Changes in extreme temperature over China when global warming stabilized at 1.5 °C and 2.0 °C

The 1.5 °C global warming target proposed by the Paris Agreement has raised worldwide attention and inspired numerous studies to assess corresponding climate changes for different regions of the world. But CMIP5 models based on Representative Concentration Pathways (RCP) are ‘transient simulations’ and cannot reflect the response of climate warming stabilized at 1.5 °C. The current work presents an assessment of extreme temperature changes in China with simulations from ‘Half a degree Additional warming, Prognosis and Projected Impacts’ (HAPPI) project specially conceived for global warming levels stabilized at 1.5 °C and 2.0 °C. When global warming stabilizes at 1.5 °C/2.0 °C, the areal-mean temperature for whole China increases by about 0.94 °C/1.59 °C (relative to present period, taken from 2006–2015). Notable increase regions are mainly found in Northwest and Northeast-North China, but warm spell duration increases mostly in Southeast China. The effect of the additional 0.5 °C warming is particularly investigated and compared between the transient and stabilized simulations. Changes of mean and extreme temperature are larger in transient simulations than in stabilized simulations. The uncertainty range is also narrower in stabilized simulations. Under stabilized global warming scenario, extreme hot event with return period of 100 years in the present climate becomes event occurring every 4.79 (1.5 °C warming level) and 1.56 years (2.0 °C warming level), extreme cold event with return period of 10 years becomes event occurring every 67 years under 1.5 °C warming and is unlikely to occur under 2.0 °C warming. For geographic distribution, the occurrence probabilities of extreme (hot and cold) events mainly change in the Tibetan Plateau, and the extreme cold events also change in Northeast and Southeast China.


Data and Methods
Data. The HAPPI datasets that we downloaded are the 3 simulations of the Tier-1 experiment: (1) present-day climate (2006-2015); (2) 1.5 °C warming level (relative to pre-industrial) for which the actual warming is about 0.7 °C if present-day is taken as reference; (3) 2.0 °C warming level (relative to pre-industrial) for which the actual warming is about 1.2 °C compared to present-day. The detailed experimental protocol can be found in Mitchell et al. 19 . Our analysis is performed on daily mean, minimum and maximum surface air temperature from CanAM4, ECHAM6-3-LR, MIROC5 and NorESM1-HAPPI models contributing to HAPPI (as shown in Table 1). Relevant diagnoses, including calculation of extreme indices, are performed on their native grids to achieve the highest accuracy possible. But to facilitate operations such as data visualization or areal average, indices calculated from different models with different resolutions are re-gridded to a common 1° × 1° grid with a bilinear interpolation scheme.
In order to assess eventual differences between transient and stabilized simulations for the half-a-degree additional warming, we also use datasets under RCP4.5 scenario from 15 models in CMIP5 (as shown in Table 2). A single member (r1i1p1) is used for each model, and the 1.5 °C/2.0 °C global warming period under transient simulations is selected as an 11-year period centered on the time of 1.5 °C/2.0 °C global warming targets, as shown in Shi et al. 15 . The same data manipulation strategy as for HAPPI is used here. That is, relevant diagnoses and indices are calculated at the native grid of each model, and final results are re-gridded to the 1° × 1° grid to facilitate a fair comparison with HAPPI. However, it is to be noted that due to different states in CMIP5 and HAPPI for their own references, they can't be compared directly. But it is fair and meaningful to compare them when considering the additional 0.5 °C warming from 1.5 to 2.0 °C.

Methods. Extreme indices.
We use four extreme temperature indices following the recommendation of the Expert Team on Climate Change Detection and Indices (ETCCDI) 28 , namely annual maximum temperature (TXx), annual minimum temperature (TNn), warm spell duration index (WSDI) and frost days (FD). The definition of these indices is shown in Table 3.
And the multi-model ensemble mean (general mean) is: We can demonstrate that the total variance of x(m, n) is the sum of internal (inter-member) variability σ N 2 and models' spread (inter-model variability) σ M 2 , calculable as:   www.nature.com/scientificreports www.nature.com/scientificreports/ Probability ratio. To assess change of occurrence probabilities of extreme events in the future warmer world, we use the concept of Probability Ratio (PR) between the two probabilities of the event in future (p 1 ) and in present day (p 0 ): It represents how much the occurrence probability of a present-day extreme event changes in a future warmer climate [31][32][33] .

