An 8-yr Meteotsunami Climatology across Northwest Europe: 2010–17

Meteotsunamis are shallow-water waves that, despite often being small (~0.3 m), can cause damage, injuries, and fatalities due to relatively strong currents (>1 m s−1). Previous case studies, modeling, and localized climatologies have indicated that dangerous meteotsunamis can occur across northwest Europe. Using 71 tide gauges across northwest Europe between 2010 and 2017, a regional climatology was made to understand the typical sizes, times, and atmospheric systems that generate meteotsunamis. A total of 349 meteotsunamis (54.0 meteotsunamis per year) were identified with 0.27–0.40-m median wave heights. The largest waves (~1 m high) were measured in France and the Republic of Ireland. Most meteotsunamis were identified in winter (43%–59%), and the fewest identified meteotsunamis occurred in either spring or summer (0%–15%). There was a weak diurnal signal, with most meteotsunami identifications between 1200 and 1859 UTC (30%) and the fewest between 0000 and 0659 UTC (23%). Radar-derived precipitation was used to identify and classify the morphologies of mesoscale precipitating weather systems occurring within 6 h of each meteotsunami. Most mesoscale atmospheric systems were quasi-linear systems (46%) or open-cellular convection (33%), with some nonlinear clusters (17%) and a few isolated cells (4%). These systems occurred under westerly geostrophic flow, with Proudman resonance possible in 43 out of 45 selected meteotsunamis. Because most meteotsunamis occur on cold winter days, with precipitation, and in large tides, wintertime meteotsunamis may be missed by eyewitnesses, helping to explain why previous observationally based case studies of meteotsunamis are documented predominantly in summer.


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Meteotsunamis are shallow-water waves with periods between 2-120 minutes that are 45 generated by moving weather systems. The atmospheric pressure and wind fields associated 46 with those weather systems can force wave growth, known as external resonance (e.g., 47 regions is that they contain a large (~10 5 km 2 ) region of shallow, gently sloping bathymetry. 69 However, a similarly large (6×10 5 km 2 ) region that is known for meteotsunamis has not been 70 represented by a regional climatology-the northwest European continental shelf (Fig. 1). 71 Climatologies are useful because they quantify conditions during which meteotsunamis occur.  it seems reasonable to assume that meteotsunami seasonality (2 min -2 h period) should not 85 be considerably different to waves of atmospheric origin with a slightly longer period (3-5 h). 86 Furthermore, a climatology of atmospherically-generated seiches in Rotterdam, which we 87 interpret as meteotsunamis, also showed that most Dutch meteotsunamis occur in autumn and 88 winter (e.g., de Jong and Battjes 2004). Clearly, there is discrepancy between the seasonality 89 of meteotsunamis in case studies, and the suggested seasonality from localised climatologies 90 (loosely referring to a long-term analysis of less than 10 tide gauges along a coastline). 91 Once the time of events are known, we can also link the conditions of their identified 92 occurrence to concurrent atmospheric conditions. One question is whether meteotsunamis 93 occur primarily with particular mesoscale weather systems. For example, meteotsunamis in the 94 Great Lakes tend to be generated by fronts, linear convective systems and non-linear 95 convective complexes rather than discrete, individual cells (e.g., Bechle et al. 2015Bechle et al. , 2016. This  Table 1. 106 To illustrate the variety of choices available within each step, consider valid choices in the 107 second step -the amplitude threshold to distinguish waves from background noise. Previous 108 studies have used a significant wave height relative to the de-tided residual noise (e.g., Bechle to produce the first regional climatology of meteotsunamis for northwest Europe and identify 122 the atmospheric phenomena that are associated with meteotsunamis. This northwest European 123 climatology will answer how frequently meteotsunamis of certain wave heights occur (size-124 exceedance rates), when they occur (diurnal and seasonal variation), and which precipitating 125 weather systems tend to co-occur with meteotsunamis. This climatology will also provide 126 evidence to test the hypothesis that linear systems tend to generate meteotsunamis.

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The structure of the rest of this article is as follows. In section 2, we describe the data, how 128 NSLOTTs and meteotsunamis were detected from this data, and the atmospheric system 129 classification scheme. Then, in section 3, we present results and discussion of the size-130 exceedance rates, seasonal and diurnal variation and atmospheric conditions. Finally, we 131 conclude in section 4.

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To produce a meteotsunami climatology, we linked NSLOTT identifications to precipitating 134 atmospheric systems that were measured by radar and identified from pre-processed images it would take to process the 1-min data manually (i.e. methods described in sections 2b and 147 2c).

