the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Jun 2022
Modelling large‐scale landform‐evolution with a stream‐power law for glacial erosion (OpenLEM v37): Benchmarking experiments against a more process-based description of ice flow (iSOSIA v3.4.3)
Jörg Robl
Stefan Hergarten
David Lundbek Egholm
Kurt Stüwe
Abstract. Following the tradition of modeling fluvial landscape evolution, a novel approach describing glacial erosion based on an empirical stream power law was proposed. This approach differs substantially from well established process-based models applied to describe glacial erosion in mountain landscapes. Outstanding computational performance but a number of potential limitations compared to process-based models requires extensive testing to evaluate the applicability of this novel approach. In this study, we test the validity of the glacial stream power law and its implementation into a 2-D landform evolution model (OpenLEM) by benchmarking it against a state of the art surface process model based on the integrated second order shallow-ice approximation (iSOSIA).
Despite completely different approaches, OpenLEM and iSOSIA predict similar ice flow patterns and erosion rates for a wide range of climatic conditions without re-adjusting a set of calibrated scaling parameters. This parameter set is valid for full glacial conditions where the entire precipitation is converted to ice but also for an altitude-dependent glacier mass balance as characteristic for most glaciated mountain ranges on Earth.
In both models characteristic glacial features, such as overdeepenings, hanging valleys, and steps at confluences emerge roughly at the same locations resulting in a consistent altitude-dependent adjustment of channel slope and relief. Compared to iSOSIA, however, distinctly higher erosion rates occur in OpenLEM at valley flanks during the initial phase of the fluvial to glacial transition. This is mainly due to the simplified description of glacier width and ice surface in OpenLEM.
In this respect, we found that the glacial stream power approach cannot replace process-based models such as iSOSIA, but is complementary to them by addressing research questions that could not previously be answered due to a lack of computational efficiency. The implementation of the glacial stream power law is primarily suitable for large-scale simulations investigating the evolution of mountain topography in the interplay of tectonics and climate. As coupling glacial and fluvial erosion with sediment transport shows nearly the same computationally efficiency as its purely fluvial counterpart, mountain range scale simulations at high spatial resolution are not exclusively restricted to the fluvial domain anymore and a series of exciting research questions can be attacked by this novel approach.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Moritz Liebl et al.
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-352', Leif S. Anderson, 12 Sep 2022
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-352/egusphere-2022-352-RC1-supplement.pdf
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AC1: 'Reply on RC1', Moritz Liebl, 30 Sep 2022
Dear Leif S. Anderson,
we thank you for your constructive and positive review. We appreciate that you find our benchmarking experiments robust and detailed. Before we get into the details when preparing a revised version, here is a brief overview of the key issues you raised that we will address.
We agree that the extensive and detailed description of each experiment makes it at some point difficult for the reader to focus on the main purpose of the benchmark study. We will try to shorten and synthesise the results of the experiments in a way that the benefits and negatives of each model are addressed more clearly.
We appreciate your comment that we should include citations in a few places to better support some statements. We will include citations in the suggested sections regarding the sensitivity of glaciers to changing mass balances and the influence of the contribution of sliding and internal deformation to total ice flow on erosion rates.
In the latter case, we now explain in more detail why the inclusion of internal deformation in an erosion model might be important. And we will clarify why the original implementation of OpenLEM (Hergarten 2021) did not consider internal deformation.
Best regards,Moritz Liebl on behalf of all co-Authors
Citation: https://doi.org/10.5194/egusphere-2022-352-AC1
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AC1: 'Reply on RC1', Moritz Liebl, 30 Sep 2022
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RC2: 'Comment on egusphere-2022-352', Eric Deal, 16 Sep 2022
In this paper, Liebl et al. compare the behaviour of the relatively well understood and physically motivated glacial erosion model iSOSIA to a new, simpler model of glacial erosion. The advantages of the simple model are that it can feasibly be run on landscape evolution timescales. The big question is then whether or not the simple model is good enough to capture the essential dynamics of glacially driven landscape evolution or not. Comparing their simple model, OpenLEM to iSOSIA is the natural step to answer this question. Overall, the authors find that many aspects of glacial landscape evolution are well replicated by the simpler model, with some important differences and caveats. They finish by using OpenLEM to run a longterm landscape evolution model complete with glacial erosion and sediment transport.
