the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Jun 2026
Focusing of Swell at the Nazaré Submarine Canyon
Abstract. Steep underwater canyons near the coast can significantly modulate the propagation of long waves. Many canyons share similar dimensions of approximately 150 meters deep thalweg at their terminus, and a sloping continental shelf of about 20 meters within hundred meters of the shoreline. Swell traveling above the shelf is refracted and reflected at the canyon edge, where the phase speed increases abruptly due to the increased depth, resulting in a significantly focused wave field. Outside Nazaré, Portugal, one of the largest near-shore canyons exist, extending to within ten meters of the shoreline. Here, some of the largest breaking waves (> 20 meters) in the world are formed. We deployed arrays of wave buoys above the canyon, and stereo cameras mounted at the cliff at Nazaré overlooking the canyon edge, allowing us to measure the wave field at far greater spatial and temporal resolution than any previous experiment. The swell propagation is modeled using ray tracing and a boundary element method. In particular, the shape of a submarine canyon’s edge in the final hundreds of meters toward the coastline is crucial for how and exactly where beams are focused towards the beach. Contrary to the popular explanation that the large waves are channeled through the canyon, we find they are refracted and reflected along the canyon edge. We find that waves longer than about 7 seconds are mostly reflected at the canyon, common to many canyons around the world. At Nazaré, optimal focusing occurs for waves arriving from about 275°–315°. This is in agreement with the experience from the surfing community which considers waves arriving from about 290°–315° to yield the biggest surf.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2778', Milan Curcic, 22 Jul 2026
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AC1: 'Reply on RC1', Gaute Hope, 01 Oct 2026
Dear Dr. Curcic,
Thank you for taking the time to review this manuscript and providing detailed
and thoughtful comments. They will make the manuscript better and more
understandable.Below we respond to each comment individually.
## 1. Comparison between buoys and ECMWF
> I appreciated the comparison between buoys and ECMWF early on in the paper. Given the space/time overlap between some buoys and stereo video (e.g, bug32 and bug56, as shown in Fig. 9), is it possible to compare instantaneous water elevations sampled by the buoys and stereo video, on both sides of the canyon edge? I think showing a comparable contrast in waves from two distinct measurement techniques would significantly strengthen one of the key findings of the paper.
There are three main limitations that are holding us back from comparing direct elevations: 1) accurate timing (approximately ~1 second, both for the stereo-video system and the buoys), 2) accurate positioning, and 3) the integration of acceleration to elevation for the buoy data.
We attempted to track the phase of the waves across the grid of buoys, but the results were ambigious. In fact, we had brought an experimental buoy with an RTK GPS unit which, in theory, would have solved all three limitations (vertical elevation accurate to approximately 20 cm), but it failed to work properly in the water for unknown technical reasons.
The integration of the elevation from acceleration is accurate enough in this case (the IMU is less accurate at low frequency waves, where the magnitude of the acceleration is smaller). However, the timing and the positioning is not accurate enough to use as a reference between buoys at this scale: in particular since the reflection and refraction of the wave field manifests as a phase shift of the wave field seen from each individual buoy, requiring even better accuracy for the absolute timing and positioning, and a model of phase-shift due to the bathymetry (we do not think our model, or any other model, is accurate enough or has an accurate enough bathymetry, sea level or estimate of the incoming waves to estimate). Prompted by this experience we have developed a buoy with far greater temporal accuracy, however to get to better spatial accuracy a RTK solution is needed (which is more expensive and require more battery, but still completely feasible).
It would be interesting to make another attempt at looking at the time series
elevation, compared between the two measurement techniques. Because of the
limitations in timing between the two systems we are unlikely to be able to
compare the phase, but we will likely be able to match the phases between the
two. Either way, this discussion is of interest to include in the
manuscript.## 2. Using stereo-video to detect reflection
> Stereo video provides instantaneous frame-by-frame height field covering the northern cliff of the canyon (e.g. Fig. 9). It's clear that it gets quiet in the canyon southeast of the cliff. Is it possible to detect actual reflection of long waves based on the evolution of instantaneous height fields? As I understand it, stereo video allows for computation of a full (3-dimensional) wavenumber-frequency spectrum, which should be able to show reflected swell off the cliff edge.
This may be possible: it would require that we have a sufficiently large
footprint on both sides of the canyon edge. It is worth exploring, but I suspect
that there is only a narrow part of the footprint on the shelf-side. Another way
to look at this could be to look at the phase-shift, due to the reflection,
between canyon and shelf side. If the wave field is not too chaotic this could
possibly provide a more robust benchmark for evaluating analytic or numerical
models for reflections of waves encountering trenches (Kirby and Dalrymple 1983; Li et al. 2021). This
would increase the scope significantly, however, we can discuss the possibility
for future work in this manuscript.
## 3. Building a (probabilistic) prediction model for wave heights given input spectra> The paper reveals high sensitivity of refraction and reflection of swell off the cliff edge to the incoming swell direction and period. From my reading of the paper, the BEM and ray-tracing models are used to make key conclusions, while the buoy and stereo video measurements provide observational support of the findings. Would it be feasible to take this a step further and use BEM+ray-tracing to build a (likely a probabilistic) prediction model for a spatial distribution of wave heights in the Nazare nearshore, given input ECMWF (or other) directional wave spectrum? If not feasible in this paper due to scope limitations, please discuss possible next steps toward such a model.
This is a good idea. I do not think the models presented here are accurate
enough to predict wave height, but we believe they capture the situations that
yield the greatest wave heights. As you point out, this may increase the scope
significantly. However, the transfer functions we have computed using the
BEM-model here are a good step on the way for this type of study. Estimating
wave height using the ray tracer requires either using the ray density as an
estimate, or exploring whether using Gaussian beams or other methods for
robustly calculating the amplitude of the rays can be useful in this situation.
We should discuss the possibility and the necessary steps for this here.
## Line specific comments & questions> L2: "thalweg" too hydrology specific for the abstract (I had to look it up); I suggest a more general language like you have on L35
Good point, at least help the reader with a general description the first time
the word is used.> L5: One of the largest in the world, correct? I think you should write "one of world's largest"
Will double check.
