Dear Dr Zemp,

Thank you very much for the revised manuscript and responses to reviewers. The manuscript presents interesting work, but I found that the revised manuscript is still hard to read and has quite a few errors and typos. The organisation of figures and appendices also needs a bit work to make thing easier for readers. Specific comments are given below.

1) Figures: I understand you probably intend to keep current Figs 4 and 5 close to Figs. 6-8 and B1-B3, but it doesn't necessarily help readers to understand the material. It is also unusual to talk about Figs. 4 and 5 in the very beginning when Figs. 1-3 are not mentioned/discussed yet. Please consider rearranging figures as the following:
* change old Fig. 4 to Fig. 1 (please consider drawing/defining boundaries of the Amazon basin and the La Plata basin in old Fig. 4, because these two basins are discussed in the very beginning)
* change old Fig. 5 to Fig. 2
* combine old Fig. 1 and 3 to Fig. 3 (it is possible to describe the concept in old Fig. 3 using the old Fig. 1; also in the old Fig.3, it doesn't make sense to explain m12 when no arrow represents m12.)
* change old Fig. 2 to Fig. 4
* combine old Fig. 6 and B1 to Fig. 5
* combine old Fig. 7 and B2 to Fig. 6
* change old Fig. 8 to Fig. 7
* change old Fig. B3 to Fig. 8
* change old Fig. B4 to Fig. 9

Appendix

2) When the text refers to Appendix very often, it probably means that the content in Appendix should be included in the main text. I suggest that at least for the short appendix (e.g., C1.1), the content can be incorporated into the main text.

3) Appendix C1.3 - "Sect. A1 and A2.1 " is mentioned, but there are no such sections. It is leftover from the previous version. Please correct it.

4) Appendix C2 - remove "(see Fig. B1)". (Throughout the manuscript, "see Fig." is often used, but the connection and key points are unclear.) Also, Page 15, line 1020, do you really mean Ej-> omega, or should it be Ei-> omega?

5) Appendix C2 - This appendix is referred on Page 5, Line 459, when talking about delta_Pc and delta_Ec. Therefore, it would make much more sense to start Appendix C2 from Eq. (C12a) and (C12b); in other words, using an "inverse" order of those equations will help the flow of this section.

6) Appendix C3.1 - I understand that the Middleman motif involves triangles; that's probably why the weights involve "the three arrows". While this motif represents "an intermediary on an alternative pathway to the direct transport..." (page 6, Line 495), shouldn't the weight be counted only when it involves the "midpoint", i.e., in and out grid cell i (two arrows rather than three)?

7) Appendix C3.1 - I don't understand what it means from Line 1053 to 1055; N is also not defined, although one can guess when reading Appendix C3.3.

8) Appendix C3.2 - I suggest replacing "t" with other variables so readers won't get confused with t in Eq. (C13). Also, Line 1064- do you mean to refer to Fig. B1 or Fig. C2?

9) Appendix C3.2 - "W_134 and "W_1234" in Fig. C2 captions don't make sense to me, and they are not consistent with Eq. (C16) either. Please double check.

10) Appendix C3.2 - Line 1096, in equation, it should be w_i, t1, not w_1, t1. Same typo in Line 1090.

11) Appendix C3.3 - B is defined as a fraction; I expect it ranges from 0 to 1 (as shown in Fig. B4). Therefore, the upper bound mentioned in Line 1114 doesn't make sense to me. Could the authors please explain it? Also, it is not clear to me why "weights" need in calculations of B and how the weights work here. Could the authors please elaborate on it?

The rest of the manuscript

12) Author contribution on page 19: I am not sure why it is needed. Please delete it.

13) Page 3, Line 259-260: please double check the sentence.

14) Could the authors please give a bit more specific definition about "the network"? Does the network include both continental and oceanic grid cells?

15) Page 6, Line 520: Could the authors please comment the contribution of motifs formed by three or more grid cells?

16) Table 2: Please add (%) in the last column heading.

17) Figs. 8 and B3: Please use different colours for the two different basins.

18) Fig. B1. Please double check the caption (delta_E_c/ E part). Also, the maximum ratio within the blue boundaries is only 35%, far below 80% as mentioned in the caption. Could the authors please clarify it?