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However, the data intervals should be short enough to identify meteotsunamis. In the US, 6-149 min data have been used in climatologies to quantify size-exceedance rates and determine  Furthermore, a climatology of relatively high-frequency waves (3-5-h periods) was 152 constructed in the UK using 15-min averaging intervals (Oszoy et al. 2016). Therefore, we 153 expected that 10-min and 15-min tide-gauge data could also be used to identify particularly 154 large non-seismic sea-level oscillations at tsunami timescales (termed NSLOTTs as in Vilibić 155 and Šepić (2017)). However, wave heights from these 10-min and 15-min datasets will likely 156 be aliased and underestimate size-exceedance rates. 8 removed for the Netherlands and Germany. No corrections were made for missing data 163 between January and December. 164 b. Isolating non-tidal waves with periods less than 120 minutes 165 First, any 120-min high-pass filtered data that had a magnitude greater than four times the 166 standard deviation of the residual was visually inspected. Upon visual inspection, data were 167 removed if corresponding to spikes, incorrect timings, missing-data replacement values, 168 inappropriate absolute sea-level elevation or jumps in data.

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After preliminary data cleaning, tidal components of the sea-level elevation and periods > 120 170 min were removed to isolate tsunami-period signals. The averaging intervals used here are 5-171 15 min and are unable to reliably show waves with periods less than 10-30 min, nor properly 172 represent wave heights with periods less than 50-150 min. As the sea-level elevation had 173 already been low-pass filtered (due to long intervals), we applied a fourth-order, zero-phase, 174 120-min high-pass Butterworth (1930) filter to retain signals with periods < 120 min.

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However, this filter did not remove all unwanted tidal noise. After high-pass filtering, there 176 were repeating wavelets with wave heights on the order of tens of centimetres (peak to trough) 177 with periods of ~90 min. These repeating wavelets were identified in the data from most tide 178 gauges. Autocorrelation of the sea-level elevation time series showed that the wavelets repeated 179 in about 12-h 25-min intervals (i.e. M2 periodicity). The wavelet amplitudes were also 180 modulated over 28 days with the spring-neap cycle. The repeating wavelets could not be fully 181 removed by first applying tidal harmonic analysis (U-tide in Python). Synthetic time series 182 (M2, M4, M6, and M8 constituents) suggested that these repeating wavelets were damped 183 higher-frequency tidal components.

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Therefore, a stacking algorithm was designed to remove the mean repeating wavelet signal at 185 12-h 25-min intervals. A stacking correction was designed to remove unwanted tidal signals 186 that high-pass filtering did not remove. First, the filtered time series were resampled at 1-187 minute intervals and separated into equal segments (e.g. 12-hr 25-min segments). Seven 188 segments were consecutively taken, and the central (fourth segment) was taken to be the  Performing this algorithm on synthetic data with four tidal coefficients suggested that the 197 stacking algorithm could remove 94% of the tidal sea-level residual that was not removed by 198 high-pass filtering. On the real data, the algorithm showed mixed success in suppressing 199 wavelets, and in the worst cases did not suppress the wavelets at all during a spring-neap cycle. 200 Therefore, peaks that were detected at the standard deviation of the signal, σ, multiplied by a 201 factor of 6 (termed 6σ), were visually inspected. If the peak was part of the repeating wavelet 202 cycle, it was removed. After this manual data processing, 71 out of the 90 tide gauges (79%) 203 were accepted for further analysis (black outline and black text in Fig. 1).

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Individual events were then grouped into NSLOTT events if they were identified at two or 213 more tide gauges within a 3-h interval (the event interval). This event interval was deemed 214 appropriate because of 10-100 km separations between tide gauges, 25-100 km h -1 shallow-215 water wave speeds, and because mesoscale atmospheric systems last a few hours. There was 216 no imposed maximum time limit for an NSLOTT event, meaning that the event interval 217 controlled the number of NSLOTT events. After this processing, the largest measured wave 218 height in an NSLOTT event was set as the NSLOTT wave height.  we resort to remotely-sensed data to identify atmospheric features.

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Specifically, weather radar can be used to remotely sense atmospheric precipitation-sized . Nevertheless, we acknowledge that using weather radar means that we may miss a 245 few meteotsunamis associated with non-precipitating weather features. 246 We used radar mosaic images across northwest Europe with 5-km grid spacing. This radar

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We decided to link a weather feature to an NSLOTT event if precipitation was over the basin 253 at least 6 h before the first detection. If there was no precipitation over water, the NSLOTT 254 was not classified as a meteotsunami, even if the wave height exceeded 0.25 m. From radar-derived precipitation, mesoscale characteristics of atmospheric systems were 257 catalogued. We classified the system motion into one of eight cardinal directions. This motion 258 was the overall motion of the system, constituting of mean flow and propagation (e.g., 259 Markowski and Richardson 2011 p. 251). If possible, we classified the type of mesoscale 260 atmospheric system based on radar morphology (Fig. 2). 261 We grouped mesoscale atmospheric systems into four classifications: isolated cells, quasi- were much smaller (order of 100-10,000 km 2 ) (cf. Fig. 2a(ii) with Fig.2d(ii)).

