Recent globally synchronous seasonal warm events unprecedented since 850 CE

Abstract

Spatially synchronous extreme warm events can amplify environmental and societal impacts by affecting multiple regions simultaneously. However, previous studies have largely focused on June–August (JJA) events during the instrumental period, limiting understanding of their seasonal prevalence and long-term evolution. Here, we examine globally synchronous seasonal warm events (GSSWEs) using seasonal mean near-surface air temperature (SAT) and introduce an Extremity Index (EI) that combines normalized local land SAT anomaly intensity with the spatial extent of land areas exceeding a specified SAT threshold. Using instrumental observations, paleo-reanalysis products and climate model simulations, we assess changes in global-land GSSWE extremity since 850 Common Era (CE). We find that GSSWEs have intensified sharply since the 1970s across all four seasons, reaching levels not found earlier in the multi-dataset records. Detection and attribution analyses indicate that anthropogenic forcing, dominated by greenhouse-gas forcing, is the main contributor to this recent intensification. Spatially, the tropics contribute greatly to the recent extremity of GSSWEs due to their lower intrinsic variability. These findings highlight that climate-risk assessment and adaptation planning need to consider the growing spatial coherence and intensity of seasonal warm extremes.

This study shows that the extremity of globally synchronized seasonal warm events has sharply intensified in recent decades, reaching unprecedented levels since 850 CE, largely driven by anthropogenic greenhouse gas forcing.

Introduction

Recent extreme warm events, particularly threshold-exceeding hot events, have drawn increasing attention due to their frequently adverse impacts on the environment and society^1–12. However, most previous studies on large-scale notable record-shattering warm events have focused on the season of June–August (JJA)^{1,2,3,5,9,11,12,13,14,15,16}, which corresponds to boreal summer and has been examined predominantly from a Northern Hemisphere extratropical perspective. The same calendar season, however, is winter in the Southern Hemisphere extratropics, and the behavior of such events there remains largely unexplored. Warm events during December–February (DJF) are also consequential, yet remain less studied globally. The rate of global land-averaged SAT increase during DJF has surpassed that during JJA^17,18. For the Northern Hemisphere, where DJF corresponds to the winter season, extreme DJF warmth may disrupt plant phenology, increase the risk of pest outbreaks, and reduce crop yields in certain regions^6,8,19–23. Of particular concern is the release of carbon from permafrost associated with extremely warm DJF seasons^8,24–27. In northern polar regions, as well as in high-mountain regions such as the Tibetan Plateau, increases in DJF SAT have emerged as an important contributor to permafrost warming^24,27–30. Concurrently, as DJF corresponds to summer in the Southern Hemisphere, extreme warm events manifest as severe heatwaves and prolonged droughts^31,32, which substantially elevate the risk of catastrophic wildfires, cause ecological degradation³³, and lead to a marked increase in heat-related morbidity and mortality³⁴. Despite these impacts, the long-term evolution and attribution of DJF warm-event extremity remain insufficiently understood.

Compared with regionally confined warm extremes, spatially synchronous extreme warm events may amplify societal impacts by affecting multiple regions simultaneously^35,36. Such events can contribute to widespread electric power outages across multiple urban areas, increasing heat exposure and heat-related mortality when external support capacity is limited^5,37. In combination with prolonged dry conditions, spatially synchronous warm extremes may also favor widespread wildfires⁵ and contribute to multiple harvest failures^5,7,38. Their frequency is expected to increase with ongoing global warming³⁹, and multiple lines of evidence indicate that anthropogenic forcing has contributed substantially to globally synchronous multiday-to-monthly extreme warm events in recent decades^40–42. Seasonal warm events represent a distinct and important class of extremes because their long duration allows impacts to accumulate over several months. Regional seasonal warm events have become more widespread and more frequent^{5,8,12,43–45} however, changes in globally synchronous seasonal warm events (GSSWEs), and their attribution, remain less well constrained. Long-term paleoclimatic data provide an essential pre-industrial context for assessing whether recent GSSWE behavior exceeds the range of natural variability, while seasonal aggregation reduces the influence of short-lived local weather fluctuations⁹. Such a long-term paleoclimatic context is crucial for evaluating whether recent GSSWE extremity exceeds the range of natural variability and for quantifying the contribution of anthropogenic forcing to recent changes.

The degree of GSSWE extremity has two complementary dimensions, namely the magnitude of global-land seasonal SAT anomalies and the spatial extent of land areas experiencing synchronous threshold-exceeding conditions. Previous studies have generally examined these dimensions separately, using either large-scale mean temperature anomalies or the proportion of grids exceeding local records^{4,5,31,37,42,43,46}. While both diagnostics are informative, each captures only one aspect of event extremity and does not by itself describe the joint expression of anomaly intensity and spatial extent. In this study, we introduce the Extremity Index (EI) as a diagnostic synthesis metric that jointly quantifies the normalized local SAT anomaly intensity across threshold-exceeding land grid cells and the actual land area affected by synchronous warmth, where threshold‑exceeding is defined relative to the local 95th percentile of the 1901–1930 baseline. Specifically, the EI is calculated by integrating, across all threshold-exceeding grid cells, the product of their normalized temperature anomaly and their actual land area, relative to the global land total (see “Methods”).

Using the EI, we examine the long-term evolution of GSSWE extremity from 850 to 2023 CE using observations, paleo-reanalysis products and global climate model (GCM) simulations. We assess seasonal prevalence across all four seasons, evaluate changes in the spatial pattern of threshold-exceeding warmth, and perform detection and attribution analyses to quantify the role of anthropogenic forcing in recent EI trends.

