Increasing central and northern European summer heatwave intensity due to forced changes in internal variability

Domain: earth_science
Published: 2025-10-30
Editorial outcome: major_revision

Abstract
In recent years, European summer heatwaves have strongly intensified due to rising anthropogenic emissions. While European summer heatwaves will continue to intensify due to the warming of summer temperatures, the effects of the changes in internal variability under global warming remain unknown. Employing five single-model initial-condition large ensembles, we find that the forced changes in internal variability are projected to intensify central and northern European summer heatwaves. Central and northern Europe will experience frequent moisture limitations, enhancing land-atmosphere feedback and increasing heat wave intensity and variability. In contrast, the forced changes in internal variability will contribute to weakening southern European summer heatwaves. Southern Europe is projected to face a more stable moisture-depleted environment that reduces extreme temperature variability and heatwave intensity. Our findings imply that while adaptation to increasing mean temperatures in southern Europe should suffice to reduce the vulnerability to increasing EuSHW intensity, in central and northern Europe adaptation to increased temperature variability will also be needed.

Introduction
With human-induced rising global mean temperatures, the intensity, frequency, and duration of extreme heat events have increased almost everywhere since the 1950s, and this positive trend is expected to continue in the coming decades1–5. Europe, in particular, has been identified as a heatwave hotspot with increasing intensity trends up to four times higher than the rest of the northern midlatitudes6,7. During the last two decades, the occurrence of multiple unprecedented European summer heatwaves (EuSHWs) (e.g. 2003, 2015, 2018, and 2022) has caused large economic, ecological, and humanitarian losses8–11.

The recent increase in EuSHW intensity has been partly explained by the forced shift in climatology towards warmer values12–15. Under rising global mean temperatures, European summer temperatures are also rising, altering the background mean state and shifting summer temperature distributions. Assuming a limited adaptation towards increasing European summer mean temperatures, the threshold at which temperatures are perceived as extreme will be time-invariant, and consequently, the positive shift in the temperature distribution leads to an increase in EuSHW intensity16. For instance, considering an ecosystem that historically lived with average summer temperatures of 20°C and extreme temperatures of 30°C, a positive shift in temperature distributions of 5°C will increase the mean to 25°C and extreme temperatures to 35°C. Although the difference between the shifted average summer temperatures and extreme temperatures has not changed from the historical period, the ecosystem will experience an increase in extreme heat if it does not adapt to the altered climatology.

In addition to the shift in the temperature distribution, the internal variability of the climate system has significantly contributed to the occurrence of recent heatwaves17–20. The variability in sea surface temperatures, soil moisture content, atmospheric dynamics, and the consequent positive feedbacks involved have been related to historical EuSHWs6,21–27. Persistent sea surface temperature anomalies in the North Atlantic, Pacific and Barents Sea have been critical to sustaining circumglobal atmospheric wavetrains and consequent long-lasting high-pressure systems over Europe, which relate to negative precipitation and soil moisture anomalies17,19,20,24,25. In transitional regimes, a decrease in soil moisture reduces evaporative cooling by reducing latent heat flux and increases temperatures by increasing sensible heat flux, feeding back onto the atmospheric circulation, further decreasing soil moisture content and amplifying the intensity of recent EuSHWs23,25.

However, under rising global mean temperatures, the background mean warming is expected to alter the mean state of the ocean, land, atmosphere and their interactions, and therefore, the variability of the climate system15,21,28–35. In the upcoming decades Europe is expected to face significant drying36,37, which, depending on the historical soil moisture mean state, could change regions from energy-limited regimes into transitional regimes, and from transitional regimes into dry regimes (Fig. 5 in ref. 23). Considering that soil moisture-temperature feedback is effective only in transitional regimes, a decrease in soil moisture content could lead to either enhanced land-atmosphere coupling and temperature variability, or diminished land-atmosphere coupling and temperature variability. An increasing temperature variability could enhance the increase in the heatwave intensity caused by the shift in temperature distributions and expand the intensity range of possible future EuSHWs increasing the risk of unprecedented EuSHWs38,39. Following the previous example of the ecosystem, if the forced changes in internal variability induce an additional 2°C increase in extreme temperatures, the difference between the shifted average summer temperatures and extreme temperatures will increase relative to historical times. Therefore, even if the ecosystem adapts to increasing mean temperatures and mitigates the effects of increasing heatwave intensity due to the distribution shift, this might not be enough to reduce the vulnerability of upcoming EuSHWs.

While it is well established in the literature that EuSHW intensity will continue to increase due to the shift in summer temperature distributions, how the forced changes in internal climate variability will affect EuSHW intensity under increasing global warming levels remains unknown. Previous studies have been limited by the short observational record that did not allow a robust sampling of EuSHWs, or by the coarse temporal resolution of climate models that did not allow the identification of heatwave events but rather an assessment of summer mean temperature metrics. Here, we employ five single model initial-condition large ensembles (SMILEs): ACCESS-ESM-1.540 (40 members), CanESM541 (50 members), EC-Earth342 (50 members), MIROC643 (50 members), and MPI-GE CMIP644 (50 members). We use all available SMILEs that provide ~50 ensemble members with daily temporal resolution for the late historical period (1970–2014) and two shared socioeconomic pathway scenarios (SSP2–4.5, and SSP5–8.5) that span until the end of the 21st century. The high temporal resolution enables us to identify heatwave events and quantify their intensity, and the ~50 ensemble members for each SMILE enable us to robustly differentiate the effects of changing internal climate variability (i.e. forced changes in internal variability) from shifting temperature distributions (i.e. forced distribution shift)45–47. Here, we investigate the changes in EuSHW intensity and their range due to forced changes in internal variability and forced distribution shift under different global warming levels.

Results
Historical and projected European summer heatwave intensity
The intensity of non-detrended EuSHWs (see methods for details) has been increasing over the past two decades leading to the three most extreme observed events in 2022, 2003, and 2015, in the respective order, and the increase is projected to continue until ~2040 regardless of the SSP scenarios for all climate models (Fig. 1a, d, g, j, m). Thereafter, the forced signal in EuSHW intensity, computed as the ensemble mean, and the range of possible future EuSHW intensity due to the internal climate variability will strongly depend on the SSP scenarios. The five climate models indicate that for the SSP2–4.5 scenario the increase in EuSHW intensity will be relatively constant, and for the SSP5–8.5 scenario the increase will be non-linear. By the end of the century, CanESM5 shows the highest forced signal in EuSHW intensity (25 times higher than the mean observed EuSHW intensity for SSP2–4.5, and 108 times higher for SSP5–8.5; Fig. 1d), followed by ACCESS-ESM-1.5 (24 times for SSP2–4.5, and 76 times for SSP5–8.5; Fig. 1a), EC-Earth3 (18 times for SSP2–4.5, and 76 times for SSP5–8.5; Fig. 1g), MIROC6 (14 times for SSP2–4.5, and 57 times for SSP5–8.5; Fig. 1j) and MPI-GE CMIP6 (9 times for SSP2–4.5, and 47 times for SSP5–8.5; Fig. 1m), in the respective order.

The range of possible future EuSHW intensity due to the internal climate variability computed as the difference between the 95th and the 5th ensemble percentile follows a similar evolution (Fig. 1a, d, g, j, m). For each model, the range increases similarly in both forcing scenarios until ~2040. However, the range of EuSHWs due to internal climate variability will diverge towards the end of the 21st century with the largest increase shown by the SSP5–8.5 scenario. ACCESS-ESM-1.5 shows the largest range that is 59 times larger than the mean observed EuSHW intensity for SSP5–8.5 (Fig. 1a), followed by MPI-GE CMIP6 (50 times larger; Fig. 1m), EC-Earth3 (47 times larger; Fig. 1g), CanESM5 (41 times larger; Fig. 1d), and MIROC6 (31 times larger; Fig. 1j). The qualitative time evolution of the forced signal and the range of possible EuSHW intensity due to internal climate variability reflects the evolution of the underlying radiative forcing, and hence, the evolution of global mean temperature anomalies.

Sensitivity of EuSHW intensity to global warming levels
We find a robust relationship between global warming levels and the forced signal in five climate models (Fig. 1b, e, h, k, n), as expected, as well as a robust relationship between global warming levels and the range of possible EuSHW intensity (Fig. 1c, f, i, l, o). We find that on the one hand, the forced signal in EuSHW intensity increases non-linearly under increasing global mean temperature anomalies. On the other hand, the range of possible EuSHWs computed as ensemble standard deviation increases linearly under increasing global mean temperature anomalies. MPI-GE CMIP6 shows the largest increase in the range of EuSHW intensity under global warming (an increase of 3.9 times the mean observed EuSHW intensity per one degree Celsius increase of global mean temperature anomalies; Fig. 1o), followed by ACCESS-ESM-1.5 (3.5 times; Fig. 1c), MIROC6 (2.8 times; Fig. 1l), EC-Earth3 (2.7 times; Fig. 1i), and CanESM5 (2 times; Fig. 1f).

The scaling of the forced signal and the range of EuSHW intensity due to internal variability with global warming anomalies are not spatially uniform (Fig. 2). Although the increase in the forced signal (Fig. 2a) and in the range of EuSHW intensity (Fig. 2b) are projected for entire Europe, the strongest increase is projected for southern Europe and the increase will gradually reduce northward. All models agree on the positive relationship between the forced signal and the range of EuSHW intensity, and global warming anomalies for the entire European domain (Supplementary Fig. 1). Yet, models differ on the magnitude of the increase. MIROC6 shows the largest increase across models in the forced signal and in the range of EuSHW intensity in southern Europe, but it also shows the most abrupt reduction of the increase northward (Supplementary Fig. 1g, h). In contrast, CanESM5 shows the least abrupt reduction of the increase northward (Supplementary Fig. 1c, d), with ACCESS-ESM-1.5 (Supplementary Fig. 1a, b), MPI-GE CMIP6 (Supplementary Fig. 1i, j) and EC-Earth3 (Supplementary Fig. 1e, f) in between.

The increase in the forced signal in non-detrended EuSHW intensity and its range is driven by the combined effects of the forced distribution shift and the forced changes in internal variability. The forced distribution shift implies that temperature distributions will shift toward positive values and thus more frequent exceeding the fixed threshold. With a fixed percentile-based heatwave threshold (i.e. assuming a constant perception of what extreme temperatures are for a given day of the summer and grid point) a positive shift in temperature distribution will lead to an increased EuSHW intensity together with an increase in their possible range, even if the internal variability remains unforced. The forced changes in internal variability imply a change in the variability of the climate system and hence, of temperatures, which could enhance or suppress the forced signal and the range of EuSHW intensity caused by the shift in temperature distributions. We next disentangle the contribution of the forced changes in internal variability from the forced distribution shift.

