We use simulations performed with CESM version 2.1.2 , which have been run in exactly the same setup as for producing the CESM2 Large Ensemble CESM2-LE;. The fully coupled simulations have 32 vertical levels and a horizontal resolution of ∼ 0.9° latitude times 1.25° longitude. They use CMIP6 historical radiative forcing until 2014 and Shared Socioeconomic Pathways (SSP) 3-7.0 radiative forcing thereafter. A four-member ensemble covering the time period 1980–2020 is considered in our analyses. In contrast to the publicly available CESM2-LE data, we stored six-hourly output of horizontal and vertical winds (u,v,ω) and temperature (T) on all 32 model levels, i.e., we retained the full vertical resolution of the model and are thus able to compute kinematic air parcel trajectories required for the Lagrangian temperature anomaly decomposition (see Sect. 2.3).

As in , we consider as heat extremes so-called TX1day events, which are identified at each grid point as the hottest day of the year based on absolute daily mean 2 m temperature, T2m, computed from the respective six-hourly values. As we consider a 41-year period, this yields 41 TX1day events per member. Note that TX1day events are identified based on absolute temperatures and not based on temperature anomalies. Evidently, various meaningful definitions of heat extremes exist and have been used previously. Here, we opt for TX1day events for the following reasons: (1) the computational demand of our analyses scales linearly with the duration of the events under consideration. That is, focusing on longer-lasting events such as TX5day events as in e.g., would be five times more costly than considering TX1day events, and would exceed the limits of computational resources available to the authors. (2) TX1day events are annual block maxima and thus lend themselves to analyses based on extreme-value statistics. (3) TX1day events have been used previously by , whose analysis serves as starting point of this study.

To decompose the near-surface T′ of the CESM2 TX1day events, we compute 15 d backward trajectories from each TX1day event, at six-hourly temporal resolution and on three vertical near-surface levels (10, 30 and 50 hPa above ground), yielding 12 trajectories per TX1day event in CESM2. Trajectories have been computed with LAGRANTO 2.0 . LAGRANTO is a versatile tool to calculate three-dimensional air parcel trajectories offline. As input fields, it uses three-dimensional winds and additional use-specific variables (in our case temperature, the model-level temperature climatology and its temporal and pressure derivatives), which are interpolated in space and time along the trajectories. Details about the numerical implementation and the versatile functionality of the tool can be found in .

We evaluate CESM2 TX1day characteristics against the latest ECMWF reanalysis ERA5 for the time period 1980 to 2020. The ERA5 data used here has been interpolated to a 0.5° latitude by 0.5° longitude grid, and is used at three-hourly temporal resolution. As for CESM2, model level data is used for the Lagrangian analyses and TX1day events are identified as in CESM2, i.e., based on daily mean T2m. To employ the Lagrangian T′ decomposition, as for CESM2, 15 d backward trajectories are computed from the same near-surface vertical levels but at three-hourly resolution, yielding 24 trajectories per ERA5 TX1day event. The results of our analyses with ERA5 have been published previously in (there the years 1979–2020 were considered).

From the description of the two datasets it becomes evident that trajectories computed with CESM2 rely on wind fields with a coarser horizontal, vertical, and temporal resolution. This means that although we apply the identical diagnostic (described in the next subsection), the comparison of the resulting T′ decomposition might be affected by the differing resolutions of the underlying datasets. We will come back to this issue in Sect. , where we perform sensitivity experiments by reducing the resolution of ERA5 fields towards the one of CESM2. For these specific experiments, we interpolated ERA5 data to various resolutions, both horizontally and vertically. Horizontal interpolation of the ERA5 data with 0.5° horizontal resolution has been done bi-linearly, to either the exact CESM2 latitude/longitude grid (Sect. ) or to a uniform 1° latitude/longitude grid (Sect. ). Vertical interpolation is less straightforward and explained in Appendix B.

To quantify the advective, adiabatic and diabatic contributions to near-surface temperature anomalies during TX1day events in the two datasets we use the Lagrangian T′ decomposition of , which relies on the computation of a large set of trajectories. The setup of these trajectories is the same for both datasets, as described above.