Results
Changes in mean and extreme temperature. Changes of annual-mean temperature over China under 1.5 °C and 2 °C global warming levels are shown in Fig. 1a,b for geographic distributions and in Fig. 1d 5,15,34 . For the half-a-degree additional warming, the geographic distribution is shown in Fig. 1c, while the areal average (yellow bars) is shown in Fig. 1d which also adds that from transient simulations (blue bar). Under the additional warming of 0.5 °C, the mean temperature increases mostly in Northwest and Northeast China by more than 0.7 °C. The mean increases are 0.65 °C (0.5-0.8 °C) and 0.78 °C (0.62-0.94 °C) for stabilized and transient simulations respectively. The difference between them is statistically significant according to a two-sample Kolmogorov-Smirnov (K-S) test (p < 0.05). The K-S test is a non-parametric test, suitable for extreme indices which generally show non-Gaussian distribution characteristics 35,36 . Figure 2 depicts changes of TXx and TNn at 1.5 °C and 2 °C warming levels, and in the case of half-a-degree additional warming in panels a, b and c respectively. The areal-mean over China increases by 0.93 °C (0.63-1.23 °C), 1.63 °C (1.33-1.93 °C) for 1.5 °C and 2 °C global warming, and the areal-mean TNn increases by 0.99 °C (0.43-1.55 °C) and 1.8 °C (1.25-2.35 °C) respectively, the magnitude of which is a little larger than TXx, indicating that global warming has more effect on extreme cold events, which is consistent with previous studies 5, 37,38 . The largest increase of TXx occurs over North China and the west of the Tibetan Plateau, with 1.1 °C/1.75 °C warmer under 1.5 °C/2.0 °C global warming levels; and TNn increases mostly in northern China, with more than 1.1 °C/2.0 °C warmer in Northwest and Northeast-North China, the spatial distribution in transient simulations also exhibits similarly 15,39 . The magnitudes of both TXx and TNn increase are higher than that for mean temperature in these areas, indicating that extreme temperature events are more sensitive to global warming.
As for the additional warming of 0.5 °C, the areal-mean TXx increases by 0.7 °C (0.43-0.97 °C) in stabilized simulations, while the increase is 0.85 °C (0.55-1.15 °C) in transient simulations (Fig. 2d); and areal-mean TNn increases by 0.81 °C (0.3-1.32 °C) and 0.94 °C (0.19-1.69 °C) respectively (Fig. 2h), it can be seen that the transient response is a little higher than the stabilized one. As shown in Fig. 2c, TXx increases more than 0.5 °C all over China under the additional half-a-degree warming, especially in Northwest China with a higher increase over 0.7 °C; TNn also has an increase of more than 0.5 °C in most regions of China, with the largest increase of more than 0.9 °C in part of Northwest and Northeast China (Fig. 2g). Figure 3 (three columns on the left) shows the projected changes of WSDI and FD under 1.5 °C/2 °C global warming levels and for the half-a-degree warming respectively, while areal-means are shown on the right with results from transient simulations added (blue bar). The areal-mean WSDI increases obviously with global warming, which is 9.9 days (7.1-12.7) and 18.1 days (14.3-21.8) respectively in 1.5 °C and 2.0 °C warmer world. There is an obvious decrease in areal-mean FD, which is 7.8 days (6.0-9.5) and 13.2 days (11.3-15.0), respectively. When considering the additional warming of 0.5 °C, the stabilized response of areal-mean WSDI shows an increase of  Fig. 1d with the yellow bars representing the change of areal-mean temperature of stabilized simulations, and the blue bar representing that of transient simulations; the error bars represent ranges of the mean ± one standard deviation (1σ), and the hatching indicates that there is significant difference between transient and stabilized simulations following a K-S test (p < 0.05). The maps were plotted with NCL 6.2.1 (free software; http://www.ncl.ucar.edu/). (2019) 9:14982 | https://doi.org/10.1038/s41598-019-50036-z www.nature.com/scientificreports www.nature.com/scientificreports/ 8.2 days (5.3-11.2), and the transient response is 9.5 days (5.3-13.8). The decrease of FD is 5.4 days (3.9-6.9) and 6.7 days (5.1-8.2) in the stabilized and transient simulations respectively. For both WSDI and FD, the response in transient simulations is larger than that of stabilized simulations (the last two bars in Fig. 3d,h).