The effects of the forced changes in internal variability
We detrend daily maximum 2m air temperature by subtracting the ensemble mean to remove the effects of the forced distribution shift, and focus on the effects of forced changes in internal variability (Fig. 3, see methods for details). The recent and projected increase in non-detrended EuSHW intensity seen in Fig. 1 is considerably reduced when removing the effect of mean temperature rise, which implies that the forced distribution shift is the main contributor to the increase in EuSHW intensity (Fig. 3a, d, g, j, m). Yet, we find a positive linear relationship between global warming levels and the forced signal in all models (Fig. 3b, e, k, n), excluding EC-Earth3 which shows a slightly negative linear relationship (Fig. 3h). The linear relationship between global warming levels and the range of detrended EuSHW intensity is consistently positive in all models (Fig. 3c, f, i, l, o). The positive linear relationship implies that the forced changes in internal variability will enhance the intensity and variability of EuSHWs caused by the temperature distribution shift, increasing the risk of unprecedented EuSHWs. MPI-GE CMIP6 shows the largest increase in the forced signal and the range of EuSHW intensity across models (an increase of 0.19 and 0.22 times the mean observed EuSHW intensity per one degree Celsius increase of global mean temperature anomalies, respectively; Fig. 3n, o), followed by ACCESS-ESM-1.5 (0.18 and 0.12 times; Fig. 3b, c), MIROC6 (0.9 and 0.11 times; Fig. 3k, l), CanESM5 (0.02 and 0.04 times; Fig. 3e, f), and EC-Earth3 (a decrease of 0.01 and an increase of 0.01 times; Fig. 3e, f).

We find a robust increase in the forced signal and the range of EuSHW intensity with global warming levels emerging from central and northern Europe (Fig. 4a, b). Considering that individual models largely disagree on the regional patterns (Supplementary Fig. 2), we define a robust change in the forced signal and the range of EuSHW intensity (non-dashed regions in Fig. 4a, b) when at least three out of the five models agree on the sign of the change and three out of the five models show significant changes at the 95% confidence level. All models except MIROC6 show a significant increase in the forced signal and the range of EuSHW intensity in central Europe, although in ACCESS-ESM-1.5 this increase is more pronounced in northern than in central Europe. Similarly, all models except CanESM5 and EC-Earth3 show a significant increase in northern Europe (Supplementary Fig. 2). The maximum positive contribution of the forced changes in internal variability to the increase in the forced signal and the range of central-northern EuSHW intensity (45°N latitude northward) is shown by ACCESS-ESM-1.5 (14% and 32%, respectively; Supplementary Fig. 3a, b), followed by MPI-GE CMIP6 (14% and 24%; Supplementary Fig. 3i, j), MIROC6 (7% and 11%; Supplementary Fig. 3g, h), EC-Earth3 (2% and 8%; Supplementary Fig. 3e, f), and CanESM5 (1% and 6%, respectively). In central and northern Europe the forced changes in internal variability will cause a faster increase of the right tail of daily maximum temperatures than the mean under increasing global warming levels (Supplementary Fig. 4), that is, an increase in temperature variability in agreement with ref. 21 and ref. 34. A faster increase of extreme summer temperatures compared to the mean lead to the positive trend of the forced signal in EuSHW intensity after detrending daily maximum temperatures. In addition, the increased temperature variability due to the forced changes in internal variability will lead to a higher fluctuation of extreme temperatures (Supplementary Fig. 5) leading to a larger range of EuSHW intensity.

In contrast, we find a robust decrease in the forced signal and the range of EuSHWs with global warming levels along the Mediterranean coastline (Fig. 4a, b). While CanESM5 and MIROC6 show a decrease confined to the southern Iberian Peninsula, Italy and Greece, ACCESS-ESM-1.5, EC-Earth3 and MPI-GE CMIP6 show also a decrease in the Mediterranean coast and the Balkans (Supplementary Fig. 2). The maximum negative contribution of the forced changes in internal variability to the increase in the forced signal and the range of southern EuSHW intensity (45°N latitude southward) is shown by ACCESS-ESM-1.5 (1% and 7%, respectively; Supplementary Fig. 3a, b), followed by EC-Earth3, MIROC6 and MPI-GE CMIP6 (equal contribution of 1% and 6%; Supplementary Fig. 3e–j), and CanESM5 (0.5% and 4%; Supplementary Fig. 3c, d). In southern Europe the forced changes in internal variability will cause a slower increase of the right tail of daily maximum temperatures than mean temperatures under global warming levels (Supplementary Fig. 4), that is, a decrease in temperature variability in agreement with ref. 48. A slower increase of extreme temperatures compared to the mean leads to a negative trend of the forced signal in EuSHW intensity after detrending daily maximum temperatures. Furthermore, the decreased temperature variability due to the forced changes in internal variability will lead to a smaller fluctuation of extreme temperatures (Supplementary Fig. 5) leading to a reduced range of EuSHW intensity.

Our results imply that while large model uncertainties exist, the forced changes in internal variability will enhance the increase in central and northern EuSHW caused by the forced distribution shift increasing the risk of unprecedented central and northern EuSHWs. In contrast, the forced changes in internal variability will partly mitigate the increase in southern EuSHW intensity caused by the forced distribution shift decreasing the risk of unprecedented southern EuSHWs. Therefore, while an adaptation to increasing mean daily maximum temperatures in southern Europe should be enough to reduce the vulnerability to upcoming EuSHWs, in central and northern European adaptation to increased variability will also be needed.

Relating the changes in EuSHW intensity to the changes in soil moisture
The regional differences in the effects of the forced distribution shift and the forced changes in internal variability on EuSHW intensity are related to the regional differences in soil moisture changes. We find a robust decrease in summer soil moisture content with increasing global warming levels in all Europe excluding some areas southeast of the Baltic Sea (Fig. 5a) which can be related to the robust projected increase in non-detrended EuSHW intensity (Fig. 2). A decrease in soil moisture would generally reduce the cooling effect of latent heat-flux and increase the heating effect of sensible heat-flux49,50, leading to the overall increase in EuSHW intensity.

Under global warming, mean summer soil moisture declines continent-wide (Fig. 5a), but its impact on interannual variability differs by region (Fig. 5b). We find a robust increase in soil moisture variability in central and northern Europe, where we also find a robust increase in EuSHW intensity and its range due to the forced changes in internal variability (Fig. 4). We also find a robust decrease in soil moisture variability in the southernmost European grid-points coherent with the areas of decreased EuSHW intensity and range due to forced changes in internal variability. Soil moisture in southern Europe is historically lower than in central and northern Europe51. A further decrease in soil moisture over southern Europe will lead to a more constant state of moisture depletion state, which means less often switching between moisture limited and energy limited states, a weaker coupling between soil moisture and extreme summer daily maximum 2m air temperature (Fig. 6a), and less effective land-atmosphere feedback (Fig. 6b), mitigating EuSHW intensity and its range due to the forced changes in internal variability. In contrast, a decrease in soil moisture over central and northern Europe will push the region to switch more often between moisture limited and energy limited states, resulting in a stronger coupling between soil moisture and extreme summer daily maximum 2m air temperature (Fig. 6a), an enhancement of land-atmosphere feedback (Fig. 6b), an increase in soil moisture variability (Fig. 5b), and an increase in the amplitude and variability of EuSHW intensity due to the forced changes in internal variability.

The inter-model differences in EuSHW intensity change due to the forced changes in internal variability (Supplementary Fig. 2) are partly related to the inter-model differences in soil moisture variability changes (Supplementary Fig. 6b, d, f, h). We find model disagreements on the sign of soil moisture variability change with global warming levels in eastern Europe, where we also find matching model disagreements on the sign of EuSHW intensity changes due to the forced changes in internal variability. ACCESS-ESM-1.5 and MIRO6 project a decrease in soil moisture variability and a decrease in EuSHW intensity and its range due to the forced changes in internal variability, while CanESM5, EC-Earth3 and MPI-GE CMIP6 project an increase in soil moisture variability and in EuSHW intensity and its range due to the forced changes in internal variability (Supplementary Fig. 2 and 6b, d, f, h, j). Yet, we also find EuSHW intensity changes that can not be explained with soil moisture changes, mainly in northern Europe. The decreased intensity simulated by CanESM5 north of the Baltic Sea (Supplementary Fig. 2c, d) cannot be explained by the decrease in soil moisture (Supplementary Fig. 6c) and the increase in variability (Supplementary Fig. 6d) under global warming. Similarly, the increased intensity simulated by MPI-GE CMIP6 in northern Europe (Supplementary Fig. 2i, j) cannot be explained by the increase in soil moisture (Supplementary Fig. 6i) and decrease in variability (Supplementary Fig. 6j) under global warming. It is likely that other factors (e.g., changes in the North Atlantic sea surface temperature or atmospheric variability) also contribute to the forced changes in internal variability, and hence affect northern EuSHW intensity.

Methods
Data
We use five single-model initial-condition large ensembles (SMILEs): ACCESS-ESM-1.5 (40 members40), CanESM5 (50 members41), EC-Earth3 (50 members42), MIROC6 (50 members43), and MPI-GE CMIP6 (50 members44). All SMILEs considered here provide daily temporal resolution for the late historical period (1970–2014) and two shared socioeconomic pathway scenarios (SSP2–4.5, and SSP5–8.5) that span until the end of the 21st century. Our main findings are robust with respect to the inclusion of SSP1–1.9, SSP1–2.6, and SSP3–7.0 scenarios. The ensemble members have identical natural and anthropogenic forcing but start from different initial conditions allowing us to robustly identify the effects of forced changes in the shift of temperature distribution and internal climate variability45–47. We test the capability of climate models to simulate the intensity of recent EuSHWs by comparing it to the daily gridded land observations E-OBS dataset for the period 1970–202282. All datasets are linearly interpolated to the MPI-GE CMIP6 grid using Climate Data Operator (CDO) command line tool. While the interpolation spatially smoothes temperatures in E-OBS, particularly over areas of complex topography, a common grid between datasets is needed to compare the spatially integrated cumulative heat.

We compute two sets (i.e. non-detrended and detrended) of daily maximum 2m air temperature (T2max) anomalies from 1970 until 2099 to remove the seasonal cycle83. The non-detrended T2max anomalies are computed in reference to a centered 15-day running window and 1985–2014 reference period. The 1985–2014 period is chosen to represent the most recent climatology within the historical simulations. The detrended T2max anomalies are computed in reference to a centered 15-day running mean averaged across all ensemble members for each corresponding day of each year and model. For E-OBS, we compute the detrended T2max anomalies in reference to a centered 15-day running mean, averaged across all climate models for each corresponding day of each year. While the non-detrended dataset retains an increasing mean temperature trend (i.e., forced distribution shift) due to global warming, in the detrended dataset the forced distribution shift is removed, isolating changes in the statistics of natural climate oscillations driven by the altered mean state (i.e., forced changes in internal variability).

We use monthly 2m air temperature to compute area-weighted global mean surface temperature anomalies (GMTA) in reference to the 1985–2014 period. For soil moisture, we use the variable mean total soil moisture content summed over all soil layers (mrso) averaged over boreal summer (June, July, August).

EuSHW definition and intensity quantification
We apply a percentile-based heatwave definition to identify boreal summer (June, July, August) heatwave days84. Percentile-based heatwave definitions consist of a temperature threshold defined by a percentile that represents the perception of extreme temperatures, and a temporal constraint to capture the persistent nature of heatwaves. For each calendar day and European land grid point (10°W–30°E, 35–70°N), a heatwave day is identified when T2max exceeds the 90th percentile based on a centered 15-day running window and 1985–2014 reference period for at least six consecutive days.

