Atmospherically driven extreme sea levels (e.g. wind storms, hurricanes), associated with flooding producing substantial damage to houses, goods, and infrastructure, are among the main hazards impacting coastal communities (Nicholls and Cazenave, 2010; Neumann et al., al., 2015). As such, meteorological tsunamis (commonly referred to as meteotsunamis) are sea level oscillations with characteristics similar to seismic or landslide tsunamis but generated by atmospheric gravity waves, frontal passages, pressure jumps, or squalls, for example, though a multi-resonant mechanism (Monserrat et al., 2006). The principal generation mechanisms are open-ocean resonance occurring between the ocean and the air pressure oscillations at timescales ranging from a few minutes to a few hours (e.g. Proudman, 1929) and coastal amplification that also includes so-called harbour resonance (Miles and Munk, 1961; Rabinovich, 2009). Locally they can be destructive, not only due to extreme sea levels (Hibiya and Kajiura, 1982; Salaree et al., 2018), but also to dangerous currents in constrictions or in coastal zones (Ewing et al., 1954; Vilibić et al., 2004; Linares et al., 2019). The strongest meteotsunami on record in the Mediterranean Sea hit Vela Luka, Croatia, in June 1978, with a wave height of 6 m (crest to trough) and a period of 18 min. The meteotsunami lasted several hours and caused USD 7 million in damage (Vučetić et al., 2009; Orlić et al., 2010).

In certain locations around the world, due to a combination of weather patterns, geography, and bathymetry, meteotsunamis can be a regularly occurring phenomenon. The Balearic Islands and Croatian coastline in the Mediterranean Sea, a few of Japan's gulfs and bays, the Great Lakes and the US East Coast, and the western Australian coastline are good examples (Pattiaratchi and Wijeratne, 2015; Rabinovich, 2020). For all these locations, despite varying intensities, meteotsunami events have the potential to generate structural damage and sometimes even human casualties. Meteotsunami early warning systems, helping the local population to prepare for these destructive events, are thus important for the coastal communities living in such places. Vilibić et al. (2016) pointed out that meteotsunami early warning systems can be created based on four approaches: (1) identification of tsunamigenic atmospheric synoptic conditions, (2) real-time detection of tsunamigenic atmospheric disturbances using a microbarograph network, (3) measurement and tracking of high-frequency sea level oscillations by high-resolution digital tide gauges, and (4) numerical simulation of meteotsunamis based on coupling of atmosphere–ocean numerical models. As it stands today, the only fully operational meteotsunami early warning system in the world is located in the Balearic Islands. It is based on forecasts given at a qualitative level with the identification of favourable synoptic conditions a few days ahead (Jansà et al., 2007; Jansà and Ramis, 2020) and with the deterministic results of the operational BRIFS (Balearic Rissaga Forecasting System, http://www.socib.eu, last access: 16 August 2021) model (Renault et al., 2011). In the Balearic Islands, probabilistic approaches have also been tested recently to narrow down the uncertainties of the meteotsunami forecasts (Vich and Romero, 2020; Mourre et al., 2020). In the US, meteotsunami early warning systems are still under development by NOAA (National Oceanic and Atmospheric Administration) and will be based on high-resolution air pressure measurements combined with forecast models (Anderson et al., 2020). Finally, the recently developed Croatian meteotsunami early warning system (CMeEWS) is based on an observational network of pressure sensors and tide gauges, as well as on the deterministic AdriSC modelling suite (Denamiel et al., 2019a) and the stochastic meteotsunami surrogate model (Denamiel et al., 2019b, 2020). It provides meteotsunami hazard assessments depending on forecasted and measured air pressure disturbances but has unfortunately not been used operationally since November 2019 due to a lack of high-performance computing resources needed to execute such a numerically demanding suite in real time.

