Summary: The manuscript presents a new dataset of climate simulations spanning approximately five hundred years, generated by the global atmospheric model of the Max-Blank Institute. This ensemble of simulations incorporates variations in external forcing and estimated sea-surface temperature and sea ice cover. The authors assess the realism of these ensembles in reproducing the mean climate, climate variations, and the frequency of heat waves. The manuscript is generally well-written, with clear figures and simulation descriptions. However, there are some concerns with specific sections, such as the one discussing heat waves. Additionally, there are some general comments for the authors to consider in the revised version.

Main points:

1) The manuscript should emphasize that these ensembles cannot capture the internal climate variability originating in the ocean. This is mentioned in the text, but it remains somehow hidden, and at some stages, it may be misleading. This point should be highlighted prominently, even in the abstract and title, as the simulations are driven on observed or reconstructed sea surface temperatures without including the possible internal variability.

2) The section on heat waves needs improvement. The section's title is misleading, as it generally refers to extreme events, not specifically heat waves. The definition of heat waves should be provided in the main text rather than in the caption of Figure 7. The underestimation of heat wave frequency and intensity before 1920 should be acknowledged more explicitly, as it is not a slight discrepancy. The text should avoid suggesting that most heat waves are caused directly by external radiative forcing, as Figure 7 indicates that they are primarily related to mean temperatures. To compare the model's ability to capture extreme events, model biases should be corrected, and heat waves could be defined separately in the reanalysis and model data. This can also be achieved by defining the 95% percentile for reanalysis and for model data separately.

Specific points:

3. The information about data assimilation and a gridded 3-dimensional dataset may not be relevant enough for this manuscript for inclusion in the abstract.

4) The sentence claiming the ensemble's capability to capture extreme events (heat waves) needs careful revision based on the aforementioned points.

5) The phrase "sampling of the supposed true state" is unclear. Clarification is needed, possibly by reformulating the sentence to avoid ambiguity. If by 'true state' the authors mean the mean climate, then this is not a random variable. It is a fixed parameter of the Earth's climate. However, if by 'true state' the authors mean the climatic probability distribution, then the sentence makes sense.

6) Section 2.2 should mention the external forcing used for the simulations upfront rather than referring to it later in the text.

7) In line 108, "set 1430-2" should likely be corrected to "set 1430-3."

8) '' forcing and the ocean boundary conditions can be detected from the subensemble means computed from each 20-member set separately (Fig. 2b & c), indicating that the ensemble size is clearly sufficient to separate forced signals from internal variability'

The distinction between internal atmospheric variability and internal climate variability with oceanic origins is important and should be clarified. The current phrasing might suggest that the ensemble captures all internal climate variability, which is not the case. 

The paper reports on the construction of a single climate model ensemble  for the period 1420 to 2009. The ensemble members have different initial  conditions but also different boundary conditions (SSTs and sea-ice) and forcings. The climate model is a coarse version of the atmospheric model  ECHAM6. The experimental design, including the initial conditions and the  forcings, isdescribed in detail. This is followed by a description of  the model behavior including the response to volcanic forcings, extremes and heat-waves.



While I value the construction of another large single-model ensemble, and this stands out by including variability related to the uncertainty  in the forcings, I cannot recommend that the paper is accepted in its present form. This is a result of the major comments mentioned below.

Major comments:



1) The paper seems to be put hastily together. The analysis and results  in  section 3.4 and 3.5  are very briefly discussed and  the methods are basically only described in the figure captions. I can understand that  the authors do not wish to present a very deep analysis of heatwaves, but what they choose to show should be adequately described.  Figure 3  is only mentioned briefly (l110) and the results are not properly described.



2) Tests of statistical significance are missing throughout the paper.  Regions with significant results should be indicated in the figures.



3) I have several comments to the construction of the additional SSTs in Section 2.2.3.  First of all the construction is not linear as claimed.  A linear model would look like SST_i = 1/3(SST_j + SST_k + SST_l).



Furthermore, I think x and t should be dropped from the formula and it should just be mentioned in the text that the construction is applied  simultaneously to  grid-points and  time.



More importantly, the authors should also be aware that their method  generates SSTs that donot have a Gaussian distribution. The distribution  of a ratio like SST_j/SST_k has heavy tails. It is difficult to see how big this problem is here, but it will also depend of the units you use  for temperature (I hope it is Kelvin).



Minor comments:



Abstract:  The data assimilation procedure is mentioned but it is  not clear if this is for the future or if it is included in the present paper.  Perhaps the abstract could be more informative on the results of the paper.



l16: This refer to single-models ensembles only. Multi-model ensembles  also include differences in physics.  I think the difference between  the two types of ensembles should be stated directly here.



l22: This sentence is not clear. .. was done by comparison with the  statistics .. Comparison with what?



l43 A  time-slice is mentioned but which time-slice.



l46: Perhaps define modern era in the text.



l57: 'last': as in latest or final?



l103: Is EVA defined anywhere?



l108: 1430-2 --> 1430-3 ?



l168: Perhaps the warming over northern Eurasia is connected to a positive  NAO.  A positive NAO is reported in observational studies the winter  after the eruptions (see, e.g., Christiansen 10.1175/2007JCLI1657.1).



Section 3.3:  How does the model reproduce the temporal characteristic  of the ENSO?  The responses in Fig. 5 seem very spatial extended. The  statistical significance is important here.



Figure 2: It is hard to see the shading in panels b and c.



Figure 4:  The statistical significance describing where this signal is different from zero should be indicated. The caption says 'ensemble  mean': I guess this is the mean of the volcanic signal over the ensemble  members and not the signal in the ensemble mean temperature. This should  be explained better.



Line 210 and Fig. 6: The description here is so brief that it is almost impossible to understand.



Section 3.5: Again, I find this much too brief to be of any value.