the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 May 2025
Impact of Noise on Landscapes and Metrics Generated with Stream Power Models
Abstract. The Stream Power Model (SPM) has become a cornerstone of quantitative geomorphology, widely used to predict landscape evolution including the generation, moderation, and lowering of Earth's topography, sedimentary flux and biogeochemical processes. It is well known that landscape geometries predicted by the SPM can be strongly influenced by noise. However, its impact on the uncertainties or probabilities of, for instance, drainage planform geometries and widely used metrics is poorly understood. Noise can be incorporated into SPM simulations in a variety of ways. For instance, random, low amplitude, topographic anomalies are often inserted into starting conditions to enhance the realism of calculated drainage networks. Spatio-temporal or quenched (frozen) noise also influence the trajectories of evolving landscapes. Our goal with this paper is to establish how noise impacts the probabilities of landscape geometries and the reliability of tectonic and erosional information recovered from them. A series of landscape evolution models are run in which different arrangements, distributions, and implementations of noise are added to models evolving under the same tectonic and erosional forcings to an equilibrium state. We quantify uncertainties that arise from incorporating different arrangements of typical (uniform; white) and naturalistic initial, quenched and spatio-temporal noise. We focus on three conclusions. First, tectonic rates and values of erosional-geometric parameters (e.g., concavity and steepness indices, Hack exponents) recovered via metrics-based approaches (e.g., slope-area, χ, length-area) are uncertain in the presence of noisy initial conditions. Recovered values from individual landscapes generated with the same distribution but different specific arrangement of noise are at least as uncertain as ranges attributed to, for instance, changes in aridity. In fact, even noise with amplitudes that are <1 % of cumulative uplift can cause tectonic rates to no longer be recoverable to within a factor of two of true values. These results emphasise the sensitivity of metrics that rely on calculating derivatives (e.g., slope-area, χ) to noise. Secondly, whilst noise can make landscape geometries highly uncertain (different in different simulations), the distributions of their geomorphic properties (e.g., hypsometries, channel length-area relationships, Hack exponents) appear to have well defined statistical properties (e.g., expected values and variance). Finally, we suggest that a useful way to assess the impact of noise on SPM predictions is to generate ensembles of hundreds to thousands of models in which different arrangements of the chosen distribution of noise are inserted. Doing so can provide means to quantify uncertainty in predicted geometries and derived metrics, which can be substantial.
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RC1: 'Comment on egusphere-2025-1953', Jeffrey Kwang, 25 Jun 2025
Review of Impact of Noise on Landscapes and Metrics Generated with Stream Power Models
Summary:
The stream power model (SPM) is a reduced complexity model that simulates the interaction between tectonics, fluvial erosion, and hillslope diffusion. Commonly, researchers using this model utilize noise in the initial topography to produce realistic-looking drainage networks. The authors further investigate the influence of noise on landscape evolution models by incorporating different noise colors (the most commonly used white, red, and blue) and noise applications (e.g., initial topography, quenched, spatio-temporal). In their numerical experiments, the authors find that noise can produce uncertainty in recovering geomorphic parameters. In some configurations, a small amount of noise was enough to make some parameters unrecoverable, such as uplift. In contrast, other metrics, such as Hack’s law exponents, were uncertain but consistent across different types of noise. The authors conclude by recommending researchers use probabilistic/ensemble approaches to modeling by running multiple instances with different randomized noise and assessing its effects on the distribution of geometric properties and computed metrics on the landscape.
Review:
The authors conduct a thorough exploration and review of the influence of noise on landscape evolution. The manuscript is well-written and easy to follow; I particularly appreciate the explanations they provide throughout the paper to provide the reader with enough context to understand some of the complex material they cover. The motivation for the paper is clear and well justified. The figures illustrate their points well; I wish more papers utilized the style and clarity of Figure 3, which is worth a thousand words (or more). I think the authors use a thoughtful approach when choosing the different types of noise and model configurations. They cover different types of noise by choosing the end-member models of blue and red noise. Within these end-members are white noise, which is commonly used by landscape evolution researchers. The different types of model configurations (i.e., square, domal, escarpment) also represent the range of configurations most modelers use. I found the results and discussion about how noise affects the landscape metrics useful and thought-provoking. The metrics are typically straightforward when used on numerical results and harder to interpret for natural landscapes. By incorporating noise and multiple ensembles in their numerical experiments, the authors provide a great framework for interpreting the uncertainty seen in natural landscapes. I agree with the authors’ recommendation to use a more probabilistic/ensemble approach to landscape evolution modeling. I support this paper for publication in its current form, but would appreciate it if the authors incorporated some of the feedback below.
