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# Changes in Northern Hemisphere temperature variability shaped by regional warming patterns

## Abstract

Global warming involves changes not only in the mean atmospheric temperature, but also in its variability and extremes. Here, we use a feature-tracking technique to investigate the dynamical contribution to temperature anomalies in the Northern Hemisphere in climate-change simulations from the Coupled Model Intercomparison Project – Phase 5 (CMIP5). We develop a simple theory to explain how temperature variance and skewness changes are generated dynamically from mean temperature gradient changes, and demonstrate the crucial role of regional warming patterns in shaping the distinct response of cold and warm anomalies. We also show that skewness changes must be taken into account, in addition to variance changes, to correctly capture the projected temperature variability response. Our findings suggest that the world may experience not only a warmer mean climate in the coming decades, but also changes in the likelihood of temperature anomalies within that climate.

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## Data availability

The datasets analysed in the current study were obtained from the World Data Center for Climate (WDCC) repository, available at http://cera-www.dkrz.de/WDCC/ui/.

## Code availability

The feature-tracking algorithm used in this study is available for download at http://www.nerc-essc.ac.uk/kih/TRACK/Track.html, by contacting K.H. (k.i.hodges@reading.ac.uk).

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## Acknowledgements

This research has been supported by the James S. McDonnell Foundation for complex systems and by the European Research Council Advanced Grant (ACRCC) ‘Understanding the atmospheric circulation response to climate change’, project 339390. The data were obtained from the World Data Center for Climate (WDCC). We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (listed in Supplementary Table 1) for producing and making available their model output. For CMIP, the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.

## Author information

Authors

### Contributions

T.T.-B., K.H., B.J.H. and T.G.S. designed the study and wrote the paper. T.T.-B. performed the data analyses.

### Corresponding author

Correspondence to Talia Tamarin-Brodsky.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Primary Handling Editors: Tamara Goldin; Heike Langenberg.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Composites of the vertical cross-section of temperature anomalies.

The composites are produced by tracking features whose maximum intensity exceeds the 75th percentile threshold, for the 850 hPa cold (first row) and warm (second row) temperature anomalies (K) during winter (DJF) for (a,e) the NH midlatitudes (30°N-70°N), (b,f) the Rockies (denoted as ‘topo’), and (c,g) east-central North America (NAEC), and (d,h) for central Europe (EUC) during summer (JJA). The cross sections are taken at the longitude of maximum intensity (i.e., the middle of the composite box). The lowest contour equals 3 K, and the contour intervals equal 1.3 K. Ly denotes the latitudinal distance (in degrees) from the center of the composite box. The vertical cross-sections show, in all cases, a strong local correlation between the surface and the 850 hPa level during extreme temperature events.

### Extended Data Fig. 2 The Eulerian temperature variability for the ERA-I reanalysis data.

The 850 hPa (a) mean temperature (K), (b) temperature variance (K2), and (c) skewness, during NH winter (DJF). Panels (d)–(f) show the same but for the summer period (JJA). These results can be compared with the same quantities from the historical CMIP5 simulations (panels a,b,e,f of Fig. 1, and panels a,e of Fig. 2 in the manuscript).

### Extended Data Fig. 3 The Lagrangian decomposition of the temperature variability for the ERA-I reanalysis data.

The mean intensities of the 850 hPa (a) cold $$(\left| {T^\prime } \right| = T_c)$$ and (b) warm $$(\left| {T^\prime } \right| = T_w)$$ anomalies (K), produced from the temperature tracking statistics, and (c) the approximate temperature skewness, $$S \approx \frac{{T_w - T_c}}{{\frac{1}{2}(T_w + T_c)}}$$, during NH winter (DJF). Panels (d)-(f) show the same but for the summer period (JJA). These results can be compared with the same quantities from the historical CMIP5 simulations (panels b,f of Fig. 2, and panels a,b,e,f of Fig. 3 in the manuscript).

### Extended Data Fig. 4 The historical (1980–1999) ensemble-mean climatologically averaged meridional and zonal temperature gradients and their projected changes (2080–2099 minus historical).

