Comparing simulated and observation-derived warming in Europe
Since 1980, much of Europe has warmed by more than 2 °C during summertime (June–August), with some areas even exceeding a warming of 3 °C in ERA5 (Fig. 1a), resulting in an almost three times larger regional warming compared to the observed global warming over that time frame (0.8 °C). Based on a state-of-the-art 49-member RCM simulation ensemble from the CORDEX experiment, however, the modeled warming signal is far weaker (blue colors in Fig. 1b). Averaged over the land areas of western West-Central Europe (WWCE; delineated in Figs. 1a–b) and gauged with linear trends, this amounts to 1.0 °C less warming than observed (ERA5, 2.3 °C). We focus our analysis on the WWCE region and provide area-averaged summer temperatures; all timeseries are smoothed and expressed as changes with respect to 1980 (see Methods for details). We note that this entails no assumption of linearity, and hence the resulting long-term temperature changes visualized in Fig. 1c are generally similar – but not identical – to linear trends. Only a few CORDEX simulations feature a warming of more than 2 °C since 1980 (purple range in Fig. 1c), and even the simulation with the strongest temperature increase (thin purple line) does not clearly exceed the reanalysis-warming. This suggests that there is a systematic bias in either (a) the prescribed forcing, (b) the regional model response to this forcing, or (c), a strong misrepresentation of the variability. The CMIP6 multi-model ensemble (green shading in Fig. 1d) also features weaker than observed trends in most simulations, yet the upper warming range is considerably higher compared to CORDEX, and the overall distribution actually includes the ERA5 data, thus not necessarily implying a demonstrated discrepancy. The CORDEX simulations also feature less warming in winter and spring than observation-derived datasets, whereas linear trends in simulated and observed fall temperature are fairly consistent (Fig. 1e). Our analysis focuses on summertime temperatures, however, because compared to other seasons, (i) summer has warmed the fastest since 1980 according to both ERA5 and E-OBS (Fig. 1e), and (ii), elevated summer baseline temperatures fuel more intense and frequent heatwaves that exert greater impacts on society and ecosystems (e.g., refs 34–36).
Revisiting the drivers of regional warming, we first examine whether insufficient background warming contributes to the summer warming discrepancy in WWCE. The background warming is indicated by linear trends in global annual mean 2m-temperatures from the corresponding driving GCM of each CORDEX simulation, and visualized together with WWCE summer warming since 1980 (purple dots in Fig. 2a). Within the CORDEX ensemble used here, forced by 8 individual GCMs, most models clearly exceed ERA5’s 1980–2022 global mean temperature increase of 0.8 °C. A majority of CMIP6 simulations also overestimate the global mean temperature change compared to ERA5, but the displayed range of background warming is substantially larger than for the CORDEX ensemble. Still, most regional temperature changes of ~1 °C or less are found in CORDEX simulations, and nearly all of these also remain below the 1:1 line, i.e. they feature less WWCE summer warming than for the entire globe throughout 1980–2022. At the other end of the simulated regional warming spectrum by the CORDEX ensemble, a handful of models manage to reproduce ERA5-like WWCE warming, but at a staggering background warming of ~1.6 °C, i.e. double the observed warming. Similarly, CMIP6 models associated with strong WWCE warming generally feature stronger than observed global mean temperature changes. These simulations agree with the observed WWCE summer warming for the wrong reason, since climate models should accurately capture the regional response to global warming (rather than to underestimate this response but simultaneously overestimate the warming at global scale).
Unraveling dynamic and regional thermodynamic warming contributions
Therefore, we continue our analysis for a subset of simulations with the most accurate background global warming compared to ERA5 (indicated by black marker edges in Fig. 2a). We find that differences in WWCE warming between simulations and the reanalysis product emerge more clearly (Fig. 2b), particularly for the CORDEX model subset. Inspecting the temporal evolution of surface net radiation for the same simulation subsets and domain (Fig. 2c), ERA5 points to a strong increase, whereas most — but not all — CORDEX simulations indicate only weak changes. This implies that most of the CORDEX ensemble members suffer from a bias in the regional thermodynamically induced trend. We examine this more closely further below, but already note that this is caused by different aerosol representations in the RCMs within CORDEX (e.g., refs. 23,24). In contrast, the CMIP6 subset used here shows no clear forcing bias. Nonetheless, the strong-observation-derived temperature rise is still not captured (cf. model median vs. ERA5 in Fig. 2c). This suggests that the sole remaining regional warming driver — atmospheric dynamics — contributes to deviating temperature trends.
