Observations of extreme wave runup events on the U.S. Pacific
Northwest coast

Li, Chuan; Özkan-Haller, H. Tuba; García-Medina, Gabriel; Holman, Robert A.; Ruggiero, Peter; Jensen, Treena M.; Elson, David B.; Schneider, William R.

doi:https://doi.org/10.5194/nhess-2020-425

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https://doi.org/10.5194/nhess-2020-425

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26 Jan 2021

Observations of extreme wave runup events on the U.S. Pacific Northwest coast

Chuan Li¹, H. Tuba Özkan-Haller^1,2, Gabriel García-Medina³, Robert A. Holman², Peter Ruggiero², Treena M. Jensen⁴, David B. Elson⁴, and William R. Schneider⁴ Chuan Li et al.

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¹School of Civil and Environmental Engineering, Oregon State University, Corvallis, OR, USA
²College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA
³Marine Sciences Laboratory, Paciﬁc Northwest National Laboratory, Seattle, WA, USA
⁴National Weather Service, National Ocean and Atmospheric Administration, Portland, OR, USA

Received: 05 Jan 2021 – Discussion started: 26 Jan 2021

Abstract. Extreme, tsunami-like wave runup events in the absence of earthquakes or landslides have been attributed to trapped waves over shallow bathymetry and long waves created by atmospheric disturbances. These runup events are associated with inland excursions of hundreds of meters and periods of minutes. While the theory of radiation stress implies that nearshore energy transfer from the carrier waves to the infragravity waves can also lead to very large runup, there have not been observations of runup events induced by this process with magnitudes and periods comparable to the other two mechanisms. This work presents observations of several runup events in the U.S. Pacific Northwest that are comparable to extreme runup events related to trapped waves and atmospheric disturbances. It also discusses possible generation mechanisms and shows that energy transfer from incident waves to bound infragravity waves is a plausible generation mechanism. In addition, a method to predict and forecast extreme runup events with similar characteristics is presented.

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Chuan Li et al.

Interactive discussion

Status: closed

RC1:
'Comment on nhess-2020-425', Anonymous Referee #1, 22 Feb 2021
General comments

This manuscript investigates the mechanisms leading to a series of very large run-up events that took place within a couple of hours at different locations along the US Pacific Northwest coast. The authors show that the series of extreme runup events coincides with the arrival of very long swells at the coast and hypothesize that these long swells were responsible for the generation of unusually large (initially bound) infragravity waves that ultimately led to the large, 5-6 min period, run-up events that were filmed by beachgoers.

The manuscript addresses a topic that is relevant to the scientific community and presents some interesting results. The analysis is however limited by the type of data that is available (e.g., no nearshore wave measurements except the 1min-resolution tide gage water level data) that prevents strong conclusions to drawn. I think that it is acceptable as long as the limitations of the analysis are clearly stated (in the core of the manuscript but also in the conclusions). This is a point that needs improvement in my opinion (see comments on below the interpretation of the DART data for instance). Furthermore, several aspects of the methodology, particularly in Section 6.2, need to be clarified and possibly contain errors (see detailed comments in the next section).

I therefore recommend major revisions.

Specific comments

The paper refers a few times to the runup of bound infragravity waves. I find the formulation confusing as the infragravity waves that run up the beach are not bound anymore (released in the surf zone).

This is coming back at different locations within the paper, in slightly different forms. For instance it is stated line 265 that “th[e] bound wave travels at the speed of the wave groups towards the shore and as a free wave […] after reflection” which is not strictly correct as IG waves are not bound until the shore. Or in line 312 the authors discuss the “dissipation of the bound infragrvaity waves” and refer to van Dongeren et al. 2007 to do so, while this paper examines dissipation close to the shoreline, i.e. at a location where the IG waves are not bound anymore.

Line 32: I don’t think the reference to Roeber and Bricker is appropriate as an example in which trapped waves lead to extreme runup (they actually explicitly state that “Resonant amplification over the reef flat […] did not contribute significantly…”).

Line 62: “the amplification of low frequency motion was found to decrease dramatically during storms”. What does that mean? How does it relate to the previous statements?

Line 106: I do not understand the sentence “Data is […] averaged over 1 minute to produce 1 min timeseries”? Is 1 minute the sampling interval or the duration? (probably the first one?)

Lines 180-182: I find that the time delay between observations of “larger than usual” oscillations at the DART sensors and at the tide gages difficult to visualize and as a result the numbers given in the text seem quite arbitrary (I could argue based on visual inspection of figure 5 that the largest waves at Garibaldi occur several hours after the point identified as the approximate onset of the anomalous water level fluctuations… which would in turn change all the time lags). As this time delay seems important to the current narrative (it is used later to support the fact that the observed large oscillations at the DART sensors could be due to IG wave reflection), it would be useful to define periods with “higher than usual magnitudes” in a more systematic way (e.g., it starts when the elevation is larger than X*std(eta)?).

Lines 191-193: As wave direction cannot be inferred from a point measurement of surface elevation/water column height, I do not think it is fair to talk about “large offshore directed waves detected at the DART bottom sensors”. It should be formulated in such a way that it is obvious that it is only a hypothesis, which, if I understand correctly, mostly relies on the fact that there is some time lag between the moment at which the largest oscillations are observed at the tidal gages and at the DART sensors. See also previous comment.

Line 194: At several tide gages (Crescent City, South Beach, Westport) the spectra seem to peak in the 13-22min band (figure 6), and not at 5 min, which suggests that the water levels at these gages (and thus possibly the runup) is dominated by motion in this lower frequency band (associated with resonance in the text). I am not sure this is consistent with the statement that resonance is of secondary importance to explain the extreme water levels. Unless the variance contained in this lower frequency peak is actually less than the variance in the 5min peak (hard to evaluate visually because of the log-scale in the frequency axis)?

Lines 195-207. There has been a number of recent publications on coastal hazards induced by meteotsunamis such as Shi et al., 2020 (Nature communications) and Anarde et al. 2020 (JGR-Oceans) that could be relevant to this discussion. For instance Shi et al., 2020 showed that both single-peak meteotsunami waves and long lasting meteotsumami wave trains could be generated (thus not only soliton like waves as mentioned in the manuscript). Anarde et al., 2020 showed that pressure disturbances much lower than the 5HPa mentioned in the manuscript could trigger significant meteotsunamis.

Lines 211-212: The fact that the long waves that are responsible for the extreme run-up events were generated as bound infragravity waves is a key result of this paper which is in my opinion not sufficiently supported. I understand that data availability limits the analyses that can be conducted, but still feel that stating that 5-min is a “plausible period for wave groups when carrier waves are 25 s” (see also line 260) is in itself not a very convincing statement (for such a key result). Have the authors considered using the measured spectra at the wave buoys to reconstruct a timeseries using a random phase (which is probably not a too bad assumption in these depths) and examine the group structure? They could for instance look at the spectrum of the envelope of such a reconstructed timeseries and check that it indeed peaks around 5 min? That would lend some additional support to the fact that such a wave field could indeed force bound waves in the proper frequency range.

Line 222: What is the typical period of the waves measured by the DART sensors during the period where they recorded at high temporal resolution? Is it indeed close to 5min and therefore consistent with the 5-min peaks in the tidal gage spectra?

Lines 276-279 (and following): van Dongeren et al. 2007 (and I expect that Battjes et al. as well, although I haven’t re-checked) used shoaling zone data in off-resonant conditions to examine the relation between the growth rate (alpha) and the normalized bed slope (beta) and demonstrate that the infragravity wave amplitude was bound between h^(-1/4) and h^(-5/2). This means that the relation between beta and alpha (that is used in this paper) was derived for conditions in which the carrier waves were not in shallow water, contrary to what is stated at the start of this paragraph (and a few times later on, e.g., line 295).