The 850 hPa (a) meridional and (b) zonal background temperature gradients (10−5 Km−1) during winter (DJF), and the corresponding projected changes in (c) and (d), respectively. Panels (e)–(h) show the same but for the summer period (JJA). Regions where more than 70% of the models agree on the sign of the gradient changes are stippled. During NH winter, the most prominent features include the weakening of both the meridional and zonal temperature gradients, although some strengthening of the meridional gradient is projected over central Europe and to its southwest (recall that negative values of the meridional temperature gradient imply poleward decreasing temperatures). During NH summer, there is a projected strengthening of the meridional gradient over central Europe, and a general strengthening of the zonal temperature gradients.

### Extended Data Fig. 5 Risk Ratio (RR) changes with or without considering kurtosis changes.

The risk ratio, calculated as the ratio of the Cumulative Density Functions (CDFs) between the historical and projected simulations, of the cold (a,c) and warm (b,d) tails, with (solid black line) or without (dashed lines) the projected kurtosis change (as done in Fig. 4j,k and Fig. 5j,k in the manuscript, but here for kurtosis changes rather than skewness changes), for east-central North America during winter (first row) and central Europe during summer (second row). This is achieved by reproducing the PDF distribution, keeping the mean, variance and skewness changes, but neglecting the kurtosis changes. Compared to the skewness, neglecting kurtosis changes leads to much smaller changes in the risk ratios associated with extreme warm and cold temperatures (even negligible for central Europe during summer).

### Extended Data Fig. 6 Historical and projected latitudinal displacements of temperature anomalies.

The latitudinal displacements of cold (left column) and warm (right column) temperature anomalies, for (a,b) anomalies in the NH (between latitudes 30° to 70°) during winter, (c,d) east-central North America during winter, and (e,f) central Europe during summer. The displacements are calculated as the latitudinal difference between the initial location of the temperature anomalies and the location during its maximum intensity, while it is inside the region box. Solid (dashed) lines denote the historical (projected) simulations. Shading denotes the 95% confidence interval. In each panel, the mean displacement is shown by the solid (dashed) vertical line for the historical (projected) simulations. The relative change in the mean value of the displacements ($$\Delta _{mean}$$) is shown in each panel. The averaged displacement of cold anomalies is negative (i.e., equatorward) while that of warm anomalies is positive (i.e., poleward) in all cases, expect for east-central North America where the averaged displacement of warm anomalies is negative (this is potentially due to the effect of the Rockies). For all cases, the averaged displacements do not change much in the projected climates, with the relative changes in the mean ranging from 3% to 18% (the latter is achieved for the east-central North America case, where the mean is close to zero, hence the relative change appears larger although the values themselves are very close to each other).

### Extended Data Fig. 7 The near-surface (T2m) winter temperature in the CMIP5 historical data (1981–1999) and its projected changes (2081–2099 minus historical).

The T2m (a) mean temperature (K), (b) temperature variance (K2), and (c) temperature skewness, during winter (DJF), and the corresponding projected changes in (d)–(f), respectively. The surface response is calculated for a subset of 16 models (denoted by * in the model list given in table S1), for which data was obtained. The winter T2m mean, variance, and skewness can be compared with the 850 hPa fields, shown in Fig. 1a,c, Fig. 1b,d, and Fig. 2a,c in the manuscript, respectively.

### Extended Data Fig. 8 The near-surface (T2m) summer temperature in the CMIP5 historical data (1981–1999) and its projected changes (2081–2099 minus historical).

The T2m (a) mean temperature (K), (b) temperature variance (K2), and (c) temperature skewness, during summer (JJA), and the corresponding projected changes in (d)–(f), respectively. The surface response is calculated for a subset of 16 models (denoted by * in the model list given in table S1), for which data was obtained. The summer T2m mean, variance, and skewness can be compared with the 850 hPa fields shown in Fig. 1e,g, Fig. 1f,h, and Fig. 2e,g in the manuscript, respectively.

## Supplementary information

### Supplementary Information

Supplementary Table 1 and derivations.

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Tamarin-Brodsky, T., Hodges, K., Hoskins, B.J. et al. Changes in Northern Hemisphere temperature variability shaped by regional warming patterns. Nat. Geosci. 13, 414–421 (2020). https://doi.org/10.1038/s41561-020-0576-3

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• DOI: https://doi.org/10.1038/s41561-020-0576-3

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