Future changes in Northern Hemisphere summer weather persistence linked 1 to projected Arctic warming .

37 Understanding the response of the large-scale atmospheric circulation to climatic change 38 remains a key challenge. Specifically, changes in the equator-to-pole temperature difference 39 have been suggested to affect the mid-latitudes, potentially leading to more persistent 40 extreme weather, but a scientific consensus has not been established so far. Here we quantify 41 summer weather persistence by applying a tracking algorithm to lower tropospheric 42 vorticity and temperature fields to analyze changes in their propagation speeds. We find 43 significant links between slower propagating weather systems and a weaker equator-to-pole 44 temperature difference in observations and models. By end of the century, the propagation 45 of temperature anomalies over mid-latitude land is projected to decrease by -3%, regionally 46 strongest in southern North America (-45%) under a high emission scenario (CMIP5 47 RCP8.5). Even higher decreases are found (-10%, -58%) in models which project a 48 decreasing equator-to-pole temperature difference. Our findings provide evidence that hot 49 summer weather might become longer-lasting, bearing the risk of more persistent heat 50 extremes. 51

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speeds of anticyclones (ccx) and warm temperature anomalies (ctx) were linearly detrended, to avoid [1]). Hence, assuming , and remain constant, we can expect changes in " to follow changes 182 in (although the relevant wavenumbers and can generally change too). In a more realistic 183 case (e.g. for Rossby waves propagating on a jet), on the right hand side of Eq.1 should be 184 replaced with the mean potential vorticity gradient, which could depend on and the meridional 185 tempereature gradient / as well. Hence, the westward self-propagation of the waves could 186 also change in response to a change in or / . Nonetheless, the results presented in the 187 Section 3 suggest that the changes in the propagation speeds indeed correlate well with the changes 188 in .
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Assuming that the eastward propagation velocity of vorticity !" and temperature anomalies $" 190 follows the troughs and ridges of propagating Rossby waves (i.e., " ≅ !" , " ≅ $" ), we can thus 191 also expect: 192 !"~; $"~. [2] 193 Above the boundary layer, the vertical shear of the zonal mean flow / can be further related 194 to the equator-to-pole temperature gradient dT/dy by the thermal wind balance: Where is the pressure, is the gas constant and is the Coriolis parameter. 3).

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The most impactful heatwaves of the past decades were not only characterized by extreme 214 temperatures, but also by their unusual persistence. To showcase the temperature anomaly tracking 215 algorithm and it's output, we provide anomaly tracks detected during two major Northern not only extreme in their intensity but also unusual in their persistence. The eastward propagation Non-peer reviewed version submitted to EarthArxiv (17.10.2020) Original manuscript in revision at Geophysical Research Letters (GRL) and will be available soon.
Please cite the published version once available. Europe and Moscow, respectively, and those tracks were also among the slowest tracks detected.

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The tracking algorithm successfully captures both the extreme intensity and the exceptional 226 persistence of these two events, which gives confidence in it's utility for examining the potential 227 changes in the persistence of such extreme events. and future projections in a high emission scenario (rcp8.5, 2081-2099). In order to analyse the Non-peer reviewed version submitted to EarthArxiv (17.10.2020) Original manuscript in revision at Geophysical Research Letters (GRL) and will be available soon.
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modelled inter-relationships and model spread, we investigate the projected changes in the zonally 280 averaged ∆dT/dy, ∆U, ∆ccx and ∆ctx, in JJA (Fig. 3) (p-value <0.05), with a R 2 value of 0.28, Fig.3a). The correlations between ∆dT/dy and ∆ccx and 284 ∆ctx are also both found to be significant at a 95% confidence level with R 2 values of 0.71 and 0.52 285 respectively, (Fig. 3b, c). In agreement with the significant correlations found in reanalysis data,

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∆U with ∆ccx and ∆ctx as well as ∆ccx with ∆ctx are found to be significantly related in models 287 ( Fig.3d-f), with highest values of described variance for ∆ccx with ∆ctx (R 2 =0.72). Thus, models 288 that project an increase of dT/dy in the mid-latitudes also tend to project an increase of U, ccx and 289 ctx, while models that project a decrease in dT/dy tend to project a decrease of U, ccx and ctx, 290 highlighting the considerable linkages between these four variables.

