Dear reviewer, 

Thank you for your thorough review and insightful comments on my manuscript. I agree that the paper would greatly benefit from additional discussion on the sources and magnitude of uncertainty in modelling exercises like this. The large data availability for this study area provides a solid foundation for addressing many of the sources of uncertainty, including the ones that you listed. I will address these sources of uncertainties and their magnitudes in the Methods, Results and Discussion Sections, and add additional Sections on uncertainty propagation and limitations of the study to the Discussion, as suggested. I will also provide quantitative and statistical evaluations of model results and their uncertainties. 

I feel that by addressing these topics in separate Sections will provide the requested information, while also not obscuring the other messages of the paper, which are the novel method of inverse modelling with OSL dates and the comparison of erosion and deposition rates. 

I have addressed your individual comments below. 

With best regards,

Marijn van der Meij 

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This study presents an interesting approach to reconstruct long term erosion rates through the use of OSL-based deposition rates and a landscape evolution model and tries to prove its suitability for this purpose. However, the manuscript and the methodology in particular, are hard to understand as well as the comparison between simulated values and OSL-based estimates. Moreover, the conclusions are hard to justify given the numerous uncertainties and unknowns, and are not sufficiently supported, in particular in a quantitative way.

The analysis and discussion of the results are often mostly qualitative and lack statistical support (for example Lines 231-234, lines 252-253, lines 257-258, lines 276-277, lines 305-312). Incorporating statistical indicators and tables illustrating the fit between simulations and OSL/FRN-based estimations, would enhance the rigor of the findings. Furthermore, a shift towards quantitative evidence would strengthen statements and conclusions, particularly regarding the suitability of ChronoLorica for upscaling geochronological data. Especially given the numerous assumptions, unknowns and uncertainties involved in this study.

Response: Based on both reviews, I will extend the manuscript with a focus on the uncertainties that come with modelling exercises like these. I will include a scatterplot that will report the fit  and errors of the model calibration, and I will provide Tables that provide the individual sources of uncertainties and their magnitude and the modelled rates and their ranges. I will also perform a point-based evaluation of experimentally-based erosion rates and modelled erosion rates. These will be compared with the landscape-scale evaluations in the original manuscript to discuss at what scales these models provide useful results and how the model results can best be evaluated. 

In the Discussion of the uncertainties I will refer to previous studies addressing uncertainties in landscape evolution modelling, such as: (Perron and Fagherazzi, 2012; Hancock et al., 2016; Temme et al., 2017; Willgoose, 2018; Barnhart et al., 2019; Kwang and Parker, 2019; Gasparini et al., 2023). Based on the new version of the manuscript, I will rewrite the conclusions with a focus on the methodology and re-evaluate the current conclusions in the light of the quantified uncertainty. I aim that the manuscript is better understandable after revision based on both reviewers’ comments. 

Please further support and clarify this statement “The initial shape of the landscape and the land use history are well-constrained, enabling accurate simulations of the landscape evolution that incorporate uncertainties in the model inputs.” At the moment I don’t see how this is possible given the high uncertainty. This is a very important assumption so it would be necessary to further explain how this shape was reconstructed and how uncertain it is, rather than citing a reference.

Response: I will extend Section 2 (Study area) with more extensive descriptions of the reconstruction of initial topography and land-use history that has been done in earlier work. These descriptions are currently provided with limited detail in different parts of the manuscript. I will rephrase this statement to: “Previous work reconstructed pre-erosion topography and land-use history of the study area, including associated uncertainties. This enabled the assessment of how uncertainties from initial and boundary conditions propagate through the model simulations, ultimately providing robust estimates of landscape evolution, erosion rates and their quantified uncertainties.”

Section 3.2 requires a figure illustrating the vertical profile with different layers and corresponding periods, as well as OSL locations. Additionally, clarification is needed regarding the exclusion of samples from the ploughed layer, particularly whether it refers to the present ploughed layer and the rationale behind this exclusion and not past ploughed layers.

Response: I will add an overview of the five sampled profiles, with their layering and ages to Section 2, as that is part of previous work that I will elaborate on more (see previous comment). I will base that Figure on Figure 3 from Van der Meij et al.,  (2019, see Figure 1 below), where I will add the sampling depths, their ages and interpretation of young and old colluvium. The sample from the current plough layer was included in the calibration after all. I will remove the statement that that wasn’t the case from the manuscript.

Figure 1: Figure 3 from Van der Meij et al.,  (2019), that will be used to illustrate the sampling depths, their ages and the interpretation of the layering. 

