Stochastic Surrogate Model for Meteotsunami Early Warning System in the Eastern Adriatic Sea
Abstract
The meteotsunami early warning system prototype using stochastic surrogate approach and running operationally in the eastern Adriatic Sea is presented. First, the atmospheric internal gravity waves (IGWs) driving the meteotsunamis are either forecasted with state-of-the-art deterministic models at least a day in advance or detected through measurements at least 2 hr before the meteotsunami reaches sensitive locations. The extreme sea-level hazard forecast at endangered locations is then derived with an innovative stochastic surrogate model—implemented with generalized polynomial chaos expansion (gPCE) method and synthetic IGWs forcing a barotropic ocean model—used with the input parameters extracted from deterministic model results and/or measurements. The evaluation of the system, both against five historical events and for all the detected potential meteotsunamis since late 2018 when the early warning system prototype became operational, reveals that the meteotsunami hazard is conservatively assessed but often overestimated at some locations. Despite some needed improvements and developments, this study demonstrates that gPCE-based methods can be used for atmospherically driven extreme sea-level hazard assessment and in geosciences in wide.
Key Points
- Design and evaluation of an innovative meteotsunami early warning system prototype using stochastic surrogate approach
- Forecast of the atmospheric internal gravity waves driving meteotsunami events with deterministic state-of-the-art models
- Stochastic surrogate model based on generalized polynomial chaos expansion methods and running at nearly no computational cost
Plain Language Summary
Atmospherically driven extreme sea-level events are one of the major threats to people and assets in the coastal regions. Assessing the hazard associated with such events together with uncertainty quantification in a precise and timely manner is thus of primary importance in modern societies. In this study, an early warning system for the eastern Adriatic meteotsunamis, destructive long waves with periods from few minutes up to an hour generated by traveling atmospheric disturbances, is presented and evaluated. The system is based on state-of-the-art deterministic atmospheric and ocean models as well as an innovative statistical model developed to forecast the meteotsunami hazard. The evaluation reveals that the meteotsunami hazard is conservatively assessed but often overestimated. This study demonstrates that the presented methodology can be used for extreme sea-level hazard assessment and in general for hazard studies in geosciences.
1 Introduction
During the past decade, meteorological tsunamis or meteotsunamis—destructive long waves in the tsunami frequency band generated by traveling atmospheric disturbances (Monserrat et al., 2006)—have become the object of an increasing number of studies all over the globe (Cho et al., 2013; Dusek et al., 2019; Masina et al., 2017; Okal et al., 2014; Olabarrieta et al., 2017; Pattiaratchi & Wijeratne, 2014; Pellikka et al., 2014; Šepić et al., 2012; Tanaka, 2010; Whitmore & White, 2014). These extreme events have the potential to produce substantial damages to houses, goods, and infrastructures (Hibiya & Kajiura, 1982; Linares et al., 2019; Salaree et al., 2018)—for example, not only more than seven million U.S. dollars have been lost in Vela Luka harbor, Croatia during the 21 June 1978 meteotsunami (Orlić et al., 2010; Vučetić et al., 2009), but human lives were also claimed. Seven people were also killed during a sunny day in 1954 (Ewing et al., 1954) in the Great Lakes near Chicago, USA. Rather than addressing a particular catastrophic event, this work focuses on the design and evaluation of an innovative meteotsunami early warning system tested in operational mode, since late 2018, in the eastern Adriatic. As fully preventing meteotsunami impact is, for now, close to impossible (Vilibić et al., 2016), the principal goal of such a system is to allow the local communities to better prepare for these destructive events (e.g., set temporary protection against flooding and waves, avoid swimming, etc.) in order to minimize the losses. However, deterministically forecasting the atmospheric disturbances responsible for meteotsunamis is challenging (Denamiel et al., 2019; Renault et al., 2011), and the uncertainties in anticipating their location and intensity as well as their relationship to flood in sensitive harbor locations must be taken into account. In addition, as meteotsunamis are rare events, which require specific model setup, for example, for the ocean, a 1-min atmospheric forcing and a resolution below 50 m in the harbors where resonance occurs, the available forecast results are generally not designed to capture them (Denamiel et al., 2019). For the Adriatic Sea, a specific numerical suite was thus implemented to deterministically forecast the atmospheric disturbances—for example, the internal gravity waves (IGWs; Vilibić & Šepić, 2009; Denamiel et al., 2019), driving the meteotsunamis along the Croatian coastline.
