The authors would like to express our gratitude to the referee for the review and the helpful comments. Revisions and replies are presented in the following.

(1) Lines 94-95: Why did you assume the wave height of the 100-year return period is 1.8 m? Have you done any probabilistic study for this assumption? Because Table 1 shows 100-year significant wave height is greater than 10 m.

Reply: Lines 94–95 (A modern surge maximum of 1.8 m a.s.l. is tentatively inferred to as the 100 year surge in this study.) are focused on the typhoon surge. The 50- and 100-year significant wave heights are presented in Table 1 and Lines 86–87.

There are previous probabilistic studies on the 50- and 100-year significant wave heights (see references in Table 1) and yet no previous probabilistic studies on the 100 year surge on the Penghu Islands. The 1.8 m a.s.l. is inferred from the modern 1.8 m surge maximum of the 2019 Typhoon Mitag among the 118 observed surges from 1997 to 2021 (Lines 91–94). This surge maximum of the period of current global warming may be very close to the 100 year surge and comparable to the maximum in the 17th century of the Little Ice Age period.

(2) Table 1 – what is “observation”? Is it the number of waves?

Reply: The ‘observation’ will be revised as ‘number of measurements’ to better label this column of the table that lists the total measurements at the selected buoys in certain months over the past 10 or 15 years.

(3) Nandasena et al. (2022) formulas do not calculate the minimum wave height but the minimum flow velocity to initiate boulder transport. Therefore, the first four formulas given in the manuscript cannot be referred from Nandasena et al. (2022). The given formulas have a significant difference (perhaps typos) compared to the formulas in Nandasena et al. (2022). Therefore, the authors must include a section to explain how they derived their equations based on Nandasena et al. (2022).

Reply: The first four formulas in this study are the modified Nott’s formulas of wave heights that were deduced from the flow velocity formulas. The flow velocity formulas were modified by a series of previous studies that took virtual boulder dimensions, maximum lifting surface, lift force, fundamental physics, effect of the bed slope, and transport mode sediment sources, transport distances, and shore slope angle into account (see references in Lines 60–64).

In the revised manuscript, Nott (2003) and Nandasena (2020) are to be added to the source references of the four formulas in the footnote of Table 2. Nandasena (2020) reviewed most of the modifications except virtual boulder dimensions that were latter examined by Nandasena et al. (2022).

(4) Line 135: Hudson formula is used for the design of armor-breakwaters against gravity waves (sea and swells). The formula was not validated for tsunamis and storms. However, Esteban et al. (2014) applied the Hudson formula to assess the damage to breakwaters by tsunamis. The authors may cite their paper to support the application of the Hudson formula in this study.

Reply: Hudson formula was only applied to the storm waves in this study (Tables 2 and 3). The application follows the study of Lorang (2011), which also used the formula and the modified Nott’s formulas on storm wave estimates (Lines 135–136).

(5) Lines 136-137: the assumption of Fr =1 and 2 for storms and tsunamis, respectively, is outdated. Because both the high-energy events can have similar Froude numbers varying from as small as 0.5 to as high as 2.5 or more. It is difficult to predict the exact Froude number at the pre-transport location of the boulders without knowing flow characteristics (flow depth and flow velocity). Therefore, the results based on this assumption have a low scientific value. Alternatively, I suggest the authors to conclude based on flow velocities if permitted.

Reply: Flow depth/wave height is derived from the estimated flow velocity and depended upon in this study on the ancient marine inundation deposits, because flow depth is considered the most useful parameter in the studies based on pre-historic events (Nandasena, 2020). In the study area, only the wave height records of historical and modern tsunamis and typhoons are available for the comparison with the calculation results and for the further discussion (Line 84–97 and Table 1).

Like the other coefficients in the formulas, Froude numbers for tsunamis and storms have not been directly estimated, not even during modern events (Nandasena et al., 2022) and the authors are aware that the formulas are under constant review and improvement (Lines 60–69).

It has been pointed out that the fixed Fr numbers produced unrealistic wave estimates for some coastal boulders (Nandasena, 2020). Nonetheless, many recent studies on ancient tsunamis and storms adopted the Fr numbers given by Nott (2003) to highlight the principal flow natures of tsunamis and storms (e.g., Gong et al., 2022; Abad et al., 2020; Callahan et al., 2021; Iwai and Goto, 2021; Gallentes et al., 2021; Lario et al., 2020; Huang et al., 2020; Roig-Munar et al., 2019; Biolchi et al., 2019). In this study, the same Fr numbers were used and incorporated with the up-to-date modifications of wave velocity formulas to deduce the minimum wave heights (see references in Lines 63–64).