Lines 291-305: I find it difficult to understand what the model is exactly doing, and even more difficult to follow the description of the model outputs that follow in the second paragraph. Some additional information is needed (see questions/remarks in bullet points below). A figure showing the cross-shore evolution of short wave and infragravity wave heights could also help.

Line 294: I would expect that the infragravity wave amplitude is calculated until the moment the short waves break, not when the infragravity wave break as stated here (as van Dongeren et al. derived eq. (3) based on shoaling zone data)?

Lines 296-298: I guess the short-wave height is shoaled according to linear wave theory until H=gamma*h? It would be good to say it explicitly.

Line 303: I find the formulation confusing. I do not expect that the model described in the paragraph above is needed to determine that 25 s waves are in shallow water for h<15m (which depends only on the dispersion relation). Also, how is this info used to determine that the infragravity waves have a 0.87 m amplitude at this depth? Does it mean that eq. (2) is used until the point where the waves enter shallow water (let’s say h/L=0.05)? In that case, does it mean that van Dongeren et al. relation is used only shoreward of that point? (while to the best of my knowledge this empirical relation was not derived using shallow water data - see also comment #11)

Lines 305 and 306: Different alpha’s are used for the 10s and 25s short wave cases. I understand that these depend on the beta-values, but how are these beta’s calculated? Do they differ only because of differences in breaking depth for the 10 and 25s short-wave periods? Or is omega, the IG wave frequency, changing as well when the carrier frequency is changing? If that’s the case, how is it changing/what is the assumption to calculate this frequency?

Line 306: an infragravity wave of amplitude 2.3 m (so 4.6 m high) in 5.8 m depth seems very large. Is it a typo or is there a problem with the model?

Line 308: It seems unlikely that waves that are 5m high offshore break at a depth of 1.8 m (I would expect the breaking depth to be closer to 6-7m). Is this a typo?

14. I have similar comments/questions on the paragraph discussing the dissipation patterns based on the beta_H-value

How is beta_H calculated in both cases? Again, beta_H depends on the infragravity wave period (or frequency), not on the short-wave period. So some explanations are missing.

According to the definition of beta_H, a larger IG wave height H means a smaller value of beta_H, and thus a smaller R (meaning more dissipation). So unless other parameters are varying (such as the long wave period), I do not understand how it can be concluded that the case with larger infragrvaity waves is dissipating the least (lines 322-324).

15. Finally, the link between dissipation and run-up does not seem that straightforward to me as we are comparing the runup of waves that have different incoming heights (and maybe period?). A wave that dissipates more can still lead to a higher runup than a smaller that would have dissipated less…

16. Lines 388-389: “This conclusion is supported by far offshore sensors which did not detect the incoming waves but did detect the returning ones…”: The formulation suggests that the authors were able to discriminate between incoming and reflected waves -> reformulate?

17. It should be clear in the conclusion that the predictor developed in this study is (likely to be) highly site-specific (depends on a dimensional parameter, involves a proportionality factor that already varies strongly along the considered stretch of coast…).

Technical corrections

“very low frequency” is usually used to describe motions happening at a much lower frequency than the long swells described in this paper, which I find a bit confusing.

Line 228: shouldn’t it be figures 8 and 9 instead of figures 9 and 10?

Line 346: I guess that sqrt(m_{-3}f_{m}^3) should be sqrt(m_{-3}) here?
Citation: https://doi.org/10.5194/nhess-2020-425-RC1
- AC1:
  'Reply on RC1', Chuan Li, 13 May 2021
  Response to general comments
  We appreciate the reviewer's assessment and the thorough review. Regarding the limitations of the analsys, we will clearly state that that only nearshore measurements available to us during this ‘experiment of opportunity’ are from the tide gages along the coast. Regarding the methodology, we will make the clarifications as the reviewer suggested. Please see our response to each specific comment below.
  Response to specific comments
  (Omited as specific comments starts with #2)
  
  This is a valid point. In our revision, we will use ‘bound infragravity waves’ to refer to incoming infragravity waves prior to incident wave breaking. We will use the terms ‘infragravity waves’ and ‘infragravity motions’ to refer to onshore movements of these low frequency waves after incident wave breaking.
  
  We agree with this assessment. In our revision, we will refer to this work as an example of large runup from energetic infragravity waves generated by abrupt breaking of incident waves.
  
  By low frequency runup we meant runup associated with infragravity wave frequencies. We will clarify this in our revision. This particular statement is not related to the previous statements but is a key finding from the previous work in discussion.
  
  We agree that this did not read very clearly in the original manuscript. In the revision, we will make it clear that the data is sampled at 1 Hz but is averaged and recorded every minute.
  
  We appreciate this comment. We will use a more quantitative measure to identify the “onset” of large water level fluctuations. We think the X*std(eta) suggestion is a good one. In the revised manuscript we will also identify the onset at each station rather than the approximate onset over all stations. This will provide more detailed analysis for each station.
  
  We agree here as well. Here, in the revision, we will not write “offshore directed” when we are describing the data itself. We will use care to differentiate what the data shows and what we are hypothesizing based on other observations and theory.
  
  We realize that the spectra indicate that at some gages there were strong water level motions in the longer, 13-22min periods. However, video footage (https://youtu.be/JMYLvSsWR_g) shows that the extreme runup events were much closer to the 5 min period. The tide gages are also well inside the inlets. As some of the videos show, the heights of the bores associated with the extreme runup events were considerably reduced as they traveled further into the inlets. Furthermore, the two gages that show the largest fluctuations – La Push and Charleston (we do not include Crescent City here because it is known to amplify shelf resonance from its harbor) – show a clearly stronger signal in the 5 min period (taking into account the log scale). We will clarify this point in our revision.
  
  We thank the reviewer for making us aware of these new works on meteotsunamis. We will cite these papers and add their results into our discussion. We note that in Shi et al., the large wave trains have periods on the order of hours (compared to our 5 min signal). We also note that the pressure disturbances in this work (<1HPa) is still on the low side of the pressures found to generate meteotsunamis in the study of Anarde et al. (~1-3HPa). The runup period (~5 min) in this work is also lower than the meteotsunami period (~20 min) in Anarde et al. However, we do think it is important to include these new papers in our discussion.
  
  We agree with this assessment and per the reviewer’s suggestion conducted a wave group period analysis. To do this, we used Kimura’s (1980) method of computing the mean wave group period directly from the energy spectra (which does not require generation of time series). We note that there is an inherent uncertainty with any method of wave group period calculations, which arises from how the wave group is defined. A wave group is usually defined as consecutive waves with wave heights above some threshold wave height. We used the significant wave height as this threshold wave height. The significant wave height is a common choice of threshold wave height (e.g., Kimura 1980, Battjes and van Vledder 1984, and Rodriguez et al. 2000), but the resulting group period can vary if a different threshold is used. Given this, we computed a mean group period of roughly 6 minutes for the low frequency swells during the period of observed large runup events. We feel that this agrees reasonably with the roughly 5-minute peaks of the tide gage water level signals.
  
  The typical period of waves measured by DART during the high temporal resolution recording was about 3.5 min. It is a bit lower than the 5 min peaks of the tide gage spectra. In the revised manuscript we will provide this information and comment that it is still a plausible period for wave groups based on our analysis from the previous comment.
  
  We thank the reviewer for this comment. We wish to note that van Dongeren et al. 2007 write that the forcing of the incident waves was off-resonant. However, the alpha parameter was measured for the entirety of the shoaling region which includes the resonant region. This is supported in section 5 of van Dongeren et al.: “… amplitude of the incoming long waves can be evaluated by fitting a function of local depth with an unknown power alpha to the observed amplitude as … in the shoaling region between x = 8 m and x = 25 m.” If we refer to van Noorloos 2003, which is the source of the physical experiment that van Dongeren uses, we see that x = 25 m (x is measured from the paddle) refers to the location of infragravity wave breaking. This shows that growth throughout the resonant conditions, all the way up to infragravity wave breaking, is considered. This is also consistent with Battjes et al. 2004 (Figure 5) which shows that they compare the amplitude growth of the infragravity waves against h^(-1/4) and h^(-5/2) all the way up to infragravity wave breaking.
  