> L7-8: "far greater spatial and temporal resolution than any previous experiment" Do you mean any previous experiment at Nazare? Better to be specific here. In general, there have been experiments with higher spatial and temporal resolution. Same comment for L22-23.
I mean experiments of refraction of canyons. The combination of spatial extent,
and the study of a real world case (as opposed to labs), with the high
resolution offered by stereo-cameras and the high-frequency buoys (and the
relative dense network of buoys) is unique. We explain better what we mean here.> L10: "beams" I suggest "wave beams" for clarity
OK.
> L16: "sometimes exceeding 30 m" Is this known or anecdotal? Same question for L19.
It has been measured by stereo-cameras or using photos and estimations based on
sufer-height in the way surf-records are established. So we are fairly confident
in the number, but we do not have a high-quality reference (yet). Will try to
moderate statement or find better reference.> L23: It's not clear yet what exactly are cut-off frequencies for short waves at this place of the paper, so I suggest rephrasing this to some simpler language.
OK.
> L28: "increasing" -> "increase"
OK.
> L31-32: Fig. 1 is great but does not show yearly events; maybe find a way to rephrase this sentence.
Good point.
> L45: "at" should be removed.
OK.
> L48-49: "The canyon originates from...". This sentence alone doesn't convey much meaning. I suggest merging it with the following two sentences to replace vague with specific.
OK.
> L73: "Above 300 m depth" I think you mean "at depth greater than 300 m", but it's not clear because "above" is ambiguous in this context (i.e. shallower is above deeper, but also wind is above the ocean, etc.)
Good point. Will clarify.
> L88-95: This paragraph would be greatly helped by including the varying-depth dispersion relation.
Yes. It's a trade-off between including too much basic theory here, bug I agree
that the depth-dependent dispersion relation is essential to this work.> L91-92: Confusing sentence; cliffs cannot be described as reflections of waves.
> L102: "long"
> L118-119: There's either a missing or an extra parenthesis in this sentence; something's a little off.All above comments should be fixed.
> L141-153: Section 2.1 I think readers would greatly benefit from a little more description of each model. References are good, but I personally wished to see at least the governing equations of BEM and ray-tracing models each, and a list of key advantages and limitations of each.
Good point. Also a trade-off between theory and space, but I agree that a little
basic introduction will help readers and avoid having to look up too much other
places.> L149-151: "dissipation of short waves" Why only short waves? Is it because the dissipation of long waves is negligible over these scales? And in what frequency band is the dissipation applied?
Yes, the dissipation as implemented here is per wavelength, which on the scale
here is small. When employed across basins or larger scales it would make more
sense. So it is applied equally across all frequencies, but does not have any
significant effect on lower frequencies.> L176: "sample the acceleration of the sea surface" They sample their own acceleration but you approximate it to that of the surface. That is fine for this application, of course, but I think better to be specific.
OK. Always good to be specific: the goal is to sample the acceleration of the
surface, so we can make this clearer.> L186: "its" -> "their"
OK.
> L190-199: An example figure of the camera field of view + variance overlay derived from stereo-video would be very helpful.
Yes. I have tried to limit the number of figures, but perhaps we can re-use one
of the stereo-video figures from further down or show a schematic. We will try
to solve this.> L250-252: Break sentence into two.
OK.
> L279: "The BEM model predicts oscillating beams in the peak period" Please expand on this. What causes the oscillations and is it realistic?
Yes, this is a key result. Agree that it needs clearer wording.
> L351: By this, do you mean waves propagating through the channel and then over the canyon cliff onto the shelf? This is an explanation I've heard. Is there any prior literature on this?
We should make this clearer. The point is that a often repeated explanation is
that swell is channeled up the canyon and is then focused when it gets closer to
the beach, we find that this is inaccurate and that a better explanation is that
the large waves are generated by waves arriving from north-west onto the
northern edge of the canyon are reflected and focused towards the beach. The
other explanation is often repeated in news articles, or YouTube explanations of
the waves at Nazare. There are few scientific articles that describe the wave
propagation, and then they are often described so broadly that this nuance is
lost.> L378: I suggest rewording "wave generation" to not confuse it with generation by wind. This sentence could begin as simply as "Large waves at Nazare are therefore..."
OK.
> Fig 1: Top panel: what is the meaning of these stats, physically? Different N appears in top panel (59770) and in the caption (72311)
There are some errors here that should be fixed. The goal of the figure is to
show how frequent and relevant large incoming waves are at Nazare, and that the
predominant direction they arrive from is almost optimal to the large waves (but
not quite) for long waves. We should re-do the figure to try and convey this
information better.> Fig 2: I think it'd be more elegant to group the photos together and describe them in a single caption. Same comment for most other figures.
Will try this, this may save some figure space as well.
> Fig. 5: Given that peak swell period is critical for the analysis of the process, I recommend adding a panel of the peak period time series (buoys + ECMWF).
True, good point.
> Fig. 7: Labels are too small to read; may need to be broken up into multiple figures. In panels (a) and (b) the units for Tp are shows as Hz instead of s.
OK.
> Fig. 9: Top 4 panels and bottom 2 panels should probably be separate figures. Bottom two panels are very busy due to colorbar and label overlays; any way to simplify them?
Will try to simplify without generating too many figures in total.
> Fig. 12: x and y axis labels are missing.
OK.
> Fig .13: This is probably three separate figures; text labels are tiny in middle panels.
Will try to simplify this without generating too many figures in total.
> Fig. 14: Labels too small.
OK.
Sincerely,
Dr. Gaute Hope## References
Kirby, James T., and Robert A. Dalrymple. 1983. “Propagation of Obliquely Incident Water
Waves over a Trench.” Journal of Fluid Mechanics 133 (August): 47–63. https://doi.org/10.1
017/S0022112083001780.Li, Yan, Yaokun Zheng, Zhiliang Lin, Thomas A. A. Adcock, and Ton S. van den Bremer. 2021.
“Surface Wavepackets Subject to an Abrupt Depth Change. Part 1. Second-order Theory.”