Regarding Figure 5, it is really hard to visualize and to understand. The comparison between spatially averaged values (simulations) and point estimates (OSL and FRN) raises questions about representativeness of single point estimates and justification. It may be more meaningful to compare simulated values at specific locations corresponding to where OSL estimates were obtained. I think that it would help to have a table comparing simulations to OSL and FRN estimates for each period. Additionally, the complexity of Figure 5 could be addressed by clarifying the meaning of dashed and solid lines (legend says one thing and the figure caption the opposite) and adjusting the x-axis scale to improve visualization. Most of OSL estimates concentrate in the right part of the figure making it really hard to visualize this part of the graph. Also, you could consider to compare simulations vs OSL estimations using a scatter plot of the correlation between them.

Response: In the original manuscript I evaluated the catchment-averaged rates of the simulations to provide insights in the overall erosion or deposition rates. Point estimates are often taken from locations where the erosion or deposition is evident, such as fully eroded soils or thick colluvium, which could overestimate erosion and deposition rates for the entire catchment. This is also visible in Fig. 5, where the experimental data generally agree with the 95th percentile of rates instead of the mean. I will expand the model evaluation using point-based evaluation of the rates to test how the model performs on a specific location and add a Discussion on what scale (point or landscape) the model results can best be interpreted. This will also include a discussion of the reliability of the geochronological tracers used.

Figure 5 indeed contains a lot of information, which I tried to present as clear as possible. I will improve its readability by log transforming the X axis to better show the more recent rates. The line types are correctly stated in the legend, the caption is wrong. I will fix that as well. 

While the study enumerates some the uncertainty sources, it misses some very important ones that should be acknowledged and addressed:

1. OSL related uncertainties e.g.: biological soil mixing (termed bioturbation), mixing by tillage causes bleaching of particles already at their erosional locations…
2. OSL-based point estimates are considered representative of the whole catchment.
3. the exclusion of water erosion contribution over 5000 years
4. The study assumes that the southwestern part of the catchment didn’t contribute to the build-up of the colluvium in the central depression.
5. FRN (Pu and Cs) related uncertainties. (Parsons and Foster, 2011 https://doi.org/10.1016/j.earscirev.2011.06.004).
6. Unknown bulk density of eroded layers
7.  …

Given the multitude of uncertainties and assumptions, it would be necessary to include a dedicated "Limitations" section outlining these factors, discussing their potential impact on the results, and suggesting avenues for future research. This section would contribute to the transparency and robustness of the study's findings.

Response: I fully agree that there could be more sources of uncertainty in my modelling study and appreciate the suggestion to address these in dedicated Sections. I will elaborate on the previously included uncertainties (initial and boundary conditions) and expand this with the points you address above. In the Methodology, I will explain how these factors could be a source of uncertainty in this study and in what way their effects could be mitigated in the present study. In the Discussion, I will elaborate on how the remaining sources of uncertainty limit the modelling and how these could be addressed in future experimental and numerical studies. I will address the different sources mentioned above in the following ways:

1. The high intensity of tillage mixing produces well-bleached samples, especially under mechanized tillage. By calibrating on the mode of the age distributions, the tillage signal is targeted, while other signals in the age distributions, for example resulting from bioturbation are ignored. 
2. The colluvium in the center of the closed catchment contains all the sediments  eroded from the slopes, which means that the colluvium contains a complete geo-archive of landscape evolution of the study area and the geochronological tracers can be used to track this evolution. By working with OSL samples from five locations at different depths, we identified spatial differences in deposition history and rates, which further increased the representativeness of the OSL dates for tracing the complex landscape evolution. 
3. As indicated in Section 2.2, the current soil profiles indicate that tillage has been the main erosion process in the catchment. While water erosion likely also occurred, particularly when the fields were fallow, its impact was probably minor due to the short slopes and the absence of rills and gullies. Assessing the impact of water erosion with the OSL tracers used in this study is challenging, since the water sediments have been deposited in the same locations as the tillage sediments, towards the centre of the depression, and reworked after by tillage. I will elaborate on this in Section 2.2 and mark this as one of the limitations of the used methodology. 
4. This assumption is based on the relatively flat topography and mostly intact soil profiles, as mentioned in Section 2.1. If this area contributed substantially to historical erosion as well, that would have reduced the erosion rates on the rest of the hillslopes. I will address the consequences of this assumptions and its possible effects in the limitations Section.
5. I was not aware of these uncertainties, but I will include them in the Discussion of the rates, while considering the critique from Parsons and Foster  (2011), the response from Mabit et al. (2013) and the experimental design of the 137Cs study in Aldana Jague et al. (2016).
6. Thank you for pointing out bulk density here and in a following comment. I actually discovered a mistake there in the model set-up. Bulk densities measured in the field from different horizons of (eroded) Luvisols and a colluvisol have bulk densities of 1.72 ± 0.11 g cm-3 (Appendix of Van der Meij et al., 2017), while the pedotransfers from Tranter et al (2007), which are normally used in the Lorica model, predict bulk densities of 1.57 ± 0.04 g cm-3. The used bulk density of 1.5 g cm-3 was from a previous study with the model, which I forgot to correct for this study. I will re-run the calibration and model runs using a bulk density of 1.72 g cm-3, based on the field measurements, and support this number using the calculations provided here. I expect little differences in the model calibration and results, as the tillage erosion is calculated based on volume instead of mass (Eq. (1)). The main differences will be in the reported rates in t ha-1 a-1 in Fig. 5, and in the ktil which were calculated from the TIpot using the bulk density. The new values will actually be closer to the values reported by Öttl et al (2024).