In order to quantify the uncertainties linked to the meteotsunami extreme sea levels, the origin, propagation, and sources of uncertainty of the complex ocean-atmosphere system must be described (Arnst & Ponthot, 2014; Bulthuis et al., 2019; Ghanem et al., 2017). In the Adriatic Sea, the location, speed, period, amplitude, and direction of the forecasted atmospheric disturbances are the primary sources of uncertainties linked to the meteotsunami events and can thus be seen as random variables characterized by their prior distributions. In the field of uncertainty quantification (Ghanem et al., 2017; Le Maître & Knio, 2010), generalized polynomial chaos expansion (gPCE) methods (Soize & Ghanem, 2004; Xiu & Karniadakis, 2002) have been widely used to build surrogate models that propagate, at nearly no computational cost, the uncertainties of a given stochastic forcing to the results of a deterministic model. Furthermore, in the past decade, gPCE methods have been applied with success in geosciences: Formaggia et al. (2013) built a surrogate model of basin-scale geochemical compaction, Wang et al. (2016) studied the acoustic uncertainty predictions, Sraj et al. (2014) estimated the wind drag parameter forcing an ocean model, Giraldi et al. (2017) documented the propagation of earthquake ocean floor displacement uncertainty to the tsunami wave parameters, and Bulthuis et al. (2019) used a surrogate model to quantify the uncertainty of the multicentennial response of the Antarctic ice sheet to climate change. Following the footsteps of these recent studies, the newly developed meteotsunami surrogate model was thus designed to propagate the known uncertainties of the atmospheric disturbances to the forecast of extreme sea levels at five sensitive locations along the Croatian coastline: Vela Luka, Vrboska, Stari Grad, Rijeka dubrovačka, and Ston (Figure 1).
In this paper, the setup of the Croatian early warning system prototype, which provides meteotsunami hazard assessments depending on the deterministically forecasted and measured atmospheric pressure waves and the stochastically deduced maximum elevation distributions derived with the surrogate model, is first described in details in section 2. In section 3, its evaluation for five different locations along the Croatian coastline is performed first, against five different historical events, and then for automatically detected events since the system became operational in late 2018. Finally, the methodological choices made to design this first meteotsunami early warning system as well as its performance and the improvements needed to increase its reliability are discussed in section 4.
2 Design of the Meteotsunami Early Warning System
2.1 Data and Models
The Croatian Meteotsunami Early Warning System (CMeEWS, Šepić et al., 2017), developed within the framework of the project MESSI (“Meteotsunamis, destructive long ocean waves in the tsunami frequency band: from observations and simulations towards a warning system,” http://www.izor.hr/messi), receives three different kind of data: (1) synoptic conditions from the Croatian Meteorological and Hydrological Service (DHMZ) operational atmospheric products, (2) high-resolution atmospheric and ocean model results provided by the Adriatic Sea and Coast (AdriSC) modelling suite (Denamiel et al., 2019), and (3) measurements from the MESSI observational network along the Adriatic coast. The synoptic data are used for a long-term qualitative forecast (at least a week) of meteotsunamigenic conditions through assessment of the synoptic meteotsunami index (Šepić et al., 2016). However, such an approach cannot be used in quantitative meteotsunami hazard assessment and forecast and is not further discussed in this paper.
The AdriSC modelling suite is composed of a basic module providing high-resolution regional atmospheric and ocean results for the entire Adriatic Sea and a dedicated meteotsunami module. The basic module uses a modified version of the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modelling system developed by Warner et al. (2010), which couples (online) (1) the Regional Ocean Modeling System (ROMS; Shchepetkin & McWilliams, 2005, 2009), with nested grids of 3 km (covering the entire Adriatic and Ionian Seas) and 1 km (covering the Adriatic Sea only), and (2) the Weather Research and Forecasting (WRF) model (Skamarock et al., 2005), with nested grids of 15 km (covering the central Mediterranean basin) and 3 km (identical to the 3-km ROMS grid). The dedicated meteotsunami module couples (offline) the WRF model, which downscales the hourly 3-km WRF results of the basic module to a 1.5-km resolution for a grid covering the entire Adriatic Sea, with the 2DDI ADvanced CIRCulation (ADCIRC) model (Luettich et al., 1991) using a mesh of up to 10-m resolution in the areas sensitive to meteotsunami hazard. In this deterministic configuration, the ADCIRC model is forced (1) every minute by the WRF 1.5-km wind and pressure fields and (2) every hour by the ROMS 1-km sea-level fields (including tides). Every day at midnight, the next 48 hr hourly forecast results from the COAWST run, as well as the 15-min forecast results from WRF 1.5 km and ADCIRC simulations for the next day, are published at http://www.izor.hr/adrisc
The MESSI observational system currently encompasses a network of sensors setup with a 1-min sampling rate and installed in areas where either the generation or the amplification of meteotsunamis are known to occur: eight air pressure sensors located in (1) Ancona, Ortona, and Vieste on the Italian coast, up to 200 km from any endangered location along the Croatian coastline, (2) Vis and Svetac in the middle of the Adriatic Sea, and (3) Vela Luka, Stari Grad, and Vrboska, which are known sensitive harbors (Figure 1) as well as two tide gauges located in the harbors of Vela Luka and Stari Grad (Figure 1).