However, the CMeEWS applications to recent meteotsunami events may surely be used to better quantify its reliability and to improve its performance. Recently, an exceptional multi-meteotsunami event, which lasted for a week between 11 and 19 May 2020, occurred in the Croatian cities of Vela Luka (VL), Stari Grad (SG), and Vrboska (Vr), located along the coasts of the Dalmatian islands in the Adriatic Sea (Fig. 1). Therefore, the deterministic and stochastic AdriSC models have been run retroactively in operational (hindcast) mode (i.e. in the exact same conditions that the daily meteotsunami forecasts would have been produced operationally) for this 11–19 May 2020 period. As quoted by Denamiel et al. (2020), forecasting the right speed and frequency (period) of the travelling atmospheric disturbances is crucial for meteotsunami hazard assessments in the harbours of Vela Luka, Stari Grad, and Vrboska. Therefore, unlike previous studies on the performances of the CMeEWS operational models, this analysis introduces the novelty of using energy banners – based on the spectral analysis of the high-pass-filtered air pressure and sea level fields – as a tool to evaluate the capacity of the AdriSC deterministic model to reproduce the frequency of the meteotsunamigenic disturbances measured during the 11–19 May 2020 period. Hereafter, the CMeEWS (including the AdriSC modelling suite, the stochastic surrogate model, and the observational network) and the methods used in the study are first presented in Sect. 2. Then, Sect. 3 describes the 11–19 May 2020 multi-meteotsunami event using eyewitness reports, available observations, and reanalysis products. The verification of the AdriSC deterministic atmospheric model is undertaken in Sect. 4, while Sect. 5 presents the main results of the study – i.e. the meteotsunami energy banners used to detect the strongest atmospheric disturbances. Finally, the stochastic meteotsunami hazard assessments, based on parameters extracted from transects selected along the energy banners, are discussed in Sect. 6, and the findings of this study are summarized in Sect. 7.

The Croatian meteotsunami early warning system (CMeEWS) receives three different kinds of data: (1) high-resolution atmospheric and ocean model results provided by the Adriatic Sea and Coast (AdriSC) modelling suite (Denamiel et al., 2019a), (2) high-frequency air pressure and sea level measurements along the Adriatic coast, and (3) meteotsunami hazard assessments based on the stochastically estimated maximum elevation distributions derived from a meteotsunami surrogate model (Denamiel et al., 2019b, 2020). The following subsections describe the different components of the CMeEWS and the methods used in this article to improve the detection and extraction of the modelled meteotsunamigenic disturbances in the atmosphere.

This long-lasting meteotsunami event was reported by the media, in particular by eyewitnesses in Vrboska with two YouTube videos (https://www.youtube.com/watch?v=vz9G5E9ravc, last access: 16 August 2021; https://www.youtube.com/watch?v=-aD9q4QMANE, last access: 16 August 2021), and by local web portals in Vela Luka and Stari Grad. In particular, Dalmacija danas (https://www.dalmacijadanas.hr/, last access: 16 August 2021) wrote on 14 May: “Changes in air pressure have a pronounced effect on the sea level in the Adriatic, which is most noticeable on the Dalmatian islands in the last two days. There is a constant change in sea level throughout the day, and today it was most pronounced in the afternoon in Vela Luka. […] the sea level fluctuated in the range of about 70 cm. The sea rose and flooded the waterfront, then receded abruptly, leaving the boats dry. The phenomenon was also recorded on Hvar, for example in Stari Grad, but it was less pronounced.” On 16 May another local web portal, Morski.hr, published an article titled Meteotsunami in Vela Luka: The sea is pouring into shops and cafes. This has been going on for three days now! The following is the testimony of a local, Ljubo Padovan. “This is something we haven't had in years and it has been going on for full three days. The sea got into some shops and cafes again. When the sea recedes, one can walk from one side of the bay to the other. The sea flooded everything again last night. The situation is not calming down even after three days; that is very unusual.”

