the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Jan 2026
Bridging the gap between weather forecasting and tsunami forecasting: a background model of the open ocean in the tsunami spectrum
Abstract. A reference power law of ω -2, where ω is angular frequency, has been traditionally used to characterize the background open ocean tsunami spectrum (BOOTS) slope from a period of 10 mins to 120 mins and that its noise profile can be assumed to be normally distributed. However, this characterization is based on data from temporary deployments of bottom pressure sensors that lasted from several weeks to 11 months and only in scattered areas of the Pacific. Here we measure the BOOTS noise profile using 1–15 years of bottom pressure recorder data sampled at 15 s from the Deep-ocean Assessment and Reporting of Tsunamis (DART) stations. We utilize probabilistic power spectral density plots to create background noise models for 34 DART stations across the Pacific basin. We find that often a simple normal probability distribution does not correctly characterize the observed background noise spectrum at periods of 120 s, 250 s, 800 s, and 2700 s. We find deviations from the expected behavior follow a strong seasonality signal due to infragravity waves. We calculate infragravity wave heights and their mean values for December, January, and February and June, July, and August. We found that meteorologically induced infragravity wave events are the largest factors in seasonal variations of the BOOTS slope and intercept, especially in the east Pacific. We show the typical meteorological systems that drive these events, and we connected tropical systems from off the coast of Mexico to infragravity wave events in the east and central Pacific. And that these infragravity wave generating events potentially affect the probability distributions of the BOOTS. Finally, we convert plot the spatial distributions of the probability distribution functions.
- Preprint
(7964 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
-
RC1: 'Comment on egusphere-2025-5764', Anonymous Referee #1, 17 Jan 2026
-
AC1: 'Reply on RC1', Sean Santellanes, 02 May 2026
The paper characterizes the background noise of the open ocean tsunami spectrum using a large dataset of DART stations. It challenges the traditional Gaussian noise assumption by demonstrating significant non-Gaussianity driven by seasonally variable infragravity waves (IGWs) linked to weather systems. This is an interesting work. However, the study would benefit from a more detailed discussion on the potential implications for forecasting models to fully support the proposed connection. Additionally, further clarification on the data selection criteria and the interpretation of the observed spectral features would strengthen the manuscript's robustness. Therefore, I recommend a Major Revision.
1. The title employs the broad phrase "Bridging the gap between weather forecasting and tsunami forecasting." The manuscript primarily characterizes
the statistical properties of background noise and the correlation between weather systems and IGWs. It does not propose a concrete forecasting model or operational framework that truly "bridges" this gap. The current title overpromises; I suggest revising it to more accurately reflect the study's scope (e.g., focusing on the characterization of noise statistics).Response: the title can be changed to the following "statistics of noise in the background open ocean tsunami spectrum in the Pacific Ocean."
2. Lines 120-121: The authors mention excluding only seismic tsunamis with Mω≥7.0, as well as landslide or volcanic tsunamis. Many earthquakes smaller than 7.0, meteotsunamis, or small-scale non-seismic events can still leave detectable signals in DART records. This could lead the authors to erroneously attribute these unremoved signals to the intrinsic non-Gaussian nature of the background noise.
Response: seismic tsunamis with <Mw7.0 are more frequent than those in the range we consider, yes. However, the radiative decay along with the increase in dispersive properties means their signals would have their signals being comparable to the background noise ~1-3 cm. In addition, the large spacing of the DART sensors mean they would only — theoretically — affect one sensor location. As for meteotsunamis and small-scale non-seismic events, no definitive climatology exists for the entire Pacific basin. Indeed, they are included in the background noise, but further research would be needed to detect them, since DART sensor data on its own is insufficient. Ideally, this process would include SWOT and general circulation models in a Bayesian process.
3. Lines 275-278: The authors observe that noise at long periods (e.g., 2700s) also deviates from a normal distribution but state directly that they "cannot determine the cause." For a paper aiming to establish a background model, leaving the noise source of a key frequency band as an "unanswerable question" is insufficient. I suggest the authors provide a deeper discussion on potential physical causes (such as residual tides, atmospheric pressure coupling, or instrument drift) rather than merely describing the phenomenon.
Response: We can add more statistical methods to establish a deeper discussion. This means including correlation coefficients with derived ocean data from the ERA5 model, which is doable.
4. Lines 279-285: The authors repeatedly emphasize that current Data Assimilation (DA) and Machine Learning (ML) algorithms may encounter difficulties in handling actual tsunami impacts due to the assumption of Gaussian distributions. The manuscript does not provide any actual examples or synthetic tests to quantify this impact. I recommend adding a simple DA experiment or synthetic test to substantiate this core argument.