It can be seen that, in terms of spatial distribution, WSDI increases mainly in the south of the Tibetan Plateau and in Southeast China, with an increase reaching 12 days, 21 days and 9 days for the 1.5 °C, 2.0 °C warming levels and the additional warming of 0.5 °C, respectively. These areas would suffer severe heat waves in the future. FD decreases in most parts of China, with the largest decrease in the Tibetan Plateau with values larger than 9 days/15 days under the 1.5 °C/2.0 °C warming levels, and larger than 7 days for the additional 0.5 °C warming, which implies that the Tibetan Plateau would be strongly affected by global warming. The transient response of WSDI and FD based on CMIP5 also exhibits similar response, as shown in Lang et al. 40 , Chen et al. 37 , Shi et al. 15 and Li et al. 41 .
When combining the stabilized response of extreme temperature in China to 1.5 °C/2.0 °C global warming with the results based on transient simulations in previous studies 11,15,41,42 , we can find that the areal-mean extreme temperatures over China show an increase larger than their global counterpart in both stabilized and transient simulations, and key regions are located in Northwest and Northeast-North China; while WSDI increases mostly in Southeast China, FD decreases mostly in the Tibetan Plateau. The results indicate that the response of these regions to global warming is robust, that is, these regions are truly more sensitive to global warming and will suffer severe effects, whether under which warming scenarios. Under the additional warming of 0.5 °C, the change of areal-mean temperature and all extreme indices are larger in transient simulations than that in stabilized simulations (the difference between them is significant in mean temperature, TXx and FD). Moreover, the uncertainty ranges of all areal-mean indices are narrower in stabilized simulations than that in  www.nature.com/scientificreports www.nature.com/scientificreports/ transient simulations, for the ensemble mean of HAPPI project (which has large ensemble members) can reduce the uncertainty caused by climate internal variability 22 . But it should be noted that in this study we only use 4 models of HAPPI project, but 15 models of CMIP5; moreover, the uncertainties of HAPPI results are composed of the spread among different models and different individuals, while the uncertainties of CMIP5 are only due to model spreads.
To quantify the two sources of uncertainty in relation to spreading among models and internal variability among different runs, we perform an analysis of variance for the temporal (whole duration of runs) and spatial (whole China) averages of different climate indices. Results are shown in Fig. 4. It can be seen that, under 1.5 °C (dark orange and light yellow) and 2.0 °C (dark red and light red) global warming, the mean temperature shows a larger inter-model spreading (60 and 67%) against internal variability. For most extreme indices, we observe a dominant internal variability, except for WSDI which shows a large spreading among models (consistent with what found in Shi et al. 15 for models running transient scenarios). For an additional warming of 0.5 °C (blue) and for all indices, the variance is mainly brought in by internal variability whose contribution is more than 85%. WSDI again shows a particular behavior with an important inter-model spreading.
Changes in occurrence probabilities for hot extremes. We firstly examine the spatial distributions of PR for extreme hot events calculated at each grid point. We used Generalized Extreme Value (GEV) approach to evaluate their probability and PR from the reference period to warming scenario. The methodology that we used is the same as in Kharin et al. 43 . It is to be noted that important biases may exist among various models and their individual members 19 , which makes the ensemble of data incoherent among them and inapplicable for a GEV distribution. To remediate this issue, we use anomalous fields calculated from each individual model, and add the general mean value just before performing the GEV fitting. After the calibration of the three free parameters of GEV (location, scale, and shape), the PR is calculated for three probabilities, 90%, 95% and 99%, respectively, corresponding to events that occur every 10, 20 and 100 years. The PR of extreme hot events increases over China with global warming (Fig. 5). It can be seen in Fig. 5a-h that the spatial patterns of PR are similar between 1.5 °C and 2.0 °C global warming, whereas the value is larger for a higher warming level and a rarer event. The PR is relatively high in the south of the Tibetan Plateau and Northwest China in a future warmer world, with occurrence probability for 100-year extreme hot event increases by 4 and 3 times in these regions respectively (that is, the return values of such event change to 25.0 and 33.3 years) under 1.5 °C global warming; and in a 2.0 °C warmer world, the occurrence probability for 100-year extreme hot event becomes 16 and 8 times respectively (the return values of 100-year extreme hot event change to 6.3 and 12.5 years). The additional warming of 0.5 °C leads to higher PR in Northwest China and the occurrence probability for 100-year extreme hot event increases by about 4 times (the return value is 25.0 years) relative to the 1.5 °C warming level.