The high level of uncertainty inherent in the study's results has significant implications for the conclusions drawn. Uncertainty introduces a degree of variability and ambiguity that can impact the reliability and generalizability of findings. In this context, the uncertainties associated with OSL-based estimates, landscape evolution modelling, and other factors may introduce limitations in the ability to make definitive conclusions about long-term erosion rates and landscape evolution dynamics and the suitability of ChronoLorica to reconstruct landscape evolution. The presence of uncertainty underscores the need for caution in interpreting the results and making conclusions.  and emphasizes the importance of considering alternative scenarios or sensitivity analyses to explore the range of possible outcomes. Moreover, it highlights the necessity for future research efforts to focus on reducing uncertainty through improved methodologies, data collection techniques, and model refinements. By acknowledging and addressing the implications of high uncertainty, the study can provide a more nuanced understanding of its findings and contribute to a more robust foundation for future research in this field.

I believe that this study would be more relevant if it would focus on the uncertainties (identifying them, discussing their potential impact on the results, which uncertainty sources are likely most influential and suggesting avenues for future research and to reduce these uncertainties) rather than on proving the ChronoLorica model as suitable or ideal to reconstruct long term erosion rates. This approach would enhance the relevance and significance of the study, providing valuable insights for the scientific community. I would also suggest a different title for this study, e.g. “Towards translating deposition rates into erosion rates with landscape evolution modelling” or “Enhancing Understanding and Addressing Uncertainties in Translating Deposition Rates to Erosion Rates with Landscape Evolution Modeling”

Response: I agree that the manuscript could benefit from a larger focus on the sources of uncertainty in such modelling exercises, especially because the data richness of the study area facilitates quantification of different sources of uncertainty in a real-world setting, where uncertainty propagation in landscape evolution models is usually assessed with numerical experiments (e.g., Perron and Fagherazzi, 2012; Kwang and Parker, 2019). However, I also believe that I present a very novel modelling approach to upscale depositional OSL age to the entire landscape, which also warrants attention in the manuscript. That is why I would like to expand the current manuscript with additional discussions on sources of uncertainties and model limitations, which should add a critical note, but not downgrade the rest of the manuscript. I will revise the Discussion, Conclusions and Title according to the added focus on uncertainties. 

Minor comments:

Lines 34-35: don’t understand this sentence

Response: With this sentence I want to indicate that cumulative historical anthropogenic erosion could explain a large share of the overall erosion in agricultural areas. I will rephrase it to: Historical anthropogenic erosion rates were significantly lower compared to modern-day rates, yet their cumulative impact over centuries of agricultural use may have contributed substantially to overall land degradation.

Lines 113-114: please add a reference to support this assumption and further explain this important assumption

Response: See my response to point 6 in the model assumptions above. 

Line 129: what is the meaning of j and J in this equation (1)?

Response: J is the number of lower lying neighbouring cells, and j is the iterator over these cells. These calculations are necessary for the diffusive distribution of tillage sediments over the lowerlying neighbouring cells. I will add this explanation to the manuscript. 

Equation 1: are the slope gradients considered the same as in present? Or in other words, do you assume that the slope gradients remain constant in time? Please clarify in the manuscript. Is the parameter p calibrated? Why? Please clarify in the text.

Response: The slope gradients change throughout the simulations, as the elevation map is updated in each calculation step based on the amount of erosion and deposition. The parameter p was set to 2, which was inherited from previous studies with Lorica, but not supported by literature (Temme and Vanwalleghem, 2016). In the new model runs, I will change the parameter to 1, which aligns with other models that simulate tillage as a diffusive process (e.g. Govers et al., 1994). I will clarify both points in the text.

Line 185: I think that you mean uncertainty analysis not sensitivity analysis.

Response: Correct. I will modify it in the manuscript. 

Lines 228-229: please add a reference to support this statement “tillage process smoothes…”

Response: I will add De Alba et al. (2004) as reference, who show with a conceptual and numerical model that tillage erodes local high spots and fills up low spots, creating a smoother topography. 

Lines 252-253: what ranges?

Response: With ranges I meant the orders of magnitude, but I will quantify this in the new version of the manuscript, including the errors of the calibration. 

Lines 261-264: these RMSE values should be first shown in the Results section

Response: I will report them in the Results. 

