The manuscript presents an analysis of PMIP4 simulations for the PI, MH and LIG and investigates the importance of the definition of the calendar. Although this has been done previously and the new results largely confirm previous ones, this new analysis is still useful as it includes an ensemble of climate model simulations and thus allows one to test the robustness of the findings over multiple models.

Major comment:

Lines 92-93: In the literature various methods are presented to adjust monthly data towards a angular calendar. In this manuscript reference is made to Rymes and Myers (2001), but how different or similar are the various methods? So for instance Bartlein and Shafer (2019) and the various other methods that they mention in their publication (Pollard and Reusch, 2002; Timm et al., 2008; Chen et al., 2011). It would be very informative for the reader to know whether the results presented in this manuscript generally hold for all those methods or if some should be avoided.

Bartlein and Shafer (2019) made their code to perform the calendar adjustment freely available and ‘user friendly’. It would be great if the same could be done with the code used in this manuscript. A reference to the code could then be added in the manuscript.

Minor comments:

Line 60: Scussolini et al. 2019 do show LIG results for precipitation and temperature for both the classical calendar and the angular calendar.

Line 72: Perhaps it is good to mention that in the results section you will first briefly describe the main features of simulated MH and LIG temperatures and precipitation (describe in more detail in previous publications) and after that you will focus on the main topic of the manuscript, namely calendar-effects.

Line 110: For consistency it would be better to mention the initialization procedure of all three transient simulations, not just for IPSL.

Line 141: Perhaps good to not only focus on the comparison to earlier work on PMIP4 results, but also shortly on previous iterations of PMIP and other projects. For instance Lunt et al., 2013; Scussolini et al. 2019.

Section 3.3: this section is rather long. Consider breaking it up in several sub-sections, for instance one on temperature, precipitation and one on using monthly data to calculate angular-seasons.

Lines 240-242: The authors say that these are ‘significant’ differences, but the meaning of the word significant is unclear and undefined in this context. Better to replace it.

Lines 347-359: these lines are rather vague. A reference is made to major model-data mismatches that are being discussed in the literature (e.g. The Holocene temperature conundrum). So what do the results of this manuscript have to add to those discussions? Can an estimate be given on the possible magnitude of calendar effects on this model-data mismatch? Or, if not, how could this be investigated in future work? Please clarify the link between the current manuscript and the work that is mentioned in this last paragraph.

Figures 5-7: It is always a difficult choice whether to show precipitation changes in units of mm/time or as percentages. The authors choose to use mm/month and as a result the tropical regions supposedly show the most marked changes in precipitation while in terms of percentages the picture might look quite different. Consider adding figures to the supplement that show percentage precipitation changes.

Technical comments:

Line 44: replace the word ‘bunch’

Lines 57-58: “hereafter referred to as fixed-length or classical calendar”. Perhaps better to use only one of the two in the remainder of the manuscript to avoid confusion.

Lines 107 & 111: use subscripts for the names of the greenhouse-gasses.

Line 130: replace ‘at the’ by ‘over’ or perhaps ‘in’?

Main article figures and supplementary figures: Just for clarity, mention in the figure captions when the figure shows multi-model-mean results.

Calendar effect is a problem in paleoclimate modelling since long. To my knowledge, there are not many studies dedicating to this topic. In this manuscript, the authors investigate the calendar effect on seasonal temperature and precipitation by using the PMIP simulations of the PI, 6ka, 127ka snapshot and the 6-0ka transient experiments. The results could be informative for paleoclimate community and let pay more attention to the calendar problem. In the meantime, some improvements would be needed for clarifications and also to make the manuscript more attractive. Please find my comments and questions here below.

General comments: 

1.    There are not many studies on the calendar effect in paleoclimate simulations. In addition to Joussaume and Braconnot 1997, Bartlein and Shafer 2019 cited in the manuscript, there are also Pollard and Reusch 2002 (https://doi.org/10.1029/2002JD002126 ), Timm et al 2008 (https://doi.org/10.1029/2007PA001461 ) and Chen et al 2010 (https://doi.org/10.1007/s00382-010-0944-6) . These studies and their findings should be mentioned in the manuscript and be compared with.