The T′ decomposition is based on the thermodynamic energy equation formulated in terms of temperature anomalies, T′, relative to a temperature climatology T‾ (hereafter referred to as the Lagrangian T′ equation, Eq. 1 in ). The Lagrangian T′ equation states that the material change of T′ in an air parcel is the sum of four terms: (1) seasonality T′, which arises from temporal changes in T‾ (i.e., climatological diurnal and seasonal cycles) but is usually small on the timescales over which near-surface T′ of heat extremes form; (2) advective T′, which is T′ arising from transport of air across horizontal gradients of T‾; (3) adiabatic T′, that is, T′ arising from vertical motion of air parcels; and (4) diabatic T′, which is T′ generated through any physical process that changes the potential temperature of an air parcel. To decompose any T′ at location x and time tX, one first computes the backward trajectory (x(t),t) of the air parcel located at x at time tX. Then, the Lagrangian T′ equation is integrated along the trajectory (x(t),t) from the time tg when T′ was last zero in that air parcel. Hereafter, we refer to tg as the “genesis time”. Formally, the decomposition of T′ can thus be written as: 1T′(x,tX)=-∫tgtX∂T‾∂tdτ-∫tgtXv∇hT‾dτ+∫tgtXκTp-∂T‾∂pωdτ+∫tgtXpp0κDθDtdτ.

Hereby v and ∇h are the horizontal wind and horizontal gradient operator, respectively, p is pressure, κ=0.286, ω is vertical motion in pressure coordinates, and θ is potential temperature (reference pressure p0 = 1000 hPa).

The temperature climatologies in CESM2 and ERA5 (T‾ERA5 and T‾CESM2) are computed as in , i.e., as a model-level T-climatology that incorporates both the climatological diurnal and climatological seasonal cycle, as well as the long-term warming trend. The subscripts ERA5 and CESM2 are hereafter omitted whenever possible without loss of clarity. Specifically, at any time step, T‾ is computed by averaging all T values from the same time of the day in a 21-calendar-day window in a 9-year running window. For instance, T‾ at 00:00 UTC on 15 July 1990 is thus computed by averaging T at all 00:00 UTC time steps for calendar days between 5 and 25 July in 1986–1994. For the first and last few years of the study period, i.e., for 1980–1983 and 2016–2020, T‾ERA5 is computed from the years 1979–1987 and 2012–2020, respectively, while for computing T‾CESM2 in 9-year windows we use data from the years 1976–2024.

For ERA5 data we evaluate Eq. () exactly as detailed in , but for CESM2 we employ a slightly modified definition of the anomaly genesis time, tg, as outlined in Appendix A, while keeping all other aspects of the method identical. This slightly modified definition of tg in CESM2 only has a marginal effect on the results presented here, but is mentioned for the sake of completeness.

Differences in TX1day T′ between CESM2 and ERA5 (CESM2 minus ERA5) as well as differences in the respective advective, adiabatic, and diabatic contributions are hereafter referred to as, e.g., ΔT′, Δ advective T′, etc. Moreover, we consider three spatiotemporal characteristics of temperature anomalies: their age, defined as A=tX-tg, the Lagrangian formation distance, D, defined as the great circle distance between x(tg) and x(tX), and the net vertical displacement since anomaly genesis, P=p(tX)-p(tg).

We begin by examining global-scale patterns in the TX1day T′ decomposition in ERA5 and CESM2 (Fig. ). The qualitative patterns in the TX1day T′ magnitude largely agree between ERA5 and CESM2 (Fig. a, b), with generally more intense TX1day events over land than over ocean and the globally most intense TX1day events over Siberia, Canada, and southern Australia. Also for the advective, adiabatic, and diabatic T′, the qualitative patterns agree between the two data sets and reveal dominant advective contributions to TX1day events in stormtrack regions, considerable adiabatic contributions over subtropical ocean regions as well as some extratropical land regions, and pronounced diabatic T′ over most tropical and extratropical land regions in both data sets (Fig. c–h).

Quantitatively, however, systematic discrepancies in both the magnitude of T′ and the contributions from the different processes to TX1day T′ are found across the globe. Averaged globally, TX1day T′ magnitudes are overestimated in CESM2 by 0.49 K (0.70 K when only considering land regions), while absolute values of the differences in ΔT′ are smaller than 1 K in 80 % of all regions below 1500 ma.s.l. (Figs. a and c), they reach substantial values in some areas. For example, in western Russia and eastern Canada, TX1day T′ in CESM2 exceeds the respective value in ERA5 by more than 3 K (Fig. a). Similarly, substantially more intense TX1day events in CESM2 are found over the eastern North Atlantic and North Pacific, off the coast of Namibia as well as in the seas south of Australia. Negative values of ΔT′ are far less widespread than positive values; they are prevalent in the Southern Ocean and in few land regions including the western United States (Fig. a).