Results shown in Fig. 5 can also be summarized in box-whisker plots as in Supplementary Fig. S1 to highlight the characteristics of PR spatial distribution in China. Under 1.5 °C warming, the median PR for 10-, 20-and 100-year TXx over China is 2.35, 2.69 and 3.68, and the range of which is 1.55-3.8, 1.64-5.06 and 1.81-11.42 respectively, with the biggest PR located in the south of the Tibetan Plateau. The values and ranges of PR are both larger under 2.0 °C global warming, indicating that the occurrence probabilities of extreme events will change a lot and the difference between regions will become larger when global warming rises from 1.5 °C to 2.0 °C.
We now investigate how extreme events would change at the national level. To do so, we make the areal average, over whole China, of TXx for each year of our considered periods. We are aware that averaging over large domain for extreme indices (such as TXx) may not have a physical significance, since they may be geographically independent for different grids. However, they may have a practical meaning for policy decision makers to have a national-level evaluation of extreme events. This gives us an ensemble of areal-mean values which forms a probability distribution. Despite the averaging operation over space, such a distribution does not pass the normality test. A GEV distribution is then used to fit the data.   www.nature.com/scientificreports www.nature.com/scientificreports/ quite large difference between the return periods under different warming levels suggests that the probability for severely extreme hot event will experience an intensive increase in higher global warming scenarios. Figure 6c shows PR for the additional 0.5 °C warming. Also shown is the counterpart from transient simulations. The occurrence probability for 10-, 20-and 100-year TXx increases by 4.40 times (4.34-4.48), 5.97 times (5.82-6.13) and 11.79 times (11.07-12.53) in stabilized simulations, respectively, while it increases by 6.38 times (6.07-6.67), 10.65 times (9.92-11.40) and 36.86 times (32.04-42.19) in transient simulations. The two modes of running simulations both suggest that limiting global warming at 1.5 °C can effectively reduce probabilities for extreme hot events. The occurrence probabilities for extreme hot events with different return periods in transient simulations are higher than that in stabilized simulations under the additional 0.5 °C warming. And the uncertainty ranges of projected occurrence probabilities for extreme hot events are obviously narrower in stabilized simulations than in transient simulations, due to the large ensemble members of HAPPI data. Figure 7 shows the spatial patterns of PR for extreme cold events in stabilized simulations. The GEV estimation is also used to evaluate the occurrence probability of TNn. Note that GEV distribution is only suitable for extreme large values, thus we simply take a negative sign for TNn when calculating PR. Considering the probability of 100-year TNn is too small and contains large uncertainty, we analyze the extreme cold event with 5-, 10-, and 20-year return periods. And we also remove the systematic biases among models in TNn series before further processing, as what we did to TXx series in Fig. 5. There are very similar spatial patterns between the 1.5 °C and 2.0 °C warming targets, whereas rarer events have much smaller values, especially over higher warming levels (Fig. 7a-h). For an extreme cold event in present climate, a smaller PR means that it has a lower probability to occur under future warming scenarios. The occurrence probabilities of extreme cold events reduce all over China (PR < 1) in warmer worlds, areas with smaller PR located in the east of the Tibetan Plateau, Northeast and Southeast China, the PR of 10-year TNn in the present climate is 0.5/0.3 under 1.5 °C/2.0 °C global warming, that is, the return period of which is 20/33 years. Under the additional 0.5 °C warming, the PR of 10-year TNn is still relatively small in the east of the Tibetan Plateau and Northeast China (PR is 0.5 approximately), indicating that a TNn event expected once every 10 years in a 1.5 °C warmer world is expected to occur about every 20 years in a 2.0 °C warming climate, suggesting that limiting global warming at 1.5 °C will reduce the change of occurrence probabilities for extreme cold events in these regions, which is also identified in Supplementary Fig. S2. It can be seen