Optimising global landscape evolution models with 10Be
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.
Gregory Ruetenik et al.
Status: final response (author comments only)
- RC1: 'Comment on esurf-2022-54', Richard Ott, 23 Nov 2022
- RC2: 'Comment on esurf-2022-54', Boris Gailleton, 06 Jan 2023
- EC1: 'Comment on esurf-2022-54', Jean Braun, 09 Jan 2023
- AC1: 'Comment on esurf-2022-54', Gregory Ruetenik, 06 Mar 2023
Gregory Ruetenik et al.
Gregory Ruetenik et al.
Viewed (geographical distribution)
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/
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.