Considering differences between CESM2 and ERA5 in the three contributions to TX1day T′ over land, they are particularly large for the adiabatic and diabatic T′ (Figs.  and a), also in regions where ΔT′ magnitudes are modest, e.g., in Europe, vast parts of Africa and Australia. Over almost all land regions, the adiabatic T′ is considerably smaller in CESM2 compared to ERA5 (Fig. c). Averaged across all land regions with altitudes below 1500 ma.s.l. in CESM2, the adiabatic T′ in CESM2 (1.69 K) is less than half that in ERA5 (3.45 K), while the diabatic T′ in CESM2 (4.61 K) is much larger than in ERA5 (2.48 K, Fig. a). Furthermore, in regions of complex topography, there is poor quantitative agreement between the two datasets regarding the TX1day T′ composition. This, however, is an expected result, as the topography is less well resolved in CESM2, with significant effects on trajectories of near-surface air parcels.

Also over ocean regions, systematic differences in the TX1day T′ composition are apparent between the two data sets. Averaged across all ocean regions, CESM2 TX1day events feature -0.29 K diabatic T′, compared to -1.21 K in ERA5 (Fig. b). Furthermore, in several subtropical and tropical ocean regions (in particular the tropical Pacific), there are larger negative advective contributions to CESM2 TX1day events compared to those in ERA5 (Fig. b). In the tropical Pacific, the more intense negative advective contributions in CESM2 are offset in part by more positive adiabatic T′. Note, however, that both the magnitude of TX1day T′ as well as its difference to ERA5 ΔT′ is small over tropical ocean regions. Interestingly, advective T′ is overestimated mainly in regions where the general amplitude of TX1day T′ is also overestimated (e.g., over eastern Canada and southern Australia; Fig. a and b).

Figure c, which shows differences of the T′ composition as a function of the magnitude of ΔT′, reveals some additional interesting aspects. Consistent with the previous discussion, differences in advective T′ are positive at the grid points with the largest differences ΔT′, and they are negative at grid points where ΔT′ is small. At these grid points the negative differences in advective T′ is mainly balanced by positive differences in diabatic T′. Interestingly, the average differences in diabatic T′ are fairly independent of ΔT′ (flat orange curve in Fig. c). In contrast, the differences in adiabatic T′ are always negative but strongly increases in magnitude at grid points with larger ΔT′, compensating the differences in diabatic T′ at the grid points with the largest values of ΔT′.

Next we consider the temporal, horizontal, and vertical scales over which near-surface TX1day anomalies form in the two data sets, by examining the Lagrangian characteristics age, A, formation distance, D, and vertical displacement since anomaly genesis, P (Figs.  and ). The large-scale patterns in A and P largely agree between the two data sets, in particular for TX1day events over land. Oldest TX1day anomalies are found in both data sets over western Russia, Greenland, and in subtropical anticyclones (Fig. a and d). However, in particular for TX1day events in the tropical Pacific, CESM2 substantially overestimates A (by up to 4 d, while in ERA5 A in these regions is typically less than 3 d, Figs. a and a, b). Nevertheless, over land regions, A differences are typically less than 10 h and the spatial patterns in A agree remarkably well between the two data sets (Fig. a and b). Similarly, also the spatial patterns in P agree very well (Fig. e and f), with globally largest P in the Mediterranean region and around major orography. Quantitatively, however, CESM2 systematically underestimates P, in particular over land regions (Fig. c), as P is 40 hPa in ERA5 and only 13 hPa in CESM2 when averaging across all TX1day events occurring at land grid points below 1500 ma.s.l. in the CESM2 topography. That is, air parcels contributing to TX1day events in CESM2 subside less after anomaly genesis than their counterparts in ERA5, which points to a different combination of physical mechanisms leading to heat extremes in CESM2 compared to ERA5.

