the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The sensitivity of Landscape Evolution Models to DEM grid cell size
Christopher J. Skinner
Thomas J. Coulthard
Abstract. Landscape evolution models (LEMs) are useful for understanding how large scale processes and perturbations influence the development of planetary surfaces. With their increasing sophistication and improvements in computational power they are finding greater uptake in analyses at finer spatial and temporal scales, however. For many LEMs, the planetary surface is represented by a grid of regularly spaced and sized grid cells, or pixels, referred to as a Digital Elevation Model (DEM), yet despite the importance of the DEM to LEM studies there has been little work to understand the influence of grid cell size (i.e. resolution) on model behaviour and outputs. This is despite the choice of grid cell size being arbitrary for many studies, with users needing to balance detail with computational efficiency. Using the global sensitivity analysis Morris Method, the sensitivity of the CAESAR-Lisflood LEM to the DEM grid cell size is evaluated relative to a set of key user-defined parameters, showing it had a similar level of influence as a key hydrological parameter and the choice of sediment transport law. Outputs relating to discharge and sediment yields remained stable across different grid cell sizes until the cells became so large that the representation of the hydrological network degraded. Although total sediment yields remained steady when changing the grid cell sizes, closer analysis revealed that using larger grid resulted in it being built up from fewer yet more geomorphically-active events, risking outputs that are ‘the right answer but for the wrong reasons”. These results are important considerations for modellers using LEMs and the methodologies detailed provide solutions to understanding the impacts of modelling choices on outputs.
Christopher J. Skinner and Thomas J. Coulthard
Status: final response (author comments only)
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RC1: 'Comment on esurf-2022-30', John Armitage, 20 Jul 2022
Review of “The sensitivity of Landscape Evolution Models to DEM grid size” by Chris Skinner and Tom Coulthard
In this manuscript the authors discuss the sensitivity of the LEM CAESAR-Lisflood to grid cell size. They find that for a series of model functions that the numerical model is roughly as sensitive to DEM resolution as two other important parameters, the sediment transport law, and the TOPMODEL m parameter (that controls the peak and recession curve for the transformation of rainfall to runoff). There is the important observation that despite resolution having some, but perhaps not a significant impact on model functions such as total sediment yield or time to peak sediment yield, there is the potential that the model gives the “right answer for the wrong reasons”.
In this manuscript the authors re-use the experimental method developed in Skinner et al. (2018) to use the Morris Method to explore the relative importance of parameters to one and other. This is achieved (please correct me if I am wrong) by first selecting a representative sample of models to run (1220 models in this case) and then plotting the standard deviation and mean effect of each parameter relative to a model function (Table 2 in the manuscript). From this the most important factors might become apparent. From reading up on the subject, I see that the Sobol method however gives a quantified effect of each parameter on the model result, however in Skinner et al. (2018) it is stated that the Morris Method is good enough given evidence from previous studies. It would be interesting to see this point demonstrated, but perhaps that is a technical point for some future study.
I think this manuscript is a useful contribution to understanding the operational use of landscape evolution models that are process based, such as CAESAR-Lisfood. From using this code, my colleagues and I have noticed that for example the Mannings coefficient needs to be adjusted if a higher resolution DEM is used to replace a coarse resolution DEM. This manuscript starts to put these sorts of “tunings” into context of the limitations of the model approach.
I have a few comments that the authors might find useful to further improve this manuscript (in no specific order):
- It would be useful to see to what extent the change in DEM resolution impacts the spatial distribution of erosion and deposition. There is a focus on the model functions in Table 2, for obvious reasons, however these are spatially lumped. The biggest advantage of using a code like CAESAR-Lisflood is it can be used to model the spatial distribution of erosion and deposition. If I were interested in only gauging station measurements of water flux and sediment yield, I could turn to one of the many 1D models that treat the river network as a line and get over the problem of resolution. Therefore, it would be ideal to get some feeling for how resolution impacts the spatial distribution of landscape change. If the authors think it possible, perhaps some analysis of the DEMs of difference between the start and of each model could be analysed. A plot of the distribution of the mean and standard deviation of elevation change for each DEM resolution? Or the same exercise for each sub-catchment in the DEM as a function of model resolution? It would be interesting to see at what resolution the spatial distribution of erosion and deposition starts to converge.
