Review of Yan et al.

I have read the manuscript, “Hybrid data-model-based mapping of soil thickness in a mountainous watershed” by Yan and colleagues. The authors present a new approach to predicting soil thickness that utilizes the strengths of both numerical and empirical relationships within a portion of the East River, CO watershed. The new data presented here are 78 auger and 54 CPT measurements for 78 locations across two aspects. Their work produces a high-resolution (0.5 m) map of soil thickness, production rates, and transport rates for the two dominate aspects. I found this paper a pleasure to read. I thought it was interesting and provided a creative approach for predicting soil thickness where other approaches have limitations. This document is well written and has a logical flow that is easy to follow; however there are sections that could use more clarification to strengthen the approach and conclusions. Overall, the work was of good quality and falls within the scope of Earth Surface Dynamics target audience. Below I have provided a brief list of major and minor comments to the manuscript. In addition I have submitted a PDF with a more complete and thorough in-text comments.

Major Comments:

Methods clarity- Though I generally understood how your models work, it was difficult to follow the step-by-step methods (i.e., when each variable/equation is used).  Could you more explicitly describe what equations (EQ1-10) and all the necessary variables (7) that the reader would need to use in your approach? At the present, I cannot tell if you calculate your 7 variables using OAT or your model, or if they already have been determine in a past study. Please clarify. Lastly, I would recommend making a diagram in the supplementary information that highlights the workflow and points to the exact equations and variables that are mentioned within the text.

Smoothing and resampling grid size- The different methods for smoothing the landscape is interesting but it’s still unclear if it’s extremely important for your study and possibly removes the focus away from the main findings. Curvature can be calculated at any resolution but what I am gathering from Sections 2.3 and 4.1 is that the authors want the highest resolution with the lowest RMSD, hence why they selected there smoothing over time approach. To my knowledge, I have not seen any studies which smooth elevation data using diffusion equations and since the authors did not mention any previous studies, I am assuming this is new. If it is not, please provide some references. I do have some concerns with this smoothing approach:

• The smoothing of the DEM uses a linear sediment transport equation when in your hybrid model you utilize non-linear sediment transport (EQ2). If the East River watershed is govern by non-linear sediment transport than your current smoothing equation is inappropriate. Could you provide your reasoning for selecting this equation?
• What values of soil diffusion coefficient (K) and time-steps are you using? I see that your model calculated K value but this happens after the original smoothing occurred. Could you clarify?
• Though this approach is interesting, I believe it would introduce more uncertainty and unnecessary complexity into your elevation data. For instance, if you were to propagate the error with every time-step (error in original DEM and K) the uncertainty would be much larger than if you were to resample or use a smoothing window. If you were to propagate the error in all your smoothing methods and provide that uncertainty with your Figure 2, it may highlight a more appropriate smoothing method and resolution.

Sensitivity analysis- I have read through Section 2.4 and Results 4.2 several times, but I am still having a difficult time wrapping my head around the 7 variables, associated uncertainties, and subsequent sensitivity. Below are my two major questions. More clarification would be greatly appreciated. Lastly, it would benefit the general audience who may not have much expertise in the OAT method (such as myself) to provide a brief explanation on how to interpret Figure 3.

• Did you personally calculate values, acquire from prior studies, or did your model generate them?
• When you apply the OAT method to determine sensitivity, was this just for the 0.5 DEM smoothed with time?

Minor Comments:

Model comparison- You predict soil thickness through your hybrid approach and the random forest approach but why not compare it with the components of your model (i.e., just predicting soil thickness using the conservation of mass models and the Patton et al. method)? In the methods you nicely lay out their limitations but you could also demonstrate it. I am particularly interested in how your model will compare with the Patton et al. method because, like your model, it can determine soil thickness across the full topography. By adding a direct comparison you might be able to see additional pros and cons of the models. At the moment there are some clear benefits of your model and worth highlighting such as: you can account for the full landscape where the conservation of mass equations cannot, the Patton et al method is limited to a 5 m resolution, and your model can determine soil production and transport rates.

