2.1 Observational and CMIP5 data

We use the Hadley Centre Global Historical Climatology Network-Daily (HadGHCND) dataset (Caesar et al., 2006) to evaluate climate model simulations for the period 1950–2014. HadGHCND is a land-only, daily gridded dataset of daily maximum and minimum temperatures from ground stations, for which daily mean temperatures are calculated by taking the average of each daily maximum and minimum temperature value for each grid cell.

The HadGHCND data are used to evaluate six individual CMIP5 models (see Table 1), which were selected based on their data availability for all of the daily climate variables being investigated. While we only show a single simulation from each model (r1i1p1), multiple ensemble runs were analysed (where available) to determine model robustness and assess internal climate variability within the models. Results of multiple ensemble runs were found to be highly correlated in both spatial pattern and magnitude of simulated changes (see Fig. S1 in the Supplement), indicating that the sensitivity of the results to internal variability within the models is small. Historical model simulations (1950–2005) are merged with Representative Concentration Pathway 8.5 (RCP8.5) simulations (2006–2099) to assess changes between the mid-20th century and early 21st century (1950–2014), as well as between the mid-20th century and late 21st century (1950–2099). For analysis of recent decades, a bilinear remapping technique is used to re-grid all models to the grid cell size of HadGHCND, that is, 2.5^∘ latitude × 3.75^∘ longitude, and masked to only cover land regions where sufficient observational data are available. We define “sufficient” as being grid cells with at least 80 % of daily data available over 1950–2014, as well as at least 50 % of data available for the first and last 10 years of observational data. For analysis of future projected changes, all models are re-gridded to a common grid size of 2.5^∘ latitude × 2.5^∘ longitude to enable inter-model comparison and analysis of the multi-model mean.

Table 1List of CMIP5 models used in this study and their institution.

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2.2 Methods

For each model simulation as well as HadGHCND, daily temperature anomalies are calculated relative to a mean annual cycle of daily mean temperatures based on the entire period of analysis (1950–2014 for analysis of recent changes and 1950–2099 for analysis of future changes). The data are then split into seasons – boreal winter (December to February – DJF), spring (March to May – MAM) and autumn (September to November – SON) – and all analyses are only applied to Northern Hemisphere land areas north of 30^∘ N. Boreal summer is not included in the analysis as it was previously found to have only small changes in cold extremes relative to the mean that were less robust across a suite of CMIP5 models (Gross et al., 2019).

For each grid cell in each dataset, the seasonal minima of daily temperature anomalies are calculated annually for 1950–2014 and 1950–2099 separately, accounting for the differences in base period selection. The seasonal minima are then averaged over two periods (1950–1981 and 1982–2014 for analysis of recent changes and 1950–1979 and 2070–2099 for analysis of future changes) to calculate changes in the anomalously coldest days. Changes in seasonal mean temperature are similarly computed from daily mean temperature data. The difference between changes in the seasonal minima and changes in the seasonal mean is then calculated, hereafter referred to as “excess changes”. The term “recent excess changes” refers to excess changes between the mid-20th century and early 21st century, while “future excess changes” refers to excess changes between the mid-20th century and late 21st century. Local significance of future excess changes is assessed by a Kolmogorov–Smirnov test (KS test) at the 5 % level.

To investigate the possible drivers of the amplified warming of seasonal cold extremes relative to the mean in the mid- to high-latitude Northern Hemisphere regions, we assess several variables available at the daily timescale in the selected CMIP5 models. This includes snow cover (CMIP5 variable name snc), snow amount (snw), and upwelling and downwelling longwave and shortwave radiation fluxes at the surface (rlus, rlds, rsus, rsds). We also assess surface albedo, calculated as the ratio of upwelling shortwave radiation and downwelling shortwave radiation, and horizontal temperature advection, which is derived for each model using the following equation:

where $\partial T/\partial t$ is the horizontal temperature advection in ^∘C s⁻¹, u and v are the zonal and meridional wind components (uas and vas, respectively), and $\partial T/\partial x$ and $\partial T/\partial y$ are the temperature gradients in the zonal and meridional direction. We refer to advection of cold air temperature hereafter as “negative temperature advection”. For surface albedo, there are some instances in high-latitude regions where values are unrealistically large, as a result of low incoming shortwave radiation values that affect the calculation of surface albedo. In any instance where surface albedo values are outside of the physically reasonable 0 to 1 range, values are set to missing. Several other daily variables were also assessed, such as surface heat fluxes and cloud cover, but were found to be of low relevance as potential drivers of cold extremes in the seasons and regions being examined.