Concerning the observations (Fig. 2), on 11 May intense high-frequency sea level oscillations reached up to 80 cm of height (crest to trough) and a 16 min period at 09:40 UTC in Vela Luka as well as 53 cm of height and a 18 min period at 11:07 UTC in Stari Grad. Additionally, all microbarographs recorded an intensification of the air pressure oscillations, with a maximum high-frequency amplitude of 3.1 hPa and a period of 13 min documented for Vela Luka. Air pressure oscillations calmed down on 12 and 13 May but, following reported flooding, increased again on 14 May, especially in Ancona and Vieste. On this day, in Vela Luka, air pressure oscillations were about 2 times weaker than on 11 May, but the height of sea level oscillations almost reached 80 cm with a 15 min period. However, in Stari Grad, sea levels oscillated between -25 and 25 cm from 08:00 to 16:00 UTC. Even though the sea level oscillations in Stari Grad harbour were 2 times smaller than during 11 May, flooding still occurred, probably due to the additional effects of tidal elevation and/or storm surge. Lower-intensity oscillations of both air pressure and sea level followed on the next days until around midnight on 16 May, when another meteotsunami event took place. For this event, air pressure oscillations were unusually low, even in Ancona, which recorded the strongest ones. However, in Vela Luka the height of the sea level oscillations went up to 80 cm with a 13 min period. Despite the reports of flooding in Stari Grad, identically to 14 May, the sea levels only oscillated between -25 and 25 cm.

The pressure oscillations did not completely vanish in the following days, and on 19 May strong air pressure disturbances with heights above 2.5 hPa occurred in Svetac, Vieste, Vis, Vrboska, and Vela Luka. However, no flooding is recorded in Vela Luka or Stari Grad where the recorded sea level oscillations did not surpass 30 and 20 cm, respectively.

The synoptic conditions over Europe derived from ERA5 reanalysis (Hersbach et al., 2020) – temperature at 850 hPa, winds at 500 hPa, and mean sea level air pressure (Fig. 3) – are extracted at times close to the flooding of Vela Luka, Stari Grad, and Vrboska harbours: in the morning on 11 May, around midday on 14 May, and around midnight on 16 May. For all the flooding events, the conditions show the advection of warm air from the Sahara towards the Adriatic at 850 hPa, associated with strong southwesterly winds at 500 hPa with speeds over 30 ms-1. Additionally, the mean sea level air pressure over the Adriatic indicates either a trough stretching from northern Europe, as on 11 May, or a cyclone that was deeper on 14 May and quite weak on 16 May. These synoptic conditions are known to occur during Mediterranean meteotsunamis (Jansá et al., 2007; Vilibić et al., 2008; Šepić et al., 2016) when atmospheric disturbances (particularly atmospheric gravity waves) can be generated along the strong frontal gradients of the jet streams, as seen in Fig. 3, and propagate over long distances in the form of so-called ducted waves (Lindzen and Tung, 1976; Monserrat and Thorpe, 1996).

The capacity of the AdriSC WRF 1.5 km and ADCIRC models to reproduce the meteotsunami events during the 11–19 May 2020 period is first assessed qualitatively by comparing the observed (in red) and modelled (in blue) time series presented in Fig. 2. It shows that the events on 11 and 16 May are completely missed by both the WRF 1.5 km and ADCIRC models. However, the meteotsunami event of 14 May is partially captured by the AdriSC model. Air pressure oscillations are indeed simulated in Vieste, Vis, Stari Grad, Vela Luka, and Vrboska, along with weaker than measured sea level oscillations in Stari Grad and Vela Luka. AdriSC model results for 12 and 13 May are generally in accordance with the measurements, with no strong oscillations of pressure and sea level, but with slightly underestimated pressure and sea level oscillations in Ancona, Vieste, and Stari Grad and overestimated pressure oscillations in Ortona. The model results for 17 May are also generally in accordance with the measurements, with underestimated pressure and sea level oscillations in Ortona, Stari Grad, and Vela Luka and overestimated pressure oscillations in Svetac. Even though the deterministic AdriSC model fails to forecast two of the three observed meteotsunami events, the event mode of the CMeEWS is triggered for all the days of the 11–19 May 2020 period except for 12 and 13 May for which no false alarms would have been triggered (Fig. S1 in the Supplement).

