At each grid point (i,j) and vertical hybrid sigma–pressure level k, we compute the temperature anomaly T′ by removing the climatological temperature Tclim from the absolute temperature T: 1T′(i,j,k)=T(i,j,k)-Tclim(i,j,k), where Tclim(i,j,k) is computed analogously to : Tclim(i,j,k) is the running mean over a 21-calendar-day and 9-year centred window of the absolute temperature at the same 3-hourly time step, resulting in an average over 189 d. Therefore, this Tclim(i,j,k) accounts for the climate change, the seasonality, and the diurnal cycle. The standard deviation of the temperature anomalies at each grid point and each vertical level σ(i,j,k) is calculated as: 2σ(i,j,k)=1Nt∑NtT′(i,j,k)2, where Nt=1533 results from the 21 d centred window across all 73 years. Although we expect that σ(i,j,k) during summer has changed with global warming, its change is small compared to the change in the mean . Studies focusing on the most extreme temperature events suggested that the standard deviation has remained roughly constant throughout this period . We, therefore, use a standard deviation that varies with the calendar day and time of the day but not throughout the years (i.e., no climate change variation), contrary to Tclim, which varies diurnally, seasonally, and inter-annually. Note that σ(i,j,k) is largest near the surface and decreases with altitude, except for polar regions (Fig. ). To account for different variabilities vertically and across the globe, we then normalise the temperature anomalies as follows: 3Tnorm′(i,j,k)=T′(i,j,k)σ(i,j,k). Therefore, we express the normalised temperature anomalies Tnorm′(i,j,k) in units of σ in the following.

In this study, we define heat extremes based on the annual maximum three-hourly 2 m absolute temperatures at each grid point, so-called TXx events. This definition corresponds to the block-maxima approach, which is commonly used in extreme value statistics and for understanding heat extremes e.g.. Note that in some regions, the TXx values are strongly influenced by inter-annual variability. Because a TXx event is defined as the single hottest three-hourly value within a given year, every year has a TXx event, even in years without any particularly hot days. Consequently, not all TXx events are exceptionally hot in a climatological sense. Furthermore, if a year has multiple distinct heatwaves, this definition considers only the single warmest event and disregards all others.

We analyse TXx events between 1951 and 2023, resulting in 73 heat extremes at each grid point. For those events, we then extract the temperature anomaly and the normalised temperature anomaly. Both the median temperature anomaly and the median normalised temperature anomaly (Fig. a, b) on the lowermost model level show meridional differences, with smaller values in the tropics compared to the mid-latitudes. While the median temperature anomalies decrease again towards the polar regions (Fig. a), the median normalised temperature anomalies further increase (Fig. b). The median magnitude of the near-surface temperature anomaly during TXx events in the mid-latitudes exceeds 8 K, which corresponds to 1.5–2.5σ in those regions. In contrast, tropical regions feature smaller temperature anomalies of up to 4 K, corresponding to 1–2σ. Polar regions exhibit temperature anomalies of 6–8 K, corresponding to 2–2.5σ.

If we assume the maximum temperature to occur within a season of approximately 90 d (see Fig. S1 in the Supplement) and the temperature distribution to be Gaussian, we expect the median σ with a 95 % probability between 2.3 and 2.5 by selecting 73 times a maximum from 90 values. Even though this σ is larger than the observed σ during TXx events in some regions, after the normalisation, most of the meridional differences disappear. Therefore, most of the meridional temperature differences occur because of climatologically different σ and less because of the underlying skewness of the distribution of extremes in each region.