Within the CMeEWS, the extreme sea-level hazard assessment relies on the newly developed meteotsunami stochastic surrogate model. This model is based on generalized gPCE methods (Soize & Ghanem, 2004; Xiu & Karniadakis, 2002), which, compared to sampling approaches (e.g., Monte Carlo simulations), are highly efficient for propagating the uncertainties of model inputs to outputs (e.g., Knio & Le Maître, 2006 and Najm et al., 2009 provide detailed discussions in the context of computational fluids applications). In this study, the stochastic surrogate model propagates the uncertainties from the meteorological input (i.e., the IGWs responsible for the meteotsunami generation) to the maximum sea levels at different locations along the Croatian coastline. The surrogate model is based on polynomials expansions that decompose into deterministic coefficients and random orthogonal bases. The coefficients, which are the projection of the maximum meteotsunami elevation distribution onto each polynomial basis, are derived from a quadrature based approximation using numerical simulations undertaken with the ADCIRC model (identical to the one used in the AdriSC modelling suite) forced only by synthetic pressure disturbances (no wind, no tide). As described in Denamiel et al. (2018), the synthetic atmospheric pressure forcing is split into (1) a mean atmospheric pressure component (P0) assumed constant over the entire Adriatic Sea and (2) a stochastic gravity wave component (PGW) depending on six stochastic parameters—start location (y0), direction (θ), speed (c), period (T), amplitude (PA), and width (d) of the disturbance. These six parameters are assumed to have uniform distributions and are defined on the following intervals: y0 ∈ [41.25o, 43.65o],
, c ∈ [15m s−1, 40m s−1], T ∈ [300s, 1800s], PA ∈ [50Pa, 400Pa], and d ∈ [30km, 150km]. Examples of synthetic gravity wave spatial and temporal properties can be visualized as supporting information (Figure S1). Practically, as the input parameters are assumed to be uniformly distributed, (1) the delayed Gauss Patterson sparse grid method (Burkardt, 2014; Novak et al., 1999; Smolyak, 1963) is applied to automatically select all the combined values of the six stochastic parameters of the synthetic pressure forcing and thus to define the number of simulations (in this study, 4,161 as the gPCE is defined for polynomial degrees up to 6) used to derive the polynomial coefficients, while (2) the random orthogonal bases are built with Legendre polynomials. The meteotsunami hazard forecast is illustrated in Figure 2 and is based on the meteotsunami stochastic surrogate model receiving atmospheric pressure field input from both (1) the WRF 1.5 km next day forecast results (brown box, Figure 2) and (2) the real-time transmitted observations from Ancona, Ortona, Vieste, Svetac, and Vis stations (green box, Figure 2).
2.2 Operational Mode
Every day, as soon as the WRF 1.5 km 1-min forecast results are available, which are at least 30 hr before any potential meteotsunami event (M) can occur, the high-pass filtered (with a 2-hr cutoff period) mean sea-level pressure (i.e., PGW for meteotsunami events) is automatically extracted (AdriSC Forecast step, Figure 2). Then, the maximum temporal rate of change (over a 4-min interval T4) of this filtered pressure, that is,
, is derived at each WRF 1.5-km grid sea point. Such a condition has been proven to be efficient for the detection of meteotsunamigenic disturbances (Vilibić et al., 2016). No later than 28 hr before any meteotsunami event, the spatial coverage (in percentage) of the WRF 1.5-km grid sea points with a maximum temporal rate above 20 Pa per 4-min interval (RM ≥ 20) is calculated (Automatic Detection step, Figure 2). If this coverage exceeds 5%, a potential meteotsunami has been detected (event mode of the warning) and an automatic email, including a figure of the distribution ofRM ≥ 20, is sent to the AdriSC team (red box, Figure 2). The threshold of 5% is prescribed, being based on the analysis of recent meteotsunami events in which reproduction by the AdriSC modelling suite has been included (Denamiel et al., 2019). Otherwise (silent mode of the warning), at this stage, it is assumed that no meteotsunami will occur in the next forecasted day (blue box, Figure 2).
In case of automatic meteotsunami detection, no later than “27 hr before any meteotsunami event,” the filtered pressure field is visualized and analyzed by the AdriSC team. If the detected pressure disturbance is recognized as an atmospheric pressure gravity wave, the ranges of variation of the forecasted wave parameters including a ±10%of the parameter interval of definition, latitude of origin (y0,F ± 0.24 ° N), direction of propagation (θF ± 0.26rad), amplitude (PA,F ± 35Pa), period (TF ± 150s), and width (dF ± 12000m), are manually estimated from the WRF 1.5 km 1-min filtered air pressure results (Manual Extraction step, Figure 1). To the best of the authors' knowledge, the technology to automatically detect and extract the parameters of the atmospheric disturbances driving the Adriatic Sea meteotsunamis is yet to be developed, and thus, for the moment, human intervention is unfortunately required in the early warning system. As the errors associated with manually deriving the speed of the gravity waves (cF) are quite large, this parameter is always taken on its full range of definition [15m s−1, 40m s−1]. At least 24 hr before the forecasted meteotsunami event, the meteotsunami stochastic surrogate model, based on gPCE, is used to deduce the meteotsunami maximum elevation distributions at different locations of interest (Hazard Forecast step, Figure 2) via the user-friendly interface developed in MATLAB (Figure 3). These distributions are derived from 20,000 random combinations of the six uniformly distributed input variables selected in the range of the extracted parameters. In order to produce a conservative estimate of the final maximum elevation expected at the locations of interest, (1) the surrogate model results below 0.1 m are ignored as irrelevant for meteotsunami hazard, and (2) the maximum tidal elevation of the forecasted 24-hr period is added to the results of the stochastic surrogate model.
