Introduction

Heatwaves, characterized by prolonged periods of abnormally high temperatures, are among the deadliest and most disruptive climate hazards globally1,2,3. There is overwhelming evidence that climate warming is causing more frequent, more intense, and longer-lasting heatwaves in the hot summer season over most regions around the world4,5,6. In contrast to the well-established knowledge of summer heatwaves, we know much less about warm spells (or heatwaves) that occur in cold winter seasons, one type of off-season events that occur outside their typical or expected seasons. This knowledge gap is of particular concern given the high vulnerability of both human and natural systems, especially challenging for communities unprepared for extremely high temperatures during traditionally cold months, where hot weather has typically not been known to occur.

Winter warm spells (or winter heatwaves) have occurred worldwide and have caused severe and, in some cases, irreversible impacts on agricultural yield, energy demand, water resources, and ecosystems7,8,9,10. One of the notable examples occurred in central-southern Queensland of Australia from August 29 to 31, 2009, and has severely disrupted agriculture by causing widespread crop failure due to water stress11. Similarly, an unexpected warm spell across the Alps in December 2015 accelerated glacier melting, causing terrestrial ecosystems exposed to unusually high temperatures12,13. Such an altered atmospheric environment can prematurely break the dormancy of woody species, leading to an early bud development7. Winter warm spells can also drive cascading events, such as snowmelt-induced flooding14, heightened wildfire occurrences15, and exacerbated drought conditions16. For example, a record-breaking winter warm spell in February 2019 over England led to arid conditions, parched fields, and widespread wildfires across East Sussex, Saddleworth Moor, and North Wales17. Other prominent examples are the 1996 winter warm spell in China18, the 2021 winter warm spells across Europe and parts of Asia19, and the hottest-ever winter temperature recorded in Australia in 202420. Winter warm spells may also have some positive aspects, such as reducing the severity of cold stress on human health and decreasing heating demand21. With growing evidence of these profound effects, winter warm spells are increasingly regarded as one of the critical climate phenomena. It is an urgent need to improve the understanding of winter warm spells to mitigate their resultant impacts effectively in a warming Earth.

Understanding winter warm spells is essential to reveal their drivers and underlying mechanisms. Most previous studies have focused on summer hot-season heatwaves and found that they are typically linked to anticyclonic circulation patterns and high-pressure systems22,23,24. These systems often lead to adiabatic subsidence, reduced cloud cover, and intense solar radiation reaching the surface23,25. Additionally, there is increasing evidence of the role of land surface processes in amplifying summer heatwaves26,27. This land-atmosphere feedback is often accompanied by reduced soil moisture and increased sensible heat flux, collectively intensifying surface warming28,29,30,31. In comparison, the physical processes driving winter warm spells are less understood. For instance, Beniston32 found that winter warm spells in the Swiss Alps are linked to the North Atlantic Oscillation, which influences snow cover and surface-atmosphere temperature feedback. Leach, et al.33 demonstrated that the winter warm spell in the Northern and Western Europe in February 2019 was associated with a narrow-tilted ridge stretching from northwestern Africa to southern Scandinavia, transporting warm subtropical air from the southwest. While these studies provide insights into the large-scale atmospheric conditions involved in specific regions, gaps remain in understanding the local processes driving winter warm spells worldwide. Yet, the quantitative attribution of the temperature anomalies during winter warm spells remains unexplored.

To address these knowledge gaps, here we investigate the occurring characteristics of winter warm spells across global land areas from 1979 to 2023, and examine their local mechanisms by quantifying the contributions of different physical processes to the temperature anomalies during warm spells based on the energy budget analysis. The temperature anomalies are decomposed into advection heating, adiabatic heating, and diabatic heating34,35,36. The diabatic heating term is further decomposed into net shortwave radiation, downward longwave radiation, surface latent heat flux, surface sensible heat flux, and ground heat exchange34. By exploring and comparing the contributions of these components, the present study aims to identify the dominant physical drivers of winter warm spells. Our findings are essential for improving the prediction of warm spell occurrence and developing effective strategies to mitigate their resultant impacts in a warming world.

Results and Discussion

Historical occurrences of winter warm spells

We begin by analyzing the multi-year climatological mean of winter warm spell metrics in the cold season (i.e., the coldest consecutive three calendar months) during 1979–2023 (Fig. 1; see Methods for details). Winter warm spells occur worldwide, with an annual average frequency of 2.02 events (Fig. 1a) and an annual participating day of 9.33 days (Fig. 1b). The average maximum duration of each warm spell event is 5.36 days (Fig. 1c), and the mean duration is 4.46 days (Fig. 1d). These winter warm spell events exhibit maximum and mean intensities exceeding 7.40 and 7.00 °C above the climatological winter temperature baseline (Fig. 1e, f).