The analysis of the physical mechanisms related to the amplified warming of cold extremes is limited to future changes, where the signal is stronger than for recent changes, and therefore shows a more robust identification of relationships. For each of the variables assessed, except temperature advection, data are evaluated on the specific day when the seasonal minima occur. For temperature advection, a 3 d average prior to the day the cold extreme occurs is used. This is because it is likely that larger changes in circulation would have more of an influence on temperature in the days leading up to the event rather than on the day of the event. A 3 d average leading up to the day of the cold event was also assessed for snow cover and albedo, but results showed no clear difference compared to using values on the exact day of the event. Excess changes are also calculated for each variable in much the same way as excess temperatures, that is, taking the difference between the value of the variable on the days of the cold extreme (or 3 d average prior to the event for temperature advection) and the seasonal mean of the variable. This essentially removes the mean from the analysis and shows regions that experience increases or decreases in conditions related entirely to the days on which the cold extremes occur.

Results of the physical relationships are presented in two ways: maps of the variables, as is shown for excess changes in temperature (to infer the similarity of spatial patterns), and scatter plots of correlations of future excess changes in cold extremes with either snow cover or albedo. The former are included in the Supplement, while the latter are included within the main body of the paper. For the scatter plots, seasonal “excess” values for the two time periods used for the future analysis are calculated as the difference between the variable value on the day the seasonal minima occur and the seasonal mean of the respective variable. For simplicity, we use the term “actual changes” to refer to changes in the actual values of the different variables on the days the cold extremes occur (or the 3 d average prior to this day for negative temperature advection). Weighted area averages of the annual excess values are then calculated for all grid boxes within a selected region that adhere to a specified condition that only includes grid cells with a statistically significant future excess change exceeding 1 ^∘C. Two regions are assessed for all models, one covering North America (30 to 70^∘ N, 168 to 52^∘ W) and the other covering much of northern Eurasia (47 to 75^∘ N, 10 to 135^∘ E) (see Fig. S2). Regressions are calculated using total least squares regression, with correlation coefficients computed using Spearman's rank correlation.

3.1 Recent changes in cold extremes relative to the mean

Historical excess changes in seasonal cold extremes relative to corresponding mean temperatures are shown for HadGHCND and the six-member multi-model mean for boreal winter, spring and autumn (Fig. 1). Maps of individual models are included as the Supplement (Figs. S3–S5). Positive values indicate regions where cold extremes have warmed more than the mean, while negative values indicate regions where cold extremes have warmed less than the mean. Stippling indicates grid cells where both five out of six models agree on the sign of excess change and where the multi-model mean agrees in sign with HadGHCND.

Figure 1Recent excess changes (1982–2014 to 1950–1981) in cold extremes (seasonal minima – seasonal mean) in HadGHCND (a–c) and the six-member CMIP5 multi-model mean (d–f) for boreal winter (a, d), spring (b, e) and autumn (c, f). Grey areas represent areas where data are missing in HadGHCND. Stippling in the multi-model mean represents grid cells where both the multi-model mean agrees in sign with HadGHCND and where at least five out of six models agree on the sign of excess change.

During winter (Fig. 1a), HadGHCND shows that cold extremes have warmed more than 1 ^∘C faster than the mean for parts of northern and eastern Canada, the western US, eastern Siberia, and parts of northern and central Eurasia. The mean has warmed more than cold extremes in parts of western Alaska and north-western Russia. In spring (Fig. 1b), much of North America shows strong positive excess changes, excluding eastern Canada, which shows some negative excess changes around −1 ^∘C. Positive excess changes over 1 ^∘C in spring are also shown for Nordic countries and eastern Russia, while central-northern Russia shows some areas of negative excess changes. In autumn (Fig. 1c), much of eastern North America, excluding eastern Canada, shows strong positive excess changes sometimes exceeding 1 ^∘C. This is similarly shown for parts of Siberia, the Nordic countries and Eurasia, while negative excess changes are evident over western Russia and parts of Europe and the Mediterranean region.