- The sensitivity analysis is carried out on an existing landscape, where the landscape features already exist. Another application of LEMs is to try and model landscape formation. Here the impact of model resolution might be more acute, as the channels have not been carved into the landscape, and the model equations are free to form the landscape features. It would be interesting to run the same sensitivity analysis on a simple slope, perhaps with some noise to localize the flow routing algorithm. This would confirm the robustness of the results from the Morris Method that suggest DEM resolution is as important as the sediment transport law and the TOPMODEL m parameter. Spatial statistics, such as the wavelength of valley spacing, could also be measured to discover if below a certain resolution the model reproduces the same topography (e.g. Armitage, ESurf, 2019; https://doi.org/10.5194/esurf-7-67-2019).
- Why was the Meyer-Peter Muller sediment transport model introduced in this study? How has it been included? What are the benifits of using it over Wilcox and Crowe? What are the drawbacks?
- I recently read the chapter “Transport of gravel and sediment mixtures”, in Sedimentation Engineering: Theories, Measurements, Modeling, and Practice, by Gary Parker (2008; https://ascelibrary.org/doi/10.1061/9780784408148.ch03). In this chapter he states that “Einstein (1950) was the first to execute such an analysis for the bed-load transport of mixtures. The relation cannot be considered appropriate for the purposes of calculation due to the gross inaccuracies in the hiding function.” I am curious as to why the Einstein model remains within this analysis if it is known to badly represent the hiding effect of large grains on smaller grains?
- In Figure 5, what is the “vegetation critical shear” and the “grass maturity”?
- I think it is important to stress that it is not surprising that outputs that are totaled over the duration of the model run are not sensitive to the DEM resolution, such as total sediment yield. The area of the catchment has not changed, and neither has the average slope of the catchment (I presume). What is more interesting is the response of the model to change, such as how well flood events are recreated. I don't feel that this is really covered by the application of the Morris Method here.
- There is a typo on line 42, “someone”.
- Why is bedrock erosion ignored? This was also the case in Skinner et al. (2018).
Summary
Overall, I think this manuscript is highly valuable, if focused to users of CAESAR-Lisflood. The results could be possibly extrapolated to other process-based models, such as LAPSUS, PARALEM (?), but this has not been tested. It could be published with some minor improvement, and act as a starting point for more research. Or with some more thought into the question of the spatial distribution of erosion and deposition could make for a bigger piece of work. I would prefer the latter, hence my choice for "major revisions" however being realistic, I would leave that choice to the authors as the day job can get in the way of big revisions.
I hope these comments are helpful.
John Armitage
IFP Energies Nouvelles, Paris.
Citation: https://doi.org/10.5194/esurf-2022-30-RC1 -
RC2: 'Comment on esurf-2022-30', Anonymous Referee #2, 16 Aug 2022
This is a methodological paper exploring the impact of grid resolution on the CAESAR-Lisflood Landscape Evolution Model. The authors use an earlier developed global sensitivity analysis, referred to as the Morris Method to evaluate the impact of grid resolution compared to user-specified model parameters. They conclude that grid resolution does not change the modeled sediment output flux, but that resolution changes the frequency of events, with fewer big events producing the same output flux. This makes the authors conclude that changing the model resolution might give “the right answer for the wrong reasons”.
The topic discussed in this manuscript is of interest to an increasing amount of people applying LEM’s. Like the authors discuss, setting the resolution of a LEM is a choice with some implications which are, in some cases, overlooked. Re-applying the Morris exercise (a similar exercise was done for parameter sensitivity in Skinner et al 2018) to test the impact of resolution is useful. Yet, I feel the manuscript should be improved at several points to make it a contribution that adds to the existing literature on LEMs.
Some points not in order of importance:
- Almost no deposition is occurring in the shown simulations (erosion = 40-60k m3 versus deposition = 0.1-0.4k m3, this is a factor 100-200 difference!). This seems problematic for the goal of this paper since I would expect grid resolution to alter deposition. If almost no deposition occurs, I am not sure this is a proper catchment to test the impact of grid resolution. Given the narrow focus of this paper (only considering CAESAR-Lisflood), at least the full spectrum of erosion and deposition should be covered. I suppose this could be solved by comparing the results in-between smaller and larger catchments.