To determine regions with similar temperature anomaly profile structures, we employ a clustering algorithm. We aim to identify “characteristic” vertical profiles during heat extremes. At every grid point and for each TXx event n (n=1, …, 73), we extract the vertical profile of temperature anomalies T′n(i,j,k) and normalised temperature anomalies T′normn(i,j,k). Figure c, d shows the T′ profile during TXx events at an exemplary grid point in central Europe (49° N, 12° E). Importantly, at each grid point, the TXx events have different normalised anomalies at the lowermost T′normn(i,j,k=0), because some events are more intense than others. To compare the associated profiles, we assume that the normalised vertical temperature anomaly profile scales with the normalised anomaly at the surface: T′normn(i,j,k)=T′normn(i,j,k=0)⋅f(k), where f(k) is the function we want to determine. Therefore, we scale each vertical profile by the lowermost normalised temperature anomaly T′normn(i,j,k=0): 4T′scaledn(i,j,k)=T′normn(i,j,k)T′normn(i,j,k=0). We express the scaled temperature anomalies in units of σ/σs in the following, where σs represents the surface standard deviation (at k=0). While T′normn(i,j,k) shows the departure from the climatology, T′scaledn(i,j,k) shows at each vertical level whether the value reached is more or less anomalous than the one at the surface (see Fig. e for an example). If Tscaled′ is smaller than one (which is typically the case), this indicates that the temperature anomaly at that level is less anomalous than the one at the surface. Furthermore, given the implied proportionality, a 2σ-event at the surface is expected to have a temperature anomaly profile twice as anomalous as that of a 1σ-event. At each grid point, the scaled T′ profiles exhibit many similarities across TXx events in different years (see Fig. e for an example). To approximate this representative profile, we compute the multi-year median scaled T′ profile (black line in Fig. e): 5T′‾scaled(i,j,k)=mediannT′scaledn(i,j,k). Note that the median is used here to provide robustness to outliers, which arise from potentially including less extreme TXx events, as discussed in Sect. .

Next, we perform a principal component analysis PCA; of T′‾scaled(i,j,k) over all land grid points to reduce the dimension of the data set, as high-dimensional phase spaces can make the k-means clustering unreliable . We retain eight principal components, which explain over 95 % of the variance (the red line in Fig. e shows an example of a PCA-based profile). The vertical profiles projected on those eight components serve as the basis for the clustering algorithm.

For the clustering, we use an area-weighted k-means approach . A suitable number of clusters is determined based on the silhouette score , which is a commonly used measure to find an optimal number of clusters e.g.. The silhouette score for the retained components of the T′‾scaled profiles peaks at three clusters, reaching a value of approximately 0.44 (Fig. a). We therefore use three clusters for the following analysis. The scikit-learn Python package served for computing the PCA, k-means clustering, and silhouette score .

Finally, for each cluster C, we define the cluster profile as the median of T′‾scaled of the grid points within this cluster, based on the full vertical profile: 6Tscaled,C′(k)=median(i,j)∈CT′‾scaled(i,j,k).

After the clustering, we want to assess how well the median cluster profile (Tscaled,C′) represents the characteristic vertical profile (T′‾scaled) at each grid point that belongs to cluster C. Furthermore, we are generally interested in how variable the temperature anomaly profiles are between TXx events at a given grid point. A classical mean squared error (MSE) decomposition into bias and variance allows us to investigate exactly these two objectives. Therefore, we calculate the MSE between the vertical temperature anomaly profile and the median cluster profile at each grid point, which we then decompose into a contribution from the squared bias of the cluster and the median vertical temperature anomaly profile, the variance of the TXx events at that grid point, and a covariance of both terms: 7MSE(i,j,k)=1Nn∑nNnT′scaledn(i,j,k)-Tscaled,C′(k)2=T′‾scaled(i,j,k)-Tscaled,C′(k)2+1Nn∑nNnT′scaledn(i,j,k)-T′‾scaled(i,j,k)2+2T′‾scaled(i,j,k)-Tscaled,C′(k)8⋅1Nn∑nNnT′scaledn(i,j,k)-T′‾scaled(i,j,k), where Nn is the number of TXx events that we consider at each grid point. The first term on the right-hand side of Eq. (8) denotes the (squared) bias of the median grid point profile relative to the cluster profile, bias2(Tscaled′), i.e. how the median for this grid point compares to the median of all other grid points in the same cluster. The second term describes the variance between TXx events (var(Tscaled′)), which is independent of our clustering as we cluster on the median profiles. The third term is the covariance term, describing the coupling between the variance and the bias. By definition, the sum of (T′scaledn(i,j,k)-T′‾scaled(i,j,k)) is equal to zero, if T′‾scaled(i,j,k) is the mean. Since we use the median, this term slightly deviates from zero, but the deviation is much smaller than the other two terms (not shown), and we will neglect it in the following: 9MSE(i,j,k)≈T′‾scaled(i,j,k)-Tscaled,C′(k)2︸bias2(T′‾scaled)+1Nn∑nNnT′scaledn(i,j,k)-T′‾scaled(i,j,k)2︸var(Tscaled′).

As already mentioned in Sect. , not all TXx events are particularly extreme. To reduce the influence of comparatively colder TXx events, which we regard as outliers, the clustering was based on the median Tscaled′ profile at each grid point. For the bias2(T′‾scaled) and var(Tscaled′) analysis, we additionally exclude the 10 coldest events from each cluster because they tend to show large deviations from the cluster median and provide little information on the most relevant, i.e., most intense heat extremes (see Fig. S4).