The CMIP5 multi-model mean shows a smoother spatial pattern overall compared with HadGHCND, with agreement between observations and the models themselves mostly in regions where the strongest positive excess changes are seen. Though underestimating excess changes in HadGHCND, there is strong agreement in both the sign of the individual CMIP5 models and with HadGHCND that cold extremes have warmed more than the mean for parts of northern and eastern Canada and northern and central Eurasia during winter (Fig. 1d). While the multi-model mean shows small negative excess changes for eastern Siberia, individual models disagree in sign, with MPI-ESM-LR showing positive excess changes in the region similar in magnitude to HadGHCND (Fig. S3). During spring (Fig. 1e), there are strong model agreement and similarities with HadGHCND for much of central Eurasia, the Nordic countries, and northern North America, with cold extremes warming between 0.4 and 0.8 ^∘C more than the mean during recent decades. Some of the individual models show stronger changes than others in these regions, such as INM-CM4 and CanESM2 (Fig. S4). Autumn shows a similar pattern to spring in the multi-model mean, with slightly more model agreement over a larger part of northern Eurasia (Fig. 1f). The models agree on the positive excess changes shown in HadGHCND over north-eastern North America, southern Greenland, the Nordic countries, Siberia and central Eurasia, though they do not capture the negative excess change over western Russia and Europe. This negative excess change, however, is shown to a lesser degree in CanESM2 and MPI-ESM-MR (Fig. S5). Though the multi-model mean underestimates the positive excess changes in HadGHCND, excess changes simulated in the individual models vary, with some resembling the magnitude shown in HadGHCND more than others.

The shoulder seasons generally show widespread positive excess changes in the multi-model mean and individual models, with agreement between models as well as with HadGHCND over much of Eurasia and northern North America. Winter also shows strong agreement over some of these regions. Across all seasons shown, the same general pattern of excess changes in cold extremes is clear, with the most prominent positive excess changes in recent decades occurring in the northern continental interiors. This motivates us to assess how cold extremes might change in the future relative to mean temperatures in the selected six climate models over the Northern Hemisphere extratropics.

3.2 Projected excess changes in cold extremes

Projections of excess changes in cold extremes comparing the mid-20th century with the late 21st century are shown for boreal winter, spring and autumn using the six-member multi-model mean (Fig. 2). Future excess changes in the individual models are included as the Supplement (Figs. S6–S8).

Figure 2Future excess changes (2070–2099 to 1950–1979) in cold extremes (seasonal minima – seasonal mean) in the six-member CMIP5 multi-model mean for boreal winter (a), spring (b) and autumn (c). Stippling indicates grid cells that are both significant at the 5 % level as assessed by a KS test and where at least five out of six models agree on the sign of excess change.

Cold extremes are projected to warm significantly more than mean temperatures across much of the Northern Hemisphere extratropics. During winter, the amplification of cold extremes relative to the mean is strongest in Alaska, eastern and western Canada, Nordic countries and north-western Eurasia, with positive excess changes exceeding 5 ^∘C in some of these locations. Similar to the historical excess changes for winter, CanESM2 projects the largest positive excess changes; however, all six of the models show positive excess changes of at least 2 ^∘C in these regions (Fig. S6). There is some variation over northern Russia and Siberia, with CNRM-CM5 showing significant negative excess changes around −1.5 ^∘C, opposed to relatively strong positive excess changes of around 3 ^∘C in CanESM2, MPI-ESM-LR and MPI-ESM-MR. The shoulder seasons also show a similar spatial pattern to historical excess changes, albeit at a greater magnitude, with positive excess changes exceeding 3 ^∘C projected for most of the Northern Hemisphere extratropics. For both spring and autumn, the largest excess changes are projected for northern North America and northern parts of Eurasia, in particular western Russia and the Nordic countries but also spreading further east in autumn into the eastern parts of Siberia. During spring, the models show some differences in southern parts of the US and Eurasia, which mostly show non-statistically significant negative excess changes (Fig. S7). In autumn, which shows the largest and most widespread excess changes, there is robust model agreement that cold extremes are projected to warm in excess of 5 ^∘C more than the mean for much of northern North America and northern Eurasia. In the individual models, the excess changes in these regions range from around 3 ^∘C in INM-CM4 to over 6 ^∘C in CanESM2 (Fig. S8).