We quantify the intensity of EuSHWs using the cumulative heat metric1. The cumulative heat is computed as a seasonal integration of heat exceeding the threshold during heatwave days. In addition, we integrate the cumulative heat over the European domain after weighting each grid point by the cosine of the latitude22. Hence, with a single number the cumulative heat accounts for the duration, spatial extent, and amplitude of all EuSHWs that occur in each summer. We refer to non-detrended and detrended EuSHW intensity to the cumulative heat computed with non-detrended T2max and detrended T2max, respectively. We scale the simulated EuSHW intensity with the mean observed EuSHW intensity (i.e., E-OBS 1970–2022).

Sensitivity of the forced signal and ensemble spread to global warming levels
For each summer the forced signal is given by the ensemble mean, and the range due to internal climate variability is given by the ensemble spread computed as ensemble standard deviation. We linearly regress the forced signal in EuSHW intensity and soil moisture to global mean surface temperature anomalies. Similarly, we regress the ensemble spread in EuSHW intensity and soil moisture to global mean surface temperature anomalies. While linear analysis assumes a consistent relationship across all warming levels, non-linear relationship might exist especially at very high warming levels. We apply a significance test at the 95% confidence level. We define a robust change when at least three out of the five models agree on the regression coefficient sign, and at least three out of the five models show statistically significant changes.

Data availability
The data generated in this study have been deposited in the public long-term archive repository of the German Climate Computing Center85 (DKRZ-LTA; https://www.wdc-climate.de/ui/entry?acronym=DKRZ_LTA_1075_ds00040). The gridded land observations E-OBS dataset is publicly available at Copernicus Climate Data Store (https://cds.climate.copernicus.eu/datasets/insitu-gridded-observations-europe?tab=download). The climate model data are publicly available at Earth System Grid Federation (ESGF) nodes (https://esgf.llnl.gov/nodes.html).

