the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Optimising global landscape evolution models with 10Be
Gregory Ruetenik
John D. Jansen
Pedro Val
Lotta Ylä-Mella
Abstract. By simulating erosion and deposition, landscape evolution models offer powerful insights to Earth surface processes and dynamics. These models are typically constructed from parameters describing drainage area (m), slope (n), substrate erodibility (K), hillslope diffusion (D), and a critical drainage area (Ac) that signifies the downslope transition from hillslope diffusion to advective fluvial processes. In spite of the widespread success of such models, the parameter values have high degrees of uncertainty mainly because the advection and diffusion equations amalgamate physical processes and material properties that span widely differing spatial and temporal scales. Here, we use a global catalogue of catchment-averaged cosmogenic 10Be-derived erosion (denudation) rates with the aim to optimise a set of landscape evolution models via a Monte Carlo based parameter search. We consider three model scenarios: advection-only, diffusion-only, and an advection-diffusion hybrid. In each case, we search for a parameter set that best approximates erosion rates at the global scale, and we directly compare erosion rates from the modelled scenarios with those derived from 10Be data. Optimised ranges can be defined for many LEM parameters at the global scale. In the absence of diffusion, n ~ 1.3, and with increasing diffusivity the optimal n increases linearly to a global maximum of n ~ 2. Meanwhile we find that the diffusion-only model somewhat outperforms the advection-only model and is optimised when concavity is raised to a power of 2. With these examples, we suggest that our approach provides baseline parameter estimates for large-scale studies spanning long timescales and diverse landscape properties. Moreover, our direct comparison of model-predicted versus observed erosion rates is preferable to methods that rely upon catchment-scale averaging or amalgamation of topographic metrics. We also seek to optimise K and D parameters in landscape evolution models with respect to precipitation and substrate lithology. These optimised models allow us to effectively control for topography and target specifically the relationship between erosion rate and precipitation. All models suggest a positive correlation between K or D and precipitation > 1500 mm yr–1, plus a local maximum at ~ 300 mm yr–1, which is compatible with the long-standing hypothesis that semi-arid environments are among the most erodible.
- Preprint
(3944 KB) -
Supplement
(240 KB) - BibTeX
- EndNote
Gregory Ruetenik et al.
Status: final response (author comments only)
-
RC1: 'Comment on esurf-2022-54', Richard Ott, 23 Nov 2022
This study by Ruetenik et al. investigates parameters of diffusion and advection models for landscape evolution, based on a global compilation of CRN erosion rates. The authors use CRN data to optimize parameters in their landscape evolution models and investigate the distribution of parameters in respect to the different models, as well as environmental variables of precipitation and lithology. The authors advertise their method as a way to more objectively select parameter values for landscape evolution models (LEMs). I believe this study is of great interest for the geomorphological community and is generally suitable for Esurf. The parameter optimization results will be of value to justify model parameter selection and offer insights into the processes driving landscape evolution. Furthermore, the dependencies of coefficients on climate and lithology have been widely discussed, and this paper offers some valuable insights here. However, I have several points concern that should be addressed before publication.
The current approach incorporates catchments with a huge variation in drainage area. This may lead to a lot of different biases, which arise from the CRN erosion rate assumptions. I would like to see, how the results look like if you only use 10-1000km² catchments, or similar. Small catchments are prone to biases of sudden sediment input or anthropogenic disturbance. Large catchments (> 500km²) typically violate the uniform quartz fertility and sediment contribution assumptions, as well as having a negligible transport time without nuclide buildup. Also, production rate uncertainties grow significantly for large catchments due to the before mentioned reasons. I understand that this will substantially decrease the quantity of data points, but might on the other hand substantially increase the data quality.
No smoothing of the landscape is mentioned. Flow paths from DEMs especially in valley bottoms tend to have large errors. These errors typically lead to a lot of slope values = 0 and a bunch of very high values (Schwanghart and Scherler, 2017). This would bias the predicted erosion rates, if no smoothing is applied before running the LEM. I hope this was addressed and not mentioned, otherwise smoothing should be applied to the flow paths and the method described.
I like the interpretation put forward to explain the variation in coefficients with precipitation (MAP). However, without further analysis this should be stated as speculation and probably reduced in text. The problem I see is that variations in lithology with MAP are not accounted for. This means that if the catchment lithologies are not homogeneously distributed among climate zones, which can happen easily due to the high clustering of CRN measurements in certain regions, one could get significant biases. Either an analysis of MAP values with respect to the lithologies would need to be added, to show that the distribution is homogeneous, or this caveat needs to be clearly acknowledged.
