2.1 Stage 1: catalogue of events

Trials for the LMTI were conducted in the UK, where there is a long history of events dating back to at least 1750 CE (Haslett and Bryant, 2009). Six main sources of UK meteotsunami events were utilised: Lewis et al. (2023a), Williams et al. (2021), Thompson et al. (2020), Long (2015), Haslett and Bryant (2009), and Dawson et al. (2000), all providing a comprehensive and coherent historical record. The collected data were analysed, with the meteotsunami identified and categorised according to a reliability and verification system adopted from Gusiakov (2021). Identified events were allocated a reliability score from 1 to 4 depending on the amount of evidence and data available across the sources (i.e., the number of components completed in the index), where 1 = doubtful (1 to 3 components), 2 = questionable (eyewitness report, 3 to 6 components), 3 = probable (newspaper report, 6 to 9 components), and 4 = definite (technical report, 9 to 12 components). Older events which are usually fragmented make it difficult to establish an informed judgement, so these were subsequently allocated a reliability score of 1; events with insufficient information remained unclassified and were considered highly uncertain.

2.2 Stage 2: meteotsunami components and values

The proposed LMTI considers 12 various components of meteotsunami and receptor site characteristics, based upon descriptions of previous global events, current thresholds used by researchers, and the characteristics of other related hazard indices (Table 1). This multifaceted approach allows for the LMTI to capture the complex dynamics of meteotsunami events and facilitate a single score which can be matched with a description on the LMTI table (Table 1). The LMTI adopts this layout to allow for an intensity evaluation based upon hazard only or receptor site only. By incorporating both parts this allows for analysis of a low height wave impacting a highly vulnerable coastline. Each component has a different threshold weighting leading to the allocation of a score from 1 to 5. These threshold weightings are calculated based on event data and other related hazard indices.

Table 1Hazard and receptor components with associated thresholds as used in the LMTI.

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2.2.3 LMTI intensity levels

Once the thresholds were determined it was possible to then propose a five-stage index. This system incorporates a scoring regime to represent the level of contribution or weighting from each component towards the overall hazard. For this reason, each component is scored separately on a level of 1 to 5, with 1 contributing least and 5 contributing most strongly. This method allows for standardisation of the index and for each component that is measured in different units to be combined. Papadopoulos and Imamura (2001) proposed a 12-level scale to measure tsunami. However, we have reduced and simplified the LMTI scale to 5 levels, as meteotsunami, being smaller in scale and more localised in impact than tsunami, do not need such a detailed breakdown.

The final meteotsunami intensity values exhibited in Table 2 contain brief descriptions highlighting the characteristics of each intensity level, which have been devised from the characteristics of historical global meteotsunami events and are based around the events ability to be measured, its impacts, and post-event actions. The five levels are portrayed in a colour-coded format as this is an effective way of communication as people tend to perceive risk better through colours, graphics, and visuals (Engeset et al., 2022).

Table 2LMTI intensity level descriptions.

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2.3 Stage 3: categorising events based on intensity: how to calculate LMTI

1. An event must be identified and verified as a meteotsunami (see Lewis et al., 2023a).

2. The 12 components are systematically allocated a score of 1 to 5 dependent on the distinct weightings of the threshold values as displayed in Table 1.

   The component scores from each of the two subsections are added together and divided by the number of component cells containing data. If a component is not present at certain locations, then the numerical score of “zero” is placed in the calculation and this does not affect the overall intensity score.

3. Scores for the two subsections are then combined to give a single score by using the following conceptual calculation in Eq. (2):

   $$\begin{array}{}\text{(2)}& \mathrm{MTI}={\displaystyle \frac{\mathrm{\Sigma }z}{Nz}},\end{array}$$

   where LMTI (meteotsunami intensity) is a function of 12 potential components, where z is component and N is the number of components.

4. The final LMTI score will be a number between 1 and 5 as shown in Table 2 and will give a standardised description of the level of intensity for that event. The higher the intensity score, the higher the level of risk.

