiment.

Panels (c) and (d) in Figs. – show the differences of the SSP5-8.5 projected changes in SST, SSS, and MLD between the all-forcing experiment and the GHG-only experiment. A two-sided t test with the null hypothesis that the GHG-only experiment and all-forcing experiment give identical ensemble mean was conducted. Dots in the maps highlight regions where the p value of the t test is smaller than 5 %, and therefore the difference is significant as compared to the variability among ensemble members.

The spatial distribution of the SSP5-8.5 projected warming, especially the polar amplification in boreal summer (Fig. b), is mostly similar between the all-forcing experiment and GHG-only experiment (not shown), with a significantly stronger magnitude in the all-forcing experiment (see the similar spatial patterns between panels c and a, and between d and b). This suggests that while GHG emissions dominate the changes in oceanic mean SST, other forcings may also be important in amplifying the changes. Similar remarks could also be made for the simulated SSS (Fig. ), though the difference of the simulated SSS between all-forcing and GHG-only experiments are more complicated. The changes in SSS are likely driven by atmospheric forcing, which is indeed evident in the bottom panel of Fig.  that the projected reduction of precipitation in the all-forcing experiment is stronger than that in the GHG-only experiment over this region. The difference in the simulated MLD (Fig. ) between all-forcing and GHG-only experiments is less obvious, especially in regions of strong currents (e.g., the Kuroshio and Gulf Stream extensions and the Southern Ocean) where the variability among ensemble members is large. We also note that the strength of the AMOC is slightly weaker in the GHG-only experiment during most of the period (Figs.  and ). This could be due to the warmer Tair (Fig. ), which would decrease North Atlantic surface density, thus, reducing deep convection and AMOC. The SSP5-8.5 all-forcing and GHG-only experiments converge toward the end of the simulations. Given that the AMOC is so weak in both experiments, this is likely nearing an “off” state.

The sea-ice extent for the SSP5-8.5 all-forcing experiment and the SSP5-8.5 GHG-only experiment is shown in the black and gray lines respectively in Fig. . Overall, the trends are similar, which is not surprising given the strong warming in both experiments. However, we do note that the Northern Hemisphere sea-ice extent in September in the GHG-only experiment decreases rapidly since 1950 and drops to nearly zero around 1990, likely a result of a much warmer state in the GHG-only experiment. The Northern Hemisphere sea-ice extent in March in the GHG-only experiment is also lower than the all-forcing experiment since around 1950, but decreases at a similar rate as the all-forcing simulation between around 2010 and 2050. It decreases rapidly starting from approximately 2050, whereas the sea-ice extent in the all-forcing experiment remains larger for another decade before dropping rapidly. Note that the warming SST in the high-latitude North Atlantic in boreal winter is actually smaller in the GHG-only experiment than in the all-forcing experiment (Fig. c). Further, the difference in the net CRE between the all-forcing experiment and the GHG-only experiment (Fig. d) over the polar regions suggests more warming from cloud radiative effect for the all-forcing experiment, which is counter to what is observed in Fig. . Therefore, the earlier decrease in Northern Hemisphere sea-ice extent in March in the GHG-only experiment may also be driven by the warmer mean climate state in the GHG-only experiments (e.g., Figs.  and ). The Southern Hemisphere sea-ice extent in both March and September is similar between the all-forcing experiment and the GHG-only experiment and only slightly smaller in the latter due to the warmer mean climate state.

The land responses were first examined by comparing the runoff distributions driven by all forcing and GHG-only forcing (Fig. ). No obvious differences can be identified between the runoff during either historical or future period. However, a noticeable deviation can be seen in the historical to future changes (i.e., between Fig. c and f). Specifically, in southern North America, southern Africa, and eastern Asia, GHG-only forcing leads to a greater decline in future runoff than all forcing condition, while in central Africa, the GHG-only forcing tends to have less runoff increase in the future than the all forcing condition. To further examine the time evolution of runoff responses in the SSP5-8.5 all-forcing experiment and the SSP5-8.5 GHG-only experiment, we applied the two-sample Kolmogorov–Smirnov (K-S) test on the annual mean runoff at grid-cell level. The two-sample K-S test has been widely applied in climate studies e.g., to examine whether two data samples are from a same distribution by comparing their empirical cumulative distribution functions (eCDFs). The null hypothesis (H0) is that the values of two data sets are from the same continuous distribution, which can be rejected at a significant level (α) if 1Dm,n>i(α)m+nm×n, where (m,n) are the sample sizes of the two samples; (Dm,n) is the distance between the eCDFs of the two samples; (i(α)) is the inverse of the Kolmogorov distribution at (α). The smaller (Dm,n), the more similarity between the to eCDFs. In this study, the K-S test was conducted for mean annual runoff at every land grid cell between the SSP5-8.5 all-forcing experiment and GHG-only experiment with (α=0.01). Similar to previous sections for other climate components, we selected two 30-year periods to represent historical (1985–2014) and future (2070–2099) conditions. In the following context we will use letter R to indicate H0 was rejected, meaning the two samples (i.e., runoff from the all-forcing experiment and GHG-only experiment) are from different distributions; and letter F to indicate H0 was fail to reject, meaning the two samples are from the same distribution. Two representative pixels were picked to further demonstrate the changes in runoff time series as well as the eCDFs for the two different directions of changing (Fig.  for F to R, and Fig.  for R to F).

The global distribution of the K-S test results for the historical period (Fig. a) were F in most areas but R in Greenland, Australia, central and northwest of North America, and eastern Asia. For the future climate projection period (Fig. b), the F area was generally expanded, indicating the difference in local runoff enlarges in the future climate projection experiments. Note that, some areas turn from R to F, such as Greenland, Australia, and Alaska, meaning that the time evolution of the local runoff from the all-forcing experiment and GHG-only experiment become closer to each other during the future climate projection period. The difference in local runoff during both time periods will contribute to the difference in the projected runoff change between the SSP5-8.5 all-forcing experiment and the GHG-only experiment (Fig. c and f). Therefore, the regions with F in either period (Fig. a and b) tend to have notable differences in the projected runoff changes shown between Fig. c and f.

The difference between the K-S test results (Fig. c) clearly shows the regions with a switch in runoff changes from the historical period to the future climate projection period, where K-S test results changed from R to F (i.e., purple regions in Fig. c). We also noticed that the K-S test results in some areas, such as central Africa, changed from F to R which is opposite to the general trend. Overall, about 14 % of the global area changed the results from F to R (orange color) and 26 % area changed from R to F (purple color) nearly doubled. This suggests that the runoff distributions from the SSP5-8.5 all-forcing experiment and GHG-only experiment tend to be more similar during the future period than during the historical period, implying that the GHG emission plays a dominant role among all forcings in terms of runoff for the future climate projection period. Instead of investigating changes in annual mean (Fig. c and f), K-S tests focus on the distributional changes and thus provide additional information associated with systematic alteration in the time series. One limitation of our current annual scale runoff analysis is that it did not fully address the snow dynamic changes, which are mostly associated with seasonal shifts in runoff due to changes in snow accumulation and melting processes, as well as snow versus rain partitioning of the precipitation . Therefore, to better understand the contribution of forcings on the runoff changes, seasonal runoff analysis will be needed in the future studies.