The manuscript by Leloup and Paillard tests the ability of a simple conceptual model to simulate Quaternary glacial cycles using different metrics of “orbital forcing” which differ by relative contributions of precessional and obliquity components. The authors used only one parameter (critical ice volume) to maximize model performance in term of a novel performance metric proposed by the authors. The main results of this study can be summarized as follows:

i) model performance does not strongly depend on whether “orbital forcing” is dominated by precession or precession is essentially absent.

ii) the transition from short to long glacial cycles in all cases can be achieved by an increase of the critical ice volume by factor 2-2.5.

While the latter is not surprising since 100/40=2.5, the first result requires more serious discussion (see below).

General comments

1. Since the review of Mikhail Verbitsky was already available at the time when I was requested to write my own, it is natural that I read his review before writing. And I must respectfully disagree with Mikhail in respect of the number of model parameters used in this study. Under “model parameters” (at least in our field) we understand parameters that can be used for model tuning. Gravity acceleration, Plank constant or Milankovitch‘ frequencies are not such parameters. This is why, formally, the Leloup and Paillard model (which is a simplified version of Parennin and Paillard mode) has only 5 parameters. In fact, the authors did not use four of them for model tuning since they used values for these parameters from a different model (Parennin and Paillard, 2003). Thus, the only parameter which the authors used for model tuning is the critical ice volume. Whether it is good on not is another issue.
2. When authors discuss the current state of our understanding of Quaternary climate variability, they are too pessimistic. The authors repeat twice (in abstract and introduction) that “the nature and physics of the [link between insolation and the glacial - interglacial cycles] remain unclear”, and “the Mid Pleistocene transition ... remain mostly unexplained”. Such statements would be, probably, appropriate in 1998 but not in 2021. Of course, some questions remain and, likely, will remain for some time but the major issues are already clear.
3. Of course, it is up to the authors to decide which model to employ, which parameters use to tune the model and which criteria use to select the optimal parameters set. However, as the result of authors’ choice, the model performance for all four “orbital forcings” for post-MPT glacial cycles are essentially the same. The authors claim that “we are able to represent the Mid Pleistocene Transition and the switch from a 41 kyr dominated record to a 100 kyr dominated record, by raising the deglaciation threshold (L. 291).” However, Fig. 4 clearly shows that this is not the case, since for three of four “orbital forcings” obliquity continues to dominate after MPT. Only for the solstice insolation, this is not the case, but then the model instead of sharp 100 kyr cyclicity simulates something which looks more like a red noise. Thus, as far as spectral properties of simulated glacial cycles are concerned, none of the model realisations is really successful. Whether this is a result of model formulation, fixing of four of five model parameters, or criteria for optimization - is not clear to me but has to be discussed in the paper.
4. As I already mentioned above, if the authors are convinced that model results are equally realistic irrespectively of whether “orbital forcing” contains a strong precessional component (solstice insolation) or almost none (ISI), then they should conclude that precession plays no role in Quaternary glacial cycles and, thus, 100 kyr cyclicity has nothing to do with eccentricity. Do the authors agree with such a statement? Please comment.
5. I do not understand what is shown in fig 1. Obviously, the figure heading (Normalized summer solstice insolation) is not applicable to the entire figure. More important is that the upper panel does NOT show summer solstice insolation. What it shows - I do not know.

Specific comments

L. 24. Milankovitch not just “popularized” this idea (which was not his own idea) but made it the key element of his ice age theory.

L. 26. “This also raises the question of what period should be defined as summer”. It should be made clear that the question of how to define “summer insolation” is relevant only for conceptual models, like one used in this study. Climate models and ESMs compute insolation at each time step for each grid-cell and do not need such prescriptions.

L. 28. This choice leads to very different forcings.

L. 41. The authors should make it very clear that they only consider here conceptual models of glacial cycles.

L. 81, 93 and 94. I fully agree with the comments by Mikhail Verbitsky

Eq. 2. Please change V to v.

Last par, p. 7. When discussing pre-MPT model performance, it is important to realise that for this period of time, LR04 stack was tuned to obliquity. This is why it is not surprising that it contains nothing apart from obliquity

L. 231. Which “data”? What “best guess” means?

L. 300. Talento and Ganopolski is now published

Review of „Influence of the choice of insolation forcing on the results of a conceptual glacial cycle model“

The manuscript is based on a simplified version of the conceptual model of Parrenin and Paillard (2003). While there are 5 tunable parameters in the model, the authors consider 4 of them as fixed and adjust the value of the fifth one (V0) in order to maximise the fit to paleo records, according to a criterion counting the failed or successful reproduction of deglaciations. The authors evaluate the different values that the parameter takes in order to optimise the fitting to the paleo data when using 4 different insolation forcings and considering different periods of time in the last 2500 kyr.

