GENERAL COMMENTS

The study uses spectrally nudged high-resolution regional climate model simulations to quantify the sensitivity of summer 2019 European heatwave to the thermodynamic effects of global warming. The simulations indicate that, under unchanged atmospheric circulation, the daily maximum temperatures experienced under the heatwaves increase by about 2 K for each 1 K of global mean temperature change, and locally up to 3 K to the east of the heatwave centre. This contrasts with the simulated temperatures earlier in the summer, which only increase at the same rate with the global mean temperature. These features, together with the increased diurnal temperature range during the heatwave periods, suggest a role for reduced soil moisture in the amplified temperature response.    

Overall, the manuscript is interesting and well-written. I only have a few minor comments and remarks on it.

DETAILED COMMENTS (substance and presentation)

1. The focus of the study should be introduced earlier. Perhaps write on L7: ... we employ an event-based storyline approach to study the 2019 summer heatwaves over Central Europe. The approach comprises three steps ....
2. "the scaling of the global mean temperature" is obscure: the global mean temperature always scales one-to-one with itself.
3. Equation (2) suggests a linear increase with height.
4. L148-149. The ensemble spread in E-OBS characterizes the observational uncertainty in individual daily temperature fields. The observational uncertainty in (e.g.) summer mean values is expected to be considerably smaller, due to cancellation of errors whose sign varies from day to day. For this reason, comparison with the E-OBS ensemble spread understates the significance of the model-to-observation biases on longer than daily time scales.
5. L237-238. The difference in warming rates might also relate to the difference in season (early vs. late summer), not only the extremeness of temperature.
6. L274-277. Is the mean scaling similar for all summer months, or does it increase from early to late summer following the decrease in average soil moisture?
7. Same as comment 2.
8. L339-341. Is this seasonal evolution of the diurnal temperature range change specific to summer 2019, or does it also occur in the other simulated years?

DETAILED COMMENTS (wording and typos)

1. aimed at estimating the effect of human-induced …
2. L34-35. contributions to
3. computationally efficient
4. L70 and later. spectrally nudged
5. and 8-20 km in the Arctic
6. Caption of Figure 3, L3. give / report the RMSD to E-OBS
7. Analogously to
8. the GER-3 simulation
9. L221-222. the longitude-latitude area
10. to the east of it?