Human-induced changes in extreme cold surges across the Northern Hemisphere

Abstract

Extreme cold surges, very large temperature drops over a short period of time, have serious impacts on human health, energy supply and ecosystems. While changes in temperature variability and cold extremes in a warming climate are well understood, changes in extreme cold surges and their driving mechanisms are not. Here we show that extreme cold surges have robustly weakened in middle-to-high latitude continents during autumn and winter but have remained almost unchanged in lower latitudes. By diagnosing near-surface thermodynamic budget, we find that this change is mainly induced by anthropogenic forcing. Greenhouse gas forcing decreases the meridional temperature gradient and associated variability in middle-to-high latitudes but has minimal impact in lower latitudes. This leads to similar spatial pattern of changes in nonlinear horizontal temperature advection that dominantly drives the extreme cold surges. Influenced by the same mechanism, extreme cold surges during winter across middle-to-high latitudes will continue to weaken in the future, with an 8%−13% reduction in their strength by the end of the century under the SSP 3-7.0 scenario.

This study shows that human-induced warming has weakened extreme cold surges in middle-to-high latitudes but has had minimal effect in lower latitudes. This is due to reduced north-south temperature differences and this pattern of change is projected to persist with future warming.

Introduction

The latest World Meteorological Organization report stated that the global average near-surface temperature in 2024 was 1.55 °C above the pre-industrial baseline¹. Warming has resulted in a reduction in cold extremes in general. The Sixth Assessment Report (AR6) of the Intergovernmental Panel on Climate Change (IPCC) has concluded that it is virtually certain the frequency and intensity of cold extremes have decreased at global and continental scales and will continue to decrease in the future². In large areas of the northern middle- and high-latitudes in winter, observed daily cold extremes have become less frequent and less severe^3–6, supported by both modeling response to Arctic sea ice loss^7–10 and model simulations forced by anthropogenic forcing¹¹. Cold extremes that were examined in those studies have mostly been defined as the annual coldest daily daytime or nighttime temperatures or relatively when daily minimum or daily maximum temperatures below their 10th percentile¹².

Despite the general focus on changes in cold extremes, limited attention has been given to past and future changes in a specific type of cold extremes—extreme cold surge—defined by sharp and large temperature drop in a day or within a few days [e.g., ^13–17]. These extreme cold surge events can have a profound impact on human health, natural ecosystems and energy supply. A sudden, large decrease in temperature over a short period can weaken the human immune system, trigger immune evasion¹⁸, and exacerbate epidemic influenza¹⁹, increasing the risk of respiratory mortality²⁰. Extreme cold surges during the cold season can also stress plants, inhibiting cold acclimation, triggering premature dormancy breaks, and inducing frost damage. These effects suppress physiological activity, disrupt biochemical metabolism, and ultimately reduce crop yields^21,22. Additionally, extreme cold surges can disrupt energy supply and transportation²³. In February 2021, a severe cold surge struck the Great Plains, causing air temperature to plummet by 20 °C within a single day. The event, compounded by inadequate preparedness, lead to widespread power outages, traffic incidents, and widespread winter storm warnings. The resulting collapse of the Texas energy infrastructure left millions of people without power, causing more damage than any disaster in the state’s history^24,25. In February 2024, record-breaking blizzards, freezing rain, and 14 °C temperature drops within one day brought massive disruption to China’s travel rush, leaving millions of people stuck on icy highways, in train stations, and at airports^26,27.

