I’ve now read the two reviews and the responses to these. For the most part, I am happy with the responses of the authors and think this is close to being ready to proceed to ESURF. The main component that I think still needs work is the sensitivity analysis. Both reviewers asked for this, and the authors responded by adding a section that shows the influence of single parameter values with all else held constant. I think this is work in the right direction, but more could be done to explain to readers how confident the authors are in the result. I suggest adding a few more sentences about how uncertain the input parameters are (temperature, precipitation and erosion) and how changing these parameters within the limits of their uncertainty modifies the results. This is more work, but I do hope that the authors have the model running and wiggling the parameters will not represent a major challenge. Doing this will give readers more confidence that the authors have correctly identified the mechanism for generating the observed pattern of terraces.
Lined comments:
Page 2 line 7: “Dominant control on escarpment rivers”: this is awkward phrasing. I would say dominant control on the geometry of these rivers, or on the incision of such rivers.
Page 2, line 12: Reference should be italic. Also, say “Since chemical weathering”.
Page 3, line 28: Ending with “point of view” is slightly awkward .Consider rephrasing.
Page 4: Line 17 and thereafter: The mentions of the parameters in the text should have the same format as in the equations, so on this line the parameters need to be italic and have their subscripts. Check throughout to make sure there are no other typos of this kind.
Page 4, line 23: The Heimsath 1997 paper is from a landscape in northern California that is not that similar to the landscapes studied here. Arjun has calculated this scalar in a number of places and I suggest adding a sentence to explain the range of these values and why you selected the one that you did. I also think in the discussion you should mention that this number can change as a function of climate change. If it is relatively easy to run the transport model, I would also suggest doing a sensitivity check of this parameter (I suspect it has only a small effect but it might be nice to demonstrate).
Page 5, section 3.1. I think this needs a bit of work. First of all, the caption to figure 5 could include some more detail. It should explain that the curves show the predicted soil thicknesses if only the listed variables change. Secondly, this plot doesn’t really tell us how certain the authors are of the predicted soil thicknesses. I think there should be a second plot that shows how the predicted curve will vary based on the maximum and minimum values of reconstructed precipitation and temperature. Also, I would mention on line 5 where the temperature effect comes from (that is, restate that it affects the maximum soil production rate).
Page 5, line 29: A citation is needed here for the modern precipitation rate.
Page 6, line 3: “Steady state is unclear in this context: if the denudation rate is increasing, how can things be steady state? Please explain.
Page 6, lines 15-16: The authors are running long term models but the variability of precipitation is from a 20 year dataset. The authors should mention how much precipitation rates are likely to have changed in the past.
Page 7, line 2: I would use the word “homogenous” rather than “invariable”.
Page 7, line 16: The authors say equation 5 is fit to the Rio Pisco, but what was fit? They then say that the b exponent is “usually” 0.5. Was 0.5 used here or was that parameter fit to field observations?
Page 10 line 4: It is not clear what distinction the authors are trying to make here. Are we supposed to understand there is some different sediment in the bedload compared to the total bedload? Are the CRN concentrations different in the bedload and in the terraces? A few extra sentences of explanation would be useful here.
Page 10 line 5: typo delete “if”.
Page 11, line 1: It seems, based on the discussion below, that the soil response time has been calculated so I think it would be better if the response time is stated explicitly here.
Figure 2: I suggest adding a sentence of explanation for the erosion rate curve in panel d.
Figure 6: An extra sentence or two of explanation for panels e and f are needed.

S. Mudd

I thank the authors for careful attention to my comments. Hopefully they agree that the extra work I requested improved the manuscript. I think this is now ready for publication. There are a few minor formatting problems in the new text on page 17 of the document with tracked changes (no superscript on mm ky-1, no space between 25 and kyr), but the typesetters will catch these. Otherwise I think it is a very nice contribution to ESURF.

I am happy to accept the manuscript for publication. During the final production stage please change the time unit from 'yr' to 'a' (respectively ka, Ma,...)