Overall the question the authors are addressing is an important one. There is a dearth of models for glacial erosion over landscape evolution timescales that are simple enough to be paired with modern fluvial erosion models. Benchmarking a proposed simple model of glacial erosion against one whose behaviour is better known and more trusted is a good step towards addressing this problem. The work is novel, and the authors demonstrate a good awareness of the state of the art. The paper is well written and logically structured; They have taken time to choose logical numerical experiments and describe them clearly. Overall, I find that the authors are aware of the shortcomings of their approach and discuss them fairly in depth. Finally, the figures are generally very well made.However, the paper is fairly long. Part of that is due to the inherent nature of a benchmarking exercise, still I urge the authors to consider two steps to shorten the paper. First, there is a slight tendency to describe the results of each experiment in detail. Perhaps some more summarizing of the results and key conclusions of each experiment would be helpful to shorten the paper throughout. Second I suggest the authors consider removing the final experiment of running a longterm model with sediment transport from the paper. It is exciting, and very interesting, but has little to do with the benchmarking. It requires the introduction of several new model components, and does not help to answer the questions posed by the authors initially. I encourage the authors to submit this work separately.
The description of how the model works is at times hard to follow. I think that a few figures/diagrams illustrating how everything comes together would be incredibly helpful. In particular in section 2.2, the description of just how flow lines come together, how Ai and ice formation rates, erosion rates and total ice flux volumes are calculated across the channel width could perhaps be aided by a diagram showing this. Also, section 4.2, a diagram describing how the climate model works in the iSOSIA model would be helpful. Finally, I have one significant issue with the paper as it is, that I would like to see addressed before publication, discussed below.
I have an issue with the treatment of channel width in the implementation of OpenLEM. Recovering channel width from a model of glacial flow and erosion requires resolving the physics of ice flow at the sub-channel scale. You should be able to model the stresses within the ice, solving for cross-channel stresses induced by lateral velocity gradients across the channel as well as lateral gradients in the ice surface elevation across the channel. As the authors themselves point out repeatedly, the SPIM does not do this for rivers, instead it assumes a constant, equilibrium channel width that is instantaneously carved by the water at all times. This makes sense, over the timescales of landscape evolution, rivers probably achieve an equilibrium hydraulic geometry effectively instantaneously. In addition, the scale of the channel is usually smaller than the resolution of the landscape, so river width is considered a sub-grid process and can be kind of forgotten about. As the authors also discuss, this is harder to do with glaciers. They have widths that are often larger than the resolution of the landscape grid. So I appreciate that this is a challenging issue that has to be addressed. However, from my perspective, what OpenLEM does is sort of pretend that the simple glacier erosion model can capture the physics of ice flow within a channel, and then try to model the evolution of a channel width over time. To me this simply doesn’t work. iSOSIA is designed to handle exactly this sort of problem, but OpenLEM is not.
OpenLEM already makes effectively all the same assumptions as the SPIM, why not assume that U shaped profiles are achieved immediately? Over landscape evolution it likely doesn’t matter that U-shaped valleys take time to form. Most importantly, I don’t think it has been shown that it is really a problem to treat glacier width as a sub-grid process. It might slightly alter the flow paths, but the tributary glaciers are all going to still flow into the trunk channel. The landscape will not visually look like a glacial one, which I think what might be driving the authors to develop the ad-hoc width treatment. But the parameters that matter at the landscape scale, such as valley elevation profiles, erosion rates, eroded volume, overall orogen height, etc. should be fine. Perhaps the authors can demonstrate that allowing glacial width to be sub-grid doesn’t work. This would be an interesting and valuable contribution, and would add a lot to the paper. Even in this case, I think there must be a better, more physically informed approach rather than modelling in-channel ice flow with OpenLEM, which is what the authors effectively do. At the end of the day, OpenLEM is simply not the tool to try to establish the evolution timescale or morphology of glacial channels, as the authors almost seem to be doing in this paper at times. As the authors say themselves: “we must keep in mind that OpenLEM is not a model for simulating ice patterns on a surface, but landform evolution.”