Future excess changes are robust and systematic, with strong model agreement that cold extremes are expected to warm more than mean temperatures for many mid- to high-latitude regions in boreal winter, spring and autumn. As in the historical excess changes, spring and autumn generally show a more widespread and systematic pattern of positive excess changes over Eurasia, Canada and Alaska; however, the projected magnitude of amplified cold extremes relative to mean temperatures exceeds 3 ^∘C for much of the Northern Hemisphere extratropics in seasons shown. To explore the possible physical mechanisms driving the amplified warming of cold extremes, we focus on the regions that show the most robust signals. The strongest excess changes across all the seasons shown are over northern Eurasia and northern North America. This is relatively consistent with the largest recent excess changes occurring in the northern continental interiors in observations and CMIP5 models, though it is much more widespread and systematic in the projected patterns.

3.3 Projected changes in advection of cold air prior to cold extremes

Due to the evidence suggesting Arctic amplification, and consequent changes in thermal advection, as a main driver of decreasing temperature variability in Northern Hemisphere regions (e.g. Screen and Simmonds, 2010; Screen, 2014; Schneider et al., 2015; Holmes et al., 2016; Rhines et al., 2017), we first consider projections of changes in temperature advection averaged over the 3 d prior to the cold event. Figure 3 shows future changes in actual and excess temperature advection in the six-member CMIP5 multi-model mean, with stippling indicating grid cells where at least five out of six models agree on the sign of change. As described in Sect. 2.2, actual changes refer to changes only in the days prior to the day of the extreme, while excess changes show the difference between the days prior to the extreme and the seasonal mean temperature advection. Results of individual models are included as the Supplement (Figs. S9 and S10).

Figure 3Projected future changes (2070–2099 to 1950–1979) in actual (a–c) and excess (d–f) negative temperature advection in ^∘C s⁻¹ in the six-member CMIP5 multi-model mean for boreal winter (a, d), spring (b, e) and autumn (c, f). Changes are calculated using the average negative temperature advection for the 3 d prior to the day the seasonal minimum occurs, with negative values indicating reductions in cold air advections and positive values indicating increases.

The most notable features occur for boreal winter, where the multi-model mean projects reductions in negative temperature advection for much of North America as well as Eurasia, corresponding to reduced advection of colder air in these regions. This is evident for changes in both actual and excess negative temperature advection, which suggests the changes are related especially to the days directly prior to the day the cold extreme occurs rather than to changes in average seasonal advection of cold air. While there is strong agreement between models regarding this, the magnitude of the reduction in the advection of cold air varies between individual models, where CanESM2 generally shows the largest reduction compared with the other models (Figs. S9 and S10). This is reflected in future excess changes in cold extremes, where CanESM2 is generally warmer than the other models during winter (see Fig. S6). For much of North America, especially the central and eastern US and south-western Canada, reductions in negative temperature advection of at least −2 ^∘C s⁻¹ are projected for the late 21st century, with the same areas showing the largest projected positive excess changes in cold extremes. This is indicative of reduced cold air temperature advection, related to both the day the cold extreme is projected to occur as well as changes in the mean seasonal temperature advection, being a dominant driver of the amplified warming of cold extremes relative to the mean during boreal winter. Similarly, the greatest decreases in negative temperature advection over the European continent occur in the Nordic countries and Eurasia, which also show high-magnitude excess warming in cold extremes during winter. This same pattern is evident across all of the selected climate models (Figs. S9 and S10). Though some reductions in negative temperature advection are shown scattered over North America and Eurasia for spring and autumn, the spatial pattern does not match with the seasonal future excess changes in cold extremes like it does for winter.

Based on these results, it is evident that a reduction in the advection of cold air is driving the projected excess changes in cold extremes over much of North America and Eurasia during winter. Both shoulder seasons, however, show a less clear signal with generally smaller changes in negative temperature advection, pointing to other mechanisms being a dominant driver of the projected amplified warming of cold extremes in spring and autumn.