2.    It is unclear for me how the conversion of temperature and precipitation on the classical calendar to those on angular calendar was made. A thorough explanation would be needed in section 2.1. Please also see some of my specific comments.

3.    The calendar effect at 6ka and 127 ka was examined using multi-model ensemble. Is the calendar effect on temperature and precipitation similar between individual models qualitatively and quantitatively speaking? Additional analysis on individual model would be interesting. Moreover, how is the calendar effect compared to the difference between models? For example, the difference between the black and pink lines in Fig.12 appears very small. It is much smaller than the model-model difference. Is such a small effect worth to be mentioned? 

4.    To which extent is the model-proxy comparison improved when calendar effect is considered? It would be interesting to show the comparison with proxy data before and after the calendar conversion. 

5.    If I understand well, the calendar effect happens mainly when the seasonal climate between two time slices is compared. Is it worth to consider it when we are interested only in the absolute climate at one given time slice? Does the calendar effect have an influence on the simulated vegetation?

6.    In section 3.4, why only analyze the temperature over continents and ice-free continents?  I would suggest to add analysis also on temperature over ocean and ice continents, which would be particularly important for Southern Hemisphere.

Specific comments: 

Line 25: change “31” to “21”; is there any other reference date that has been used by other model groups? Is there a reason to use March 21 or other date as the reference date?

L32: change “with a periodicity of about 100,000 years” to “with major periodicities of about 400,000 and 100,000 years (Berger, 1978, https://doi.org/10.1175/1520-0469(1978)035<2362:LTVODI>2.0.CO;2; Berger and Loutre, 1991, https://doi.org/10.1016/0277-3791(91)90033-Q)”. The 400 ka periodicity is more important than the 100 ka one. 

L33: what does “periods of perihelion and aphelion” mean? 

L34:  0.0167, 0.0189, and 0.0397 are the values at a given date or an average over a given period? Please make it clear in the manuscript. 

L37: with a “major” period of 41,000 years

L39: Note that 19,000 and 23,000 years are the major periodicities of climatic precession, not of astronomical precession. Please clarify it in the manuscript and cite Berger (1978) where these periodicities were calculated for the first time. 

L46: Indicating 6ka for MH and 127 ka for LIG could be misleading, because MH and LIG are more than these two dates.

L51:  Herold et al 2012 (https://doi.org/10.1016/j.quascirev.2012.08.020 ) and Nikolova et al 2013 (doi:10.5194/cp-9-1789-2013 ) are among the early studies on simulating the 127ka climate and describing its insolation pattern, and deserve to be cited here. Please also be more precise about "enhanced seasonal cycles". In Nikolova et al 2013, it is found a larger seasonal contrast in northern hemisphere but a reduced one in the southern hemisphere.

L67: “we perform …” is unclear for me. Please give more explanation.

Section 2.1: Is the calendar conversion method used in this study similar to those used in the five studies mentioned in my major comment 1? 

L79: is it necessary to mention “Northern Hemisphere”?

L85: “orbital period” is confusing. I assume T is the number of days in one year.

Equation 2: Please explain what is the principle on which Equation (2) is built.

Equation 3: It is unclear how equation (3) is obtained. Please also give an equation explicitly relating tp to true anomaly.

L94-96: Please be more precise on how each season is defined from the true anomaly that is calculated in equation (3).

L119: you mean “ increased summer insolation”?

L124: Please explain what is the delayed effect.

L143: It is unclear how this calculation has been done, and how the dates in table 2 are obtained. More explanation is needed.

L145-146: isn't the velocity always greater at perihelion than at aphelion, whatever at today or any time in the past?

L235: It is good to refer to Rymes and Myers 2001 when use monthly values for calendar corrections, but it would be helpful for the reader if some information is given on how to transform monthly values to daily values.

L280: any idea of why there is a model-dependency of the calendar effect?

Section 4: discussion and conclusion are mixed up, better to be separated.

L297: what does “the phasing of the insolation curve” mean?  Does calendar effect have an influence on the phasing between insolation and temperature, precipitation in the Holocene transient simulation?  