Detailed comments
Line 70 - Can the authors say how Hergarten 2021 was different than Deal and Prasicek 2021?
Line 167 - I am not a fan of Ai. I think it makes the erosion law seem more similar to the stream power model and easier to handle than it actually is. The ice flux Qi only reflects topography in a complex way, incorporating topography itself, but also climate and the properties of the ice flow itself. This is in contrast to the rather direct relationship between topography and catchment area for rivers. If I’m not mistaken, Ai even decreases downstream at times below the ELA. I think it would be better to use something like Qi to make this more clear.
Line 182 - Is this the steepest descent of ice surface or bedrock surface?
Line 183 - What is meant by catchment size equivalents? Does this mean a volumetric flux dh/dt*w = pi*w - div(pi*A) or something like this? How do the units work out? I think it would be helpful to write out equation 2 again in the catchment-size equivalents form, it is not quite clear to me how this is working.
Figure 5 - Why does the linear climate model lead to ice profiles that seem so ragged compared to the nonlinear models?
Figure 6b - I’m wondering about the ice in the three lowest elevation tributaries. Why is there ice filling these valleys, but no ice coming from upstream? Is it just flow up valley from the main trunk channel? What is it about OpenLEM that allows this but not iSOSIA?
Citation: https://doi.org/10.5194/egusphere-2022-352-RC2 -
AC2: 'Reply on RC2', Moritz Liebl, 30 Sep 2022
Dear Eric Deal,
we thank you for thoroughly reviewing our manuscript and for providing constructive comments. Before we prepare a detailed revised version, we will briefly address the main points you raised. Most comments are very useful to the reader's understanding and we are happy to include them.
As also pointed out by the first reviewer, the manuscript is rather long. We will shorten the description of the benchmark experiments by first summarizing the main findings of each experiment and then explaining how we arrived at these findings in a shortened version. In this way the advantages and disadvantage of each model should be addressed more clearly. Then the scope of the study should be clear: benchmarking and evaluating of existing models.
We agree that additional figures/diagrams would help the reader to understand more clearly how the two models function. We are trying to create a figure that compares both models along a small section of the glacier showing the direction of the ice flow and how the flow lines come together.
Although including the last experiment makes the manuscript longer, we think it is reasonable to keep it as it shows exactly the field of application OpenLEM is intended for. We have structured the study in a way that the first set of benchmark experiments is conducted in settings intended for a process-based model such as iSOSIA to show how a topography based model such as OpenLEM performs in these settings. This helps to make the shortcomings of OpenLEM even more visible. Unfortunately, benchmarking the two models on scales of the last experiment is not possible due to the high computational cost of iSOSIA. This highlights the weaknesses of process-based models and strengthens the request to develop and test simpler models such as OpenLEM.
The major criticisms you made (in particular in the second half of your review) are more about the theoretical description of one model (OpenLEM), and not about the results of the benchmark experiments. We would like to emphasize that this study is not about the further development of one of the two models but only about the comparison of published, existing codes. In order to achieve a balanced benchmarking, we have asked the "masterminds" behind iSOSIA (David Egholm) and OpenLEM (Stefan Hergarten) to conduct this study together with us.
