the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Feb 2026
Tide of the Time: Global tidal characteristics observed from in-situ measurements
Abstract. Tide gauges have been critical sources for sea level research, enabling the development of tidal theory and an understanding of local variations that occur across the global oceans. Tides play important roles in a variety of oceanographic and geodetic applications, and characterising their spatial variability is valuable for applications ranging from fishing to flood risk management. This manuscript presents the coastal characteristics of ocean tides based on 3,591 high-frequency tide gauge observations from the recently updated GESLA-4 database. These characteristics range from tidal datums such as Mean High Water (MHW) and the Great Diurnal Range to metrics like the Age of the Tide, Form Factors, Dodginess, updated amplitude trend estimates, and new insights into the regional duration of high tides. Our analysis finds that 125 out of 237 long-time series show statistically significant trends in one or more constituents, from -1.47 mm/yr to +1.80 mm/yr, while the duration of the high-water stand during spring tides is shown to vary from 1 to 14 hours, for an inundation depth of 20 cm. It is anticipated that the results presented will be useful not only to tidal experts but also to a wide range of cross-disciplinary researchers and local communities, aiding their understanding of a vital component of the global Earth system.
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Status: open (until 01 Apr 2026)
- RC1: 'Comment on egusphere-2026-346', Thomas Monahan, 26 Feb 2026 reply
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RC2: 'Comment on egusphere-2026-346', Haidong Pan, 28 Feb 2026
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This paper investigated global tidal features using 3591 high-frequency tide gauges, which is helpful for improving our understandings of global tidal dynamics and the validation of tidal models. I want to express my gratitude to the authors for their long-term efforts in establishing the tidal observation dataset and the harmonic constant dataset, from which the whole tidal community benefits. The paper I think is well-written, thus, it can be accepted after minor revisions.
Specific comments:
Line6, Abstract, ‘Dodginess’ is not a common concept, which may need some further explanation
Line60,Section 2 ‘Data and methodology’ can be divided into two sub-sections.
Line65, may be a table can better show the improvement and differences of different versions of GESLA.
Line85, Eq.(1),classical harmonic analysis model uses ordinary least squares (OLS) to solve unknown tidal parameters, which are sensitive to outliers. Leffler and Jay (2009) introduced iteratively reweighted least squares (IRLS) to replace OLS in harmonic analysis, which can effectively eliminate the influences of background noises. Pan et al. (2025, doi: https://doi.org/10.1007/s10236-024-01652-5) identified significant timing errors in 35 tide gauges from the UHSLC, with these errors potentially altering tidal amplitude estimates of main constituents by more than 10 mm. Notably, at specific tide gauges, such as Tanjong Pagar and Manila, abnormal tidal amplitude changes caused by timing errors can be larger than 50 mm. The use of IRLS can remove the interference from timing errors. Since parts of GESLA data are obtained from UHSLC, such timing errors are also inherited. It is suggested that you can use IRLS rather than OLS in performing harmonic analysis.
L114, inter-annual tidal variability can be driven by climate modes, such as ENSO (see Devlin et al. 2014, doi: https://doi.org/10.1007/s10236-014-0741-6 ; Pan et al., 2025, doi:https://doi.org/10.1016/j.pocean.2024.103410).
L124, although astronomical tides in the Baltic Sea and Black Sea are generally weak, it is suggested that these tide gauges should be retained for two reasons: First, tides in parts of these sea areas may be significant. Second, local radiational tides such as S1 and S2 may be significant, which can also provide important tidal information.
Figure 1, not MKS, but MKS2.
L160-162, Figure 2, it is interesting that at some tide gauges, K2, P1 and Q1 have the largest amplitudes, which are unusual. I suggest that you can list tidal constants (as well as the uncertainties) of major constituents at these unusual tide gauges in tables (may be in the Appendix). Although K2 and P1 amplitudes are large, they may not past the significance test. Nevertheless, it is necessary to further explore these tide gauges.
Figure 4B, revise title ‘Tidal band’ as ‘Dominant tidal band’. Also, how do you define ‘dominant’? Are there any quantified numerical values?
Figure 5A, in the colorbar, the maximum value of tidal form factor (FF) is set as 5, which may mislead the readers that the maximum FF among 3591 tide gauges is only 5. However, this is not true, for example, FF at Hon Dau (UHSLC ID: 650a) can exceed 14.
L228, it is better to provide a map of tidal level variations at these tide gauges, to illustrate dodgy tidal regimes. Also, how the definition of ‘dodginess’ (namely, Eq.2) is proposed?
L359-361, it is important to provide the uncertainties (95% confidence intervals) of amplitude trends.