L330-331: Please explain why a different definition of season is used in this study, is there any advantage?

L352: The analysis of this study shows that the calendar effect is most important in autumn. Then would the model-proxy comparison be significantly affected if proxy records mainly reflect summer temperature?  

This paper documents in detail the calendar effects on analyses of paleoclimate simulations for the mid-Holocene (MH), the Last Interglacial (LIG) and pre-industrial periods as well as for transient simulations. Indeed, due to the slow variations of the Earth’s orbital parameters, the position of seasons is modified within the ellipse, affecting the length of the seasons. This effect has been documented in Joussaume and Braconnot (1997) and more recently in Bartlein and Shafer (2019) but is usually not accounted for. This paper uses the most recent simulations of PMIP4 with coupled models and allows to revisit this question. Indeed, at the time of PMIP1, in Joussaume and Braconnot (1997), sea surface temperatures were prescribed to today, thus including a hidden present-day calendar in past climate simulations. Moreover, the paper presents results from transient simulations. These results deserve to be published although some improvements of the text would help its readability.

• There is a need to better explain how the 90° angular seasons are positioned relative to the vernal equinox which provides the reference for dates (March 21^st), the way the seasons are computed is not fully clear in the paper
• Concerning the simulations used, it would be good to summarize the PMIP4 boundary conditions in section 2.2 and explicit whether the three transient simulations use the same boundary conditions and whether they differ or not with PMIP4 for the mid-Holocene.
• The use of angular seasons is indeed more appropriate when comparing seasons from different periods in paleoclimate simulations, however, it would be good to add some elements in the discussion on possible implications for the model-proxy data comparisons.
• Moreover, you have made the choice to define 4 times 90° angular seasons and to compare to pre-industrial, but nothing is said on how you would compare to present-day. In Joussaume and Braconnot (1997), the choice was to use the same angular seasons as used today (even if they are not perfect 90° angles) to ensure consistency with present-day. It could be interesting to add some discussion on the impact of those different choices.
• In the discussion, it would also be interesting to know if some of the forcing or boundary conditions of simulations may still keep some memory of the present-day calendar (e.g., prescribed vegetation or aerosols) and may add some bias in the analyses.
• The text needs some reading to correct some sentences, some are mentioned below.

Specific comments:

L12: The largest difference occurs in autumn is related to the choice of a fixed date for the vernal equinox, this should be made clearer in this sentence

L16: the conclusion on using monthly data is not clear in the abstract, you should add compared to using daily data

L24: “is highly depends” should be “highly depends”

L25: March 21^st and not 31 !

L30: the classical reference is rather to Berger (1978) than 1977

L44: modelling groups and not model groups

L48: I do not think we can say that the MH and LIG are chosen due to their great potential to resemble future scenarios. Please reconsider this statement

L50: receive more insolation in summer and less in winter is only true for the Northern Hemisphere

L83 to L86: a drawing to explain M and E is missing. It could be added at least in the supplementary material

L102: IPSL is the name of the institution not of the model (IPSL-CM)

L132: Sahel and not Sahal

Table 2: mentions that the present-day calendar is not an angular one and should be corrected: could that correction be described ?  at least in supplementary ?

L155-156: you compare in the following angular (adjusted) versus calendar (non adjusted), as is chosen on the figures as well, whereas in this sentence you reverse the comparison. Please take care to avoid changing the reference to help the reader.

L180: It is expected to have continents reacting faster than oceans to solar forcing due to the differences in heat capacity.

L312: Use of daily data “can completely erase the bias” is strange, isn’t it the definition of what is called the bias in the paper ? I guess you mean that compared to daily data, using monthly data do not completely erase the bias ?

L332: indeed, in Joussaume and Braconnot (1997) the choice is made to use the same seasons as defined today to be compatible with the present-day reference. It would be useful to discuss more the implication of your choice if you want to compare to today.

L352: when considering proxy-data we may have to rather consider bioclimatic indicators which are less dependent on the artificial definition of seasons, eg when considering the growing degree-days

Fig 3: legend of third column is angular minus classical and not classical minus angular