Thank-you for your revised manuscript. I am asking for a few minor revisions.

All three referees commented on the models producing features (especially a “hotspot in the Southern Ocean west of South America” – referee 1) where there are no fCO2 data. You really should respond to these comments in the final text – the comments will be public and readers will be able to judge your responses. I think you can look at the independent (input) variables: do these extrapolated fCO2 features correspond to features in one or more input variables? Especially important for confidence in the models: is the set of input variable values closely approximated somewhere else so that the model features where there is not fCO2 data are in fact constrained by fitted fCO2 data?

Page 2 equation (1). Referee 3 commented on your use of a single value of trend for all locations. You have partly answered this at the end of section 5 but you should relate the statements there to the referee’s question. “normalisation” does not make a clear link.

Page 2 equation (2) and dSST. I suspect that dSST is not described properly in the text. “difference between the monthly and annual means of SST” is not continuous, it means 12 discrete values, same values on January 1 and January 31 and different values on January 31 and February 1. But your response says you are avoiding this problem.

Section 4. Perhaps there should he sub-headings to make clearer that page 3 lines 20-25 are about SVM, page 4 lines 1-15 are about FNN and page 4 lines 16-25 are about SOM.

Appendix A3. I think the kernel function definition (A15) should come directly after A(9) where φ is introduced.

Equations (A12) and (A14). Somehow “c” seems to have been replaced by “α” but the relation between them is not stated.

Dear Authors
Thank-you for your revisions. Here follow just a few "technical corrections". In addition I expect that the copy editor will make some changes to the use of English, so after copy-editing you should check that the final version says what you intend.
Yours sincerely
John Huthnance

Page 4
Line 17. Usually "trial-and-error"
Line 19. "determined . ."

Page 5
Line 2. ". . goodness of fit by . ."
Line 30. ". . non-normalized . ."

Page 6 line 18 and reference Dee at al. 2011. I think you copied the reference from somewhere that indexed authors' affiliations with "a", "b", "c" etc. The last letter needs to be removed from the name of each author. Eg. the first author was "Dee", the third author was definitely Adrian Simmons etc.

Page 7 lines 13, 16. Better "over-fitting", "over-interpolation", "over-extrapolation"

Page 8 line 11. Better ". . is smaller than to all other . ."

Page 9
Lines 15, 19. In "w'" the "'" symbol should be as in (A6).
Line 24. Omit second "in".
Page 13 line 27. Omit "1" at end of "Le Quere".