Influence of network geometry on long-term morphodynamics of alluvial rivers

McNab, Fergus; Schildgen, Taylor F.; Turowski, Jens Martin; Wickert, Andrew D.

doi:https://doi.org/10.5194/egusphere-2025-2468

Preprints

https://doi.org/10.5194/egusphere-2025-2468

Preprints

10 Jun 2025

| 10 Jun 2025

Influence of network geometry on long-term morphodynamics of alluvial rivers

Fergus McNab, Taylor F. Schildgen, Jens Martin Turowski, and Andrew D. Wickert

Abstract. Alluvial rivers respond to external forcings such as variations in sediment supply, water supply and base level by aggrading, incising and adjusting the rates at which they transport sediment. These processes are recorded by landforms, such as terraces and fans, that develop along stream courses, and by stratigraphy in downstream sedimentary basins. Many concepts we use to interpret such records are derived from models that treat alluvial rivers as single streams: for example, the length of an alluvial river has been shown to set its response time to external forcing. However, alluvial rivers in nature exist within interconnected networks, complicating the application of such concepts to real systems. We therefore adapted a model describing long-profile evolution and sediment transport by transport-limited, gravel-bed alluvial rivers to account for network structure, and explored the response of large numbers of synthetic networks to sinusoidally varying sediment and water supply. We show that, in some respects, networks behave similarly to single-segment models. In particular, properties that integrate across the entire network, such as the total sediment output, are well predicted by single-segment models. We used this behaviour to define an empirical network response time, and show that this response time scales with network mean length, or the mean distance from all a network's inlets to its outlet. Nevertheless, interactions between segments do lead to complex signal propagation within networks: amplitudes and timings of aggradation and incision vary between minor tributaries and major trunk streams, and between upstream and downstream parts of the network, in ways that depend on that individual network's structure. We conclude that, while single-segment models may be useful for some applications, detailed studies of specific catchments require a modelling framework that accounts for their specific network structure.

Received: 27 May 2025 – Discussion started: 10 Jun 2025

Competing interests: One of the authors is a member of the editorial board of Earth Surface Dynamics.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 21304 KB)

Supplement (66806 KB)

Download & links

Preprint (21304 KB)
Metadata XML
Supplement (66806 KB)
BibTeX
EndNote

Fergus McNab, Taylor F. Schildgen, Jens Martin Turowski, and Andrew D. Wickert

Status: final response (author comments only)

CC1:
'Comment on egusphere-2025-2468', Alan Howard, 10 Jun 2025

The authors might want to consider the similarity of the authors procedures and conclusions regarding alluvial channel network evolution in response to sediment input changes (step, pulse, sinusoidal) to those of the attached paper. Also the research by Doug Jerolmack and others on "shredding" of environmental signals in alluvial systems seems appropriate to this paper.

Citation: https://doi.org/10.5194/egusphere-2025-2468-CC1
- AC1: 'Reply on CC1', Fergus McNab, 18 Jul 2025
  
