|Thank you for the opportunity to review this re-submission. The paper has been fundamentally re-written, and examines detailed records of grain size from 21 rivers along the Peruvian margin crossing about a 10° range of latitudes. This is a valuable set of data and the authors have worked hard to collect it. In their analyses, they use correlation coefficients to compare their sedimentological measurements with environmental parameters including seismicity, erosion rates, river discharge, and catchment slopes. They identify some ambiguous relationships, and suggest that the grain size exported by these catchments is controlled by both sediment supply processes and sediment transport processes, perhaps involving migrating gravel fronts. Unfortunately, this manuscript still has some major weaknesses. It oversells weak correlations that may themselves be inappropriate, and the interpretations and conclusions are still vague and unconvincing, and in some places contradictory.|
My review has three parts:
 Detailed comments for those sections of the paper where I think there are significant problems.
 Minor comments by line number.
 Some suggestions about different ways the authors could look at their data. It is clear that a great deal of time and effort has gone into collecting this valuable data set, and I would love to see it published. I’m trying to provide some constructive ways forward in case the authors find this helpful.
 Comments by section:
Tectonics and geological setting:
Section 1.1 provides some good information about the geological context, but more is needed. Firstly, I am confused about the boundaries of the tectonic domains. The authors describe a change in the degree of interseismic coupling between north and south, specifically with high coupling and high seismicity south of 13-16 °S, and low coupling and low seismicity to the north. The authors cite a paper by Nocquet et al. (2014), but this paper does not contain data as far south as 13-16 °S, and instead appears to place the gap in seismicity at 3-10 °S. Almost all of the catchments in this study area are south of 10 °S, so it needs to be clarified where this boundary is. I’m struggling to reconcile the data in Nocquet et al. (2014) with the statements in this section. This needs to be cleared up. Second, Fig. 3 shows a long-wavelength feature in the slope data (panel G), from 7 to 14 °S; what is this? It has quite a significant amplitude, with slopes almost doubling in the centre, but it isn’t discussed. This could be significant – see my later suggestions. Finally, what timescale do the historical earthquake records average over? Is this sufficient to compare with grain size data?
Section 4.1.2. “Absence of gravels in rivers between 15.6 °S and 13.7 °S:
I’m not convinced by the arguments in this section. The authors propose that this sub-group of catchments lack gravel bars potentially because they have been lengthened by tectonic deformation, which resulted in a pulse of uplift and enhanced erosion, and the gravel-sand transition simultaneously migrated upstream into the catchments. Do the authors expect the gravel-sand transition to migrate upstream in response to enhanced erosion? This seems counterintuitive to me, and also contradicts the interpretations they make about grain size correlating (weakly) with sediment flux (e.g., Fig. 5a). Also, Fig. 4 shows the fining rates are fairly low in this landscape, with D50 only decreasing by a few mm over >100 km. How far upstream do the authors propose the gravel-sand transition has migrated in order to supply only sand at their sampling location? How much have these catchments supposedly been lengthened? As it stands, this section raises more questions than it answers.
I recommend the authors take a look at Lamb, M.P. and Venditti, J.V., 2016, The grain size gap and abrupt gravel-sand transitions in rivers due to suspension fallout, Geophysical Research Letters, 43, doi: 10.1002/2016GL068713. This paper discusses gravel-sand transitions and suggests they arise because of changes in bed shear velocity (the wash load hypothesis). Are there any reasons why these catchments might have different bed shear velocities? Perhaps the framework in this paper can help the authors develop a more robust argument, if they do want to invoke gravel-sand transitions here. At the moment this section seems contradictory and unintuitive.
A more minor point: this argument is repeated all over again in section 4.1.3 from lines 318-323, and this repetition is not needed.
Section 4.1.4. “Supply control on the grain size pattern”.
This section overstates some of the results. Lines 329-331: “the positive correlation between the size of the D50 and the morphometry of these basins” – there is no correlation between D50 and slope, so do the authors mean with catchment area? This is still a weak correlation, so I think this statement is over-selling the relationship. Especially given the authors then claim “environmental factors exert a major control on the pattern of the D50 encountered for the rivers in western Peru”. These are weak correlations, not evidence for “major control”. Also lines 332-335: “it is very likely that the bulk supply of hillslope-derived sediment to the trunk stream increases with larger basin size, mean basin slope and basin-averaged denudation rate” – there seems to be no correlation between D50 and mean slope, so how can this explain the grain size patterns? The relationships that can be drawn from the data are being overstated.