3.4 Projected changes in snow cover and surface albedo associated with cold extremes

Many of the grid cells showing significantly strong excess changes are located in regions that experience high seasonal snow cover. Snow cover and associated surface albedo feedbacks therefore play a major role in temperature variability in these regions, but it is not clear if this relationship extends to the amplified warming of cold extremes relative to local mean temperatures, and the seasonal influence remains uncertain. The subsequent results show scatter plots of excess changes in cold extremes and snow cover (Fig. 4) and surface albedo (Fig. 5). As outlined in Sect. 2.2, these changes are calculated for the exact day when the cold extreme occurs. Projections of changes in actual and excess snow cover and surface albedo for the days of the cold extreme are included as the Supplement (Figs. S11 and S12 and S13 and S14, respectively). For additional information on the snow–temperature relationship, future changes in snow amount are also included as the Supplement (see Figs. S15 and S16).

Figure 4Scatter plots showing annual values of excess temperatures in cold extremes for each season on the y axis, and annual values in each season of actual snow cover (snow cover values on the day the cold extreme occurs) on the x axis (a, c, e, g, i, k). Panels (b, d, f, h, j, l) show values of excess snow cover on the x axis (i.e. snow cover on the day of the extreme – mean seasonal snow cover). Each row represents a different season: boreal winter (DJF) (a, b, g, h), spring (MAM) in (c, d, i, j) and autumn (SON) in (e, f, k, l). Each point is an area average of two regions (see Fig. S2): North America (a–f) and northern Eurasia (g–l). The straight lines indicate the regression slope for each model calculated using total least squares regression. Correlation coefficients are shown at the top of each panel, with the different colours indicating the model. The asterisk ^* indicates significance at the 5 % level.

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Figure 5As Fig. 4, but for surface albedo.

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For both regions, mostly significant negative correlations between snow cover and excess cold extremes are shown for all seasons, aside from excess snow cover in boreal winter. During winter in the North America region (Fig. 4a–f), all models show significant negative correlations of at least −0.74 for actual snow cover (Fig. 4a); however, all models except CSIRO-Mk3-6-0 show significant positive correlations for excess snow cover (Fig. 4b). From Figs. S11 and S12, parts of North America, particularly southern Alaska, southern Canada and along the north-western coast of the US, show projected decreases in actual snow cover but slight increases in excess snow cover. This suggests that the feedback between snow cover and the projected amplified warming of cold extremes is related to overall reductions in the seasonal mean snow cover during winter rather than to decreases in snow cover on the day the cold extreme occurs. Negative correlations in spring and autumn are generally stronger than they are for winter, in both actual and excess snow cover (Fig. 4c, e and d, f respectively), with the greatest overall correlations projected for autumn. Again, this is reflected in the maps, where actual snow cover is projected to decrease around 40 % for much of Alaska and northern Canada during the autumn, while decreasing somewhat less and slightly further south during spring (Fig. S11). Smaller decreases are projected for excess snow cover, compared with actual snow cover, excluding Alaska, which shows mostly small increases during spring (Fig. S12), implying that projected decreases in the overall mean state of snow cover are related to projected excess changes more than to decreases in snow cover on the day of the extreme. Northern Eurasia (Fig. 4g–l) shows similar correlations to that of North America. The overall largest correlations between snow cover and excess cold extremes occur in autumn (Fig. 4k and l), with some models, for example, CanESM2 and CNRM-CM5, showing correlations as high as −0.91 (Fig. 4k). In these models, decreases in snow cover over 45 % are shown for parts of western Russia and Scandinavia (Fig. S11). Correlations are slightly lower for spring (Fig. 4i), with the largest projected spring decreases in actual snow cover shown for the Nordic countries and central or eastern Europe, with no substantial changes in Siberia (Fig. S11). This is reflected in projected changes in actual snow amount (Fig. S15), with increases shown for regions that project no changes in snow cover. The lack of snow cover changes in the coldest climates, such as in Siberia, is likely due to the trade-off between increasing temperatures that shorten the snow season and increased moisture-holding capacity which leads to greater snowfall in these regions (e.g. Krasting et al., 2013; Mankin and Diffenbaugh, 2015). Correlations with excess snow cover in spring (Fig. 4j) are substantially smaller for most models, compared with actual snow cover, with parts of northern Russia showing small increases in snow cover (Fig. S12) and snow amount (Fig. S16).

Figure 6Projected changes in the timing of the anomalously coldest day of the season between 2070–2099 and 1950–1979 in the six-member CMIP5 multi-model mean for boreal winter (a), spring (b) and autumn (c). Positive values indicate grid cells where the anomalously coldest day occurs later in the season, while negative values indicate grid cells where the anomalously coldest day occurs earlier in the season. Stippling indicates where at least five out of the six models agree on the sign of change.