  We welcome Alan Howard's interest in our manuscript and thank him for drawing our attention to two important omissions.
  First, Howard refers to similarities between our analysis and that of an earlier paper of his (Howard, 1982). Indeed, we were aware of this contribution, and it was an oversight not to cite it in our previous draft. In the context of, first, a generic linear system, and, second, a long-profile evolution model for sand-bed alluvial rivers, Howard (1982) identifies several aspects of the general behaviour that we discuss. In particular, he shows how the extent to which the system can achieve equilibrium with a given change in boundary conditions depends on the system’s response timescale. His solution for the response to a sinusoidal forcing takes a similar form to ours (M^cNab et al., 2023), including a factor scaling the forcing amplitude to the response amplitude (the ‘magnitude factor’ or, in our terminology, ‘gain’) and a phase shift or lag. He further shows, for an example channel network, that downstream lag times are reduced and the response therefore more uniform along stream relative to the single-segment case, which is also a general feature of our simulations. We do, however, reach different conclusions regarding network response times, which we find to be shorter for networks than for single reaches of the same maximum length, while Howard (1982) finds them to be longer. Clearly, this prior work is relevant to our study. In our revised manuscript, we will give it proper acknowledgment, both in our introductory discussion of previous work and throughout the paper with respect to specific results, including but not limited to the key points we summarised above. We believe this added context will help strengthen and broaden our argument.
  Second, Howard suggests that some discussion of the concept of signal ‘shredding’ in sedimentary systems, as originally proposed by Jerolmack and Paola (2010), is warranted. This concept builds from the observation that sediment transport in many environments is a threshold process subject to large fluctuations, and states that, if an external signal is imposed with a timescale and amplitude similar to the timescales and amplitudes of these internal fluctuations, it will not be transmitted through the system (i.e., it will be ‘shredded’). Importantly, this process is distinct from the diffusive damping or buffering we observe for high frequency variation in sediment supply and low frequency variation in water supply. The model we apply is deterministic, assuming steady flow conditions during bankfull floods (Wickert and Schildgen, 2019), and we set sediment and water supply to vary smoothly with constant intermittency. We justify this approach with the observation that alluvial channels efficiently adjust their widths in response to short-term hydraulic variation, resulting in a more ‘linear’ relationship between water and sediment discharge than might otherwise be expected (e.g., Phillips and Jerolmack, 2016). Indeed, terrace records with Milankovitch periodicities do imply that these rivers can respond systematically to external change (e.g., Tofelde et al., 2017). Nevertheless, it is clear that large fluctuations in sediment transport do occur (e.g., associated with storms, landslides or avulsions), and that these fluctuations will have an effect, particularly on timescales similar to or shorter than channel-width adjustment. Such fluctuations may particularly influence patterns of sediment output, where extreme events can have amplitudes much larger than the background transport rate, in contrast with long-profile evolution. These processes will introduce additional timescale limiting transmission of external signals through alluvial valleys, linked to the repeat time of the largest sediment-transport events (Jerolmack and Paola, 2010; see also Griffin et al., 2023). Placing tighter constraints on both this timescale and our deterministic T_eq in real systems is critical for understanding the relative importance of each process (an important advantage of our physically based, network approach). In our revised manuscript, we will explicitly note our steady flow assumption where we introduce the model, and include a brief consideration of the implications of this simplification in an additional subsection of the Discussion.
  References
  Howard, A.D., 1982, ‘Equilibrium and time scales in geomorphic systems: Applications to sand-bed alluvial streams’, Earth Surface Processes and Landforms, v. 7, p. 303-325, doi:10.1002/esp.3290070403.
  Griffin, C., Duller, R.A. and Straub, K.M., 2023, ‘The degradation and detection of environmental signals in sediment transport systems’, Science Advances, v. 9. p. eadi8046, doi:10.1126/sciadv.adi8046.
  Jerolmack, D.J. and Paola, C., 2010, ‘Shredding of environmental signals by sediment transport’, Geophysical Research Letters, v. 37(19), p. L19401, doi:10.1029/2010GL044638.
  M^cNab, F., Schildgen, T.F., Turowski, J.M. and Wickert, A.D., 2023, ‘Diverse responses of alluvial rivers to periodic environmental change’, Geophysical Research Letters, v. 50., p. e2023GL103075, doi:10.1029/2023GL103075.
  Phillips, C.B. and Jerolmack, D.J., 2016, ‘Self-organization of river channels as a critical filter on climate signals’, Science, v. 352, p. 694-697, doi:10.1126/science.aad3348.
  Tofelde, S., Schildgen, T.F., Savi, S., Pingel, H., Wickert, A.D., Bookhagen, B., Wittmann, H., Alonso, R.N., Cottle, J. and Strecker, M.R., 2017, ‘100 kyr fluvial cut-and-fill terrace cycles since the Middle Pleistocene in the southern Central Andes, NW Argentina’, Earth and Planetary Science Letters, v. 473, p. 141-153, doi:10.1016/j.epsl.2017.06.001.
  Wickert, A.D. and Schildgen, T.F., 2019, ‘Long-profile evolution of transport-limited gravel-bed rivers’, Earth Surface Dynamics, v. 7, p. 17-43, doi:10.5194/esurf-7-17-2019.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2468-AC1
RC1:
'Comment on egusphere-2025-2468', Anonymous Referee #1, 05 Jul 2025

Referee report on

Influence of network geometry on long-term morphodynamics of

alluvial rivers

by

McNabe et al.
The manuscript presents an extended follow-up of the authors' 2023 GRL

on "Diverse Responses of Alluvial Rivers to Periodic Environmental

Change". The authors explore the parameter space of an erosional

longitudinal profile model for alluvial rivers. In the current

manuscript, the main focus is to explore how network properties and

lateral sediment supply influence the evolution in comparison to

single profile models.
While the paper is rather extensive and contains some overlap with the

previous publication, its text is well-written, and the methods and

steps of the analysis are clearly explained. However, a clearer

separation of the new content from the previous results would be

helpful.
For example, the section "background" ends in line 171, and Section 4,

including "numerical results," repeats several findings already

reported in the 2023 manuscript (c.f. Fig. 4 closely resembles a

combination of Fig. 2 and Fig. 3 of the 2023 paper).
Also, the section "Approach" outlining the course of the paper is

somehow squeezed in between two modeling sections.
I would suggest moving the approach section to the end of the

introduction, outlining explicitly which part comes from Wickert and

Schildgen (2019) (the basic profile equilibrium equations), which has

been derived in Mc Nab et al. (2023) (single segment solution) and

what is the actual new part of the paper (lateral along segment inputs

and network considerations).