L376, the title of section 7 ‘A note on river tides’ may be not suitable, you can change as ‘A note on tides in fluvial estuaries’ since tide gauges along the river channel are excluded in your analysis.
L401, NSTIDE, not subscript
Citation: https://doi.org/10.5194/egusphere-2026-346-RC2 -
RC3: 'Reply on RC2', Haidong Pan, 28 Feb 2026
reply
In Eq.2, A means tidal amplitudes. But in Eq.(1), you use H to denote amplitudes. To keep consistency, I suggest you use H in Eq.2.
Citation: https://doi.org/10.5194/egusphere-2026-346-RC3
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RC3: 'Reply on RC2', Haidong Pan, 28 Feb 2026
reply
Data sets
Tidal characteristics from tide gauge data M. Hart-Davis et al. https://www.seanoe.org/preview/111620?token=oJhIGBczw4FcCtYXEJM9qcLzk4qVlDRg
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- 1
This manuscript presents a global analysis of tidal characteristics from a recently expanded global database of tide gauges. Due to the relevance of coastal tides for a wide-range of communities, particularly with the new SWOT satellite, I think this is a timely and important contribution. Furthermore, I believe that this manuscript has the potential to be a key reference for these communities for a long time to come. The following points are mostly minor, but I think the authors should carefully revise the manuscript to ensure it has the potential impact that it can have in line with the suggestions below. I suggest minor revisions.
Main Critique:
The text reads somewhere between a review paper, a foundational textbook, and a journal paper on tides from tide gauges (with some very interesting results in trends and time at high tide). The unfortunate aspect of doing all three is that it leaves more to be desired from each one.
For example, the section on data and methodology reads less like a summary of data and methodology and more like a section which introduces the basics of tidal analysis and gauge datasets. In fact, there are many missing details regarding the methodology (see later comments) which are needed to ensure replication. My suggestion is to choose one or the other, either strip back the very general and light overview in favor of a comprehensive methodology, or put the methods in the appendix and keep the general introduction to tides. The latter would make it easier to present both a foundational description of the basics of tides, and the characteristics they have globally.
Beyond the methods, I suggest the authors make clear exactly what role this paper is to have: a review of things we can, and have, learned from global tide gauges along-side some new insights.
The remaining points are organized according to the section they come from.
Section 4:
This section presents a useful overview of various tidal characteristics and the way we quantify them. While the details are well covered, for non-tidal readers this is a deluge of information baked into notation and jargon that does not become more intuitive with the global figures. An easy fix could be to include supplementary figures which visualize what these quantities amount to for representative problems. The authors already do this in Figure B1, but I think even more value would come from some of the more advanced characteristics. Figure 1 of Phil’s Differences between Mean Tide Level and Mean Sea Level paper is a fantastic example of how this might be done.
Tidal Durations:
I think this is extremely useful and interesting to the flood community, but I wish there was a bit more discussion of the why. E.g. it seems relatively obvious a diurnal tide would spend a bit longer at a peak than a semi-diurnal one. What superposition of constituents creates especially long peaks? Are there any interesting mechanisms at play? This doesn’t require a massive rejig of the figures, but at least an effort at explaining to readers where these discrepancies come from, perhaps through a simple synthetic example in the appendix from two representative sites.
“Globally, the coastal tides evaluated stay within 1 cm of their peak from 0.2 to 3.5 hours, with a mean of 1.0 hours. The time spent within 20 cm of the peak varies from 1 to 14 hours, with a mean of 4.7 hours.” Please consider presenting distributions on Figure 7 in the form of a histogram with the mean plotted on it. Given this is a strictly positive statistic, and likely heavy tailed, is it appropriate to present a mean only?
It is obvious that this is relevant for inundation, but I think even a back of the napkin calculation of how would greatly increase the impact of these results. My suggestions would be to consider a place with considerable sunny day flooding like the East coast of the US where there are well documented future estimates of sunny day flooding frequency that would be straightforward to translate to time at high water. Discrepancies in the shape around the high-water would therefore lead to large discrepancies in the durations of future floods.
The authors also allude to tide-surge interaction here “Additionally, tidal properties interact with storm surge to produce a composite wave; generally speaking, the longer the high-water stand, the longer the ensuing high-water period during a storm may be, given equal meteorological forcing.” A brief discussion of how longer or shorter high-water stands interact with the surge component would be interesting. For example the sqrt(gH) dependence, and 1/H dependence of wind stress would yield very different interaction characteristics.