Although extreme cold surges, driven by cold air outbreaks, can exert disproportionate socioeconomic impacts on Northern Hemisphere continents, our understanding about their past changes and future responses to warming remains limited. While several studies have analyzed changes in cold surges across parts of East Asia^14–17, generalizing these findings is challenging due to different definitions of cold surges, and cold surge defined in some studies may not be relevant to impacts. Previous studies have shown a decrease in intra-seasonal winter temperature variability—often defined by temperature anomalies from their daily climatology—across middle- to high-latitude regions^28–36. Some studies have attributed this decrease to human activity^28,33,35, possibly through a reduction in the mean temperature gradient²⁹. Changes in distributional properties, such as variance and skewness, may be used to infer changes in the intensity of cold or warm anomalies in daily temperature³⁷. However, because daily temperatures are not independent and identically distributed random variables—there is a strong autocorrelation in daily temperature as well as an annual cycle in daily temperature variance—and because extreme cold surges occur at the tail end of the distribution of day-to-day temperature variation, it is not possible to infer changes in extreme cold surges solely from changes in daily temperature variance and skewness. In fact, some researchers argue that warming-induced changes in the Arctic may result in changes in atmospheric circulation (e.g., warmer or disrupted stratospheric polar vortex^38–40, nonlinear feedback of suppressed synoptic eddy activities⁴¹) favor southward intrusions of cold air from the Arctic^38,40–42, that ultimately lead to more frequent cold surges.

The lack of knowledge of how extreme cold surges have responded to global warming in the Northern Hemisphere motivates us to investigate this phenomenon and its underlying physical mechanisms. Using modern reanalysis product and observational data, we examine the long-term changes in extreme cold surges during cold seasons, defined by the seasonal maxima of daily temperature drop. We find a strong decrease in extreme cold surge intensity in the middle-to-high latitudes, while lower latitudes exhibit little changes–contrasting with the hemispheric-scale warming of extreme cold temperatures. To detect human influence on historical trends, we use a signal-to-noise analysis and large ensemble simulations of climate models forced with individual external forcings as well as the combined effect of all external forcings. Unlike previous detection and attribution studies that aim at separating the contribution of external forcing from internal variability (noise), we take an additional step by analyzing the near-surface thermodynamic budget^43,44 to diagnose the dynamical and thermodynamical processes involved—offering a deeper understanding. Finally, we project future changes in extreme cold surges by comparing the ensemble-mean intensities between the historical period and future period.

Results

Historical changes in extreme cold surges

Figure 1 a, b illustrate the spatial maps of linear trends in extreme cold surge intensity over land from 1960 to 2022, based on the European Center for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) dataset. Extreme cold surge intensity is defined as the daily temperature tendency (∂T/∂t) on the day with the strongest daily temperature drop within the season (Methods). The intensities of extreme cold surges show statistically significant weakening trend. Specifically, an increasing trend in ∂T/∂t indicates a less intense temperature drop. This weakening is evident over high latitudes during autumn and extends farther into the middle latitudes in winter, encompassing most regions of Eurasia and North America. Over the past 60 years, there was a 1 to 2 °C decrease trend of extreme temperature drop in the middle-to-high latitudes (between 50 °N and 80 °N). This weakening is noteworthy, considering the average extreme cold surge intensity during 1960–2022 is in the range between 8–12 °C over the region. In contrast, extreme cold surge intensity in lower latitudes (between 20 °N and 50 °N) shows minor change, although localized increases have been detected, such as in western North America during autumn. Overall, 20.3% and 14.3% of grid boxes in the middle-to-high latitudes show a statistically significant (at the 5% level) weakening of extreme cold surge intensity in fall and winter, respectively, while only 4.2% and 3.6% show a significant increase. A field significance test⁴⁵ confirms that the weakening of extreme cold surge intensity is statistically significant at the 5% level. In contrast, changes in the lower latitudes are more mixed, with fewer than 5% of grid boxes showing statistically significant weakening or strengthening in either seasons, indicating that changes in extreme cold surge intensity in lower latitudes are not statistically significant. In certain countries like China, cold surge alerts are issued when temperature also drops to specific thresholds, such as daily minimum temperatures below 4 °C or 0 °C¹³. Additionally, we compute the trends in extreme cold surge intensity when daily minimum temperatures fall below 4 °C and 0 °C, respectively. Supplementary Fig. 1 displays results that closely mirror the patterns observed in Fig. 1a, b. To simplify the presentation, we primarily focus on results based on seasonal maximum daily temperature drops, irrespective of the magnitude of the daily minimum temperature. The use of observation-based Berkeley Earth gridded daily temperature data produces comparable results (Supplementary Figs. 2a, b), reinforcing the confidence in the ERA5 reanalysis dataset’s ability to capture long-term changes in extreme cold surge intensity. The conclusions regarding the weakening of extreme cold surges remain consistent when trends are computed based on daily minimum surface air temperature, the maximum temperature drop over three days, or the seasonal strongest cold temperature advection (Supplementary Figs. 2c–h). This pattern is distinct from trends in seasonal coldest daily minimum surface air temperature, which demonstrate warming across the land (Supplementary Figs. 2i, j).