Code availability
The code used in this study86 is publicly available in the GitHub repository (https://github.com/gbeobidearsuaga/EuSWH_projection_IV_2025).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of “Increasing central and northern European summer heatwave intensity due to forced internal variability changes”\nGeneral comments：\nThis manuscript uses four single-model large ensembles (ACCESS-ESM1.5, CanESM5, MIROC6, MPI-GE CMIP6) under\nSSP2-4.5 and SSP5-8.5 to disentangle the contributions of a positive shift in summer temperature distributions (“forced\ndistribution shift”) versus forced changes in internal variability on future European summer heatwave (EuSHW) intensity. The\nkey finding is that, under warming, central and northern Europe will experience amplified EuSHW intensity and variability\ndue to moisture-limited land–atmosphere feedbacks, whereas southern Europe may see dampened extremes under more\npersistent drought. This work offers important insights for regional adaptation strategies. However, significant revisions are\nrequired to address omitted literature, clarify methodological details, and bolster the robustness of the conclusions. I\nrecommend Major Revision.\nMajor comments:\n1. The Introduction and Discussion must be expanded to acknowledge and compare with the following pivotal studies,\nwhich directly address the relative contributions of external forcing versus internal variability to extreme heatwaves in\nNorthern Hemisphere—spanning Europe, southern China, and western North America (e.g., Zhang et al., 2023; Gong et al.,\n2024; Ma et al., 2024a, 2024b; Sarah et al., 2024). These works have rigorously attributed major recent heatwave events,\nquantified the respective roles of internal variability and external forcing, and clarified the underlying mechanisms driving\nextreme heatwaves. Including these references will enrich the manuscript’s contextual framework and provide readers with a\ncomprehensive overview of the latest advances in heatwave attribution and dynamics across the Northern Hemisphere.\n2. Lines 104–105: The term “mean observed EuSHW intensity” is not tied to a specific period. Clearly state the exact years\nand observational dataset (e.g. E-OBS 1950–2022, or 1985–2014) used to compute this baseline. This precision is essential\nfor reproducibility and for interpreting the scaling of future projections.\n3. The causal chain—radiative forcing → global mean temperature anomalies → forced signal in EuSHW intensity →\nchanges in internal variability—is too condensed. How greenhouse gas and aerosol forcings drive global mean temperature\nanomalies. How temperature anomalies translate into ensemble-mean heatwave intensity (“forced signal”). How the same\nwarming alters statistics of internal variability via land–atmosphere and circulation feedbacks. A brief schematic or boxed\nequation could help clarify these steps.\n4. Different models yield varying magnitudes—and sometimes opposite signs—of forced-variability changes across regions.\nProvide regression slopes of detrended EuSHW intensity versus global mean temperature anomalies. Diagnose the\ndominant physical drivers (soil moisture feedback or circulation patterns) that underlie those sensitivities. Discuss whether\ninter-model divergence stems from land-surface parameterizations, convection schemes, or differences in SST\nvariability. A summary table or supplementary figure would greatly enhance transparency.\n5. Fig. 4b shows limited regions of great than 3-model agreement on increased detrended EuSHW intensity, raising\nconcerns about reliability. Please discuss how the spatial extent of “non-dashed” regions informs confidence in projections.\nCould you explain why only these four SMILEs were chosen? For instance, would adding other large‐ensemble datasets\n(e.g., CESM2 or EC‐Earth) expand or shift the regions showing robust agreement? Consider evaluating each model’s\nhistorical performance in simulating heatwave characteristics—such as by comparing simulated versus observed intensity—\nand then either applying skill‐based weights or presenting performance metrics to justify the focus on regions with strong\nmulti‐model agreement.\n6. The phrase “the decrease in European summer soil moisture has an opposite effect on soil moisture variability changes in\ndifferent European regions” is confusing. Please rewrite more clearly, for example: “Under global warming, mean summer\nsoil moisture declines continent-wide (Fig. 5a), but its impact on interannual variability differs by region: central and northern\nEurope exhibit increasing soil-moisture variability, whereas southern Europe shows a reduction in\nvariability (Fig. 5b).” Make sure to link these contrasting variability responses explicitly to the divergent heatwave outcomes.\n7. The authors state throughout the manuscript that future forced changes in internal variability will amplify European\nheatwaves, but they do not specify which internal‐variability factors change significantly under warming to drive these\nextremes. The paper lacks any discussion of the dynamical mechanisms underpinning extreme heatwaves. The discussion\nacknowledges North Atlantic SST and broad atmospheric dynamics but omits other important circulation drivers. Please add\na paragraph on additional large-scale climate factors known to modulate European heatwaves. For example: Ural blocking\nevents and their projected frequency changes. Arctic sea-ice loss and its teleconnections via the jet stream. North Atlantic\nOscillation (NAO) and Scandinavian pattern dynamics under warming. Discuss how changes in these climate modes could\ninteract with forced internal variability to influence future EuSHWs.\n8. The phrase “forced internal variability change” is cumbersome and potentially confusing. Consider rephrasing to “forced\nchange in internal variability,” and define your terms clearly in the Introduction or Methods.\nReferences:\nZhang, X., et al., 2023: Increased impact of heat domes on 2021-like heat extremes in North America under global warming.\nNature Communications, 14, 1690.\nGong, H., et al., 2024: Attribution of the August 2022 Extreme Heatwave in Southern China: Role of Dynamical and\nThermodynamical Processes. Bulletin of the American Meteorological Society, 105, E193-E199.\nMa, K., et al., 2024: Anthropogenic forcing intensified internally driven concurrent heatwaves in August 2022 across the\nNorthern Hemisphere. npj Climate and Atmospheric Science, 7, 290.\nMa, K., et al., 2024: Attribution of the concurrent extreme heatwaves in Northern Europe and Northeast Asia in July 2018.\nAtmospheric Research, 307, 107506.\nPerkins-Kirkpatrick, S., et al., 2024: Extreme Terrestrial heat in 2023. Nature Reviews Earth & Environment, 5, 244-246.", "reviewer_2": "The study effectively leverages single-model initial condition large ensembles (SMILEs) with daily temporal resolution,\nwhich is a robust methodological choice to disentangle the effects of forced distribution shifts from changes in internal\nvariability. This addresses a key limitation of previous studies that relied on shorter observational records or coarser model\nresolutions.\nThe article clearly identifies soil moisture dynamics and land-atmosphere feedbacks as the primary drivers behind the\nregional differences in heatwave intensity and variability. The explanation that southern Europe, already moisture-depleted,\nexperiences reduced temperature variability due to consistent aridity, while central/northern Europe's increased soil\nmoisture variability leads to enhanced land-atmosphere feedback, is a strong scientific argument.\nThe distinction between the nonlinear increase in EuSHW intensity and the linear increase in their intensity range with\nglobal warming levels is an important nuance, highlighting not just hotter extremes but also greater unpredictability.\nHowever, there are several issues that need to be address before being considered for publication.\n1. While the paper defines \"Forced Internal Variability Change\", a more explicit and concise explanation of what \"forced\ninternal variability change\" is (e.g., changes in the statistics of natural climate oscillations driven by the altered mean state)\nearly in the introduction or methods would enhance clarity for a broader audience. This would clarify how it differs from\nunforced, natural internal variability.\n2. The text mentions \"push the region to switch more often between moisture limited and energy limited states.\" A brief,\nmore mechanistic explanation of how Soil Moisture Feedback in Central/Northern Europe is switching specifically amplifies land-\natmospheric feedback and increases temperature variability would be beneficial (e.g., how the shift between latent and\nsensible heat fluxes is enhanced).\n3. The conclusion briefly touches on adaptation. Expanding the discussion to consider the socio-economic implications of\nincreased variability in central/northern Europe (e.g., challenges for infrastructure, agriculture, health systems, and\nemergency response beyond just temperature adaptation) could strengthen the real-world relevance.\n4. While the paper states the forced distribution shift is the \"main contributor,\" providing a more quantitative comparison of\nthe relative magnitudes of change attributed to each factor (perhaps a percentage contribution where possible) would offer a\nclearer picture of their respective importance.\n5. If feasible, a conceptual diagram or schematic illustrating the different soil moisture regimes and how they lead to\ncontrasting temperature variability responses in the north/center versus south of Europe could significantly aid\nunderstanding.\n6. While the chosen SMILEs are well-established, a brief justification for their selection could be added. Are they chosen to\nrepresent a range of climate model sensitivities, or for their specific characteristics (e.g., representation of land-atmosphere\ncoupling)?\n7. While stating linear interpolation using CDO is fine, mentioning the potential implications of interpolating E-OBS to the\nMPI-GE CMIP6 grid, especially if there are significant resolution differences, would be useful. Were any other interpolation\nmethods considered, and if so, why was linear chosen?\n8. The text mentions computing anomalies to \"remove any bias that might arise when computing the intensity of EuSHWs\ndue to the seasonal cycle.\" However, when comparing model output to E-OBS, direct biases in temperature magnitudes or\nvariability might exist between models and observations. While not the primary focus, a brief comment on how these\npotential biases are handled or if they are assumed to be less relevant for anomalies and trends would be beneficial.\n9. A short rationale for choosing the 1985-2014 reference period for percentile calculations would be useful. This is a\ncommon choice, but explaining why this particular period was chosen over others (e.g., for its representativeness or data\navailability) can strengthen the methodology.\n10. For the detrended E-OBS anomalies, it states \"in reference to a centered 15-day running window over all ensemble\nmembers from all models for each year.\" Given E-OBS is observational, it doesn't have \"ensemble members.\" It likely refers\nto averaging over different historical realizations or perhaps the temporal mean. Clarification here would be helpful.\n11. For \"spatially weighted global mean surface temperature anomalies (GMTA),\" specifying the weighting (e.g., area-\nweighted) would ensure precision, although it's generally assumed for GMTA.\n12. The study uses SSP2-4.5 and SSP5-8.5. While these cover a range of plausible futures, it's worth noting that\nconclusions are bound to these specific scenarios and might not fully capture outcomes under very low emission pathways\nor other highly uncertain future scenarios. So it is suggested to consider other scenarios that lies in between them.\n13. Soil moisture is defined as \"fraction of water accumulated in the root zone relative to the water capacity.\" This is a\nstandard definition, but the precise depth of the root zone and what \"water capacity\" refers to (e.g., field capacity, total pore\nspace) can vary between models and influence results. A brief acknowledgment of this model-specific variability would be\nappropriate.\n13. While linear regression of heatwave intensity/range to GMTA is a useful approach, it assumes a consistent relationship\nacross all warming levels. While justified in the results (linear for range, non-linear for forced signal), acknowledging that\ncomplex, non-linear relationships might be present, especially at very high warming levels, could be a minor limitation.\n14. The study focuses on daily maximum 2m air temperature. While this is appropriate for heatwaves, other metrics like\nduration/return period of heatwaves could also have significant impacts and might be influenced differently by internal\nvariability changes.\n15. The paper explicitly states that some observed changes in EuSHW intensity cannot be solely explained by soil moisture\nvariability changes (e.g., CanESM5 north of the Baltic Sea, MPI-GE CMIP6 in northern Europe). This suggests that other\nfactors, such as North Atlantic sea surface temperature variability or atmospheric circulation changes, play an unquantified\nrole, indicating an incomplete understanding of all drivers. Some discussion or explanation (with results if available) is\nbeneficial for the readers.\n16. The definition of heatwaves using a fixed percentile (assuming a \"time-invariant\" perception of extreme temperatures)\nis a common approach but represents a simplified view of adaptation. Real-world adaptation might involve shifting thresholds\nas societies acclimatize, which could alter the perceived intensity and impact of future heatwaves. A short analysis with\nvariable percentiles may be beneficial for the study.", "reviewer_3": "The intensity and frequency of heatwaves in Europe have significantly increased in recent decades, drawing widespread\nattention from the academic community. While most studies focus on the impact of anthropogenic forcing on heatwaves, this\nstudy investigated the influence of internal variability on heatwave variability in central and northern Europe. They also\nindicated the important role of soil moisture in the changes of European heatwave intensity. However, the conclusions\ndrawn in this study exhibit apparent inter-model inconsistencies and lack solid mechanistic analysis, which raises major\nconcerns in my view, as detailed below.\n1. This study primarily highlights the importance of internal variability in the long-term changes of European heatwaves.\nHowever, as seen in Figure 1, the influence of external forcing remains dominant. It is recommended to include a discussion\non the relative impacts of external forcing versus internal variability.