Tidal Trends:
There is not enough information about how uncertainties are estimated for the trends, or the estimator employed for the harmonic analysis, or indeed the final estimated uncertainties. One cannot evaluate the veracity of the statistical significance if this information is not included. See Innocenti et al. 2022, Monahan et al 2025 etc. for relevant discussion on uncertainty estimation in tidal estimators. Further, all estimates need to be reported with uncertainties. It also needs to be made clear whether the subsequent description of globally observed trends are computed exclusively from the statistically significant trends, or all of the trends. Given this, the revised manuscript should also report the confidence in this by incorporating the uncertainty. Figure 8 should also be modified to reflect the uncertainties, cross-hatching, opacity, size, etc. would all be welcome to reflect the confidence in the individual estimates to the readers.
Previously in the manuscript it is also stated that there are numerous duplicate records in the database. Are these accounted for in the processing? If you state that 52 and 53% of the trends are significant without removing duplicates, the true geographically balanced estimate may differ.
Given the massive variability in trends, does it make sense to report global average statistics? Again, histograms on the plots would be useful in confirming whether a mean is appropriate to report here. Additionally, if you state qualitatively that there are regionally coherent trends, this needs to be quantitatively supported in the text:
“For the S2 tide, clear region-specific changes in the tides can be observed, particularly positive trends on the west coast of America” of _____ +/- ____ mm/year. This doesn’t need to be done everywhere, but it is worth citing the main areas as these trends will likely spur future work.
I am sympathetic to the need to do batch processing of gauge estimated trends for a paper like this; however, the potential for systematic errors to crop up in the gauge estimates cannot be ignored. The manuscript as written mentions these errors but does not meaningfully engage with them. If the trends reported are intended to be released and used by the public, some attempt needs to be made to reconcile this. For this work, one need not identify all such gauges, but using this manuscript as a means of flagging this potential issue will be valuable to future tidal researches in order to prevent inaccurate trends from being presented.
Given the authors focus on tide gauges, and that this manuscript is in some sense an overview of the use of these data in tidal research, it would seem useful to summarize some of the primary ways that errors manifest in these data and how they differ from say altimetry or bottom pressure sensors, etc.
River Tides
It is unclear why this section has been included in the manuscript as written. River tides are both interesting and important in many regions as the authors rightly point out. However, the authors do not present any results beyond an abbreviated summary of the interesting characteristics of tidal rivers. Simply summarizing these mechanisms is not novel, nor particularly useful for the manuscript if not backed up by some observations of this in the tide-gauge data globally. I suggest the authors either add a figure which explicitly looks at river characteristics, including the mechanisms they discuss using NS_Tide, CWT_Multi, or even response based approaches (e.g. RTide) or they remove the section entirely and remark that this warrants future work. Certainly, an entire manuscript could be dedicated to global tidal river characteristics from gauges.
Conclusion
Further to my main criticism, throughout the manuscript I found myself questioning what the intent of the manuscript is. At some points it appears to be trying to be something like an abbreviated textbook where various global tidal characteristics and mechanisms are discussed. At other points, such as for trends and the times at high-water it seems to present interesting scientific results. The conclusion did not reconcile this dilemma.
If this is intended to be a review paper on what we can understand about tides from tide gauges I think this is great, but the authors should consider speaking about the open challenges in tidal research from these data. This goes well beyond purely observational dataset gaps which are emphasized in the present conclusion. What more is there to be done with tide gauges beyond what was presented here?
Pedantic points:
When introducing equation 3 (age of semidiurnal tide), include the full description of the symbols used in the equation before “alternatively”. Can be confusing if readers don’t see an explanation for S_S2, S_M2. (you do this correctly in Equation 4).
“It is probably true to say that this diurnal age parameter is made much less use of now in scientific studies than the semidiurnal age of the tide.” Either remove statements like this or qualify them: e.g. Due to ____ the diurnal age of the tide is less relevant.
“A complementary tidal statistic to this analysis is whether the superposition of semidiurnal and diurnal constituents tends to produce especially large high waters or is more biased toward low outliers; readers are referred to the discussion by Byun et al. (2023) for more information on this” Why not include this? Most of the other statistics are not novel so why refer readers away for this one especially given its relevance for flooding?
It would be helpful to have a table in the appendix which contains each of the tidal characteristics and their definition so that readers can easily see them in one place.
Final thoughts:
I think this paper has potential to be an excellent summary of what we can learn about tides from global tide-gauge measurements – and that it will be very successful. In all, I think these revisions are actually fairly minor and mainly just require more information on methods, reporting of uncertainties, and a rejigging of the text to make the goals of the paper more clear.
-TM
Innocenti et al 2022: Analytical and residual bootstrap methods for parameter uncertainty assessment in tidal analysis with temporally correlated noise
Monahan et al 2025: Tidal Corrections From and for SWOT Using a Spatially Coherent Variational Bayesian Harmonic Analysis