The main conclusions are that:

1. Independently of which of the 4 insolation forcings is used, it is possible to find values of V0 (changing in time) in order to provide a reasonable fit of the model output to the paleo records.
2. For all the forcings, to increase the accuracy of the fit to paleo data, the value of V0 increases after MPT.

I think the manuscript is interesting and well written. However, I have some questions and suggestions of some extra analysis to include.

General comments

1. I think that it should be clearly stated in the abstract, introduction and conclusions that the paper will focus on the deglaciation threshold V0, while keeping all the other 4 model parameters constant. In particular, I find the sentence “to be able to reproduce the frequency shift over the Mid Pleistocene Transition, the deglaciation threshold needs to increase over time, independently of the summer insolation used as input” misleading if it is not pointed out that all the other parameters are fixed. If temporal changes in the other parameters were also allowed, then the frequency shift over the MPT could potentially also be reproduced via other changes.
2. How do the results change if you consider the insolation at 50°N, as in Caulder’s model, instead of 65°N?
3. What happens if you decompose the summer solstice insolation into its precession and obliquity components and use each of them as forcing in your model? By the results shown in the manuscript, the ISI above 300W/m2 forcing (which contains almost no precessional signal) still produces what the authors deem a “good fit to data”. Therefore, I think that a clean separation into the precessional and obliquity components of, let’s say, summer solstice insolation could be a clean experiment to compare with.   
4. Will the results be the same with a different fitting criterion? For example, if instead of the defined c, the criterion for the optimisation is to maximise the correlation between time-series of normalized paleo and modelled ice volume, how do the results change? It is obvious that the correlation measure will penalise the ISI above 300W/m2 forcing, as it clearly cannot reproduce the variability at the 100 kyr frequency. 
5. I am interested in knowing more about the optimisation procedure. For each period and insolation forcing, did you any optimisation algorithm or trial and error?
6. How do you define the “Best fit over the Quaternary”? (Section 3.2) This is not explained. I assume the authors use a V0 that changes with time (5 different values, in the 5 different periods considered), is that correct? Please, make explicit.
7. For the “Best fit over the Quaternary” the authors use a V0 that changes with time. As a benchmark, I think the authors should also show how the performance with a changing V0 compare with the one of a constant V0. Please, repeat the optimisation procedure using the whole 0-2500 kyr BP period and provide the optimised constant V0 and corresponding model output. Please add these curves for each forcing in Figure 4. Also add in Figs. 1 and 2 the corresponding optimal constant-over-time V0 and accuracy when considering the entire 0-2500 kyr period.

Specific comments

L 25-26: “…due to reduced summer insolation, at latitudes typical of Northern Hemisphere ice sheets, 65° N.” I suggest to change for “…due to reduced summer insolation, at latitudes of the Northern Hemisphere critical for ice sheet growth (65°N).”

L 38: independent --> independent

L 49: the more insolation --> the highest insolation

L 53: more adapted --> better

L 71: explicitely --> explicitly

L 77-77: In Equation (1) the labels (g) and (d) are misplaced

L 80: “…a typical latitude for Northern Hemisphere ice sheets.” This part of the sentence has already been used in the introduction, no need to repeat it.

L 93-93: “The importance of orbital forcing alone seems able to start a glaciation” This sentence does not make sentence, please reformulate.

L 169: “In order to study the evolution of the optimal model parameters over the Quaternary…” Please correct to indicate that only V0 is being optimised.

L 170: periods --> period

L 173: “…the best fit parameters…” please modify to indicate only V0 is being fit

L 183-184: “The model state was compared to the middle of the deglaciation.” I don’t understand this sentence

L 233: varying --> varying

L 242: varies --> varies

L 273-274: “To model future natural evolutions of the climate system, one would need to take into account for possible evolutions of the V0 threshold.” Please acknowledge that, possibly, the other parameters might as well change.

L 283: Also add here Talento and Ganopolski, 2021 as reference.

L 287: “…very few tunable parameters… ” in fact, you should clarify that you tune only 1 parameter.

Section 2.4: I think a plot of the d18O record used with indications of the start and end of deglaciations, according to your criterion, is due here. Or at least refer the reader to this information in figure 3.

Figure 1: Normalized to what? by standard deviation? Please clarify. The ylabel in blue line must be corrected.

Why show only until 1000 kyr BP when the totality of the Quaternary (0-2500 kyr BP) is the focus on the rest of the paper? Please show the plot considering 0-2500 kyr BP.

In all the text: The acronym ISI was introduced in line 5, but frequently not used afterwards.

When starting a new paragraph, sometimes there is an indent, sometime there is not.