\n2. As seen in Figure 2, the regions with the highest range of heatwaves caused by internal climate variability are mainly\nconcentrated in southern Europe. However, the range of detrended heatwave intensity resulting from forced changes in\ninternal variability predominantly occurs in central-northern Europe. Further analysis and discussion are required to provide\nsome explanations.\n3. The main conclusion of this study is that the increasing heatwave intensity linked to forced changes in internal variability\nprimarily occurs in central-northern Europe, which could result in a faster increase in extreme values compared to the mean.\nHowever, this conclusion is largely based on four single-model initial-condition large ensembles, and the results from these\nfour models appear inconsistent (Supplementary Figure 2). Among the four models, the positive contributions of forced\nchanges in internal variability can be found in northern, central, and southern Europe. This inconsistency significantly\nundermines the reliability of the conclusion, which is my primary concern regarding this paper.\n4. The authors attempted to link the effects of forced changes in internal variability with soil moisture changes. However, as\nanalyzed in the paper, soil moisture changes often fail to explain heatwave variability. Moreover, the conclusion that \"In\ncentral and northern Europe, a decrease in soil moisture will cause the region to switch more frequently between moisture-\nlimited and energy-limited states, amplifying land-atmosphere feedbacks...\" lacks in-depth mechanistic analysis.\nFor instance, no supporting evidence is provided to demonstrate that soil moisture actually enhances land-atmosphere coupling\nin these regions.\n5. Why were only four models used? Could the number of models be increased to obtain more reliable conclusions?"}, "author_response": "Detailed response to reviewers\nReviewers comments are shown in blue, author responses are shown in black, and the line numbers\nreference the revised version of the manuscript without track changes.\nReviewer #1:\nThis manuscript uses four single-model large ensembles (ACCESS-ESM1.5, CanESM5, MIROC6,\nMPI-GE CMIP6) under SSP2-4.5 and SSP5-8.5 to disentangle the contributions of a positive shift\nin summer temperature distributions (“forced distribution shift”) versus forced changes in internal\nvariability on future European summer heatwave (EuSHW) intensity. The key finding is that, under\nwarming, central and northern Europe will experience amplified EuSHW intensity and variability\ndue to moisture-limited land–atmosphere feedbacks, whereas southern Europe may see dampened\nextremes under more persistent drought. This work offers important insights for regional adaptation\nstrategies. However, significant revisions are required to address omitted literature, clarify\nmethodological details, and bolster the robustness of the conclusions. I recommend Major Revision.\nWe thank the reviewer for their time and for the thoughtful and constructive comments. We have\naddressed each of the reviewer’s points and revised the manuscript accordingly. Specifically, we\nhave included the missing literature, clarified methodological details, and strengthened the\nrobustness of our conclusions by incorporating an additional model and conducting further analysis.\nWe believe that the reviewer’s comments and suggestions have significantly improved the\nmanuscript.\nMajor comments:\n1. The Introduction and Discussion must be expanded to acknowledge and compare with the\nfollowing pivotal studies, which directly address the relative contributions of external forcing\nversus internal variability to extreme heatwaves in Northern Hemisphere—spanning Europe,\nsouthern China, and western North America (e.g., Zhang et al., 2023; Gong et al., 2024; Ma et al.,\n2024a, 2024b; Sarah et al., 2024). These works have rigorously attributed major recent heatwave\nevents, quantified the respective roles of internal variability and external forcing, and clarified the\nunderlying mechanisms driving extreme heatwaves. Including these references will enrich the\nmanuscript’s contextual framework and provide readers with a comprehensive overview of the\nlatest advances in heatwave attribution and dynamics across the Northern Hemisphere.\nWe thank the reviewer for highlighting these relevant studies. In response, we have added a new\nparagraph in the Introduction (L49-59), incorporating the suggested literature to discuss the role of\ninternal variability in recent heatwaves.\n2. Lines 104–105: The term “mean observed EuSHW intensity” is not tied to a specific period.\nClearly state the exact years and observational dataset (e.g. E-OBS 1950–2022, or 1985–2014) used\nto compute this baseline. This precision is essential for reproducibility and for interpreting the\nscaling of future projections.\nWe thank the reviewer for pointing out the missing specification of the time period. We have now\nclarified this in the Methods section (L417-418) by adding the following sentence: “We scale the\nsimulated EuSHW intensity with the mean observed EuSHW intensity (i.e., E-OBS 1970-2022).”\n3. The causal chain—radiative forcing → global mean temperature anomalies → forced signal in\nEuSHW intensity → changes in internal variability—is too condensed. How greenhouse gas and\naerosol forcings drive global mean temperature anomalies. How temperature anomalies translate\ninto ensemble-mean heatwave intensity (“forced signal”). How the same warming alters statistics\nof internal variability via land–atmosphere and circulation feedbacks. A brief schematic or boxed\nequation could help clarify these steps.\nWe thank the reviewer for the helpful comments, and we agree that the mentioned causal chain in\nthe original manuscript was too condensed. We have expanded the Introduction to provide a more\ndetailed explanation of how global warming could influence EuSHW intensity.\nIn the second paragraph of the Introduction (L36-47), we describe how global warming is affecting\nEuropean summer mean temperatures (i.e., forced distribution shift), and how this background\nwarming might influence EuSHW intensity. In the third paragraph (L49-59), we highlight the\nimportant role of internal variability in recent and historical EuSHWs. In the fourth paragraph (L61-\n77), we elaborate on how global warming may also drive changes in internal variability through\nland-atmosphere and circulation feedbacks, thereby affecting both the intensity and variability of\nfuture EuSHWs.\n4. Different models yield varying magnitudes—and sometimes opposite signs—of forced-\nvariability changes across regions. Provide regression slopes of detrended EuSHW intensity versus\nglobal mean temperature anomalies. Diagnose the dominant physical drivers (soil moisture\nfeedback or circulation patterns) that underlie those sensitivities. Discuss whether inter-model\ndivergence stems from land-surface parameterizations, convection schemes, or differences in SST\nvariability. A summary table or supplementary figure would greatly enhance transparency.\nWe thank the reviewer for the valuable suggestion.\nWe provide the regression slopes of detrended EuSHW intensity integrated over Europe versus\nglobal mean temperature anomalies, scaled using the mean observed EuSHW intensity (i.e., E-OBS\n1970-2022), in L174-179. We believe these scaled regression slopes offer a clearer interpretation\nthan the absolute spatially integrated cumulative heat, which can exceed 1000 °C – values that may\ninitially appear counterintuitive. When spatial integration is not required (i.e., grid-point-level\nanalysis), we present the regression slopes of detrended EuSHW intensity versus global mean\ntemperature anomalies (Fig. 4 and Supplementary Fig. 2).\nWe carefully considered the suggestion to diagnose the physical drivers (thermodynamic vs.\ndynamical), but ultimately decided not to pursue this direction. The aim of our manuscript is to\ninvestigate how EuSHW intensity is expected to change due to the forced changes in internal\nvariability. Our analysis suggests that changes in soil moisture variability can generally explain the\nregional patterns in EuSHW intensity changes, consistent with the findings from Vogel et al. (2017)\nand Maraun et al. (2025). While we agree that a dedicated analysis of thermodynamic and dynamic\ncontributions would be highly valuable, such an analysis would shift the focus of the manuscript\nand it is out of scope of the present work.\nInstead, we have considerably expanded the discussion to consider how the changes in atmospheric\ncirculation might also contribute to changes in EuSHWs (L334-347). Following the reviewer’s\nsuggestion, we also extended the discussion regarding inter-model difference, including possible\ncontributions from land-surface parameterizations, convection schemes, and differing projected\natmospheric responses to global warming (L321-324 and L343-347).\n5. Fig. 4b shows limited regions of great than 3-model agreement on increased detrended EuSHW\nintensity, raising concerns about reliability. Please discuss how the spatial extent of “non-dashed”\nregions informs confidence in projections. Could you explain why only these four SMILEs were\nchosen? For instance, would adding other large‐ensemble datasets (e.g., CESM2 or EC‐Earth)\nexpand or shift the regions showing robust agreement? Consider evaluating each model’s\nhistorical performance in simulating heatwave characteristics—such as by comparing simulated versus\nobserved intensity—and then either applying skill‐based weights or presenting performance metrics\nto justify the focus on regions with strong multi‐model agreement.\nWe thank the reviewer for suggesting the inclusion of EC-Earth3. We have now incorporated EC-\nEarth3 into our analysis, which increased the extent of the “non-dashed” areas in Fig. 4 and\nimproved the robustness of our results regarding changes in EuSHW intensity driven by forced\nchanges in internal variability.\nUnfortunately, CESM2 provides the required daily-resolution data for only a few number of\nensemble members. We identified only one member available at the DKRZ node and four at the\nNCL node. As shown by Milinski et al. (2020), robust detection of forced changes in internal\nvariability requires approximately 50 ensemble members. Therefore, CESM2 and other SMILEs\nwith considerably fewer than 50 ensemble members at daily resolution are not suitable for inclusion\nin this study. We have clarified our selection criteria for SMILEs in L87-93.\nTo assess each model’s performance in simulating the observed spatially integrated EuSHW\nintensity trend over 1970-2022, we present in Response Fig. 1 the distribution of ensemble\nmembers for each model. All models capture the recent increase in EuSHW intensity within their\nensemble spread. While most of ensemble members of ACCESS-ESM1-5 and CanESM5 seem to\noverestimate the trend, the observed trend lies near the center of the ensemble distribution for EC-\nEarth3, MIROC6, and MPI-GE CMIP6.\nWe also evaluated each model’s performance at the grid-point level. In Response Fig. 2 we show,\nfor each model and grid-point, the percentile position of the observed EuSHW intensity trend within\nthe ensemble distribution (e.g., red indicates that most ensemble members fall below the observed\ntrend, blue indicates that most ensemble members are above the observed trend, and dashed grid\npoints indicate that the observed EuSHW intensity trend is outside the ensemble spread). We find\nthat, while models seem to underestimate trends in western and eastern Europe and overestimate in\nnorthern and southern Europe, all model are able to capture the observed heatwave intensity trend\nacross nearly all grid points.\nGiven that observations represent only one possible realization of the climate system, and all\nmodels capture the observed trends within their ensemble spread, we cannot definitely assess which\nmodel performs best. An alternative would be to undertake a process-based evaluation, assessing\neach model’s performance in simulating the processes relevant for EuSHWs. This would involve\nevaluating the representation of soil moisture and atmospheric dynamics, ocean-atmosphere\ninteraction and feedbacks, and land-atmosphere interaction and feedbacks, among others. However,\nevaluating only a subset of these processes could lead to biased or misleading model rankings, as\ndifferent models could simulate different processes better. A comprehensive process-based\nevaluation, while highly valuable, is out of scope of the present study.\nResponse Figure 1: Model evaluation of the EuSHW\nintensity trend, expressed as spatially integrated cumulative\nheat trend over the period 1970-2022. The observed trend (E-\nOBS) is shown alongside the ensemble distribution of\nsimulated trends for: a) ACCESS-ESM1-5; b) CanESM5; c)\nEC-Earth3; d) MIROC6; e) MPI-GE CMIP6.\nResponse Figure 2: Model evaluation of the EuSHW intensity trend at\nthe grid-point level, expressed as cumulative heat trend over the period\n1970-2022. The color bar indicates the percentile within the ensemble\ndistribution where the observed EuSHW intensity trend lies. Red shades\nindicate that most ensemble members are below the observed trend, blue\nshades indicate they are above, and dashed grid points show where the\nobserved trend falls outside the ensemble spread. Models shown: a)\nACCESS-ESM1-5; b) CanESM5; c) EC-Earth3; d) MIROC6; e) MPI-GE\nCMIP6.\n6. The phrase “the decrease in European summer soil moisture has an opposite effect on soil\nmoisture variability changes in different European regions” is confusing. Please rewrite more\nclearly, for example: “Under global warming, mean summer soil moisture declines continent-wide\n(Fig. 5a), but its impact on interannual variability differs by region (Fig. 5b). We find a robust increase in soil moisture\nvariability in central and northern Europe, where we also find a robust increase in EuSHW intensity\nand its range due to the forced changes in internal variability (Fig. 4)...”\nThank you, we have rephrased the sentence accordingly (L239-242) as follows: “Under global\nwarming, mean summer soil moisture declines continent-wide (Fig. 5a), but its impact on\ninterannual variability differs by region (Fig. 5b). We find a robust increase in soil moisture\nvariability in central and northern Europe, where we also find a robust increase in EuSHW intensity\nand its range due to the forced changes in internal variability (Fig. 4)...”\n7. The authors state throughout the manuscript that future forced changes in internal variability will\namplify European heatwaves, but they do not specify which internal‐variability factors change\nsignificantly under warming to drive these extremes. The paper lacks any discussion of the\ndynamical mechanisms underpinning extreme heatwaves. The discussion acknowledges North\nAtlantic SST and broad atmospheric dynamics but omits other important circulation drivers. Please\nadd a paragraph on additional large-scale climate factors known to modulate European heatwaves.