Fig. 1: Observed climatology of global winter warm spells.
figure 1

Maps showing the climatological mean of annual mean frequency (a), participating days (b), maximum duration (c), mean duration (d), maximum intensity (e), and mean intensity (f) of winter warm spells over global land areas during 1979–2023. The embedded bar chart shows the climatology of the corresponding characteristics in different climate zones (G: global, Tr: tropical zone, A: arid zone, Te: temperate zone, P: polar zone, and C: cold zone). The latitudinal curves accompanying the maps show the zonal means of the climatology of the corresponding characteristics, and the shading indicates the spread of zonal mean values (mean ± s.d.).

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Distinct regional patterns are evident across different latitudinal and climate zones (Fig. 1), with the tropical zone exhibiting the highest values for all metrics except for intensity. Specifically, winter warm spells are more frequent and more persistent in the tropical zones such as central Africa, South Asia, and parts of South America, where both frequency (Fig. 1a) and participating days (Fig. 1b) exhibit the regional maximum. The mean frequency and participating days of warm spells in the tropical zone are 2.26 events and 10.62 days, which are 1.18 and 1.22 times higher than the global average (1.92 events and 8.73 days), respectively. This suggests that the tropical zone is particularly vulnerable to frequent and prolonged winter warm spells, likely due to relatively more stable atmospheric conditions that may favor and maintain warmer-than-average environments37. In addition, regions such as northern South America, northern Africa, and southwestern Asia experience extended winter warm spell durations, with both maximum and mean durations exceeding the global average. Conversely, both maximum and mean intensities of winter warm spells increase with latitude in the two hemispheres, reaching a maximum in high latitudes of the Northern Hemisphere. The highest values for both maximum and mean intensities are observed in the polar zone, with intensities reaching 13.20 °C and 12.52 °C, respectively (Fig. 1e, f). This larger intensity in higher latitudes is likely linked to stronger temperature variabilities in these regions38. Comparatively, winter warm spells in the tropical zone show markedly smaller maximum (2.31 °C) and mean intensity (2.16 °C). It is due to that the temperature variability and seasonal cycle are small, even a moderate temperature increase will cause warm spell occurrence37,39. These patterns highlight that while tropical regions experience more frequent and longer-lasting winter warm spells, polar regions are characterized by more intense temperature anomalies.

To examine the temporal changes in winter warm spells, we calculate the annual time series of spatially-averaged warm spell metrics over global land grid cells from 1979 to 2023. As shown in Fig. 2, all metrics except for intensity exhibit significant increasing trends at the 0.05 level, indicating a notable intensification of winter warm spell events since the 1980s. Specifically, the global mean annual frequency of winter warm spells has risen by 0.224 events per decade (Fig. 2a), accompanied by an increase in the annual participating days by 1.347 days per decade (Fig. 2b). The duration of these warm spells has also lengthened, with both maximum and mean durations prolonging by 0.360 and 0.134 days per decade, respectively (Figs. 2c, d). These intensifying trends are also seen in all climate zones (Supplementary Fig. 1). Notably, tropical warm spells exhibit the strongest upward trends in the frequency (0.541 events per decade), participating days (3.056 days per decade), and maximum duration (0.656 days per decade), which are 2.41 times, 2.27 times, 1.82 times the corresponding magnitudes of global mean trends, respectively. The greatest increases in mean duration of warm spells are seen in the temperate zone (0.187 days per decade), followed closely by that in the tropics (0.176 days per decade). Enhanced frequency and prolonged duration of these events indicate that traditionally cold seasons where hot weather has been previously known not to occur are now experiencing warmth, potentially disrupting energy demand21, agricultural cycles11, and public health40 in winter. The annual maximum and mean intensity exhibit significant decreasing trends of 0.305 °C and 0.334 °C per decade, respectively (Figs. 2e, f). The decrease in the intensity, despite overall winter warming, can be explained by the inverse relationship between warm spell intensity and their frequency (or duration)41. For each warm spell event, intensity is defined as mean temperature exceedance relative to the threshold by averaging all days during the event, and the annual maximum (mean) intensity is derived from the intensities of all events occurring in the same year. Thus, as the number of warm spell days increases, a decrease in the intensity can be expected. These trends suggest a shift towards more frequent and longer-lasting winter warm spells, underscoring the influence of climate warming on winter temperature extremes. This shift emphasizes the growing vulnerability of global land areas to extreme temperatures beyond the typical warm season, underlining the urgent need to explore the different contributions of potential drivers of winter warm spells.