Line 284: “one main process”? why can we ignore the effect of water erosion? please further support this statement. When you refer to “independent data”, do you mean radionuclides-based estimations? Yes, independent but uncertain (Parsons and Foster, 2011 https://doi.org/10.1016/j.earscirev.2011.06.004). Please mention and consider this uncertainty in the study.

Response: See my response to points three and five in the list of uncertainty sources.

References

Aldana Jague, E., Sommer, M., Saby, N. P. A., Cornelis, J.-T., Van Wesemael, B., and Van Oost, K.: High resolution characterization of the soil organic carbon depth profile in a soil landscape affected by erosion, Soil and Tillage Research, 156, 185–193, https://doi.org/10.1016/j.still.2015.05.014, 2016.

Barnhart, K. R., Glade, R. C., Shobe, C. M., and Tucker, G. E.: Terrainbento 1.0: A Python package for multi-model analysis in long-term drainage basin evolution, Geoscientific Model Development, 12, 1267–1297, 2019.

De Alba, S., Lindstrom, M., Schumacher, T. E., and Malo, D. D.: Soil landscape evolution due to soil redistribution by tillage: a new conceptual model of soil catena evolution in agricultural landscapes, CATENA, 58, 77–100, https://doi.org/10.1016/j.catena.2003.12.004, 2004.

Gasparini, N. M., Barnhart, K. R., and Forte, A. M.: Short Communication: Motivation for standardizing and normalizing inter-model comparison of computational landscape evolution models, Physical: Landscape Evolution: modelling and field studies, https://doi.org/10.5194/esurf-2023-17, 2023.

Govers, G., Vandaele, K., Desmet, P., Poesen, J., and Bunte, K.: The role of tillage in soil redistribution on hillslopes, European Journal of Soil Science, 45, 469–478, https://doi.org/10.1111/j.1365-2389.1994.tb00532.x, 1994.

Hancock, G. R., Coulthard, T. J., and Lowry, J. B. C.: Predicting uncertainty in sediment transport and landscape evolution–the influence of initial surface conditions, Computers & geosciences, 90, 117–130, 2016.

Kwang, J. S. and Parker, G.: Extreme Memory of Initial Conditions in Numerical Landscape Evolution Models, Geophysical Research Letters, 46, 6563–6573, https://doi.org/10.1029/2019GL083305, 2019.

Mabit, L., Meusburger, K., Fulajtar, E., and Alewell, C.: The usefulness of 137Cs as a tracer for soil erosion assessment: A critical reply to Parsons and Foster (2011), Earth-Science Reviews, 127, 300–307, https://doi.org/10.1016/j.earscirev.2013.05.008, 2013.

Öttl, L. K., Wilken, F., Juřicová, A., Batista, P. V. G., and Fiener, P.: A millennium of arable land use – the long-term impact of tillage and water erosion on landscape-scale carbon dynamics, SOIL, 10, 281–305, https://doi.org/10.5194/soil-10-281-2024, 2024.

Parsons, A. J. and Foster, I. D. L.: What can we learn about soil erosion from the use of 137Cs?, Earth-Science Reviews, 108, 101–113, https://doi.org/10.1016/j.earscirev.2011.06.004, 2011.

Perron, J. T. and Fagherazzi, S.: The legacy of initial conditions in landscape evolution, Earth Surface Processes and Landforms, 37, 52–63, https://doi.org/10.1002/esp.2205, 2012.

Temme, A. J. A. M. and Vanwalleghem, T.: LORICA – A new model for linking landscape and soil profile evolution: development and sensitivity analysis, Computers & Geosciences, 90, 131–143, https://doi.org/10.1016/j.cageo.2015.08.004, 2016.

Temme, A. J. A. M., Armitage, J., Attal, M., Gorp, W. van, Coulthard, T. J., and Schoorl, J. M.: Developing, choosing and using landscape evolution models to inform field-based landscape reconstruction studies, Earth Surface Processes and Landforms, 42, 2167–2183, https://doi.org/10.1002/esp.4162, 2017.

Tranter, G., Minasny, B., McBratney, A. B., Murphy, B., McKenzie, N. J., Grundy, M., and Brough, D.: Building and testing conceptual and empirical models for predicting soil bulk density, Soil Use and Management, 23, 437–443, https://doi.org/10.1111/j.1475-2743.2007.00092.x, 2007.

Van der Meij, W. M., Temme, A. J. A. M., Wallinga, J., Hierold, W., and Sommer, M.: Topography reconstruction of eroding landscapes–A case study from a hummocky ground moraine (CarboZALF-D), Geomorphology, 295, 758–772, https://doi.org/10.1016/j.geomorph.2017.08.015, 2017.

Van der Meij, W. M., Reimann, T., Vornehm, V. K., Temme, A. J. A. M., Wallinga, J., van Beek, R., and Sommer, M.: Reconstructing rates and patterns of colluvial soil redistribution in agrarian (hummocky) landscapes, Earth Surface Processes and Landforms, 44, 2408–2422, https://doi.org/10.1002/esp.4671, 2019.