Line 10-12: It should be mentioned that many LEMs simulate erosion processes with the Stream Power Incision Model (SPIM) and therefore need these parameters as input. It should not necessarily be assumed that all LEMs run this way, because there are also transport-limited or combined approaches.
Line 22: Somewhat outperforms? Please, be specific.
Line 73: Denudation is more correct than erosion in most cases. However, if you were to be strict, neither of the two terms would be correct (e.g. due to mass loss below the attenuation length of cosmogenic nuclides). The best strategy could be to have a very brief definition of what is meant by denudation or erosion, describe why a certain term is used, and then be consistent, and also remove the parenthesis in the abstract.
Line 79-81: This is more of a comment. It makes me slightly uncomfortable that two of the main assumptions are being highlighted here, for reasons that are not apparent to me, and other important assumptions (quartz fertility, uniform contribution of stream sediment proportionally to local denudation rate and area) are being folded away into the next sentence.
Line 107: There are more processes that can affect the value of n. For instance, incision process (Whipple et al., 2000), but also other flow resistance parameters, or other processes creating incision thresholds (Lague et al., 2005).
Line 155: Not sure it matters for the general outcome of the study, but SRTM30 vertical errors are many times higher than for COP30. I think the whole community should move away from using SRTM data.
Line 161-164: I think it would be more beneficial if you could make this comparison with COP30 and COP90 data, or simply use those.
Line 165: In general, very small catchments (< 10 km²) will be more prone to disturbances by recent mass wasting (Yanites et al., 2009). It might be worth checking how/if results change if you include those catchments.
Line 190: Please list the used likelihood function as an equation. As a reader, I do not want to look it up in a separate paper.
Are uncertainties of observed erosion rates taken into account? Do you draw normally distributed observed erosion rates, or do you use the observations uncertainty in the likelihood function? Uncertainties on the observations should be taken into account in some way.
Line 230: I am not a climate specialist, but from what I get WorldClim is a bit outdated and newer, higher-resolution rasters are available (e.g. CHELSA).
Line 237: This equation includes the assumption that precipitation scales linearly with discharge. This caveat should be acknowledged.
Figure 4a: I suggest to change the color map to a perceptually uniform, colorblind-friendly color map.
Figure 5: This figure is very interesting! A color bar for MAP is missing. Also, it might be more informative to have 3 panels instead of one combined. Then the uncertainties can be shown. The current representation does not allow to assess how robust this pattern with MAP really is compared to the scatter.
Section 4.3: Also these findings are very interesting. Similarly, to figure 5 , having individual plots with uncertainties would give the reader a better understanding of the uncertainties in the analysis. Some of your findings here are quite surprising, such as the highly erodible carbonate rocks. Some of the general tendencies differ from similar studies relating topography to rock erodibility on a global-scale (Moosdorf et al., 2018; Ott, 2020). The findings here, should be discussed in light of previous work.
References: I think a mistake happened with the Marder and Gallen 2022 reference. It’s cited as published in JGR:Solid Earth, when in fact it seems like it is only available as prepint on EarthArxiv. https://eartharxiv.org/repository/view/3139/
References:
Lague, D., Hovius, N. and Davy, P.: Discharge, discharge variability, and the bedrock channel profile, J. Geophys. Res. Earth Surf., 110(F4), 4006, doi:10.1029/2004JF000259, 2005.
Moosdorf, N., Cohen, S. and von Hagke, C.: A global erodibility index to represent sediment production potential of different rock types, Appl. Geogr., 101, 36–44, doi:10.1016/j.apgeog.2018.10.010, 2018.
Ott, R. F.: How Lithology Impacts Global Topography, Vegetation, and Animal Biodiversity: A GlobalâScale Analysis of Mountainous Regions, Geophys. Res. Lett., 47(20), doi:10.1029/2020GL088649, 2020.
Schwanghart, W. and Scherler, D.: Bumps in river profiles: Uncertainty assessment and smoothing using quantile regression techniques, Earth Surf. Dyn., 5(4), 821–839, doi:10.5194/esurf-5-821-2017, 2017.
Whipple, K. X., Hancock, G. S. and Anderson, R. S.: River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation, Geology, 112(3), 490–503, doi:10.1130/0016-7606(2000)112<490:RIIBMA>2.0.CO;2
Yanites, B. J., Tucker, G. E. and Anderson, R. S.: Numerical and analytical models of cosmogenic radionuclide dynamics in landslide-dominated drainage basins, J. Geophys. Res., 114(F1), 12857, doi:10.1029/2008JF001088, 2009.