Fig. 2: Long-term changes of global winter warm spells.
figure 2

Time series of the spatially-averaged annual mean of frequency (a), participating days (b), maximum duration (c), mean duration (d), maximum intensity (e), and mean intensity (f) of winter warm spells over global land areas from 1979 to 2023. The straight line indicates the linear trend, and the shading indicates the corresponding 90% confidence interval. Slope and p-value estimates for the trend per decade are given in parentheses.

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Decomposition of temperature anomalies during winter warm spells

During winter warm spells, positive temperature anomalies are observed across global land areas, with notable regional variations in the magnitude of these anomalies (Fig. 3a). To investigate the underlying mechanisms responsible for winter warm spells, we decompose these tempearature anomlies into three key components, namely, advection heating (Fig. 3b), adiabatic heating (Fig. 3c), and diabatic heating (Fig. 3d). Advection heating results from the horizontal movement of air masses, typically transporting warm air from lower to higher latitudes, or cooler air in the opposite direction42. As shown in Fig. 3b and Table S1, advection heating of winter warm spells in the tropics tends to have a weak negative contribution to temperature anomalies (−0.126 °C). This is likely caused by that cooler air masses from higher latitudes suppress surface warming, partially because horizontal temperature gradients are smaller in the tropical atmosphere due to the weaker Coriolis parameter near the equator43,44. In the non-tropics, winter warm spells experience considerable warming, partially due to the advection of warm air masses from the tropics to mid-to-high latitudes (0.122 °C), which was also observed during the Antarctic warm spell of March 202245. Across different non-tropical regions, the contribution of advection heating varies noticeably. Specifically, advection heating contributes positively to temperature anomalies in cold (+0.281 °C), temperate (+0.120 °C), and polar zones (+0.056 °C), whereas it has a negative contribution to warm spells in arid zones (−0.058 °C) (Fig. 3k and Table S1). Adiabatic heating, resulting from the compression and warming of descending air masses, is also a key contributor to temperature anomalies in high-latitude and high-altitude regions (Fig. 3c), which is consistent with the findings of Kim, et al. 36. The contribution of adiabatic heating is particularly pronounced in polar (+5.984 °C) and cold zones (+1.236 °C), for instance, in regions including Greenland, the west coasts of North America, and elevated terrains including the Rocky Mountains, Tibetan Plateau, and Andes, where sinking air masses warm markedly, thereby amplifying temperature increases.

Fig. 3: Decomposition of temperature anomalies during winter warm spells.
figure 3

a, Temperature anomalies of winter warm spells over global land areas during 1979–2023. The decomposition of temperature anomalies into the contributions of advection heating (b), adiabatic heating (c), and diabatic heating (d). The decomposition of the diabatic heating term into the contributions of net surface shortwave radiation (e), surface downward longwave radiation (f), surface latent heat flux (g), surface sensible heat flux (h), and ground heat flux (i). Regions with the composite mean not passing the 0.1 significance level by the Student′s t-test are masked out. j Boxplot showing the regional mean of the temperature anomalies and its decomposition into the contribution of different heating terms to winter warm spells in the tropics (pink bar) and non-tropics (grey bar). k, l Boxplot showing the regional mean of the temperature anomalies and its decomposition into the contribution of different heating terms to winter warm spells across different climate zones. The centerline indicates the median value, the box bounds depict the 25th and 75th percentile values and the whiskers indicate the lower and upper quartiles±1.5 times the interquartile range of the decomposition of temperature anomalies.

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Although both advection and adiabatic heating contribute to the temperature anomalies during winter warm spells, their magnitudes are much smaller than those of diabatic heating, which increases the air temperature to 7.801 °C (Fig. 3d). That is, positive temperature anomalies during winter warm spells in most global land areas are predominantly driven by diabatic heating, which represents the direct energy exchange between the Earth’s surface and the atmosphere46. This heating term is thus decomposed into (see Methods) net shortwave radiation (Fig. 3e), downward longwave radiation (Fig. 3f), latent heat flux (Fig. 3g), sensible heat flux (Fig. 3h), and ground heat flux (Fig. 3i). Among these surface processes, net shortwave (Fig. 3e) and downward longwave radiations (Fig. 3f) are the primary drivers of warming temperatures.

