This paper by Polanco et al investigates the effect of load-induced flexural isostasy and hydro-isostasy on a passive margin system using a numerical model. The authors find that the rate and response times of these processes greatly affect delta stacking pattern, progradation distance as well as extent and duration of unconformities etc. Specifically, the paper concludes that changes in sea level fluctuation during both greenhouse and icehouse times may have resulted in vertical motions that influenced the dynamics of the delta system through isostatic response. The paper is very well written and the figures are generally clear, although there are many figures compared to the length of the manuscript and some can be used as supporting material. Below I have listed some key points that I think should be addressed.

In the introduction, the section covered by lines 35-43 marks the transition from general introduction to the purpose of the study. But in line 44, the authors continue the general introduction comparing glacial margins, sea level fluctuations and isostasy. In line 61, the authors again go into the purpose of the study a second time. I suggest a restructuring of the introduction so that the general introduction is kept separate from the purpose and aim of this study.

In terms of terminology, terms like “Isostatic adjustment”, “flexural response”, “flexural loading”. “flexural subsidence”, “flexural adjustment”, “flexural isostasy” and other similar terms are just variably throughout the paper, but no definition or clarification of these terms are given. Do they all refer to the same process? I suggest that the authors define these terms early in the paper to avoid confusion.

Section 4.1 is called “Flexural isostatic effects on delta morphology and stratigraphic evolution”, and also the caption in Figure 8 points to the difference in river morphology in the flexural vs non-flexural model. However, the authors never explain what the effect on delta or river morphology actually is in Section 4.1. Nor is the stratigraphic evolution described in any detail. The plots in Fig 8b shows river mouth locations, but the differences and implications are not discussed. Except for the fact that non compensated models prograde farther into basin, what are these results telling us?

Another relevant issue is the scale and rate of flexural adjustment to sea level fluctuations. In Section 4.2, for example, is stated that “significant bidirectional flexural compensation can take place at high frequencies”. Even if it is demonstrated that the compensation is coeval with deposition, the amount of vertical movement is not discussed. Figures 5 and 7 suggest that the amplitudes are very high, several hundred meters! Figure 10 implies that a 100 m sea level fall will give an isostatic response of about 10 m, however, actual values are not presented or discussed by the authors. It would be useful to discuss how much accommodation is ascribed to flexural loading and how much is described to sea level fluctuations so that the reader can get an impression of the relative contribution of the two processes.

In the “Results and discussion “section, I also would have liked to see a more concrete discussion on the implication on real systems. In addition to a discussion on the actual rates and amplitudes, as mentioned above, it would be interesting to discuss the interplay between long-term load-induced flexural isostasy vs more short-lived hydro-isostasy. The authors mention that it can enhance valley incision during falling sea level and aggradation during transgression, but are there other consequences of this? For example, will the combined rate of subsidence or uplift be the same across the delta? Can one expect that transgression and increase in accommodation occurs faster in one region compared to another?

More detailed comments:

Line 72: “thermally mature passive margin”, what is a thermally mature margin?

Line 87: Compaction is described together with local controls like growth faults and salt tectonics, but will of course be at the scale of the entire sedimentary wedge.

Line 256: Can you be more specific with the use of accommodation here? Accommodation can be many things. Here I guess you are referring to accommodation created by longer term hydrological  and flexural isostasy. You are not referring to rapid changes in sea level, which also can create rapid changes in accommodation that are not filled immediately.

Figure 4. Which map does the scale bar called ‘Discharge’ refer to?

Figure 5, (d) and (e). The amplitude of flexural uplift and subsidence is almost 1 km in (d), and several hundred meters in (e), whereas the amplitude of sea level variations is 100 m. Values of up to 1 km in response to hydro-isostatic loading does not match up. Perhaps I have misunderstood the figure. Otherwise, please check labels and/or scales.

Figure 6. Check label, should f5Mkyr be f5Myr? Explain what arrows point to

Figure 8. Subplots (a), (b) and (c) are not discussed in the text. Black bars on model outputs, are they scale bars as shown to the left? Please explain in the caption. First line of caption, what is (f) referring to? In description of (c), what is a “de-trended river mouth trajectory”? In this bar plot, it would perhaps be easier to just measure the distance to the shelf break?

Figure 10. ‘Left’, ‘middle’ and ‘right’ does not explain the position of the three plots

Figures 8-15. Consider making some of these figures supplementary material. In many cases, like Figs 11, 12 and 13, they supplement the discussion, but they are not discussed or referred to in any detail in the text.