  We appreciate this feedback from the reviewer and agree that the wording in the model portion should be improved. We will include a figure of the model result in our revised manuscript (see reply to reviewer #2). Specific points are addressed below.
  
  As we stated in our reply two comments above, the growth parameter alpha was considered in van Dongeren et al. 2007 up until infragravity wave breaking. In fact, Figure A1 in van Dongeren et al. shows that infragravity wave amplitude growth persists past incident wave breaking.
  
  The reviewer’s statement is correct: the short-wave height is shoaled using linear wave theory until H=gamma*h. We will state this explicitly in our revision.
  
  We thank the reviewer for this comment and agree that the wording can be improved. Indeed, as the reviewer wrote, we simply use dispersion to determine the depth at which 25 s waves enter shallow water. We will make it clear that this isn’t a result of our simple model, but rather just from dispersion. The reviewer is correct in that equation 2 is used until the incident waves are in shallow water, and that the van Dongeren et al. relation is used shoreward of it. We show in our response to #11 (regarding lines 276-279) that the empirical relation was derived from shallow water data, as the term non-resonant was used to refer to the forcing of incident waves. This was likely written as such in order to show that the entirety of resonant growth is captured.
  
  Beta is calculated using equation (3), i.e β = h_x / ω √g/h where ω is the IG wave radial frequency. We assume 12 waves per wave group in both 10s and 25s short-wave cases. Hence, ω is also changing. We will make this assumption clear in the revision.
  
  We thank the reviewer for this comment. First, we’ve gone back to the model and improved its formulation. Instead of using a deep-water formulation for infragravity waves from offshore to shallow water, we are now using a formulation (also from Longuet-Higgins and Stewart 1962, equation 3.26) that is valid for all water depths. We now compute maximum infragravity wave heights of roughly 6.5 m and 1.1 m respectively for 25 s and 10 s incident waves. There are no published field data of infragravity waves for 25 s incident waves of 5 m wave height on very low sloping beaches that we know of. However, there are field data for smaller waves on similar beaches. For example, Fiedler et al. 2018 (Fig. 2) show a maximum a maximum cross-shore infragravity wave height of about 0.9 m at roughly 5 m water depth. This is for a case (refer to their Fig. 1) with approximately 10 s period, 3 m wave height offshore incident waves. When we ran their case, we computed maximum infragravity wave height of about 1.1 m at roughly 6.3 m water depth. We feel that our model compared reasonably here.
  
  This is indeed a typo. The breaking depth the incident waves for this case is about 9.9 m. 1.8 m was the breaking depth for the infragravity wave (2.4 m in the revised model). We will correct this in the revision.
  
  We thank the reviewer for this comment, and address them below for each specific point.
  
  We thank the reviewer for catching this as well. As we described in a previous comment, these calculations are based on omega (infragravity wave frequency). We calculated this by assuming 12 waves per group. We omitted this in the original manuscript and will add this information in the revision.
  
  The reviewer is correct that a larger IG wave height does indeed lead to greater dissipation. We currently do not mention this in the paper and will state this in the revision. However, the reason why we end up with less dissipation with 25 s waves compared to 10 s waves is that omega (infragravity wave frequency) is lower for the 25 s waves.
  
  The point that we are trying to make is that infragravity waves associated with 25 s incident waves are much larger, but also dissipates less, than that associated with 10 s incident waves. We will make this more clear in our revision.
  
  We agree that this is not well-worded. We meant to write that the lack of strong signals prior to the observations of extreme runup events onshore imply that the incoming waves were not detectable at the far offshore sensors. The strong signals that were detected at the far offshore sensors were detected after the extreme runup events were first observed onshore, which implies that these were the returning waves.
  
  We agree with this assessment and will include this description in our revision.
  
  Response to technical corrections
  We agree on the confusion caused by the term “very low frequency” and will rephrase as “low frequency swell.” The reviewer is also correct on figures 8 and 9 versus 8 and 10. The reviewer is also correct on sqrt(m_{-3}). These will be corrected in the revision.
  
  Citation: https://doi.org/10.5194/nhess-2020-425-AC1
RC2:
'Comment on nhess-2020-425', Anonymous Referee #2, 01 Apr 2021

he paper here does a lot of work to bring together all of the data for some extreme wave runup events, and then performs some analysis. The work with the data is very good, but the analysis is not.

The best work done by the authors is represented in Figure 14 where they show how low-frequency weighted moments of offshore waves relate to onshore RMS fluctuations of onshore tide gauges. This is useful, but not entirely clear as it would have been better to compare results using the m-3 moment to results using other spectral moments. sqrt(m-3) is linearly proportional to wave height. The authors suggest results but don't actually show anything definitively. The proportionality is also dimensional, which is a real problem. If the mechanism proposed here is true, then it should be able to be reduced to a dimensionless fit, but the authors state that this does not work. Why? This question must be answered.

A second issue, not addressed here, is that all tide gauges have stilling wells that deliberately filter out higher frequency water level fluctuations. I am not sure of the frequency response, but am certain that higher frequency components will be more damped than lower frequency components. For this reason the lower frequency components will be disproportionaly represented in the signals. How do the authors account for this?

I have harsh words for the model presented here. The authors claim it is simple, but do not give anywhere near enough information for a reviewer or reader to be able to evaluate it or reproduce it. I can't evaluate the details of what this model is or how it was produced, so can't evaluate its appropriateness or accuracy or even all assumptions included in the model. I could not reproduce it even though I am familiar with this area. It also makes impossible predictions. A carrier wave amplitude of 2.5m at 25s is stated to reach an infragravity amplitude of 2.3m by 5.8m depth. This is wrong. We know that it doesn't happen because it would be observed instantly and would be the overwhelming feature. If the phenomenon were correct, it would also have to occur for low amplitude shorter period waves that occur all the time and it doesn't. As one final note, the authors refer to the wave amplitude, but don't even say whether this refers to the amplitude of the RMS wave, the significant wave, or something else. This model needs work.

Citation: https://doi.org/10.5194/nhess-2020-425-RC2
- AC2: 'Reply on RC2', Chuan Li, 13 May 2021
  