We notice that the contributions of surface heating are contrasting between tropical and non-tropical regions. Net shortwave radiation plays a dominant role in elevating temperatures (+3.424 °C) during winter warm spells in the tropics (Fig. 3e and Table S1), whereas it generally exerts a cooling effect in non-tropics except for southwestern North America and parts of western and southern Eurasia. This cooling effect is particularly pronounced in polar (−0.211 °C) and cold zones (−0.365 °C). Downwelling longwave radiation predominantly drives increases in temperature in non-tropical regions (+10.263 °C), particularly in polar zone (+15.794 °C) (Fig. 3f, l, and Table S1), aligning with previous studies47. By contrast, the contribution of downward longwave radiation to temperature anomalies during tropical winter warm spells is relatively weaker (1.246 °C). Latent and sensible heat flux anomalies (Fig. 3g, h, and Table S1) also play roles in modulating temperature changes. Both latent and sensible heat fluxes generally have cooling effects in tropical regions (−1.029 °C and −1.037 °C), while the latter contributes significantly to warming in non-tropics (+1.696 °C), especially in the cold zone (+2.437 °C). Ground heat flux typically has a cooling effect on winter warm spells in all climate zones (Fig. 3i and Table S1), with the strongest cooling effect observed in polar regions (Fig. 3l). Overall, the temperature anomalies during winter warm spells in the tropics are primarily driven by net solar radiation, while regions outside the tropics experience stronger contributions from downwelling longwave radiation (Fig. 3j).

Possible causes of heating processes

To further examine how local conditions contribute to the heating processes reported above, we apply a composite analysis method48,49 to examine the changes and evolutions of relevant variables associated with winter warm spells (Fig. 4). Cloud cover is a key factor modulating the effects of radiation fluxes on temperature anomalies. As shown in Fig. 4a, cloud cover exhibits positive anomalies in tropical regions and negative anomalies in non-tropical regions. This discrepancy aligns with the regional differences in the diabatic heating term of net solar radiation between tropical and non-tropical warm spells (recall Fig. 3e). In the tropics, reduced cloud cover during warm spells allows more solar radiation to reach the surface, directly intensifying surface heating. In contrast, non-tropical warm spells are associated with decreased solar radiation, which is largely due to high solar zenith angles in the cold season and even a presence of the polar night in high-latitudes (e.g., polar regions). Over these non-tropical regions, increased cloud cover further reduces incoming solar radiation at the surface. Simultaneously, cloudier skies reduce nighttime cooling by trapping more atmospheric heat, thus enhancing downward longwave radiation50. The added heat from increased downward longwave radiation in non-tropical regions helps elevate surface warming despite reductions in direct solar radiation (recall Fig. 3f).

Fig. 4: Composite anomalies of key variables associated with winter warm spells.
figure 4

The composite mean anomalies of total cloud cover (a), total precipitation (b), relative humidity (c), moisture divergence (d), soil moisture (e), and evaporation (f) associated with winter warm spells. Regions with the composite mean not passing the 0.1 significance level by Student′s t-test are masked out. The embedded boxplot chart shows the regional mean of the anomalies of corresponding variables associated with warm spells in the tropics (pink bar) and non-tropics (grey bar). The centerline indicates the median value, the box bounds depict the 25th and 75th percentile values, and the whiskers indicate the lower and upper quartiles±1.5 times the interquartile range of the composite mean anomalies.

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The formation of cloud cover is closely linked to precipitation and atmospheric moisture, both of which play crucial roles in inducing temperature changes during winter warm spells. As shown in Figs. 4b, d, precipitation and relative humidity exhibit significant positive anomalies in high-latitude regions of the Northern Hemisphere and negative anomalies in low- and mid-latitudes, particularly in tropical regions. In the tropics, suppressed precipitation and humidity collectively inhibit cloud formation, thereby increasing solar radiation reaching the surface. Additionally, anomalous moisture divergence is seen over the tropics (Fig. 4d), creating a drier atmosphere that intensifies winter warm spell activities. Such a hot and dry environment under clear skies can cause potential impacts on societies and ecosystems by inducing water scarcity, wildfire risks, and crop yield reduction51,52. In non-tropical regions, increased cloud cover and moisture convergence (i.e., negative divergence) create a more humid atmospheric condition. A cloudier and wetter atmosphere traps more outgoing longwave radiation and then re-emits it to the surface, thus increasing air temperatures near the surface49. Concurrently, increased air temperatures enhance the emitted longwave radiation into the surface, further contributing to surface heating53.

Dry atmospheric conditions over the tropics lead to negative soil moisture anomalies (Fig. 4e), limiting the available moisture for evaporation (Fig. 4f)54 and subsequently reducing latent heat flux released from the surface55. This reduction (i.e., upward heat transport from surface to atmosphere) weakens the cooling effect of evaporation56. Additionally, negative anomalies in sensible heat flux in the tropics indicate an increased heat transfer from the surface to the overlaying atmosphere, further warming near-surface air temperatures, and favoring the occurrence of winter warm spells in these areas. In non-tropical regions, especially high latitudes, soil moisture tends to exhibit positive anomalies, likely due to localized surplus rainfall (recall Fig. 4b).

