The Effect of Forced and Unforced Variability on Heat Waves, 1 Temperature Extremes, and Associated Population Risk in a CO 2 - 2 Warmed World

25 This study investigates the impact of global warming on heat and humidity extremes by 26 analyzing 6-hourly output from 28 members of the Max Planck Institute Grand Ensemble driven 27 by forcing from a 1%/year CO 2 increase. We find that unforced variability drives large changes 28 in regional exposure to extremes in different ensemble members, and these variations are mostly 29 associated with ENSO variability. However, while the unforced variability of the climate can 30 alter the occurrence of extremes regionally, variability within the ensemble decreases 31 significantly as one looks at larger regions or at a global population perspective. This means that, 32 for metrics of extreme heat and humidity analyzed here, forced variability of the climate is more 33 important than the unforced variability at global scales. Lastly, we found that most heat wave 34 metrics will increase significantly between 1.5°C and 2.0°C, and that low GDP regions shows 35 significant higher risks of facing extreme heat events compared to high GDP regions. 36 Considering the limited economic adaptability of population to heat extremes, this reinforces the 37 idea that the most severe impacts of climate change may fall mostly on those least capable to 38 adapt. 39 population data the Socioeconomic Data and Applications (SEDAC, 2018) to the heat indices The in year 2015 at 30 × 30 ′′ spatial resolution, and we averaged and re-gridded to the 1.875° 1.875° grid of the MPI model by summing the values in grid boxes surrounding the MPI grid centers. In our population-weighted calculations, we assume that the relative of remains into the


Introduction 40
The long-term goal of the 2015 Paris agreement is to keep the increase in global 41 temperature well below 2°C above pre-industrial levels, while pursuing efforts and to limit the 42 warming to 1.5°C. Given that no one lives in the global average, however, understanding how 43 these global average thresholds translate into regional occurrences of extreme heat and humidity 44 is of great value (Harrington et al., 2018). Various studies have reported that regional extreme 45 heat events and heat waves will not only be more frequent, but also more extreme in a warmer 46 world. This was discussed in various assessment and reports such as US National Climate Many criteria and indices have been used to assess extreme heat, such as the absolute 51 increase of maximum temperature from the reference period (Wobus et al., 2018), risk ratio 52 (Kharin et al., 2018), and heat wave magnitude index (Russo et al., 2017). In this study, we 53 utilize four locally defined heat wave indices from Fischer and Schär (2010) and Perkins et al. 54 (2012) of duration, frequency, amplitude, and mean. We also focus on consecutive-day extremes, 55 which are known to cause more harm than single-day events ( The CDF-t method (Michelangeli et al., 2009) is used to bias correct each ensemble 155 member of the 1% runs. CDF-t method finds the transformation function that maps the 156 cumulative density function (CDF) of a GCM to the CDF of a historical reanalysis data in a 157 reference period, which is year 39-53 in 1% runs and 2003-2017 for ERA-Interim reanalysis 158 data. This function is then applied to the 1% runs to generate bias-corrected fields. For the values 159 that fall outside the limits of the CDFs in the reference period, linear extrapolation is used. CDF-t 160 is known to realistically correct the temperature and precipitation output of GCMs, especially for 161 extreme events (Vrac et al., 2012;Watanabe et al., 2012). 162 Bias correction via CDF-t is done for t2m and d2m, and then rh and w2m are calculated 163 with these bias-corrected fields. The bias is reduced significantly for all regions for both t2m and 164 w2m (Figures 1c, 1d, 2a-2d). The bias in w2m is mostly caused by the small remaining biases in 165 t2m and d2m, which are amplified in the w2m calculation. Hereafter, '1% runs' will refer to the 166 bias-corrected 1% runs. 167 Since the 1% runs are CO2-only forcing, without aerosol forcing, one might wonder 168 whether the temperature extremes estimated by these models would apply to a world with a more 169 realistic forcing that includes aerosols. To determine this, we have compared monthly average 170 and monthly maximum temperatures from an ensemble of 100 RCP 8.5 scenario runs from the 171 MPI-GE to the same quantities estimated from the 1% ensemble. If we compare the ensembles 172 at points in time when they have 1.5, 2, 3, and 4°C of ensemble-and global-average warming, 173 we find very small regional differencesthe regional ensemble averaged maximum and mean 174 temperature difference was less than 0.5°C in all regions. Alternatively, since we bias-corrected 175 the 1% CO2 runs to reanalysis data, which contains aerosol forcing, our bias-corrected 1% CO2 176 9 runs can be understood as a continuously warming climate driven by CO2, with effect of aerosols 177 fixed at 2003-2017 period. 178 179