  We thank the reviewer for their assessment. We recognize that the analysis could be made clearer, further elaborated, and aided by inclusion of additional figures. We aim to do this in our revision. Please see our responses below for some clarifications.
  Regarding low frequency moments: we do compare results from m-3 to m0, which shows that m-3 performs better (lines 345-346). We have also tried other spectral moments, such as m-1 and m-2. We can add comparisons between these moments and m-3 in the revision as well. Regarding a non-dimensional proportionality, we have computed a relationship in which both parameters in x and y are in dimensions of m (see attached Figure 1). We note that the relationship is not quite as strong as the dimensional relationship. Nonetheless, we think this shows that a reasonable non-dimensional relationship does exist. We will add this to the revision.
  Regarding tide gages: the reviewer is correct that higher frequency water level fluctuations are filtered out. The tide gages samples at 1 Hz and report averages over 1 min. However, the extreme runup events captured on video show that their frequency is much longer than the frequencies of incident waves. As we stated in the paper, the frequency of the extreme runup events in the videos are close to the roughly 5 minutes peaks from the tide gages. We will further clarify this point in our revision.
  We appreciate the reviewer’s comment regarding our model. We’ve in fact gone back to the model and improved its formulation due to the reviewer’s comments. Instead of using a deep-water formulation for the infragravity waves from offshore to shallow water, we are now using a formulation (also from Longuet-Higgins and Stewart 1962, equation 3.26) that is valid at all water depths:
  ζ = - 1/ 2 g a² (2c_g / c - 1 / 2 ) / (gh - c_g²)
  where ζ is the infragravity wave water level, g is acceleration of gravity, a is incident wave amplitude, h is water depth, c_g is group celerity, and c is incident wave celerity. We also feel that the description of our model simulation could be made much clearer, which we will do in our revision.
  The model is simple in the sense that it is essentially the analytical solution of infragravity wave water level given by Longuet-Higgins and Stewart (1962) using our environmental conditions. Except here we limit the growth rate when incident waves are in shallow water, per the laboratory results of Battjes et al. (2004) and van Dongeren et al. (2007). Please see Figures 2 and 3 (attached) for results from our model, which we will include in our revised manuscript. Figure 2 shows the incident wave amplitude profile while Figure 3 shows the infragravity wave amplitude profile. We use linear wave theory to compute the incident wave amplitudes, which are then used to calculate radiation stress. The radiation stress is then used in Longuet-Higgins and Stewart’s (1962) analytical solution to calculate infragravity wave water levels. The infragravity wave water levels are then used to calculate infragravity wave amplitude (Figure 3). We do not attempt to calculate the infragravity wave amplitude once the infragravity wave is expected to break (based on a wave height to water depth ratio of 0.5, changed from 0.78 in the previous version). The dashed line shows when incident waves reach shallow water. The dotted line shows when incident waves start to break.
  As a result of this analysis, we compute maximum infragravity wave heights of roughly 6.5 m and 1.1 m respectively for 25 s and 10 s incident waves. We agree that 6.5 m is a rather large infragravity wave, but we think that a large infragravity is to be expected since the observed extreme runup events were also very large. However, we also feel that our model compares reasonably well against field data. For example, Fiedler et al. 2018 (in their Fig. 2) measured a maximum cross-shore infragravity wave height of close to 0.9 m at roughly 5 m water depth from approximately 10 s and 3 m offshore waves (their Fig. 1). When we ran their case, we computed maximum infragravity wave height of about 1.1 m at roughly 6.3 m water depth.
  
  Citation: https://doi.org/10.5194/nhess-2020-425-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (09 Jun 2021) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (20 Jul 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (03 Aug 2021) by Joanna Staneva

ED: Reconsider after major revisions (further review by editor and referees) (11 Aug 2021) by Piero Lionello(Executive Editor)

AR by Chuan Li on behalf of the Authors (13 Aug 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (26 Aug 2021) by Joanna Staneva

RR by Anonymous Referee #1 (07 Oct 2021)

Suggestions for revision or reasons for rejection

Overall the manuscript has significantly improved. Most of my comments have been appropriately addressed in the revised manuscript. The remaining comments I have are all related to Section 6.2 in which the ‘simple’ IG model is presented and used as an attempt to explain the large run-up events. The description of the wave model itself is now much clearer, but I still have issues with the last part that links the model output (H_ig at the breakpoint) to beta_H and ultimately to the run-up.

• First of all, as also recognized by the authors, Beta_H is defined in van Dongeren et al. using the IG wave height “near the shoreline”. Although I recognize it is quite a vague definition, calculating beta_H from IG wave characteristics at a depth of 9-13 m depth as done in the present manuscript does not seem appropriate, so I am not sure that it is a good idea to use it as such for a quantitave

• Defining the IG wave period as 12 times the incoming wave period as a general rule of thumb (applicable for different wave periods) seems rather arbitrary. I realize that the authors need to make a choice here but I think they should comment a little bit more on it (or recognize explicitly the limitations of this choice/possible implications).

• I could not find back the values of beta_H given by the authors based on the info given in the text. Actually, based on the definition of beta_H and the fact that the IG period is defined as 12 times the incident wave period, I would expect that [beta_H for T=25s]/[beta_H for T=10s]=2.5 (as the IG wave height is approx. the same in both cases), which does not appear to be the case.

• Assuming I made a mistake and that the values of beta_H are indeed 0.49 and 0.89 as stated in the manuscript, the associated reflection coefficients according to van Dongeren would then be 0.15 and 0.5 (not given in the manuscript), which means that in both cases quite a lot of dissipation takes place. So I do not think the authors can claim lines 349-350 that the IG waves for a 25s carrier wave show a “low dissipation” for instance.

• I do not understand the reasoning lines 347-349 leading to the conclusion that the energy available for run-up is 3.5 times larger when the incident waves are 25 s instead of 10 s, so I cannot judge of its validity.
Actually, I am wondering if the authors are not trying to push too far their simple modelling approach (i.e. not only to estimate Hig but also the runup induced by these long waves). An alternative would be to use a numerical wave-resolving model which could be used over the same simplified bathymetry for waves of same Hs but different peak periods (assuming a given spectral shape). Anyway, if the authors decide to stick to their simplified approach the points raised above should be addressed.

• Lines 349-352: Overall I am not sure we can really support the statement of dissipation based on the videos. In particular I do not think that the fact that the run-up front slows down (or does not slow down) on the video recordings is a good indication of wave dissipation (or absence thereof). I would say that it depends mostly on the timing with respect to the run-up/run-down cycle.

Other comment:
Line 262: the authors need to give some more details on the “simple shelf geometry” they use in their calculations to make their results reproducible.

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RR by Anonymous Referee #3 (03 Mar 2022)

ED: Reconsider after major revisions (further review by editor and referees) (04 Mar 2022) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (14 Apr 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (16 Apr 2022) by Joanna Staneva

RR by Anonymous Referee #1 (28 Apr 2022)

ED: Reconsider after major revisions (further review by editor and referees) (10 May 2022) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (14 May 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (17 May 2022) by Joanna Staneva

ED: Reconsider after major revisions (further review by editor and referees) (07 Jul 2022) by Piero Lionello(Executive Editor)

ED: Referee Nomination & Report Request started (12 Jul 2022) by Piero Lionello

RR by Anonymous Referee #1 (29 Jul 2022)

Suggestions for revision or reasons for rejection

Unfortunately the authors' explanations on the calculation of the nearshore IG wave height did not alleviate my concerns. I now understand how the authors conducted their calculations, but I still do not understand the underlying reasoning. I am actually now convinced that it is incorrect.

I have been hesitating between recommending minor or major revisions but picked minor at the end as the majority of the paper is now of publishable quality. However, as stated above, it still contains some incorrect reasoning which in my view needs to be corrected (or removed) before publication.

-----
Below a new attempt to explain why I think the proposed approach is not correct.

The first part of the idealized modelling exercise leads to an estimate of the incoming IG wave height at the short wave breakpoint (called Hmax in the manuscript), which is located in about 10 m depth for the conditions considered here. This I can follow and it makes sense to me.

What does not make sense to me is how the authors use this Hmax (defined in ~10m depth) and a reflection coefficient R defined near the shoreline (so much more onshore, let's say in ~1m depth) to define the incoming wave height near the shoreline H, i.e. why it would make sense to assume that H=R*Hmax.

The reflection coefficient R is a function of the incoming and reflected wave heights at the location where this reflection coefficient is defined, in that case near the shoreline. While I agree that H in 1m depth will somehow depend on the wave height Hmax more offshore, there is no straightforward relation between the two as far as I know, and the reflection coefficient R in ~1m depth cannot be used to express how the incoming wave height decays between 10m and 1m depth.

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ED: Reconsider after major revisions (further review by editor and referees) (29 Jul 2022) by Piero Lionello

Dear Author:
Unfortunately, the concerns of Reviewer#1 have not been completely solved by your answer. Specifically, the reviewer is not convinced that the procedure that you use for defining the value of the coefficient R relating H, incoming wave height near the shoreline, to Hmax in 10m depth is correct.