Results

Evaluating the Extremity Index (EI) against its component diagnostics

Changes in the magnitude of the global-land mean of seasonal SAT anomaly relative to the 1901–1930 reference period do not consistently align with changes in the ratio of threshold-exceeding areas (RTEA) (Fig. 1 and Supplementary Fig. S1). This indicates that large-scale mean warmth and threshold-exceeding spatial extent describe related but distinct aspects of GSSWE extremity. Although the bivariate distributions (Fig. 1a, d and Supplementary Fig. S1a, d) show a positive correlation between global-land mean SAT anomaly and the RTEA (P < 0.01), the two metrics are not interchangeable for extremity evaluation; notable outliers occur not only in DJF and JJA, but also in MAM (March–May) and SON (September–November). In DJF 1968/69 and 1985/86 (Fig. 1b, c), RTEA values were similar, at approximately 24%, whereas global-land mean SAT anomalies differed substantially, from –0.58 °C in 1968/69 to 0.68 °C in 1985/86. Similarly, in JJA 1937 and 1993 (Fig. 1e, f), global-land mean SAT anomalies were both close to 0.3 °C, whereas the threshold-exceeding spatial extent differed by 15.63 percentage points. These contrasts demonstrate that global-land mean SAT anomaly magnitude and threshold-exceeding extent can capture distinct facets of event extremity. Relying on the SAT anomaly alone can obscure years with extensive threshold-exceeding grids but modest global-land mean anomalies, whereas RTEA alone does not account for differences in local anomaly intensity within the threshold-exceeding grids. This motivates a combined diagnostic that integrates these two metrics.

Fig. 1. Relationship between global-land mean near-surface air temperature (SAT) anomaly, threshold-exceeding area and Extremity Index (EI) for globally synchronous seasonal warm events (GSSWEs) during 1901–2023 Common Era (CE).

a, d Bivariate distribution of global-land mean SAT anomalies relative to 1901–1930 CE and the ratio of threshold-exceeding areas (RTEA) for December–February (DJF) (a) and June–August (JJA) (d). b, c Spatial patterns of SAT anomalies and threshold-exceeding grids for DJF 1968/69 (b) and DJF 1985/86 (c). e, f Spatial patterns of SAT anomalies and threshold-exceeding grids for JJA 1937 (e) and JJA 1993 (f). The four selected events are highlighted in a and d with bold outlines. Point colors in a and d represent the EI, calculated from normalized threshold-exceeding SAT anomalies and area-weighted threshold-exceeding extent (see “Methods”). Annotated labels and black lines indicate the range of one variable, SAT anomaly or RTEA, when the other is held approximately constant. Numbers in b, c, e and f denote the area-weighted global-land mean SAT anomaly and RTEA of each event; dots indicate threshold-exceeding grids. All analyses are based on CRU TS v4.08 observations.

To evaluate whether the EI provides information beyond its component diagnostics, we compared event rankings based on global-land mean SAT anomaly, RTEA and EI (Supplementary Fig. S2 and Supplementary Table S1). These comparisons show that the three metrics are related but not interchangeable, and that certain seasons are ranked differently depending on whether large-scale mean warmth, threshold-exceeding spatial extent, or their joint expression is emphasized. For example, in DJF 2006/07 (Supplementary Fig. S2a), global-land mean SAT anomaly ranked 3rd whereas RTEA ranked 8th, indicating strong large-scale warmth but a more limited simultaneous threshold-exceeding area. The EI ranked this event 6th, reflecting its intermediate position when both local anomaly intensity and threshold-exceeding spatial extent are considered together. Likewise, in JJA 2022 (Supplementary Fig. S2b), global-land mean SAT anomaly ranked 4th, whereas RTEA ranked 12th, while the EI ranked the event 5th owing to the high anomaly intensity within the threshold-exceeding grids. These ranking differences indicate that the EI captures aspects of seasonal extremity not fully represented by global-land mean SAT anomaly or RTEA alone. We therefore interpret the EI as a synthesis diagnostic that complements, rather than replaces, separate analyses of anomaly magnitude and threshold-exceeding area. Consistent with DJF and JJA, similar ranking divergences are observed in MAM and SON. Global-land mean SAT anomaly and RTEA show substantial mismatches in identifying extreme events (Supplementary Fig. S2c, d).

In some cases, EI can even identify events that SAT anomalies alone fail to capture. For instance, in DJF 2009/10, the global-land mean SAT anomaly ranks only 22nd among all DJF seasons since 1901, whereas EI ranks 3rd, because this season exhibited extensive and spatially synchronous threshold-exceeding warmth across multiple regions. This underscores that moderately warm years globally can still represent exceptional synchronous seasonal extremes when spatial coherence is taken into account.

To determine whether such rank misalignments are systemic or merely isolated anomalies, we evaluated the rank consistency between the two metrics using a parallel trajectory alignment approach under both zero-tolerance and tolerant frameworks (Supplementary Figs. S3–S5).

When isolating the top 10% observational EI events under a strict zero-tolerance criterion (exact rank matching), rank alignment is remarkably poor (Supplementary Fig. S3). For DJF, the exact matching rate is only 25.0%, with the traditional SAT ranking yielding a 50.0% underestimation rate and a 25.0% overestimation rate (Supplementary Fig. S3a). For JJA, the exact match rate is likewise 25.0%, accompanied by an underestimation rate of 50.0% (Supplementary Fig. S3b). MAM and SON demonstrate highly similar characteristics, with exact match rates limited to 16.7% and 33.3%, respectively (Supplementary Fig. S3c, d).