Journal of Fluid Mechanics 915 (May): A71. https://doi.org/10.1017/jfm.2021.48.Citation: https://doi.org/10.5194/egusphere-2026-2778-AC1
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AC1: 'Reply on RC1', Gaute Hope, 01 Oct 2026
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RC2: 'Comment on egusphere-2026-2778', Anonymous Referee #2, 21 Sep 2026
The authors have presented a very interesting study revealing the mechanism behind the formation of the large breaking waves near Nazare, through both measurements and numerical modelling. The founding is quite interesting, for a long-axis wave, refraction seem to be the main cause, but for north-western waves, reflection becomes another important factor in addition to refraction. That said, here are some comments for the manuscript:
1) It's suggested to make a table to summarize the three experiments in Sec 3.1, including their durations, principal wave directions and other relevant information, so it’s easier to follow the setups in the following sections - especially the following discussions don’t strictly follow the experiment-by-experiment sequence, e.g. Fig.7 only exp 1 & 2, Fig, 10 only exp 3. And two wave conditions are presented while three experiments are presented, the connection can be also summarized so the readers have a clear reference when reading the results.
2) in figure 7 a), the white color label for depth is not visible in the legend, it’s recommended to use a different color or put a background color on the legend
3) The phenomena described are very complex and nonlinear, are the deployed ray tracing and BEM methods sufficient to capture the complexity. Would it be beneficial to use other 3D fully nonlinear models, if so, which parameters or phenomena will benefit from the fully nonlinear modeling - or in another words, what could be the limiting factors in the presented numerical methods for this phenomenon.
4) During the measurements or analysis, was there any hints on the current-induced effects? The drifting of the buoys itself may be a combination of nonlinear wave effect or current, since that area is also known to have strong longshore current, as they authors have also pointed out. Since current is not the main study here, the authors could address it as an outlook what could change or can be done about it.
Citation: https://doi.org/10.5194/egusphere-2026-2778-RC2 -
AC2: 'Reply on RC2', Gaute Hope, 03 Oct 2026
Dear reviewer,
Thank you for taking the time to review this manuscript and providing detailed
and thoughtful comments. They will make the manuscript better and more
understandable.Below we respond to each comment individually.
> The authors have presented a very interesting study revealing the mechanism behind the formation of the large breaking waves near Nazare, through both measurements and numerical modelling. The founding is quite interesting, for a long-axis wave, refraction seem to be the main cause, but for north-western waves, reflection becomes another important factor in addition to refraction. That said, here are some comments for the manuscript:
> 1) It's suggested to make a table to summarize the three experiments in Sec 3.1, including their durations, principal wave directions and other relevant information, so it’s easier to follow the setups in the following sections - especially the following discussions don’t strictly follow the experiment-by-experiment sequence, e.g. Fig.7 only exp 1 & 2, Fig, 10 only exp 3. And two wave conditions are presented while three experiments are presented, the connection can be also summarized so the readers have a clear reference when reading the results.
Good point. In line with other reviewer comments we will try to make the
presentation of data and results more clear and organized.> 2) in figure 7 a), the white color label for depth is not visible in the legend, it’s recommended to use a different color or put a background color on the legend
Good point.
> 3) The phenomena described are very complex and nonlinear, are the deployed ray tracing and BEM methods sufficient to capture the complexity. Would it be beneficial to use other 3D fully nonlinear models, if so, which parameters or phenomena will benefit from the fully nonlinear modeling - or in another words, what could be the limiting factors in the presented numerical methods for this phenomenon.
The ray tracing and BEM model study the effect in terms of relatively simple
refraction and reflection. More advanced models would surely be beneficial, but
would require more detailed input data in terms of bathymetry and input wave
field. Uncertainties in these will also be present in the results. I think doing
this type of simulation study is outside the scope of this study, but we can
discuss it more clearly at the end. It would be a very interesting way to
continue this work.> 4) During the measurements or analysis, was there any hints on the current-induced effects? The drifting of the buoys itself may be a combination of nonlinear wave effect or current, since that area is also known to have strong longshore current, as they authors have also pointed out. Since current is not the main study here, the authors could address it as an outlook what could change or can be done about it.
Yes, the buoys were likely drifting mainly from the wind (they drift at about 3%
of the wind speed). Some rip-current effects seemed to present intermittently,
transporting the buoys offshore. However, the measurements we have were not
sufficiently detailed to understand what was going on. These effects do point
towards wind-induced current, and some wave-induced (infra-gravity / swash)
current from the waves. We can try to discuss this, but it is almost
speculation so we will be moderate in our statements.Sincerely,
Dr. Gaute HopeCitation: https://doi.org/10.5194/egusphere-2026-2778-AC2
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AC2: 'Reply on RC2', Gaute Hope, 03 Oct 2026
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RC3: 'Comment on egusphere-2026-2778', Anonymous Referee #3, 22 Sep 2026
This manuscript studies the complex interactions between long-period swell waves and the complex bathymetry of Nazaré Canyon, which are responsible for the exceptionally large waves at Praia do Norte that have become well known through XXL wave surfing. These interactions are investigated using observations from drifting wave buoys and a stereo-video system, combined with numerical ray tracing and a Boundary Element Method (BEM).
The analysis is interesting and clearly illustrates several of the physical processes involved in the formation of multiple high wave peaks at Praia do Norte. I also acknowledge the substantial amount of work that must have been required to collect the observations.
My main concern is the organization of the manuscript. In its current form, it is often difficult to identify the specific aim of individual sections and to follow the progression of the scientific argument. I strongly recommend reorganizing the sections and subsections and clarifying the purpose of each of them. A more conventional Introduction–Methods–Results–Discussion–Conclusions structure, with additional subsections where appropriate, would improve the readability of the manuscript.
Several figures also require revisions.
Major comments
- Organization and structure of the manuscript
As stated in my introduction, the manuscript would benefit substantially from a clearer overall structure. Several paragraphs contain enough material to constitute sections or subsections by themselves but are currently embedded within much longer sections. This makes it difficult for the reader to identify the main message and follow the progression of the manuscript.