Willgoose, G.: Principles of Soilscape and Landscape Evolution, University Press, Cambridge, 2018.

Dear reviewer, 

Thank you for the extensive review of my manuscript. While I appreciate the time and effort you have invested in this review, I have to disagree with your major comments. I will explain below.

In your review, you state that “The author claims that the OSL technique provides deposition rates, when this is not true, the technique directly gives the degree of mixing in the soil. The deposition or erosion rates in each soil profile are calculated from the burial age obtained with OSL techniques using models” and that therefore “the approach of the study based on depositional data calculated with the OSL technique and translating them into erosion is not correct”. I have to disagree here. OSL dating was originally developed for determining burial ages of sediment layers, from which deposition rates can be directly calculated by dividing the sampling depth by the burial age, no models needed. Only later on, with the development of single grain OSL dating, the technique became suitable for studying soil mixing (Rhodes, 2011). The studies that you cite indeed use OSL dating for tracing and modelling soil mixing, but use single-grain luminescence dating for this purpose. This requires a very different experimental design, and serves a different purpose, than the study from which I used the OSL dates (Van der Meij et al., 2019). These samples were collected to measure burial ages and determine deposition rates instead of soil mixing rates. For this purpose, the samples were measured on small aliquots instead of single-grains. 

In the current manuscript, I determine hillslope erosion rates through inverse modelling. I calibrate the deposition process of the model on the OSL dates and infer the erosion rates based on the model simulations. This could be compared to the studies that you cite, that also rely on models to determine rates of soil transport, either vertical or lateral. The main difference is that my study is performed in a landscape with changing boundary conditions. This means that the landscape is not in steady state, which was a necessary assumption in all the studies that you cite. That is why I used a process model that can simulate landscape evolution in such transient landscapes (Van der Meij et al., 2023). 

Working in transient landscapes with spatially explicit models requires reconstructing the initial and boundary conditions, which introduces uncertainty. This uncertainty does not come from “insufficient OSL data”, but mainly from the initial and boundary conditions. These uncertainties have a large effect on the model outcomes, but they are realistic and necessary to report. It is important to note that large uncertainties are not unique to my study. The papers that you address also contain large uncertainties. For example, the very uncertain parameter estimates in Román-Sanchez et al. (2019) prohibit a reliable estimate to whether a profile is actually eroding or receiving sediments. Therefore, I have to disagree that  “The OSL technique is a precision study”, because working with OSL samples is inherently uncertain. Working with changing boundary conditions in transient landscapes adds to this uncertainty. 

Based on my response to your review here, and to the specific comments below, I believe that I have showed that the modelling approach is actually correct based on the available data and the transient landscape setting. The associated uncertainty is inherent to working with OSL dating and reconstructed initial and boundary conditions, and should therefore be included and presented as well. By revising the manuscript based on your and the other reviewer’s comments, I will improve its readability, making it easier to understand. I will explain the differences between my study and the previous modelling studies that you address in more detail, while also discussing the different sources of uncertainty, their magnitude and the limitations of the study in more detail.

With best regards,

Marijn van der Meij

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Translating deposition rates into erosion rates with landscape evolution modeling

This study attempts to calculate deposition rates based on OSL converted to erosion rates by inverse modeling with the ChronoLorica soil-landscape evolution model.

Main comment:

The OSL technique can give burial age and vertical mixing rates in a soil profile. The burial age can be used to calculate both vertical soil mixing, erosion and deposition rates using models and both transport equations in the same profile according to previous published studies (see below). Therefore, the approach of the study based on depositional data calculated with the OSL technique and translating them into erosion is not correct. Furthermore, a linear transect of soil profiles in which the erosion of upslope profiles could affect the deposition of downslope profiles is not examined, therefore, there is no certainty that the erosion produced in a profile coincides with the deposits. of another profile down the slope, since they are not linear transects. The orientation and slope of the studied profiles are also not presented. On the other hand, I am concerned about the great uncertainty in this study.  If there is already an error in the calculation of deposition rates, that error will be carried over and will be greater for the calculation of erosion rates. The OSL technique is a precision study and is used as a tracer to calculate the ratios of vertical mixing, erosion and deposition at the profile level (downscaling), but a spatially distributed calculation propagates the error on a large scale and to avoid this, it would be necessary of a greater distribution of profiles calculated with the OSL technique, which is difficult due to the costs of the OSL technique. Furthermore, OSL sampling must be done at various depths of each profile, a fact that has not been expressed by the author either.

for all that has been expressed in this review, the current approach of the manuscript, methodology and results cannot be published. The initial approach is not correct and there is a lack of precision in the model.

Moreover, through the manuscript, the text is difficult to understand, it is not clearly expressed in a way that is understandable to the reader.

Response: See my response above.