Fig. 1. Historical trends in extreme cold surge intensity (daily ∂T/∂t) from 1960 to 2022.

a Autumn and (b) winter trends based on ERA5 reanalysis. c–h as in (a, b), but for the ensemble-mean trends derived from simulations conducted with the CESM2, CanESM5 and MIROC6 models under historical ALL-forcing. The unit is Kday⁻¹decade⁻¹. Black dots in (a) and (b) mark trends significant at the 5% level. Black dots in (c–j) indicate at least 75% of members of the large ensembles agree on the sign of trends.

Large ensemble simulations using three earth system models–CESM2, CanESM5 and MIROC6–under historical all forcing (ALL) reveal a consistent pattern of changes in extreme cold surge intensity (Fig. 1c–h). The results from these simulations are consistent among models being used, and also consistent with observational data. In regions where observations show consistent weakening of extreme cold surge intensity, the model simulations also show agreement across different model ensembles. This suggests that the observed weakening in extreme cold surge intensity is a robust feature of the climate’s response to external forcing, rather than a manifestation of internal variability within the climate system. In lower latitudes, a slight increase in extreme cold surge intensity during autumn is evident in simulations conducted with MIROC6 and CESM2. However, this increase is absent during winter in these simulations and it is not seen in either autumn or winter in the simulations conducted with CanESM5. This indicates that the observed slight increase in extreme cold surge intensity in lower latitudes is not a robust feature of climate’s response to external forcing (see also trends from individual members in Supplementary Fig. 3).

Human influence on changes in extreme cold surges

The strong similarity between the observed and simulated responses under ALL forcing in changes to extreme cold surge intensity in middle-to-high latitudes highlights a key role of external forcing in these observed changes. To determine the level of significance and the timeframe when human influence on extreme cold surge intensity may emerge, we compared trends (signal) in observations with the variability of trends (noise) in model simulations, producing signal-to-noise ratios for trends estimated for periods starting in 1960 and ending in various years. A similar comparison was also conducted for trends computed from individual model runs (Methods). Results are plotted in Fig. 2. It appears that signals in the ERA5 data in the middle-to-high latitudes became statistically significant starting in 2005 when compared with noise simulated by CESM2 and MIROC6 for both winter and fall. Signals become significant starting in 2015 in autumn and starting in 2010 in winter when compared with noise simulated by CanESM5. These findings clearly indicate the robust emergence of the signal in ERA5 data, despite some uncertainty regarding the timing of emergence when compared with noise simulated by different models. Additionally, the signal-to-noise ratios based on ERA5 data are well within the range of signal-to-noise ratios when individual model runs are used to estimate signals, demonstrating consistency between model-simulated response and observations.

Fig. 2. Signal-to-noise ratio of trends in extreme cold surge intensity as a function of record length, for periods starting in 1960 or 1961 and ending in the year indicated on the x-axis.

Results for area-averaged cold surge intensity over 50^∘N–80^∘N are shown in the left two columns (a, b, e, f, i, j), while those for the 20^∘N–50^∘N average appear in the right two columns (c, d, g, h, k, l). The top, middle, and bottom panels present results when simulations using CESM2, CanESM5, and MIROC6 are employed to compute the noise in trends, respectively. Values for autumn are shown in (a, e, i), while those for winter appear in (b, f, j). Signals (trends) derived from ERA5 reanalysis are depicted as thick solid lines, whereas those computed from individual model runs are shown in gray. The magenta line represents the threshold at which the signal is statistically significant at the 5% level.