Feedback:
- Line 107 – 100 x 100 cells. Do you think this is a large enough grid to capture enough complexity in the drainage network? By eye, it looks as though the maximum stream order in the drainage networks is around 3 or 4.
- Figure 1 – Do you expect your result to change much if you opt to not fill in the sinks?
- Line 116 – “purposefully simple” – Great way to explain your approach for the modeling framework.
- Line 118 – “100 MYR” – This seems excessive? With an uplift rate of 0.2 m/kyr, one relief unit (~1200m) would take 6 MYR to erode through. Typically, landscapes reach a quasi-steady state around 2 relief units, but 100 MYR is ~17 relief units. It might be useful to describe the model behavior (Line 416 to 423) in terms of relief units to relate the model parameters to the time.
- Line 306 – typo – “river being in a cell is calculated by DIVIDING the number of times”
- Figure 9 – Great figure.
- Line 455-457 – Wow, I did not expect the drainage basins to be statistically different between the different types of noise.
- Line 475 – The no-noise figures are an important addition.
- Line 560 – Why did you decide to add noise that is 0 to 1 m instead of -0.5 to 0.5 m? While I think it is easy to follow when the noise is averaged, it essentially adds ~0.5m per time step (25% of the uplift rate). It would be easier to make your points about uplift recovery on Figure 17g and 18g if it averaged around 0m. Is it another way to interpret Scenario B and C as a noisy constant spatial uplift rate from 0.2 to 0.25 m/kyr and a noisy spatiotemporal uplift rate from 0.2 to 0.25 m/kyr, respectively?
- Figure 17b and 18b – It seems like the relief of the landscape is around ~1250 m from the color scalebar. This also seems constant across Scenario A, B and C. Shouldn’t the relief in Scenario B and C be higher because of the added noise component. Since 0.5 meters, on average, are being added every timestep, 10 kyr, the apparent uplift rate should be 0.25 m/kyr. If relief scales linearly with the uplift rate, then landscapes in Scenario B and C would be about 25% taller, right?
- Line 613 – Which supplementary information figure are you referring to?
- Line 667 – I found this result so strange that it was not just offset by the mean value of the noise addition. I was excited to read about this in the discussion (mentioned on line 579 to 580), but I was a little disappointed by the explanation here. I think Scenario C had an offset because the apparent uplift rates varied around 0.25 m/kyr due to the spatiotemporal noise configuration. Over enough timesteps this should average to 0.25 m/kyr in most locations. In contrast, this averaging does not happen in Scenario B. Do you think this might have something to do with the disparity?
- Line 719-720 – Can you cite Kwang et al. 2021, who show how numerical models remove memory of initial conditions with lateral erosion.
Citation: https://doi.org/10.5194/egusphere-2025-1953-RC1 -
RC2: 'Comment on egusphere-2025-1953', Stuart Grieve, 04 Aug 2025
This manuscript presents a diverse series of numerical experiments, designed to explore the influence of initial conditions (eg topographic noise) on topographic metrics extracted from DEMs generated using typical landscape evolution modelling approaches. The authors do an excellent job in drawing together a wide range of scenarios, ensembles and models into a coherent message. When I initially read the abstract I was worried that so many permutations would become unwieldy, but the clear and systematic organisation of the experiments and the discussion of their outcomes leads the reader well and arrives at clear, justified conclusions. The authors find that differing initial noise types and parameters can have a meaningful impact on the recovery of tectonic information using common approaches including chi and slope-area analysis is challenging. However they also demonstrate that the distributions of geomorphic properties (hypsometry, Hack relationships) remain stable across varying types and applications of noise into landscape evolution models. The manuscript concludes by making some clear recommendations about the need to generate ensembles of models as a way of quantifying the uncertainties inherent in landscape evolution modelling.