Additional investigations into the difference in the day-to-day evolution of anomalies in these related fields between tropical and non-tropical regions are also crucial for understanding their contributions to winter warm spells. Here we examine the temporal evolution of the spatially-averaged processes associated with winter warm spells across tropics and non-tropics, spanning from six days prior to the onset (i.e., −6) to six days after the end (i.e., +6) of winter warm spells at a daily interval. As shown in Fig. 5, the changes in the anomalies of related atmospheric variables associated with winter warm spells are nearly opposite between the tropics and the non-tropics.

Fig. 5: Daily evolution of the regional mean of composite anomalies of key variables associated with winter warm spells.
figure 5

The daily evolution of the regional mean of composite anomalies of moisture divergence (a), total precipitation (b), total cloud cover (c), relative humidity (d), soil moisture (e), and evaporation (f) from 6 days before the onset to 6 days after the end of identified winter warm spells in the tropics (pink line) and non-tropics (grey line). Note that the label “Onset” denotes the day when the warm spell event starts, “− 2” denotes two days before the onset, and so on; “End” denotes the day when the warm spell event ends, “+2” denotes two days after the end, and so on.

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Prior to the onset of winter warm spells in the tropics, moisture divergence exhibits positive anomalies and precipitation shows negative anomalies (Fig. 5a, b). The moisture divergence and reduced precipitation contribute to a dry atmospheric condition (Fig. 5d), thus inhibiting cloud formation (Fig. 5c). The inhibited cloud suggests a potential increase in surface solar radiation under clear skies. In comparison, the magnitude of negative precipitation anomalies in non-tropics is relatively smaller than in tropics, indicating that non-tropical winter warm spells experience relatively weaker dry conditions than tropical events (Fig. 5d). Then, the anomalies of precipitation and moisture divergence in both tropical and non-tropical regions begin to exhibit opposite changes three days prior to the winter warm spells.

In the tropics, the moisture shifts from a state of divergence to convergence, corresponding to precipitation anomalies becoming positive from Day –3 to Day –2 (Fig. 5a, b). This transition reduces the magnitude of negative cloud cover anomalies (Fig. 5c). However, due to that increased precipitation and moisture convergence exist for only one day, relative humidity anomalies remain negative (Fig. 5d). Two days before the onset of winter warm spells, positive divergence anomalies along with negative precipitation and cloud cover anomalies tend to intensify until the warm spell onset (Fig. 5a–c), further enhancing solar radiation (Supplementary Fig. 2e) and amplifying surface warming. Although these changes tend to weaken after the warm spell onset, relative humidity anomalies continue to decrease (Fig. 5d), creating a favorable condition to maintain the warm spell events. The peak of the negative relative humidity anomalies is observed during the warm spell episodes (Fig. 5d), indicating that tropical regions are enveloped by an exceptionally dry and hot atmosphere. Additionally, soil moisture anomalies remain negative throughout the entire warm spell period from Day –6 to Day +6, and they intensify two days before the onset and reach their lowest values at the warm spell termination (Fig. 5e). This amplified soil moisture depletion causes an intensification of negative evaporation anomalies (Fig. 5f), suggesting that the atmosphere is too dry to evaporate despite rising temperature. The reduction in evaporation weakens latent heat flux (Supplementary Fig. 2g), thus reducing the evaporative cooling at the surface55. When the warm spell event terminates, moisture divergence anomalies reach zero (Fig. 5a), suggesting that the atmospheric moisture flow is approaching equilibrium. This change implies that the dry conditions exacerbated by the warm spell are beginning to be mitigated as the net outflow of moisture decreases, potentially leading to increased precipitation57 (Fig. 5b).

In non-tropical regions, moisture divergence anomalies tend to be negative from Day –3 to the day when warm spell terminates (Fig. 5a). It suggests that non-tropical winter warm spells are associated with anomalous moisture convergence, corresponding to positive precipitation anomalies (Fig. 5a, b). The anomalies of cloud cover shift from negative to positive states before the warm spell onset (Fig. 5c). The positive anomalies of cloud cover intensify until the warm spell terminates, thereby reducing incoming solar radiation at the surface (Supplementary Fig. 2e). Despite the reduction in solar radiation, increased clouds and atmospheric moisture strengthen the re-emission of longwave radiation from atmosphere to the surface (Supplementary Fig. 2f), thus causing elevated temperatures near the surface49. Additionally, soil moisture anomalies remain negative throughout non-tropical warm spell events, although the magnitude of these negative anomalies tends to decrease from the day before the warm spell onset to the day after its end (Fig. 5e). This change in soil deficit is accompanied by the state of evaporation anomaly shifting from positive to negative (Fig. 5f).