Keep the sections concise and omit the title "results" when talking

about previous findings, even if they are extended with more detailed

plots, etc. Explicitly refer to the parts that are different from Mc

Nab et al. (2023) (such as lateral sediment input) and what is the

same. For example, it looks like Fig. 2(a) describes the model used

in Mc Nab et al, 2023, and (b) an extension with lateral inputs. But

it is not clear where "network geometry" comes into play.
Maybe it would be good to have a third plot of a "junction" outlining

the last step from single profile to combined profiles, forming a

network.
Note that this last step is not trivial, as it requires the

conservation of several quantities to be satisfied at each junction.
At some point, I simply gave up trying to decipher what is from Mc Nab

et al. (2023) and what is new, and jumped to Sec. 5.
A table summarizing the parameter space may also be useful.

Note that there is a typo in L 200: 10^{-2} = 10^2.
Line 320: Sentence: "We set segment lengths to a uniform value of 5 km

and supply water and sediment only at the valley inlets (Figure

7a,e)", However, when looking at Fig. 7a the segments are of very

different lengths, which is confusing.
While the visualization on a square lattice is simple, a more

"realistic" network geometry (with constant segment lengths in the

case of 7a and adjusted junction angles) may be easier for the

reader to understand.
There should be some tools from complex networks, which may help to

visually construct a network of nodes (junctions) and edges of fixed

size.
Similarly, I could not interpret the main plots in panels (e-h).

For visualizing the network, order, and discharge, one could opt for a

plotting scheme, where the line width of the network changes with

order and the color indicates the discharge.
Fig. 7 i-l: It's not very clear to me how downstream distance,

elevation, and stream order are so uniquely related. Note, for one pair

of distance/elevation, one could imagine finding channels with very

different stream order, which is not what the figure suggests.

In L 340-385, the authors describe different characteristics of

network trees, however, it remains unclear how they actually create

synthetic networks obeying these constraints, e.g., one could use OCN

networks or RSN (Seth A. Veitzer, Vijay K. Gupta, 2000), or other

techniques to create stream networks with a specific Tokunaga

connectivity and then add geometric lengths to the reaches according

to some Horton scaling relation.
Figs. 9, 10, and 11 suggest that there is almost no difference between

simulations with and without along-stream supply, thus the

along-stream supply may be negligible, particularly downstream in the

network.
Maybe it would be interesting to plot the difference between with and

without an along-stream supply. I also would expect that the along stream

component is more important in lower-order streams because at some

point, the fraction between upstream sediment input and lateral input

may be dominated by the upstream sediment supply.

L 495: Sentence: "It is impractical to show here results from each of

the 796 networks we tested; we do, however, provide a script in the

accompanying software repository allowing interested readers to plot

the entire dataset". Are Figs. 14/15 typical examples of the full

dataset? If so, it would be good to state this explicitly, because

although it is impractical to show all 796 plots, readers may still be

interested in seeing representative examples without downloading and

invoking a complex software tool.
L. 600: structure dependence: it may be interesting (maybe not here in

this manuscript) to see if and how different structure classes

described by OCN, Tokunaga parameters etc have similar behavior or

not. (see comment above)

Citation: https://doi.org/10.5194/egusphere-2025-2468-RC1
- AC2: 'Reply on RC1', Fergus McNab, 18 Jul 2025
  