The maximum elevation distribution depending on the interval of definition of the atmospheric wave parameters is generated and a first warning provides, at each location of interest, (1) the probability of the expected maximum elevation derived from the surrogate model and (2) the deterministic maximum elevation from the ADCIRC model run, which is also taken into account during the decision process for timely managing the hazard. Finally, it is planned that once the early warning system will be fully operational (24/7 watch or fully automated procedure), in the 2-hr period before the forecasted meteotsunami event (i.e., the estimated time for the atmospheric disturbances to cross the Adriatic Sea from the Italian cost), the 1-min air pressure measurements from Ancona, Ortona, Vieste, Svetac, and Vis will be analyzed by the AdriSC team, and if any pressure gravity wave is detected, amplitude and period will be extracted from the observations (PA,M, TM). These parameters will then be used as constant values in the stochastic surrogate model and new maximum elevation distributions will be produced with 20,000 random combinations of the three remaining uniformly distributed input variables selected in the range of the parameters extracted from the model results (y0,F, θF, dF). The final meteotsunami warning using the updated distribution of the maximum elevation (including maximum tidal elevation) will then be ready to be published and accessible to users.
3 Evaluation of the Meteotsunami Early Warning System
3.1 Evaluation Against Historical Events
The first evaluation of the CMeEWS is performed against well-recorded events that took place, before the early warning system became operational, at five locations of interest: Vela Luka, Rijeka dubrovačka, Stari Grad, Vrboska, and Ston (Figure 1). In 2014, two strong events happened at the end of June (Šepić et al., 2016), with reported maximum elevations of 1.5 m in Vela Luka, 0.5 m in Stari Grad, 0.75 m in Vrboska, and 1.75 m in Rijeka dubrovačka on June 25, and of 0.5 m in Ston on June 26. In summer 2017, tsunami-like waves were also generated and observed in Stari Grad on June 28 (maximum elevation of 0.75 m; Denamiel et al., 2019) as well as on June30 during the night (http://www.izor.hr/meteotsunami; maximum elevation of 0.32 m measured at 18:30 UTC) and in Vrboska on July 1 (maximum elevation of about 0.75 m). Finally, on 31 March 2018, a meteotsunami wave with maximum reported sea elevation of 0.5 m flooded Stari Grad (Denamiel et al., 2019). For five of these events, the deterministic results of the AdriSC meteotsunami forecast component have already been evaluated against a set of 48 air pressure sensors and 19 tide gauges (Denamiel et al., 2019). This evaluation highlighted that the WRF 1.5-km model used in the AdriSC modelling suite presents some skills in forecasting the IGWs responsible for the observed meteotsunamis (i.e., the IGWs were always forecasted by the model but their intensity or direction of propagation may not have been reproduced perfectly). However, it also revealed that the slightest shift in location of the modelled atmospheric disturbances resulted in the incapability of the ADCIRC model to reproduce the observed meteotsunamis in the deterministic mode of the forecast. The stochastic approach was thus developed to counter these shortcomings.
In this study, the stochastic surrogate model of the CMeEWS is also tested against these five events in order to assess its capability to provide relevant warning to the public. In addition, as the pressure sensors only became operational at the end of 2017, the atmospheric wave parameters used in the stochastic surrogate model are only extracted from the WRF 1.5 km 1-min high-pass filtered atmospheric pressure results. Finally, the meteotsunami impact highly depends on the location of interest because (1) observations have shown that extreme meteotsunami elevations present significant spatial variations in the eastern Adriatic Sea (Šepić et al., 2016), and (2) flooding, the main hazard caused by meteotsunamis, depends on the geomorphology/harbor design (Denamiel et al., 2018). In addition, due to the design of the surrogate model (i.e., uniform prior distribution of the parameters), a majority of the stochastic combinations lead to small oscillations (maximum elevations below 0.2 m as seen in Figure 3) while only about 10% lead to meteotsunami conditions. In this study, it is thus assumed that flooding occurs when at least 10% of the stochastic surrogate model maximum elevations reach more than 1.05 m in Vela Luka, 0.65 m in Rijeka dubrovačka, 0.55 m in Vrboska, 0.45 m in Stari Grad, and 0.35 m in Ston. These threshold values are prescribed considering the resilience of the coastline in these locations (e.g., the salt plant located in Ston is the least resilient to strong sea-level changes and meteotsunami waves), which in turn is largely defined by the real meteotsunami hazard (e.g., the community of Vela Luka is the most resilient to meteotsunami hazard, as they were hit by the strongest meteotsunami events along the Croatian coastline, Orlić, 2015).