\nFor example: Ural blocking events and their projected frequency changes. Arctic sea-ice loss and its\nteleconnections via the jet stream. North Atlantic Oscillation (NAO) and Scandinavian pattern\ndynamics under warming. Discuss how changes in these climate modes could interact with forced\ninternal variability to influence future EuSHWs.\nWe thank the reviewer for the valuable suggestion. We have now expanded both the Introduction\nand the Discussion sections to incorporate the dynamical mechanisms underlying heat extremes.\nIn the Introduction (L49-59), we now describe how anomalous sea surface temperatures can\nmodulate atmospheric circulation, and how such circulation anomalies can lead to heatwaves\nthrough land-atmosphere feedbacks. Furthermore, in the Discussion (L334-347), we elaborate on\nhow atmosphere dynamics are expected to evolve under global warming, and how these\natmospheric changes may contribute to both the forced changes in internal variability and the\nprojected changes in European summer heatwave intensity. We also discuss how these dynamical\nshifts may contribute to inter-model differences and overall uncertainty.\n8. The phrase “forced internal variability change” is cumbersome and potentially confusing.\nConsider rephrasing to “forced change in internal variability,” and define your terms clearly in the\nIntroduction or Methods.\nThank you for the suggestion. We have rephrased “forced internal variability change” to “forced\nchanges in internal variability” throughout the manuscript, including in the title. Additionally, we\nhave defined more clearly the terms “forced distribution shift” and “forced changes in internal\nvariability” - please see our response to the first comment for more details).\nReferences:\nMaraun, D., Schiemann, R., OssN, A. & Jury, M. (2025). Changes in event soil moisture-\ntemperature coupling can intensify very extreme heat beyond expectations. Nat. Commun. 16, 734.\nVogel, M. M., Orth, R., Cheruy, F., Hagemann, S., Lorenz, R., van den Hurk, B. J., & Seneviratne,\nS. I. (2017). Regional amplification of projected changes in extreme temperatures strongly\ncontrolled by soil moisture‐temperature feedbacks. Geophysical Research Letters, 44(3), 1511-\n1519.\nMilinski, S., Maher, N., & Olonscheck, D. (2020). How large does a large ensemble need to be?.\nEarth System Dynamics, 11(4), 885-901.\nReviewer #2 (Remarks to the Author):\nThe study effectively leverages single-model initial condition large ensembles (SMILEs) with daily\ntemporal resolution, which is a robust methodological choice to disentangle the effects of forced\ndistribution shifts from changes in internal variability. This addresses a key limitation of previous\nstudies that relied on shorter observational records or coarser model resolutions.\nThe article clearly identifies soil moisture dynamics and land-atmosphere feedbacks as the primary\ndrivers behind the regional differences in heatwave intensity and variability. The explanation that\nsouthern Europe, already moisture-depleted, experiences reduced temperature variability due to\nconsistent aridity, while central/northern Europe's increased soil moisture variability leads to\nenhanced land-atmosphere feedback, is a strong scientific argument.\nThe distinction between the nonlinear increase in EuSHW intensity and the linear increase in their\nintensity range with global warming levels is an important nuance, highlighting not just hotter\nextremes but also greater unpredictability.\nHowever, there are several issues that need to be address before being considered for publication.\nWe thank the reviewer for their time and for the thoughtful and constructive comments. We have\naddressed each of the reviewer’s points and revised the manuscript accordingly. Specifically, we\nhave conducted three new analyses: (1) we quantified the percentage contribution of forced changes\nin internal variability; (2) we tested the robustness of our results by including three additional SSP\nscenarios; and (3) we assessed the impact of using a variable percentile threshold.\nIn addition, we have expanded the Introduction and Discussion sections to clarify key terms and to\nincorporate the underlying dynamical and thermodynamical mechanisms driving heat extremes,\namong other improvements.\nWe believe that the reviewer’s comments and suggestions have significantly strengthened the\nmanuscript.\n1. While the paper defines \"Forced Internal Variability Change\", a more explicit and concise\nexplanation of what \"forced internal variability change\" is (e.g., changes in the statistics of natural\nclimate oscillations driven by the altered mean state) early in the introduction or methods would\nenhance clarity for a broader audience. This would clarify how it differs from unforced, natural\ninternal variability.\nWe thank the reviewer for the valuable suggestion. As a response, we have made a more explicit\nexplanation of what “forced changes in internal variability” are in the Methods section (L392-395)\nby adding “… in the detrended dataset the forced distribution shift is removed, isolating changes in\nthe statistics of natural climate oscillations driven by the altered mean state (i.e., forced changes in\ninternal variability).”.\nIn addition, we have expanded the Introduction section. In the second paragraph of the Introduction\n(L36-47), we describe how global warming is affecting European summer mean temperatures (i.e.,\nforced distribution shift), and how this background warming might influence EuSHW intensity. In\nthe third paragraph (L49-59), we highlight the important role of internal variability in recent and\nhistorical EuSHWs. We dedicate the fourth paragraph (L61-77) to the forced changes in internal\nvariability. Here, we elaborate on how global warming may also drive changes in internal variability\nthrough land-atmosphere and circulation feedbacks, thereby affecting both the intensity and\nvariability of future EuSHWs.\n2. The text mentions \"push the region to switch more often between moisture limited and energy\nlimited states.\" A brief, more mechanistic explanation of how Soil Moisture Feedback in\nCentral/Northern Europe is switching specifically amplifies land-atmospheric feedback and\nincreases temperature variability would be beneficial (e.g., how the shift between latent and sensible\nheat fluxes is enhanced).\nWe thank the reviewer for the constructive suggestion. We have now included a mechanistic\ndescription of how soil moisture amplifies EuSHWs in transitional regimes by reducing the\nevaporative cooling (i.e., latent heat flux) and increasing sensible heat flux (55-59). We also clarify\nthat soil moisture-temperature feedback is effective only in transitional regimes. Additionally, we\nexplain that projected future drying in Europe could cause some regions to either enter or exit\ntransitional regimes, thereby increasing or decreasing land-atmosphere coupling and temperature\nvariability (L63-69).\n3. The conclusion briefly touches on adaptation. Expanding the discussion to consider the socio-\neconomic implications of increased variability in central/northern Europe (e.g., challenges for\ninfrastructure, agriculture, health systems, and emergency response beyond just temperature\nadaptation) could strengthen the real-world relevance.\nWe thank the reviewer for the valuable suggestion. We have now expanded the Discussion section\nto include the socio-economic implications of increased variability in central and northern Europe\n(L355-356).\n4. While the paper states the forced distribution shift is the \"main contributor,\" providing a more\nquantitative comparison of the relative magnitudes of change attributed to each factor (perhaps a\npercentage contribution where possible) would offer a clearer picture of their respective importance.\nWe thank the reviewer for the valuable suggestion. In response, we have conducted a new analysis\nto quantify the percentage contribution of forced changes in internal variability to the changes in\nEuSHW intensity and its range under rising global warming levels. We have included a new figure\nillustrating these contributions (Supplementary Figure 3) and now report the maximum positive and\nnegative contributions for each model in the manuscript (L189-194 and L208-212).\n5. If feasible, a conceptual diagram or schematic illustrating the different soil moisture regimes and\nhow they lead to contrasting temperature variability responses in the north/center versus south of\nEurope could significantly aid understanding.\nWe thank the reviewer for the suggestion. Conceptual diagrams illustrating different soil moisture\nregimes and their implications for land-atmosphere feedbacks have already been published. We\nrefer readers to one such example, shown in Fig. 5 of Seneviratne et al. (2010) (L63-66).\n6. While the chosen SMILEs are well-established, a brief justification for their selection could be\nadded. Are they chosen to represent a range of climate model sensitivities, or for their specific\ncharacteristics (e.g., representation of land-atmosphere coupling)?\nWe thank the reviewer for the valuable comment. We have used all available SMILEs that provide\nthe required variables at daily temporal resolution for the SSP2-4.5 and SSP5-8.5 scenarios, each\nwith approximately 50 ensemble members. As demonstrated by Milinski et al. (2020), robust\ndetection of forced changes in internal variability requires around 50 ensemble members. We now\nprovide a justification for our model selection in L87-93.\n7. While stating linear interpolation using CDO is fine, mentioning the potential implications of\ninterpolating E-OBS to the MPI-GE CMIP6 grid, especially if there are significant resolution\ndifferences, would be useful. Were any other interpolation methods considered, and if so, why was\nlinear chosen?\nWe thank the reviewer for the constructive comment. Given that more advanced interpolation\nmethods do not stand out as much more superior than simpler approaches (Hofstra et al., 2008),\nwe choose the commonly used linear interpolation for its relative simplicity and low computational\ncost. While we acknowledge that interpolation can have implications – particularly for high-\nresolution datasets over regions with complex topography - a common grid across datasets is\nnecessary to enable comparison of spatially integrated cumulative heat (L380-382).\n8. The text mentions computing anomalies to \"remove any bias that might arise when computing the\nintensity of EuSHWs due to the seasonal cycle.\" However, when comparing model output to E-\nOBS, direct biases in temperature magnitudes or variability might exist between models and\nobservations. While not the primary focus, a brief comment on how these potential biases are\nhandled or if they are assumed to be less relevant for anomalies and trends would be beneficial.\nWe thank the reviewer for the valuable comment. We agree that the original sentence “… to remove\nany bias that might arise …”, was misleading. Following Brunner et al. (2024), we removed the\nseasonal cycle to eliminate a statistical artifact that arises when applying a running window for\nthreshold calculation. Since we do not apply any bias correction to the temperature magnitude or\nvariability relative to observations, we have revised the sentence to “We compute two sets (i.e. non-\ndetrended and detrended) of daily maximum 2m air temperature (T2max) anomalies from 1970\nuntil 2099 to remove the seasonal cycle” (L384-385).\n9. A short rationale for choosing the 1985-2014 reference period for percentile calculations would\nbe useful. This is a common choice, but explaining why this particular period was chosen over\nothers (e.g., for its representativeness or data availability) can strengthen the methodology.\nWe thank the reviewer for the valuable comment. We have now included the following sentence in\nL387-388: “The 1985-2014 period is chosen to represent the most recent climatology within the\nhistorical simulations.”\n10. For the detrended E-OBS anomalies, it states \"in reference to a centered 15-day running window\nover all ensemble members from all models for each year.\" Given E-OBS is observational, it doesn't\nhave \"ensemble members.\" It likely refers to averaging over different historical realizations or\nperhaps the temporal mean. Clarification here would be helpful.\nWe thank the reviewer for the valuable comment. We have clarified this in L390-391 by revising the\nsentence to: “For E-OBS, we compute the detrended T2max anomalies in reference to a centered\n15-day running mean, averaged across all climate models for each corresponding day of each year.”\n11. For \"spatially weighted global mean surface temperature anomalies (GMTA),\" specifying the\nweighting (e.g., area-weighted) would ensure precision, although it's generally assumed for GMTA.\nWe thank the reviewer for this comment. We have now revised the original sentence from “spatially\nweighted global mean surface temperature anomalies (GMTA)” to “area-weighted global mean\nsurface temperature anomalies (GMTA)” in L397-398.\n12. The study uses SSP2-4.5 and SSP5-8.5. While these cover a range of plausible futures, it's\nworth noting that conclusions are bound to these specific scenarios and might not fully capture\noutcomes under very low emission pathways or other highly uncertain future scenarios. So it is\nsuggested to consider other scenarios that lies in between them.\nWe thank the reviewer for the valuable suggestion. To assess the robustness of our results, we tested\nthe sensitivity to scenario choice by including three additional SSP scenarios. We used MPI-GE\nCMIP6 model, as it consistently provides the necessary data and 50 ensemble members across five\nSSP scenarios: SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5.\nAs shown in Response Fig. 3 and 4, the inclusion of the three additional SSP scenarios has minimal\nimpact on changes in non-detrended EuSHW intensity and its range. Specifically, both the forced\nsignal and the ensemble spread at the end of the 21st century consistently decrease from SSP5-8.5 to\nSSP1-1.9 (Response Fig. 3a). The forced signal and ensemble spread in EuSHW intensity\n(Response Fig. 3b,c) also show a very similar increase under global warming when compared to\nresults using only two SSP scenarios. For example, the change in ensemble spread is of 2372 °C per\ndegree of global warming, compared to 2340 °C per degree of global warming using five SSP\nscenarios. The spatial distribution of changes in EuSHW intensity under global warming levels\nshow virtually identical patterns (Response Fig. 4a,b).