The signal-to-noise ratios computed for the area between 20 °N and 50 °N (right two columns of Fig. 2) are not significantly different from what would be expected due to natural variability. This suggests that the sporadic trends seen in either the ERA5 data or model simulations for the lower latitudes are unlikely forced by external forcing. While there appears to be a slight uptick in the signal-to-noise ratio during DJF when noise is estimated using CESM2 or MIROC6 simulations, this does not seem to be significant, as the signal-to-noise ratio generally does not exceed the threshold continuously (Fig. 2d, h).

Anthropogenic greenhouse gases (GHGs) are the primary external forcing responsible for the weakening of extreme cold surge intensity in the middle-to-high latitudes, as shown in CESM2 large ensemble simulations (Fig. 3). The linear trends of extreme cold surges in the ALL-forcing experiments are consistent with that of response to GHG forcing, whereas the change due to anthropogenic aerosol (AAER) forcing are of opposite sign. We note strengthening in response to AAER forcing can be of similar magnitude to the weakening under GHG forcing in some places. However, this is mainly due to the much stronger climatological cold surge intensity in the AAER forcing simulations, which results from colder background temperatures (Supplementary Fig. 4). When changes in extreme cold surge intensity are expressed relative to their long-term climatology, the magnitude under GHG and ALL forcing are similar, while those under AAER forcing are minimal (Supplementary Fig. 5). We also note that the magnitude of cold surge intensity weakening under GHG forcing is not always greater than that under ALL forcing. Sampling uncertainty may have played a role, as there is considerable spread in the model-simulated responses across different model runs under the same forcing (Fig. 2). Other external forcings, such as biomass burning aerosols play negligible roles in influencing the strengths of cold surges. In contrast, extreme cold surges intensity in the lower latitudes exhibits only minor changes in response to external forcing, consistent with observations.

Fig. 3. Ensemble-mean trends in extreme cold surge intensity in CESM2 simulations under different external forcings.

Trends for fall are shown in the left panel (a, c, e, g, i), while those for winter appear in the right panel (b, d, f, h, j). ALL, GHG, AAER, BMB, and EE represent historical ALL forcing, greenhouse gas forcing, anthropogenic aerosol forcing, biomass burning aerosols, and other external forcing, respectively. The unit is Kday⁻¹decade⁻¹. Black dots indicate at least 75% of members of the large ensembles agree on the sign of trends.

Physical mechanisms of changes in extreme cold surges

We use the near-surface thermodynamic heat budget to understand physical mechanisms relevant to the daily air temperature drop during the extreme cold surge days. Figure 4a, d display winter composite maps of the thermodynamic heat budget on extreme cold surge days, derived from the ERA5 reanalysis. Extreme cold surge intensity is primarily driven by horizontal temperature advection across most middle-to-high latitudes. Diabatic heating plays a secondary role. The residual term, which includes adiabatic processes, exerts strong influence near major topography such as Tibet Plateau and the Rockies. Model simulations yield consistent results, supporting a dominant role of temperature advection in driving change of extreme cold surge intensity. The composite spatial patterns and amplitudes of horizontal temperature advection closely resemble those of the maximum temperature drop in CESM2 large ensemble (Fig. 4e, f), underscoring the pivotal role of temperature advection in the changes in extreme cold surge intensity in model-simulated response to external forcing. The findings are consistent when analyzed with autumn data (Supplementary Fig. 6).

Fig. 4. Physical mechanisms driving extreme cold surges.

a–d Composite maps of the near-surface thermodynamic heat budget during extreme cold surge days based on ERA5 reanalysis for winter (DJF): (a) daily temperature tendency, b horizontal temperature advection, c diabatic heating, and (d) residual term including adiabatic processes. e, f As in (a, b) but for the ensemble mean of the CESM2 large ensemble simulation. The unit is K day⁻¹.

Further decomposition analysis shows that nonlinear temperature advection (advection of temperature gradient anomaly by anomalous flow) is the dominant contributor to the changes of total temperature advection (Supplementary Figs. 7, 8). Comparison of the trends in nonlinear temperature advection from both ERA5 reanalysis and CESM2 large ensemble (Fig. 5a, b) with the trends in extreme cold surge intensity (Fig. 1b,d) reveals that the nonlinear temperature advection is the dominant contributor to changes in extreme cold surge intensity.