In addition, as the thresholds dependent on the meteotsunami impact at the five studied locations, their values will most probably be re-evaluated in the near future when more well-documented meteotsunami events in the eastern Adriatic will become available.
- 25 June 2014: for Vela Luka, Rijeka dubrovačka, Vrboska, and Stari Grad, which all have been reported to be flooded (Šepić et al., 2016). This is in accordance with the forecasted deterministic ADCIRC maximum elevation results (1.45 m in Vela Luka, 0.80 m in Rijeka dubrovačka, 0.65 m in Stari Grad and 0.55 m in Vrboska),
- 26 June 2014: for Vela Luka, Vrboska, and Ston but following eyewitness reports, only Ston experienced flooding, which was accurately forecasted with the deterministic ADCIRC maximum elevation of 0.55 m;
- 28 June 2017: for Vela Luka, Stari Grad, and Vrboska but following eyewitness reports, only Stari Grad experienced flooding. The deterministic results obtained with the ADCIRC model forecasted an elevation of only 0.35 m in Stari Grad, which would not have been enough to cause flooding;
- 1 July 2017: for Vrboska, which was the only place flooded during this event. The deterministic ADCIRC model forecasted a 1-m maximum elevation in Vela Luka but did not capture proper meteotsunami amplification in Vrboska;
- 31 March 2018: for all the five locations but following eyewitness reports, only Stari Grad experienced flooding. The deterministic ADCIRC model did not reproduce at all this event (only 0.25 m forecasted in Stari Grad).
| 25/06/14 | 26/06/14 | 28/06/17 | 01/07/17 | 31/03/18 | |||
|---|---|---|---|---|---|---|---|
| Range of the input parameters |
Latitude (°N) |
Minimum | 42.34 | 41.25 | 42.24 | 41.25 | 42.03 |
| Maximum | 43.20 | 41.70 | 43.13 | 42.81 | 42.79 | ||
|
Amplitude (Pa) |
Minimum | 60 | 255 | 85 | 100 | 85 | |
| Maximum | 320 | 340 | 185 | 275 | 215 | ||
|
Direction (rad) |
Minimum | -0.17 | 0.08 | -0.17 | 0.35 | 0.26 | |
| Maximum | 0.35 | 0.60 | 0.70 | 1.04 | 0.78 | ||
|
Period (s) |
Minimum | 300 | 330 | 1290 | 300 | 330 | |
| Maximum | 1230 | 630 | 1800 | 1410 | 1350 | ||
|
Width (km) |
Minimum | 30 | 30 | 88 | 30 | 30 | |
| Maximum | 54 | 54 | 112 | 92 | 54 | ||
| Probability (%) | Vela Luka | P(ξmax ≥ 1.05m) | 12 | 10 | 20 | 7 | 19 |
| R. dubro. | P(ξmax ≥ 0.65m) | 17 | 1 | 5 | 3 | 12 | |
| Stari Grad | P(ξmax ≥ 0.45m) | 25 | 0 | 15 | 2 | 25 | |
| Vrboska | P(ξmax ≥ 0.55m) | 10 | 16 | 50 | 10 | 23 | |
| Ston | P(ξmax ≥ 0.35m) | 7 | 27 | 7 | 2 | 11 | |
- Note. Range of atmospheric gravity wave parameters (start location, amplitude, direction, period, and width) extracted from the Weather Research and Forecasting 1.5-km forecast model results and probability (in percent) of the maximum meteotsunami elevation surpassing the flooding threshold defined at five different locations (Vela Luka, Rijeka dubrovačka, R. dubro., Stari Grad, Vrboska, and Ston). When the probabilities are above or equal to 10% (highlighted in bold), the meteotsunami warning is triggered. In addition, probabilities at locations at which flooding has been reported by eye-witnesses during the events are highlighted in italics.
In summary, for the five studied historical events, the surrogate model of meteotsunami maximum elevation is capable of forecasting the meteotsunami hazard in the areas that were flooded, which was not always the case of the deterministic ADCIRC model (Denamiel et al., 2019). Unfortunately, for many events, it also predicts flooding in areas where no meteotsunami impact was reported.