The end of the Introduction should also provide a brief overview of the manuscript structure and explain how the different methodological components—drifting buoys, stereo-video observations, ray tracing, and BEM simulations—contribute to answering the scientific question of the paper. The authors should better explain why each of these approaches is required. In particular, what information is provided by the stereo-video system that cannot be obtained from the buoys? What does ray tracing provide that the BEM does not, and vice versa? Would the main conclusions of the manuscript still be reached if one of these components were unavailable?
- Reference figure for Nazaré Canyon
I strongly recommend introducing, preferably as Figure 1, a simple reference map showing the bathymetry of Nazaré Canyon. This figure could include the main geographical features and rocks referred to throughout the manuscript, the relevant segments or "hotspots" of the canyon, the main canyon axis and turns, and potentially the locations of the buoy and stereo-camera deployments. This figure would provide a geographical reference that could be used throughout the manuscript
Specific comments
I recommend stating the scientific questions and/or objectives explicitly in both the Abstract and the Introduction.
**L.4:** Replace "outside" with "in."
**L.9:** Consider replacing "In particular" with "We show in this manuscript that..." or equivalent wording.
**L.20:** Reference needed.
**L.22–23:** Please provide examples from the literature of studies that have performed this type of experiment.
**L.24:** Add a comma before "and."
**L.28:** "wave amplitude."
**L.31–32 and Figure 1:** I do not think the current figure is the most appropriate way to demonstrate that high-wave events occur every year. I recommend introducing a temporal dimension. For example, rather than showing statistics over the complete 2009–2025 period, the authors could show annual statistics or annual means.
**L.32:** Please specify that you are referring to waves formed at Praia do Norte.
**Figure 1b:** Consider providing a bin-averaged representation.
**Figure 2e:** "One camera of the stereo-camera system."
**Figure 2:** Question for the editors: Is the current organization of the panels consistent with Ocean Science format? Should the individual panel titles instead be incorporated into the main figure caption?
**L.44:** The gradient of which quantity?
**L.45:** I recommend avoiding adverbs and simplifying the sentence. For example: "We are therefore able to distinguish the effect of canyon geometry on wave focusing, which appears to be more efficient at Nazaré than at the La Jolla and Scripps canyons."
**L.48–49:** I suggest removing the sentence beginning "The canyon originates from a complicated history of different processes active for different periods..." unless this information is directly relevant to the subsequent discussion.
**L.71:** Consider removing "The canyon is not connected to a river system …” unless this information is important for the analysis.
**L.73–75:** Please support this statement with a reference.
**L.76–77:** Please support this statement with a reference. If Tyler et al. (2009) supports it, consider combining the two sentences.
**L.78–79:** "The canyon terminus is about 200 meters west of the lighthouse (150 meters south of the lighthouse)." Please clarify: 150 or 200 m?
**L.81:** Remove "And" at the beginning of the sentence.
**L.89:** You could mention that this behavior is consistent with Airy linear wave theory in shallow water.
**L.89:** Add a comma after "at Nazaré."
**L.90:** Figure 2a and Figure 3b.
**L.92–94:** The sentence explaining the dependence of refraction and reflection on wave period is convoluted and should be simplified. Also, replace "phase speed" with "the phase speed of the incident waves" where appropriate.
**L.100:** Why are phase-resolving wave models not used for this study? Please briefly discuss this methodological choice and the advantages/limitations of the selected approaches relative to phase-resolving models.
**L.100:** Start a new paragraph at "As the water depth decreases..."
**Equations (1–2):** Please define all variables. Add a comma after Equation (1).
**L.118–119:** Please specify that h is the depth. Please carefully check the the deep- and shallow-water approximations and the associated kh limits. (Long waves/deep water waves —> large kh)
Because canyon width is discussed immediately before this point, I also recommend reorganizing these lines to avoid ambiguity between canyon width and water depth.
**L.120:** Are you referring to the same specific canyons or to the same type of coastal canyons? Please clarify.
**L.120:** "Several" and "different" are somewhat redundant here; one is sufficient.
**L.134–139:** I appreciate this paragraph because it helps illustrate the wave-reflection criterion. However, the transition from the preceding paragraph is difficult to follow. I recommend introducing it more explicitly or rewriting the beginning of the paragraph to provide a clearer transition.
**L.140:** This paragraph is difficult to follow. Several concepts require further explanation, including "interference pattern" (are these caustics?), "source field," the processes responsible for dissipation, and what is meant by waves being "summed incoherently." I also recommend shortening some of the long sentences.
**L.141:** Please provide additional details about the ray-tracing method. For example, what differential equations are solved?
**L.158:** Please explain why crest length are relevant here.
**L.161:** Please choose between either \(\mathrm{Var}(\phi_i)\) or \(\sigma_\phi\). Base on equation (3), I think \(\mathrm{Var}(\phi_i)\) is the most relevant.
**L.174:** What causes the buoys to drift across the canyon—surface currents, wind, wave-induced drift, or a combination of these? This appears to be answered around line 182; I recommend to combine the two sentences
**L.177:** "integrated twice over time."
**L.184:** "Relatively mellow" should be quantified.
**L.186:** Remove "therefore."
**L.197:** How was the elevation of the camera system measured?
I recommend adding a subsection for the description of the instruments.
**L.200:** Keep "the" before the first occurrence of "refraction zone" and remove it where unnecessary in subsequent occurrences.
**L.201:** Add a comma before "and."
**L.201:** Instead of "not particularly large, their periods were sufficiently long," please provide quantitative values.
**L.206–207:** Readers may be curious about the offshore drift of the buoys. I recommend referring to Figure 6a here.
**L.209:** ECMWF wave data are not perfect. Please provide a more quantitative and qualitative assessment of the differences between ECMWF and the observations.
**Figures 4 and 5:** Please revise the zenith/azimuth tick labels of the polar plots to avoid overlap.
**L.215–216:** "The peak wave direction travels almost along the canyon axis, slightly from the north" should be rewritten. A direction does not "travel." Consider quantifying the angular difference, e.g., "The peak wave direction and the canyon axis are aligned within approximately X°."