I will comment throughout the manuscript:

Abstract:

Line 10-11 The author claims that the OSL technique provides deposition rates, when this is not true, the technique directly gives the degree of mixing in the soil. The deposition or erosion rates in each soil profile are calculated from the burial age obtained with OSL techniques using models (see literature below).

Introduction:

Line 42 The author claims that radiocarbon or OSL provide deposition ratios, that is not correct. It provides information on grain mixing, and that result translates into burial age. Then, with burial age data and a model, you can get bioturbation, erosion and deposition ratios. There are previous studies calculating this.

Response: OSL dating and radiocarbon dating do actually provide deposition ages and deposition rates, see my response above. The literature that you cite are very specific studies designed for studying soil mixing using single-grain OSL dating. That’s a completely different research design for different objectives than the data that I’m working with.

More information:

Johnson MO, Mudd SM, Pillans B, Spooner NA, Keith Fifield L, Kirkby MJ, Gloor M. 2014. Quantifying the rate and depth dependence of bioturbation based on optically-stimulated luminescence (OSL) dates and meteoric 10Be: quantifying the rate and depth dependence of bioturbation. Earth Surface Processes and Landforms 39: 1188–1196. https://doi.org/10.1002/esp.3520.

Furbish DJ, Roering JJ, Almond P, Doane TH. 2018a. Soil particle transport and mixing near a hillslope crest: 1. Particle ages and residence times. Journal of Geophysical Research: Earth Surface 123: 1052–1077. https://doi.org/10.1029/2017JF004315

Furbish DJ, Roering JJ, Keen-Zebert A, Almond P, Doane TH, Schumer R. 2018b. Soil particle transport and mixing near a hillslope crest: 2. Cosmogenic nuclide and optically stimulated luminescence tracers. Journal of Geophysical Research: Earth Surface 123: 1078–1093. https://doi.org/10.1029/2017JF004316

A Román‐Sánchez, A Laguna, T Reimann, JV Giráldez, A Peña, T Vanwalleghem., Bioturbation and erosion rates along the soil–hillslope conveyor belt, part 2: Quantification using an analytical solution of the diffusion–advection equation. Earth Surf. Processes Landforms 44, 2066–2080 (2019).

Harrison J. Gray, Amanda Keen-Zebert, David J. Furbish, Gregory E. Tucker, Shannon A. Mahan, Depth-dependent soil mixing persists across climate zones, Proceedings of the National Academy of Sciences, 10.1073/pnas.1914140117, 117, 16, (8750-8756), (2020).

Line 58-59 Indeed, the author refers to uncertainty

Response: I’m not sure what you mean with this comment.

Line 65 Is the study area now in use as agricultural land? This is not clear here

Response: The study area was under agricultural use until it was taken into use as landscape laboratory. Now, only parts of the catchment are agriculturally cultivated. I will clarify this in the text.

Figure 1 How many OSL samples were taken and at what depth. To do an OSL sampling and for the result and reconstruction of the grain mixture to be reliable, it is necessary to take samples at different depths in each profile.

Response: Fig. 1 shows the five sampling locations. For each location, 5-8 samples were taken from different depths. This is stated in Section 3.2 and visible in Fig. 3, but I will clarify this in the study area description, including a Figure showing sampling depths, corresponding ages and interpretation of the stratigraphy. 

Methods

Line 117-119  This paragraph is not understood

Response: This paragraph explains that the three-dimensional model architecture makes it possible to simulate OSL ages at different depths in different soils. This makes it possible to compare measured OSL ages at different depths with the simulated ones. This is what I did in this study. I will rephrase this paragraph. 

Line 120-128 The approach shown by the author is quite confusing. On the one hand, the author poses the plowing process as 1 soil mixing and 2 erosion-deposit - linear diffusion.

The transport in case 2 is not only diffusion transport, there is a lateral transport.

Response: Tillage actually has these two effects. On the one hand, the mixing of the topsoil homogenizes these layers into a uniform plough layer. On the other hand, the ploughing triggers lateral soil movement, also called tillage erosion. This movement is modelled using a diffusion-type equation, where the soil transport is a function of the slope gradient (e.g. Govers et al., 1994). This lateral diffusive transport is different from vertical diffusive transport in the context of soil mixing. I will clarify this in the manuscript.  

Line 135-138 Stochastic process increases uncertainty, the exact method is not shown here

Response: Because the model works with a finite number of particles, a stochastic approach is required to determine whether a particle is transported from a layer together with the bulk sediment. I will add the equation that is used to determine the probability whether a particles is transported together with the transported mass of soil material: P_transport = sand transported [kg] / total sand present [kg]. Uncertainty is constrained by simulating a large number of particles per layer (~150). 

Line 141-144 To select an average of the soil properties is to increase the uncertainty.  The use of the OSL technique for this purpose loses accuracy when used at the landscape level.