This widespread misalignment is further corroborated across the full 123-year historical record (1901–2023 CE) under the same zero-tolerance criterion, where strict rank equality drops to a minimum for DJF and JJA, with MAM and SON showing parallel trends of low consistency (Supplementary Fig. S4). Even when incorporating a ±1 rank tolerance across the full sequence, structural mismatches remain predominant across all four seasons, with DJF and SON presenting the highest rates of overestimation and underestimation by the SAT-alone metric (Supplementary Fig. S5).

This multi-tiered, full-sequence comparison shows that seasons with moderate global-land mean SAT anomalies can nevertheless exhibit severe spatially synchronous extremes. Thus, relying exclusively on mean SAT anomalies may miss coherent large-scale extremes, supporting the usefulness of EI as a complementary diagnostic for climate-risk assessment and adaptation planning.

Recent intensification of spatially synchronous seasonal warm events

The EIs calculated from observations, paleo-reanalysis products and GCM simulations for 850–2023 CE consistently indicate a marked increase in GSSWE extremity since the 1970s (Figs. 2 and S6; Supplementary Texts S1 and S2). This increase is evident across all four seasons, in DJF and JJA (Fig. 2) as well as in MAM and SON (Fig. S6), and reaches levels that are not found earlier in the multi-dataset records. We further identified high-GSSWE seasons by applying a 5% threshold to the multi-dataset weighted-average EI series, defined as the top 5% of EI values over 850–2023 CE. Before 1970 CE, only 18% of DJF years and 15% of JJA years exceeded this threshold, whereas after 1970 CE, 89% of DJF years and 86% of JJA years did so. EI values remained comparatively low before the 1970s in both seasons, indicating limited spatial extent and/or lower intensity of threshold-exceeding warmth. By contrast, the late 20th century and early 21st century are characterized by a marked increase in the mean level of EI (Fig. 2). This pattern is robust to alternative threshold choices (Supplementary Fig. S7). The turning points identified using the mean-based regime-shift algorithm occur around the 1970s in both seasons (see “Methods”), supporting the interpretation of a recent transition in the extremity of GSSWEs. Accompanying this rise in mean extremity, the variance of the EI also increases. The 30-year running variance suggests a shift in the trend of EI variances around the turning point, and this shift reaches statistical significance (Supplementary Fig. S8; see “Methods”). Before the turning point, the running variance remains comparatively low, whereas after the turning point, it appears to increase markedly and persistently (Supplementary Fig. S8). These changes imply that recent GSSWEs are characterized not only by higher mean extremity but also by greater variability in seasonal-scale threshold-exceeding warmth. The role of external forcing in this transition is assessed in the detection and attribution analysis below.

Fig. 2. Long-term evolution of the Extremity Index (EI) for globally synchronous seasonal warm events (GSSWEs) during December–February (DJF) and June–August (JJA) since 850 Common Era (CE).

a DJF. b JJA. Insets show the observational period 1901–2023 CE. EIs are derived from three observational products (CRU TS v4.08, BEST and HadCRUT5), two paleo-reanalysis products (PHYDA and ModE-RA), a weighted ensemble of seven global climate models (GCMs) and a weighted mean across the millennium-length datasets, including paleo-reanalysis products and GCM simulations (see “Methods”). Solid lines show annual EIs, shaded areas indicate the range across the seven GCMs, and dots mark detected turning points. Colors distinguish datasets. Hollow circles indicate the detected turning points based on the main STARS cut-off length of L = 60 years, and the colors distinguish different datasets.

Anthropogenic contribution to the increased extremity of GSSWEs

To detect the anthropogenic influence on the abrupt escalation of EI since the 1970s, we perform detection and attribution analyses using separate forcings to assess the changes in the EI trend since 1901 CE (i.e., a longer period to quantify anthropogenic contributions to EI regime shifts; see “Methods”). The non-overlapping 5-year-mean series of the EI derived from observations shows that the EI of GSSWEs increased by 0.39 in DJF and by 0.33 in JJA from 1901 to 2020 CE (Fig. 3a, b). Before the turning point in the 1970s, the EIs in both seasons exhibit negligible trends; thereafter, they increase rapidly. The observed EI evolution in both DJF and JJA is broadly consistent with the simulated responses derived from the ensemble mean of seven evaluated GCMs under all external forcings (ALL), anthropogenic forcing alone (ANT), and greenhouse gas forcing alone (GHG; see “Methods”; Supplementary Fig. S9), although the models tend to slightly underestimate the most recent observed increase. By contrast, the simulated EI responses under natural forcing alone (NAT) and anthropogenic aerosol forcing alone (AA) remain comparatively weak during the analysis period.

Fig. 3. Detection and attribution of Extremity Index (EI) trends in seasonal warm events, 1901–2020 Common Era (CE).

a, b Non-overlapping 5-year mean EI from CRU observations and simulations driven by different external forcings, based on the ensemble mean of eight global climate models (GCMs), for December–February (DJF) (a) and June–August (JJA) (b). Shading shows the simulated range across GCMs. c, d factors from one-, two- and three-signal detection and attribution analyses of EI trends in DJF (c) and JJA (d). Horizontal lines indicate best estimates of the scaling factors; bars denote 5–95% confidence intervals. e Attributable EI trends for DJF (left) and JJA (right), with corresponding 5–95% uncertainty ranges.