Review of ESurf-manuscript #2023-53 (The flexural isostatic response…)

The isostatic response to deltaic sediment (un)loading is relevant for studies of the stratigraphic record as well as for understanding flooding hazards in modern deltas. Polanco et al. highlight the need to include flexural responses to both sediment and water loading along continental margins, something that may not yet be the norm in stratigraphic modeling (although I must admit that I haven’t followed this literature very closely in recent years). They do so by coupling a landscape evolution model with a flexure model. Among others, they find that flexural compensation leads to more complete stratigraphies and more limited horizontal shifts of facies belts. As the authors state (lines 116-118) the goal is not to test the model versus observational data, but rather to develop hypotheses that can be examined by means of future empirical studies.

I focus here mainly on some broader issues, along with a few more detailed comments. However, I must add that I struggled with several of the figures and tables, where information was sometimes hard to decipher if not confusing. By way of example, the caption of Fig. 10 talks about a left, right, and middle panel (but that’s not how the figure is arranged; please use a, b, c) and they mention a dashed grey line which I didn’t see. I think I know what they mean, but the reader shouldn’t have to be guessing. There is also a dark brown layer in the lower panel that is not explained. I would urge the authors to carefully examine all figures and tables for such problems; again, I did not try to identify all these issues (but see my comments below about the tables).

My main comment concerns the role of hydro-isostasy which I believe is more complex than suggested. The authors appear to emphasize the effect in the full marine realm where indeed the result of sea-level fall may be uplift (and vice versa). However, the opposite is typically the case along the landward portion of the continental margin (due to lateral flow in the asthenosphere) as widely shown by the mid- to late-Holocene sea-level change in the Southern Hemisphere. This is why some prefer the term “continental levering” (e.g., Mitrovica and co-workers). The implications of this for the present analysis are potentially significant, because any given sea-level change would affect the sediment-dispersal system differently (in fact, in opposite ways) depending on location. Since this is not discussed by the authors, I’m not sure it is something the model incorporates. Figs. 12 and 13 appear to suggest that there would be no hydro-isostatic effect landward of the shoreline. This needs to be addressed; not least because it may have implications for the self-sustaining feedback mechanisms described in lines 242-244. In short, I suspect the story may be a bit more complicated.

The authors use a fairly thin elastic thickness for the lithosphere (50 km) compared to what is commonly done in GIA models. However, since their focus is on relatively long timescales, they could benefit from the inference by Wolstencroft et al. (2014; their Section 5.3) that the elastic thickness decreases over longer timescales due to flow (i.e., a lower viscosity) in the lower lithosphere. That study found values near 100 km for the Holocene, but closer to 50 km for timescales extending into the last interglacial.

Does BADLANDS include waves, tides, and shelf currents? This may not be critical for the present study, but it would be good to know (in lines 130-131 there is mention of further details in a data repository which I couldn’t find).

The manuscript includes fifteen figures and two tables, which is a lot compared to the length of the text. I believe a portion of this could be moved to supplementary information without any harm. For example, are Figs. 11, 12, and 13 all necessary in the main paper? And how about Table 1?

Line 56: model predictions by Ivins et al. (2007) produced subsidence rates that are far higher than observations due to input sediment loads that were off by an order of magnitude. Instead, I suggest Jurkowski et al. (1984, JGR) who pioneered this type of work in this region and came to better results. Among others, they demonstrated the presence of a peripheral bulge associated with a deltaic depocenter and explained this mechanistically, well before others did (lines 80-81).

Line 92: A better reference than Jankowski et al. (2017) would be Keogh et al. (2021, JGR-ES) which explored this issue in much more detail.

Line 101: <1-2 mm/yr is a bit ambiguous; here I think they can safely say <1 mm/yr.

Line 122: Fig. S1?

Lines 154-155: can this be documented in supplementary information?

Fig. 3: needs work; for example, fonts are too small.

Fig. 5: the caption refers to Fig. 1, but presumably this should be Fig. 4?

Tables 1 & 2: in their present form, these tables are a bit cryptic and hard to interpret for the reader. Please avoid acronyms whenever possible (it’s hard to relate to “f5Myr A25m”) and river mouth lengths of >2000 km sound strange. I assume this is the entire river length? It would be much better to use “river-mouth transit distances” as in the main text. And what is “mean maximum accumulation”? Is it the mean or the maximum? I’m sure there are reasons for terms like these; they just need to be explained.

Torbjörn Törnqvist