3.2 Evaluation in Operational Mode
Since September 2018, the CMeEWS is tested in operational mode, but meteotsunami warnings are not yet released to the public. After nearly a year of run, meteotsunami hazard forecasts were performed with the surrogate model forced by both deterministic model results and measurements, for several events presenting the required meteotsunamigenic conditions (Table 2).
| 29/10/18 | 09/07/19 | 10/07/19 | 02/08/19 | |||||
|---|---|---|---|---|---|---|---|---|
| R1 | R2 | R1 | R2 | R1 | R1 | |||
| Range of the input parameters | Latitude (°N) | Minimum | 41.25 | 43.40 | 43.17 | 42.54 | ||
| Maximum | 41.49 | 43.65 | 43.65 | 43.02 | ||||
| Amplitude (Pa) | Minimum | 86 | 80 | 175 | 135 | 172 | 53 | |
| Maximum | 173 | 245 | 400 | 123 | ||||
| Direction (rad) | Minimum | 1.31 | -0.26 | -0.26 | -0.26 | |||
| Maximum | 1.57 | 0.26 | 0.26 | 0.26 | ||||
| Period (s) | Minimum | 390 | 600 | 1530 | 1800 | 750 | 450 | |
| Maximum | 870 | 1800 | 1230 | 750 | ||||
| Width (km) | Minimum | 30 | 38 | 48 | 38 | |||
| Maximum | 54 | 62 | 72 | 62 | ||||
| Probability (%) | Vela Luka | P(ξmax ≥ 1.05m) | 10 | 6 | 0 | 0 | 0 | 1 |
| R. dubro. | P(ξmax ≥ 0.65m) | 7 | 1 | 1 | 1 | 1 | 26 | |
| Stari Grad | P(ξmax ≥ 0.45m) | 29 | 14 | 19 | 29 | 2 | 21 | |
| Vrboska | P(ξmax ≥ 0.55m) | 29 | 25 | 8 | 20 | 1 | 0 | |
| Ston | P(ξmax ≥ 0.35m) | 11 | 5 | 0 | 0 | 0 | 10 | |
- Note. R1 stands for a meteotsunami hazard forecast forced with input parameters extracted from the Weather Research and Forecasting 1.5-km numerical model, while R2 hazard forecast uses air pressure amplitude and period extracted from the measurements and imposed as constant values, if a pressure disturbance is captured by the microbarographs, providing the final meteotsunami hazard. When the probabilities are above or equal to 10% (highlighted in bold), the meteotsunami warning is triggered. In addition, probabilities at locations at which flooding has been reported by eye-witnesses during the events are highlighted in italics.
The first event occurred on 29 October 2018 in the evening during the Vaia storm, but was not publicly reported as a meteotsunami. The switch of the warning system to event mode was triggered by (1) a 32% spatial coverage for RM ≥ 20 and (2) the analysis of the WRF 1.5-km filtered Mean Sea Level (MSL) pressure, which revealed the presence of several high-frequency atmospheric disturbances travelling northwards from Vieste to the Croatian coastline (as can be seen in Figure S10). However, only relatively small sea-level oscillations were deterministically forecasted with the ADCIRC model in the studied harbors along the track of the pressure disturbance (Vela Luka, Stari Grad, and Vrboska). The first hazard forecast, based on the numerical results (Figure S9), triggered the meteotsunami warning for all the locations except Rijeka dubrovačka (R1, Table 2 and Figure S11). The analysis of the filtered pressure measured at Vieste and Svetac (Figure 6), which were the stations closest to the forecasted track of the pressure disturbances, showed that several IGWs of about 80 Pa of amplitude and 10 min of period were recorded between 18:00 and 22:00 UTC.
After the hazard forecast was updated based on these measured values, the warning only remained for Stari Grad and Vrboska (R2, Table 2 and Figure S12). After the event, filtered sea level measured at Vela Luka and Stari Grad (Figure 6) revealed that high-frequency oscillations with the respective periods of about 12 and 25 min occurred at both locations and generated the respective maximum elevations of 0.48 m at 20:30 UTC and 0.26 m at approximately 18:45 UTC. If the maximum tidal elevation (about 0.16 m for both locations during this event) is added, then the total elevation reached 0.64 m in Vela Luka, which is not enough to generate flooding, and 0.42 m in Stari Grad, which is slightly below the 0.45-m threshold that is used for the meteotsunami hazard warning. Unfortunately, no sea-level measurements were available in Vrboska, and similarly to Stari Grad, even if a small meteotsunami had occurred, it is unlikely that its effect could be visually distinguished from the impact of the Vaia storm.
The next events all took place during summer storms in July and August 2019, when unfortunately, the Ancona microbarograph stopped transmitting data. Between the 9 and 10 July 2019, the Adriatic region experienced severe storms, which brought heavy rains, hurricane force downbursts, tornadoes, and the largest hailstorm ever recorded to date along the Italian coast. For both days, the event mode of the early warning system was triggered as (1) the spatial coverage for RM ≥ 20 reached 22% and 44%, mostly due to the passage of the storm, and (2) the analysis of the WRF 1.5-km filtered MSL pressure showed the presence of high-frequency atmospheric disturbances with amplitudes greater than 150 Pa, travelling eastwards from Ancona to the Croatian coastline (as can be seen in Figures S13 and S14).