Overall, I believe this is an excellent contribution which is a good fit for Esurf and will be of wide relevance to the landscape evolution modelling community, as well as the broader geomorphology community.
General comments
My only reservation with this work is in the choice to generate noise in the range 0-1m rather than centring the noise distribution around 0 for scenarios B and C. As you highlight in Section 4.4.1 this means that you are only ever adding elevation to your models, which feels like a poor representation of geomorphic processes which roughen landscapes. I would be reassured by some tests that demonstrate that this choice of constructive noise is not driving the results we see in scenarios B and C. Or alternatively, some more discussion about the use of noise within the discipline showing that standard practice is to lock noise to the range 0-1.
Something that I think could merit some additional discussion is the potential sensitivity of some of your metrics to the channel extraction threshold. In general we would expect that the most dynamic parts of a landscape are the first order basins and channels, so things like approximations of steady state in channels may vary based on the threshold used. I'm not asking for another parameter to be added to your models, but some reflection in the discussion could be interesting.
You ascribe the spike pattern observed in Figure 9 to the use of D8 flow routing and a square grid. You could quickly test this by running the D-infinity landlab component on a bunch of your DEMs to see if that is enough to smooth out the spike across all noise types.
A very minor point, but throughout the manuscript, you present and discuss the three colours of white noise in different orders. For example Figure 4 goes white, blue, red; Figure 6 goes red, white, blue; Section 2.2.2 goes white, red, blue. There's a lot of data being presented in this manuscript, so sticking to one consistent order will make it slightly easier for the reader to follow things.
Line by line comments
In addition to the comments above, I have some more general minor line by line comments:
Line 46 - "noise to inserted" is missing a word.
Line 86 - You discuss steady state in detail later (which I really enjoyed), but it would be good to add a citation here and a little more detail to outline what definition(s) you are using in this study.
Line 113 - The units for K are missing their numerator.
Line 171 - A note to highlight how good it is to see the practice of recording or fixing seeds discussed!
Table 1 - It wasn't clear to me when reading the manuscript, what scenarios A, B and C refer to here. I think they are defined later in the manuscript, but that definition needs to come before their first use.
Figure 8b - Missing values on y-axis.
Line 325 - "calculated from channel lengths and areas" This should read "and basin areas", so that there is no confusion about the calculation of channel areas.
Line 354 - "a value often used in studies of real landscapes" - this needs a citation to at least one of these studies.
Figure 11g - The hack exponents for the largest basins reported here seem to sit considerably outside the norm. I did some work last year (https://doi.org/10.1029/2024GL111220) looking at Hack's exponents on a global scale only saw values that high when very odd things were happening. Is there a morphometric explanation for these values?
Code
It is great to see the code associated with this manuscript available online, and citable. I have gone through the code on github and it is well written and structured, and reflects the analyses described in the manuscript. To aid reproducibility it would also be helpful to record the package versions python versions you are using within a readme, in case future upgrades break things in your code.
-- Stuart GrieveCitation: https://doi.org/10.5194/egusphere-2025-1953-RC2 - AC1: 'Comment on egusphere-2025-1953', Matthew Morris, 22 Aug 2025
Status: closed
-
RC1: 'Comment on egusphere-2025-1953', Jeffrey Kwang, 25 Jun 2025
Review of Impact of Noise on Landscapes and Metrics Generated with Stream Power Models
Summary:
The stream power model (SPM) is a reduced complexity model that simulates the interaction between tectonics, fluvial erosion, and hillslope diffusion. Commonly, researchers using this model utilize noise in the initial topography to produce realistic-looking drainage networks. The authors further investigate the influence of noise on landscape evolution models by incorporating different noise colors (the most commonly used white, red, and blue) and noise applications (e.g., initial topography, quenched, spatio-temporal). In their numerical experiments, the authors find that noise can produce uncertainty in recovering geomorphic parameters. In some configurations, a small amount of noise was enough to make some parameters unrecoverable, such as uplift. In contrast, other metrics, such as Hack’s law exponents, were uncertain but consistent across different types of noise. The authors conclude by recommending researchers use probabilistic/ensemble approaches to modeling by running multiple instances with different randomized noise and assessing its effects on the distribution of geometric properties and computed metrics on the landscape.