\nSimilarly, Response Fig. 5 and 6 demonstrate that these additional SSP scenarios also have little\neffect on the changes in detrended EuSHW intensity and its range. Again, both the forced signal and\nensemble spread at the end of the 21st century show a consistent decrease from SSP5-8.5 to SSP1-\n1.9 (Response Fig. 5a). The change in the ensemble mean is of 104 °C per degree of global\nwarming using two SSP scenarios, and 105 °C per degree of global warming using five (Response\nFig. 5b). Likewise, the change in the ensemble spread is of 119 °C per degree of global warming\nusing two SSP scenarios, and 133 °C per degree of global warming using five (Response Fig. 5c).\nThe spatial distribution of changes in EuSHW intensity under global warming levels remains\npractically unchanged compared to the results based on only two SSP scenarios (Response Fig.\n6a,b).\nWe therefore conclude that our main findings are robust with respect to the inclusion of SSP1-1.9,\nSSP1-2.6, and SSP3-7.0, as now stated in L373-374.\nResponse Figure 3: Changes in European summer heatwave (EuSHW) intensity for MPI-GE\nCMIP6. a) Observed, historical and projected non-detrended EuSHW intensity expressed as\ncumulative heat in the left y-axis and scaled it to the observed historical mean (1970-2022) in the\nright y-axis. Solid lines indicate the ensemble mean, the shading indicates the 5th and 95th\npercentile, and the right vertical bars indicate the 5th and 95th percentile for the last 20 years of\nthe historical simulation and each shared socioeconomic pathway (SSP1-1.9, SSP1-2.6, SSP2-4.5,\nSSP3-7.0, and SSP5-8.5) scenarios; b) the forced signal (i.e., ensemble mean) of non-detrended\nEuSHW cumulative heat scaled to global mean temperature anomalies (GMTA) relative to 1985-\n2014 for SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios (2014-2100); c) the\nrange (i.e., ensemble spread computed as ensemble standard deviation) of non-detrended EuSHW\ncumulative heat due to internal variability scaled to GMTA relative to 1985-2014 for SSP1-1.9,\nSSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios (2014- 2100).\nResponse Figure 4: Spatial distribution of changes in European summer heatwave\n(EuSHW) intensity under global warming levels for MPI-GE CMIP6. Regression\ncoefficients for the period 2014- 2100 and for SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and\nSSP5-8.5 scenarios between global mean temperature anomalies relative to 1985-2014\nand; a) the forced signal (i.e., ensemble mean) of non-detrended EuSHW cumulative heat;\nb) the range (i.e., ensemble standard deviation) of non-detrended EuSHW cumulative heat\ndue to internal variability. In the non-dashed regions the model shows significant changes\nat the 95% confidence level.\nResponse Figure 5: Changes in European summer heatwave (EuSHW) intensity due to forced\nchanges in internal variability for MPI-GE CMIP6. a) Detrended observed, historical and\nprojected EuSHW intensity expressed as cumulative heat in the left y-axis and scaled it to the\nobserved historical mean (1950-2022) in the right y-axis. Solid lines indicate the ensemble mean,\nthe shading indicates the 5th and 95th percentile, and the right vertical bars indicate the 5th and\n95th percentile for the last 20 years of the historical simulation and each shared socioeconomic\npathway (SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) scenarios; b) the forced signal\n(i.e., ensemble mean) of detrended EuSHW cumulative heat scaled to global mean temperature\nanomalies (GMTA) relative to 1985-2014 for SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-\n8.5 scenarios (2014-2100); c) the range (i.e., ensemble spread computed as ensemble standard\ndeviation) of detrended EuSHW cumulative heat due to internal variability scaled to GMTA relative\nto 1985-2014 for SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios (2014-2100).\nResponse Figure 6: Spatial distribution of changes in European summer heatwave\n(EuSHW) intensity due to forced changes in internal variability under global warming\nlevels for MPI-GE CMIP6. Regression coefficients for the period 2014- 2100 and for\nSSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios between global mean\ntemperature anomalies relative to 1985-2014 and; a) the forced signal (i.e., ensemble\nmean) of detrended EuSHW cumulative heat; b) the range (i.e., ensemble standard\ndeviation) of detrended EuSHW cumulative heat due to internal variability. In the non-\ndashed regions the model shows significant changes at the 95% confidence level.\n13. Soil moisture is defined as \"fraction of water accumulated in the root zone relative to the water\ncapacity.\" This is a standard definition, but the precise depth of the root zone and what \"water\ncapacity\" refers to (e.g., field capacity, total pore space) can vary between models and influence\nresults. A brief acknowledgment of this model-specific variability would be appropriate.\nWe thank the reviewer for this valuable comment. We now only use the mrso variable (total soil\nmoisture content summed over all soil layers, and not in the root zone as mistakenly written before).\nThis change was necessary because EC-Earth3 does not provide soil water capacity (mrsofc), which\nprevents us from calculating the fraction of water accumulated. We are aware of the importance of\nnormalizing total soil moisture content by soil water capacity before comparing model results, as\nmodels can differ in both their mean values and variability. However, since water capacity is\nconstant over time, the regression analysis is minimally affected, and our results remain consistent\nwith those presented in the previous version. The changes are now reflected L398-400.\n13. While linear regression of heatwave intensity/range to GMTA is a useful approach, it assumes a\nconsistent relationship across all warming levels. While justified in the results (linear for range,\nnon-linear for forced signal), acknowledging that complex, non-linear relationships might be\npresent, especially at very high warming levels, could be a minor limitation.\nWe thank the reviewer for the comment. We have added the following sentence in L425-427:\n“While linear analysis assumes a consistent relationship across all warming levels, non-linear\nrelationship might exist specially at vey high warming levels.”\n14. The study focuses on daily maximum 2m air temperature. While this is appropriate for\nheatwaves, other metrics like duration/return period of heatwaves could also have significant\nimpacts and might be influenced differently by internal variability changes.\nWe thank the reviewer for this relevant and insightful comment. We agree that alternative heatwave\nmetrics could yield valuable insight. However, the metric used in our study (i.e., the cumulative\nheat), already integrates key aspects of heatwaves, including duration, magnitude and spatial extent.\nWhile examining how the forced changes in internal variability affects individual components of\ncumulative heat would indeed be interesting, such an analysis would significantly extend the\nmanuscript and lies beyond the scope of our current study. We have therefore chosen not to pursue\nthis additional analysis at this stage.\n15. The paper explicitly states that some observed changes in EuSHW intensity cannot be solely\nexplained by soil moisture variability changes (e.g., CanESM5 north of the Baltic Sea, MPI-GE\nCMIP6 in northern Europe). This suggests that other factors, such as North Atlantic sea surface\ntemperature variability or atmospheric circulation changes, play an unquantified role, indicating an\nincomplete understanding of all drivers. Some discussion or explanation (with results if available) is\nbeneficial for the readers.\nWe thank the reviewer for this constructive suggestion. We now expanded both the Introduction\nand the Discussion sections to incorporate the dynamical mechanisms underlying heat extremes.\nIn the Introduction (L49-59), we now describe how anomalous sea surface temperatures can\nmodulate atmospheric circulation, and how such circulation anomalies can lead to heatwaves\nthrough land-atmosphere feedbacks. Furthermore, in the Discussion (L334-347), we elaborate on\nhow atmosphere dynamics are expected to evolve under global warming, and how these\natmospheric changes may contribute to both the forced changes in internal variability and the\nprojected changes in European summer heatwave intensity. We also discuss how these dynamical\nshifts may contribute to inter-model differences and overall uncertainty.\n16. The definition of heatwaves using a fixed percentile (assuming a \"time-invariant\" perception of\nextreme temperatures) is a common approach but represents a simplified view of adaptation. Real-\nworld adaptation might involve shifting thresholds as societies acclimatize, which could alter the\nperceived intensity and impact of future heatwaves. A short analysis with variable percentiles may\nbe beneficial for the study.\nWe thank the reviewer for this thoughtful suggestion. While our analysis uses a fixed-percentile\nheatwave definition, which inherently assumes no adaptation to rising temperatures, applying this\ndefinition to detrended daily maximum 2m air temperatures does account for adaptation to\nincreasing mean temperatures (i.e. adaptation to shifting temperature distribution). We agree that\nfuture societies may also acclimatize to rising extreme temperatures, which could further alter the\nperceived heatwave intensity and require an analysis using variable percentiles.\nWe have conducted a new analysis using a variable percentile, the 90th percentile based on a\ncentered 31-year running window, applied to the non-detrended daily maximum 2m air\ntemperatures. This approach assumes adaptation to rising extreme temperatures. The results show\ngenerally weaker and statistically non-significant changes in EuSHW intensity at the 95%\nconfidence level across models (Response Fig. 7 and 8), compared to results obtained with the fixed\nthreshold and detrended daily maximum 2m air temperatures. We would like to emphasize that the\nlarger extent of dashed area in Response Fig. 7 is due to more non-significant areas in individual\nmodels (as shown in Response Fig. 8), rather than more spatial disagreement in the sign of the\nregression coefficients.\nWeaker changes are expected: if future societies adapt to rising extreme temperatures, the relative\nimpact of future EuSHWs would resemble that of present-day events. Similarly, the lack of\nstatistical significance is also expected. As shown by Milinski et al. (2020), approximately 50\nensemble members are required to robustly quantify changes in internal variability (i.e., changes in\nthe standard deviation of a distribution). Accurately capturing changes above the rising 90th\npercentile and their effect on EuSHWs would therefore require a much larger ensemble. Thus, the\nabsence of statistical significance does not necessarily imply the absence of actual changes; rather,\nit reflects an insufficient number of ensemble members to detect them robustly.\nAlthough these results are not robust due to the limited ensemble size, the regional patterns of\nEuSHW intensity changes (Response Fig. 8) resemble those associated with forced changes in\ninternal variability (Fig. 4): the increase in EuSHW intensity is concentrated in central and northern\nEurope, while the decrease is observed in southern Europe (Response Fig. 8). This consistency\nsupports our main conclusions. Nonetheless, we have chosen not to include this analysis in the\nmanuscript, as the moving percentile does not fully capture the nature of changes in internal\nvariability.\nResponse Figure 7: Spatial distribution of changes in European summer\nheatwave (EuSHW) intensity under global warming levels using a variable\nheatwave percentile. Multi-model mean of regression coefficients for the period\n2014- 2100 and for SSP2-4.5 andSSP5-8.5 scenarios between global mean\ntemperature anomalies relative to 1985-2014 and; a) the forced signal (i.e.,\nensemble mean) of EuSHW cumulative heat; b) the range (i.e., ensemble spread\ncomputed as ensemble standard deviation) of EuSHW cumulative heat due to\ninternal variability. In the non-dashed regions at least three out of the five models\nagree on the regression coefficient sign, and at least three out of the five models\nshow significant changes at the 95% confidence level.\nResponse Figure 8: Spatial distribution of changes in\nEuropean summer heatwave (EuSHW) intensity under global\nwarming levels using a variable heatwave percentile.\nRegression coefficients for the period 2014- 2100 and for SSP2-\n4.5 and SSP5-8.5 scenarios between global mean temperature\nanomalies relative to 1985-2014 and; a) the forced signal (i.e.,\nensemble mean) of EuSHW cumulative heat for ACCESS-ESM-\n1.5; b) the range (i.e., ensemble spread computed as ensemble\nstandard deviation) of EuSHW cumulative heat due to internal\nvariability for ACCESS-ESM-1.5; c,d) same as a,b) but for\nCanESM5; e,f) same as a,b) but for EC-Earth3; g,h) same as\na,b) but for MIROC6; i,j) same as a,b) but for MPI-GE CMIP6.\nThe non-dashed regions show significant changes at the 95%\nconfidence level.\nReferences:\nBrunner, L., & Voigt, A. (2024). Pitfalls in diagnosing temperature extremes. Nature\nCommunications, 15(1), 2087.\nHofstra, N., Haylock, M., New, M., Jones, P., & Frei, C. (2008). Comparison of six methods for the\ninterpolation of daily, European climate data. Journal of Geophysical Research: Atmospheres,\n113(D21).\nMilinski, S., Maher, N., & Olonscheck, D. (2020). How large does a large ensemble need to be?.\nEarth System Dynamics, 11(4), 885-901.\nSeneviratne, S. I., Corti, T., Davin, E. L., Hirschi, M., Jaeger, E. B., Lehner, I., ... & Teuling, A. J.\n(2010). Investigating soil moisture–climate interactions in a changing climate: A review. Earth-\nScience Reviews, 99(3-4), 125-161.\nReviewer #3 (Remarks to the Author):\nThe intensity and frequency of heatwaves in Europe have significantly increased in recent decades,\ndrawing widespread attention from the academic community. While most studies focus on the\nimpact of anthropogenic forcing on heatwaves, this study investigated the influence of internal\nvariability on heatwave variability in central and northern Europe. They also indicated the important\nrole of soil moisture in the changes of European heatwave intensity. However, the conclusions\ndrawn in this study exhibit apparent inter-model inconsistencies and lack solid mechanistic analysis,\nwhich raises major concerns in my view, as detailed below.\nWe thank the reviewer for their time and for the thoughtful and constructive comments. We have\naddressed each of the reviewer’s points and revised the manuscript accordingly. Specifically, we\nhave incorporated an additional model to strengthen the robustness of our conclusions, and\nconducted two new analyses: (1) quantified the percentage contribution of forced changes in\ninternal variability; (2) quantified the changes in land-atmosphere coupling and feedback under\nglobal warming, which support the changes in EuSHW intensity driven by forced changes in\ninternal variability.