Furthermore, for the formation distance D, considerable differences are apparent already in its large-scale patterns (Fig. c and d). Over vast tropical and subtropical ocean regions, D in CESM2 exceeds D in ERA5 by more than 1000 km (Fig. b), which in many regions constitutes a difference of more than 100 %. That is, while in ERA5 TX1day T′ over tropical and subtropical oceans form over hundreds to typically less than 1500 km, the CESM2 TX1day T′ in the same region form over several thousand kilometers. Hereby, the overestimation in D is particularly large for TX1day events in the tropical Pacific, in agreement with the overestimation of the age, A, in this region (Fig. a and b). Clearly, these large discrepancies in the spatiotemporal characteristics of TX1day T′ over tropical and subtropical oceans are worrying and warrant further investigation. Nevertheless, note that over land regions the patterns of D are qualitatively similar in the two data sets, and they even quantitatively rarely differ by more than 250 km. Moreover, over land even comparatively small-scale spatial variations in D are often reproduced, e.g., in Spain, where TX1day events feature D of less than 1000 km in both data sets, while in Scandinavia D typically exceeds 1500 km.

So far our analyses have revealed that (a) CESM2 overestimates the magnitude of TX1day events in many regions, and, moreover, these particular regions feature also larger advective T′ in CESM2 compared to ERA5. (b) CESM2 systematically overestimates the diabatic contribution and underestimates the adiabatic contribution to TX1day T′, in particular over land regions. (c) Over land regions, A and D of TX1day T′ are comparable between CESM2 and ERA5 (not over oceans, however), while P is substantially underestimated in CESM2, which is consistent with the underestimated adiabatic T′. In the remainder of this paper we focus on the key findings (a) and (b) and further investigate their potential causes.

Next, we focus on the differences in the physical mechanisms during TX1day events in CESM2, and examine potential causes of Δ adiabatic T′ and Δ diabatic T′. Specifically, we examine two hypotheses: (a) the differences in adiabatic and diabatic T′ could result from resolution differences between the two data sets (assuming that the resolution of the wind fields impacts the trajectories' (vertical) motion); (b) the overestimation of diabatic T′ in CESM2 is related to a different partitioning of heat fluxes (i.e., stronger sensible and weaker latent heat fluxes) during and preceding TX1day events in CESM2 compared to ERA5, as suggested for other models in previous studies e.g.,.

The differences in the magnitude and physical mechanisms leading to heat extremes in CESM2 identified in this study relate to several known deficiencies in current climate models: Positive biases in the magnitude of simulated heat extremes have been documented previously for CMIP5 and 6 models . However, the spatial patterns of these biases considerably differ depending on the model (compare Fig. a in this study with Fig. 1h in ), and depending on whether the heat extreme magnitude is quantified with absolute values or anomalies . Here we find that differences in TX1day magnitude between CESM2 and ERA5 are related to differences in the circulation conditional to TX1day events, at least when aggregating over all land regions below 1500 ma.s.l. Subsequent studies should thus assess whether this is also the case for other climate models and, if so, examine in detail the flow features within which heat extremes form in regions of overestimated heat extreme magnitude.

Importantly, however, the differences in the TX1day T′ magnitude are far smaller (15 % when considering all land regions below 1500 ma.s.l.) compared to differences in the composition of their respective T′ (-51 % for adiabatic T′ and +86 % for diabatic T′ in the same region). Rather worryingly, our results thus suggest that CESM2 reproduces the magnitude of TX1day T′ rather well, however, the relative contributions of physical mechanisms are strongly biased compared to ERA5 and thus the TX1day events partly occur for the wrong reasons – at least in several land regions.

This may have implications for the robustness of heat extreme projections under future warming. For instance, in regions of large Δ diabatic T′, intensifying land–atmosphere interactions could affect simulated heat extremes more strongly than in reality, yielding erroneous projections of heat extremes under global warming. However, such effects would likely also depend on the (observed and simulated) base state regarding soil moisture, as further drying in already too dry regions may be underestimated in simulations . Likewise, projected changes in atmospheric blocking (which are currently rather uncertain) and, related to that, changes in subsidence warming might have little effect on changes in simulated heat extremes under global warming, due to the widespread underestimation of adiabatic T′ over most land regions. Evidently, the results of this study should be considered when pondering about changes in heat extremes under global warming, in particular if they are related to intensifying land–atmosphere interactions e.g.,, or changes in blocking .