To assess how bias2(T′‾scaled) and var(Tscaled′) vary vertically, we average the MSE vertically over the PBL, the free troposphere, and above the tropopause separately. As the clustering and previous analyses have been performed on hybrid sigma-pressure levels, we need to interpolate the profiles onto pressure levels. First, we compute the squared error for each TXx event and grid point on hybrid sigma-pressure levels. Then, we linearly interpolate the squared error values of each TXx event between the surface pressure and the PBL height pressure, the PBL height pressure and the tropopause pressure, and the tropopause pressure and the minimum pressure, respectively. Finally, at each grid point, we compute the MSE over all TXx events within each of the three layers: 10MSElayer(i,j)=1pmax⁡-pmin⁡∫pmin⁡pmax⁡var(Tscaled′)(i,j,p)dp+1pmax⁡-pmin⁡∫pmin⁡pmax⁡bias2(T′‾scaled)(i,j,p)dp, where we integrate the pressure between the minimum and maximum pressures (pmin⁡ and pmax⁡) of each layer and take its average before averaging the individual events.

Aside from the squared bias and variance computations for the scaled temperature anomaly profiles, we also compute the squared bias and variance analogously for the normalised temperature anomaly profiles. To deduce a normalised Tnorm,C′ from the scaled Tscaled,C′ at a given grid point, we multiply Tscaled,C′ with the near-surface Tnorm′ of the TXx events: 11T′norm,Cn(i,j,k)=Tscaled,C′(k)⋅T′normn(i,j,k=0).

The area-weighted k-means clustering of the vertical profiles of T′‾scaled reveals three distinct clusters (Fig. ). The spatial distribution of the clusters closely follows the climate zones, which constitutes a first key result of this study. This meridional pattern implies that our clustering grouped tropical regions in cluster 1, the mid-latitudes in cluster 2, and polar regions in cluster 3 (Fig. a). Hereafter, we will refer to these clusters as the tropical, mid-latitude, and polar clusters, respectively. Having distinct clusters for the climate zones highlights distinct processes leading to heat extremes in the tropics, mid-latitudes, and polar regions, and this therefore suggests that this is by far the dominant distinction compared to regional variations inside each climate zone. This is also recognised in the existing literature on heat extremes in the tropics, mid-latitudes, and polar regions e.g..

In the tropical cluster, we find that the positive temperature anomalies are confined to the near-surface and lower troposphere, with the highest temperature anomalies at about 900 hPa. In contrast, the mid- and upper-troposphere do not exhibit any temperature anomaly. The maximum boundary layer height, based on the Richardson number criterion , varies in these regions on days with TXx events roughly between 700 and 500 hPa (Fig. a). Since our temperature anomaly within the tropics is confined to about 600 hPa, this indicates that the temperature anomalies are restricted to the PBL. Note that not all tropical regions feature such deep PBLs, which are most frequent in arid subtropical regions (Fig. a). Due to variations of the PBL height, the interquartile range of Tscaled′ between model levels 100 and 120 is larger in the tropical compared to the other clusters (Fig. b). However, the fact that across the tropics, TXx temperature profiles have no anomaly in the free troposphere leads to the tropical and subtropical regions being clustered together. The absence of an upper-level temperature anomaly is consistent with the weak horizontal temperature gradient in the tropical free troposphere. This gradient is typically weak since gravity waves efficiently adjust the free-tropospheric temperature profile to a moist adiabatic profile throughout the tropics . Recent research on tropical heat extremes suggested that they occur during periods of suppressed moist convection, caused either by reduced near-surface moisture or the entrainment of dry air . This suppression allows for the development of a deep PBL through dry convection within the PBL, facilitating the accumulation of heat and resulting in the high temperature anomalies observed in this cluster's distinct vertical profile.

Similar to the tropical cluster, the mid-latitude cluster features a deep layer of uniform and extremely high temperature anomalies near the surface (Fig. b, c). However, in contrast to the tropical cluster, it exhibits vertically deep temperature anomalies that extend throughout the troposphere. The temperature anomaly profile is bottom-heavy, with the largest temperature anomalies in terms of Tscaled′ and T′ near the surface and in the lower troposphere since the standard deviation decreases from the surface to the free troposphere (Fig. ). The same structure with the largest anomalies near the surface but still vertically deep anomalies was also noted by during extreme summers, during recent record-shattering heatwaves, and during European heat extremes. The presence of these deep temperature anomalies suggests that heat extremes in the mid-latitudes are more vertically organised than those over the tropics, likely due to dynamical coupling with the upper-level anticyclonic flow. Aside from the vertically organised behaviour of the mid-latitude cluster, it is particularly striking that, despite well-documented regional differences in the relative importance of different processes for the formation of mid-latitude heatwaves e.g., the vertical profiles in all these regions ultimately end up in the same mid-latitude cluster, underscoring their commonality in terms of vertical structure compared to other climate zones.