In terms of the minimum tsunami wave height, the height increases when Fr number decreases at a constant wave velocity. In the results of this study, the 0.33–0.51 m wave height for initiating sliding and rolling is smaller than the 0.69 m boulder height and appears unrealistic according to Nandasena (2020). It suggests that the minimum depth of the supercritical flow (Fr=2) should add up to 0.69 m to overtop the boulder, or the flow could be less supercritical (1<Fr<2) and the minimum wave height may be comparable to the storm wave height and reach 2.03 m (Table. 3). Both of the conditions remain supportive of our inference that the minimum wave height of sliding–rolling transport is incapable of the 2.5 m high CTB deposition. In addition, the minimum wave height of the less supercritical flow (1<Fr<2) to initiate the saltation transport is larger than the 2.13–2.29 m height of the supercritical flow (Fr=2) and may reach 9.16 m (Table 3). This is also supportive of our inference that the tsunami waves for the boulder deposition may be huge and significantly overflow the 2.5 m high clifftop.

As for the storm waves, the flow velocity is expected to be higher in the E-W direction parallel to the CT Channel than that in the southward/shoaling direction to the boulder outcrop studied (Fig. 2). In this shallow interisland channel (<4.5 m deep), the shoaling flow may be prone to the relatively low supercritical to critical regime. In some cases, the storm wave overwash can be highly supercritical (Fr>2) and the onshore flows can be also supercritical (1<Fr<2; Cox et al., 2020). The supercritical overwash may result in the unrealistic minimum wave height <0.69 m in the study (Nandasena, 2020). The less supercritical storm onshore flow with the realistic minimum wave height of 0.69 m (Fr=1.6) requires a 1.5–2.65 m water depth at wave break (Lines 354–357) which mostly exceeds the shallow inundated supratidal zone (<2.0 m deep) during the rare 1.8 m high 100-year surge with the 0.2 m higher sea level in the 17th century (Fig. 2C). Or, the waves will break early in the inundated intertidal zone, attenuate rapidly and exponentially landwards (Lines 204–207), and are incapable of the 2.5 m high supratidal boulder deposition.

(6) Table 3: Some tsunami periods are highly unrealistic. For example, 3.4 S, and 3.6 S. Tsunamis are considered long-period waves. The calculated numbers fall in short-period waves. The authors need to declare which formulas used to calculate wave period (Lorang or Barbano) and describe their results carefully following the established scientific definitions.

Reply: The formulas used to calculate wave periods are declared in Table 2. The authors do agree that the tsunami waves with 3.4 and 3.6 s periods in the supratidal zone are undistinguishable from the storm waves. It may indicate that the present formulas need to be improved to better estimate the tsunami waves in the supratidal setting, which is out of the scope of the present study. Or the successive shortening of the estimated period in the intertidal–supratidal zone probably responds to the deceleration of the tsunami wave during shoaling that also causes a landward decrease in wavelength alongside an increase in the wave height (Table 2 and Lines 244–245).

References

Abad, M., Izquierdo, T., Caceres, M., Bernardez, E., and Rodriguez-Vidal, J.: Coastal boulder deposit as evidence of an ocean-wide prehistoric tsunami originated on the Atacama Desert coast (northern Chile), Sedimentology, 67, 1505-1528, 10.1111/sed.12570, 2020.

Biolchi, S., Furlani, S., Devoto, S., Scicchitano, G., Korbar, T., Vilibic, I., and Sepic, J.: The origin and dynamics of coastal boulders in a semi-enclosed shallow basin: A northern Adriatic case study, Marine Geology, 411, 62-77, 10.1016/j.margeo.2019.01.008, 2019.

Callahan, G., Johnson, M. E., Guardado-France, R., and Ledesma-Vazquez, J.: Upper Pleistocene and Holocene Storm Deposits Eroded from the Granodiorite Coast on Isla San Diego (Baja California Sur, Mexico), Journal of Marine Science and Engineering, 9, 10.3390/jmse9050555, 2021.

Cox, R., Ardhuin, F., Dias, F., Autret, R., Beisiegel, N., Earlie, C. S., Herterich, J. G., Kennedy, A., Paris, R., Raby, A., Schmitt, P., and Weiss, R.: Systematic Review Shows That Work Done by Storm Waves Can Be Misinterpreted as Tsunami-Related Because Commonly Used Hydrodynamic Equations Are Flawed, Frontiers in Marine Science, 7, 10.3389/fmars.2020.00004, 2020.

Gallentes, A. T., Manglicmot, M. T., Gong, S. Y., Hu, H. M., Shen, C. C., and Siringan, F. P.: Coral boulder transport and gravel bar formation by storms in Lumaniag village, Batangas, northwestern Philippines, Geomorphology, 376, 10.1016/j.geomorph.2020.107554, 2021.