Measured and modelled composites of air pressure frequency–time spectrograms in the eastern, middle, and western Adriatic Sea (Figs. 4–6) are thus used to quantitatively compare the energy content of the meteotsunamigenic disturbances as observed by the microbarographs and forecasted with the WRF 1.5 km model at grid points W1–W7, M1–M2, and E1–E6, in addition to grid points next to microbarograph stations as described in Sect. 2. Overall, no pronounced energy peaks are found in the spectrograms, which is typical for spectra of air pressure characterized by a number of oscillatory movements with no dominant period (Monserrat and Thorpe, 1992; Zemunik et al., 2020). Additionally, in operational mode, the CMeEWS would have provided warnings for a full day (next 30 h period including night hours past midnight) and not for a precise time. It may thus be noticed that, despite this analysis being temporal, discussions about the differences between modelled and measured timing of the meteotsunami events are not relevant for the model verification.

For 11 May, the highest energies from the observed composite are located at Ortona with frequencies below 1.5×10-3 Hz (11 min period) and around 1.8×10-3 Hz (9.25 min period) for the western Adriatic region, at Svetac with frequencies below 1.0×10-3 Hz (16.5 min period) for the middle Adriatic region, and at Vela Luka with frequencies below 1.1×10-3 Hz (15 min period) as well as with 1.4×10-3 Hz (12 min) and 1.9×10-3 Hz (8.8 min) frequencies for the eastern Adriatic region. For this event, the WRF 1.5 km model produces substantially lower energies at the same frequencies as the observed composite at E1, located far northwest from Vela Luka, but with high energies at frequencies up to 1.1×10-3 Hz (15 min period) in the western Adriatic, up to 0.8×10-3 Hz (20.8 min period) in the middle Adriatic, and at 1.0×10-3 Hz (16.5 min period). This implies that the modelled atmospheric disturbances are less energetic and located further north compared to the observed ones.

During the calm period between 12 and 13 May, the energy of the observed spectrograms is much lower than during the meteotsunami events. The model produces extremely low energies for both days in all regions, with high energies at frequencies up to 2.0×10-3 Hz only in Ortona, in the western Adriatic region, on the evening of 13 May.

However, on 14 May, the highest energy values from the observed composite are found at Vieste with frequencies below 0.7×10-3 Hz (24 min period) for the western Adriatic region, at Vis with frequencies below 0.55×10-3 Hz (30 min period) for the middle Adriatic region, and at Stari Grad with frequencies below 0.5×10-3 Hz (33 min period) for the eastern Adriatic region. The highest energies simulated by the model are located at W3 with frequencies up to 1.8×10-3 Hz (9.25 min period) for the western Adriatic region, at Vis with frequencies up to 1.1×10-3 Hz (15 min period) for the middle Adriatic region, and at E6 located south from Stari Grad with frequencies up to 1.5×10-3 Hz (11 min period) for the eastern Adriatic region. It is unlikely that the modelled atmospheric disturbance can travel from W3 to E6 by diagonally crossing the middle Adriatic region. The results are thus probably coming from more than one atmospheric disturbance that occurred during 14 May and changed energies when crossing the Adriatic.

For 15 and 16 May, the energies of the observed composite are higher than during the calm background period (between 12 and 13 May) but lower than during the meteotsunami events. For 15 May, the model produces high energies at frequencies up to 2.0×10-3 Hz (8 min period) at W1 in the western Adriatic region. However, this disturbance does not propagate to the east as the spectrograms in the middle and eastern Adriatic regions have extremely low energy. Energy in the model for 16 May is negligible in the western Adriatic region, but for the middle and eastern Adriatic regions high energies at frequencies below 1.5×10-3 Hz are found at M1 and E2, respectively. In other words, even though the meteotsunami event of 16 May is missed by the AdriSC model (Fig. 2), the WRF 1.5 km model simulates a strong meteotsunamigenic disturbance shifted northwestward compared to the observations.