For the polar cluster, we also find temperature anomalies that extend throughout the troposphere, similar to the mid-latitude cluster (Fig. b, c). However, the layer near the surface with extremely high Tscaled′ is much thinner at high latitudes. As discussed in the introduction, climatologically, polar regions feature strong temperature inversions over the cold surface, leading to thin stable boundary layers with relatively small temperature variability (see Figs. b and ). Therefore, the large near-surface temperature anomalies in the TXx profiles could hint at the erosion of this inversion layer and the mixing down of warmer air during heat extremes. This finding aligns with and , who showed the erosion of the near-surface temperature inversion during the 2022 Antarctica heatwave. The mid- and upper-tropospheric normalised temperature anomalies are relatively weak compared to the near-surface anomalies. Given the large temperature anomalies near the surface, scaling with Tnorm′(k=0) scales the full profile more drastically, leading to lower normalised values in the free-troposphere compared to the mid-latitude cluster.

In the upper troposphere and lower stratosphere, profiles of the polar and in particular the mid-latitude clusters feature negative T′‾scaled above 250–300 hPa. These negative values are most likely due to the upward shift of the tropopause, associated with the upper-level anticyclones during heat extremes e.g.. Therefore, virtually all positive temperature anomalies during TXx events are confined to the troposphere, and the negative anomalies above emerge as a consequence of the elevated tropopause. Weaker negative temperature anomalies for the polar cluster likely arise from weaker anticyclonic flow anomalies. The tropics also feature a small negative temperature anomaly around the tropopause height, consistent with the cooling of the lower stratosphere in response to tropospheric warming .

With our procedure, some regions are classified in somewhat unexpected clusters. For instance, in Europe, both the Iberian Peninsula and the west coast of France stand out as being assigned to the tropical cluster rather than the mid-latitude cluster (Fig. a). TXx events over the Iberian Peninsula feature a deep PBL and a vertically uniform layer of elevated scaled temperatures extending from the surface to 700 hPa (Fig. c, d). At the same time, there is also an upper-level temperature anomaly near the tropopause, similar to the mid-latitude cluster, even though this temperature anomaly is weaker and confined to the upper troposphere. While heat extremes in mid-latitude regions are typically linked to atmospheric blocking, over the Iberian Peninsula, they are more often associated with subtropical ridges e.g.. In addition, and reported that heat extremes over the Iberian Peninsula are frequently accompanied by Saharan plumes of warm air in the free troposphere. Therefore, TXx events in this region feature a hybrid structure, combining characteristics of both the tropical and mid-latitude clusters. Another unexpected classification occurs in Greenland (Fig. a). Despite its snow cover, cold near-surface conditions, and a shallow PBL, TXx events over a large part of Greenland are classified as being in the mid-latitude rather than the polar cluster. Examining individual grid points over Greenland (Fig. b–e) reveals that the mid-latitude classified grid points feature a weaker vertical gradient of the temperature anomalies near the surface compared to those in the polar cluster. However, the near-surface layer with uniform temperature anomalies at the Greenland grid points classified as mid-latitude is shallow compared to the median of the mid-latitude cluster. Nevertheless, the temperature anomalies in the free troposphere are higher, similarly to the mid-latitude cluster, which likely leads to the mid-latitude classification. A third unexpected classification arises in South America, where parts of Uruguay and southern Brazil are in the polar cluster (Fig. a). Comparing the cluster median profile and the profiles at the considered grid points reveals that even though the temperature anomalies in the PBL deviate considerably from the polar cluster, the free-tropospheric temperature anomalies are similar to the polar cluster and, thus, smaller than in the mid-latitude cluster (Fig. d). The different characteristics of this region likely come from the different seasonality of the TXx events compared to the monsoon region further north (see Fig. S1) and the reduced co-location of upper-level blocking anticyclones during these events compared to the region further south . Note that, aside from unexpected clusters in these regions, elevated regions generally cluster with their “expected cluster”, indicating that topography itself does not affect the clustering (Figs. a and ). Generally, we expect some grid points to feature a mix of characteristics of the three clusters, especially at the intersection between two clusters. Despite its caveats (e.g. due to the limitation to three clusters only), the clustering provides a coherent and informative overall picture of the vertical temperature anomaly structure. We will further discuss the spatial variability within the clusters (and therefore, the robustness of the cluster profiles) together with the variability of individual TXx events in Sect. .

