I read the manuscript by Turowski et al. with great interest. It presents significant efforts to characterize the width evolution of channel belts using a comprehensive approach that integrates analytical solutions, numerical models, flume experiments, and field data. Although well-crafted overall, the manuscript would benefit from improved readability in later sections.

Major comments.

(1) Clarification of river types/planforms that create the channel belt. The manuscript effectively presents analytical solutions in a step-by-step manner that is easy to follow. However, it remains unclear whether these solutions are intended for meandering rivers or braided rivers. This distinction is crucial as the manuscript appears to alternate between discussing belt width evolution in both types of channels. If the authors believe that the differences between these river planforms are not significant, please articulate this argument early in the manuscript and support it with evidence. The described workflow seems more akin to a single-thread channel that widens the belt through a random walk process, raising questions about its applicability to multiple-thread river channels. Clarity on this point in the introduction, methodology, results, and discussion sections would greatly enhance the manuscript’s impact.

(2) Detail and clarity in later sections.

The manuscript maintains excellent readability up to Chapter 3, after which the presentation becomes more abstract and details become sparse. Specifically, Section 3.2 leaves readers uncertain about the types of rivers that produce the discussed floodplains and whether these are confined or unconfined settings. This section would benefit from additional background information. The Results chapter is notably brief, and the figures often include minimal descriptive text, sometimes limited to a single sentence or solely interpretations. While I understand there is much information in the captions, a more thorough description of each figure within the text would help readers follow the narrative more effectively and discern whether there is consistency across different data sets.

Specific comments

Abstract: The abstract contains numerous technical terms that may not be accessible to a broader audience, such as "first passage time" and "sediment residence time." Please consider providing brief definitions of these terms within the text constraints.

Line 9: It's not necessary for floodplains to form exclusively during channel migration; overbank flooding is a predominant factor.

Line 27-28: The comparison is made between the model and field and flume data. Could you clarify how analytical solutions compare?

Line 28: temporal evolution “of” channel belts – off is missing.

Line 57: braiding river – braided river

Line 334: “structures a distance b from the river” -- “structures located a distance b from the river”

Line 374: when mentioning these ratios, suggest clarifying these are for unconfined, moderately confined, or highly confined scenarios to provide context for the chosen values.

Section 3.2: This section is too brief to provide a clear understanding of the comparisons being made.

Section 3.3: The experiments concern braided rivers, but it remains unclear whether the random walk model applies to the same river types.

Results chapter: Please describe each figure in detail before discussing comparisons or discrepancies. This approach will help readers better understand the visuals and their significance.

Figure 2a: in the legend, Hw = 1, 10, 100, which should likely be Hw/h, I assume. Also, please mention these ratios in the caption and ideally link them with confinement and unconfinement.

Figure 3a: consider using drift distance, since displacement is not mentioned or defined earlier.

Line 542: Lancaster et al. work is not presented, although its inconsistency with the results is suggested. Please clarify why the three digitized datasets were selected and their differences from Lancaster et al.'s work.

Line 551: Insert “where” before “both channels in confined valleys”

Conclusions: The conclusion seems too general and does not succinctly summarize the findings of this study. It reads more like an overview of the study's significance. Please highlight the key findings here.

I thoroughly enjoyed reading this manuscript. Turowski et al. present a thorough and detailed exploration into an analytical framework to model the evolution of river channel belts using the statistics of a random walk process. The authors suggest that channel-belts evolve in three phases, a linear expansion, exponential growth, and drift, each with unique statistical properties. The model itself is intuitive and the authors are quite successful in clearly walking the reader through its formulation. The manuscript provides an extremely strong motivator for future work including opportunities for its validation in natural rivers, and its utility in alluvial river restoration and risk quantification. I believe that the model is an important contribution and a paper in this style will be of broad interest to those working within river landscapes. I have one major comment and a few minor comments with the current version.