Gong, S. Y., Liu, S. C., Siringan, F. P., Gallentes, A., Lin, H. W., and Shen, C. C.: Multiple severe storms revealed by coral boulders at Pasuquin, northwestern Luzon, Philippines, Palaeogeography Palaeoclimatology Palaeoecology, 606, 10.1016/j.palaeo.2022.111195, 2022.

Huang, S. Y., Yen, J. Y., Wu, B. L., and Shih, N. W.: Field observations of sediment transport across the rocky coast of east Taiwan: Impacts of extreme waves on the coastal morphology by Typhoon Soudelor, Marine Geology, 421, 18, 10.1016/j.margeo.2019.106088, 2020.

Iwai, S. and Goto, K.: Threshold flow depths to move large boulders by the 2011 Tohoku-oki tsunami, Scientific Reports, 11, 10.1038/s41598-021-92917-2, 2021.

Lario, J., Spencer, C., Bardaj, T., Marchante, A., Garduo-Monroy, V. H., Macias, J., and Ortega, S.: An extreme wave event in eastern Yucatan, Mexico: Evidence of a palaeotsunami event during the Mayan times, Sedimentology, 67, 1481-1504, 10.1111/sed.12662, 2020.

Nandasena, N. A. K.: Chapter 29 - Perspective of incipient motion formulas: boulder transport by high-energy waves, in: Geological Records of Tsunamis and Other Extreme Waves, edited by: Engel, M., Pilarczyk, J., May, S. M., Brill, D., and Garrett, E., Elsevier, 641-659, https://doi.org/10.1016/B978-0-12-815686-5.00029-8, 2020.

Nandasena, N. A. K., Scicchitano, G., Scardino, G., Milella, M., Piscitelli, A., and Mastronuzzi, G.: Boulder displacements along rocky coasts: A new deterministic and theoretical approach to improve incipient motion formulas, Geomorphology, 407, 10.1016/j.geomorph.2022.108217, 2022.

Roig-Munar, F. X., Rodriguez-Perea, A., Vilaplana, J. M., Martin-Prieto, J. A., and Gelabert, B.: Tsunami boulders in Majorca Island (Balearic Islands, Spain), Geomorphology, 334, 76-90, 10.1016/j.geomorph.2019.02.012, 2019.

The authors appreciate the thorough review and suggested revisions of the referee that will certainly help to improve the manuscript and its readership.

There are three major comments in the results of the review, which are responded in the following.

(1) The paper reports on matrix-supported boulder… On this basis alone I am convinced that these are tsunami deposits rather than typhoon deposits.

Reply: The authors are encouraged by the positive comment on one of the major contributions of the present study, i.e., presenting facies constraints on the sediment transport of the paleotsunami gravels and basalt boulders on the Penghu Islands (Line 22).

(2) I also believe the authors should established a more solid comparison with similar deposits and their characteristics, as this is would strengthen the argumentation of the paper.

Reply: The candidate marine deposits investigated in the study were compared with the tsunami deposits in Hawaii (Lines 300–302) based on the study of Paris et al. (2018) that was suggested by the referee for the authors to look at. The candiate deposits were also compared to the tsunami deposits on the Japan Sea and Pacific coasts of Hokkaido (Fujiwara and Kamataki, 2008; Nanayama and Shigeno, 2006). The common occurrences of articulated bivalves and stranded pumices in the candidate deposits and the tsunami deposits on the Pakistan coast (Lines 374–376; Donato et al., 2008) and on the northern coast of Taiwan (Lines 310–311; Yu et al., 2022) were also presented.

        The other suggested references of the Canary Islands and Cape Verde are valuable. Among them, the studies of Perez-Torrado et al. (2006) and Madeira et al. (2020) present detailed facies characteristics and also occurrences of articulated bivalves will be cited in the revised manuscript.

(3) Below are a few passages of the text that I suggest revising, given that they are (in my view) confusing and not very clear, as well as a few minor language edits I suggest.

Reply: The authors are indebted to the referee for the editing advices. Most of them are to be accommodated and the responses are here listed.

Line 76 – remove the comma after "The Taiwan Strait"

Reply: Removed as suggested.

Line 77 - what do you mean by "dominant water depth"? Average water depth? Please be more objective here

Reply: The ‘dominant water depth’ of the Taiwan Strait is from 20 to 80 m, as shown by the water depth contours in the cited figure of Fig.1a.

Line 78 – what do you mean by "more than 90 units of Miocene basalt platform"? I really do not understand what the authors mean here... the term "units" in geology generally refers to stratigraphic units, yet I presume the authors here use the term with the meaning of individual boulders or clasts... so I suggest revising this to a more objective term – perhaps "more than 90 boulders derived from the Miocene basaltic platform"?

Reply: The units will be replaced by pieces.