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If there were multiple precipitating weather systems, those that occurred for longer times and 280 were closer to the time and location of meteotsunami detection were favoured for classification.

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As there was uncertainty classifying the precipitating system morphologies, a confidence was 282 assigned to each system classification. Classification confidence did not affect meteotsunami 283 identification but if the wave occurred more than 6 h from the system and there were multiple 284 systems in quick succession, or if the final system classification could have been in three or 285 more categories, then the system type was "unclassified". Conversely, "Confidently" classified 286 systems (which we further analyse) all occurred within 3 h of the meteotsunami and were firmly 287 in one classification. Once the mesoscale systems were classified, the concurrent synoptic 288 atmospheric environments for a subset of meteotsunami-generating mesoscale systems were 289 found from ERA5 reanalysis data (Copernicus Climate Change Service 2017).

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To summarise, we classify an NSLOTT as a non-tidal wave with a 2-120-min period and a 291 wave height (peak to trough) that is ≥ 6σ of the sea-level residual. The sea-level residual is the 292 sea-level elevation with as much tidal signal suppressed as possible, through both 120-min 293 high-pass filtering and a stacking algorithm. An NSLOTT also had to have its signal identified 294 at ≥ 2 tide gauges within 3 h. Requiring two tide gauges to measure an event to classify as an 295 NSLOTT may result in conservative estimates of meteotsunami recurrence rates (e.g. tide 296 gauges in Ireland and Lerwick). For the purposes of this climatology, a meteotsunami is an 297 NSLOTT that had a minimum calculated 0.25-m wave height (i.e. a high-amplitude NSLOTT) 298 and occurred within 6 h of a precipitating atmospheric system. Atmospheric systems were then 299 classified into one of four system morphologies, and only systems that were confidently 300 classified are presented.

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A total of 13 080 initial detections exceeded the 6σ-threshold (Table 2). From these initial  Meteotsunamis larger than 0.5 m were mainly identified in France (51%) and Ireland (36%) 336 and were only detected at 14 out of 71 tide gauges (bold location names in Fig. 1). Of the four 337 meteotsunamis that were larger than 1 m, one was identified at Dunmore East (station 86) and 338 three were identified at Le Havre (station 9).

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Countries with smaller data intervals (5-6 min) had lower annual size-exceedance rates for 340 smaller thresholds than countries with larger data intervals (Fig. 3,). In other words, smaller 341 NSLOTTs were detected less often with smaller data intervals (see Appendix F of Williams 342 (2020) for more detail). Wave-height aliasing likely meant that NSLOTTs exceeding 0.1 m 343 were identified more frequently with longer data intervals. This increase in small NSLOTT 344 identifications occurred because aliasing had two effects. First, the 6σ thresholds were lower 345 with longer data intervals than with shorter data intervals, implying that more, smaller 346 NSLOTTs were identified at tide gauges with longer data intervals. Second, because wave 347 heights were aliased, fewer large waves were identified that met the 0.25-m minimum 348 NSLOTT wave height. In locations with shorter data intervals, larger waves were identified as 349 NSLOTTs, even though there were other smaller detections.  (Table 1)

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Across every country, more meteotsunamis were identified in winter than any other season 410 (Fig. 4). In Ireland and the UK, 58-59% of all meteotsunamis were identified in winter, and 411 44-46% occurred in December and January. In France, Belgium, the Netherlands, and 412 Germany most meteotsunamis also occurred in winter (43-46% of all meteotsunamis).

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Every country apart from the UK had an annual cycle with a single winter peak and the fewest 414 meteotsunamis in either spring or summer (Fig. 4). The season with fewest meteotsunamis was 415 between 0-15% of each country's total meteotsunami count. In contrast, the UK showed an 416 annual cycle with a secondary summer peak. Even though only 32 meteotsunamis were 417 recorded in the UK, summertime meteotsunamis were identified in 5 out of 8 years.

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All detections related to high-amplitude NSLOTTs were then grouped by hour (e.g., 1400-419 1459 UTC) and month (e.g., Jan), allowing analysis of both seasonal and diurnal variation. In 420 total, 1368 detections were analysed. Again, there was strong seasonal variation, with over 421 52% of detections occurring in winter and only 7% in summer (Fig. 5). A higher winter 422 maximum and lower summer minimum were found by analysing all of the available detections 423 than by grouping the detections as a single event with the largest wave height, because more 424 tide gauges identified a 6σ-event per high-amplitude NSLOTT during winter than summer.
Thus, winter events were detected more frequently and by more tide gauges than summer 426 events.