Further one-signal detection and attribution analyses (see “Methods”) indicate that the ALL, ANT and GHG response patterns of the EI are detectable in both DJF and JJA, whereas NAT and AA are not detected in the one-signal analyses (Fig. 3c, d). Here, detection is inferred when the 5–95% confidence interval of the scaling factor lies above zero, and attribution is supported when this interval includes unity. The observed EI trend is attributable to ALL in both seasons, with scaling factors close to unity, indicating broad agreement between simulated and observed responses and supporting the role of external forcing in driving the recent EI trend. The best estimates of the GHG scaling factors are below unity in both seasons, indicating that the model-simulated GHG response is stronger than observed. To further distinguish the contributions of ANT and NAT, we conducted a two-signal analysis by regressing the observations simultaneously onto the ANT and NAT responses. In both DJF and JJA, ANT is distinguishable from NAT. The ANT-forced response in JJA is underestimated, consistent with the one-signal analysis. Three-signal analyses further show that GHG can be separately detected from AA and NAT in DJF. In JJA, both GHG and AA are detectable, indicating seasonal differences in the separability of aerosol and greenhouse-gas influences. The estimated quantitative contributions of different forcings to the EI trend (see “Methods”) indicate observed trends of 0.091/decade in DJF (95% confidence interval: 0.075–0.11/decade) and 0.115/decade in JJA (95% confidence interval: 0.094–0.14/decade) during 1901–2020 (Fig. 3e). The attributable trends for ALL, ANT and GHG are close to the observed trends, whereas NAT contributes little to the observed increase. AA has a negative contribution, consistent with an offsetting aerosol influence. The ANT-induced EI trends are 0.078/decade in DJF (95% confidence interval: 0.066–0.09/decade) and 0.096/decade in JJA (95% confidence interval: 0.08–0.112/decade). Under GHG forcing alone, the EI trends are 0.09/decade in DJF (95% confidence interval: 0.07–0.116/decade) and 0.13/decade in JJA (95% confidence interval: 0.1–0.16/decade), accounting for approximately 79% and 112% of the observed trends in DJF and JJA, respectively. These results indicate that greenhouse-gas forcing is the dominant contributor to the observed increase in GSSWE extremity since the 1970s.

Temporal changes in spatial patterns of EI of GSSWEs

To characterize the spatial evolution of GSSWEs, we analyzed gridded cumulative counts of threshold-exceeding warm events across successive 150-year intervals from 850 to 1899 CE and for the recent 1900–2023 CE interval (Figs. 4a–g, i–o and 4h, p). The 150-year window length was chosen to reduce the influence of interdecadal variability while retaining sufficient temporal resolution to compare broad phases of the last millennium. Across the pre-1900 intervals, threshold-exceeding events remain spatially fragmented, with cumulative counts and zonal means generally low (Fig. 4a–g, i–o). By contrast, the 1900–2023 CE interval shows a marked increase in threshold-exceeding frequency despite its shorter duration (Fig. 4h, p). MAM and SON follow the same spatial and latitudinal trajectory, shifting from modest pre-1900 conditions to elevated post-1900 levels (Supplementary Fig. S10). This recent increase is visible across latitudes and is particularly pronounced in the Tropics. Together, these results suggest an increasing spatial coherence of seasonal threshold-exceeding warmth, with a strong tropical contribution to the recent rise in GSSWE extremity.

Fig. 4. Spatial and latitudinal evolution of cumulative threshold-exceeding frequency of seasonal warm events over the past millennium.

a–g, i–o Spatial distribution of cumulative threshold-exceeding frequency across seven successive 150-year intervals from 850 to 1899 Common Era (CE), shown for December–February (DJF) (a–g) and June–August (JJA) (i–o). h, p Cumulative threshold-exceeding frequency for 1900–2023 CE in DJF (h) and JJA (p). Insets show the latitudinal profiles of zonal-mean cumulative threshold-exceeding counts, calculated by averaging nonzero cumulative counts across 1° × 1° grid cells at each latitude. The cumulative threshold-exceeding count at each grid cell is calculated as the sum of annual weighted threshold-exceeding events over the specified period.

We further characterized this transition in extremity of seasonal warm events by investigating the spatial synchrony of the timing of EI maxima at the grid level, comparing the recent interval with any single earlier 150-year interval, and by examining such synchrony in two typical periods of the last millennium, namely the Medieval Climate Anomaly and the Little Ice Age⁴⁷ (Supplementary Fig. S11). The results indicate that during the Medieval Climate Anomaly (850–1300 CE) and the Little Ice Age (1301–1900 CE), the timing of peak seasonal EI was highly asynchronous in not only DJF and JJA but also MAM and SON (Supplementary Fig. S11a, d, g, j). In contrast, when evaluating the entire 850–2023 CE period, a global synchronization in peak timing emerges across all seasons (Supplementary Fig. S11c, f, i, l). A large fraction of the global land area records its millennium-maximum EI within the interval after 1900 CE. This transition from more asynchronous peak timing during earlier periods to greater clustering of peak EI in the recent interval indicates that the recent intensification of GSSWEs involves both higher cumulative frequency and increased spatial coherence in the timing of peak seasonal extremity.

To further characterize the latitudinal profile of GSSWEs, we partitioned the global land surface, excluding Antarctica, into four latitudinal zones: the Northern Frigid Zone (60°N–90°N), Northern Temperate Zone (30°N–60°N), Tropics (30°N–30°S), and Southern Temperate Zone (30°S–60°S). The millennial latitudinal decomposition of EI based on 30-year running means from the multi-dataset ensemble of paleo-reanalyses and GCM simulations (Supplementary Figs. S12 and S13) provides temporal context for the recent spatial changes. Throughout 850–1899 CE, seasonal EI values remained comparatively low across all latitudinal zones, with no single zone showing a persistent lead. A coherent increase emerges during the twentieth century and accelerates after the 1970s across all latitudinal zones, both in JJA and DJF. Both CRU observations and the multi-dataset ensemble indicate a particularly strong recent increase in the Tropics. This suggests that the recent rise in GSSWE extremity reflects broad latitudinal intensification with an important tropical contribution, rather than a response dominated only by northern mid- and high-latitude SAT anomalies.