In a next step, we thus disentangle the 1980–2022 summer warming in WWCE into a dynamic and a thermodynamic component using dynamical adjustment for ERA5 and climate model simulations (see Methods). With this approach, we first estimate the impact of large-scale circulation changes over Europe — represented with 500-hPa geopotential height fields — on mean WWCE summer temperatures, i.e. the dynamical contribution to the total regional warming (schematically represented in Fig. 3a). The thermodynamic contribution is then obtained as the residual, and corresponds to the combined effects of the background global warming and the regional thermodynamic forcing (i.e., mostly increasing net radiation). Since WWCE only represents 0.19% of the global area, we consider the global-scale mean temperature rise as a background effect that contributes to — yet is effectively independent from — the regional warming itself. Fig. 3b visualizes total summer warming over 1980–2022 for model simulations, again for subsets of the CORDEX and CMIP6 ensembles constrained by background warming, and ERA5. For the latter, circulation changes act to increase the regional temperature change by 0.74 °C, which is nearly one third of the total warming (Fig. 3c). Most CMIP6 simulations feature positive, but generally far weaker dynamic contributions, leading to an underestimation of the temperature increase. These findings are consistent with a recent study that suggests dynamics as the main “culprit” for discrepancies between observed and simulated trends in heat extremes33. Given that the dynamic contribution to summer warming in WWCE is a manifestation of unforced internal variability, dynamically inflicted differences between ensemble mean and observed temperature trends do not imply systematic model biases.
Still, as a clear majority of the CORDEX simulations features slightly negative dynamical contributions to the summer warming, this causes an even stronger underestimation of the temperature trend. The difference in dynamical contributions between these model ensemble subsets should be interpreted with caution; the 15 RCM simulations used here are driven by 2 GCM simulations that largely prescribe the large-scale atmospheric flow within the respective RCM domain boundaries37, such that there are effectively only 2 independent circulation realizations. The 15 GCM simulations that form the CMIP6 subset, on the other hand, all feature a freely evolving global atmosphere, which explains why the portrayed range is wider than for the CORDEX RCMs. This also holds for the entire (unconstrained) model ensembles (SFig. 1), and although the overall difference between simulated dynamical warming is smaller than for the subsets shown in Fig. 3c, the CORDEX models still largely feature negative (ensemble mean -0.05 °C) and hence even weaker contributions than the CMIP6 ensemble (+0.16 °C on average). This does not explain the entire discrepancy with respect to the observed warming, however, since the CMIP6 and CORDEX subsets also underestimate the thermodynamic warming (Fig. 3d) by -0.17 and -0.38 °C on average.
The strong thermodynamic bias apparent for the CORDEX models, being driven by simulations with nearly identical background warming as across the CMIP6 subset (markers with black dots in Fig. 2a), must have a regional origin. More available surface net radiation boosts the surface turbulent heat fluxes, which is known to (i) directly impact air temperatures through surface sensible heating, and (ii), further enhance the net radiation through surface latent heating by the associated moistening of the atmosphere and resulting water-vapor feedback20. We thus relate the regional thermodynamic warming, obtained by removing the background warming from the total thermodynamic warming (shown in Fig. 3d), to changes in the surface net radiation in WWCE. A relatively linear relationship emerges (markers and fitted green line in Fig. 4a), with a temperature sensitivity of about 0.5 °C for a 10 W/m2 net radiation change, which is also the case when fitting the total thermodynamic warming to regional net radiation changes (SFig. 2). Following the aerosol representation classification of ref. 24, the CORDEX models with constant aerosols feature weak, mostly positive surface net radiation trends (red markers in Fig. 4a). The remaining CORDEX simulations with time-evolving aerosols, on the other hand, exhibit net radiation increases broadly consistent with ERA5 (blue markers in Fig. 4a). A budget analysis performed for ERA5 and all available simulations — regardless of background warming — reveals that changes in WWCE surface net radiation are predominantly fuelled by enhanced downward shortwave radiation, and to a lesser extent downward longwave radiation (Fig. 4b), as previously reported20. This does, of course, not hold for the CORDEX simulations that (by design) neglect long-term decreases in aerosol concentrations over Europe since the 1980s, resulting in a comparatively miniscule shortwave forcing as reported previously (e.g., ref. 23).