Fig. 5. Contributions of temperature gradient and wind to nonlinear temperature advection.

a Trends in nonlinear temperature advection based on ERA5 reanalysis for winter (DJF). c, e As in (a), but showing contributions from changes in temperature gradient and wind, respectively. b, d, f As in a, c, e but for the CESM2 ensemble-mean results. The unit is Kday⁻¹decade⁻¹.

Nonlinear temperature advection $v^{\prime }d{T}^{\prime }/dy$ involves both a dynamical factor (e.g., atmospheric circulation characterized by wind $v^{\prime }$) and a thermodynamical factor (e.g., temperature gradient anomaly $d{T}^{\prime }/dy$)⁴⁶. However, fully disentangling the dynamical and thermodynamical effects is inherently difficult, as variability in the temperature gradient also reflects wind variability (i.e., large change in temperature gradient due to passing of a frontal system is affected by frontal wind). Nevertheless, it is possible to separate the contribution primarily due to changes in $\mid v^{\prime }\mid$ from the remainder, which can be approximately regarded as contribution from temperature gradient changes (Methods). Figure 5 and Supplementary Fig. 9 display changes in these components based on ERA5 reanalysis and CESM2 simulations. The long-term trends in nonlinear temperature advection (Fig. 5a, b) are predominantly driven by changes in the temperature gradient (Fig. 5c, d). Wind-related factors contribute to regional decreasing trends over Europe and slight increasing trends in parts of North America in the ERA5 reanalysis (Fig. 5e), yet their effects are negligible in the model simulated mean responses (Fig. 5f). This suggests that low-frequency natural variability may have led to a reduction in extreme cold surge intensity in certain regions of North America, while contributing to a slight strengthening over Europe. Signal-to-noise analysis of the 50 °N–80 °N averaged nonlinear temperature advection and its associated contributions from the temperature gradient and wind (Supplementary Fig. 10) confirms a detectable human-induced change in nonlinear temperature advection, as well as in its temperature gradient component. However, human-induced changes in the wind component are not detectable. Overall, there is a lack of evidence supporting a human-induced circulation change that could have resulted in changes in extreme cold surge intensity. Nonetheless, natural variability in circulation may have moderated human-induced weakening of extreme cold surge intensity in parts of middle-to-high latitudes (Fig. 5e, f).

An alternative explanation for the changes in extreme cold surge intensity is that $\frac{d{T}^{\prime }}{dt}\approx -\frac{d\eta }{dt}\frac{d\overline{T}}{dy}$, according to Taylor’s expression, $T^{\prime }\approx -\eta \frac{d\overline{T}}{dy}$, where η is a meridional displacement of air masses, and $\frac{d\overline{T}}{dy}$ is the mean temperature gradient^29,46. Regionally averaged cold surge intensity is, in general, significantly correlated with the regionally averaged seasonal-mean temperature gradient. In the ERA5 data, the correlation coefficients for the middle-to-high latitudes are 0.69 and 0.34 for fall and winter, respectively. The corresponding correlation coefficients are 0.47 and 0.15, respectively, after temporal trends in both series are removed. The correlation coefficients for the lower latitudes are 0.32 and 0.57 for fall and winter, even after temporal trends are removed in both series. Extreme cold surge intensity and averaged seasonal-mean temperature gradient are also significantly correlated in large ensemble members, with the smallest correlation coefficient in lower latitude in fall, at 0.26, after model simulated responses represented by the model ensemble mean are removed from corresponding series. The highest correlation coefficient is obtained for the middle-to-high latitudes in winter. Overall, correlations are overwhelmingly higher in the middle-to-high-latitude regions, though the correlations can be higher in the lower latitudes in a sizable number of runs (Supplementary Fig. 11). The correlation coefficient between extreme cold surge intensity and temperature gradient in the model ensemble-mean response is high, with values range from 0.67 to 0.97.