I append below the comment of reviewer#1. Please reply to it and modify accordingly the manuscript. The manuscript and your answer will be returned to the reviewer. Note that this formally requires that this is considered a "major review". However, the text concerned is very limited and the reviewer will likely consider very quickly your answer. In absence of further objections ai think the procedure can be completed within a short time.

Best regards
Piero Lionello

The reviewer writes that:

>>>>>>
Unfortunately, the authors' explanations on the calculation of the nearshore IG wave height did not alleviate my concerns. I now understand how the authors conducted their calculations, but I still do not understand the underlying reasoning. I am actually now convinced that it is incorrect.

[... the paper ] still contains some incorrect reasoning which in my view needs to be corrected (or removed) before publication.

[...]

The first part of the idealized modelling exercise leads to an estimate of the incoming IG wave height at the short wave breakpoint (called Hmax in the manuscript), which is located in about 10 m depth for the conditions considered here. This I can follow and it makes sense to me.

What does not make sense to me is how the authors use this Hmax (defined in ~10m depth) and a reflection coefficient R defined near the shoreline (so much more onshore, let's say in ~1m depth) to define the incoming wave height near the shoreline H, i.e. why it would make sense to assume that H=R*Hmax.

The reflection coefficient R is a function of the incoming and reflected wave heights at the location where this reflection coefficient is defined, in that case near the shoreline. While I agree that H in 1m depth will somehow depend on the wave height Hmax more offshore, there is no straightforward relation between the two as far as I know, and the reflection coefficient R in ~1m depth cannot be used to express how the incoming wave height decays between 10m and 1m depth.

<<<<<<

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AR by Chuan Li on behalf of the Authors (25 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (07 Sep 2022) by Piero Lionello

RR by Anonymous Referee #1 (30 Sep 2022)

Suggestions for revision or reasons for rejection

I think the manuscript is now almost ready for publication, after a few last (minor) adjustments listed below.

• Calculation of infragravity wave height over the profile

The approach followed to estimate a nearshore IG wave height is now clear. I think this part is now publishable provided that the authors add a few sentences to further highlight the limitations of their approach. Besides the use of a very simple model to describe IG shoaling for instance, other important limitations include the fact that the IG wave period, which is a key parameter in several stages in the modeling exercise, is arbitrarily estimated as 12 times the short wave period, and the fact that full modulation of the wave field is assumed (so amplitude varying between H and 0) which means that the IG wave forcing is (severely) overestimated.

• Calculation and use of the reflection coefficient

The link between reflected IG wave height (defined as R*Hig) and runup (explained around line 405 of the ‘track-changed’ manuscript) is not obvious to me. I think the authors should either add references to back up their claim with references, or to simply remove the part of the manuscript discussing the reflection coefficient (and its use as measure for run-up) which is in my view not convincing (as is) and not key to the story.

As a side note (only relevant if the authors decide to keep the part involving the reflection coefficient), the authors derived their own estimate of the relation between R and beta_H based on van Dongeren et al. (2007)’s figure (R=0.5*beta_H) because according to them this relationship is not given in the paper. That’s incorrect: R is explicitly defined in van Dongeren’s paper as R=0.2*pi*beta_H^2.

• Besides that, the revised part of the manuscript contains several typos (units are not provided, spaces are missing, etc.) that need to be fixed.

Hide

ED: Publish subject to minor revisions (review by editor) (09 Oct 2022) by Piero Lionello

Dear Author:
The reviewers has evaluated positively the latest version of your manuscript, which I consider now publishable subject to minor revisions (review by the editor).

It is important that you consider the following suggestions of the reviewer.

• Calculation of infragravity wave height over the profile.
This part is now publishable provided that the authors add a few sentences to further highlight the limitations of their approach. Besides the use of a very simple model to describe IG shoaling for instance, other important limitations include the fact that the IG wave period, which is a key parameter in several stages in the modeling exercise, is arbitrarily estimated as 12 times the short wave period, and the fact that full modulation of the wave field is assumed (so amplitude varying between H and 0) which means that the IG wave forcing is (severely) overestimated.

• Calculation and use of the reflection coefficient.
The link between reflected IG wave height (defined as R*Hig) and runup (explained around line 405 of the ‘track-changed’ manuscript) is not obvious. The authors should either add references to back up their claim with references, or to simply remove the part of the manuscript discussing the reflection coefficient (and its use as measure for run-up) which is not convincing (as is) and not key to the story.

As a side note (only relevant if the authors decide to keep the part involving the reflection coefficient), the authors derived their own estimate of the relation between R and beta_H based on van Dongeren et al. (2007)’s figure (R=0.5*beta_H) because according to them this relationship is not given in the paper. That’s incorrect: R is explicitly defined in van Dongeren’s paper as R=0.2*pi*beta_H^2.

• The revised part of the manuscript contains several typos (units are not provided, spaces are missing, etc.) that need to be fixed.

Please provide a revised version (which accounts for all reviewers’ comments), a copy of your manuscript where all your changes are annotated and the list of your detailed answers to the reviewers’ comments.

Best regards
Piero Lionello

Hide

AR by Chuan Li on behalf of the Authors (19 Oct 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (24 Oct 2022) by Piero Lionello

ED: Publish as is (24 Oct 2022) by Piero Lionello(Executive Editor)

Interactive discussion

Status: closed

RC1:
'Comment on nhess-2020-425', Anonymous Referee #1, 22 Feb 2021
General comments

This manuscript investigates the mechanisms leading to a series of very large run-up events that took place within a couple of hours at different locations along the US Pacific Northwest coast. The authors show that the series of extreme runup events coincides with the arrival of very long swells at the coast and hypothesize that these long swells were responsible for the generation of unusually large (initially bound) infragravity waves that ultimately led to the large, 5-6 min period, run-up events that were filmed by beachgoers.

The manuscript addresses a topic that is relevant to the scientific community and presents some interesting results. The analysis is however limited by the type of data that is available (e.g., no nearshore wave measurements except the 1min-resolution tide gage water level data) that prevents strong conclusions to drawn. I think that it is acceptable as long as the limitations of the analysis are clearly stated (in the core of the manuscript but also in the conclusions). This is a point that needs improvement in my opinion (see comments on below the interpretation of the DART data for instance). Furthermore, several aspects of the methodology, particularly in Section 6.2, need to be clarified and possibly contain errors (see detailed comments in the next section).

I therefore recommend major revisions.

Specific comments

The paper refers a few times to the runup of bound infragravity waves. I find the formulation confusing as the infragravity waves that run up the beach are not bound anymore (released in the surf zone).

This is coming back at different locations within the paper, in slightly different forms. For instance it is stated line 265 that “th[e] bound wave travels at the speed of the wave groups towards the shore and as a free wave […] after reflection” which is not strictly correct as IG waves are not bound until the shore. Or in line 312 the authors discuss the “dissipation of the bound infragrvaity waves” and refer to van Dongeren et al. 2007 to do so, while this paper examines dissipation close to the shoreline, i.e. at a location where the IG waves are not bound anymore.

Line 32: I don’t think the reference to Roeber and Bricker is appropriate as an example in which trapped waves lead to extreme runup (they actually explicitly state that “Resonant amplification over the reef flat […] did not contribute significantly…”).

Line 62: “the amplification of low frequency motion was found to decrease dramatically during storms”. What does that mean? How does it relate to the previous statements?

Line 106: I do not understand the sentence “Data is […] averaged over 1 minute to produce 1 min timeseries”? Is 1 minute the sampling interval or the duration? (probably the first one?)