The top GSSWEs and their spatial characteristics

Because the highest EI values occur after the 1970s (Fig. 2 and Supplementary Fig. S8), we examined the spatial characteristics of four representative recent events: the two highest-EI events in DJF and the two highest-EI events in JJA identified from CRU observations during 1901–2023 CE (Fig. 5). These events are selected by EI rank. The gridded EI for each event is calculated as the product of the threshold-exceeding normalized seasonal SAT anomaly and the actual grid-cell area, divided by total global land area (Fig. 5a, d, g, j and Supplementary Fig. S14a, d, g, j; see “Methods”). The two highest-EI DJF events occurred in 2015/16 and 2019/20, with global EI values of both 0.40 and threshold-exceeding land-area fractions of 74.40% and 72.87%, respectively (Fig. 5a, b, d, e). Similarly, the two highest-EI JJA events occurred in 2021 and 2023, with global EI values of 0.39 and 0.51 and threshold-exceeding land-area fractions of 74.97% and 81.74%, respectively (Fig. 5g, h, j, k). The spatial patterns in MAM and SON align with those of DJF and JJA. The highest-EI MAM events occurred in 2016 and 2020, and the highest-EI SON events in 2023 and 2020 (Supplementary Fig. S14), all characterized by extensive threshold-exceeding areas and broad latitudinal coverage. This further establishes that recent high-EI GSSWEs are a multi-season phenomenon with consistently widespread spatial coherence. These events represent the highest EI-ranked GSSWEs in the observational record and are used here to illustrate the spatial pattern of recent high-EI seasons.

Fig. 5. Spatial characteristics of the top two highest-Extremity Index (EI) globally synchronous seasonal warm events in December–February (DJF) and June–August (JJA) during 1901–2023 Common Era.

a, d, g, j Grid-level EI for the two highest-EI DJF events, 2015/16 (a) and 2019/20 (d), and the two highest-EI JJA events, 2021 (g) and 2023 (j). Numbers in the lower-left corner indicate the total EI of each event. b, e, h, k Spatial distributions of threshold-exceeding grids for the same events. Numbers in the lower-left corner represent the area-weighted ratio of threshold-exceeding areas. c, f, i, l Proportion of threshold-exceeding area within each latitudinal zone relative to its own land area and to the global total threshold-exceeding area.

To quantify the latitudinal characteristics of these extreme events, we calculated two complementary metrics: the proportion of threshold-exceeding land area within each latitudinal zone, normalized by the land area of that specific zone to ensure cross-zonal comparability; and the contribution of each zone to the global RTEA, normalized by the total global land area (Fig. 5c, f, i, l and Supplementary Fig. S14c, f, i, l). The result shows that during these high-EI events, more than half of the land area in each latitudinal zone experienced threshold-exceeding warmth, indicating widespread spatial coherence. In DJF, the highest within-zone fractions occurred in the Northern Temperate Zone, reaching 82.9% in 2015/16 and 84.3% in 2019/20. In JJA, threshold-exceeding coverage was also high across nearly all latitudinal zones, with the Tropics attaining the largest within-zone fraction during 2023 (84.7%), while the Northern Temperate Zone showed the highest within-zone fraction in 2021 (80.1%). These examples indicate that recent high-EI GSSWEs involve contributions from both tropical and northern temperate land areas. Although the latitude band with maximum coverage varies by season and event, the widespread threshold-exceeding area distinguishes recent high-EI seasons from the more spatially fragmented record occurrence seen earlier in the millennium.

Discussion

Background variability in SAT anomalies plays a key role in shaping the latitude profile of seasonal EI. Although mean seasonal SAT anomalies associated with threshold-exceeding events are larger in the northern mid-to-high latitudes (30–90°N) and smaller in low-latitude regions (30°S–30°N) (Supplementary Fig. S15a, b, h, i), threshold-exceeding events occur more frequently in low-latitude regions (Supplementary Fig. S15c, d, j, k). This contrast primarily reflects strong spatial heterogeneity in seasonal SAT variability (Supplementary Fig. S15e, f, i, m). In the northern mid-to-high latitudes, variability is enhanced by synoptic‑scale baroclinic instability and thermal advection^48,49, further amplified by low effective heat capacity⁵⁰. In contrast, low-latitude variability is suppressed by strong convective adjustment and weak temperature-gradient constraints^51,52, lowering the threshold so that smaller anomalies produce more frequent exceedances, consistent with more pronounced warming signals relative to local variability⁵³. Therefore, accounting for background variability is essential when developing metrics for GSSWEs and compound climate extremes, whose spatiotemporal proximity is expected to increase in a warming climate³⁹. The EI addresses this by normalizing grid-cell anomaly intensity before aggregating across threshold-exceeding areas. Regional decomposition further shows that the EI is not dominated by large absolute SAT anomalies in the northern mid-to-high latitudes (Supplementary Fig. S15g, n). Instead, slightly higher EI values occur in low latitudes, where threshold-exceeding events are more frequent and spatially extensive, indicating that their contribution to global-land extremity is not underestimated. The enhanced contribution from low latitudes to the recent rise in GSSWE extremity is also observed in MAM and SON, consistent with the findings for DJF and JJA (Supplementary Fig. S16).