These results imply that winter warm spells in the tropics are evolving with the formation of a hot and dry clear sky with decreases in precipitation, cloud cover, atmospheric humidity, and soil moisture, which are favorable to enhance solar radiation received by the surface and warm the near-surface air (Fig. 6a). Whereas, non-tropical winter warm spells exhibit an analogously opposite evolution pattern characterized by increases in precipitation, cloud cover, and relative humidity, as well as an enhanced downwelling longwave radiative heating (Fig. 6b). While warm spells in both tropical and non-tropical regions are accompanied by depletions in soil moisture, those in tropics have much more substantial drying in soils, corresponding to anomalous moisture convergence there.

Fig. 6: A conceptual diagram of contrasting physical processes for tropical and non-tropical winter warm spells.
figure 6

The diagram summarizes the physical processes underlying winter warm spells in the tropics (a) and non-tropics (b). The blue downward arrow indicates a decrease, and the red upward arrow indicates an increase.

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Conclusions

We have examined the occurring characteristics of global winter warm spells during 1979–2023, and revealed the physical processes contributing to these events based on the energy budget analysis. Our examinations show that winter warm spells occur more frequently and persist longer in the tropics. Over the past decades, these events have become more often and more persistent, highlighting a growing risk of winter warm spells with profound implications for ecosystems, human health, and societal sectors.

Contrasting physical processes driving winter warm spells in tropical and non-tropical regions are conceptualized in Fig. 6. Diabatic heating emerges as a dominant factor contributing to positive temperature anomalies during winter warm spells across most global land areas, with substantial contributions from net shortwave and downwelling longwave radiations. The contributions of these processes are region-dependent, and exhibit contrasting differences between the tropics and non-tropics. In the tropics, surface warming during winter warm spells is mainly attributed to increased clear-sky incoming solar radiation, accompanied by drying soil and atmosphere. By contrast, non-tropical winter warm spells are primarily driven by increased downwelling longwave radiation and sensible heat flux under a cloudier and wetter environment.

We note that compared with winter warm spells, the distinction between tropical and non-tropical mechanisms is much less pronounced in summer heatwaves (Supplementary Figs. 3–4). During summer heatwaves, both tropical and non-tropical regions experience amplification of diabatic heating, which is generally driven by intensified solar radiation due to reduced cloud cover, along with widespread soil and atmospheric drying—mechanisms well documented in Röthlisberger and Papritz58. This finding is in line with Lhotka and Kyselý59, who reported that soil moisture is crucial for summer heatwave events, particularly for near-surface atmospheric heatwaves. In contrast to winter warm spells, the role of longwave radiation in summer heatwaves is relatively weak.

In addition to local physical processes, remote factors such as the Arctic amplification, Rossby wave train, sea surface temperature anomalies (e.g., El Niño-Southern Oscillation) are also likely linked to warm spells. These linkages have been confirmed in the summer season60,61,62, but it is unclear whether the relationship is applicable to the warm spells in cold winter seasons. Comparing the roles of local and remote climate factors in modulating the warm spells between summer and winter seasons is essential to improving our understanding of season-dependent extreme events. We have noticed an intensifying trend of more often and more persistent winter warm spells, particularly in tropical regions. The underlying causes and potential impacts of this intensifying trend need to be further explored in the future. Understanding these impacts is critical for developing effective adaptation strategies and minimizing the risks posed by winter warm spells. Our research underscores a pressing urgency to improve the understanding of the behaviors of emerging off-season extreme weather and climate events that occur outside their typical or expected occurrence seasons, and to mitigate their resultant impacts in a warming world.

Methods

Datasets

In this study, we identify winter warm spells (also known as winter heatwaves) using daily mean temperature (Tmean), which is calculated from hourly 2 m air temperature data from the ERA5 reanalysis dataset provided by the European Center for Medium-Range Weather Forecasts, covering the period from 1979 to 202363. To explore the underlying physical mechanisms of winter warm spells and to attribute the temperature anomalies, we also use skin temperature (Ts), total cloud cover (TCC), surface net shortwave radiation (SWR), surface downward longwave radiation (LWR), total precipitation (TP), relative humidity (RH), surface soil moisture (SM), surface latent heat flux (LHF), surface sensible heat flux (LHF), and surface pressure (Ps) from the single-level ERA5 dataset. Additionally, we incorporate geopotential height at 250 hPa, and air temperature (\({T}_{{pl}}\)), and vertical velocity (\({\omega }_{{pl}}\)) at 950 hPa, 850 hPa, 750 hPa, 650 hPa, and horizontal wind components (\({u}_{{pl}}\) and \({v}_{{pl}}\)) at various pressure levels. These variables collectively capture the dynamic and thermodynamic characteristics of the atmosphere and the surface, providing a comprehensive understanding of the conditions driving warm spells. Note that radiations and heat fluxes in this study are defined as positive downward (i.e., from the atmosphere to the surface). All data are interpolated onto a spatial resolution of 2.5° × 2.5°. We note that using different spatial resolutions (e.g., 1° × 1° and 2.5° × 2.5°) yield a consistent result of the climatological patterns and long-term trends (Supplementary Figs. 5–6).