Given that the extent of the troposphere varies meridionally, one might wonder whether the identified clusters simply reflect this variation in tropopause height. We therefore performed three sensitivity tests: (i) without an area-weighting of the grid points, (ii) with an area-weighting but with profiles that are capped in the mid-troposphere by only including the lowermost hybrid sigma–pressure levels (levels 90–137), and (iii) without an area-weighting where the profiles are vertically scaled and capped at the tropopause by linear scaling between the surface and the dynamical tropopause. The first test reveals a similar peak of the silhouette score (Fig. S2a), while the second shows a peak at four to five clusters, and the third one shows no peak and generally lower silhouette scores (Fig. S2b, c). The approaches produced very similar global distributions of the clusters and median cluster profiles when constraining the number of clusters to three, except for the second test, which features no polar but two tropical clusters (Fig. S3). We conclude from these tests that the clusters are not an artefact of varying tropopause height, but instead they capture differences in vertical temperature anomaly profiles that reveal distinct dynamics leading to the formation of heat extremes.

To better understand the temporal evolution of the vertical structure of TXx events, we next examine the genesis and decay of temperature anomalies in the days preceding and following the events, respectively (Fig. ). Even though the mechanisms forming near-surface heat extremes in the three clusters vary considerably, all three clusters experience an increase in the temperature anomaly within 5 d before the TXx event from an approximately climatological profile (close to zero anomalies at most levels) to the previously discussed profiles on the day of the TXx events (Fig. a–c).

Heat extremes in the tropics are characterised by a gradual and uniform increase in the temperature anomaly below 600 hPa (Fig. c). This suggests a local heat accumulation within the boundary layer, likely due to reduced soil and PBL moisture . Mirroring the genesis phase, the decay of heat extremes in the tropics is characterised by a gradual decrease in the temperature anomaly within the PBL (Fig. f).

In contrast, the genesis of heat extremes in the mid-latitudes is characterised by a full tropospheric warming (Fig. b). In the period from 5 to 1 d before the TXx event, the scaled temperature anomaly increases uniformly throughout the troposphere. This vertically deep warming likely indicates an influence of large-scale atmospheric dynamics that preconditions the vertical profile before reaching the peak surface temperatures. One day before the TXx event, the temperature in the mid- to upper-troposphere nearly reached its final temperature anomaly, while the surface temperature anomaly still deviates strongly from the one during the TXx event. This suggests that the final warming occurs predominantly in the lower troposphere and PBL, presumingly due to land–atmosphere feedbacks, but potentially also due to amplified subsidence, as noted by for the 2021 PNW heatwave. The evolution of temperature anomalies aligns with the evolution of recent heatwaves in the mid-latitudes, which also featured first a full tropospheric warming followed by a low-level intensification .

After TXx events in the mid-latitudes, a strong decrease in temperature anomaly is observed first within the PBL, while the temperature anomalies above 800 hPa decrease more slowly (Fig. e). Note that the TXx event is the hottest time step by definition. Therefore, we expect a decrease in the near-surface temperature afterwards. However, principally anomalous temperatures can remain after a TXx event. found that thunderstorms and frontal passages terminate heat extremes in central Europe, which aligns with the occurrence of precipitation after TXx events and their termination through moist convection, suggested by . Aside from the specific termination processes, the longer-lasting temperature anomalies in the upper levels might also represent the different lifetimes of upper-level anticyclones and heat extremes.