Future projections

The initial-condition large ensembles project a continued weakening of extreme cold surges in middle-to-high latitude regions during the future period 2065-2099, compared to the recent past (1980–2014). As shown in Fig. 6, by the end of the 21st century, all models project a weakening of extreme cold surges in these regions, although the level of weakening varies, with the strongest reduction projected by the highest sensitivity model CanESM5^47,48. Extreme cold surge intensity over 50 °N–80 °N latitudes is projected to weaken by 4.37% in autumn and 7.83% in winter in the CESM2 large ensemble, by 13.13% in autumn and 13.36% in winter in the CanESM5 large ensemble, and by 9.90% in autumn and 9.30% in winter in the MIROC6 large ensemble. The magnitude of projected changes in the CESM2 large ensemble is smaller than that in other model ensembles, despite the high climate sensitivity of CESM2⁴⁸. The cause of this discrepancy is unclear, but we note that the climatological cold surge intensity in the CESM2 large ensemble is also weaker than in the other two large ensembles. These projected reductions in extreme cold surge strength are consistent with projected magnitude in the reduction of horizontal temperature gradient (Supplementary Fig. 12). In contrast, extreme cold surges in lower latitudes are projected to change little, in agreement with the minimal changes projected for the horizontal temperature gradient.

Fig. 6. Projected changes in extreme cold surge intensity from 1980–2014 to 2065–2099, based on large ensemble simulations from three models: CESM2, CanESM5, and MIROC6.

a–c Projected changes for autumn (SON), and (d–f) for winter (DJF). The unit is K day⁻¹. Black dots indicate at least 75% of members of large ensembles agree on the sign of change.

Future projections under the SSP1-2.6 and SSP5-8.5 scenarios show patterns similar to those observed under SSP3-7.0 scenario, with a moderate reduction under SSP1-2.6 and a stronger reduction under SSP5-8.5 scenario (Supplementary Figs. 13, 14 and Supplementary Table 1). In particular, the intensity of extreme cold surges during winter across middle-to-high latitudes is projected to weaken by 3−7% under SSP1-2.6 and by 10−15% under SSP5-8.5 scenarios.

Discussion

Amid the weakening of extreme cold temperatures worldwide², the exceptional nature of recent impactful extreme cold surges, particularly the 2021 Great Plains cold event, where a record-breaking temperature drop triggered cascading failure of interconnected energy systems, and the 2024 cold event in China, which massively disrupted transportation during a peak travel period, raise important questions about past and future changes in extreme cold surges. We show that over the past 63 years, extreme cold surges have weakened in the middle-to-high latitudes during autumn and winter but have changed little in lower latitudes. The decrease in extreme cold surge intensity is caused by human-induced warming, which reduces the horizontal temperature gradient, thereby weakening nonlinear temperature advection in the middle-to-high latitudes. While in the lower latitudes, temperature gradient is small, there is thus a small room for it to change. Consequently, the change in cold surge intensity is also minimal. This understanding is consistent with the observed decrease in daily and sub-seasonal temperature variability in middle-to-high latitudes and their human causes^32–34, but does not support the speculation of increasing rapid temperature changes globally by Lee³⁶. While it has been argued that the increasing trend of daily temperature variability³⁴ and rapid temperature flips⁴⁹ in lower latitudes of Northern Hemisphere may have significant implications, this increase in daily temperature variability may not have resulted in a detectable strengthening of extreme cold surges in the past, as the horizontal temperature gradient is small in these regions. Our study also highlights that the latitudinally non-uniform change in extreme cold surges is in stark contrast with the hemispheric-scale warming in seasonal/annual minimum temperature². Model simulations project that this historical pattern of changes in extreme cold surges will continue in the future. This indicates that events like the 2021 Great Plains cold surge and the 2024 cold surge in China will likely decrease in magnitude over the coming decades.