Furthermore, very large differences between CESM2 and ERA5 were found for TX1day events over tropical and subtropical oceans in terms of the Lagrangian age, A, and the formation distance, D, of the respective temperature anomalies. While the magnitude of TX1day events is modest in these regions, these differences are still worrying, as they point to a rather different physical mechanism leading to TX1day events in CESM2 compared to ERA5 in these regions. Specifically, these differences imply that in CESM2 anomalously warm air (which later contributes to TX1day events) is transported over longer distances and time periods than in ERA5. Various factors could contribute to such differences, for instance too strong trade winds , or an erroneous representation of low clouds, which affects the surface radiation budget in these regions . We note that these results about oceanic TX1day events do not necessarily translate to the process relevant for marine heat waves. Given the much longer timescale of these heat waves, potential model biases associated with their occurrence would need to be studied separately.

Moreover, the analyses presented here suffer from at least three caveats, which should be considered when interpreting our results. Firstly, the analyses presented in Fig.  hint to one cause of the considerable Δ diabatic T′, but do not quantify the effect of a potentially biased partitioning of sensible and latent heat fluxes during heat extremes. Subsequent studies could attempt to further decompose the diabatic T′, e.g., by considering heating tendencies from ERA5 and climate models along air parcel trajectories, as has been done in for one specific numerical weather prediction model. Such even more detailed Lagrangian analyses could further pinpoint the physical causes of the considerable Δ diabatic T′ found in this study. Secondly, we performed analyses with only one model, which prevents making any general statements about the physical mechanisms leading to heat extremes in state-of-the-art models. Clearly, our analyses should be repeated in subsequent studies with various models. However, such analyses are currently severely hampered by the lack of publicly available high-frequency and vertically complete climate model data, which is a prerequisite for computing air parcel trajectories needed for our Lagrangian decomposition of T′. We thus urge the climate modeling community to provide such high-frequency (at least six-hourly output) and vertically complete data (i.e., from all model levels) for at least a few decades of simulations per model (e.g., one member covering the last few decades), such that our analyses could be repeated with other models and that a more robust understanding could be established of the capability of climate models in simulating the physics of heat extremes. Thirdly, We acknowledge that with the approach of we cannot exclude the possibility that some of the differences we identify for TX1day events also emerge when comparing CESM2 and ERA5 mean circulation and heat fluxes (i.e., differences might not be specific to TX1day events). Yet, for addressing the question “Do heat extremes in CESM2 form for the right physical reasons?” it is important to unravel the full biases in the functioning of heat extremes.

Finally, we mention that an alternative Lagrangian approach to decompose temperature anomalies during heat extremes into advective, adiabatic and diabatic components has recently been proposed by , who found that “horizontal transport is attributed the primary role for heat extremes globally”. At first sight, this finding contrasts Fig.  and the results of . However, in our view, this contrast emerges from the fact that the two studies, and , addressed slightly different research questions: Recall that assessed whether temperature anomalies contributing to heat extremes at a particular location X form because (a) air from a climatologically warmer region reaches location X, (b) because air subsides prior to the heat extreme, or (c) because that air is heated diabatically. In some contrast, compared the Lagrangian characteristics of air contributing to heat extremes at a location X to Lagrangian characteristics of “climatological” air at location X. Thereby, they construct their “Lagrangian climatology” from air parcels with any temperature anomaly (hot and cold). That is, they assess how anomalous the horizontal transport, adiabatic warming or cooling, and diabatic heating or cooling is compared to climatological air see Sect. 4 in. Evidently, their research question differs from that of .

Nevertheless, we do note that the finding of that “horizontal transport is attributed the primary role for heat extremes globally” contrasts a vast body of literature that highlights the key role for the formation of heat extremes of adiabatic warming e.g., and of diabatic warming e.g.,. We propose that the seeming unimportance of adiabatic and diabatic warming for heat extremes in the analyses of might be a consequence of the definition of their “Lagrangian climatology”. Recall that compared adiabatic warming of air parcels contributing to heat extremes (i.e., anomalously warm air) with the adiabatic warming of all air parcels arriving at a certain location, including often anomalously cold airstreams like dry intrusions , which for buoyancy reasons are expected to subside more strongly than anomalously hot air. Nevertheless, this does not exclude the possibility that (the comparatively modest) subsidence warming of already anomalously warm air in an anticyclone might be key to the formation of near-surface heat. Similarly, sensible heating of near-surface air is strongly influenced by the temperature contrast between near-surface air and the Earth's surface. The larger that contrast, the larger the heating/cooling heating rates far larger than those contributing to heat extremes are observed, for instance, during cold air outbreaks over warm ocean surfaces, e.g.,. Therefore, diabatic heating of already anomalously hot air through sensible heat fluxes from the surface is unlikely to be large compared to that of climatological or anomalously cold air. This, however, again does not render the diabatic heating of anomalously warm air unimportant for near-surface heat. Again, the choice of “Lagrangian climatology” by likely explains the contrast between their result (diabatic heating is largely unimportant for heat extremes, their Fig. 3c) with the results of previous studies suggesting the opposite e.g.,.