On 17 May the highest energies from the observed composite are located at Ortona for the western Adriatic region, at Vis for the middle Adriatic region, and at Stari Grad for the eastern Adriatic region. High energies are also found in the modelled composite at up to 2.2×10-3 Hz (7.5 min period) at W4 for the western Adriatic region, up to 1.8×10-3 Hz (9 min) at Svetac for the middle Adriatic region, and up to 1.0×10-3 Hz (16.5 min period) at E5 for the eastern Adriatic region. The spatial layout of the highest-energy points again illustrates the limitations of the applied methodology when multiple disturbances are simulated. Nevertheless, obtained results imply that the different disturbances in the model are more energetic than the ones observed by the microbarographs.

More energy is found in the observed spectrograms for 18 May than during the calm background period but less than during the meteotsunami events. The model, however, produces high energies at high frequencies of about 2.0×10-3 Hz (8 min period) at W6 for the western Adriatic region and 1.75×10-3 Hz (9.5 min period) at E4 for the eastern Adriatic region. The atmospheric disturbance energy at M2 is higher for the middle Adriatic region than for the western and eastern Adriatic regions, particularly for lower frequencies.

Conditions were again more energetic on 19 May, with the highest energies in the observed composite at frequencies up to 1.5×10-3 Hz (11 min period) at Vieste and Vela Luka and up to 1.25×10-3 Hz (13 min period) at Svetac. The model fails to reproduce these disturbances and only simulates high energies at W7, at the southernmost point of the studied area.

Briefly, periods between 10 and 20 min – typical of meteotsunamigenic disturbances – are found to often occur in the analysis of the frequency–time spectrogram composites (Figs. 4 to 6). Additionally, systematic biases exist in the forecasted atmospheric disturbances, as they are often simulated further northwest than the observed ones. Finally, this analysis has demonstrated that the Adriatic high-frequency sea level oscillations of 11–19 May 2020 were induced by atmospheric forcing of diverse spatial and temporal characteristics.

Given the lack of reliability of the deterministic AdriSC model to properly forecast spatial and temporal characteristics of the multi-meteotsunami event during the 11–19 May 2020 period, the warnings released by the CMeEWS would have fully relied on the results of the stochastic surrogate model forced with input parameters extracted from the WRF 1.5 km simulations. The values of the six stochastic parameters – which serve as input for the stochastic surrogate model – are derived from the modelled meteotsunamigenic disturbances. The meteotsunami energy banners, including their impact on the ocean, are thus documented along the selected transects where these parameters are extracted. As described in Sect. 2, the operational sampling criterion (hereafter referred as air pressure variance), the new transect sampling criterion, the atmospheric and ocean spectrograms, and the Proudman resonance along the most energetic transects are displayed in Figs. 7–11 and in the Supplement (Figs. S2–S15) for each day of the multi-meteotsunami event.

For 11 May, the modelled air pressure variances (Figs. 7, S2, and S3, top left panel) and the associated new transect sampling criterion (Figs. 7, S2, and S3, top right panel) indicate maximum meteotsunami energy banners located too far northwest from Vela Luka, Vrboska, and Stari Grad harbours, where the meteotsunami event is observed. Nevertheless, the atmosphere over the two selected transects is highly energetic and the pronounced disturbances travel with a speed between 12.5 and 33.32 ms-1 over relatively shallow areas. Despite the Proudman resonance being possible over a large section of the transects, the energy transferred to the ocean is not substantial anywhere but near the coast.