Review:
The authors conduct a thorough exploration and review of the influence of noise on landscape evolution. The manuscript is well-written and easy to follow; I particularly appreciate the explanations they provide throughout the paper to provide the reader with enough context to understand some of the complex material they cover. The motivation for the paper is clear and well justified. The figures illustrate their points well; I wish more papers utilized the style and clarity of Figure 3, which is worth a thousand words (or more). I think the authors use a thoughtful approach when choosing the different types of noise and model configurations. They cover different types of noise by choosing the end-member models of blue and red noise. Within these end-members are white noise, which is commonly used by landscape evolution researchers. The different types of model configurations (i.e., square, domal, escarpment) also represent the range of configurations most modelers use. I found the results and discussion about how noise affects the landscape metrics useful and thought-provoking. The metrics are typically straightforward when used on numerical results and harder to interpret for natural landscapes. By incorporating noise and multiple ensembles in their numerical experiments, the authors provide a great framework for interpreting the uncertainty seen in natural landscapes. I agree with the authors’ recommendation to use a more probabilistic/ensemble approach to landscape evolution modeling. I support this paper for publication in its current form, but would appreciate it if the authors incorporated some of the feedback below.
Feedback:
- Line 107 – 100 x 100 cells. Do you think this is a large enough grid to capture enough complexity in the drainage network? By eye, it looks as though the maximum stream order in the drainage networks is around 3 or 4.
- Figure 1 – Do you expect your result to change much if you opt to not fill in the sinks?
- Line 116 – “purposefully simple” – Great way to explain your approach for the modeling framework.
- Line 118 – “100 MYR” – This seems excessive? With an uplift rate of 0.2 m/kyr, one relief unit (~1200m) would take 6 MYR to erode through. Typically, landscapes reach a quasi-steady state around 2 relief units, but 100 MYR is ~17 relief units. It might be useful to describe the model behavior (Line 416 to 423) in terms of relief units to relate the model parameters to the time.
- Line 306 – typo – “river being in a cell is calculated by DIVIDING the number of times”
- Figure 9 – Great figure.
- Line 455-457 – Wow, I did not expect the drainage basins to be statistically different between the different types of noise.
- Line 475 – The no-noise figures are an important addition.
- Line 560 – Why did you decide to add noise that is 0 to 1 m instead of -0.5 to 0.5 m? While I think it is easy to follow when the noise is averaged, it essentially adds ~0.5m per time step (25% of the uplift rate). It would be easier to make your points about uplift recovery on Figure 17g and 18g if it averaged around 0m. Is it another way to interpret Scenario B and C as a noisy constant spatial uplift rate from 0.2 to 0.25 m/kyr and a noisy spatiotemporal uplift rate from 0.2 to 0.25 m/kyr, respectively?
- Figure 17b and 18b – It seems like the relief of the landscape is around ~1250 m from the color scalebar. This also seems constant across Scenario A, B and C. Shouldn’t the relief in Scenario B and C be higher because of the added noise component. Since 0.5 meters, on average, are being added every timestep, 10 kyr, the apparent uplift rate should be 0.25 m/kyr. If relief scales linearly with the uplift rate, then landscapes in Scenario B and C would be about 25% taller, right?
- Line 613 – Which supplementary information figure are you referring to?
- Line 667 – I found this result so strange that it was not just offset by the mean value of the noise addition. I was excited to read about this in the discussion (mentioned on line 579 to 580), but I was a little disappointed by the explanation here. I think Scenario C had an offset because the apparent uplift rates varied around 0.25 m/kyr due to the spatiotemporal noise configuration. Over enough timesteps this should average to 0.25 m/kyr in most locations. In contrast, this averaging does not happen in Scenario B. Do you think this might have something to do with the disparity?
- Line 719-720 – Can you cite Kwang et al. 2021, who show how numerical models remove memory of initial conditions with lateral erosion.
