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.

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.