Notably, while the period since 1900 exhibits the highest and most spatially synchronous frequency of threshold-exceeding warm events globally, regional hot features also occurred during earlier periods. For instance, a prominent peak appears in the northern subtropics (15°N–30°N) during earlier historical DJF and MAM periods, as well as in SON (Fig. 4a–g and Supplementary Fig. S10a–g, i–o), whereas after 1900 this latitudinal zone shifts to a trough (Fig. 4h and Supplementary Fig. S10h, p). Although this historical peak does not surpass modern levels, consistent with the dominant role of recent anthropogenic warming, the lower mean SAT during the 1901–1930 reference period may have allowed the relatively warm intervals of the pre-1900 era to stand out more prominently. The specific reasons for these earlier regional events warrant further investigation.

Several heat-related indices have already been applied in studies of societal and ecological impacts. The daily-scale Excess Heat Factor⁵⁴, for instance, has been extended to multi-country health impact assessments⁵⁵ and heatwave exposure analyses in European urban areas⁵⁶. In contrast, the EI proposed here is designed for seasonal-scale analyses over long time series and large spatial domains. In the future, the EI could be extended to other climate variables, such as precipitation or drought, or to specific impact sectors, such as assessing the risk of simultaneous extreme heat across major global breadbaskets⁵⁷ or integrating with ecosystem response studies, including shifts in species distribution and phenology⁵⁸. Subsequent research may further test the applicability of the EI across different regions, variables and impact sectors. At the present stage, our results should be interpreted as evidence of physical changes in the intensity and spatial extent of seasonal threshold-exceeding warmth, rather than as a direct quantification of societal risk. Nevertheless, the stronger relative extremity identified in the Tropics is relevant for future impact-oriented research, particularly because many tropical countries have high exposure and more limited adaptive capacity⁵⁹. Overlooking regional differences in the frequency and intensity of threshold-exceeding conditions may therefore contribute to an underestimation of future heat-related risks. These findings highlight the importance of linking physical diagnostics of GSSWEs with impact assessment and adaptation research.

Methods

Observational datasets

Three gridded observational datasets of monthly near-surface air temperature (SAT) were used to assess the robustness of the observed changes in this study. The first observational dataset is the Climatic Research Unit gridded Time Series v4.08 (CRU TS v4.08, abbreviated as CRU) dataset⁶⁰, which provides land-only SAT observations (excluding Antarctica) at 0.5° by 0.5° resolution for 1901–2023 CE. The second observational dataset is the Berkeley Earth Surface Temperature (BEST) dataset⁶¹, which provides global land and ocean SAT data at a spatial resolution of 1° × 1° from 1850 to 2024 CE. The third observational dataset is the Met Office Hadley Center/Climatic Research Unit gridded dataset of global historical SAT anomalies, version 5.0.2.0 (HadCRUT5)⁶², which provides global land and ocean SAT anomalies at 5° × 5° resolution from 1850 to 2024 CE. Because the CRU dataset has higher spatial resolution and complete land coverage for the study domain, it is better suited for analyzing spatially synchronous seasonal warm events and serves as the primary observational dataset used in this study. The BEST and HadCRUT5 datasets were used to validate the CRU-based results and to extend the paleo-reanalysis products, the Paleo Hydrodynamics Data Assimilation product (PHYDA)⁶³ and Modern Era Reanalysis (ModE-RA)⁶⁴, to 2023, respectively (see details in Supplementary Text S1). We consistently used seasonal mean temperature from these datasets as the analysis variable.

Paleo-reanalysis products

Two gridded paleo-reanalysis products, PHYDA⁶³ and ModE-RA⁶⁴, which provide monthly or seasonal T_mean fields, were used in this study to analyze the temporal evolution of GSSWEs. The PHYDA reanalysis dataset provides 2-m SAT data at ~2° spatial resolution for JJA and DJF, spanning from 1 to 2000 CE⁶³. The ModE-RA is a global monthly paleo-reanalysis dataset covering 1421–2008 CE at 1.875° by 1.875° resolution⁶⁴. We compared EIs derived from PHYDA and ModE-RA with observation-based EIs and found good agreement, supporting their reliability (see details in Text S1).

Climate model simulation datasets

Monthly T_mean data derived from global climate models (GCMs) that participated in Phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6)^65,66 were used to analyze the changes in GSSWEs over the last millennium and for detection and attribution. Specifically, monthly T_mean data derived from two CMIP6 and five CMIP5 GCMs (Supplementary Table S2), using consistent ensemble members across the past1000, historical and SSP2-4.5/RCP4.5 simulations, were used to analyze the evolution of GSSWEs since 850 CE (Supplementary Fig. S17).

To ensure a consistent multi-dataset comparison over the longest possible period while maintaining at least two independent data sources at the beginning of the record, we set the starting year of our analysis to 850 CE. This choice is motivated by the fact that the CMIP past1000 model simulations begin in 850 CE, and the PHYDA paleo-reanalysis product also provides continuous data from 850 CE onward. For the ModE-RA reconstruction, which starts in 1421 CE, we use its original start year without extrapolation. For the detection and attribution analysis of changes in GSSWE extremity, we used monthly T_mean simulations from eight GCMs participating in the CMIP6 Detection and Attribution Model Intercomparison Project (DAMIP)⁶⁷ (Supplementary Table S3). These simulations include all external forcings (ALL), natural forcings only (NAT), greenhouse-gas forcing only (GHG), anthropogenic aerosol forcing only (AA), and pre-industrial control (piControl) runs, allowing the roles of different external forcings to be assessed. To sample internal variability more consistently, we retained only models that provided three ensemble members for each external-forcing experiment, using matching ensemble members across simulations within each model (Supplementary Text S2).