Response: A simple data assimilation experiment with mixed statistics is no small feat. The usual development of data assimilation schemes for non-Gaussian statistics involves characterising noise and phenomena statistics, which begets a toy model demoing the mathematical structure, which then begets the full structure. Overall, these specific comment presents an idea that is a future research direction; however, it is outside the scope of the study. All non-Gaussian mixture models must reduce to a Gaussian structure to be consistent with the mathematical literature.
5. Figures 7 & 8: The authors shows that weather systems drive changes in background noise primarily by visually comparing snapshots of specific meteorological events with DART noise spectra. A few case studies are insufficient to prove that these are the "largest factors." I suggest calculating the correlation coefficients between meteorological parameters (such as significant wave height or wind speed) and DART background noise parameters over the entire time series to provide statistical backing.
Response: We can add more statistical methods to establish a deeper discussion. This means including correlation coefficients with derived ocean data from the ERA5 model, which is doable.
Another avenue would be the inclusion of SWOT data to account for the internal tides. However, its data are temporally much less in scope. It can be used to test the statistics the cases we have presented in the manuscript.6. Figure 9: I suggest explicitly marking the time points of "Sensor Upgrade" or "Old Sensor / New Sensor" with arrows or text boxes directly in Figure 9.
Response: Yes, this fix can be implemented.
7. Figure 11: The use of multiple shapes combined with various colors to distinguish different distributions appears visually cluttered, making it difficult to distinguish patterns, especially when the map is zoomed out. Consider simplifying the classification scheme or using more distinct color contrasts to improve readability.
Response: Yes, this fix can be implemented.
Citation: https://doi.org/10.5194/egusphere-2025-5764-AC1
-
AC1: 'Reply on RC1', Sean Santellanes, 02 May 2026
-
RC2: 'Comment on egusphere-2025-5764', Anonymous Referee #2, 03 Feb 2026
This study focuses on the tsunami forecasting and weather forecasting. Leveraging long-term, widely covered data from Deep-ocean Assessment and Reporting of Tsunamis (DART) stations, it reveals the non-normal distribution characteristics of Background Open Ocean Tsunami Spectrum (BOOTS) noise and the driving role of infragravity waves (IGWs). Addressing the application limitations of data assimilation and machine learning in tsunami forecasting, the research points out the challenges posed by non-normal noise distributions to traditional Gaussian-assumption algorithms, thereby providing critical foundational data support and insights for the subsequent optimization of tsunami impact forecasting models. This is an interesting work, but enhancements are needed in the description of technical details and the physical interpretation of certain conclusions. I recommend a Major Revision. Specific recommendations are as follows:
1. Clarify the potential physical mechanisms underlying the non-normal distribution of noise in long periods. Verify the causal relationship between IGWs and the non-normality of BOOTS noise through quantitative analyses (e.g., correlation coefficients, regression models) rather than relying solely on correlation inferences.
2. Supplement the optimal selection criteria for probability distribution function fitting, the specific thresholds and procedures for tsunami signal removal in IGW height calculations, and the parameter setting basis for key methods such as Multitaper Power Spectral Density (MT-PSD) to improve the reproducibility of the study.
3. The impact of meteorological systems can be further analyzed. Distinguish the differences in the effects of various meteorological systems (such as cyclones, tropical storms) on noise distributions, and clarify their action thresholds to enhance the practicality of the conclusions.
4. If data availability permits, to improve the generalizability of the conclusions, propose follow-up research plans that extend the study to other oceans and integrate additional observation methods, enhancing the completeness of the research.
5. The writing expression can be further optimized. Strengthen the interpretation of figures and tables, and organize the discussion section in a structured manner to clearly present the research innovations, limitations, and future directions.Citation: https://doi.org/10.5194/egusphere-2025-5764-RC2 -
AC2: 'Reply on RC2', Sean Santellanes, 02 May 2026
This study focuses on the tsunami forecasting and weather forecasting. Leveraging long-term, widely covered data from Deep-ocean Assessment and Reporting of Tsunamis (DART) stations, it reveals the non-normal distribution characteristics of Background Open Ocean Tsunami Spectrum (BOOTS) noise and the driving role of infragravity waves (IGWs). Addressing the application limitations of data assimilation and machine learning in tsunami forecasting, the research points out the challenges posed by non-normal noise distributions to traditional Gaussian-assumption algorithms, thereby providing critical foundational data support and insights for the subsequent optimization of tsunami impact forecasting models. This is an interesting work, but enhancements are needed in the description of technical details and the physical interpretation of certain conclusions. I recommend a Major Revision. Specific recommendations are as follows:
1. Clarify the potential physical mechanisms underlying the non-normal distribution of noise in long periods. Verify the causal relationship between IGWs and the non-normality of BOOTS noise through quantitative analyses (e.g., correlation coefficients, regression models) rather than relying solely on correlation inferences.
Response: Yes, this can be done using the ERA5 dataset. The variables to test correlation coefficients and regression models are total wave height, swell period, and wind speed 2 m.