Heat wave indices 180
Identification of heat waves is done in several steps. First, we smooth a daily maximum 181 temperature (determined form 6-hourly temperatures) using a 15-day moving window for the 182 first 5 years of 1% runs, which is the period before significant warming has occurred. This was 183 done at each grid points, followed by a framework from Fischer and Schär (2010). Then, also for 184 each grid point, the 90 th percentile of smoothed daily maximum temperature for the first 5 years 185 was calculated. This value is used as a threshold for the heat waves. After calculating the 186 threshold, we calculate the heat wave days, defined as days that exceeds the threshold for three 187 or more consecutive days (Baldwin et al., 2019). 188 We then define four indices to represent the characteristics of these heat waves.  Table  196 l.  4.1. Impact of unforced variability of climate on regional heat extremes 221 To investigate the impact of unforced variability on more regional heat extremes, we 222 select 15 large cities spread around the world (Fig. 3a). Power spectra of the PCs are plotted in Figure 5. Overall, the spectra of the deadly day 262 PCs look very much like the spectrum for ENSO, but does not have the ~20-year peak of the 263 PDO spectrum. This tells us that, in this model at least, the variability in the occurrence of 264 deadly days in these large cities is strongly regulated by ENSO. The third deadly day PC has 265 lower correlations with ENSO or PDO index and a peak at both the ENSO period a slightly 266 13 longer period than ENSO, about 10 years, so it is harder to draw firm conclusions about the 267 mechanism behind it. 268 The tropical night PCs also show peaks at ENSO periods (Fig. 5b)  shows distinct geographical characteristics, as summarized in Table 2 (the result of clustering  286 shows little difference between the ensemble members). As might be expected, each cluster 287 shows a different evolution of heat extremes in warmer world (Figure 7). Although the warming 288 signal is largest in the polar regions (Figure 6b Turning to deadly days (Fig. 7i), we find a substantial increase occurs in cluster 1 after 298 1.5°C of warming; this is important because it gives additional support for the Paris Agreement's 299 aspirational goal of limiting global warming to 1.5°C. Almost all of the increases in deadly days 300 are in low latitudes (cluster 1, 2, and 3). For tropical nights, low latitudes as well as deserts 301 (cluster 4) contribute most of the increase. These regions also show more rapid increases when 302 global average warming exceeds 1.5-2°C. 303 Figure 7 also shows the spread in within the ensemble for each metric and cluster. We 304 find that the spread for a cluster is generally smaller than the differences between the clusters. 305 This suggests that the differences obtained are not due to interannual variability. 306 We also generated indices weighted by population. Heat wave indices for the 90 th 307 percentile of population (meaning 10% of the population is exposed to higher values) and 308 median of the population are depicted in Figure 8. Figure 8a shows that with 4°C of warming, 309 10% of the Earth's population will experience heat waves lasting 131 days, and half of the 310 population will experience heat waves around 64 days long. These are large increases over 311 present-day values of 35 days and 17 days. Notably, the average of the standard deviation 312 between the ensembles during 150-yr period are 6.7 days and 3.4 days for the 90 th percentile and 313 median, respectively. This is significantly smaller than values from the regional analyses of cities 314 in Figure 3, where the unforced variability can make a huge difference in the occurrence of heat 315 waves. 316 The rate of increase of HWDw2m and HWFw2m in Fig. 8 accelerates when global average 317 warming exceeds 1-1.5°C. Given that the planet has already warmed about 1°C above pre-318 industrial, this suggests that the world may be on the cusp of a rapid increase in wet-bulb 319 extremes. This is related to the increased slope in Figure 7, in which cluster 1 and 2's values of 320 HWDw2m and HWFw2m increase rapidly between 1.5C and 2.5°C of global warming. At warmer 321 temperatures, HWDw2m and HWFw2m reach a plateau, since values over 300 days per year means 322 there is little room for additional increase. For HWAt2m/w2m and HWMt2m/w2m, the increase is 323 mostly linear. Also note that at 4°C of global warming, HWAw2m reaches 30°C, which while not 324 immediately fatal to humans may nevertheless indicate great difficulty for even a developed 325 society to adapt to. 326 Currently, 5% of the total population faces more than 180 deadly days and 302 tropical 327 nights per year. This grows to 204 and 333 days, respectively, at 1.5°C warming. With 2°C of 328 global warming, half of the population will face 2 months of deadly days every year and with 329 2.5°C of global warming, and 5% of the population will be in an environment where every day in 330 a year is a tropical night. With 2°C of global warming, the minimum ensemble member of 331 deadly days and tropical nights is above the maximum ensemble of the current climate. Further 332 details are also shown in Table 3. 333 It is notable that, although there is a large spread between the ensemble members in each 334 city (Figure 3), the spread in the clusters (Figure 7) and population-weighted metrics (Figure 8) 335 16 is not as large. This emphasizes that the effect of unforced variability might be large in small 336 regions, but as the region expands, opposite signs of variability cancel, so area-average 337 variability decreases. This is also found in Table 3, where in each case, the standard deviation 338 between ensembles is less than 10% of the average. This indicates that internal variability will 339 play a minor role in determining global exposure to temperature thresholds, although different 340 people may be affected in different climate realizations.