Next, the sentence from lines 341-344 needs to be clearer. Are the authors suggesting that the catchments with coarser grain sizes experience El Niños and extreme rainfall events with a greater sensitivity than the catchments with finer grain sizes? I find this to be very unlikely, not to mention the lack of correlation between sediment flux, water discharge and any of the grain size percentiles.
Finally, the paragraph from lines 345-364 isn’t very clear either. My understanding is that the authors propose the coarser-grained catchments are experiencing a downstream shift in the position of gravel fronts, due to greater sediment supply from hillslope sources. However Fig. 5a shows that catchments can have a large D50 with either a very low sediment flux or a very high sediment flux (the full range), and Table 3 shows that no grain size percentiles correlate with catchment slopes. The authors imply that denudation rates act as a proxy for the amount of hillslope-derived sediment, but this isn’t necessarily the case. Furthermore, it might be that slopes act to perturb sediment flux (and grain size) above thresholds, e.g., some threshold angle for landslides and debris flows. In this case a simple correlation (like Table 3) might not reveal whether there is a threshold-controlled grain size response to hillslope processes, because below the threshold you wouldn’t even expect a correlation. More careful thinking is needed about the processes the authors are invoking to explain the grain size patterns.
Section 4.1.5. “Hydrological control on the grain size distribution”
Line 373-374. “grain sizes correlate with the shear stress values”. The relationships in Fig. 5b-c look quite tenuous to me. If you took away the one point with very large grain size the correlations might even become negative? I think the text is overselling the data here, and this section is unsatisfying because  the plots in Fig. 5 are not conclusive, and  because the previous section suggested that grain size is limited by hillslope sediment supply. It’s difficult to explain the data as both supply-limited and transport-limited at the same time. Also, the average particle size apparently isn’t correlated with either water discharge or shear stress, so I’m really not convinced at all that it’s possible to infer “a hydraulic control on grain size distribution of the Peruvian rivers” as the authors claim.
Section 4.2. “Transport distance and slope angle controls on sphericity”
Lines 394-398. Recycling particles from a terrace surely won’t make them more spherical, because while the particles are being stored they aren’t being abraded. Lines 405-406. The authors propose that in catchments with steeper slopes, denudation rates will be faster and transport distances will be shorter. Table 3 shows no correlation between slope and denudation rate (or sediment flux). This may be because slopes influence denudation rates non-linearly (see my earlier comment about the potential role of thresholds in this landscape), but either way this section seems to contradict the author’s use of correlations and their data. Furthermore, it is unclear to me how steeper slopes will reduce the transport distance of material. Residence time yes, but not distance.
 Minor comments:
Lines 75-81. This sentence is very long and needs to be broken up. It also sounds like the authors expect grain size to be limited by all different factors at once. If “grain size… reflects the ensemble of mechanisms at work”, then all of those mechanisms are limiting grain size together, e.g. the grain size characteristics are both supply-limited and transport-limited at the same time. The authors should think about whether this is really what they mean.
Line 92. Trujillo isn’t marked on the map. As was suggested in the first round of review, it would be helpful to refer to towns that are marked on the map.
Line 93. “…up to 100 km broad coastal forearc plain”. Is this 100 km wide? Long?
Line 120. “Andean” should be changed to “Andes”.
Line 140. As was pointed out in the first round of review, “strong precipitation rates” implies a high intensity of rainfall, which isn’t the same as a greater overall amount. Consider “high precipitation rates” instead.
Line 144. “to reach” should be “from reaching”.
Line 145-147. This sentence about ocean currents should be supported by a reference.
Line 148-149. Again, like in the first round of review, please be careful about equating El Niño with ENSO. El Niño is one state of the ENSO, but they’re not the same thing.
Line 161. “We will use” – I recommend sticking to one tense here, present is probably best. See also line 163, “sampling sites were situated” – use the present tense, because the sites are still there.
Lines 164-166. Again, see my point for lines 75-81, which also applies here. Do the authors expect grain size to record all environmental “conditions and forces” at the same time? Put another way, is grain size simultaneously supply-limited and transport-limited?
Line 187. Percentiles should be plural.
Line 204. The authors refer to a paper by Reber et al. (in press) – I still think it would be good to briefly say how much time the discharge records cover (1 year, 100 years? Which years, i.e. are they biased by El Niño?), and in general terms where the stations are (e.g., near the catchment mouths or higher up in the catchments, are they are in similar places in each catchment?). It doesn’t need to be a detailed account of every station, but very briefly the reader needs to know, in this paper, whether the data record a meaningful period of time and can be fairly compared between catchments. This only needs 1 or 2 sentences.
Lines 208-211. This sentence is really unclear. Sediment flux can indeed affect grain size fining rates, but why does this principle mean denudation rates are variable in this study area?