Several ad-hoc assumption, in particular the the finite valley width, were ultimately the reasons we undertook this benchmark study in the first place, prior to adopting this new approach to describing glacial erosion. With this study, we show quantitatively how the very simple implementation of finite valley width in OpenLEM affects erosion rates and landscape patterns, which can than be discussed on a solid scientific basis instead of a gut feeling that it may not work properly. We also came to the conclusion that the treatment of OpenLEM in respect to the evolution of the glacial cross-valley geometry is a major shortcoming describing the evolution of glacial landforms but not necessarily describing the topographic evolution of entire mountain ranges.
We address this limitation along with its ad-hoc assumptions as a starting point for describing the models. However, we feel that going into the basic implementations of the models and modifying them as suggested is beyond the scope of a benchmark study. The limitations we identified in our benchmark study, which were also addressed in the review, provide a good basis for further model improvements, which the main developers of the codes will be happy to address in future releases. Again, our work aims to help potential users to decide which model is suitable for the particular problem that they would like to solve.
Best regards,
Moritz Liebl on behalf of all co-AuthorsCitation: https://doi.org/10.5194/egusphere-2022-352-AC2
-
AC2: 'Reply on RC2', Moritz Liebl, 30 Sep 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-352', Leif S. Anderson, 12 Sep 2022
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-352/egusphere-2022-352-RC1-supplement.pdf
-
AC1: 'Reply on RC1', Moritz Liebl, 30 Sep 2022
Dear Leif S. Anderson,
we thank you for your constructive and positive review. We appreciate that you find our benchmarking experiments robust and detailed. Before we get into the details when preparing a revised version, here is a brief overview of the key issues you raised that we will address.
We agree that the extensive and detailed description of each experiment makes it at some point difficult for the reader to focus on the main purpose of the benchmark study. We will try to shorten and synthesise the results of the experiments in a way that the benefits and negatives of each model are addressed more clearly.
We appreciate your comment that we should include citations in a few places to better support some statements. We will include citations in the suggested sections regarding the sensitivity of glaciers to changing mass balances and the influence of the contribution of sliding and internal deformation to total ice flow on erosion rates.
In the latter case, we now explain in more detail why the inclusion of internal deformation in an erosion model might be important. And we will clarify why the original implementation of OpenLEM (Hergarten 2021) did not consider internal deformation.
Best regards,Moritz Liebl on behalf of all co-Authors
Citation: https://doi.org/10.5194/egusphere-2022-352-AC1
-
AC1: 'Reply on RC1', Moritz Liebl, 30 Sep 2022
-
RC2: 'Comment on egusphere-2022-352', Eric Deal, 16 Sep 2022
In this paper, Liebl et al. compare the behaviour of the relatively well understood and physically motivated glacial erosion model iSOSIA to a new, simpler model of glacial erosion. The advantages of the simple model are that it can feasibly be run on landscape evolution timescales. The big question is then whether or not the simple model is good enough to capture the essential dynamics of glacially driven landscape evolution or not. Comparing their simple model, OpenLEM to iSOSIA is the natural step to answer this question. Overall, the authors find that many aspects of glacial landscape evolution are well replicated by the simpler model, with some important differences and caveats. They finish by using OpenLEM to run a longterm landscape evolution model complete with glacial erosion and sediment transport.
Overall the question the authors are addressing is an important one. There is a dearth of models for glacial erosion over landscape evolution timescales that are simple enough to be paired with modern fluvial erosion models. Benchmarking a proposed simple model of glacial erosion against one whose behaviour is better known and more trusted is a good step towards addressing this problem. The work is novel, and the authors demonstrate a good awareness of the state of the art. The paper is well written and logically structured; They have taken time to choose logical numerical experiments and describe them clearly. Overall, I find that the authors are aware of the shortcomings of their approach and discuss them fairly in depth. Finally, the figures are generally very well made.However, the paper is fairly long. Part of that is due to the inherent nature of a benchmarking exercise, still I urge the authors to consider two steps to shorten the paper. First, there is a slight tendency to describe the results of each experiment in detail. Perhaps some more summarizing of the results and key conclusions of each experiment would be helpful to shorten the paper throughout. Second I suggest the authors consider removing the final experiment of running a longterm model with sediment transport from the paper. It is exciting, and very interesting, but has little to do with the benchmarking. It requires the introduction of several new model components, and does not help to answer the questions posed by the authors initially. I encourage the authors to submit this work separately.