in Fig. S2   www.nature.com/scientificreports www.nature.com/scientificreports/ To understand how extreme cold events would change at the national level, the PR and PDF for areal-mean TNn series are shown in Supplementary Fig. S3. As in Fig. S3a, the right shift of the PDF indicates an increase of TNn with global warming, which also suggests that the occurrence probabilities of present extreme cold events may become very small in the warmer worlds. The shape of PDF curves doesn't change much, meaning that there are no obvious changes in variability of TNn under stabilized simulations. When global warming stabilized at 1.5 °C, the PR for 5-, 10-and 20-year TNn is 0.23 (0.21-0.24), 0.15 (0.14-0.17) and 0.10 (0.08-0.11), respectively; and in a 2.0 °C warmer world the PR for TNn with different return levels is 0.039 (0.034-0.044), 0.013 (0.010-0.018) and 0.003 (0.001-0.006) respectively ( Supplementary Fig. S3b). It can be seen that the values of PR for TNn will be smaller with higher global warming levels and rarer extreme cold events. For example, the areal-mean extreme cold event expected every 10 years in the present climate is expected about every 67 years under stabilized 1.5 °C global warming, while under 2.0 °C warming the return period of which will be more than 700 years, meaning that such extreme cold event is unlikely to happen in a 2.0 °C warmer world.

Changes in occurrence probabilities for cold extremes.
For the additional 0.5 °C warming, the PR for 5-, 10-and 20-year TNn is 0.33 (0.32-0.34), 0.25 (0.23-0.67) and 0.2 (0.16-0.21) respectively relative to that under stabilized 1.5 °C global warming; while in transient simulations, the PR for TNn with different return levels is 0.32 (0.26-0.38), 0.29 (0.21-0.37) and 0.29 (0.18-0.42) respectively ( Supplementary Fig. S3c), the results between different return periods are similar and hold wider uncertainty ranges than stabilized results, due to the quite small ensemble members compared to HAPPI simulations. Both of the warming simulations indicate that occurrence probabilities for extreme cold events will be mitigated when limiting global warming at 1.5 °C.

conclusions
In this study we used HAPPI datasets to analyze the response of extreme temperature in China when global warming stabilizes at 1.5 °C/2.0 °C, and compared the response difference between stabilized and transient simulations under the additional 0.5 °C warming. Main results are as follows: The HAPPI experimental design, with a large ensemble size, allowed us to decompose the total variance into a part related to inter-model variability and another related to internal variability. This decomposition serves as a surrogate to estimate uncertainties of climate projections. In the case of 1.5 °C and 2.0 °C warming levels, the two variances are roughly equal (about 50% each) for the mean temperature, WSDI and FD, while the internal variability dominates for TXx and TNn. In the case of additional half-a-degree warming, the internal variability is clearly dominant over the inter-model variability (80 versus 20%) for most variables (except for WSDI which shows half-and-half). 4. The PR of extreme hot/cold events will increase/decrease under global warming. There is larger change of occurrence probabilities in higher global warming levels, especially for rarer extreme events. For geographic distribution, the occurrence probabilities for TXx are higher in the south of the Tibetan Plateau, where the return period of 100-year TXx changes to 25/6.3 years under stabilized 1.5 °C/2.0 °C global warming; the occurrence probabilities for TNn change mostly in the east of the Tibetan Plateau, Northeast and Southeast China, where the 10-year TNn event becomes 20/33 years, which can be inferred that limiting global warming at 1.5 °C can reduce the change of occurrence probabilities for extreme temperature events. For the national averaged extreme events, the return period of 100-year TXx over China changes to 4.79 and 1.56 years under stabilized 1.5 °C and 2.0 °C global warming, and the return period of 10-year TNn changes to 67 years and more than 700 years; for the additional warming of 0.5 °C, the uncertainty ranges of PR for areal-mean TXx and TNn are obviously narrower in stabilized simulations than that in transient simulations.

Data availability
The datasets generated and analyzed during the current study are available from the corresponding author on request.