2. Supplement the optimal selection criteria for probability distribution function fitting, the specific thresholds and procedures for tsunami signal removal in IGW height calculations, and the parameter setting basis for key methods such as Multitaper Power Spectral Density (MT-PSD) to improve the reproducibility of the study.
Response: We can supplement the selection criteria for the PDF fitting. We can further clarify that for the IGW height calculations that times corresponding to tsunamigenic events, as defined in the manuscript, did not factor into the calculations. We can detail the key settings used in the MT-PSD code.
3. The impact of meteorological systems can be further analyzed. Distinguish the differences in the effects of various meteorological systems (such as cyclones, tropical storms) on noise distributions, and clarify their action thresholds to enhance the practicality of the conclusions.
Response: Yes, we can add in the effects of various meteorological systems (such as extra-tropical cyclones and tropical cyclones). However, adding in action thresholds is outside the scope of this study. Decisions would need to be held on what it means to be practical from these datasets, which are outside the science considered here.
4. If data availability permits, to improve the generalizability of the conclusions, propose follow-up research plans that extend the study to other oceans and integrate additional observation methods, enhancing the completeness of the research.
Response: We can add in a discussion on the combination of SWOT, hi-resolution pressure data, and ERA5 data. The DART sensor data are the longest climatology of pressure data for the Pacific, which can be useful for testing the other observations of next generation ocean observation platforms.
5. The writing expression can be further optimized. Strengthen the interpretation of figures and tables, and organize the discussion section in a structured manner to clearly present the research innovations, limitations, and future directions.
Response: Yes, this can be made further efficient.
Citation: https://doi.org/10.5194/egusphere-2025-5764-AC2
-
AC2: 'Reply on RC2', Sean Santellanes, 02 May 2026
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 1,093 | 670 | 119 | 1,882 | 90 | 82 |
- HTML: 1,093
- PDF: 670
- XML: 119
- Total: 1,882
- BibTeX: 90
- EndNote: 82
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
The paper characterizes the background noise of the open ocean tsunami spectrum using a large dataset of DART stations. It challenges the traditional Gaussian noise assumption by demonstrating significant non-Gaussianity driven by seasonally variable infragravity waves (IGWs) linked to weather systems. This is an interesting work. However, the study would benefit from a more detailed discussion on the potential implications for forecasting models to fully support the proposed connection. Additionally, further clarification on the data selection criteria and the interpretation of the observed spectral features would strengthen the manuscript's robustness. Therefore, I recommend a Major Revision.
1. The title employs the broad phrase "Bridging the gap between weather forecasting and tsunami forecasting." The manuscript primarily characterizes the statistical properties of background noise and the correlation between weather systems and IGWs. It does not propose a concrete forecasting model or operational framework that truly "bridges" this gap. The current title overpromises; I suggest revising it to more accurately reflect the study's scope (e.g., focusing on the characterization of noise statistics).
2. Lines 120-121: The authors mention excluding only seismic tsunamis with Mω≥7.0, as well as landslide or volcanic tsunamis. Many earthquakes smaller than 7.0, meteotsunamis, or small-scale non-seismic events can still leave detectable signals in DART records. This could lead the authors to erroneously attribute these unremoved signals to the intrinsic non-Gaussian nature of the background noise.
3. Lines 275-278: The authors observe that noise at long periods (e.g., 2700s) also deviates from a normal distribution but state directly that they "cannot determine the cause." For a paper aiming to establish a background model, leaving the noise source of a key frequency band as an "unanswerable question" is insufficient. I suggest the authors provide a deeper discussion on potential physical causes (such as residual tides, atmospheric pressure coupling, or instrument drift) rather than merely describing the phenomenon.
4. Lines 279-285: The authors repeatedly emphasize that current Data Assimilation (DA) and Machine Learning (ML) algorithms may encounter difficulties in handling actual tsunami impacts due to the assumption of Gaussian distributions. The manuscript does not provide any actual examples or synthetic tests to quantify this impact. I recommend adding a simple DA experiment or synthetic test to substantiate this core argument.
5. Figures 7 & 8: The authors shows that weather systems drive changes in background noise primarily by visually comparing snapshots of specific meteorological events with DART noise spectra. A few case studies are insufficient to prove that these are the "largest factors." I suggest calculating the correlation coefficients between meteorological parameters (such as significant wave height or wind speed) and DART background noise parameters over the entire time series to provide statistical backing.
6. Figure 9: I suggest explicitly marking the time points of "Sensor Upgrade" or "Old Sensor / New Sensor" with arrows or text boxes directly in Figure 9.
7. Figure 11: The use of multiple shapes combined with various colors to distinguish different distributions appears visually cluttered, making it difficult to distinguish patterns, especially when the map is zoomed out. Consider simplifying the classification scheme or using more distinct color contrasts to improve readability.