In the calculation of the index, the scores are expressed with decimal places as shown in Table S1 for example, LMTI 1.3 or LMTI 3.4. This enables a fine resolution for quantifying and comparing intensity and impact for research purposes. The presentation of the final intensity score is represented as a whole number, where the index is typically rounded to the nearest integer, for example, LMTI 1 or LMTI 3. This simplified representation provides a clear categorisation to present to the public, stakeholders, and decision makers.

3.1 UK meteotsunami intensity

The trial run of the LMTI provided valuable insights into UK meteotsunami events. A total of 100 events were analysed. Amongst these events, Level 2 meteotsunami accounted for 69 % of the occurrences (Fig. 2). This finding suggests that the UK is prone to moderate-intensity meteotsunami. Level 1 (minimal) meteotsunami represented 12 % of events, in particular between 2009 and 2015. Level 3 (high) meteotsunami accounted for 16 % of the events especially between 1883 and 1932. Finally, the results revealed a small number of severe intensity events (Level 4) which appeared in the hazard subsection, with all three events occurring in the winter months and along the Bristol Channel.

Figure 2Hazard, receptor, and LMTI scores for UK meteotsunami (1750 to 2022).

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The results highlighted in Supplementary 1 show that the number of unreliable meteotsunami (those classified as 1 = doubtful and 2 = questionable) decreases over time, with none recorded after 1968. A total of 67 % of the events were classified as definite meteotsunami having been attributed a high reliability score of 4. This enhanced reliability is apparent in the record starting in 2008, which is an indication of the abundance of data with increasing instrumentation.

The distribution of meteotsunami hotspots was also identified through the application. The southwest region of England exhibited a concentration of all levels of intensity type events, with the Bristol Channel exhibiting the only Level 4 type events. The south of England and north of Scotland also demonstrated notable meteotsunami activity, in particular Level 2 (moderate) intensity events (Fig. 3). These hotspots highlight the regions most at risk from meteotsunami occurrence and provide a valuable insight for future coastal management.

Figure 3Geographical distribution of UK meteotsunami, with the number of events and the final LMTI intensity level shown at each location. Full results are in Table S1. Base map © Crown copyright and database rights 2022 Ordnance Survey (100025252).

3.2 Global expansion of the index

The findings from the trial implementation of the LMTI in a global context demonstrated that the index has the potential for adoption into other coastal regions prone to meteotsunami. Results for events such as Vela Luka (Croatia) in 1978, Nagasaki (Japan) in 1979, and Ciutadella (Menorca) in 2006 all scored as expected with a Level 3 on the scale in line with the observed data. The event in 2017 in Dayyer (Persian Gulf) scored a Level 4; this was particularly deadly as it occurred in an area that was not accustomed to experiencing extreme wave events, and so consequently the infrastructure and population were not prepared. It occurred at 08:00 LT (local time), a few hours after a thunderstorm and it was calm, so people were starting their day unaware of any issue. On the LMTI a Level 3 and 4 equates to high intensity, where large debris is deposited from high-velocity water flow and there is a threat to life and assets (Table 2). On the opposite end of the intensity scale at Level 1, corresponding to minimal intensity events which are only detectable on instruments and with no impact to life or assets, we find events such as Pellinki (Finland) in 2010. If we compare these results to the intensity scale proposed by Vilibić et al. (2021), we find a correlation. According to Vilibić et al. (2021) Vela Luka, Croatia (1978), Ciutadella, Menorca  (2006), and Pantano do Sul, Brazil (2009) were all allocated an intensity Level 4. LMTI scored these events at 3.8, 3.6, and 3.5 respectively. Cassino beach (Brazil) in 2014, Zandvoort (the Netherlands) in 2017, and Mali Losinj (Croatia) in 2007 were allocated a Level 3 according to Vilibic̈ et al. (2021). LMTI scored these events at 3.2, 3.1, and 3 respectively. Arraial do Cabo (Brazil) in 2002 and Lagos (Portugal) in 2010 were both allocated 2 by Vilibić et al. (2021). LMTI scored these events at 2.2 and 2 respectively. Finally, the Persian Gulf event of 2017 was allocated a Level 5, and LMTI scored it at 4.3.