Model validation- I have no doubt that your hybrid approach is appropriate for other locations, given your reasonable results, but this has not been actually tested. A cross site comparison would be beneficial, specifically in sites that the Patton et al. approach is limited (watersheds with broad distributions of curvatures and avaible data) (i.e., Gordon Gulch, CO; Coos Bay, OR; Marshal Gulch, AZ). This would validate your models versatility and provide an additional comparison between the models.

Defining- Many of your symbols (i.e., E_thre) and specialized vocabulary (i.e., curvature) are missing definitions. Geomorphology is becoming increasingly interdisciplinary. Please insure you have clearly defined the words and the equations used. See PDF for in-text examples.

Figures- Overall, the figures are helpful to understand and progress the reader through the manuscript; however, minor edits will greatly benefit their readability. Please see comments in PDF for figure comments.

The study site appears to be the bottom and adjacent toe slopes of a valley that was glaciated in late Quaternary time. I write “appears to be” because I do not know the glacial geology of this region but merely note that large moraines are present elsewhere in the valley in Google Earth imagery. The equations of this paper are applicable to hillslopes dominated by soil production and colluvial and overland flow sediment transport processes and where an approximate balance between the erosion caused by those processes and rock uplift has been achieved. Glacial erosion and/or deposition is not considered, yet these are possibly the dominant processes in this study site.   

Indirect measurements of soil thickness can be useful in augmenting measurement of soil thickness in excavated soil pits, but it is inadvisable to use such methods in isolation. Augering and penetration methods are generally considered to be minimum values in rocky soils because the auger or penetrometer can be stopped by gravel. The study would be strengthened by reporting observations from soil pits at representative locations so that the nature of the soil-saprolite contact and the presence/absence of any glacial tills in the study site can be ascertained.

The authors state that the study site is in a soil-thickness steady state condition but Fig. S2 shows that this not to be the case. That figure shows the average soil thickness in a simulation increasingly steadily at the time (20 ky) when a steady state condition has purportedly been achieved. In stating that this figure demonstrates soil thickness steady state, I presume that the authors are referring to the fact that the rate of soil production is in decline. However, the rate of soil production is still far from zero and the rate of soil production for the simple case of a horizontal surface will result in a similar decline even as the soil thickness approaches infinity given sufficient time. Moreover, the average soil thickness should not be used to infer steady state because decreasing soil thickness in one area may be balanced out by increasing soil thickness elsewhere.        

The authors state (line 35) that the mass conservation method can return no finite soil thickness but this has not been demonstrated. Without such a demonstration application of the Patton method seems premature. If the model is applicable to the study site and correctly parameterized it should return a finite soil thickness value. Perhaps the model was unable to achieve such a steady state because the actual study site is not in steady state (e.g. recently glaciated) or because the authors used an inappropriate method for computing discharge by overland flow (d8 or steepest descent, as shown in Fig 1.)). In any case the paper would be strengthened by applying the model to the study site with appropriate assumptions first (see Pelletier et al., JGR, 2011 for examples of soil production and transport modeling without a steady state assumption) and then using the Patton method if and only if the model can be demonstrated to produce no adequate solution for any reasonable set of parameter values.

Some examples of unclear or incorrect methodology, incorrect units, parameter values that are very different from the literature, etc.: 1) please state how eqn. (7) was solved to determine h; this is the heart of the modeling and it is difficult to evaluate the paper without any mention of the solution method, 2) the drainage map in Fig. S1 suggests that D8 or steepest descent is used to determine sediment flux by overland flow; this method is incapable of modeling discharge by overland flow; D-infinity or another multiple flow direction routing algorithm must be used, 3) the h_0 value of 0.1-0.125 m is much smaller than other studies; h_0 typically ranges from 0.2-0.5 m, see papers by Heimsath et al.; 4) what is the relation of Bp to P_0? only P_0 appears in the equations yet only Bp appears in Fig. 3; if these are related by the bulk density ratio, as I would have thought, why is one larger on the n-facing side while the other is larger on the s-facing side? 5) values of alpha and beta are not reported, 6) the parameter a has incorrect units (must be L^2 since the product of a and curvature (units of 1/L) results in units of L).  7) In Fig. 7, what is the meaning of negative soil transport rate?