Definition of winter warm spells

A winter warm spell (or winter heatwave) event is defined when daily Tmean exceeds its corresponding calendar 90th percentile values for at least three consecutive days41,64 within the cold season (Supplementary Fig. 7). The cold season is determined as the coldest consecutive three-month period in each grid cell. Specifically, for each calendar month, we first calculate its multi-year climatological mean temperature, then calculate the three-month mean of the local climatology of temperature (i.e., October-November-December [OND], November-December-January [NDJ], December-January-February [DJF], January-February-March [JFM], and so forth). We then determine the three-month period with the lowest temperature as the cold season for each grid cell. The calendar-specific percentile is calculated based on a 15-day moving window of daily Tmean centered on each calendar day (i.e., seven days before and after) over the reference period of 1981–2010 (i.e., a set of 15 days × 30 years = 450 days)24. This definition strictly requires three consecutive days with temperature exceeding the threshold, and we do not merge the events that are separated by one- or two-day gap. To assess the winter warm spell activities, we calculate six warm spell indices (Table S2)24 including frequency (events), participating days (days), maximum duration (days), mean duration (days), maximum intensity (°C), and mean intensity (°C). We also calculate the spatially-averaged means for different climate zones identified by the Köppen-Geiger climate classification system65 (Supplementary Fig. 8). The linear trends of these warm spell indices are estimated by the simple linear regression, with statistical significance evaluated using the modified nonparametric Mann-Kendall test66.

Decomposition of temperature anomalies during winter warm spells

The physical processes contributing to the occurrence of warm spells can be separated into horizontal advection of air from climatologically warmer regions, adiabatic warming from the subsiding motion of air, and diabatic heating due to the radiations and heat fluxes62. Therefore, to further understand the atmospheric dynamics and surface energy processes contributing to winter warm spells, we decompose the near-surface temperature anomalies (\(\Delta {T}_{2m}\)) into three components: horizontal temperature advection heating (\(\Delta {T}_{{advec}}\)), adiabatic heating (\(\Delta {T}_{{adiab}}\)), and diabatic heating (\(\Delta {T}_{{diab}}\)) at each grid cell across the globe34,58. The decomposition is expressed as34,35

$$\Delta {T}_{2m}=\Delta {T}_{{advec}}+\Delta {T}_{{adiab}}+\Delta {T}_{{diab}}$$
(1)

This approach allows us to quantify the relative contributions of these processes to the temperature anomalies during winter warm spells.

Advection heating (\(\Delta {T}_{{advec}}\)) represents the horizontal transport of heat, and is calculated based on the horizontal wind components (\({u}_{{pl}}\), \({v}_{{pl}}\)) and temperature gradients in pressure coordinates34:

$$\Delta {T}_{{advec},{pl}}=-\Delta t\,\left({u}_{{pl}}\frac{\partial {T}_{{pl}}}{\partial x}+{v}_{{pl}}\frac{\partial {T}_{{pl}}}{\partial y}\right)$$
(2)

where \({u}_{{pl}}\) and \({v}_{{pl}}\) are the zonal and meridional wind components, respectively; \(\frac{\partial {T}_{{pl}}}{\partial x}\) and \(\frac{\partial {T}_{{pl}}}{\partial y}\) are the temperature gradients in the zonal and meridional directions; and \(\Delta t\) is the time step (i.e., one day in this study); \({pl}\) denotes the given pressure level.

Adiabatic heating (\(\Delta {T}_{{adiab}}\)) denotes the vertical motion-induced temperature changes34, which is calculated as34:

$$\Delta {T}_{{adiab},{pl}}=-\Delta t\,{\omega }_{{pl}}\left(k\frac{{T}_{{pl}}}{{P}_{s}}+\frac{\partial {T}_{{pl}}}{\partial p}\right)$$
(3)

where \({\omega }_{{pl}}\) and \({T}_{{pl}}\) are the vertical velocity and air temperature at a given pressure level, respectively; \({P}_{s}\) is the surface pressure, and \(k\) is Poisson’s constant (i.e., 0.286). \({\omega }_{{pl}}k\frac{{T}_{{pl}}}{{P}_{s}}\) describes the ideal adiabatic temperature change resulting from vertical motion in the atmosphere. \({\omega }_{{pl}}\frac{\partial {T}_{{pl}}}{\partial p}\) quantifies how the vertical motion of air interacts with the existing vertical temperature gradient (i.e., \(\frac{\partial {T}_{{pl}}}{\partial p}\)) to cause temperature changes.