Lines 180-182: I find that the time delay between observations of “larger than usual” oscillations at the DART sensors and at the tide gages difficult to visualize and as a result the numbers given in the text seem quite arbitrary (I could argue based on visual inspection of figure 5 that the largest waves at Garibaldi occur several hours after the point identified as the approximate onset of the anomalous water level fluctuations… which would in turn change all the time lags). As this time delay seems important to the current narrative (it is used later to support the fact that the observed large oscillations at the DART sensors could be due to IG wave reflection), it would be useful to define periods with “higher than usual magnitudes” in a more systematic way (e.g., it starts when the elevation is larger than X*std(eta)?).

Lines 191-193: As wave direction cannot be inferred from a point measurement of surface elevation/water column height, I do not think it is fair to talk about “large offshore directed waves detected at the DART bottom sensors”. It should be formulated in such a way that it is obvious that it is only a hypothesis, which, if I understand correctly, mostly relies on the fact that there is some time lag between the moment at which the largest oscillations are observed at the tidal gages and at the DART sensors. See also previous comment.

Line 194: At several tide gages (Crescent City, South Beach, Westport) the spectra seem to peak in the 13-22min band (figure 6), and not at 5 min, which suggests that the water levels at these gages (and thus possibly the runup) is dominated by motion in this lower frequency band (associated with resonance in the text). I am not sure this is consistent with the statement that resonance is of secondary importance to explain the extreme water levels. Unless the variance contained in this lower frequency peak is actually less than the variance in the 5min peak (hard to evaluate visually because of the log-scale in the frequency axis)?

Lines 195-207. There has been a number of recent publications on coastal hazards induced by meteotsunamis such as Shi et al., 2020 (Nature communications) and Anarde et al. 2020 (JGR-Oceans) that could be relevant to this discussion. For instance Shi et al., 2020 showed that both single-peak meteotsunami waves and long lasting meteotsumami wave trains could be generated (thus not only soliton like waves as mentioned in the manuscript). Anarde et al., 2020 showed that pressure disturbances much lower than the 5HPa mentioned in the manuscript could trigger significant meteotsunamis.

Lines 211-212: The fact that the long waves that are responsible for the extreme run-up events were generated as bound infragravity waves is a key result of this paper which is in my opinion not sufficiently supported. I understand that data availability limits the analyses that can be conducted, but still feel that stating that 5-min is a “plausible period for wave groups when carrier waves are 25 s” (see also line 260) is in itself not a very convincing statement (for such a key result). Have the authors considered using the measured spectra at the wave buoys to reconstruct a timeseries using a random phase (which is probably not a too bad assumption in these depths) and examine the group structure? They could for instance look at the spectrum of the envelope of such a reconstructed timeseries and check that it indeed peaks around 5 min? That would lend some additional support to the fact that such a wave field could indeed force bound waves in the proper frequency range.

Line 222: What is the typical period of the waves measured by the DART sensors during the period where they recorded at high temporal resolution? Is it indeed close to 5min and therefore consistent with the 5-min peaks in the tidal gage spectra?

Lines 276-279 (and following): van Dongeren et al. 2007 (and I expect that Battjes et al. as well, although I haven’t re-checked) used shoaling zone data in off-resonant conditions to examine the relation between the growth rate (alpha) and the normalized bed slope (beta) and demonstrate that the infragravity wave amplitude was bound between h^(-1/4) and h^(-5/2). This means that the relation between beta and alpha (that is used in this paper) was derived for conditions in which the carrier waves were not in shallow water, contrary to what is stated at the start of this paragraph (and a few times later on, e.g., line 295).

Lines 291-305: I find it difficult to understand what the model is exactly doing, and even more difficult to follow the description of the model outputs that follow in the second paragraph. Some additional information is needed (see questions/remarks in bullet points below). A figure showing the cross-shore evolution of short wave and infragravity wave heights could also help.

Line 294: I would expect that the infragravity wave amplitude is calculated until the moment the short waves break, not when the infragravity wave break as stated here (as van Dongeren et al. derived eq. (3) based on shoaling zone data)?

Lines 296-298: I guess the short-wave height is shoaled according to linear wave theory until H=gamma*h? It would be good to say it explicitly.

Line 303: I find the formulation confusing. I do not expect that the model described in the paragraph above is needed to determine that 25 s waves are in shallow water for h<15m (which depends only on the dispersion relation). Also, how is this info used to determine that the infragravity waves have a 0.87 m amplitude at this depth? Does it mean that eq. (2) is used until the point where the waves enter shallow water (let’s say h/L=0.05)? In that case, does it mean that van Dongeren et al. relation is used only shoreward of that point? (while to the best of my knowledge this empirical relation was not derived using shallow water data - see also comment #11)

Lines 305 and 306: Different alpha’s are used for the 10s and 25s short wave cases. I understand that these depend on the beta-values, but how are these beta’s calculated? Do they differ only because of differences in breaking depth for the 10 and 25s short-wave periods? Or is omega, the IG wave frequency, changing as well when the carrier frequency is changing? If that’s the case, how is it changing/what is the assumption to calculate this frequency?

Line 306: an infragravity wave of amplitude 2.3 m (so 4.6 m high) in 5.8 m depth seems very large. Is it a typo or is there a problem with the model?

Line 308: It seems unlikely that waves that are 5m high offshore break at a depth of 1.8 m (I would expect the breaking depth to be closer to 6-7m). Is this a typo?

14. I have similar comments/questions on the paragraph discussing the dissipation patterns based on the beta_H-value

How is beta_H calculated in both cases? Again, beta_H depends on the infragravity wave period (or frequency), not on the short-wave period. So some explanations are missing.

According to the definition of beta_H, a larger IG wave height H means a smaller value of beta_H, and thus a smaller R (meaning more dissipation). So unless other parameters are varying (such as the long wave period), I do not understand how it can be concluded that the case with larger infragrvaity waves is dissipating the least (lines 322-324).

15. Finally, the link between dissipation and run-up does not seem that straightforward to me as we are comparing the runup of waves that have different incoming heights (and maybe period?). A wave that dissipates more can still lead to a higher runup than a smaller that would have dissipated less…

16. Lines 388-389: “This conclusion is supported by far offshore sensors which did not detect the incoming waves but did detect the returning ones…”: The formulation suggests that the authors were able to discriminate between incoming and reflected waves -> reformulate?

17. It should be clear in the conclusion that the predictor developed in this study is (likely to be) highly site-specific (depends on a dimensional parameter, involves a proportionality factor that already varies strongly along the considered stretch of coast…).

Technical corrections

“very low frequency” is usually used to describe motions happening at a much lower frequency than the long swells described in this paper, which I find a bit confusing.

Line 228: shouldn’t it be figures 8 and 9 instead of figures 9 and 10?

Line 346: I guess that sqrt(m_{-3}f_{m}^3) should be sqrt(m_{-3}) here?
Citation: https://doi.org/10.5194/nhess-2020-425-RC1
- AC1:
  'Reply on RC1', Chuan Li, 13 May 2021
  Response to general comments
  We appreciate the reviewer's assessment and the thorough review. Regarding the limitations of the analsys, we will clearly state that that only nearshore measurements available to us during this ‘experiment of opportunity’ are from the tide gages along the coast. Regarding the methodology, we will make the clarifications as the reviewer suggested. Please see our response to each specific comment below.
  Response to specific comments
  (Omited as specific comments starts with #2)
  
  This is a valid point. In our revision, we will use ‘bound infragravity waves’ to refer to incoming infragravity waves prior to incident wave breaking. We will use the terms ‘infragravity waves’ and ‘infragravity motions’ to refer to onshore movements of these low frequency waves after incident wave breaking.
  
  We agree with this assessment. In our revision, we will refer to this work as an example of large runup from energetic infragravity waves generated by abrupt breaking of incident waves.
  
  By low frequency runup we meant runup associated with infragravity wave frequencies. We will clarify this in our revision. This particular statement is not related to the previous statements but is a key finding from the previous work in discussion.
  
