The Author are expected to heavily revise the manuscript before it can be further considered for publication.
I recommend them to carefully consider all the comments raised by the reviewers after a very good and accurate work.
In the replies to the reviewers' comments, the Authors often recall the main focuses of the paper: 1) how to include, in the most effective way, the available data as simulation conditioning, and 2) how to build a TI that is capable to reproduce the geological features which are expected to appear in the realizations. This is probably considered to be not sufficient and quantitative assessment of the results should be seriously considered.

The two Referees gave opposite assessments of the manuscript (accept vs. very major revision) and therefore I read it again very carefully. Also, I deeply reconsidered the comments to the original submission. After this examination, I agree with Referee #1, and I stress that some of his comments were raised also by other Referees during the first stage of the manuscript assessment and found limited answer in the revised manuscript. Therefore, the acceptance of the paper for publication requires that the manuscript's revision properly and fully complies with the Referee's comments. I expect that the Authors' efforts will yield a revised version which enhances the paper quality.

The paper has been improved during the revisions, but I agree with the basic complaints from one of the Referees and therefore I think that the Authors can provide a final revision, which properly accounts for those comments.

In their answer to one of the comments by Reviewer #2, the Authors claim that "This paper is about: (i) the development of a methodological framework...". However, such a methodological framework is not clearly described and discussed. They added some sentences in the introductory section, where the proposed methodology is sketched in a couple of paragraphs (from page 2, line 30, to page 3, line 13). The rest of the paper is strictly related to the specific test, apart from some methodological aspects which are somehow hidden in section "5 Defining MPS input information".
My basic suggestion to the Authors is to rewrite those sentences and to add a section, immediately after "1 Introduction", specifically devoted to the clear and thorough description of the methodological framework. This section should include all the methodological material about the proposed approach which is of general validity and not strictly related to the specific example.
Moreover, section "4 Establishing framework-model constraints" could be inserted as a sub-section in one of the other sections.
A final technical remark: in figures 11 and 19 the measurement units of the x-axes ("size of the sand bodies") are missing; meters, I suppose.

The paper has been revised and slightly reorganized by the Authors in such a way as to conform with the expected quality standard for publication on HESS.
In particular, the new section "2 Methodological framework" and the workflow in Figure 1 clarify the proposed method, which was originally hidden in the description of the specific case study, and will permit the reader to test the method with other data sets.
I provide below a few technical comments.
1) Page 2, lines 27 to 31. Substitute this paragraph, possibly with the following:
"In the present study, we describe a strategy to develop effective and realistic 3D TIs based on iterative modification of the TI images, so that general features of the unconstrained realizations meet the expected properties. Such an approach permits to analyse the coupled effects of the investigated TI and of the specific implementation of the MPS algorithm. Moreover, the tests performed in this paper show that few unconstrained realizations per tested TI are sufficient to obtain a correct assessment of the general features common to all the realizations."
2) Page 3, line 3. Substitute "the borehole" with "boreholes".
3) Page 4, lines 3 to 4. Susbtitute "in our way to proceed", possibly with "in this framework".
4) Page 4, line 6. Substitute "an initial TI attempt", possibly with "an initial tentative TI". Moreover, it is necessary (i) to give an idea of the procedure to be adopted for the iterative adjustment of the TI and/or (ii) to clarify if such an adjustment can be done in an objective way or with a trial-and-error approach.
5) Page 4, line 8. I suggest to erase the sentence in parentheses, because the effect that some modifications on the TI have on conditioned realizations, depends on the conditioning data, above all on their density, and therefore it would be necessary to explicitly state under which consditions this statement is correct.
6) Page 4, lines 10 to 11. Please, rephrase the sentence "For example,... sand bodies", possibly as "For example, in the present article, updates were based on the size, elongation, and compactness of the resulting sand bodies and on the visual analysis of a single realization per considered TI."
7) Page 4, line 12. Please rephrase "visible to the modeller building the TI and studying the realizations".
8) Page 4, lines 15 and 16; page 5, line 9; page 7, lines 1 and 3; page 8, line 26; page 11, line 23; page 12, line 4; page 16, lines 14, 29 and 31. Substitute "borehole", possibly with "borehole data", "borehole logs", etc.
9) Page 4, line 19. Is "adjoining" the right word?
10) Page 4, line 25. Erase "of".
11) Page 5, line 3. Add "at large scale" after "are spatially varying", or provide a similar modification.