Following the study of Tian, et al. 34, the calculations of advection heating and adiabatic heating are performed at four pressure levels (i.e., 950 hPa, 850 hPa, 750 hPa, and 650 hPa), covering the lower and mid-troposphere. The selection of pressure level (i.e., \({pl}\)) depends on the surface pressure of the location where winter warm spell events occur, which is influenced by topography. Specifically, for warm spell days with surface pressure exceeding 900 hPa (82.04% of cases), the 950 hPa level is selected. In cases where surface pressures range from 800–900 hPa (11.96% of cases), 700–800 hPa (3.48% of cases), and below 700 hPa (2.52% of cases), the corresponding pressure levels are set as 850 hPa, 750 hPa, and 650 hPa, respectively.

To calculate the diabatic heating during winter warm spells, we assume that the changes in air temperature due to diabatic processes (\(\Delta {T}_{{diab}}\)) are highly correlated with the variations in skin temperature (\(\Delta {T}_{{skin}}\))67. Their relationship is represented by a factor \(f\), which quantifies how skin temperature variations translate into the changes in air temperature (Eq. (4))68, and is typically assumed to be 1 in previous studies34,35,68.

$$\Delta {T}_{{diab}}=f{{\cdot }}\Delta {T}_{{skin}}$$
(4)

Based on land surface energy, the diabatic heating process can be further decomposed as follows:

$${H}_{g}={H}_{s}+{H}_{{ld}}+{H}_{{lu}}+{H}_{{lh}}+{H}_{{sh}}$$
(5)

where \({H}_{s}\) is the net solar radiation, \({H}_{{ld}}\) and \({H}_{{lu}}\) are the downward and the emitted upward longwave radiations, respectively, \({H}_{{lh}}\) and \({H}_{{sh}}\) are the surface latent and sensible heat fluxes, respectively. Note that all radiation and flux terms are downward positive.

Taking the differential of both sides in Eq. (5), the changes in surface energy budget can be written as

$${\Delta H}_{g}={\Delta H}_{s}+{\Delta H}_{{ld}}+{\Delta H}_{{lu}}+{\Delta H}_{{lh}}+\Delta {H}_{{sh}}$$
(6)

Expressing \({H}_{{lu}}\) as \(\sigma \cdot {T}_{{skin}}^{4}\) where \(\sigma\) is the Stefan-Boltzmann constant (i.e., 5.67×10−8W m−2 k−4), and taking its differential, Eq. (6) can be written as

$${\Delta T}_{{skin}}=\frac{({\Delta H}_{s}+{\Delta H}_{{ld}}+{\Delta H}_{{lh}}+\Delta {H}_{{sh}}-{\Delta H}_{g})}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}$$
(7)

With Eqs. (4) and (7), we can thus decompose the changes in air temperature driven by diabatic processes as the terms of \(\frac{{\Delta H}_{s}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\) (net shortwave radiation heating), \(\frac{{\Delta H}_{{ld}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\) (downward longwave radiation heating), \(\frac{{\Delta H}_{{lh}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\) (latent heat flux heating), \(\frac{{\Delta H}_{{sh}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\) (sensible heat flux heating), and \(\frac{{\Delta H}_{g}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\) (ground heat flux heating).

In summary, the contributions to the temperature anomalies during winter warm spells are decomposed into \(\Delta {T}_{{advec},{pl}}\), \(\Delta {T}_{{adiab},{pl}}\), \(\frac{{\Delta H}_{s}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\), \(\frac{{\Delta H}_{{ld}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\), \(\frac{{\Delta H}_{{lh}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\), \(\frac{{\Delta H}_{{sh}}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\), and \(\frac{{\Delta H}_{g}}{4\sigma \cdot {\bar{T}}_{{skin}}^{3}}\).

Composite analysis of relevant variables

To determine the dominant drivers of winter warm spells, we employ composite analysis to examine the key atmospheric and surface variables during these events48,49. In this analysis, we first calculate the daily anomalies of each variable by removing the climatological seasonal cycle from the original daily series. The seasonal cycle is obtained from the multi-year average for each calendar day over the reference period of 1981–2010, with a 15-day rolling mean applied to exclude possible short-term fluctuations24,69,70. We then average the daily variable anomalies during all participating days of a winter warm spell event, and the resulting event-level averages are further averaged across all events with equal weight to produce the composite mean for all warm spell events. The statistical significance of these composite means is estimated by a two-tailed Student’s t-test.