Definition of the Extremity Index (EI)

We propose an Extremity Index (EI) to quantify the extremity of GSSWEs, calculated as follows. First, for each grid cell and each season, we determine whether the temperature in a given year exceeds the local 95th percentile threshold calculated over the reference period (1901–1930 CE). We selected this period as the climatology baseline because it is the earliest interval covered by the primary observational dataset (CRU TS v4.08), thereby providing a consistent, observationally anchored baseline across instrumental, paleo-reanalysis, and model-based analyses. Meanwhile, this period is also characterized by a relatively low mean SAT level, and selecting it as the reference period more effectively captures the fluctuations of early GSSWEs; it also represents a suitable reference period in studies of long-term temperature change⁶⁸. Only threshold-exceeding grid cells are included in the subsequent analysis, whereas non-threshold-exceeding grid cells contribute zero. For these threshold-exceeding years, the temperature anomaly series at each grid cell is normalized to the range [0, 1] using the minimum and maximum anomaly values among all threshold-exceeding years at that grid cell. Then, for each year, we take the normalized anomaly intensity of each threshold-exceeding grid cell as a coefficient, multiply it by the actual area of that grid, sum over all threshold-exceeding grid cells, and finally divide by the total available land area. This yields the annual EI, with grid-cell area calculated from its latitudinal and longitudinal bounds using the spherical trapezoid formula. The formula for the EI calculation is as follows:

$${\mathrm{EI}}_{ij}=\frac{{\sum }_{l=1}^L{A}_l\cdot I_{l,i,j}\cdot N_{l,i,j}}{A_{i,j}}$$ 1

Where ${\mathrm{EI}}_{ij}$ represents the extremity index of the GSSWEs in season i and year j. $A_l$ represents the actual area of the l-th terrestrial grid cell (excluding Antarctica); $I_{l,i,j}$ is the threshold-exceeding indicator function, which takes the value 1 if the temperature of the l-th grid cell in season i and year j exceeds the 95th percentile of the reference period (1901–1930) for that grid, and 0 otherwise; $A_{i,j}$ denotes the total available land area (excluding Antarctica) for season i and year j, with grid cells containing missing data excluded consistently from both the numerator and denominator. In the calculation by latitudinal zone, the $A_{i,j}$ represents the total land area within that latitudinal zone. $N_{l,i,j}$ represents the normalized temperature anomaly coefficient, calculated as follows:

$$N_{l,i,j}=\frac{{\mathrm{anomaly}}_{l,i,j}-\min \left({\mathrm{anomaly}}_l\right)}{\max \left({\mathrm{anomaly}}_l\right)-\min \left({\mathrm{anomaly}}_l\right)}$$ 2

Where ${\mathrm{anomaly}}_{l,i,j}$ denotes the temperature anomaly of grid cell l in season i of year j (relative to the mean of the reference period 1901–1930 CE), and $\min \left({\mathrm{anomaly}}_l\right)$ and $\max \left({\mathrm{anomaly}}_l\right)$ are the minimum and maximum values of the anomalies among all threshold-exceeding years for grid cell l and season i.

To resolve the spatial pattern of GSSWEs, we further define a grid‑level EI. Specifically, for each land grid cell $l$ in season $i$ of year $j$, the grid-level EI is defined as:

$${\mathrm{EI}}_{lij}=\frac{A_l{I}_{l,i,j}\cdot N_{l,i,j}}{A_{i,j}}$$ 3

Thus, the EI characterizes the extremity of GSSWEs in both the temporal dimension (i.e., normalized SAT anomaly intensity relative to the reference period) and the spatial dimension, represented by the area of simultaneous threshold-exceeding grid cells. Larger EI values, therefore, indicate seasons in which threshold-exceeding warmth is both more spatially extensive and more intense relative to local background conditions.

Millennial-scale multi-model weighted averaging and spatial analysis

To obtain a spatially robust multi-model estimate of grid-level threshold-exceeding events over the past millennium, we developed a grid-cell-specific weighting scheme based on the Critical Success Index (CSI)⁶⁹. This weighting gives greater influence to models that more accurately reproduce the observed occurrence of threshold-exceeding grid cells during the common observational period. For each of the seven climate models, we compared the simulation-based threshold-exceeding indicator with observations from CRU TS v4.08 during the common period of 1901–2023 CE. For each grid cell n, the CSI for model m is defined as:

$${\mathrm{CSI}}_m\left(n\right)=\frac{\mathrm{hits}}{\mathrm{hits}+\mathrm{misses}+\mathrm{false}}$$ 4

where hits are grid-years where both the model and the observations indicate a threshold-exceeding event, misses are grid-years where the observations indicate a threshold-exceeding event but the model does not, and false alarms are grid-years where the model indicates a threshold-exceeding event but observations do not. The CSI values for the seven models are then normalized to sum to 1 for each grid cell, yielding a grid-specific weight $w_m\left(l\right)$:

$$w_m\left(l\right)=\frac{{\mathrm{CSI}}_m\left(l\right)}{{\sum }_{k=1}^8{\mathrm{CSI}}_k\left(l\right)}$$ 5

In addition, for grid cells correctly identified as threshold-exceeding (hits), we computed the spatial correlation coefficient between the grid-level EI derived from model simulations and the observations to ensure consistency in intensity. This correlation was used as a diagnostic assessment of intensity consistency, whereas the CSI-based weights were used for the fused grid-level EI calculation.

The fused grid-level EI for each year t is then calculated as:

$${\mathrm{gridEI}}_{\mathrm{fused}}\left(n,t\right)=\sum _{m=1}^8{w}_m\left(n\right)\cdot {\mathrm{gridEI}}_m\left(n,t\right)$$ 6

Where ${\mathrm{gridEI}}_m\left(n,t\right)$ is the grid-level EI from model m, defined as:

$${\mathrm{gridEI}}_m\left(l,t\right)=\frac{A_l\cdot I_m\left(l,t\right)\cdot N_{m,l,t}}{\sum _l{A}_l}$$ 7

Here, $A_l$ is the actual area of grid cell l, $I_m\left(l,t\right)$ indicates whether the seasonal SAT exceeds the 95th percentile of the 1901–1930 reference period (0 or 1), and $N_{m,l,t}$ is the normalized seasonal SAT anomaly scaled between 0 and 1.