**Figure 6a:** There appears to be an optical image underneath the bathymetric field. I recommend removing it. A coastline contour could be added instead if useful.
**Figure 6b:** Please rewrite the caption. Specify whether the quantity is the wave-energy spectrum or the power spectral density of sea-surface elevation.
**L.216–218:** Based on Figure 6a, the buoys appear to be located north of the canyon rather than directly above it during Experiment 1.
**L.223:** Avoid wording such as "not very trustworthy." Please state more precisely what the limitation is and, if possible, quantify the uncertainty.
**L.226:** Please justify the selected window length. Is it a compromise between stationarity of the wave field and including a sufficient number of periods? The selected time window appears relatively short and may reduce the frequency resolution of individual spectra.
**L.229:** From which dataset is the peak period Tp obtained—ECMWF or the deployed buoys? Over what time interval is T_p calculated?
**L.230:** Please clarify "first drift" and "second drift." Do these correspond to the first and second experiments?
**L.234:** Should "Figure 6d" be "Figure 7"?
**General comment on the spectrograms:** Please guide the reader more explicitly through these figures. Around what value does the variance oscillate? What are the relevant time intervals? Providing times that can be directly identified in the figures would make the discussion much easier to follow.
**L.238–241:** This paragraph is unclear and should be rewritten.
**L.242–252:** This paragraph should be rewritten for clarity. In addition, the panels referred to here (Figure 9a–c) need axes. What is the time window used to infer the stereo-video variances maps?
**L.258:** Avoid "more or less unperturbed”, be quantitative.
**L.260:** Please guide the reader more explicitly. Which buoy(s) should be examined?
**L.263:** Please clarify what is meant by "calculating the wave field."
**L.263:** Retain the BEM acronym once it has been defined.
**L.265–275:** This paragraph is difficult to understand and introduces several concepts that have not been sufficiently explained beforehand, including "high" and "low," phase shifts, and wave crests. I recommend rewriting the paragraph and introducing these concepts more clearly before using them to interpret the results.
**L.290:** How can Doppler shifting affect the measured spectrum? Please provide references supporting this discussion. (Colosi et al. 2023?)
**L.291:** Please provide a clearer marker for the location of the Guilhim rocks in Figure 2a. Also, the markers for the artificial reef and rocks appear identical and should be differentiated.
**L.301:** Why is T_{m02} used rather than T_{m0m1}or T_{01}? Please provide the equation used to compute the selected mean period and briefly justify this choice.
**L.313:** "and thus alters the reflection or refraction here." I do not understand the causal relationship. How does the initial refraction subsequently alter reflection/refraction? Please clarify.
**Figure 12:** Some middle panels contain color bars. Please revise the layout. The shoaling-coefficient panels should also use the same color scale/colormap to facilitate direct comparison.
**Figure 13:** Could the correspondence between panels (e) and (f) be made clearer? Please also provide axes for panels (a–d). Figure 13 seems to be a screenshots of another document. Please correct.
**Figure 14:** Please provide units on the panels and revise the layout so that tick labels and text are readable. The peak wave frequencies/directions in the polar plots should also be clearly visible. Could markers be added to the map to identify the locations associated with the secondary and tertiary peaks discussed in the text?
**L.332:** I recommend removing "from 255" and "from 305" and using a single directional convention consistently throughout the manuscript.
**L.332:** Is the angle 75° or 95°? The upper-left panel appears to indicate 95°. Please check for consistency.
**General comment on the stereo-camera results:** It should be made explicit that the variance maps derived from the stereo-camera observations represent temporally averaged variance.
**L.351–353:** There is a syntax issue; please rephrase the sentence.
**L.352:** Is Figure 5b the most relevant figure to support this statement? I also recommend adding a line or segment to the polar plot showing the main axis of Nazaré Canyon.
**L.353:** Please check whether Figure 4b is indeed the intended reference.
**L.363:** Could the canyon bathymetry/depth be superimposed on this figure? This would make it easier to relate the wave response to the underlying topography. Check Irving et al. 2025 (Supporting figures, Nazare’s Case)
**L.365:** Could the authors provide an approximate depth threshold below which realistic waves become sensitive to bathymetric variations?
**L.373:** Add a comma before “and a boundary element."
**L.376:** I am not convinced that the second (2) element listed here represents one of the main results of the analysis. Please reconsider its prominence or explain more clearly how it follows from the results.
**L.385:** Could this point be supported by a sensitivity analysis, potentially provided in the Supplementary Information?
**L.390:** Regarding currents, are observations or previous analyses of coastal currents available for this region? Are tidal currents the dominant currents in the study area? A simple scaling estimate of current-induced refraction based on realistic current gradients encountered by the waves would help assess whether neglecting currents is justified.
**L.397:** The term "full wave model" is somewhat counterintuitive because neither a phase-resolving nor a spectral wave model appears to be used here. Please consider another expression.
**L.174:** Based on the figure, the deployed buoys appear more aligned than arranged in a cross-pattern. Please revise the description or clarify the intended geometry.
**L.440-441:** Could the authors propose an observational or numerical experiment that could test this interpretation?
Citation: https://doi.org/10.5194/egusphere-2026-2778-RC3 -
AC3: 'Reply on RC3', Gaute Hope, 03 Oct 2026
Dear reviewer,
Thank you for taking the time to review this manuscript and providing detailed
and thoughtful comments. They will make the manuscript better and more
understandable.Below we respond to each comment individually.
> This manuscript studies the complex interactions between long-period swell waves and the complex bathymetry of Nazaré Canyon, which are responsible for the exceptionally large waves at Praia do Norte that have become well known through XXL wave surfing. These interactions are investigated using observations from drifting wave buoys and a stereo-video system, combined with numerical ray tracing and a Boundary Element Method (BEM).
> The analysis is interesting and clearly illustrates several of the physical processes involved in the formation of multiple high wave peaks at Praia do Norte. I also acknowledge the substantial amount of work that must have been required to collect the observations.
> My main concern is the organization of the manuscript. In its current form, it is often difficult to identify the specific aim of individual sections and to follow the progression of the scientific argument. I strongly recommend reorganizing the sections and subsections and clarifying the purpose of each of them. A more conventional Introduction–Methods–Results–Discussion–Conclusions structure, with additional subsections where appropriate, would improve the readability of the manuscript.