Line 232. “at 106 km river upstream” – this wording can be improved.
Line 233. “for the Pacific coast” should be “from the Pacific coast”.
Line 312. “Infer” means to deduce something, but here the authors are speculating. I would change to “expect” or something similar.
Line 313. “Increase *in* earthquake frequency”.
Line 399. The 2016-2017 winter was not really an El Niño. There were restricted temperature anomalies that are sometimes called a “coastal El Niño”, but this is not the same as an actual El Niño, e.g., the Niño 3.4 box showed neutral anomalies. The warm water only pooled around southern Ecuador and northern Peru.
Lines 421-427. This really isn’t “unravelled” in this paper. Wouldn’t flattening the fabric of a clast reduce the c-axis, which isn’t measured here? Either way, there’s no explanation for the lack of correlation between slope and sediment flux or denudation rate, which seems counterintuitive given that sediment flux should relate to the residence time of clasts. This is more a hypothesis than a conclusion.
Line 427-428. “the ensemble of erosional and sediment transport processes have reached an equilibrium at the scale of individual clasts”. It’s not clear what this actually means.
Lines 429-430. “the clast fabric of the channel fill has dynamically adjusted to water and sediment flux and their specific timescales”. This is also unclear. What timescales are being referred to here? What does it mean to say a “clast fabric has dynamically adjusted”?
Fig. 1. The latitude ticks are horizontal while the maps are actually rotated with respect to north, and I’m struggling to identify the latitudes of the catchments. The northernmost catchment looks to be around 9 °S on these maps, but plots at about 7 °S in Fig. 3. The coordinate system of the map could be clearer.
Fig. 1C. Around line 132 the authors describe a major N-S gradient in rainfall rates of ~1000 mm/yr. I can’t see evidence for this on the map, and the rainfall rates in the catchments look very uniform. If there is a major N-S gradient it’s hidden in the colour scale – consider using a different colour scheme that shows more variation between 0-1000 mm/yr. Also, the caption misspells “extent”.
Fig. 2. The figure caption has an open bracket.
Fig. 3. It’s unhelpful that the town names don’t match Fig. 1.
 General suggestions:
Here I am making some general suggestions to the authors, which they can take or leave as they like. I think a better way to interpret the grain size data would be to start with the D50 record in Fig. 3h and look at the spatial patterns. Most of the catchments have a uniform D50 of 2-3mm, and there are two places where there are peaks above this baseline. One is around 11-12 °S, and these catchments are the smaller ones between Lima and Huaraz that don’t seem to cross the western escarpment, while the others do. I suggested looking at this in my original review, and it still seems to me that this particular peak in grain size could be related to the catchments being shorter and steeper and not crossing the escarpment, but I’m not familiar enough with the area to develop this further. The authors should think about it, also because these catchments lie right in the centre of the long-wavelength feature visible in the slopes (Fig. 3g). If slopes are mediating grain size via a threshold effect, this could explain why the grain size peak is quite narrow and restricted to only the zone with the highest slopes and these shorter catchments in exactly this location.
The second peak is around 16-17 °S and coincides with a big spike in the mean annual water discharge. It could be that the correlation coefficients don’t show a relationship between grain size and water discharge because the authors are plotting loads of noise against itself (most of the catchments have a baseline discharge of 10-20 m3/s), but if they look across latitudes there seems to be an obvious response here. Where discharge jumps up to ~80 m3/s, D50 jumps up to ~6 mm.
Examining these two features in the grain size data would be a better way forward. They are similar in amplitude (D50 increasing by a factor of 2x to 3x, which is significant), but presumably result from different triggers – one to do with discharge (the zone where discharge spikes is where the rivers move coarser material), and the other potentially due to the catchments shortening, not crossing the escarpment, and having the greatest slopes. Both of these responses (to discharge and slopes) could be non-linear and involve thresholds, so the authors need to think about whether simple correlation coefficients are suitable for exploring this (I think not), and whether the relationships get obscured by just doing bulk correlations between all the other catchments as well, when actually the grain size responses are limited to just a few catchments.
If this is correct, then you have two cases where grain size is similarly perturbed (perhaps by thresholds), but as a result of very different perturbations. That’s important, because many studies use grain size perturbations to infer climatic/tectonic forcings, but this would suggest both can have similar effects in the sedimentary record that might be difficult to tell apart. Furthermore, the positions of these grain size peaks make sense, suggesting that this is a robust data set that has been measured with great care in the field. The authors have done a great job putting the data set together, now they need to write a paper that does all their hard work justice.