Validation was a critical step in assessing the accuracy and applicability of the index. This procedure involved ensuring that the index accurately reflected the observed and recorded data for the event that it was quantifying. For example, there was the well-documented and well-researched event at Vela Luka (Croatia) on 21 June 1978, where in the early evening the bay experienced a 6 m water level change with accompanying strong currents which inundated 650 m inland. The impact was large-scale damage and loss of assets as well as contamination of the bay, with belongings and chemicals washed out by the retreat of the water. Fortunately, due to the quick thinking of residents there were no fatalities and minimal injuries (Vučetić et al., 2009). The LMTI allocated a Level 3.8 to this event (Level 3 bordering on Level 4), which is described in Table 2 as “violent movement and damage to infrastructure and assets. Pollution by contaminants. Fast flowing velocity with deep water exceeding past flood risk defences”. The LMTI result and description accurately reflect the data for this event.

To demonstrate validation at the lower end of the index and a different geographical location, the event at Arraial do Cabo (Brazil) on 7 September 2002 is given as an example. At 12:00 UTC and low tide, a series of unusual sea level oscillations at the maximum height of 0.7 m occurred in the harbour. They were initiated by a sharp air pressure change (5 mbar h⁻¹) associated with an offshore weather system. Even though water velocity was strong, no damage to assets or injury/loss of life was reported (Candella and de Araujo, 2021). The LMTI allocated this event a Level 2.2, which as described in Table 2 is an event that is “visible in instruments and observations, causing slight disruption, with small debris and rarely a threat to life and assets”. The intensity level and description reflect the observed data for this event. However, even though the LMTI's ability to assess meteotsunami intensity was validated and demonstrated through this trial run, as the sample size is so small this will require further testing to ensure complete confidence.

Level 5 events are expected to be of a rare occurrence in the current climate. If one were to occur it would be distinguishable from the other levels by the extensive and long-term destruction of assets and loss of life that it would enforce on the shoreline.

4.1 The LMTI and UK meteotsunami

Upon successful implementation of the LMTI in the UK, results have shown that meteotsunami have tended to be of moderate intensity with an overall Level 2. Table 2 describes a Level 2 type event as representing visibly on instruments but rarely a threat to life. Coastal communities will experience a slight disruption including flooding, the movement of small-sized debris, and shallow-water flow, which will usually be accompanied by other hazards such as precipitation and lightning. The identification of south-western England and Scotland as hotspots underscores the importance of the ability to run comparisons between regions and events, allowing researchers to track changes in meteotsunami frequency, intensity, and spatial distribution over time. This hotspot tendency is most likely due to the dominant weather direction coming in from the west, off the Atlantic Ocean, and from strong convective storms building over Spain and France during the summertime.

The rareness of the combination of atmospheric, marine, and topographical factors required for meteotsunami propagation is why Level 4 (severe) events are small in quantity and observed at a limited number of locations. The strongest intensity meteotsunami tend to appear in funnel-shaped bays and harbours with a wide shelf, which is necessary for Proudman resonance to occur and for the transfer energy from the atmosphere to the water. The western English Channel is sufficiently wide and deep, with a shoaling coastline for meteotsunami to become well developed. The noticeable run of Level 3 and Level 4 hazard events that occurred between 1883 and 1932 also coincided with a series of severe storms. The runs of Level 1 hazard events between 2009 and 2015 are again due to a series of severe storms, but in this instance, we can extrapolate a more accurate picture due to the emergence of more refined quantitative data.

It is likely that the data for higher intensity meteotsunami events such as a Level 3 would have a more extensive historical record compared to lower-level events such as a Level 1. This pattern can be attributed to the fact that major events tend to have a more significant impact and are therefore more likely to be documented. The index has become more “complete” over recent years due to advancements in measurement and monitoring and an increase in the level of scientific interest and awareness.