Methods

Reanalysis and observations

We use daily-mean near-surface air temperature at 2 meters, zonal and meridional wind at 10 meters, diabatic heating rate at model surface level, and near-surface maximum and minimum air temperature from the ERA5 reanalysis⁵⁰ on the 1^∘ × 1^∘ longitude-latitude grids. We focus on the period of 1960–2022 as the observational data since 1960 is more reliable owning to the improved observational networks. Only the autumn (September to November) and winter (December to February) seasons are analyzed, because winter has the most intense cold surges followed by autumn. To test the robustness of our results, we also employ gridded observations of daily near-surface temperature from Berkeley Earth from 1960 to 2021⁵¹.

Modeling experiments

We use output from initial-condition large-ensembles from three coupled atmosphere-ocean models: CESM2⁵², CanESM5⁵³ and MIROC6⁵⁴. Each experiment consists of 50 ensemble members with historical forcing from 1960 to 2014, followed by Shared Socioeconomic Pathways 3-7.0 (SSP3-7.0) future radiative forcing scenarios until 2022. We use simulations under SSP3-7.0, as ensemble members from these simulations provide all the required variables. Projections under SSP1-2.6 and SSP5-8.5 scenarios are also briefly discussed for comparison.

In addition to the ALL-forcing experiments, four experiments with single forcing from CESM2 were examined for the driver of extreme cold surge trend: only greenhouse gases evolving (15 members), only anthropogenic aerosols evolving (20 members), only biomass burning aerosols evolving (15 members) and everything else evolving (15 members).

Each ensemble member of a climate model differs by only small changes in initial conditions, and thus the differences between ensemble members represent the internal variability of the climate system⁵⁵. For future changes by the end of the 21st century, we calculate the difference between the historical period (1980–2014) and the future period (2065-2099).

Identification of extreme cold surges

The World Meteorological Organization considers a cold wave as a cold extreme associated with a sharp and significant drop of air temperatures persisting for more than a day⁵⁶. Considering the impacts, the China National Standard¹³ classifies a cold surge based on temperature drop of more than 8, 10 or 12 degrees Celsius during a period of 1, 2, or 3 days, respectively, with the daily minimum temperature also falling below 4^∘C. Cold alerts may also be issued when temperature drop does not reach those thresholds. In this study, we use the seasonal largest daily-mean surface air temperature drop to represent “extreme cold surges”. Specifically, we first calculate the time derivative of daily-mean surface air temperature using the central difference method in each season, obtaining 91(or 90) daily temperature derivatives for autumn(or winter). We then identify the minimum temperature derivative within each season and define the extreme cold surge intensity as the value of the temperature derivative on that day.

Signal-to-noise calculation

To test whether the observed trends are statistically significant, we compute the signal-to-noise ratios of extreme cold surge trends. Here, the signal-to-noise ratio is defined as the ratio between the linear trend magnitudes of the observed cold surge intensity and the standard deviation of the linear trends for the time series of the same length, estimated separately from each climate model in the large ensembles. More specifically, the observed cold surge intensity is calculated as the area-weighted average of extreme cold surge intensity over 50 °N–80 °N (or 20^∘N–50^∘N) using ERA5 reanalysis data. The noise time series for each model is calculated by subtracting the ensemble mean from of the 50 °N–80^∘N (or 20^∘N–50^∘N) averaged extreme cold surge intensity time series in individual ensemble members. Since each ensemble member differs by only small changes in initial conditions, and thus these noise time series represent the internal variability of the climate system. Signal-to-noise ratios are then analyzed as a function of increasing record length for trends for the periods starting from 1960, with a minimum record length of 15 years. We consider the trend to be statistically significant if the signal-to-noise ratio exceeds 1.645, based on one-sided Student’s t-test. The time of detection is determined by the first year where the signal-to-noise ratio surpasses this threshold and remains above it thereafter.

Physical origin of extreme cold surges

We employ the near-surface thermodynamic heat budget^43,44 to explain the changes of temperature tendency in the extreme cold surge days. Specifically, the near-surface thermodynamic equation can be expressed as:

$$\frac{\partial T}{\partial t}=-\mathbf{V}\cdot \nabla T+\frac{Q}{c_p}+Res,$$ 1

where T is the daily near-surface temperature, V is the daily near-surface vector wind,  ∇ is the horizontal gradient operator. We approximate the near-surface fields with 2-meter temperature and 10-meter wind, respectively, which is similar to the results obtained from using temperature and winds in the lowest model level. Q is the daily diabatic heating, c_p is the specific heat of dry air. Res denotes residual term, including the vertical temperature advection and adiabatic heating. The heating rate from diabatic heating $\frac{Q}{c_p}$ is estimated as the mean temperature tendency due to parametrisations at the lowest model level following Clark and Feldstein⁴³. This term and the residual term play secondary roles as the leading thermodynamic balance of extreme cold surge is between the temperature tendency and horizontal advection (Fig. 4).

