Paper provides rather detail descriptions of used climate model and parameter calibration procedure.

However, in my view it requires some clarifications and revision before publication.

Authors say in Abstract:  

“We show that two very different future projections to a given emission scenario can be obtained using emissions from the IPCC Sixth Assessment Report (AR6) (fair-calibrate v1.4.0) and from updated emissions datasets through 2022 (fair-calibrate v1.4.1) for similar climate constraints in both cases.”

However, simulations presented in the paper were done not only using different parameters distributions but also very different emission scenarios (Fig 11).  Moreover, in section 4 authors mentioned difference in future emission while explaining difference between results of v1.4.1 and v1.4.0 ensembles.

  I think simulations with v1.4.0 set of model parameters need to be redone with different emissions scenarios. As I understand, historical simulations used to derive final parameters distributions were run until 2022 using historical plus SSP2-4.5 from AR6. It looks logical to produce another set of harmonized SSP emissions using 2022 SSP2-4.5 emissions instead of historical and repeat v1.4.0 ensemble with these emissions. It should make comparison cleaner. It also would be interesting to mention distribution of which model parameters are most sensitive to changing historical emissions.

Specific comments.

Page 7. Line 185.  Reference to fig S1 is confusing.

Page 10 line 254.

concentrations of methane are in approximate equilibrium with pre-industrial concentrations.

It should be:

concentrations of methane are in approximate equilibrium with pre-industrial emissions.

Page 11

 line 267 should be  fig. S3,

 line 269 should be fig S4b

Lines 271-273

“As 1750 emissions are subtracted from the total to report changes away from a pre-industrial equilibrium, the change in emissions (1750–2022) in v1.4.1 from PRIMAP-Hist is smaller than in v1.4.0, leading to longer atmospheric lifetimes necessary to reproduce concentrations.”

According to Fig. S4b, 1750 CH4 emissions are larger in v1.4.1 than in v1.4.0. If 1750 CH4 concentration are identical in both cases, it will require large CH4 lifetime is for v1.4.1 for concentration to be in equilibrium with emissions. Please comment.

Page 20.

“841 is one more than a highly composite number and allows many quantiles of the full distribution to correspond to a single ensemble member at each point in time.”

Needs explanation.

Page 21. Line 464

“The disagreement in the upper bound of ERFaci is large in absolute terms but small in relative terms.”

It seems to be other way around.

Page 21. Line 477

“Firstly, concentration (not emissions) driven runs were used to derive the IPCC warming ranges, which excludes the impact of carbon cycle sensitivity uncertainty on a future spread in CO2 concentrations and thus over-constraining the uncertainty range.”

IPCC ranges for SSP scenarios, shown in tables 5 and S4, are not from AR6 Table 4.2, which shows ranges based on CMIP6 model simulations, but from Table 4.5, which shows Assessment results for 20-year averaged GSAT change, based on multiple lines of evidence.

The study proposes a new version of the FaIR simple climate model. It uses a Bayesian framework to estimate the parameters of the FaIR model and clearly explains the differences between fair-calibrate v1.4.0 and fair-calibrate v1.4.1. I enjoyed studying the entire manuscript. I have a few comments listed below.

• Can you please provide a flowchart of the working principle of fair-calibrate v1.4.1?
• If I understood correctly, the authors have used kernel density estimation as a prior distribution in the Bayesian framework. KDE can be very sensitive to outliers and data sparsity. Could you please discuss this in the manuscript?
• Can you please explain how you preserve the correlation structure between parameters while sampling parameters (section 3.2)?
• Can you please provide a table indicating the prior distribution of different parameters and the parameters of prior distributions?
• Can you please comment on the sensitivity of the parameters sampled using the MCMC approach?
• Is there any reason why you selected gaussian distribution (section 3.3.2)? Have you performed any goodness of fit tests?
• The authors have used RMSE as a constraint to reject ensemble members. Is it possible to use correlation as a metric to select ensemble members? Different metrics target different errors, and restricting it to a single metric might lose some information.