The manuscript by Anan et al. is a useful addition to the literature, clearly laying out the issues of model uncertainty and the relatively sparse data available to compare to those models. The methodology used has been used before, by the authors, to reconstruct LGM conditions. Here they apply the same methodology to the mid Piacenzian (Pliocene).

The paper is a useful example of the methodology and poses questions that should be followed up by those looking at Pliocene and other deep-time climates. There are a number of minor issues, enumerated below, that detract from the overall message. If one is going to compare different proxy data sets, an attempt should be made to use as close to apples vs apples as one can get. A comparison of the PlioVAR and PRISM allkenone compilations, which use basically the same data, would be more informative if the same resolution was chosen. Instead of comparing the data from ± 10 kya windows around 3.205 Ma, a comparison was made using ±10 kya for one data set and ±15 kya for the other. This may not make much difference but could have been avoided. 

Figure 4 shows anomaly maps for (a) PRISM4, (b) PlioVAR Mg/Ca and (c) PlioVAR ALL. It would be helpful to see a plot of PlioVAR Uk37 for comparison (I think this is Figure 1 (b)). Having it side by side as part of Figure 4 would make visual comparison of the different data sets more productive. The differences between PlioVAR Uk37 and PRISM4 are minor, and both show marked differences compared to PlioVAR Mg/Ca. This isn't a surprise and is nicely documented quantitatively, but seeing adjacent images would help.

The conclusion that the models may be underestimating polar amplification isn't much of a surprise to the community, but it is useful to document it as the authors have. Likewise, much is made of the mismatch between Mg/Ca and alkenone based SST estimates. This is nothing new, having been discussed in more detail in countless previous papers. 

References need to be double checked. Many are missing .doi or web addresses, punctuation, etc. 

Individual notes:

Page 4, line 2:

This appears to be a simple misunderstanding, but Bragg (2014) could not have used PRISM4 data since those data were not available prior to 2016 and SST estimates shown in  Foley and Dowsett (referred to here as PRISM4), were not produced until 2019.

Page 4, lines 18-19:

Why use the PRISM4 community sourced verification data with a 30K window to compare to PLIOVAR's 20K window when PRISM also, in the same release, produced a version with a ±10K window?

Page 4, lines 28-29:

The PlioVAR interval is slightly narrower only due to your choice of the 30 kyr window rather than the identical 20 kyr window provided in Foley and Dowsett (2019).

Page 5, lines 26-27:

You should probably cite a couple of the many available references that previously documented differences between Mg/Ca and alkenone based SST estimates in Pliocene and Pleistocene sequences.  

Page 5, lines 30-34:

This is an interesting point and it would be helpful if it was addressed in this paper. Foley and Dowsett (2019) is a compilation of previously published alkenone data and it would be useful to know whether the sites not in common with PlioVAR are from a particular region, particular lab, etc. 

Page 7, lines 33-35:

As in one of the comments above, comparing alkenone and Mg/Ca based SST estimates is like apples and oranges. They are measuring different things and while both are calibrated to mean annual SST, the literature is ripe with examples of the two providing discordant estimates. On page 8 of this manuscript you indicate some possible reasons for Mg/Ca data being less reliable, the same reasons that have been stated by many authors in the past. Maybe move those up to page 7 and provide citations to earlier works?

Page 9, line 17:

I think you just made a simple typo with the citations. If you are referring to the PRISM4 compilation you must mean Haywood et al. 2020 (not 2010).   

References

Foley and Dowsett 2019 needs a doi. (also needs spelling, checked etc.)

Huang et al. 2017 needs a doi.  (https://doi.org/10.1175/JCLI-D-16-0836.1)

Müller et al. 1998 needs a doi. (10.1016/S0016-7037(98)00097-0 )

Salzmann et al. 2013 needs a doi. (10.1038/nclimate2008)

Sherwood et al. 2020 needs a doi.