Analysis on GDP per capita 350
It is well-known that not everyone is equally vulnerable to extreme weather, with rich, 351 developed countries having more resources to deal with extreme events. In that context, global 352 gridded GDP per capita is used to calculate average risk at each level of wealth. The ensemble-353 average result is depicted in Figure 9, which shows the increased number of deadly days and 354 tropical nights that each level of economic level experience relative to today's current level of 355 global warming. This plot assumes that the distribution of population and GDP remains fixed 356 through time. 357 With 0.5°C increase of global warming, population in lowest 10% of GDP will face 28 358 more deadly days and 22 more tropical nights increasing compared to present day. In contrast, 359 the richest 10% will experience 5 and 3 more deadly days and tropical nights for the same 360 warming. At 3°C above current temperatures (about 4°C above preindustrial temperatures), the 361 population with the lowest 10% of GDP will experience154 and 162 more days of deadly days 362 and tropical nights compared to today's climate. On the other hand, population with the highest 363 10% of GDP will experience an increase of 26 and 30 days for the same warming. The regions 364 that contribute the most for the low GDP percentiles are Tropical Africa, including Republic of 365 the Congo, Kenya, Uganda, Ethiopia, and Sudan, which are in clusters 1 and 2 in our cluster 366 analysis. The maximum difference of heat wave days between the ensembles is less than 25% for 367 all GDP and global warming levels. 368 369

Energy demand on large cities 370
Annual CDD and HDD have been calculated for the 15 cities in section 4.1. Fig. 10  371 shows the percent change of CDD and HDD at 1.5°C , 2.0°C , 3.0°C , and 4.0°C relative to the 372 pre-industrial CDD and HDD values (average of first 5 year of 1% CO2 runs). This was done for 373 each city, and for each ensemble member. In 1.5°C , 2.0°C, 3.0°C , and 4.0°C warming, CDD in 374 15 cities increases by 26%, 38%, 60%, and 82%. This suggests an enormous increase in energy 375 required for cooling. In contrast, energy demand on cold days (HDD) decreases by 51%, 60%, 376 68%, and 75%, compared to pre-industrial baseline, suggesting a partially offsetting decrease in 377 energy required for heating. The spread between the ensemble members is small compared to the 378 average of the ensembles, except for Moscow. 379 Large percentage increases in CDD for Moscow is the result of low pre-industrial CDD 380 values, so that (relatively) small increases in CDD correspond to large fractional changes, as well 381 as large differences between ensemble members. The ensemble spread of HDD in Moscow is 382 also large, compared to other cities. This is not due to low values of HDD -Moscow has highest 383 HDD value among 15 cities (4062 days °C per year in pre-industrial condition)but rather that 384 unforced variability of the climate is more important for HDD than CDD values for Moscow. 385 386

Conclusion 387
In this study, we found that extreme heat events will become more frequent and severe in 388 a continuously warming world. In a warmer world, duration, frequency, amplitude, and mean of 389 extreme heat and humidity events increase, especially in low-latitude regions. In some of the 390 regions, wet bulb temperature will reach upper 20s, which is above the level that significantly 391 impact human mortality. We also find and quantify the impact of forced change and unforced 392 variability on the extreme heat events. 393 Our results show that ENSO is the dominant mode of unforced variability impacting the 394 occurrence of extreme heat and humidity events and that events tend to be synchronous in 15 395 large cities we chose. But while the impact of unforced variability might be significant 396 regionally, it narrows down when one looks at larger aggregate regions. 397 Looking at the population-weighted stats, we found that with 1.5°C of global average 398 warming, over 10% of population will face heat waves of 42°C temperature, and 27°C wet bulb 399 temperatures. With 4°C warming, 10% of population will face 45°C temperature and 29°C wet 400 bulb temperature. Also, even with 1.5°C of warming, which is about 0.5°C higher than the 401 current level, 5% of the population will face more than 200 days of deadly days and over 300 402 days of tropical nights per year. With 4°C of warming, 10% of the population will experience 403 over 300 days of deadly days and over 330 days of tropical nights per year. Given these two 404 metrics are based on human mortality, this may have significant impact on human health 405 globally. 406 Sorting heat and humidity events by wealth, we found that increasing frequency and 407 severity of extreme events will fall mostly on the poorest people. Given underdeveloped 408 countries' lack of ability to endure climate extremes, and that they have contributed the least to 409 climate change, this introduces a profound moral dimension to the problem. Another uncertainty is that our runs are continuously warming, and it is possible that an 420 equilibrium world at any given temperature may experience different occurrence of extremes 421 than in the runs in this paper. Additionally, since an increasing proportion of the population lives 422 in dense metropolitan areas, there is also the possibility that actual heat and humidity extremes 423 that populations experience could be more severe than the gridded data due to local phenomena 424 such as the urban heat island effect (Murata et