Citation: https://doi.org/10.5194/esurf-2022-54-RC1 -
RC2: 'Comment on esurf-2022-54', Boris Gailleton, 06 Jan 2023
Ruetenik et al. introduce and apply a method to find optimal parameter values in Landscapes Evolution Models using a global 10Be compilation. They use a Montecarlo approach to run multiple one-time-step simulations to find the values of m, n, K, D minimizing the differences between simulated erosion rates and apparent erosion rates measured by CRN. They finally group the results by lithological and climatic domains to investigate the behaviour of optimal parameters function of these variables. I believe it offers a novel way to calibrate model parameters and even highlight interesting patterns about the behaviour of the stream power law and hillslope diffusion parameters correlated with precipitation patterns. I suggest this work is suitable for publication in esurf and will benefit the geomorphological community, however, I have two concerns about the method itself and the analysis of the results as well as other minor comments that I suggest should be addressed prior to publication. The manuscript is relatively short, which is not an issue, but could benefit from additional information and sensitivity analysis to clarify the method and its potential/limitation. Please find bellow my different comments.
Boris Gailleton
Main concerns:
One of the main advantages of the method according to the authors is the consideration of all the pixels in the investigated catchments, as opposed to only considering fluvial processes like Harel et al., 2016 or Marder and Gallen (2022). However, this also raises a number of questions as 10Be data is sampled at the river mouth. First, rivers are by nature only representing a minority of pixels in the catchments and are therefore under-represented statistically-speaking. Secondly, the connectivity with the sampling site will be significantly different between river processes and hillslope processes: rivers “instantly” transmit the sediments to the sampling sites while hillslopes may be disconnected. The models proposed in this study seem to assume that any change in the current topography through time is instantly transmitted to the outlet of the river, which may be true on a landscape simulated only with the stream power law and linear hillslope diffusion, but more difficultly on a real landscape. Finally, the authors present a method running LEMs on one snapshot of the (current) topography, while cosmogenic nuclides integrate larger time scales. Stochastic events (e.g., monsoon, landsliding) and/or complex sediment dynamics (e.g., recycling, residence time, intermediate traps) induce potentially significant variability in the signal (see Dingle et al., 2018 for an extreme example: https://doi.org/10.5194/esurf-6-611-2018, 2018). I acknowledge these are challenging points to include in the actual simulations - especially because the process laws of the models do not explicitly account for the sediment flux (they only express vertical topographic changes) - but I suggest it is not sufficiently discussed or addressed in the manuscript in its current form.
My other main concern is about the results, expressed in Figure 2, 3, 4, 5 and 6. It is not entirely clear whether the method picks a set of parameters, runs this same set for all the 3618 selected catchments, and calculates the global performance of this set of parameters; or if the Montecarlo process is done for each basin separately and then averaged. In other words, it is not entirely clear what these points exactly represents. In any cases, I suggest it would be relevant to show and discuss the breakdown of the global datasets: one could expect an average best parameter to be misrepresentative of the whole variability: multiple clusters could eventually emerge. This is also applicable to the Lithology and Climate comparisons: grouping metamorphic rocks into a unique category can be misleading as one would expect a very different rock strength via K (or even erosion processes via n) in a schist domain vs a gneiss domain – while both metamorphic. On the opposite, showing that the best-fit parameters are relatively constant in different contexts would be an important finding.
Other comments:
- There is a missing subsection title in the method part, when describing fluvial and hillslope processes.
- I find the use of the term “concavity” for the non-linear hillslope diffusion equation a bit confusing as it commonly refers to river processes – as stated in the manuscript. I would recommend using “hillslope concavity” or another term to avoid any confusion.
- The “non-linear hillslope diffusion” term can also refer to Roering et al. (1999) type of laws – that include a critical slope component in the equation. While p indeed makes the equation non-linear, it would be relevant to explicitly state the difference with the more common (in my experience at least) alternatives like Roering et al., 1999.
- The ratio between m/n is set to 0.45. While the average is in accordance with most of the literature, this value can vary quite significantly (this is acknowledged in the manuscript, and for example Wobus et al, 2006 suggest a 0.3-0.6 range using theoretical prediction, Harel et al., 2016 0.51 +/- 0.14 based on geomorphometrics and Gailleton et al., 2021 details significant variations at global scale). I am not suggesting to rerun the full analysis for ranges of m/n, but I would recommend to at least test the sensitivity of the prediction to this ratio in at least one site or one subset of the study. I believe the study would be more robust and if the method is resilient to this ratio, it would represent a notable advantage over others.