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Assessing changes in ∆dT/dy shows that the models do not agree on the sign of the 292 projected future changes in summer (Fig. 3a-c). To further investigate this, the models are split Non-peer reviewed version submitted to EarthArxiv (17.10.2020) Original manuscript in revision at Geophysical Research Letters (GRL) and will be available soon.
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Please cite the published version once available.  to-pole temperature difference in models. In the spirit of a storyline approach, we classify the 324 models by their future projection of / and investigate the spatial patterns of ∆ccx and ∆ctx for 325 models that show increasing and decreasing trends separately, in addition to a multi-model mean 326 (Fig.4). A mean warming is found for the multi-model mean, but models that predict a decreasing 327 temperature gradient tend to be generally much warmer compared to models that project an 328 increasing temperature gradient (Fig.4a-c). Land areas and the Mediterranean are hotspots for 329 future warming in all three cases, but an amplified warming at higher latitudes is only projected 330 for the ∆dT/dy <0 subset, as expected (Fig. 4b). Multi-model mean fields of ∆ccx show a slow-331 down across most of the mid-latitude land areas and a northward shift in U over the North Atlantic, 332 in agreement with earlier studies (36), while U over the Pacific is found to be less affected (Fig.   333 4d). We find a robust signal of decreasing ∆ccx over land area when analysing ∆dT/dy <0 models 334 only (Fig. 4e), compared to ∆dT/dy >0 models (Fig. 4f). The poleward shift in over the North Non-peer reviewed version submitted to EarthArxiv (17.10.2020) Original manuscript in revision at Geophysical Research Letters (GRL) and will be available soon.
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bearing the risk of more persistent hot extremes across mid-latitude land area, especially over 388 southern North America, where model agreement is most robust.

390
In this study we take a novel approach to investigate weather persistence, by applying a 391 tracking algorithm on vorticity and temperature fields in observations and climate models. We find considerations based on linear Rossby wave theory (Fig. 2). Our results imply that summers with 400 warmer temperatures in the Arctic could feature more persistent, slower-moving weather patterns 401 and surface temperature in the mid-latitude. In contrast, we find that upper tropospheric 402 temperature gradients to be unrelated to weather persistence as given by a slow-down of the 403 eastward propagation ccx and ctx (Fig. S3-S6).

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It is important to note that no straightforward causal arguments can be made based on the 405 regression analysis presented here. Given that mid-latitude weather systems also transfer heat 406 poleward, more persistent weather could also increase the transport of heat into higher latitudes 407 (41, 42), thus contributing to AA in addition to contributions from e.g. albedo changes due to  Non-peer reviewed version submitted to EarthArxiv (17.10.2020) Original manuscript in revision at Geophysical Research Letters (GRL) and will be available soon.
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Contents of this file
Figures S1 to S13 Table S1 Section on statistical methods     anomalies are shown in red (blue) while the zero-line is shown in grey, with a distance of 1ms -1 ) for (a) all models, (b) models that project a decreasing temperature gradient    Fig. 2 is provided as dashed lines. When adjusting the p-values for false discovery rate due to multiple testing, no significant trends are identified in accordance with the non-significant trends observed in the zonal mean ( Fig. S2a,b).

Statistical Methods.
We probe the relationships between dT/dy, U, ccx and ctx using a linear regression model, assuming a Gaussian behavior (i.e. the samples are normaly distributed) for each of the investigated measures, using the lm() function from the R-package stats (31). A quantile-quantile plot in figure S12 show that the assumption of Gaussianity is justified.
Statistical significance is tested against the null-hypothesis of no correlation between to variables. The probability of observing a specific result by chance is provided by the pvalue, where a p-value < 0.05 is considered statistically significant. To test the quality of a linear fit we use the coefficient of determination R 2 , which provides the magnitude of variance of one variable which can be related to the variance of the other variable in question.
Figure S12. Quantile-Quantile plots, of / , , ccx and ctx from ERA-Interim (1981-2014, also see Fig.2), which provide a visual test the correlation of a sample with a normal distribution. A 45° reference is provided as a grey dotted line. As most of the points fall on the line, we can assume the samples to come from a normal distribution. Figure S13. Quantile-Quantile plots of ∆ / , ∆ , ∆ccx and ∆ctx from CMIP5 (1981-2014, also see Fig.3) to test if they follow normal distributions. A 45° reference is provided as a grey dotted line. As most of the points fall on the line, we can assume the samples to come from a normal distribution.
Table S1. Projected regional changes of ccx and ctx in the multi-model mean and for subsets of models classified by their projected trends of dT/dy comparing the historic and end-of-the century period (historical , 1981(historical , -2004(historical , vs. RCP8.5, 2081(historical , -2099.