4.2 Application of the LMTI

Motivated by the absence of a formalised way of quantifying meteotsunami intensity, in this paper we have presented the new LMTI, which will allow for comparative analysis between regions prone to meteotsunami, and it is offering a standardised communication media to eliminate any confusion and inconsistency. Having started from a zero position the authors have based the LMTI on the already widely accepted and used Papadopoulos and Imamura (2001) tsunami index and the ITIS-2012 tsunami index (Lekkas et al., 2013). Both indices are heavily reliant on qualitative perceptions based around the impact on people and places. The latter, however, does incorporate quantitative data on the physical characteristics in the form of wave height, run-up, and the number of fatalities. Neither index accounts for variables such as resonance or local geomorphology.

The traditional concept of an intensity scale measures the effects of hazards but not its strength (Gusiakov, 2009). The LMTI has evolved this concept to incorporate the physical components of the hazard. This allows for further investigation into not just why certain areas are more prone but also into the dynamics of the meteotsunami at the shoreline. The index is different from other hazard indices as it does not require sophisticated technology and it allows for the analysis of both the hazard and the receptor site to provide a more holistic view of meteotsunami risk. Understanding how these events have behaved and evolved historically can be a precursor to establishing future trends and highlight issues to promote forward thinking in terms of coastal planning. One of the primary strengths of the LMTI lies in its adaptability and potential for global application. As the field of meteotsunami forecasting and warning progresses, the LMTI will no doubt play an important role in assisting in this process. While the index was developed and trialled in the UK due to its long history of events, records, and data availability, its underlying principles and methodology can be applied to other meteotsunami-prone regions worldwide.

4.3 Constraints and limitations

While the expected results from the LMTI implementation are encouraging, there are certain limitations that should be considered. The availability and quality of historical data may vary across regions, with events missing and the severity of other events being underrepresented due to incomplete datasets. This may potentially affect the applicability in certain areas. Addressing this limitation requires efforts to enhance data collection and establish robust monitoring networks.

The index contains two thresholds that rely on qualitative descriptors, and many of the historical accounts used may have been subjective in nature, especially with documents such as pamphlets and newspapers tending to misreport, exaggerate, or invent characteristics to boost sales. Results have revealed that the further back in time you go, the less available and reliable the accounts become. However, as time progresses this will be remedied with improved quantitative data collection methods.

Finally, sea level, shoreline slope, and elevation in historical times would have been different from present day, and the geometric and topographic nuances of an area can have effects on the propagation of waves. As adjustment of this is beyond the scope of this study; we must assume a static shoreline position based up on current data. Despite the limitations, the index proves to be a useful indication of meteotsunami intensity, and these limitations should not be an issue in moving forward as data become more available and at a higher frequency.

4.4 Further work

Successful implementation of the LMTI in the UK has yielded results that can be used to champion the need for higher-frequency data sampling on tide gauges and for the consideration of the inclusion of meteotsunami into coastal management regimes. As this paper introduces the first evolution of the LMTI, we can offer potential strategies for calibrating and improving the index, in particular for use in a more global context. Primarily, the incorporation of more data from recent observed events and more global events will improve the calibration and reliability. The present evolution of the LMTI requires instantaneous air pressure readings to indicate sudden changes. However, as wave height is proportional to integrated air pressure over time, it may be more appropriate to alter this component to incorporate air pressure over time.

Expanding the index to include resonances such as Proudman, Greenspan, and harbour Q factor may provide valuable information about the potential amplification or dampening effects within a particular location. However, whilst this offers a valuable insight, its practical implementation would require advanced numerical modelling techniques with reliable and detailed data on bathymetry, morphology, and atmospheric conditions. These data may not be available for all affected locations, and by adding complex resonances this could potentially hinder the practicality and usability of the index, making it harder to interpret and less accessible to decision makers.