Line 81 – the authors describe sea-level fall... I presume they refer to local relative sea-level fall... is this correct? Please be more precise/objective and state if you refer to relative or eustatic sea level, and please provide more information as to the nature of this sea-level change (climate-related? Subsidence/uplift related?)

Reply: It will be revised as ‘local sea level’.

It was previously reported that the Holocene local sea level changes in the Penhu Islands area were dominated by the global sea level (eustatic) fluctuations due to the local tectonic quiescence. Please see Lines 80–84 and references therein.

Line 110 - another reference to largest boulder unit... again I presume the authors refer to a particular clast or boulder and not a unit composed of boulders... if so please remove the term "unit" from this phrase.

Reply: Removed as suggested.

Line 111 – I find the following phrases really confusing "The cliff-top boulders are supported by a gravel and mud matrix that forms a lateral gravel layer (MECT-1) that pinches out from 2.5 to 4.0 m a.s.l. Marine shells and rounded pumice pebbles that are abundant in both matrix and gravel layer, and are also found on modern beaches in the region (Fig. 3b), are absent in the underlying basalt basement, basal soil, and overlying angular-gravel colluvium." Could you please reformulate these phrases and make it more concise? 

Here is a possible suggestion: "The cliff-top boulders are supported by a gravel and mud matrix that forms a laterally-continuous layer (MECT-1) with variable thickness and extending from 2.5 to 4.0 m a.s.l. Marine shells and rounded pumice pebbles are also abundant in the matrix, can be also found on modern beaches in the region (Fig. 3b), but are distinct from the underlying basalt basement, and are absent in the basal soil and overlying angular-gravel colluvium."

Reply: The suggestion is appreciated and will be adopted with a slight modification to feature the ‘pinch-out’ bedform which marks the minimum run-up height.

Lines 119-121 – change the existing phrase to "An intertidal rock exposure that is located 0.5 m below sea level and is covered by isolated and stacked boulders of sizes and shapes that are comparable to the CTB may be the source of the studied boulder (Fig. 3d)"

Reply: The lines are rephrased as ‘An intertidal rock exposure with well-developed joint fractures may be the boulder source for being covered by boulders that are comparable in size and shape to the CT boulder (Fig. 3d).

Lines 173-175 – this phrase is also very confusing... I suggest changing "better obtain" to "understand"... also, what do you mean by "during a marine event"? Are you referring to a storm? A typhoon? Another tsunami? please be more concise...

Reply: The ‘obtain’ will be replaced as suggested. The ‘gravel layers that were deposited during a marine event’ will be revised as ‘gravel layers that contain sediment of marine origin’.

Lines 200-203 – similar to my comment to line 81, I find the statement "During this period, the maximum water depth in the CT Channel could increase from 2.5 to 4.5 m because the sea level was approximately 0.2 m higher than it is at present" confusing... first I would suggest changing "could increase from 2.5 to 4.5 m" to "was 2.5 to 4.5 m higher than today". Presumably you are also referring to relative sea-level change – could you be more precise/objective here?

Reply: The ‘sea level’ will be revised as the ‘local sea level’.

The authors tried to precisely express that the maximum water depth in the CT Channel could increase from 2.5 to 4.5 m. It is 2.5 m measured in the fair-weather condition by the authors and may be 4.5 m at the occurrence of 100 year surge with the higher local sea level in the 16th–17th centuries (Fig. 2a).

Lines 213-214 – I also find this phrase really confusing and grammatically incorrect: "The CTB is floored by the pumice-bearing gravel and mud matrix above the cliff basement (Fig. 4d) and the gravel layer are matrix-supported" – could you please revise this phrase to improve clarity?

Reply: The lines are rephrased as ‘The CTB is underlain by the matrix of pumice-bearing gravel and mud above the cliff basement (Fig. 4d) and the matrix laterally forms a mud-supported gravel layer (Fig. 3a–b).

Finally, in my view the text overuses acronyms/abbreviations, making it really difficult to read... the use of acronyms/abbreviations is useful economy of speech tool that can help the reading of a manuscript, but its overuse can make a text harder to read, especially when many abbreviations are very similar and some are really unnecessary... for example, why abbreviate "marine event"? (I also suggest being more concise with this term)? The manuscript possibly contains more than 10 different abbreviations, which in my view affects its readership, so I suggest the authors to revise this...

Reply: The authors appreciate the advice.

The CTB for CT boulder will be removed.

The use of ‘marine event’ and ‘ME’ will be removed in the revised manuscript. The coding and naming of the key gravel layers will be largely removed (Fig. 5a). The MESGS-a and b layers are revised as the upper and lower SGS layers, respectively. The MESG-a and b layers are revised similarly.

Only the common abbreviations may be preserved, such as a.s.l. for above sea level.