The horizontal temperature advection anomaly in equation (1) can be further decomposed to three components: advection of temperature gradient anomaly by mean flow, advection of mean temperature gradient by anomalous flow and advection of anomalous temperature gradient by anomalous flow.

$${\left(-\mathbf{V}\cdot \nabla T\right)}^{\prime }=-\overline{\mathbf{V}}\cdot \nabla T^{\prime }-{\mathbf{V}}^{\prime }\cdot \nabla \overline{T}-{\mathbf{V}}^{\prime }\cdot \nabla T^{\prime }$$ 2

Decomposition of wind and temperature gradient contributions to nonlinear temperature advection

Nonlinear temperature advection involves both a dynamical factor (e.g., atmospheric circulation characterized by wind $\mid v^{\prime }\mid$) and a thermodynamical factor (e.g., temperature gradient $d{T}^{\prime }/dy$)⁴⁶. To quantify their relative contributions, we decompose the nonlinear temperature advection into two components: contribution primarily due to changes in $\mid v^{\prime }\mid$ and the remainder. More specifically, following the method used in previous studies^57,58, the nonlinear temperature advection can be written as $-v^{\prime }\frac{d{T}^{\prime }}{dy}=\mid v^{\prime }\mid \frac{-v^{\prime }\frac{d{T}^{\prime }}{dy}}{\mid v^{\prime }\mid }=\mid v^{\prime }\mid T_y$, where prime denotes the deviation from the climatology $\overline{\left(\right)}$, and thus $\mid v^{\prime }\mid$ represents the magnitude of anomalous wind. T_y is the anomalous temperature gradient weighted by anomalous wind speed. Changes of nonlinear temperature advection $\mathrm{\Delta }\left(\mid v^{\prime }\mid T_y\right)$ can be further decomposed as

$$\mathrm{\Delta }\left(\mid v^{\prime }\mid T_y\right)={\underbrace{\mathrm{\Delta }\mid v^{\prime }\mid \overline{T_y}}}_{wind}+{\underbrace{\left(\mathrm{\Delta }\left(\mid v^{\prime }\mid T_y\right)-\mathrm{\Delta }\mid v^{\prime }\mid \overline{T_y}\right)}}_{temperaturegradient},$$ 3

where the first term on the right-hand side of equation (3) denotes the changes of nonlinear temperature advection due to the changes of anomalous wind. The second term on the right-hand side denotes the difference between the total changes of nonlinear temperature advection and the wind component, and thus can be roughly considered as a thermodynamical contributor primarily due to changes in temperature gradient.

Author contributions

Y.N.: Conceptualization, Formal analysis, Visualization, Writing - original draft. Y.S. and X.Z.: Conceptualization, Writing - review & editing. G.C.: Writing - review & editing. All authors contributed to the investigation, discussed the results, and approved the final manuscript.

Peer review

Peer review information

Nature Communications thanks Yongkun Xie and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The ERA5 reanalysis data used in this study is available at 10.24381/cds.bd0915c6. Berkeley Earth observations are available at http://berkeleyearth.org/archive/data/. The CESM2 data are available at https://www.cesm.ucar.edu/community-projects/lens2/data-sets. The CanESM5 and MIROC6 data are available at https://esgf-node.llnl.gov/search/cmip6/.

Code availability

The key codes for trend calculation, significance testing, signal-to-noise analysis and temperature advection decomposition are provided in the Supplementary Code. Additional code to reproduce the figures of this study is available upon request from the corresponding author.

Competing interests

The authors declare that they have no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-62576-2.