It has been challenging to organize this in a easy-to-follow way, the current
method tries to organize the manuscript between the two main situations we have
measured: waves arriving from along-axis and waves arriving cross-axis to the
canyon. We can try to present the experiments and data first, and then analyse
the two situations afterwards. This would make it easier to keep track of the
experiments as well. Whether we end up with an organization based on the wave
direction or based on the experiment order, we will try to make it clearer and
less confusing.> Several figures also require revisions.
OK. This is in line with other review comments too. We will improve.
> Major comments
> - Organization and structure of the manuscript
> As stated in my introduction, the manuscript would benefit substantially from a clearer overall structure. Several paragraphs contain enough material to constitute sections or subsections by themselves but are currently embedded within much longer sections. This makes it difficult for the reader to identify the main message and follow the progression of the manuscript.Understood, we will work on the organization and attempt to make clearer as
described above.> The end of the Introduction should also provide a brief overview of the manuscript structure and explain how the different methodological components—drifting buoys, stereo-video observations, ray tracing, and BEM simulations—contribute to answering the scientific question of the paper. The authors should better explain why each of these approaches is required. In particular, what information is provided by the stereo-video system that cannot be obtained from the buoys? What does ray tracing provide that the BEM does not, and vice versa? Would the main conclusions of the manuscript still be reached if one of these components were unavailable?
Good point, we will give an overview of what will follow, but try to not make it
too lengthy.> - Reference figure for Nazaré Canyon
> I strongly recommend introducing, preferably as Figure 1, a simple reference map showing the bathymetry of Nazaré Canyon. This figure could include the main geographical features and rocks referred to throughout the manuscript, the relevant segments or "hotspots" of the canyon, the main canyon axis and turns, and potentially the locations of the buoy and stereo-camera deployments. This figure would provide a geographical reference that could be used throughout the manuscript
Yes, the plan was that Figure 2a would do this. Ideally, a 3D sketch with
correct bathymetry would give a good overview and provide a useful
illustration for the future. We will try to impement these suggestions, keeping
in mind some time and cost limitations on how this can be done.> Specific comments
>
> I recommend stating the scientific questions and/or objectives explicitly in both the Abstract and the Introduction.Ok. Will do.
> **L.4:** Replace "outside" with "in."
Ok.
> **L.9:** Consider replacing "In particular" with "We show in this manuscript that..." or equivalent wording.
Ok.
> **L.20:** Reference needed.
Ok. Partly we show this here through the main directions of large swell events
and the bathymetric effects. Perhaps best left for the conclusion and the
abstract.> **L.22–23:** Please provide examples from the literature of studies that have performed this type of experiment.
Ok. The NCEX studies previously mentioned do this.
> **L.24:** Add a comma before "and."
Ok.
> **L.28:** "wave amplitude."
Ok.
> **L.31–32 and Figure 1:** I do not think the current figure is the most appropriate way to demonstrate that high-wave events occur every year. I recommend introducing a temporal dimension. For example, rather than showing statistics over the complete 2009–2025 period, the authors could show annual statistics or annual means.
We will re-work this figure, this is clearly confusing to many readers.> **L.32:** Please specify that you are referring to waves formed at Praia do Norte.
Ok.> **Figure 1b:** Consider providing a bin-averaged representation.
Ok.
> **Figure 2e:** "One camera of the stereo-camera system."
Ok.
> **Figure 2:** Question for the editors: Is the current organization of the panels consistent with Ocean Science format? Should the individual panel titles instead be incorporated into the main figure caption?
> **L.44:** The gradient of which quantity?
Will fix.
> **L.45:** I recommend avoiding adverbs and simplifying the sentence. For example: "We are therefore able to distinguish the effect of canyon geometry on wave focusing, which appears to be more efficient at Nazaré than at the La Jolla and Scripps canyons."
Good suggestion.
> **L.48–49:** I suggest removing the sentence beginning "The canyon originates from a complicated history of different processes active for different periods..." unless this information is directly relevant to the subsequent discussion.
Will check and possibly re-word. Some readers appreciate this context, some do
not.> **L.71:** Consider removing "The canyon is not connected to a river system …” unless this information is important for the analysis.
Similar to above.
> **L.73–75:** Please support this statement with a reference.
Will do, this is the same as the following paragraph (Tyler et al., 2009).
> **L.76–77:** Please support this statement with a reference. If Tyler et al. (2009) supports it, consider combining the two sentences.
Ok.
> **L.78–79:** "The canyon terminus is about 200 meters west of the lighthouse (150 meters south of the lighthouse)." Please clarify: 150 or 200 m?
Will fix.
> **L.81:** Remove "And" at the beginning of the sentence.
Ok.
> **L.89:** You could mention that this behavior is consistent with Airy linear wave theory in shallow water.
Yes.
> **L.89:** Add a comma after "at Nazaré."
Ok.
> **L.90:** Figure 2a and Figure 3b.
Will specify.
> **L.92–94:** The sentence explaining the dependence of refraction and reflection on wave period is convoluted and should be simplified. Also, replace "phase speed" with "the phase speed of the incident waves" where appropriate.
Ok. Will clarify.
> **L.100:** Why are phase-resolving wave models not used for this study? Please briefly discuss this methodological choice and the advantages/limitations of the selected approaches relative to phase-resolving models.
The BEM-model is phase-resolving. It would make sense to do a study using
established phase-resolving models. The main reason is that this would
significantly increase the scope, a secondary reason is that these models
generally require a well constrained bathymetry and input spectrum. Since there
are large uncertainties here, the results of these models are less likely to be
relevant and would possibly require significant tuning and trial-and-error.
We therefore choose more conceptual models here, ray tracing and BEM to
interpret the phenomena in terms of refraction and reflection. However, it would be a natural next step to try and study the Nazare-waves in better detail. We do mention this in the conclusion, but we can make this clearer up front so that the choices are understandable.> **L.100:** Start a new paragraph at "As the water depth decreases..."