However, for these 2 days, similarly to the Vaia storm, the deterministic ADCIRC model only forecasted relatively small oscillations in the harbors of Vela Luka, Stari Grad, and Vrboska located along the track of the pressure disturbances. For 9 July 2019, the first hazard forecast, based on numerical model results, triggered the meteotsunami warning in Stari Grad (R1, Table 2 and Figure S15). In addition, the analysis of the filtered pressure measured at Ortona, Vieste, Svetac, and Vis stations (Figure 7) clearly showed an atmospheric disturbance of about 135 Pa and 30-min period travelling eastward from Svetac to Vis between 17:30 and 18:30 UTC. As both Ortona and Vieste are located south from the forecasted track of the pressure disturbances, the pressure waves recorded at these stations were assumed to be incapable to affect Stari Grad harbor where the warning was issued. Based on the final hazard assessment (R2, Table 2 and Figure S16) updated with the values extracted from the Svetac and Vis stations, the Stari Grad warning was confirmed and an additional warning was triggered for Vrboska. During the evening of the 9 July 2019, a meteotsunami occurred in the harbor of Stari Grad, where the promenade was flooded (https://www.dalmacijadanas.hr/meteoroloski-tsunami-na-hvaru-more-se-povuklo-za-vise-od-metra). The analysis of the filtered sea levels in Stari Grad (Figure 7) confirmed the presence of a 1.05-m height and 25-min period meteotsunami wave just before 19:00 UTC. During the event, the measured maximum elevation reached 0.47 m, which is, even without adding the maximum tidal elevation, beyond the threshold value of 0.45 m defined for meteotsunami warning. Sea-level oscillations were also recorded in Vela Luka (Figure 7), but the maximum elevation never surpassed 0.25 m. Finally, no meteotsunami was reported in Vrboska, and thus, the warning was most probably too conservative for this location. For 10 July 2019, the forecasted meteotsunami conditions were similar to the ones obtained from the previous day, except concerning the periods of the disturbances, which were all below 18 min instead of the measured 30 min. As meteotsunami are extremely sensitive to the period of the atmospheric disturbances, no warning was triggered by the hazard forecast based on these numerical results (R2, Table 2 and Figure S17). In addition, the monitoring of the air pressure measurements did not show any disturbance with period greater than 18 min, and no meteotsunami was reported in the studied locations.
Two more storms took place in the Adriatic Sea during 13 and 28 July 2019 (not presented in this study) and both triggered the event mode of the warning system, but conditions for these storms were extremely similar to the 10 July 2019 event and the hazard forecast based on both numerical results and measurements did not trigger any meteotsunami warning.
Finally, the last event occurred on 2 August 2019 just before a storm that swept the eastern Adriatic coast, where falling trees blocking roads, damaged power distribution lines, and flooding were reported in the media. The event mode was triggered by (1) a 19% spatial coverage for RM ≥ 20 and (2) the analysis of the WRF 1.5-km filtered MSL pressure, which revealed that a high-frequency atmospheric disturbance was travelling eastwards around 10:00 UTC in the middle of the Adriatic (about 42.77°N of latitude), from the Italian to the Croatian coasts (as can be seen in Figure S18). The forecasted meteotsunami hazard based on these numerical results was quite high, and warnings were triggered for Rijeka dubrovačka, Stari Grad, and Ston (R1, Table 2 and Figure S19). Similarly to the other events, the deterministic results of the ADCIRC model only forecasted some oscillations of small amplitude in the harbors of interest. Due to technical problems, the Ortona and Vela Luka stations were not transmitting data during this event; thus, the analysis of the filtered pressure was based on measurements at Svetac and Vis (Figure 8). Interestingly, some disturbances were indeed travelling eastwards during August 2 between 10:00 and 12:00 UTC. However, their amplitude was below 50 Pa and they were not capable of generating strong oscillations and/or flooding along the Croatian coast. The warnings were thus canceled, and in fact, no meteotsunami was reported for this event. Finally, the biggest atmospheric disturbance—which generated some moderate oscillations (about 0.15 m of amplitude) in the harbor of Stari Grad, as can be seen in the filtered sea-level data (Figure 8)—was recorded between 20:00 and 22:00 UTC during the peak of the storm.
For this event, the assessment of the meteotsunami hazard was first largely overestimated due to the deterministic forecast of pressure disturbances capable of generating strong sea-level oscillations in the eastern Adriatic, but as the measured pressure disturbances were far smaller than expected, no meteotsunami occurred.
The evaluation of the CMeEWS in operational mode highlights that the microbarograph network plays a crucial role in terms of delivering the final warnings and confirms that the surrogate model forecasts the meteotsunami hazard in a conservative way even during storms events which, in the eastern Adriatic, are not the classical generation mechanism of the meteotsunamigenic pressure disturbances.
4 Discussion and Conclusions
Notwithstanding major research efforts, the scarcity of the measurements and the reliability of the numerical models in meteotsunami studies are still major restrictions for hazard assessment and forecast, and even more for risk management (e.g., for the determination of a 100-year meteotsunami event). Based on lessons from river flooding hazard warning systems designed and evaluated in hydrological studies (e.g., Beven, 2006; Sivakumar, 2008), two major conclusions can be drawn: (1) The promotion of uncertainty analysis of measurements and modelled results is of crucial importance for hazard assessment and forecast, and (2) the effectiveness of the warning systems is not determined only by the predictive accuracy of the models, but also by the lead time and the available social response set.