For 14 May, several modelled atmospheric disturbances are located in the middle Adriatic region (Figs. 8 and S4–S6 in the Supplement, top left panel). The location of the highest air pressure variances and the associated new transect sampling criterion (top panels, Fig. 8), as well as the speed of the tracked most energetic disturbance of 27.9 ms-1, make this disturbance a good candidate for causing the meteotsunamis that flooded Vela Luka, Vrboska, and Stari Grad harbours on this day. Nevertheless, the transect is in deep water with changing bathymetry, and therefore the Proudman resonance is only likely to happen over a small part of the transect, while other effects, including edge waves, strong topographical enhancement, and refractions on the islands in the pathway of atmospheric disturbances, may be important for the generation of meteotsunami waves in the middle Adriatic (Šepić et al., 2016). Higher energies in the atmosphere, but not in the ocean, can be found on spectrograms of transects in Figs. S4 and S6. These disturbances are located too south or too north of the domain to cause meteotsunamis in the harbours of interest. Also, the speeds of the tracked disturbances in Figs. S4 and S5 are not within the range of speeds of meteotsunamigenic disturbances.

Two atmospheric disturbances are tracked for 15 May and presented in Figs. 9 and S7 in the Supplement. The maximum air pressure variance (Fig. 9, top left panel) and the associated maximum in the new transect sampling criterion (Fig. 9, top right panel) are located too northwest to have caused the Vela Luka and Stari Grad flooding on the night of 15 to 16 May. Also, despite the high energies in the atmosphere, no transfer to the sea can be seen along the transect, being restricted just near the coast. This is probably due to the low speed of the disturbance (i.e. 10.5 ms-1) and the depth (i.e. over 100 m) along the transect. Spectrograms in Fig. S7 display high energies and a strong ocean response at the beginning of the transect but negligibly small energy values on the rest of the transect, which is a good example of a dissipating disturbance. The low speed of the atmospheric disturbance of only 11.6 ms-1 and the lack of flat seabed could explain such behaviour.

Three disturbances are analysed for 16 May and presented in Figs. 10, S8, and S9. Two northwestwardly shifted atmospheric disturbances (Figs. 10 and S8) are extremely energetic, and the transfer of energy to the sea is strong at the beginning of the transects. Speeds of the disturbances, of 7.1 and 11.3 ms-1, are low compared to the normal speeds for meteotsunamigenic disturbances. The southern disturbance (Fig. S9) has a greater speed of 25 ms-1, but the atmosphere is not highly energetic and the transfer of energy to the sea is not strong anywhere but near the coast. This is displayed in the top panels and in spectrograms of Fig. S9. It should be noticed that the air–sea interaction is the strongest over the area where Proudman resonance is likely to happen.

For 17 May, two of three modelled atmospheric disturbances (Figs. S10 and S11) are located where they could have caused meteotsunamis along the eastern Adriatic coastline. However, the speeds of these disturbances, ranging from 10.3 to 12.1 ms-1, are too low and the atmosphere and the sea are not as energetic as they are over the transect analysed in Fig. 11. The atmosphere is extremely energetic over the selected transect and, since energy is well transferred to the ocean, high energies occurred for high frequencies in the ocean too. Spectrograms in Fig. 11 show that ocean's response to atmospheric disturbance is pronounced over the whole transect, but it is the strongest over the section which satisfied the Proudman resonance conditions. The disturbance travelled at 27.8 ms-1, but as seen in the top panels, it is again located in the northern part of the middle Adriatic.

For 18 May, the modelled atmospheric disturbances (Figs. S12–S14) cross the middle Adriatic from southwest to northeast, over the common path of meteotsunamigenic disturbances. Speeds of the tracked disturbances vary from 20.2 to 30.3 ms-1. Even though the atmosphere is energetic for the transects presented in Figs. S12 and S14, the energy of the sea is not significantly higher than for the transect in Fig. S13, with low energy in the atmosphere. Therefore, despite the appropriate speeds and locations of the meteotsunamigenic disturbances, the energy is not well transferred from the atmosphere to the sea and no meteotsunami event is modelled.