Ok.
> **Equations (1–2):** Please define all variables. Add a comma after Equation (1).
Ok.
> **L.118–119:** Please specify that h is the depth. Please carefully check the the deep- and shallow-water approximations and the associated kh limits. (Long waves/deep water waves —> large kh)
Ok.
> Because canyon width is discussed immediately before this point, I also recommend reorganizing these lines to avoid ambiguity between canyon width and water depth.
Good point.
> **L.120:** Are you referring to the same specific canyons or to the same type of coastal canyons? Please clarify.
Will clarify.
> **L.120:** "Several" and "different" are somewhat redundant here; one is sufficient.
Ok.
> **L.134–139:** I appreciate this paragraph because it helps illustrate the wave-reflection criterion. However, the transition from the preceding paragraph is difficult to follow. I recommend introducing it more explicitly or rewriting the beginning of the paragraph to provide a clearer transition.
Ok, will do.
> **L.140:** This paragraph is difficult to follow. Several concepts require further explanation, including "interference pattern" (are these caustics?), "source field," the processes responsible for dissipation, and what is meant by waves being "summed incoherently." I also recommend shortening some of the long sentences.
Will re-work this text to make it clearer.
> **L.141:** Please provide additional details about the ray-tracing method. For example, what differential equations are solved?
Will briefly explain this and provide a reference for more information.
> **L.158:** Please explain why crest length are relevant here.
Yes, will do.
> **L.161:** Please choose between either \(\mathrm{Var}(\phi_i)\) or \(\sigma_\phi\). Base on equation (3), I think \(\mathrm{Var}(\phi_i)\) is the most relevant.
Ok.
> **L.174:** What causes the buoys to drift across the canyon—surface currents, wind, wave-induced drift, or a combination of these? This appears to be answered around line 182; I recommend to combine the two sentences
Yes, will discuss this and combine.
> **L.177:** "integrated twice over time."
Ok.
> **L.184:** "Relatively mellow" should be quantified.
Ok.
> **L.186:** Remove "therefore."
Ok.
> **L.197:** How was the elevation of the camera system measured?
From the topographic map, will clarify.
> I recommend adding a subsection for the description of the instruments.
Ok.
> **L.200:** Keep "the" before the first occurrence of "refraction zone" and remove it where unnecessary in subsequent occurrences.
Ok.
> **L.201:** Add a comma before "and."
Ok.
> **L.201:** Instead of "not particularly large, their periods were sufficiently long," please provide quantitative values.
Yes, good point.
> **L.206–207:** Readers may be curious about the offshore drift of the buoys. I recommend referring to Figure 6a here.Good point.
> **L.209:** ECMWF wave data are not perfect. Please provide a more quantitative and qualitative assessment of the differences between ECMWF and the observations.
Ok, will try to do that.
> **Figures 4 and 5:** Please revise the zenith/azimuth tick labels of the polar plots to avoid overlap.
Yes, will improve.
> **L.215–216:** "The peak wave direction travels almost along the canyon axis, slightly from the north" should be rewritten. A direction does not "travel." Consider quantifying the angular difference, e.g., "The peak wave direction and the canyon axis are aligned within approximately X°."Will re-word and verify.
> **Figure 6a:** There appears to be an optical image underneath the bathymetric field. I recommend removing it. A coastline contour could be added instead if useful.
Ok, will try to make this figure clearer. Obtaining good and recent coastline
contours have not been easy (the one from the bathymetry is not very accurate).
Can check if OpenStreetMap vectors are better.> **Figure 6b:** Please rewrite the caption. Specify whether the quantity is the wave-energy spectrum or the power spectral density of sea-surface elevation.
Ok.
> **L.216–218:** Based on Figure 6a, the buoys appear to be located north of the canyon rather than directly above it during Experiment 1.
They started out above the canyon and drifted north. Will try to improve figure.
> **L.223:** Avoid wording such as "not very trustworthy." Please state more precisely what the limitation is and, if possible, quantify the uncertainty.
Ok, good point.
> **L.226:** Please justify the selected window length. Is it a compromise between stationarity of the wave field and including a sufficient number of periods? The selected time window appears relatively short and may reduce the frequency resolution of individual spectra.
Exactly. The frequency resolution is improved by the high sample rate of the
buoys (52 Hz), will clarify.> **L.229:** From which dataset is the peak period Tp obtained—ECMWF or the deployed buoys? Over what time interval is T_p calculated?
ECMWF. Will clarify. It was relatively similar, and since the buoys are affected
by the near-shore effects ECMWF was considered more appropriate as an estimate
of the incoming field.> **L.230:** Please clarify "first drift" and "second drift." Do these correspond to the first and second experiments?
We sometimes did several drifts in the same experiments, will clarify.
> **L.234:** Should "Figure 6d" be "Figure 7"?
Both do show the effect. Figure 6d show that using buoy data only above the
canyon capture little low-frequency energy. Figure 7 shows it more clearly for
all buoys. Will clarify.> **General comment on the spectrograms:** Please guide the reader more explicitly through these figures. Around what value does the variance oscillate? What are the relevant time intervals? Providing times that can be directly identified in the figures would make the discussion much easier to follow.
Yes. Will do, they are not so common so will spend some time explaining them.
> **L.238–241:** This paragraph is unclear and should be rewritten.
Ok. Will re-word.
> **L.242–252:** This paragraph should be rewritten for clarity. In addition, the panels referred to here (Figure 9a–c) need axes. What is the time window used to infer the stereo-video variances maps?Ok. The time window was about 10 minutes, will check and specify.
> **L.258:** Avoid "more or less unperturbed”, be quantitative.
Ok.
> **L.260:** Please guide the reader more explicitly. Which buoy(s) should be examined?
Ok. Will clarify.
> **L.263:** Please clarify what is meant by "calculating the wave field."Ok.
> **L.263:** Retain the BEM acronym once it has been defined.
Ok.
> **L.265–275:** This paragraph is difficult to understand and introduces several concepts that have not been sufficiently explained beforehand, including "high" and "low," phase shifts, and wave crests. I recommend rewriting the paragraph and introducing these concepts more clearly before using them to interpret the results.