Response: I had to take the average, because there is no detailed information on the spatial distribution of parent material properties available. The reported parent material properties are all near to the average values, suggesting that it is quite homogeneous (Appendix of Van der Meij et al., 2017). This part of the model set-up does not influence the experimental or simulated OSL technique. 

Figure 2, Line 165-181. As shown in the Figure 2 and text, indeed, all the processes represented in this manuscript have high uncertainty. Where is the uncertainty analysis? It is necessary to make a table and represent all the uncertainty of each process.

Response: The uncertainty is visualized in Fig. 5B, but I agree that it can be more visible. I will add a Table reporting the uncertainty contributions from initial and boundary conditions, as well as other sources of uncertainty. 

Results

Line 190-193 and Figure 3. This section is difficult to understand. The author is supposed to be calculating erosion-deposition ratios, why is he calibrating age? If the age is not simulated, the age is obtained from the OSL technique.

Response: The model simulates the redistribution of luminescence particles, which behave the same as quartz or feldspar particles in real landscapes. This means that they build up a luminescence age after transport and stabilization. For the model calibration, I compare these simulated ages with experimental OSL ages  from Van der Meij et al. (2019). Based on these deposition ages, which were used to calculate deposition rates, I can infer erosion rates on the hillslope through the inverse modelling. I will better reflect this in the manuscript and title, for example by rephrasing it to something like: “Translating deposition ages into erosion rates with landscape evolution modelling”.

Line 197-205 What are the tillage parameters? Once again, this text is quite confusing and lacks coherence in this section.

Response: The tillage parameters have been explained in the Methods section (Section 3.1.2, lines 125-129), and in Section 3.2 (Inverse modelling) I explain that these parameters have to be calibrated for the different land-use periods. This is also visualized in the workflow in Figure 2. I believe that this parameter has been explained well enough in the Methods Section, so that I can just report their calibrated values in the Results Section.

Line 218 “Erosion and deposition rates”

Response: I’m not sure what you mean with this comment. 

Line 222 What erosion and deposition ratios are obtained? the author says 1 cm per year but this value is not shown correctly in the graph (Figure 5).

Response: I will report minimum, maximum, mean and standard deviations of the rates for each period in a separate table, to better communicate the results of the study. The 1 cm per year refers to an extreme value, which actually is the peak in the orange line on the right side of the graph.

Figure 5:

Graph legend color does not display correctly "Total deposition"

Response: This is actually the same colour as the purple polygons in the graph. 

Also, in figure 5 the caption description does not correspond to the legend and figure "dashed and solid lines".

Response: The legend displays the right line types. I will modify this in the caption. 

The error of each experimental data (OSL, Pu) should be represented, otherwise it is not possible to evaluate the uncertainty from which we start.

Response: I will include the uncertainties associated with these experimental data. 

Why in this graph is Pu 239+240, 14C, 10Be also represented, if for comparison the author is supposed to use results from the OSL technique? It is quite confusing

Response: The OSL dates have been used to calibrate the model, so they are not independent data for the evaluation of the model. That is why I use additional independent data sources, such as ^239+240Pu, ¹³⁷Cs, ¹⁴C and ¹⁰Be, which are all available for the study area. This was already explained in Section 3.4 (Evaluation). 

This model has a large uncertainty in the Medieval, it does not fit the data. Uncertainty is also high in initial and boundary conditions

Response: Yes, as explained in the manuscript and throughout this review, the reconstructed initial and boundary conditions come with uncertainty. This uncertainty propagates into the model results, which is unavoidable when working with uncertain initial and boundary conditions. It is actually more transparent to report this uncertainty than to take averages or ignoring these sources of uncertainty. The high uncertainty in the period of 200-900 CE is due to the uncertain transition from ard plough to mouldboard plough. 

It is quite confusing and does not explain why there are so many OSL data in Figure 5A (triangle symbol) when in the experimental sampling there are only 5 (Figure 1).

Why there are so many OSL samples (triangles) accumulated close to 2000 years and the rest of the graph only approximately 9 between -3000 and 1500 years. This brings a large uncertainty over time between -3000 and 1500 years which makes the model unreliable.

Response: Figure 1 shows the locations of the dates cores and pits. Per location we took 5-8 samples, as explained in Section 3.2 and visible in Figure 3. Most of these dates are relatively young, because most colluvium was formed in recent times under mechanized agricultural use (~1800 CE to the present, Van der Meij et al., 2019). The numbers of datings per period were also reported in Section 3.2. As mentioned before, I will better introduce the datings and their ages in Chapter 2. I will log transform the X axis of Figure 5 to better visualize the more recent times, which indeed have a higher concentration of dating. 