The presented prototype of meteotsunami early warning system combining deterministic and stochastic hazard assessment was designed to address such concerns. In particular, the very first use of a gPCE-based surrogate model to derive atmospherically driven extreme sea-level hazard was motivated by the successful application of such methods for uncertainty quantification in a wide range of areas including mechanics, engineering, water resources, and geosciences (e.g., Foo et al., 2007; Giraldi et al., 2017; Rupert & Miller, 2007). The main advantages of this kind of approach are (1) the propagation of the uncertainties associated with the atmospheric disturbances (e.g., location, direction, and speed) to the maximum elevation results, (2) the potentiality of using both deterministic forecast results and measurements to provide the surrogate model input parameters, and (3) the few minutes of computation needed to assess, with a large number of samples and no additional deterministic simulation, the hazard of any studied event (e.g., meteotsunami). However, the main disadvantages are that the surrogate model (1) only relies on ocean numerical results forced by synthetic atmospheric disturbances (e.g., idealized pressure waves) and (2) requires a large number of synthetic simulations to be built with good enough accuracy (e.g., in this study, 4,161 simulations were used to build the model with approximately 80% accuracy). Additionally, in operational mode, the early warning system currently presents three major weaknesses. First, due to the high resolution of the deterministic models and thus the relative slowness of the system, the early forecast of the meteotsunami hazard (at least 24 hr prior to any event) is only derived once from numerical results obtained 2 days in advance. This means that the first warnings are always based on conditions forecasted from a 72-hr old assimilation cycle, which can lack accuracy, particularly during extreme events. Second, human intervention is still required in the present setup of the early warning system in order to extract the IGW parameters from the deterministic forecast. And third, to be able to provide the final meteotsunami warnings derived from hazards forecasted with input parameters extracted from the measured mean sea-level air pressures along the Italian coast and the middle Adriatic, the microbarograph data should be analyzed in a timely manner with efficient operational tools which, in the CMeEWS, are still under development.
On one hand, the evaluation of the early warning system with five well-recorded events demonstrates that (1) the IGWs driving the eastern Adriatic meteotsunamis are always forecasted and well detected, and (2) the meteotsunami hazard derived only from the deterministic model results is conservative but tends to be largely overestimated in certain locations such as Vela Luka or Vrboska. On the other hand, the evaluation in operational mode highlights the importance of (1) taking into account the uncertainties associated with the forecasted meteotsunamigenic atmospheric disturbances particularly during storm events when the deterministic model lacks of accuracy, (2) updating the final warnings using meteotsunami hazards based on input parameters extracted from the measured pressure disturbances, and (3) extending and maintaining the measurement network (microbarographs and tide gauges) along the Italian and Croatian coastlines in order to produce more accurate hazard assessments and to better understand how and where the system failed. Following these conclusions, to improve the accuracy of the warnings, for all potential future events, (1) the system should be thoroughly re-evaluated, (2) the measurements recorded by the microbarographs should be used in a timely manner to derive the final hazard assessment, (3) the flooding criteria and the input parameter ranges of the surrogate model should be finely tuned as more data will become available, and (4) ultimately, once the prototype will be fully tested, the meteotsunami warnings will not only be triggered when more than 10% of the maximum elevations surpass the thresholds defined at the sensitive locations, but their strength (yellow, orange, and red) will also be defined depending on the detailed statistical information (maximum, 75th percentile, mean, median, etc.) extracted from the extreme sea-level distributions.
Finally, the CMeEWS combining 1-min air pressure measurements—accurate but scarcely spread along the Italian coast and the middle Adriatic Sea, state-of-the-art deterministic models dedicated to meteotsunami forecast but computationally costly and slow and a newly developed stochastic surrogate model—running at nearly zero cost but yet to be fully tested, highlights the need to use real time high-temporal resolution observational networks for regional early warning systems in the Mediterranean and presents an alternative way to deal with atmospherically driven extreme sea-level hazard assessment.
Acknowledgments
Acknowledgement is made for the support of the ECMWF staff, in particular Xavier Abellan, as well as for ECMWF's computing and archive facilities used in this research, which has been supported by projects MESSI (UKF Grant 25/15), ADIOS (Croatian Science Foundation Grant IP-2016-06-1955), and ECMWF Special Project (The Adriatic decadal and inter-annual oscillations: modelling component). The authors would also like to thank the two anonymous reviewers for their valuable contributions. The MATLAB interface developed for the stochastic surrogate model, including the gPCE coefficients needed to create the meteotsunami maximum elevation distributions at the five studied locations, as well as the WRF 1.5-km filtered results of sea surface pressure can be obtained under the Open Science Framework (OSF) FAIR data repository at https://osf.io/jysqu/ (doi:10.17605/OSF.IO/JYSQU).