- Catchment size (related to previous comment): this is a very small catchment. At high resolution the topological network is strongly altered because of the limited catchment area. In my opinion, a study focusing on one single LEM, should cover a larger domain of catchment areas to study the role of changing grid resolution. Using larger catchment sizes would also resolve the issue on deposition, I assume.
- From reading the title, I was expecting a study that would cover the impact of model resolution in general. However, this paper focuses on one particular model (CAESAR-Lisflood). It would have been more interesting to see a contribution spanning a wider range of models but focusing on one LEM is acceptable. However, it should be indicated as such in the title. Also, I would like to see a discussion on how these findings can be extrapolated to other LEM’s. One more comment regarding the title: it is a little weird to use an abbreviation (DEM) in the title. Why not using ‘spatial model resolution’ or ‘grid resolution’ rather than DEM grid cell size? DEM resolution might be controlled by other factors such as the resolution of the source data the DEM was built from. When you say model grid resolution, you avoid this confusion.
- From the model description, it is unclear whether bedrock incision is simulated. How is sediment being produced? Is the full model domain supposed to be sediment (transport limited behavior versus detachment limited behavior? ) or is there a conversion mechanism to transform bedrock into sediment (fluvial bedrock incision, landslides,…). Do you assume an initial soil cover where the sediment is derived from? This might be described in the original CAESAR publications but would be good to summarize here.
- Over what timescales do observations hold and how sensitive are they to the initial boundary condition (DEM). More broadly speaking, several LEMs are used to create synthetic landscapes to test specific scenarios. What happens if CAESAR-Lisflood is used to generate synthetic landscapes and how sensitive are these kinds of landscapes to changes in resolution (e.g. in terms of fluvial network).
- The introduction should be structured better. Now it reads as an enumeration of various studies, but I miss a good story line here. It would be helpful to provide an overviewing first paragraph where the authors summarize what they will discuss and for which types of models. Next discuss these points and clarify what is known from these studies and what the knowledge gaps are. From there move towards the final paragraph outlying what will be done in this paper. Also, this work builds on Skinner et al. It would be useful to provide a summary of their main findings and explain how this manuscript builds on those using various grid resolutions.
- Grid resolution is one thing, numerical methods another. The latter is not mentioned in the manuscript but is critically important regarding grid resolution: some numerical methods will be more sensitive to grid resolution than others. The paper would benefit from details on the numerical implementation of the model as well as details on the temporal properties of the simulations. Numerical methods determine the sensitivity of LEMs to grid resolution. Finite Difference Methods will respond differently to changing resolutions compared to Finite Volume Methods or Finite Element Methods. Moreover, I am wondering how the numerical model advances in time: is a forward difference scheme used or a more complex scheme (e.g. Runge Kutta,…)? Related to that: provide details on the timescale over which this model is run and the timesteps being used. In terms of model performance, as shown and as expected, models run faster at lower resolution. Should be good to discuss whether the model allows parallelization and how that alters performance for various grid sizes.
- Figure 1 is hard to interpret before reading the methods section. This figure comes directly from Skinner et al and I see little value in doing so. Rather provide the readers with a synthetic figure overviewing the method and move it to the methods section. One suggestion would be to replace this figure with a synthetic figure that describes 3-5 cases (dots on the graph). For every case, the authors can explain what a high mean versus standard deviation imply, and how it should be interpreted.
- Would be good to explain the different transport formulas and how they behave differently. It might be explained elsewhere but knowing how they work is critical to understand what is going on in this study so please summarize.
- Stream network analysis: it is obvious that you lose details when coarsening a DEM, no modelling is needed to show that. What would be an interesting exercise is to run a synthetic LEM using a variable resolution and to check how the stream network comes out. Checking the order might be one metric to look at, but you could also consider evaluating the drainage density. This exercise could also be tested on drainage basins of various sizes (see before).
- Fewer yet more erosive events: is there a process-based explanation for this? Generally, with decreasing resolution, gradient decreases. Intuitively, I would expect this to result in decreasing erosion rates for single erosive events rather than increasing events. Some background on how erosion works in CAESAR-Lisflood might clarify this. Are there thresholds involved in the erosion mechanisms implemented?
Minor and line comments: see annotated PDF for details.
- AC1: 'Comment on esurf-2022-30', Christopher Skinner, 20 Dec 2022
Christopher J. Skinner and Thomas J. Coulthard
Christopher J. Skinner and Thomas J. Coulthard
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