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Throughout the year, there was a weak diurnal cycle, with detections peaking in the afternoon 428 (30%) and falling overnight (23%) (Fig. 5). Most meteotsunamis occurred in winter, primarily 429 in the afternoon, although there was also a secondary winter peak overnight. The diurnal cycle 430 was about 5-6 times weaker than the seasonal cycle and was slightly variable throughout the 431 year. For example, the overnight peak occurred between winter and autumn, but not spring or 432 summer.  We suggest that this discrepancy in the seasonality between case studies and climatologies is 448 not explained because meteotsunamis are larger in summer than winter. In this study, in France  Noticeably, none of the 32 meteotsunamis in the Netherlands were in summer (Fig. 4) (Table 2). High-amplitude NSLOTTs without co-occurring 475 precipitation may have been formed by non-precipitating atmospheric phenomena or by non-476 atmospheric phenomena (e.g., landslides). There was no significant difference between the 477 mean wave heights of NSLOTTS without a coincident precipitating system and NSLOTTS 478 with a coincident precipitating system (p > 0.09). There was also no significant difference 479 between meteotsunami wave heights for different mesoscale system classifications (p > 0.26).  In these instances, it was unclear whether these generating systems were more similar to non-   (Fig. 6a). Fewer classifications were non-linear clusters (44, or 17%) and 496 isolated cells (10, or 4%). However, the variation within this average shows both seasonal and regional variation. There were strong seasonal patterns of meteotsunamis generated by quasi- 498 linear systems and open cells (Fig. 6b). Both quasi-linear systems and open cells followed an 499 annual cycle with most occurring in winter and fewest in summer, whereas the isolated cells 500 and non-linear clusters had no clear cycle (Fig. 6b). 501 Regionally, locations with more meteotsunamis tended to have higher counts of every 502 classification, but those with proportionally more wintertime meteotsunamis (e.g., Ireland and 503 the UK) tended to have even more open-cell classifications (Fig. 6c). Non-linear cluster 504 identifications tended to increase with total number of meteotsunamis, remaining between 14-505 22% for every country apart from the Netherlands (4%). Quasi-linear system classifications 506 also increased with larger totals, with the exception of Ireland, which had fewer quasi-linear 507 classifications than Belgium. However, despite similar seasonal patterns between countries,  they also cover a smaller area than other systems and because they may have lower surface 534 pressure gradients and wind stresses. 535 We suggest that using radar to classify meteotsunamis is about as successful as using in situ 536 surface pressure and wind speed measurements. We linked 92% of NSLOTTs exceeding 0.25 537 m to weather systems using the radar method. Comparably, in the Great Lakes, fewer quasi-linear systems and 9 events with summertime quasi-linear systems. We examined sea-557 level pressure, 500-hPa geopotential height, the temperature difference between 850 hPa and 558 the sea surface (ΔTSS), and convective available potential energy (CAPE) (Fig. 7).

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All synoptic environments indicated that the dominant synoptic weather feature at the time of 560 meteotsunami detection were extratropical cyclones north or west of the UK (Fig. 7). Although 561 sea-level low-pressure centers were associated with all meteotsunamis and favoured westerly 562 geostrophic flow, the associated extratropical cyclones were farther north and about 20 hPa 563 deeper in winter than in summer (Figs. 7ai, 7bi and 7ci). The mean lower-and middle-564 tropospheric winds were also supportive of eastward-moving mesoscale precipitation systems. 565 We also infer lower tropospheric static instability with open cells and winter quasi-linear 566 systems, as indicated by warmer surface waters compared to lower-tropospheric air (i.e. ΔTSS 567 < -13°C, Figs. 7bi and 7bii) (e.g., Holroyd 1971). Moderate CAPE over ocean occurred for the 568 winter meteotsunamis (Figs. 7ci and 7cii), whereas stronger CAPE over land occurred for the 569 summer meteotsunamis (Fig. 7ciii).

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This study has produced a regional climatology of meteotsunamis across northwest Europe.

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Through a combination of manual filtering, automatic peak detection and a stacking algorithm 594 designed to remove tidal signals, 13 080 events greater than a 6σ-threshold were identified  We recognise that relatively long intervals in tide gauges were used to study meteotsunamis 609 compared to elsewhere. We suggest that, the 15-min data interval in the UK is too long to here, 1-min data may need automated methods with rigorously removed tidal signals.

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Despite the large intervals used, we expect that the seasonal cycle extracted is valid, as there is 618 no reason to expect seasonal bias in aliasing from tide-gauge measurements. Furthermore, all 619 seasonal analyses from tide gauges tended to agree. In Ireland, France, Belgium, the 620 Netherlands and Germany, there was a single annual cycle, with most meteotsunamis in winter 621 (42-59%) and fewest in spring or summer (0-15%). There was also a diurnal cycle, with most 622 between 1200-1859 UTC (30%) and fewest between 0000-0659 UTC (23%).

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To understand which mesoscale weather phenomena were associated with the meteotsunamis,