The distribution of datings results from the presence of older and younger colluvial layers. The older colluvial layers are buried below the young colluvium and have a much smaller volume. Consequently, the number of older samples is lower than the number of younger samples. For more information on this, I refer to the original study (Van der Meij et al., 2019). In this study, I use these previously published OSL dates for a modelling exercise, and despite being a small study area, it already includes a substantial number of OSL samples (32 samples, 27 used in this study). The goal was to use previously published information, not gathering new data. The OSL dates from 3000 BCE to 1500 CE are well distributed over this period, so I would disagree that these bring “large uncertainty”. I would rather argue that the high number of samples in recent times reduces uncertainty in this period, because there is more information available. 

Discussion

The author includes in the discussion aspects that should be in the results, for example, line 268, 300,317, etc

Response: I will move these results to the Results section.

throughout the discussion, the author repeats and is aware of the large uncertainty in the model and repeats several comments on results that should be in the results section. This uncertainty is due to insufficient OSL data. In addition, as I indicated above, samples must be taken at different depths to have an accurate reconstruction. Furthermore, a linear transect of soil profiles in which the erosion of upslope profiles could affect the deposition of downslope profiles is not examined, therefore, there is no certainty that the erosion produced in a profile coincides with the deposits. of another profile down the slope, since they are not linear transects. Indeed, the author confirms that the deposition ratio cannot be used to calculate erosion.

Response: I have addressed most of these comments above. Regarding the linear transect of soil profiles, it doesn’t make sense to perform conventional OSL dating on hillslope deposits, as there are no depositional sediments to date. An approach used in Johnson et al. (2014) and Román-Sanchez et al (2019) would not work here, as the landscape is not in steady state. Also, these studies do not actually couple erosion and deposition profiles directly, but estimate erosion /deposition rates for individual landscape positions. By modelling landscape evolution with a process model, erosion and deposition locations are actually connected by the sediment flow. The model works with a  conservation of mass, so there is also a physical constraint.

Therefore, I would argue that a spatially distributed landscape evolution model actually better represents erosion and deposition processes, compared to the profile analyses in the referenced studies. Furthermore, the catchment is a closed depression, with a much larger hillslope area compared to the depositional area. A linear transect therefore does not represent direct coupling of erosion and deposition, as the hillslope sediments converge to the smaller depositional area. Because of this, the depositional sediments represent a large, wedge-shaped section of the hillslope, not only the linear transect above. Simulating erosion and deposition processes with a process model accounts for the differences in source area and sink area of the sediments. 

For all the above reasons, the model is neither accurate nor reliable and the manuscript lacks a correct approach as I have explained and, finally, the text is difficult to understand, it is not clearly expressed. Therefore, this manuscript in this form cannot be published.

References

Govers, G., Vandaele, K., Desmet, P., Poesen, J., and Bunte, K.: The role of tillage in soil redistribution on hillslopes, European Journal of Soil Science, 45, 469–478, https://doi.org/10.1111/j.1365-2389.1994.tb00532.x, 1994.

Johnson, M. O., Mudd, S. M., Pillans, B., Spooner, N. A., Keith Fifield, L., Kirkby, M. J., and Gloor, M.: Quantifying the rate and depth dependence of bioturbation based on optically-stimulated luminescence (OSL) dates and meteoric 10Be, Earth Surface Processes and Landforms, 39, 1188–1196, https://doi.org/10.1002/esp.3520, 2014.

Rhodes, E. J.: Optically Stimulated Luminescence Dating of Sediments over the Past 200,000 Years, Annu. Rev. Earth Planet. Sci., 39, 461–488, https://doi.org/10.1146/annurev-earth-040610-133425, 2011.

Román-Sánchez, A., Laguna, A., Reimann, T., Giraldez, J., Peña, A., and Vanwalleghem, T.: Bioturbation and erosion rates along the soil-hillslope conveyor belt, part 2: quantification using an analytical solution of the diffusion-advection equation, Earth Surface Processes and Landforms, 44, 2066–2080, https://doi.org/10.1002/esp.4626, 2019.

Van der Meij, W. M., Temme, A. J. A. M., Wallinga, J., Hierold, W., and Sommer, M.: Topography reconstruction of eroding landscapes–A case study from a hummocky ground moraine (CarboZALF-D), Geomorphology, 295, 758–772, https://doi.org/10.1016/j.geomorph.2017.08.015, 2017.

Van der Meij, W. M., Reimann, T., Vornehm, V. K., Temme, A. J. A. M., Wallinga, J., van Beek, R., and Sommer, M.: Reconstructing rates and patterns of colluvial soil redistribution in agrarian (hummocky) landscapes, Earth Surface Processes and Landforms, 44, 2408–2422, https://doi.org/10.1002/esp.4671, 2019.

Van der Meij, W. M., Temme, A. J. A. M., Binnie, S. A., and Reimann, T.: ChronoLorica: introduction of a soil–landscape evolution model combined with geochronometers, Geochronology, 5, 241–261, https://doi.org/10.5194/gchron-5-241-2023, 2023.