The description of how the model works is at times hard to follow. I think that a few figures/diagrams illustrating how everything comes together would be incredibly helpful. In particular in section 2.2, the description of just how flow lines come together, how Ai and ice formation rates, erosion rates and total ice flux volumes are calculated across the channel width could perhaps be aided by a diagram showing this. Also, section 4.2, a diagram describing how the climate model works in the iSOSIA model would be helpful. Finally, I have one significant issue with the paper as it is, that I would like to see addressed before publication, discussed below.
I have an issue with the treatment of channel width in the implementation of OpenLEM. Recovering channel width from a model of glacial flow and erosion requires resolving the physics of ice flow at the sub-channel scale. You should be able to model the stresses within the ice, solving for cross-channel stresses induced by lateral velocity gradients across the channel as well as lateral gradients in the ice surface elevation across the channel. As the authors themselves point out repeatedly, the SPIM does not do this for rivers, instead it assumes a constant, equilibrium channel width that is instantaneously carved by the water at all times. This makes sense, over the timescales of landscape evolution, rivers probably achieve an equilibrium hydraulic geometry effectively instantaneously. In addition, the scale of the channel is usually smaller than the resolution of the landscape, so river width is considered a sub-grid process and can be kind of forgotten about. As the authors also discuss, this is harder to do with glaciers. They have widths that are often larger than the resolution of the landscape grid. So I appreciate that this is a challenging issue that has to be addressed. However, from my perspective, what OpenLEM does is sort of pretend that the simple glacier erosion model can capture the physics of ice flow within a channel, and then try to model the evolution of a channel width over time. To me this simply doesn’t work. iSOSIA is designed to handle exactly this sort of problem, but OpenLEM is not.
OpenLEM already makes effectively all the same assumptions as the SPIM, why not assume that U shaped profiles are achieved immediately? Over landscape evolution it likely doesn’t matter that U-shaped valleys take time to form. Most importantly, I don’t think it has been shown that it is really a problem to treat glacier width as a sub-grid process. It might slightly alter the flow paths, but the tributary glaciers are all going to still flow into the trunk channel. The landscape will not visually look like a glacial one, which I think what might be driving the authors to develop the ad-hoc width treatment. But the parameters that matter at the landscape scale, such as valley elevation profiles, erosion rates, eroded volume, overall orogen height, etc. should be fine. Perhaps the authors can demonstrate that allowing glacial width to be sub-grid doesn’t work. This would be an interesting and valuable contribution, and would add a lot to the paper. Even in this case, I think there must be a better, more physically informed approach rather than modelling in-channel ice flow with OpenLEM, which is what the authors effectively do. At the end of the day, OpenLEM is simply not the tool to try to establish the evolution timescale or morphology of glacial channels, as the authors almost seem to be doing in this paper at times. As the authors say themselves: “we must keep in mind that OpenLEM is not a model for simulating ice patterns on a surface, but landform evolution.”
Detailed comments
Line 70 - Can the authors say how Hergarten 2021 was different than Deal and Prasicek 2021?
Line 167 - I am not a fan of Ai. I think it makes the erosion law seem more similar to the stream power model and easier to handle than it actually is. The ice flux Qi only reflects topography in a complex way, incorporating topography itself, but also climate and the properties of the ice flow itself. This is in contrast to the rather direct relationship between topography and catchment area for rivers. If I’m not mistaken, Ai even decreases downstream at times below the ELA. I think it would be better to use something like Qi to make this more clear.
Line 182 - Is this the steepest descent of ice surface or bedrock surface?
Line 183 - What is meant by catchment size equivalents? Does this mean a volumetric flux dh/dt*w = pi*w - div(pi*A) or something like this? How do the units work out? I think it would be helpful to write out equation 2 again in the catchment-size equivalents form, it is not quite clear to me how this is working.