Decreases in snow cover imply that reductions in surface albedo are a likely factor contributing to the amplified warming of cold extremes relative to the mean. Correlations between surface albedo and excess cold extremes (Fig. 5) indeed show strong similarities with those of snow cover, with the largest negative correlations shown for boreal autumn for both North America (Fig. 5a–f) and northern Eurasia (Fig. 5g–l). As shown for snow cover, the strongest overall projected decreases are shown for actual changes in surface albedo over Alaska, northern Canada and Eurasia during autumn months (Fig. S13). Differences in the magnitude and sign between actual surface albedo and excess surface albedo are also clear (Figs. S13 and S14). Mostly positive correlations with excess surface albedo are shown for winter for both regions (Fig. 5b and h). During boreal winter in high-latitude regions, solar insolation is low, so it is expected that surface albedo is less of a factor in driving excess changes in cold extremes during the winter months.

There is a clear relationship between decreases in snow cover, associated lower albedo and the amplified warming of cold extremes for many regions in the Northern Hemisphere mid-latitudes to high latitudes. While negative correlations are shown for actual snow cover and excess cold extremes during winter for both North America and Eurasia, projected decreases in actual snow cover, as shown in the maps in Fig. S11, are generally much smaller than they are for both shoulder seasons, especially autumn months which show the overall largest decreases and highest correlations with excess temperatures in cold extremes. Much of this relationship between snow cover, surface albedo and excess temperatures in cold extremes is a consequence of overall decreases in the mean state of both snow cover and surface albedo rather than decreases in snow cover specifically on the day in which the cold extreme occurs. This is consistent across the selection of CMIP5 models used in this study.

3.5 Projected changes in the timing of anomalously cold days

The amplified warming of cold extremes projected for much of the Northern Hemisphere mid-latitudes to high latitudes is related to excess heat near the land surface that acts to decrease the severity of the anomalously coldest days of the season. During spring and autumn, much of this is likely a consequence of less snow cover and lower albedo, leading to increases in absorbed shortwave radiation at the surface and consequently amplifying the warming of cold extremes, creating a positive feedback within the system. In addition to these relationships, we also analysed an increase in net radiation on the days of the cold extremes in both shoulder seasons, with increases in incoming shortwave radiation being the largest contributor (not shown). These increases are, however, largely attributable to temporal shifts in the occurrence of the largest negative temperature anomalies in the shoulder seasons.

Figure 6 shows the projected change in the timing of the seasonal minimum of daily anomalies in the six-member multi-model mean (see Fig. S17 for individual model results). Positive values indicate grid cells where the coldest days are projected to occur later in the season, while negative values indicate grid cells where the coldest days are projected to occur earlier in the season. Changes in the anomalously coldest winter day are mostly small with little model agreement, except for far-eastern Canada where the coldest winter days are projected to occur between 8 and 16 d earlier in the season (Fig. 6a). The shoulder seasons both show more significant shifts in the timing of the anomalously coldest days. For much of the Northern Hemisphere mid- to high latitudes, excluding the most southerly parts, the Mediterranean region and parts of Greenland, the anomalously coldest days are projected to occur later in the season during spring (Fig. 6b). In some regions, such as central-western Europe and eastern Canada, the anomalously coldest spring days are projected to occur more than 20 d later in the late 21st century, compared to those simulated in the mid-20th century. Some models, such as CanESM2, project over a 30 d shift in the timing of spring cold extremes in these areas (Fig. S17). During autumn (Fig. 6c), the anomalously coldest days are projected to shift to earlier in the season for most high-latitude regions in the Northern Hemisphere. For example, in the multi-model mean, the anomalously coldest days are projected to occur up to about 30 d earlier than they did in the mid-20th century in some regions in northern Canada and northern Eurasia. This change in the timing of anomalously cold days suggests an overall flattening of the seasonal cycle in these extratropical Northern Hemisphere regions. Coupled with the cold extremes warming at a faster rate than average temperatures, this suggests these regions will generally experience a longer-duration warm season and a shorter-duration cold season, in confirmation with previous studies (e.g. Dwyer et al., 2012; Chen et al., 2019).