The striking discrepancy of shortwave forcing in CORDEX simulations with and without time-evolving aerosols implies that the downward shortwave radiation increase evident for ERA5 and CMIP6 is largely caused by temporally evolving aerosol attenuation. Additional analyses presented in the Suppl. Information confirm that cloud-related shortwave radiation changes are minor (+1 W/m2) compared to aerosol effects (+21.3 W/m2) for ERA5 (SFig. 3a). This is in line with evidence for decadal variations in observed shortwave radiation since the mid-20th century in West-Central Europe being primarily human-induced21 (rather than, e.g., caused by changes in cloudiness). While CMIP6 models tend to have stronger cloud contributions than ERA5, aerosols remain the key driver of increasing shortwave radiation (SFig. 3b). This further substantiates that neglecting time-evolving aerosols causes a lack of regional thermodynamic forcing (and resulting warming response). Before we proceed with our analysis for WWCE, we note here that European aerosol concentrations are largely attributable to domestic emissions, which are highest in eastern and southeastern parts of the continent38. Consequently, at the eastern edge of our analysis region, and particularly even further to the east, downward shortwave trends for 1980–2022 are underestimated more severely in simulations with constant aerosol forcing than in any other part of Europe (Fig. 4c). In terms of the impact on temperature trends, our analysis region with an average bias of ~0.6 °C is more affected than southern or northern Europe (Fig. 4d), but even stronger biases emerge to the east with local exceedances of 1 °C, consistent with the pattern in shortwave trend biases (Fig. 4c) and aerosol emissions38.
Quantifying the aerosol forcing-induced warming mismatch
Building on the disentangled temperature contributions from the dynamical adjustment we summarize our findings for WWCE in Table 1, always based on averages for the respective models and using ERA5 as a reference to calculate biases. As previously noted, the dynamical contribution is generally much weaker across both the CMIP6 and CORDEX ensembles, causing a mean temperature trend underestimation of 0.58 °C and 0.79 °C, respectively. However, we focus on the thermodynamic warming here, since this is what each model simulation — and, contrary to the dynamic warming, especially the ensemble mean — should capture. For the CMIP6 ensemble, there is a slight positive thermodynamic bias, whereas it is negative for the CORDEX simulations, despite the fact that both model ensembles have a mean background warming excess of about 0.3 °C that counteracts the remaining (or residual) negative thermodynamic bias. We estimate the regional thermodynamic bias using the relationship between thermodynamic warming (i.e., the slope shown in Fig. 4a) for the CORDEX subset, and the respective mean net radiation trend discrepancy with respect to ERA5 for the entire CORDEX ensemble and all subgroups. Similarly, using the slope determined analogously to Fig. 4a for the CMIP6 subset (SFig. 4), we obtain the regional thermodynamic bias for the CMIP6 models based on mean 1980–2022 changes in summer net radiation. Whereas this reveals only slight biases for the CMIP6 models, for the CORDEX models, our estimates of the regional warming bias are clearly negative for the entire ensemble (-0.47 °C), the subset (-0.37 °C) and its subgroup with constant aerosol representations only (-0.61 °C). Only the subgroup with time-evolving aerosols does not suffer from a clear bias (-0.01 °C). The respective residual thermodynamic biases are all within ±0.1 °C, which suggests that it is indeed a general lack of increasing net radiation — in turn due to a majority of the RCMs relying on constant aerosols — that causes most of the thermodynamic warming underestimation. The extent of the bias depends on the composition of the respective ensemble; for our 49-member CORDEX ensemble consisting of 35 RCM simulations with constant aerosols, it amounts to about 0.5 °C on average. Comparing the thermodynamic biases between the two subgroups with constant and evolving aerosols, we find a total (& residual) thermodynamic difference of 0.59 °C, and a regional thermodynamic difference estimated through net radiation changes of 0.60 °C. In other words, neglecting long-term changes in aerosols reduces the total thermodynamic warming by 35%–40%.
Table 1: Summer warming in WWCE between 1980 and 2022 for model simulations and ERA5, disentangled into dynamical and thermodynamic (TD) contributions (see Methods). The total bias with respect to the thermodynamic warming in ERA5 is shown, further disentangled into a background warming (BW) bias and a residual. The latter roughly corresponds to — but is obtained independently from — our estimate of the regional thermodynamic bias, which we estimate by converting simulated net radiation trend differences with respect to ERA5 into warming biases. The total, dynamic and thermodynamic warming are estimated with a linear trend and represent the respective total 1980–2022 changes, and all values are shown in °C.