  We agree that this did not read very clearly in the original manuscript. In the revision, we will make it clear that the data is sampled at 1 Hz but is averaged and recorded every minute.
  
  We appreciate this comment. We will use a more quantitative measure to identify the “onset” of large water level fluctuations. We think the X*std(eta) suggestion is a good one. In the revised manuscript we will also identify the onset at each station rather than the approximate onset over all stations. This will provide more detailed analysis for each station.
  
  We agree here as well. Here, in the revision, we will not write “offshore directed” when we are describing the data itself. We will use care to differentiate what the data shows and what we are hypothesizing based on other observations and theory.
  
  We realize that the spectra indicate that at some gages there were strong water level motions in the longer, 13-22min periods. However, video footage (https://youtu.be/JMYLvSsWR_g) shows that the extreme runup events were much closer to the 5 min period. The tide gages are also well inside the inlets. As some of the videos show, the heights of the bores associated with the extreme runup events were considerably reduced as they traveled further into the inlets. Furthermore, the two gages that show the largest fluctuations – La Push and Charleston (we do not include Crescent City here because it is known to amplify shelf resonance from its harbor) – show a clearly stronger signal in the 5 min period (taking into account the log scale). We will clarify this point in our revision.
  
  We thank the reviewer for making us aware of these new works on meteotsunamis. We will cite these papers and add their results into our discussion. We note that in Shi et al., the large wave trains have periods on the order of hours (compared to our 5 min signal). We also note that the pressure disturbances in this work (<1HPa) is still on the low side of the pressures found to generate meteotsunamis in the study of Anarde et al. (~1-3HPa). The runup period (~5 min) in this work is also lower than the meteotsunami period (~20 min) in Anarde et al. However, we do think it is important to include these new papers in our discussion.
  
  We agree with this assessment and per the reviewer’s suggestion conducted a wave group period analysis. To do this, we used Kimura’s (1980) method of computing the mean wave group period directly from the energy spectra (which does not require generation of time series). We note that there is an inherent uncertainty with any method of wave group period calculations, which arises from how the wave group is defined. A wave group is usually defined as consecutive waves with wave heights above some threshold wave height. We used the significant wave height as this threshold wave height. The significant wave height is a common choice of threshold wave height (e.g., Kimura 1980, Battjes and van Vledder 1984, and Rodriguez et al. 2000), but the resulting group period can vary if a different threshold is used. Given this, we computed a mean group period of roughly 6 minutes for the low frequency swells during the period of observed large runup events. We feel that this agrees reasonably with the roughly 5-minute peaks of the tide gage water level signals.
  
  The typical period of waves measured by DART during the high temporal resolution recording was about 3.5 min. It is a bit lower than the 5 min peaks of the tide gage spectra. In the revised manuscript we will provide this information and comment that it is still a plausible period for wave groups based on our analysis from the previous comment.
  
  We thank the reviewer for this comment. We wish to note that van Dongeren et al. 2007 write that the forcing of the incident waves was off-resonant. However, the alpha parameter was measured for the entirety of the shoaling region which includes the resonant region. This is supported in section 5 of van Dongeren et al.: “… amplitude of the incoming long waves can be evaluated by fitting a function of local depth with an unknown power alpha to the observed amplitude as … in the shoaling region between x = 8 m and x = 25 m.” If we refer to van Noorloos 2003, which is the source of the physical experiment that van Dongeren uses, we see that x = 25 m (x is measured from the paddle) refers to the location of infragravity wave breaking. This shows that growth throughout the resonant conditions, all the way up to infragravity wave breaking, is considered. This is also consistent with Battjes et al. 2004 (Figure 5) which shows that they compare the amplitude growth of the infragravity waves against h^(-1/4) and h^(-5/2) all the way up to infragravity wave breaking.
  
  We appreciate this feedback from the reviewer and agree that the wording in the model portion should be improved. We will include a figure of the model result in our revised manuscript (see reply to reviewer #2). Specific points are addressed below.
  
  As we stated in our reply two comments above, the growth parameter alpha was considered in van Dongeren et al. 2007 up until infragravity wave breaking. In fact, Figure A1 in van Dongeren et al. shows that infragravity wave amplitude growth persists past incident wave breaking.
  
  The reviewer’s statement is correct: the short-wave height is shoaled using linear wave theory until H=gamma*h. We will state this explicitly in our revision.
  
  We thank the reviewer for this comment and agree that the wording can be improved. Indeed, as the reviewer wrote, we simply use dispersion to determine the depth at which 25 s waves enter shallow water. We will make it clear that this isn’t a result of our simple model, but rather just from dispersion. The reviewer is correct in that equation 2 is used until the incident waves are in shallow water, and that the van Dongeren et al. relation is used shoreward of it. We show in our response to #11 (regarding lines 276-279) that the empirical relation was derived from shallow water data, as the term non-resonant was used to refer to the forcing of incident waves. This was likely written as such in order to show that the entirety of resonant growth is captured.
  
  Beta is calculated using equation (3), i.e β = h_x / ω √g/h where ω is the IG wave radial frequency. We assume 12 waves per wave group in both 10s and 25s short-wave cases. Hence, ω is also changing. We will make this assumption clear in the revision.
  
  We thank the reviewer for this comment. First, we’ve gone back to the model and improved its formulation. Instead of using a deep-water formulation for infragravity waves from offshore to shallow water, we are now using a formulation (also from Longuet-Higgins and Stewart 1962, equation 3.26) that is valid for all water depths. We now compute maximum infragravity wave heights of roughly 6.5 m and 1.1 m respectively for 25 s and 10 s incident waves. There are no published field data of infragravity waves for 25 s incident waves of 5 m wave height on very low sloping beaches that we know of. However, there are field data for smaller waves on similar beaches. For example, Fiedler et al. 2018 (Fig. 2) show a maximum a maximum cross-shore infragravity wave height of about 0.9 m at roughly 5 m water depth. This is for a case (refer to their Fig. 1) with approximately 10 s period, 3 m wave height offshore incident waves. When we ran their case, we computed maximum infragravity wave height of about 1.1 m at roughly 6.3 m water depth. We feel that our model compared reasonably here.
  
  This is indeed a typo. The breaking depth the incident waves for this case is about 9.9 m. 1.8 m was the breaking depth for the infragravity wave (2.4 m in the revised model). We will correct this in the revision.
  
  We thank the reviewer for this comment, and address them below for each specific point.
  
  We thank the reviewer for catching this as well. As we described in a previous comment, these calculations are based on omega (infragravity wave frequency). We calculated this by assuming 12 waves per group. We omitted this in the original manuscript and will add this information in the revision.
  
  The reviewer is correct that a larger IG wave height does indeed lead to greater dissipation. We currently do not mention this in the paper and will state this in the revision. However, the reason why we end up with less dissipation with 25 s waves compared to 10 s waves is that omega (infragravity wave frequency) is lower for the 25 s waves.
  
  The point that we are trying to make is that infragravity waves associated with 25 s incident waves are much larger, but also dissipates less, than that associated with 10 s incident waves. We will make this more clear in our revision.
  
  We agree that this is not well-worded. We meant to write that the lack of strong signals prior to the observations of extreme runup events onshore imply that the incoming waves were not detectable at the far offshore sensors. The strong signals that were detected at the far offshore sensors were detected after the extreme runup events were first observed onshore, which implies that these were the returning waves.
  
  We agree with this assessment and will include this description in our revision.
  
  Response to technical corrections
  We agree on the confusion caused by the term “very low frequency” and will rephrase as “low frequency swell.” The reviewer is also correct on figures 8 and 9 versus 8 and 10. The reviewer is also correct on sqrt(m_{-3}). These will be corrected in the revision.
  