In this study the physical mechanisms leading to heat extremes simulated with CESM2 are evaluated, by comparing near-surface T′ during TX1day events. In a four-member CMIP-type CESM2 simulation as well as in ERA5, the T′ is decomposed into its advective, adiabatic, and diabatic contributions, as computed in . This comparison reveals a good qualitative agreement in the large-scale patterns of TX1day T′ and its contributions: (i) In both datasets we find more intense TX1day events over land (peak intensities in western North America and Russia exceeding 10 K) than over ocean (least intense TX1day events over tropical and subtropical oceans, with lowest TX1day T′ magnitudes of less than 1 K); (ii) advective contributions dominate the TX1day T′ over extratropical storm track regions, where in both data sets air moves poleward on near-surface levels before approaching the respective heat extreme location; (iii) in both data sets, adiabatic T′ is large for TX1day events in the regions of the climatological subtropical anticyclones, as well as over northern hemispheric extratropical land regions; and (iv) diabatic T′ is generally positive over land and small or negative over oceans in both data sets, and in both data sets particularly large in subtropical dry regions, such as Australia.

Quantitatively, however, there are large discrepancies between the datasets regarding the advective, adiabatic, and diabatic contributions to TX1day T′, and, moreover, CESM2 overestimates the magnitude of TX1day T′ in numerous regions, in particular in the mid-latitudes (averaged globally, the difference in Δ TX1day T′ is 0.49 K, which is 15 % of the global average of TX1day T′ in ERA5). Interestingly, regions with large differences in TX1day T′ also feature large (and same-signed) differences in the advective T′, suggesting a tight relationship between the two. Detailed analyses of the underlying causes for the differences in advective T′ reveal that at a regional scale, differences in circulation leading to the TX1day events (i.e., differences in the air parcel trajectories) and differing horizontal gradients of T‾ contribute both to the differences in advective T′, albeit with larger contributions from circulation differences when aggregating over all land areas below 1500 ma.s.l.

Furthermore, CESM2 systematically underestimates the adiabatic T′ over land (averaged globally across land regions below 1500 ma.s.l., the difference in Δ adiabatic T′ is -1.77 K or a 51 % underestimation compared to ERA5), and systematically overestimates the diabatic T′ over most land and ocean regions (Δ diabatic T′ of 2.13 K averaged over land regions below 1500 ma.s.l., overestimation of 86 %). The underestimation of the adiabatic T′ is related to less subsidence between tg and tX for air contributing to TX1day events in CESM2 compared to ERA5. For TX1day events over land, the average P is 40 hPa, while in CESM2 it is only 13 hPa (note that peak values of P exceed 150 hPa in either data set, though). At the current time it is unclear why CESM2 underestimates the subsidence involved in heat extreme formation. Experiments with trajectories based on ERA5 wind fields interpolated to fewer vertical levels indicate that vertical resolution is not a major reason for this underestimation.

The overestimation of the diabatic T′ in CESM2 was investigated at six selected grid points in regions of peak Δ diabatic T′. In all six cases, differences in diabatic T′ appear to be related to a different partitioning of surface heat fluxes in upwind regions during TX1day events. Hereby, the (upward) sensible heat fluxes in most upwind regions of the respective locations are larger in CESM2 than in ERA5, while the converse is true for the latent heat fluxes. This finding is consistent with numerous previous studies who documented a similarly biased land–atmosphere coupling during heat extremes in current climate models .

We draw the following conclusions from the results presented and discussed above:

It is reassuring to see that CESM2 adequately reproduces the large-scale patterns in TX1day T′ and its contributions. This is particularly noteworthy, as the advective, adiabatic, and diabatic T′ are highly derived quantities resulting from Lagrangian diagnostics. Their qualitatively adequate representation in CESM2 testifies to the ability of this model to realistically simulate regional variations in the processes leading to heat extremes.