|
Total warming
|
Dynamic warming
|
TD warming
|
Total TD bias
|
Backgr. warm. bias
|
Resid. bias
|
Rnet-based TD bias
|
ERA5
|
2.33
|
0.74
|
1.59
|
|
|
|
|
CORDEX
|
1.32
|
-0.05
|
1.37
|
-0.22
|
+0.33
|
-0.55
|
-0.47
|
CORDEX subset
|
1.06
|
-0.16
|
1.21
|
-0.38
|
+0.08
|
-0.46
|
-0.37
|
CORDEX aerEvo
|
1.42
|
-0.16
|
1.57
|
-0.02
|
+0.08
|
-0.10
|
-0.01
|
CORDEX aerCon
|
0.81
|
-0.16
|
0.98
|
-0.61
|
+0.08
|
-0.69
|
-0.61
|
CMIP6
|
1.85
|
0.16
|
1.69
|
+0.10
|
+0.32
|
-0.22
|
+0.04
|
CMIP6 subset
|
1.71
|
0.29
|
1.42
|
-0.17
|
+0.03
|
-0.20
|
+0.04
|
It is difficult to quantify this precisely, since model errors and possibly other factors also play a role (otherwise the residual and regional thermodynamic bias estimates would be identical), but our analysis conclusively demonstrates that the thermodynamic warming underestimation by the CORDEX ensemble is largely attributable to simplistic aerosol representations. To our knowledge, previous analyses either examined the impact of aerosol representation in multi-model CORDEX ensembles on past (and projected) shortwave radiation changes23,24, or investigated the influence on temperature in climate projections25,39. Besides these studies, model experiments with a single RCM suggest that nearly a quarter of the simulated 1980–2012 annual mean warming in Europe is achieved by aerosol changes40. Even though comparing this to our estimate based on several models and a different analysis period is not straightforward, it is plausible that we obtain an even stronger aerosol effect on temperature changes than ref. 40: incoming shortwave radiation in mid-to-high latitudes is most intense and exerts the strongest influence on air temperatures during summertime (e.g., ref. 41). Our results suggest that the summertime warming in WWCE in RCMs without time-evolving aerosols — the majority of models participating in the CORDEX initiative — is largely driven by the background warming, as the regional thermodynamic forcing and resulting warming is widely underestimated.
On the other hand, the RCMs with long-term aerosol changes simulate almost the same thermodynamic warming as obtained from ERA5 (cf. dashed lines in Fig. 5a). While these models reach the observation-derived 1980–2022 temperature change attributable to thermodynamics (yellow line in Fig. 5a) on average in the year 2026 (i.e. 4 years too late), it takes 13 years longer for the simulations based on constant aerosols. As such, and despite being forced with a high-emission scenario, the RCMs with constant aerosol forcing only reach the current observed summer warming by about 2039. Crucially, the mismatch introduced by neglecting long-term aerosol changes relative to simulations that account for it increases throughout the ongoing century, reaching about 1.5 °C (and close to 2 °C) in terms of mean (median) in 2100 (cf. red and blue boxplots in Fig. 5a). This range is consistent with ref. 25, even though the authors assessed surface rather than air temperature changes, and employed a different CORDEX model ensemble.
Finally, we also explore how the lack of local thermodynamic forcing due to neglecting aerosol trends affects summer temperatures at different timescales, from seasonal to daily (Fig. 5b). Unlike for the multi-model averages, the observation-derived 1980–2022 warming for the 5 hottest consecutive days outpaces both changes at shorter and longer timescales. We would not expect the latter if the warming was entirely driven by thermodynamics, and hence consider this an independent line of evidence that dynamics contributed to the summer warming in WWCE. Moreover, we note that the hottest sub-monthly periods occur most frequently in July and August for WWCE, whereas the observed monthly mean warming is clearly highest in June (SFig. 5), fuelled by strong dynamic contributions. Consequently, discrepancies between ERA5 and CORDEX simulations also increase from 10/15-d periods towards the (90-d) seasonal scale. Comparing the mean warming rates of the two CORDEX subgroups, the hottest 10-d period per year increased by about 2 °C and 1 °C for CORDEX simulations with and without time-evolving aerosols, respectively, and the resulting ~1 °C difference implies an even stronger absolute thermodynamic contribution than for summer mean temperatures at ~0.6 °C. While the relative contribution to the total warming does not vary much as much across timescales, but tends to exceed 40%, it is not obvious why a long-term modulation of shortwave — and ultimately net — radiation trends by aerosols enhances temperatures during the hottest sub-monthly time periods more than across the entire summer. We argue that aerosol representation-inflicted biases should emerge most clearly in cloud-free conditions, which are closely related to the large-scale circulation patterns — typically atmospheric blockings — that enable heatwaves in WWCE (e.g., ref. 42). Moreover, the same analysis performed for 1980–2099 shows that at the end of the century (under a scenario assuming further decreases in aerosol emissions), aerosol-related temperature biases exceed 2 °C for the hottest multi-day periods up to 15 days.