Major comments:

The loose structure of the latter half of the manuscript (section 3 and onwards) could be improved, specifically focusing on grouping similar points of focus and adding more detail. Some examples of how the current framing needs more detail and structure:

1. Section 3 includes the set up to the external procedures and datasets used to validate the model. I agree that validation for the model is integral for the success of the paper, but the authors need to flesh out how these datasets/numerical procedures can validate the analytical model. There is no discussion of how success will be evaluated. This section should tell the readers how they should know the analytical model does a good job at representing reality.
2. The results section (section 4) is currently formatted as a grouping of figures. I would expand this section to walk through what the figures are showing. If section 3 is set up well, this could include things like descriptions of r-squared values between the numerical and analytical results.
3. As a reader, there seems like there could be a distinction between the validation of the model and the application of the model. To explain what I mean by this, the numerical simulations (section 3.1) and the examination of the Bufe 2016, 2019 experiments (section 3.3) are great examples of opportunities to validate the model. On the other hand, the sediment residence times seems like a natural application of the model, using it as a tool for geochemistry, not just geomorphology. In the current version of the manuscript, these components are grouped together in shared sections. I think some clarity could be gained by separating the ideas of validation and application in the text. One could even section out the paper to have a specific validation section, then a specific application section, which could help break up the results into a natural structure and motivate expanding section 3.

Minor comments:

1. The introduction could use a stronger statement as to why predictions and theory for the evolution channel-belts are important. The authors could lean on the value of the predictive model specifically. A model connecting channel-belt width through time to hydraulic variables has direct applications in quantifying floodplain risk and management (forward model), as well as to back out hydraulic properties (or even relative migration timescales) from direct measurements of channel-belt widths in fluvial strata (inverse model). There are a couple places in the text (outside of the introduction) where this type of implication/context is given in more detail. I would suggest moving those to the set-up of the paper.
2. Be explicit about planform applicability. The fact that it works for the Bufe experimental data suggests that the model is widely applicable, but it would be nice throughout the model set up do discuss explicitly that planform differences are an important consideration. Intuition suggests to me at least, that delta_T (delta_t) should be different depending on if a river has a single, or more than one active thread.

Line-by line comments:

Eqs (7) and (8) – I may be unfamiliar with standard notation, but the left side of equations could be more descriptive. Instead of PDF_exponential, they could be PDF_TW and PDF_dx respectively. The functional form of the PDF is anyhow seen on the right side. Would help connect the probability functions to what they represent in the equation (not just vis-à-vis the text).

L227: Keep language consistent around unconfined and confined channel belt. Should be formalized in the set up. “Unconfined plane” is a new way of referring to this.

Section 2.3.3: The section is clear. The derivation of c, while cool to see how it falls out of the model, could be moved to a supplement to simplify text.

L311: “Knowledge of this distance…” exactly the type of language that could be rolled into the motivation to the problem (section 1). Having this already known to the reader would mean you could jump right into the derivation after the topic sentence.

L:321 should the “(eq. 15)” be “(eq. 20)?”

L376: “limiting the channel-belt width to the steady-state width by adjusting the other side of the valley.” This is an interesting assumption to keep examining because there are so many unknowns at play. For a numerical (or analytical) model, regardless if vegetation recolonizes the other side of the channel-belt, in terms of its evolution, it’s still part of the same channel-belt even though it is statistically unlikely that it would be visited by the channel. This remains true for a natural channel-belt between avulsion events. I don’t have much intuition outside of unconfined channel belts, but I would not take the channel belt width preservation to be a widely valid assumption.

L395: No topic sentence as to why the authors are leveraging this experimental dataset. The opening paragraph to the section simply states that the “results are compared to two separate types of data… (ii) the temporal evolution…in the experiments of Bufe et al…” I know implicitly that it’s to validate the model against scarce empirical data, but the authors never explicitly state as much. This relates to my major comment.

Results section: Check figure numbers throughout this section.

L416: This should be Fig. 7 not Fig. 6.

Fig. 7: It’s unclear to me why you are only fitting the drift phase to the data? Given the long experimental run times relative to the mobility, shouldn’t you be able to recognize all three phases of growth and evolution?

L554-560: If you aren’t going to discuss q_L, and I agree that it’s not necessary, you can remove this text and simply set up a topic sentence (and section heading) about k.

L571: The switch between the statement touching on directly estimating k, and an empirical model for λ is sudden and not set up well. This paragraph could use a topic sentence for what this derivation is arriving at.

Section 5.5: Would the authors make the suggestion that their simplifying assumptions of independent cross-sections wouldn’t lead to fruitful results when examining 2d planform changes?