Ok, will do.
> **L.290:** How can Doppler shifting affect the measured spectrum? Please provide references supporting this discussion. (Colosi et al. 2023?)
It will shift the spectrum towards higher or lower frequencies. Will clarify and
refer.> **L.291:** Please provide a clearer marker for the location of the Guilhim rocks in Figure 2a. Also, the markers for the artificial reef and rocks appear identical and should be differentiated.
Yes, see comment regarding figure at beginning.
> **L.301:** Why is T_{m02} used rather than T_{m0m1}or T_{01}? Please provide the equation used to compute the selected mean period and briefly justify this choice.
Ok.
> **L.313:** "and thus alters the reflection or refraction here." I do not understand the causal relationship. How does the initial refraction subsequently alter reflection/refraction? Please clarify.
The sloping edge initially refract the waves, before they encounter the even
steeper edge towards the canyon floor. The first effect is best described as
refraction, the second as reflection. The initial refraction cause greater
reflection since the incidence angle is increased.
> **Figure 12:** Some middle panels contain color bars. Please revise the layout. The shoaling-coefficient panels should also use the same color scale/colormap to facilitate direct comparison.Ok.
> **Figure 13:** Could the correspondence between panels (e) and (f) be made clearer? Please also provide axes for panels (a–d). Figure 13 seems to be a screenshots of another document. Please correct.
Ok, will improve figures.*> *Figure 14:** Please provide units on the panels and revise the layout so that tick labels and text are readable. The peak wave frequencies/directions in the polar plots should also be clearly visible. Could markers be added to the map to identify the locations associated with the secondary and tertiary peaks discussed in the text?
Yes, will improve. Discrete markers will improve the figure.
> **L.332:** I recommend removing "from 255" and "from 305" and using a single directional convention consistently throughout the manuscript.
Ok.
> **L.332:** Is the angle 75° or 95°? The upper-left panel appears to indicate 95°. Please check for consistency.
Will double-check this.
> **General comment on the stereo-camera results:** It should be made explicit that the variance maps derived from the stereo-camera observations represent temporally averaged variance.
Yes. This is important, because the buoys show spatial variance change, so
together they provide more convincing evidence.> **L.351–353:** There is a syntax issue; please rephrase the sentence.
Will check.
> **L.352:** Is Figure 5b the most relevant figure to support this statement? I also recommend adding a line or segment to the polar plot showing the main axis of Nazaré Canyon.
Yes, good point. Will check if there is a better figure.
> **L.353:** Please check whether Figure 4b is indeed the intended reference.
Will double check.
> **L.363:** Could the canyon bathymetry/depth be superimposed on this figure? This would make it easier to relate the wave response to the underlying topography. Check Irving et al. 2025 (Supporting figures, Nazare’s Case)
Yes, can try to add the outline of the canyon edge.
> **L.365:** Could the authors provide an approximate depth threshold below which realistic waves become sensitive to bathymetric variations?
Yes, we have simulations earlier in the manuscript that can support this.
> **L.373:** Add a comma before “and a boundary element."
Ok.
> **L.376:** I am not convinced that the second (2) element listed here represents one of the main results of the analysis. Please reconsider its prominence or explain more clearly how it follows from the results.
True, this is not a result, but an argument for a result. Will make clear that
this is supporting another statement.> **L.385:** Could this point be supported by a sensitivity analysis, potentially provided in the Supplementary Information?
It would be very interesting to investigate this further, I am reluctant to
increase the scope of this study by including it here. We could list as an
interesting study for further work, especially together with other
phase-resolving models like e.g. REEF3d.> **L.390:** Regarding currents, are observations or previous analyses of coastal currents available for this region? Are tidal currents the dominant currents in the study area? A simple scaling estimate of current-induced refraction based on realistic current gradients encountered by the waves would help assess whether neglecting currents is justified.
It is likely difficult to get good current estimates that cover the entire area
of this study, but we could try to do obtain some estimates of the current if
available in other studies. It is likely that this will still remain an
uncertainty, especially since the waves themselves generate significant currents
in the area of reflection.> **L.397:** The term "full wave model" is somewhat counterintuitive because neither a phase-resolving nor a spectral wave model appears to be used here. Please consider another expression.
Ok. Will be more specific.
> **L.174:** Based on the figure, the deployed buoys appear more aligned than arranged in a cross-pattern. Please revise the description or clarify the intended geometry.
Yes, they were initially deployed in a cross pattern. We can show this better in
the figure.> **L.440-441:** Could the authors propose an observational or numerical experiment that could test this interpretation?
At this scale, this is challenging. Perhaps stereo-camera data comparing planar
waves and intersected waves can show whether those that are intersecting can
sustain greater heights before breaking. It would require correcting for wave
height and period differences. Advanced non-linear wave models may also be able
to reproduce the results of McAllister. We will try to discuss this.
Sincerely,
Dr. Gaute HopeCitation: https://doi.org/10.5194/egusphere-2026-2778-AC3
-
AC3: 'Reply on RC3', Gaute Hope, 03 Oct 2026
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- 1
I apologize for the delay with the review as it overlapped somewhat with my summer vacation.
This paper describes the measurements and modeling of ocean swell as it approaches and transforms over the submarine canyon in front of Nazare, Portugal. This is an oceanographically fascinating region that features unusually large and 3-dimensional breaking waves. The region is also important in the XXL surf community & industry, tourism, etc. The combination of measurements and modeling are to my knowledge unprecedented for this area. The modeling experiments are appropriate and interesting. The paper is overall well written and straightforward to read, however, it does occasionally get a tedious because of a complex subject matter. The paper illuminates the role of wave refraction and reflection off the canyon cliff and coherent interference toward the occurrence of very large and steep, pyramid-like waves that are seen at Nazare. I believe this paper makes a great leap forward toward better understanding the behavior of waves at Nazare and other similar coastal locations with submarine canyons. It does leave some questions unanswered, but that I think should be straightforward to address. Most figures need some lift and formatting changes to improve readability.
Significant comments & questions
Line-specific comments & questions
Milan Curcic, University of Miami