  We thank the Anonymous Reviewer for their constructive comments. In particular, they highlight several points in our manuscript where greater clarification is needed. We will respond directly to each of the Reviewer’s comments and detail changes made later in the context of a revised manuscript. Here, we provide brief explanations on two important issues, in case they are also points of confusion for other readers of the Preprint.
  First, the Reviewer notes that, in our comparison (Section 4.3) between single-segment models with upstream supply (i.e., all sediment and water supplied only at the valley inlet) and along-stream supply (i.e., sediment and water also added along stream), it was not always clear which results were new and which were taken from an earlier paper of ours (M^cNab et al., 2023). The earlier paper focuses on the upstream supply case, and provides analytical solutions for gain and lag as functions of distance downstream and forcing period. All results for upstream supply models shown here were computed using these analytical expressions and so are ultimately derived from our earlier analysis (though the presentation differs in some cases). We believe that the rwo cases need to be presented together in order to facilitate an effective comparison. Nevertheless, we acknowledge that the distinction between new and existing results is important and will ensure that it is made explicitly in our revised manuscript.
  Second, the Reviewer notes: “‘We set segment lengths to a uniform value of 5 km and supply water and sediment only at the valley inlets (Figure 7a,e)’. However, when looking at Fig. 7a the segments are of very different lengths, which is confusing.” We apologise for this confusion. In the schematic network diagrams in Figure 7a-d, only the horizontal lines represent valley segments – the vertical lines have no physical meaning and are only used to connect the horizontal segments. We chose this representation to maintain a consistent “downstream distance” axis and thus facilitate comparison with the other plots in Figure 7 (and elsewhere in the manuscript). We acknowledge, however, that the scheme was not clearly enough explained, and that alternative renderings may be more intuitive. We will carefully consider the Reviewer’s suggestions for this Figure when revising the manuscript.
  References
  M^cNab, F., Schildgen, T.F., Turowski, J.M. and Wickert, A.D., 2023, ‘Diverse responses of alluvial rivers to periodic environmental change’, Geophysical Research Letters, v. 50., p. e2023GL103075, doi:10.1029/2023GL103075.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2468-AC2
RC2: 'Comment on egusphere-2025-2468', Alan Howard, 18 Jul 2025

The paper is well-written, the citations to previous literature are extensive, the methodology as presented in the paper is clear, the simulations concerning single channel and stream network response to sinusoidal variation of water and sediment supply are comprehensive, and the conclusions of the paper seem reasonable.
My main comment concerns incomplete references to some relevant past research on the patterns of response of both single channels and networks to various types of perturbations in the forcing factors of water and sediment inputs as well as base level changes. In particular, Howard (1982, ESPL, 7, 303-325) conducted simulations of the response of both single channel and channel networks to sinusoidal variations in water and sediment yield, as well as response to impulse inputs and base level changes. The channel and network response time is discussed in detail. This modeling was in the context of sand-bed channel systems so that that threshold of motion was not a factor. The application in that paper was primarily on concepts of grade and equilibrium in geomorphic systems, but the computational and analytic treatments for sand bed channels are very similar in conclusions to the present paper. That paper did not consider changes in valley and channel width in response to the modeled responses, e.g., it did not consider channel narrowing in response to incision or changes in channel planform. A particular correspondence between the present paper and Howard (1982) is the change between close adjustment of channel response to low frequency inputs and the strong averaging (or muting of response) to high frequency variation.
The paper could also reference other recent research on filtering of channel responses to upstream inputs due to network response time, such as the Jerolmack and Paola (2010, GRL, 37 L19401) concept of signal “shredding”.
Reviewer: Alan Howard

Citation: https://doi.org/10.5194/egusphere-2025-2468-RC2

Fergus McNab, Taylor F. Schildgen, Jens Martin Turowski, and Andrew D. Wickert

Supplement

https://doi.org/10.5194/egusphere-2025-2468-supplement

Model code and software

Software and data supplement to 'Influence of network geometry on long-term morphodynamics of alluvial rivers' by McNab et al. (2025, EGUsphere) Fergus McNab https://doi.org/10.5281/zenodo.15524965

Fergus McNab, Taylor F. Schildgen, Jens Martin Turowski, and Andrew D. Wickert

Viewed

Total article views: 408 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
337	57	14	408	27	12	28

HTML: 337
PDF: 57
XML: 14
Total: 408
Supplement: 27
BibTeX: 12
EndNote: 28

Views and downloads (calculated since 10 Jun 2025)

Month	HTML	PDF	XML	Total
Jun 2025	137	31	8	176
Jul 2025	91	19	6	116
Aug 2025	109	7	0	116

Cumulative views and downloads (calculated since 10 Jun 2025)

Month	HTML	PDF	XML	Total
Jun 2025	137	31	8	176
Jul 2025	91	19	6	116
Aug 2025	109	7	0	116

Viewed (geographical distribution)

Total article views: 396 (including HTML, PDF, and XML) Thereof 396 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 30 Aug 2025

Short summary

Alluvial rivers form networks, but many concepts we use to analyse their long-term evolution derive from models that treat them as single streams. We develop a model including tributary interactions and show that, while patterns of sediment output can be similar for network and single-segment models, complex signal propagation affects aggradation and incision within networks. We argue that understanding a specific catchment's evolution requires a model with its specific network structure.


Total:	0
HTML:	0
PDF:	0
XML:	0