|The authors answered to all my comment, and I thank them for taking them into account.|
I still have 3 minor and 1 major comments bellow.
= minor =
"More specifically, with only a few uncertain data, it is expected that the reconstruction based on our data assimilation method may show less variance than reconstructions provided by some other methods (as observed previously; e.g. Goosse et al. 2010). Nevertheless, we did not discuss much this point in the manuscript as it critically depends on the uncertainty of the input data, that is itself not well known. »
Can you add a short sentence on this point in the text, maybe in the discussion?
= minor =
In the text, at the end of Section 3.1:
« Considering all particles weights, we can compute a weighted average, providing a reconstruction for this time step. In this study, the ensemble members are derived from three climate model outputs: ECHAM5-MPI/OM (Sjolte et al., 2018), ECHAM5-wiso (Steiger et al., 2017) and iHadCM3 (Tindall et al., 2009; Holloway et al., 2016b). »
As models have already been presented with more details in Section 1.2, I suggest to change for something like:
« Considering all particles weights, we can compute a weighted average, providing a reconstruction for this time step. In this study, the ensemble members are derived from the three isotope-enabled climate model outputs ECHAM5-MPI/OM, ECHAM5-wiso and iHadCM3, presented at Section 1.2. »
= major =
« Throughout the text we mainly focused on the iHadCM3 model because, in contrast to the other isotope-enabled models (ECHAM5-wiso and ECHAM5/MPI-OM), iHadCM3 offers an ensemble of simulations, which is a significant advantage for data assimilation.
We added a few words on the reason of our choice at the end of the section 3.1.:
“Because iHadCM3 offers an ensemble of seven simulations, while the other isotope-enable models have only a single realization, we mainly focus on the iHadCM3 outputs in the manuscript. Dealing with an ensemble instead of a single simulation increases the probability of finding model results close to the assimilated records during the data assimilation process.” »
I computed the number of years by simulation:
ECHAM5-MPI/OM: 800–2000 = 1200 years
ECHAM5-wiso: 1871–2011 = 141 years
iHadCM3: seven x 1851-2003 = 7 x 153 years = 1071 years
If indeed ECHAM5-wiso gives a much lower number of particles than ECHAM5-MPI/OM and iHadCM3, you did not quantify how much the long simulation from ECHAM5-MPI/OM covers less internal variability than iHadCM3. I am not convinced it is necessarily true. The reason for which you chose to focus on iHadCM3 seems weak to me. One can wonder if it is related to the fact that iHadCM3 DA is the only reconstruction for which using both δ18O and SMB gives better results than δ18O alone for West Antarctica.
To answer to this comment, I suggest to include the results of the 3 models, or at least results of ECHAM5-MPI/OM together with iHadCM3, to draw your conclusions. I believe your results are robust, and the fact that it remains robust for the 3 models for East Antarctica and all-Antarctica is a strong assessment of it in my point of view (Table S4).
In particular I think Table S4 should replace Table 1 and be commented in the text, and Fig. 6 should be updated to include ECHAM5-MPI/OM.
= minor =
In Figure 7 vs. Fig. S11, the red shaded area show larger spread for iHadCM3 DA than for ECHAMwiso DA. This is logical as you show 1-sigma of model particles, and the number of particules is much lower in ECHAMwiso than in iHadCM3. But ideally the shaded area should reflect this, giving more uncertainty on reconstructions coming from ECHAMwiso, no? Can you compute a metric of the uncertainty of your DA reconstruction that decreases with increasing number of particle?