Using this fused product, we computed cumulative threshold-exceeding frequency over 150-year intervals from 850 to 1899 CE and over the period 1900–2023 CE. We also derived the zonal mean cumulative threshold-exceeding frequency as a function of latitude to examine latitudinal coherence.

Turning point identification

We used sequential t-test analysis of regime shifts⁷⁰ (STARS; significance level P = 0.01; Huber’s weight parameter = 1) to detect turning points in the seasonal EI time series over the last millennium. STARS sequentially tests for step-like shifts in the mean under a prescribed cut-off length (L), flags candidate shift years based on a t-test critical departure from the current regime mean, and confirms them using the regime shift index (RSI), which quantifies the persistence of the shift over the subsequent L-year window. Given the millennium-long record (850–2023 CE) and our focus on persistent shifts in the extremity of GSSWEs over the last millennium, rather than short-lived fluctuations, we set the cut-off length to L = 60 years. Sensitivity tests using alternative cut-off lengths (L = 50 and L = 70 years) yielded consistent results (Supplementary Table S4). We defined the turning point as the year with the largest RSI, or, when two adjacent candidate years had comparable RSI values, we reported the earlier year as the turning point and noted the uncertainty in Supplementary Table S4.

Detection and attribution of changes in EI trend

Anthropogenic signal detection and quantitative attribution for changes in the EI trend of GSSWEs were performed based on observations and GCM simulations driven by different external forcings using the formal optimal fingerprint methodology^71,72. The approach represents observed changes as a linear combination of various external forcings and internal variability.

$$\mathrm{y}=\beta \left(\mathrm{x}-\vartheta \right)+\epsilon$$ 8

Where $\mathbf{y}$ refers to a vector of the observed EI trend, and$\mathbf{x}$ denotes the signal patterns of different forcings derived from the ensemble mean of seven model simulations (Supplementary Text S2, Supplementary Fig. S9 and Supplementary Table S3). $\vartheta$ represents noise from internal variability in the corresponding signal patterns. $\beta$ denotes the corresponding scaling factors and $\mathrm{\epsilon }$ signifies the regression residual. The scaling factor and its uncertainty were determined using the ordinary least-squares method^71,72. The covariance structure of the noise terms was estimated from a long-term unforced climate control simulation (i.e., piControl). The vectors for EIs derived from observations and GCM simulations with different forcings were calculated with consecutive non-overlapping five-year averages over the analysis period 1901–2020 CE (24 × 5 years). The five-year averages were used to suppress natural variability, especially at interannual timescales^71,72. Correspondingly, the piControl simulations were divided into multiple non-overlapping 120-year segments, with the final segments shorter than 120 years being discarded. All of the detection and attribution analyses were performed using the code provided in reference⁷¹.

Based on the detection results, the attributable changes in the observed EIs were calculated by multiplying the linear trends of the external forcing component by the corresponding scaling factors (best estimate and uncertainty range). The ALL and ANT scaling factors derived from one-signal analysis were used to compute the attributable changes, whereas the quantitative contributions of NAT, GHG and AA were estimated using the results from three-signal analysis.

Author contributions

J.D.: Conceptualization, Methodology, Writing—original draft, Writing—review & editing. F.H. and Y.Z.: Methodology, Data acquisition, Visualization, Writing—original draft, Writing—review & editing. S.C. and A.W: Visualization, Writing—original draft, Writing—review & editing. C.X., J.L., B.D., F.C.L., E.X., and P.A.S.: Writing—review & editing, discussing, interpretation and finalising the results.

Peer review

Peer review information

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

Data availability

All instrumental observations, paleo-reanalysis products and model simulations used in this study are publicly available as follows. Instrumental observations: CRU TS v4.08, https://crudata.uea.ac.uk/cru/data/hrg/cru_ts_4.08/; BEST, https://berkeley-earth-temperature.s3.us-west-1.amazonaws.com/Global/Gridded/Land_and_Ocean_LatLong1.nc; HadCRUT5, https://www.metoffice.gov.uk/hadobs/hadcrut5/data/HadCRUT.5.0.2.0/analysis/HadCRUT.5.0.2.0.analysis.anomalies.ensemble_mean.nc. Paleo-reanalysis products: PHYDA reanalysis data, DJF: https://www.ncei.noaa.gov/pub/data/paleo/reconstructions/steiger2018/da_hydro_DecFeb_r.1-2000_d.05-Jan-2018.nc; JJA: https://www.ncei.noaa.gov/pub/data/paleo/reconstructions/steiger2018/da_hydro_JunAug_r.1-2000_d.05-Jan-2018.nc; ModE-RA reanalysis dataset, https://www.ncei.noaa.gov/pub/data/paleo/gcmoutput/ModE/ModE-RA/ensstat/ModE-RA_ensmean_temp2_anom_wrt_1901-2000_1421-2008_mon.nc. Model simulations: CMIP5 model data, https://esgf-node.llnl.gov/projects/cmip5/; CMIP6 model data, https://esgf-node.llnl.gov/projects/cmip6/. Furthermore, the processed data and source data underlying the figures generated in this study are available in the Zenodo repository at https://doi.org/10.5281/zenodo.21179138.

Code availability

All analytical codes are available at Zenodo (https://doi.org/10.5281/zenodo.21179138).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-76985-4.