- To echo a comment about smoothing the DEM from Reviewer #1: the location of the river network is of prime importance as it define the transition between advective and diffusive processes. However, the choice of methods and their implications is not very detailed for (i) the preprocessing of the dem to remove local minima (or smooth the data) and (ii) the flow topology (D8). These can significantly affect the location of the rivers and the proportion of river pixels, especially in the case of lower-relief areas. Another point that would deserve a mention is the flow direction. Steepest descent algorithm reduces the river as 1D series of pixels with the same area no matter the drainage area. Because the process equations used to calculate E_predicted depends on the location of the river I believe this is an important point to raise – for example mentioning alternative like D_inf or multiple flow directions which would change the ratio rivers/hillslope. Again, I am not suggesting to rerun all the analysis with a different topology, but more to address this point in the method or discussion part.
- While some parameters benefit from the Montecarlo “brute-force” approach, others can be estimated through other means and optimize the process – especially because this approach is applied on real topography rather than simulated ones. For example, it is possible to estimate ranges of possible m/n and Ac through geomorphometry (e.g., Mudd et al., 2018, Wobus et al., 2006). It is also possible to directly determine the location of the river network (and therefore a more natural delimitation between hillslopes and fluvial processes) and bypass the need of Ac (e.g., Clubb et al. 2014).
- The parameter p is both used for the precipitations in equation 8 and the (hillslope) concavity exponent. I suggest to at least use a capital letter P for precipitations or another notation to avoid confusion.
- It is unclear in the method section whether the model considers spatial variations in K_lith, D and p (precipitation). If it does not, it can be an important point of discussion: catchments showing significant lithologic contrasts can really obscure the reading of geomorphometrics (e.g., Gailleton et al., 2021b - https://doi.org/10.1029/2020JF005970).
Minor comments:
l.40: I agree. I would also add a technical limitation to the parameter values: some are inter-connected - for example a value of K is only valid in a given context, and if n, m or other associated laws are modified a new K needs to be constrained.
l. 43: “vital” may be a bit of an exaggeration in my opinion, maybe “natural” or “crucial”?
l.107: “discharge” more than “flood” variability?
l.109: Harel et al. 2016 also reports significant variability in this value, also suggested by Gailleton et al. 2021 from geomorphometrics.
l. 112: As long as K remains constant (can be good to remind that).
l.139: While in line with the median in our global compilation, we also highlighted how variable this ratio could be (or at least its expression in the shape of the topography – which might not always reflect their translation into m/n when the system is significantly transient).
l.200: It is not clear what K* represents at this point of the manuscript. Please clarify.
l.232: missing “s” in variation.
l.246: refer to equation.
l.293: I disagree with this sentence: Harel et al., 2016 calculate ksn from M_chi using the method detailed in Mudd et al., 2014. M_chi is the gradient of a statistically segmented Chi-elevation River profile and is equal to ksn if A_0 = 1, otherwise proportional to it to a factor A_0. M_chi is then directly relatable to K and n within the stream power referential via the same relationship” M_chi = (E/(K * A0^m))^1/n.
l.295-300: while Harel et al., 2016 indeed only consider the fluvial section of the landscape, they do integrate spatial variation of ksn within a basin and calculate it for each river pixel. I suggest rephrasing/reworking the whole paragraph comparing the results with Harel et al., 2016.
l.301: Braun and Willett, 2013 barely mention linear diffusion, I suggest to use more relevant reference(s).
Citation: https://doi.org/10.5194/esurf-2022-54-RC2 -
EC1: 'Comment on esurf-2022-54', Jean Braun, 09 Jan 2023
I thank the two reviewers for their useful and supportive comments. I strongly encourage the authors to prepare a response to the reviewers comments and concerns, in particular where they request a more detailed explanation of aspects of the methods, as well as a more in-depth discussion on how some limitations of the cosmogenic nuclide method of estimating erosion rate and the way the various morphometric parameters are computed from DEMs may affect their conclusions, especially if these factors could lead to biases.
Citation: https://doi.org/10.5194/esurf-2022-54-EC1 - AC1: 'Comment on esurf-2022-54', Gregory Ruetenik, 06 Mar 2023
Gregory Ruetenik et al.
Gregory Ruetenik et al.
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 640 | 159 | 14 | 813 | 43 | 2 | 6 |
- HTML: 640
- PDF: 159
- XML: 14
- Total: 813
- Supplement: 43
- BibTeX: 2
- EndNote: 6
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1