\nIn addition, we have expanded the Introduction and Discussion sections to clarify the effects of\nforced distribution shift and forced changes in internal variability on the EuSHW intensity range.\nWe also discuss the potential contribution of atmospheric circulation changes to the projected\nchanges in EuSHW intensity, which may explain why changes in soil moisture variability do not\nalways align with changes in EuSHW intensity.\nWe believe that the reviewer’s comments and suggestions have significantly improved the quality\nand clarity of the manuscript.\n1. This study primarily highlights the importance of internal variability in the long-term changes of\nEuropean heatwaves. However, as seen in Figure 1, the influence of external forcing remains\ndominant. It is recommended to include a discussion on the relative impacts of external forcing\nversus internal variability.\nWe thank the reviewer for the valuable suggestion. In response, we have conducted a new analysis\nto quantify the percentage contribution of forced changes in internal variability to the changes in\nEuSHW intensity and its range under rising global warming levels. We have included a new figure\nillustrating these contributions (Supplementary Figure 3) and now report the maximum positive and\nnegative contributions for each model in the manuscript (L189-194 and L208-212).\n2. As seen in Figure 2, the regions with the highest range of heatwaves caused by internal climate\nvariability are mainly concentrated in southern Europe. However, the range of detrended heatwave\nintensity resulting from forced changes in internal variability predominantly occurs in central-\nnorthern Europe. Further analysis and discussion are required to provide some explanations.\nWe thank the reviewer for the constructive comment. We would like to clarify that the change in the\nrange of heatwave intensities shown in Fig. 2 are driven by the combined effects of the forced shift\nin temperature distribution and forced changes in internal variability, with the former being the\ndominant factor. Notably, an increase in the range of EuSHW intensity could arise solely from the\nforced shift in temperature distribution. As temperature distributions shift towards higher values, the\nheatwave threshold -defined as the fixed 90th percentile relative to 1985-2014 reference period-\nremains constant, assuming limited adaptation to rising temperatures. As a result, exceedances of\nthis threshold become more frequent, and the potential variability in heatwave intensity increases.\nConsequently, the contribution of internal variability to heatwave events becomes more\npronounced, even if the internal variability itself is not forced. We have clarified this in L150-159\nand L282-287.\n3. The main conclusion of this study is that the increasing heatwave intensity linked to forced\nchanges in internal variability primarily occurs in central-northern Europe, which could result in a\nfaster increase in extreme values compared to the mean. However, this conclusion is largely based\non four single-model initial-condition large ensembles, and the results from these four models\nappear inconsistent (Supplementary Figure 2). Among the four models, the positive contributions of\nforced changes in internal variability can be found in northern, central, and southern Europe. This\ninconsistency significantly undermines the reliability of the conclusion, which is my primary\nconcern regarding this paper.\nWe thank the reviewer for raising this concern. We have now included an additional SMILE, EC-\nEarth3, which increases the extent of the non-dashed areas in Fig. 4 and strengthens the robustness\nof our results regarding changes in EuSHW intensity driven by forced changes in internal\nvariability.\nUnfortunately, other SMILEs such as CESM2 provide the required daily-resolution data for only a\nfew number of ensemble members. As shown by Milinski et al. (2020), robust detection of forced\nchanges in internal variability requires approximately 50 ensemble members. Therefore, CESM2\nand other SMILEs with considerably fewer than 50 ensemble members at daily resolution are not\nsuitable for inclusion in this study. We have clarified our selection criteria for SMILEs in L87-93.\nWhile the inclusion of EC-Earth3 has expanded the area showing robust EuSHW intensity changes,\ninter-model inconsistencies naturally remain. Due to data constraints preventing the inclusion of\nadditional SMILEs, we have responded to the reviewer’s concern by expanding the Discussion\nsection regarding inter-model differences. This includes potential contributions from different land-\nsurface parameterizations, convection schemes, and differing projected atmospheric responses to\nglobal warming, all of which might contribute to divergent regional responses to forced changes in\ninternal variability (L321-324 and L343-347).\nMore importantly, we would like to highlight that our multi-model mean findings align with the\nclassical conceptual framework in hydrology (Seneviratne et al., 2010), which suggests that soil\nmoisture feedbacks can either be amplified or reduced under declining mean soil moisture,\ndepending on the evapotranspiration regime (L63-69). While the regional assessment on how\nEuSHW intensity will change due to the forced changes in internal variability (e.g., the latitude at\nwhich the increasing EuSHW intensity becomes negative) is very uncertain and model dependent,\nthe fact that a latitude at which EuSHW intensity changes from positive to negative should exist is\nmuch more certain. We believe that the agreement between the multi-model mean analysis and\nclassical conceptual framework in hydrology strengthens of our main conclusion.\n4. The authors attempted to link the effects of forced changes in internal variability with soil\nmoisture changes. However, as analyzed in the paper, soil moisture changes often fail to explain\nheatwave variability. Moreover, the conclusion that \"In central and northern Europe, a decrease in\nsoil moisture will cause the region to switch more frequently between moisture-limited and energy-\nlimited states, amplifying land-atmosphere feedbacks...\" lacks in-depth mechanistic analysis. For\ninstance, no supporting evidence is provided to demonstrate that soil moisture actually enhances\nland-atmosphere coupling in these regions.\nWe thank the reviewer for the valuable comment. We agree that changes in soil moisture variability\ndo not always explain changes in EuSHW intensity due to the forced changes in internal variability,\nparticularly over northern Europe. This point is now clearly stated in L326-328.\nWhile the mean state of the ocean and atmosphere is changing under global warming, their\nvariability may also be altered, potentially enhancing or suppressing the increase in EuSHW\nintensity driven by the forced distribution shift. One example is the change in meridional\ntemperature gradients in the lower and upper troposphere, which affects mid-latitude atmospheric\ncirculation and, consequently, the intensity of EuSHWs.\nAlthough the simulated mid-latitude atmospheric circulation response to these gradient changes\nvaries across models, and may contribute to the inter-model uncertainties found in our study,\nrecent studies suggest that the summer North Atlantic Oscillation (SNAO) will exhibit a positive trend\nunder global warming (Liu et al, 2025; Mitevski et al., 2025). Since the positive phase of SNAO is\nassociated with northwestern EuSHWs, this trend could help explain our finding that northern\nEuSHWs are expected to intensity driven by forced changes in internal variability.\nWe have expanded the Discussion section to address the potential contributions of atmospheric\ncirculation changes to the projected changes in EuSHW intensity, the inter-model differences, and\nthe overall uncertainty (L334-347).\nAdditionally, we conducted two supplementary analyses to support that the changes in soil moisture\nvariability are associated to changes in land-atmosphere coupling and feedback, and thus to changes\nin EuSHW intensity.\nWe compute land-atmosphere coupling as the correlation between the 90th percentile of daily\nmaximum temperature and summer mean soil moisture across ensemble members, and regress this\ncorrelation against global mean temperature anomalies. Similarly, we define land-atmosphere\nfeedback as the slope of the linear regression between the same variables, which we also regress\nagainst global mean temperature anomalies.\nOur results show that under global warming, both the correlation (Response Fig. 9a) and linear\nregression (Response Fig. 9b) become more positive in southern Europe. Since soil moisture and\ntemperature are typically anti-correlated (i.e., while soil moisture decreases temperature increases),\na more positive correlation and regression slope indicate a weakening of land-atmosphere coupling\nand feedback. In contrast, the correlation and regression slope become more negative in central and\nnorthern Europe, indicating a strengthening of land-atmosphere coupling and feedback.\nWe have included an additional figure to the supplementary material showing changes in land-\natmosphere feedback and coupling under increasing global warming levels (Supplementary Figure\n6), and have added the relevant text to the manuscript in L245-256.\nResponse Figure 9: Spatial distribution of changes in land-atmospheric coupling and\nfeedback under global warming levels. Multi-model mean of regression coefficients\nfor the period 2014-2100 and for SSP2-4.5 and SSP5-8.5 scenarios between global\nmean temperature anomalies relative to 1985-2014 and; a) land-atmospheric coupling\ncomputed as the correlation between 90th percentile summer (June, July, August) daily\nmaximum 2m air temperatures and summer mean soil moisture; b) land-atmospheric\nfeedback computed as the linear regression between 90th percentile summer daily\nmaximum 2m air temperatures and summer mean soil moisture. In the non-dashed\nregions at least three out of the five models agree on the regression coefficient sign,\nand at least three out of the five models show significant changes at the 95%\nconfidence level.\n5. Why were only four models used? Could the number of models be increased to obtain more\nreliable conclusions?\nWe thank the reviewer for the constructive comment. We have now incorporated EC-Earth3 into our\nanalysis, which improved the robustness of our results. As stated in the response to the third\ncomment, to our knowledge there are no other SMILEs that fulfill the criteria to robustly identify\nthe forced changes in internal variability.\nReferences:\nLiu, Q., Bader, J., Jungclaus, J. H., & Matei, D. (2025). More extreme summertime North Atlantic\nOscillation under climate change. Communications Earth & Environment, 6(1), 474.\nMilinski, S., Maher, N., & Olonscheck, D. (2020). How large does a large ensemble need to be?.\nEarth System Dynamics, 11(4), 885-901.\nMitevski, I., Lee, S. H., Vecchi, G., Orbe, C., & Polvani, L. M. (2025). More positive and less\nvariable North Atlantic Oscillation at high CO2 forcing. npj Climate and Atmospheric Science, 8(1),\n171.\nSeneviratne, S. I., Corti, T., Davin, E. L., Hirschi, M., Jaeger, E. B., Lehner, I., ... & Teuling, A. J.\n(2010). Investigating soil moisture–climate interactions in a changing climate: A review. Earth-\nScience Reviews, 99(3-4), 125-161."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all my concerns, I thus recommend it for publication in current form.", "reviewer_2": "The authors have revised the manuscript carefully. The manuscript can be accepted in the current form.", "reviewer_3": "I appreciate the authors' efforts in revising the manuscript based on the feedback. The paper is now substantially stronger, and most of my comments have been well-addressed. I would be happy to recommend acceptance once the following minor comments are resolved.\n1. L186-187: “All models excluding MIROC6 show a significant increase in the forced signal and the range of EuSHW intensity in central Europe”, this description is not accurate. In my view, significant increase in ACCESS-ESM-1.5 primarily appears in northern Europe rather than in central Europe.\n2. Supplementary Fig. 6: Should be added as a main figure since it presents one of the key conclusions.\n3. The distinct modulation of future heatwaves by soil moisture and land-atmosphere feedback across different regions can be supported by a recent publication (Cai et al. 2024: Pronounced spatial disparity of projected heatwave changes linked to heat domes and land-atmosphere coupling)."}, "author_response": "Detailed response to reviewers\nReviewers comments are shown in blue, author responses are shown in black, and the line numbers\nreference the revised version of the manuscript.\nReviewer #1:\nThe authors have addressed all my concerns, I thus recommend it for publication in current form.\nWe thank the reviewer for their time. We are pleased to have addressed all of their concerns.\nReviewer #2:\nThe authors have revised the manuscript carefully. The manuscript can be accepted in the current\nform.\nWe thank the reviewer for their time. We are pleased to have addressed all of their concerns.\nReviewer #3:\nI appreciate the authors' efforts in revising the manuscript based on the feedback. The paper is now\nsubstantially stronger, and most of my comments have been well-addressed. I would be happy to\nrecommend acceptance once the following minor comments are resolved.\nWe thank the reviewer for their time and for the thoughtful and constructive comments. We have\naddressed each of the reviewer’s points and revised the manuscript accordingly.\n1. L186-187: “All models excluding MIROC6 show a significant increase in the forced signal and\nthe range of EuSHW intensity in central Europe”, this description is not accurate. In my view,\nsignificant increase in ACCESS-ESM-1.5 primarily appears in northern Europe rather than in\ncentral Europe.\nWe thank the reviewer for this comment. We have now modified the sentence to “All models except\nMIROC6 show a significant increase in the forced signal and the range of EuSHW intensity in\ncentral Europe, although in ACCESS-ESM-1.5 this increase is more pronounced in northern than in\ncentral Europe.” (L186-188).\n2. Supplementary Fig. 6 should be added as a main figure since it presents one of the key\nconclusions.\nWe thank the reviewer for the suggestion. We have now added the Supplementary Fig. 6 to the main\nmanuscript as Fig. 6.\n3. The distinct modulation of future heatwaves by soil moisture and land-atmosphere feedback\nacross different regions can be supported by a recent publication (Cai et al. 2024: Pronounced\nspatial disparity of projected heatwave changes linked to heat domes and land-atmosphere\ncoupling).\nWe thank the reviewer for suggesting this relevant publication. We have cited the publication in\nL310-314."}]

Decision letter