For 19 May there is only one modelled disturbance, travelling at 19.4 ms-1 far south of the analysed region (Fig. S15). The energy content of both the atmosphere and the sea is low for the selected transect, but some air–sea interactions take place at the eastern end of the transect (top right panel, Fig. S15).

Averaged air pressure variance and the averaged new transect sampling criterion derived from all the extracted transects between 11 and 19 May 2020 are presented in Fig. 12, together with the selected transects. The transects are classified into four different categories emphasizing the strength of the atmospheric disturbances as well as the energy transfer from the atmosphere to the ocean. The most intense atmospheric activity and air–sea interactions are located across the middle Adriatic region. Additionally, despite relatively low averaged air pressure variances, the averaged values of the new transect sampling criterion are the highest along the Dalmatian islands and the middle Adriatic Italian coastline. These results thus confirm that the intensity of the atmospheric disturbances is less important than the resonance – i.e. appropriate speed, period, and depth along the transects (Denamiel et al., 2020) – and, of course, the bathymetry.

Briefly, the presented results of the travelling air–sea meteotsunami energy banners show that the ocean model response to the atmospheric forcing highly depends on both the location and the frequency of the meteotsunamigenic disturbances, which are in our study often modelled too northwest of the most affected locations. Finally, the introduced new transect sampling criterion does not seem to overall facilitate the decision-making process in terms of the transect selection, since all the transects selected by this criterion would have also been selected following the highest values of air pressure variances only. Even though for some events (e.g. Figs. 9–11) the new criterion highlights the strength of the air–sea interactions, these interactions are located along the same transects as captured by the highest values of the air pressure variance. As efficiency is important in an early warning system, it can thus be concluded that the use of the ocean model results to better select the transect with maximum meteotsunami generation is not necessary in operational mode, since it would be more time-consuming with no significant value added to the process of the transect selection.

The analysis presented in previous sections has proven that the operational deterministic AdriSC model is not capable of properly reproducing the meteotsunami events of the 11–19 May 2020 period. However, parameters like location, amplitude, direction, speed, period, and width can be extracted from the atmospheric disturbances produced by the WRF 1.5 km model and used as inputs for the stochastic surrogate model. For the 11–19 May 2020 period (with the exception of 12 and 13 May), the stochastic surrogate model is thus run for Vela Luka, Stari Grad, and Vrboska with input variables from the atmospheric disturbances selected for each day along the transects presented in the previous section. The probabilities of the maximum elevation surpassing the flooding threshold are presented in Table 2.

For the 11–19 May 2020 period when flooding and strong sea oscillations were reported for Vela Luka, Stari Grad, and Vrboska (in italics, Table 2), the meteotsunami warning would have been triggered in Vela Luka and Vrboska for all the events, but only for 11 May in Stari Grad. The results found in Stari Grad are, however, in good agreement with the moderate oscillations (amplitude of 25–30 cm) of the high-pass-filtered sea levels extracted between 14 and 16 May at the tide gauge location. Additionally, the meteotsunami warning would have been wrongly triggered on 17 and 19 May in Vela Luka and 15, 16, 17, and 19 May in Vrboska when no flooding was reported. It is worth noticing that, for 17 and 19 May 2020, the forecasted meteotsunamigenic conditions capable of triggering the event mode of the CMeEWS are, in fact, in good agreement with the strong air pressure oscillations observed along the western Adriatic coast (Fig. 2). Additionally, as already shown in Denamiel et al. (2019b), false alarms are easily triggered in Vrboska. This may be linked to either the poor representation of the Vrboska geomorphology within the ADCIRC model used to create the surrogate model or the choice of the flooding threshold and should therefore be further investigated.