Similar to the mid-latitudes, heat extremes in the polar cluster exhibit first a uniform warming throughout the troposphere (Fig. a). The difference in the vertical profile compared to the mid-latitude cluster emerges about 1 d before TXx events, when the temperature anomaly in the lowermost 50 hPa increases very strongly. found a strong advective contribution to near-surface temperature anomalies during heat extremes in polar regions. Furthermore, according to , a strong upper-tropospheric ridge and the associated poleward transport of warm and moist air masses are responsible for extreme melting events in Greenland. Therefore, we hypothesise that the deep temperature anomaly profiles that we observe in the polar cluster likely originate from strong advection. Aside from the deep temperature anomalies, the near-surface evolution of T′‾scaled, as already discussed before, hints towards the rapid erosion of the above-ground temperature inversion layer. The intrusion of warm and moist air above the inversion can lead to its erosion through changes in the surface energy balance, rather than increased shear-driven turbulent mixing within the inversion layer . This erosion of the surface temperature inversion during our TXx events in the polar cluster is likely similar to observed, recent polar heatwaves. During the days after polar TXx events, the near-surface temperature anomalies continuously fade away. In contrast, the upper-level temperature anomaly decreases more slowly (Fig. d). Both suggest the restoration of a near-surface temperature inversion after a TXx event, which was also observed after the East Antarctica heatwave in 2022 .

Up to this point, our analysis focused on a k-means clustering with three clusters, which is the number of clusters for which the ratio of the within-cluster similarity and the between-cluster dissimilarity is the largest. As a refinement, we extend the analysis to six clusters. This choice is motivated by the consideration that by doubling the number of clusters, we can examine whether each of the three original clusters is partitioned into two sub-clusters, or whether qualitatively new groupings emerge.

The six resulting clusters from the area-weighted k-means clustering show, similarly to the three clusters, the major climate zones (compare Figs. a and a). Compared to the original clustering with three clusters, the refined clustering results in two clusters with tropical characteristics, three with mid-latitude characteristics, and one with polar characteristics. Hereafter, we focus on the different climate characteristics separately.

In the tropical regions (Fig. d), we find a distinction between regions with deeper PBLs with positive T′ (tropics 2) and regions with a less deep layer with positive T′ (tropics 1), while the profiles look similar above 500 hPa (no anomalies in both clusters). Comparing these clusters to the soil moisture regimes of , we find that the regions with the shallower PBL are often situated in regions classified in a wet or transitional-wet regime, whereas the tropics 2 cluster is located in regions classified in the dry or transitional regime, especially over deserts, i.e. below the descending branch of the Hadley cell. In dry regions, the sensible heat fluxes are stronger than in wet regions, as a larger fraction of the net radiation is converted into sensible heat flux e.g.. This larger heat transfer into the atmosphere leads to a deeper PBL .

All mid-latitude clusters feature deep temperature anomalies (Fig. c), but the mid-latitude 1 cluster has a stronger vertical decrease of T′‾scaled, while clusters mid-latitude 2 and 3 exhibit a more vertically uniform anomaly profile. The layer of high temperature anomalies near the surface is shallower in mid-latitude 3 compared to mid-latitude 2. The stronger vertical gradient in T′‾scaled between 800 and 600 hPa in the mid-latitude 1 cluster indicates that its temperature anomalies are more concentrated near the surface. Furthermore, the deeper uniform layer of T′‾scaled in this cluster near the surface suggests a deeper PBL and suggests that surface processes may be more important. In contrast, the stronger upper-tropospheric anomalies in cluster mid-latitude 2 and mid-latitude 3 are likely linked to stronger anticyclones or atmospheric blocks, as also indicated by a strong negative anomaly above the tropopause. also differentiated European heat extremes by their vertical temperature distribution and noted that heat extremes with amplified temperature anomalies near the surface were often preconditioned by low soil moisture. Furthermore, according to , large parts of the mid-latitude 1 cluster regions are located in the transition soil moisture regime, while the mid-latitude 2 and mid-latitude 3 cluster regions are in the wet regime. Connecting this knowledge with our clusters, the mid-latitude 1 cluster, with its deeper PBL, has likely stronger sensible heat fluxes and, thus, a stronger land-atmosphere coupling due to drier soil moisture conditions.

Considerable changes occur in climatic transition zones between the original three-cluster and the extended six-cluster categorisation. In these regions, some grid points change their cluster type. For example, the Iberian Peninsula, which was initially part of the tropical cluster, has now shifted to the mid-latitude 1 cluster with weak temperature anomalies in the upper troposphere and deep PBL anomalies, which fits better with the observed Tscaled′ of that region (see grey shading in Fig. c, d). Similarly, the South American regions, which were assigned to the polar cluster due to their weak upper-level temperature anomalies, are now classified as mid-latitude 1.

The polar cluster is similar to the polar cluster of the original clustering (Figs. a and a). Having only one polar cluster in the refined clustering suggests that the variability between polar grid points is comparatively small due to the shallow near-surface layer with high temperature anomalies.

In the remaining parts of the paper, we return to the analysis of the original classification with three clusters.