  Citation: https://doi.org/10.5194/nhess-2020-425-AC1
RC2:
'Comment on nhess-2020-425', Anonymous Referee #2, 01 Apr 2021

he paper here does a lot of work to bring together all of the data for some extreme wave runup events, and then performs some analysis. The work with the data is very good, but the analysis is not.

The best work done by the authors is represented in Figure 14 where they show how low-frequency weighted moments of offshore waves relate to onshore RMS fluctuations of onshore tide gauges. This is useful, but not entirely clear as it would have been better to compare results using the m-3 moment to results using other spectral moments. sqrt(m-3) is linearly proportional to wave height. The authors suggest results but don't actually show anything definitively. The proportionality is also dimensional, which is a real problem. If the mechanism proposed here is true, then it should be able to be reduced to a dimensionless fit, but the authors state that this does not work. Why? This question must be answered.

A second issue, not addressed here, is that all tide gauges have stilling wells that deliberately filter out higher frequency water level fluctuations. I am not sure of the frequency response, but am certain that higher frequency components will be more damped than lower frequency components. For this reason the lower frequency components will be disproportionaly represented in the signals. How do the authors account for this?

I have harsh words for the model presented here. The authors claim it is simple, but do not give anywhere near enough information for a reviewer or reader to be able to evaluate it or reproduce it. I can't evaluate the details of what this model is or how it was produced, so can't evaluate its appropriateness or accuracy or even all assumptions included in the model. I could not reproduce it even though I am familiar with this area. It also makes impossible predictions. A carrier wave amplitude of 2.5m at 25s is stated to reach an infragravity amplitude of 2.3m by 5.8m depth. This is wrong. We know that it doesn't happen because it would be observed instantly and would be the overwhelming feature. If the phenomenon were correct, it would also have to occur for low amplitude shorter period waves that occur all the time and it doesn't. As one final note, the authors refer to the wave amplitude, but don't even say whether this refers to the amplitude of the RMS wave, the significant wave, or something else. This model needs work.

Citation: https://doi.org/10.5194/nhess-2020-425-RC2
- AC2: 'Reply on RC2', Chuan Li, 13 May 2021
  
  We thank the reviewer for their assessment. We recognize that the analysis could be made clearer, further elaborated, and aided by inclusion of additional figures. We aim to do this in our revision. Please see our responses below for some clarifications.
  Regarding low frequency moments: we do compare results from m-3 to m0, which shows that m-3 performs better (lines 345-346). We have also tried other spectral moments, such as m-1 and m-2. We can add comparisons between these moments and m-3 in the revision as well. Regarding a non-dimensional proportionality, we have computed a relationship in which both parameters in x and y are in dimensions of m (see attached Figure 1). We note that the relationship is not quite as strong as the dimensional relationship. Nonetheless, we think this shows that a reasonable non-dimensional relationship does exist. We will add this to the revision.
  Regarding tide gages: the reviewer is correct that higher frequency water level fluctuations are filtered out. The tide gages samples at 1 Hz and report averages over 1 min. However, the extreme runup events captured on video show that their frequency is much longer than the frequencies of incident waves. As we stated in the paper, the frequency of the extreme runup events in the videos are close to the roughly 5 minutes peaks from the tide gages. We will further clarify this point in our revision.
  We appreciate the reviewer’s comment regarding our model. We’ve in fact gone back to the model and improved its formulation due to the reviewer’s comments. Instead of using a deep-water formulation for the infragravity waves from offshore to shallow water, we are now using a formulation (also from Longuet-Higgins and Stewart 1962, equation 3.26) that is valid at all water depths:
  ζ = - 1/ 2 g a² (2c_g / c - 1 / 2 ) / (gh - c_g²)
  where ζ is the infragravity wave water level, g is acceleration of gravity, a is incident wave amplitude, h is water depth, c_g is group celerity, and c is incident wave celerity. We also feel that the description of our model simulation could be made much clearer, which we will do in our revision.
  The model is simple in the sense that it is essentially the analytical solution of infragravity wave water level given by Longuet-Higgins and Stewart (1962) using our environmental conditions. Except here we limit the growth rate when incident waves are in shallow water, per the laboratory results of Battjes et al. (2004) and van Dongeren et al. (2007). Please see Figures 2 and 3 (attached) for results from our model, which we will include in our revised manuscript. Figure 2 shows the incident wave amplitude profile while Figure 3 shows the infragravity wave amplitude profile. We use linear wave theory to compute the incident wave amplitudes, which are then used to calculate radiation stress. The radiation stress is then used in Longuet-Higgins and Stewart’s (1962) analytical solution to calculate infragravity wave water levels. The infragravity wave water levels are then used to calculate infragravity wave amplitude (Figure 3). We do not attempt to calculate the infragravity wave amplitude once the infragravity wave is expected to break (based on a wave height to water depth ratio of 0.5, changed from 0.78 in the previous version). The dashed line shows when incident waves reach shallow water. The dotted line shows when incident waves start to break.
  As a result of this analysis, we compute maximum infragravity wave heights of roughly 6.5 m and 1.1 m respectively for 25 s and 10 s incident waves. We agree that 6.5 m is a rather large infragravity wave, but we think that a large infragravity is to be expected since the observed extreme runup events were also very large. However, we also feel that our model compares reasonably well against field data. For example, Fiedler et al. 2018 (in their Fig. 2) measured a maximum cross-shore infragravity wave height of close to 0.9 m at roughly 5 m water depth from approximately 10 s and 3 m offshore waves (their Fig. 1). When we ran their case, we computed maximum infragravity wave height of about 1.1 m at roughly 6.3 m water depth.
  
  Citation: https://doi.org/10.5194/nhess-2020-425-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (09 Jun 2021) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (20 Jul 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (03 Aug 2021) by Joanna Staneva

ED: Reconsider after major revisions (further review by editor and referees) (11 Aug 2021) by Piero Lionello(Executive Editor)

AR by Chuan Li on behalf of the Authors (13 Aug 2021) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (26 Aug 2021) by Joanna Staneva

RR by Anonymous Referee #1 (07 Oct 2021)

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RR by Anonymous Referee #3 (03 Mar 2022)

ED: Reconsider after major revisions (further review by editor and referees) (04 Mar 2022) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (14 Apr 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (16 Apr 2022) by Joanna Staneva

RR by Anonymous Referee #1 (28 Apr 2022)

ED: Reconsider after major revisions (further review by editor and referees) (10 May 2022) by Joanna Staneva

AR by Chuan Li on behalf of the Authors (14 May 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (17 May 2022) by Joanna Staneva

ED: Reconsider after major revisions (further review by editor and referees) (07 Jul 2022) by Piero Lionello(Executive Editor)

ED: Referee Nomination & Report Request started (12 Jul 2022) by Piero Lionello

RR by Anonymous Referee #1 (29 Jul 2022)

Suggestions for revision or reasons for rejection

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ED: Reconsider after major revisions (further review by editor and referees) (29 Jul 2022) by Piero Lionello

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AR by Chuan Li on behalf of the Authors (25 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (07 Sep 2022) by Piero Lionello

RR by Anonymous Referee #1 (30 Sep 2022)

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ED: Publish subject to minor revisions (review by editor) (09 Oct 2022) by Piero Lionello

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AR by Chuan Li on behalf of the Authors (19 Oct 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (24 Oct 2022) by Piero Lionello

ED: Publish as is (24 Oct 2022) by Piero Lionello(Executive Editor)

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Chuan Li et al.

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In this work, we examine a set of observed extreme, non-earthquake/landslide related wave runup events. Runup events with similar characteristics have previously been attributed to trapped waves over shallow bathymetry and long waves created by atmospheric disturbances. However, we find that neither mechanisms were likely at work in the observations we examined. We show that instead, these runup events were more likely due to energetic growth of bound infragravity waves.


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