In the Adriatic Sea, recurrent meteotsunami events are known to strongly impact the way of life of the coastal communities, particularly in the Dalmatian islands where they can generate serious flooding. In this study, the capacity of the Croatian meteotsunami early warning system (CMeEWS), which provides meteotsunami hazard assessments depending on the deterministically forecasted and measured air pressure disturbances and the stochastically deduced maximum elevation distributions derived with the surrogate model, is examined. As it is no longer operational, the capacity of the CMeEWS is evaluated retroactively for the multi-event of 11–19 May 2020. This event is of particular interest because meteotsunamigenic synoptic patterns over the Adriatic were present during a prolonged period of about 5 to 10 d, which was not previously observed for any meteotsunami. During this period, intense high-frequency air pressure and sea level oscillations were observed and recorded in the middle Adriatic, with maximum sea levels reached on 11, 14, and 16 May in Vela Luka, Stari Grad, and Vrboska.

One of the main originalities of this study is that the performances of the CMeEWS operational models – i.e. the WRF 1.5 km atmospheric model and the ADCIRC ocean model from the AdriSC modelling suite – are assessed via energy banners. Analysis of composites of frequency–time spectrograms has shown that the deterministic models are generally not capable of reproducing the meteotsunami events in affected bays but can produce strong meteotsunamigenic disturbances often shifted northwestward from them. It was demonstrated that, even though the strongest atmospheric activity was modelled in the middle Adriatic along common air pressure disturbance pathways, the meteotsunami events were always missed by the ADCIRC ocean model at Vela Luka and Stari Grad during the 11–19 May 2020 period due to a shift in location of the modelled atmospheric disturbances. This most probably indicates that the frequency of the air pressure disturbances is not properly reproduced by the WRF 1.5 km model, posing the question of the appropriateness of state-of-the-art atmospheric models in terms of their resolution and set-up (Horvath and Vilibić, 2014). Finally, this study also highlighted the fact that using the ocean model results in combination with the atmospheric model results with the so-called new transect sampling criterion does not help to improve the selection of atmospheric conditions needed to feed the stochastic meteotsunami surrogate model. However, due to the systematic error link to the shift of the disturbances towards the north, it may be envisioned in the future to apply a correction concerning the starting point location before using the surrogate model.

Given these results, the following question can be raised: should the ADCIRC ocean model be run in operational mode within the CMeEWS, or should the meteotsunami hazard assessments be derived solely with the stochastic surrogate model? In the presented case, as the deterministic ocean model fails for all events due to a shift in the location of the modelled atmospheric disturbances, the question is easily answered. And, in general, due to the uncertainties associated with operational modelling of meteotsunamigenic disturbances, the stochastic approach has proven to be an optimal option. Nevertheless, the ADCIRC ocean model can still be used for other hazards, such as extreme storm surges associated with wind waves, and not only for meteotsunami events.

Concerning the evaluation of the stochastic model fed by the extracted meteotsunamigenic air pressure conditions along the selected transects, in most of the cases and despite some false alarms, the coastal communities of Vela Luka, Stari Grad, and Vrboska would have been warned of potential meteotsunami events if the CMeEWS had been operational. Even though warning effectiveness highly depends on resident trust, which can be easily eroded due to false alarms and/or missed events, the uncertainty faced by the Croatian coastal communities during the 11–19 May 2020 period and reported by several local newspapers is probably far worse. The meteotsunami surrogate model, even if not perfect due to not including the storm surges in Stari Grad, for example, has thus proven to be extremely useful and reliable for this multi-meteotsunami event.

The complexity of forecasting the precise location, intensity, and speed of the atmospheric disturbances triggering the most extreme sea level events around the world is one of the biggest issues faced by the meteotsunami community. In consequence, different approaches have been recently implemented within the two existing meteotsunami early warning systems in the Mediterranean Sea (Denamiel et al., 2019, Mourre et al., 2020, Romero et al., 2020). To conclude, as operational models often fail to properly forecast extreme events, the continuous development of stochastic approaches – such as the meteotsunami surrogate model within the CMeEWS – described in Denamiel et al. (2021) should be an avenue explored by the extreme sea level community in order to improve early warning systems.