Citation: https://doi.org/10.5194/egusphere-2025-1953-RC1 -
RC2: 'Comment on egusphere-2025-1953', Stuart Grieve, 04 Aug 2025
This manuscript presents a diverse series of numerical experiments, designed to explore the influence of initial conditions (eg topographic noise) on topographic metrics extracted from DEMs generated using typical landscape evolution modelling approaches. The authors do an excellent job in drawing together a wide range of scenarios, ensembles and models into a coherent message. When I initially read the abstract I was worried that so many permutations would become unwieldy, but the clear and systematic organisation of the experiments and the discussion of their outcomes leads the reader well and arrives at clear, justified conclusions. The authors find that differing initial noise types and parameters can have a meaningful impact on the recovery of tectonic information using common approaches including chi and slope-area analysis is challenging. However they also demonstrate that the distributions of geomorphic properties (hypsometry, Hack relationships) remain stable across varying types and applications of noise into landscape evolution models. The manuscript concludes by making some clear recommendations about the need to generate ensembles of models as a way of quantifying the uncertainties inherent in landscape evolution modelling.
Overall, I believe this is an excellent contribution which is a good fit for Esurf and will be of wide relevance to the landscape evolution modelling community, as well as the broader geomorphology community.
General comments
My only reservation with this work is in the choice to generate noise in the range 0-1m rather than centring the noise distribution around 0 for scenarios B and C. As you highlight in Section 4.4.1 this means that you are only ever adding elevation to your models, which feels like a poor representation of geomorphic processes which roughen landscapes. I would be reassured by some tests that demonstrate that this choice of constructive noise is not driving the results we see in scenarios B and C. Or alternatively, some more discussion about the use of noise within the discipline showing that standard practice is to lock noise to the range 0-1.
Something that I think could merit some additional discussion is the potential sensitivity of some of your metrics to the channel extraction threshold. In general we would expect that the most dynamic parts of a landscape are the first order basins and channels, so things like approximations of steady state in channels may vary based on the threshold used. I'm not asking for another parameter to be added to your models, but some reflection in the discussion could be interesting.
You ascribe the spike pattern observed in Figure 9 to the use of D8 flow routing and a square grid. You could quickly test this by running the D-infinity landlab component on a bunch of your DEMs to see if that is enough to smooth out the spike across all noise types.
A very minor point, but throughout the manuscript, you present and discuss the three colours of white noise in different orders. For example Figure 4 goes white, blue, red; Figure 6 goes red, white, blue; Section 2.2.2 goes white, red, blue. There's a lot of data being presented in this manuscript, so sticking to one consistent order will make it slightly easier for the reader to follow things.
Line by line comments
In addition to the comments above, I have some more general minor line by line comments:
Line 46 - "noise to inserted" is missing a word.
Line 86 - You discuss steady state in detail later (which I really enjoyed), but it would be good to add a citation here and a little more detail to outline what definition(s) you are using in this study.
Line 113 - The units for K are missing their numerator.
Line 171 - A note to highlight how good it is to see the practice of recording or fixing seeds discussed!
Table 1 - It wasn't clear to me when reading the manuscript, what scenarios A, B and C refer to here. I think they are defined later in the manuscript, but that definition needs to come before their first use.
Figure 8b - Missing values on y-axis.
Line 325 - "calculated from channel lengths and areas" This should read "and basin areas", so that there is no confusion about the calculation of channel areas.
Line 354 - "a value often used in studies of real landscapes" - this needs a citation to at least one of these studies.
Figure 11g - The hack exponents for the largest basins reported here seem to sit considerably outside the norm. I did some work last year (https://doi.org/10.1029/2024GL111220) looking at Hack's exponents on a global scale only saw values that high when very odd things were happening. Is there a morphometric explanation for these values?
Code
It is great to see the code associated with this manuscript available online, and citable. I have gone through the code on github and it is well written and structured, and reflects the analyses described in the manuscript. To aid reproducibility it would also be helpful to record the package versions python versions you are using within a readme, in case future upgrades break things in your code.
-- Stuart GrieveCitation: https://doi.org/10.5194/egusphere-2025-1953-RC2 - AC1: 'Comment on egusphere-2025-1953', Matthew Morris, 22 Aug 2025
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