Figure 5 - Why does the linear climate model lead to ice profiles that seem so ragged compared to the nonlinear models?
Figure 6b - I’m wondering about the ice in the three lowest elevation tributaries. Why is there ice filling these valleys, but no ice coming from upstream? Is it just flow up valley from the main trunk channel? What is it about OpenLEM that allows this but not iSOSIA?
Citation: https://doi.org/10.5194/egusphere-2022-352-RC2 -
AC2: 'Reply on RC2', Moritz Liebl, 30 Sep 2022
Dear Eric Deal,
we thank you for thoroughly reviewing our manuscript and for providing constructive comments. Before we prepare a detailed revised version, we will briefly address the main points you raised. Most comments are very useful to the reader's understanding and we are happy to include them.
As also pointed out by the first reviewer, the manuscript is rather long. We will shorten the description of the benchmark experiments by first summarizing the main findings of each experiment and then explaining how we arrived at these findings in a shortened version. In this way the advantages and disadvantage of each model should be addressed more clearly. Then the scope of the study should be clear: benchmarking and evaluating of existing models.
We agree that additional figures/diagrams would help the reader to understand more clearly how the two models function. We are trying to create a figure that compares both models along a small section of the glacier showing the direction of the ice flow and how the flow lines come together.
Although including the last experiment makes the manuscript longer, we think it is reasonable to keep it as it shows exactly the field of application OpenLEM is intended for. We have structured the study in a way that the first set of benchmark experiments is conducted in settings intended for a process-based model such as iSOSIA to show how a topography based model such as OpenLEM performs in these settings. This helps to make the shortcomings of OpenLEM even more visible. Unfortunately, benchmarking the two models on scales of the last experiment is not possible due to the high computational cost of iSOSIA. This highlights the weaknesses of process-based models and strengthens the request to develop and test simpler models such as OpenLEM.
The major criticisms you made (in particular in the second half of your review) are more about the theoretical description of one model (OpenLEM), and not about the results of the benchmark experiments. We would like to emphasize that this study is not about the further development of one of the two models but only about the comparison of published, existing codes. In order to achieve a balanced benchmarking, we have asked the "masterminds" behind iSOSIA (David Egholm) and OpenLEM (Stefan Hergarten) to conduct this study together with us.
Several ad-hoc assumption, in particular the the finite valley width, were ultimately the reasons we undertook this benchmark study in the first place, prior to adopting this new approach to describing glacial erosion. With this study, we show quantitatively how the very simple implementation of finite valley width in OpenLEM affects erosion rates and landscape patterns, which can than be discussed on a solid scientific basis instead of a gut feeling that it may not work properly. We also came to the conclusion that the treatment of OpenLEM in respect to the evolution of the glacial cross-valley geometry is a major shortcoming describing the evolution of glacial landforms but not necessarily describing the topographic evolution of entire mountain ranges.
We address this limitation along with its ad-hoc assumptions as a starting point for describing the models. However, we feel that going into the basic implementations of the models and modifying them as suggested is beyond the scope of a benchmark study. The limitations we identified in our benchmark study, which were also addressed in the review, provide a good basis for further model improvements, which the main developers of the codes will be happy to address in future releases. Again, our work aims to help potential users to decide which model is suitable for the particular problem that they would like to solve.
Best regards,
Moritz Liebl on behalf of all co-AuthorsCitation: https://doi.org/10.5194/egusphere-2022-352-AC2
-
AC2: 'Reply on RC2', Moritz Liebl, 30 Sep 2022
Peer review completion
Journal article(s) based on this preprint
Moritz Liebl et al.
Model code and software
egusphere-2022-352 Moritz Liebl https://doi.org/10.5281/zenodo.6557805
Video supplement
egusphere-2022-352-videos Moritz Liebl https://doi.org/10.5281/zenodo.6557805
Moritz Liebl et al.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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