A Tsunami Warning System Based on Offshore Bottom Pressure Gauges and Data Assimilation for Crete Island in the Eastern Mediterranean Basin

The Eastern Mediterranean Basin (EMB) is under the threat of tsunami events triggered by various causes including earthquakes and landslides. We propose a deployment of Offshore Bottom Pressure Gauges (OBPGs) around Crete Island, which would enable tsunami early warning by data assimilation for disaster mitigation. Our OBPG network consists of 12 gauges distributed around Crete Island, with a 100‐km interval, based on three criteria to select the locations. The station network must have a good azimuthal coverage and have enough (>50 km) distance from the coast, and the OBPGs are placed at the locations where the most energetic wave dynamics occur, which is confirmed by Empirical Orthogonal Function (EOF) analysis of pre‐calculated tsunami scenarios. We demonstrate three test cases comprising a hypothetical seismogenic tsunami in east Sicily, a hypothetical landslide tsunami in the Aegean Sea, and the real tsunami event of the May 2020 off the Crete earthquake. Our designed OBPG network achieves an accuracy of 88.5% for the hypothetical seismogenic tsunami and 87.3% for the hypothetical landslide tsunami with regard to the forecasting of first tsunami peak. For the real event of May 2020, it predicts the tsunami arrival at tide gauge NOA‐04 accurately; the observed and forecasted amplitudes of the first wave are 5.0 cm and 4.5 cm, respectively. The warning lead time for the May 2020 event was ~10 min. Therefore, our results reveal that the assimilation of OBPG data can satisfactorily forecast the amplitudes and arrival times for tsunamis in the EMB.


Introduction
Tsunamis in the Eastern Mediterranean Basin (EMB) have raised significant concern over the past years, in particular following the July 2017 Bodrum-Kos (Turkey-Greece) and the May 2020 off the Crete earthquakes and tsunamis (Figures 1 and 2) Papadopoulos et al., 2020;Yalciner et al., 2017). In the catalogue of tsunamis in the Mediterranean Sea, Soloviev (1990) identified numerous tsunami events in the Aegean Sea, Sea of Crete, and other locations in the EMB. The southern Greece, including Crete Island, the Cyclades, and the Dodecanese Islands, is among the most active regions in terms of seismicity. The main cause of tsunami generation in this region is tectonic activity associated with strong earthquakes . For example, earthquakes often occur in the south-central Aegean Sea. The 1956 Amorgos earthquake (Mw 7.7-7.8) (Figure 1) was the largest one to strike Greece in the 20th century. The 1956 earthquake generated a strong tsunami that affected the northern shores of Crete Island. In Heraklion, the largest city in Crete, the 1956 tsunami arrived with a 2-m runup height and inundated 30 m inland. In Souda, a port city in the northwest of Crete Island, the measured tsunami runup height was 1.5 m (Okal et al., 2009). To the south of Crete Island, there is an active tsunamigenic zone of the Hellenic subduction zone (Figure 1) which has produced many large, shallow, and intermediate-depth earthquakes in the past (Papadopoulos, Daskalaki, Fokaefs, & Giraleas, 2007). For instance, the AD 365 earthquake (Mw 8.4) in the southwestern Crete Island was felt throughout the eastern Mediterranean Sea. Its tsunami inundated coastal sites in Africa, the Adriatic Sea, Greece, and Sicily and drowned thousands of people (Shaw et al., 2008). Moreover, the tsunamigenic zone in the east Aegean Sea also has a very high tsunami potential.
The two recent events in the EMB region are the July 2017 Bodrum-Kos earthquake (Mw 6.6; Dogan et al., 2019;Yalciner et al., 2017) and the May 2020 off the Crete earthquake (Mw 6.6; The United States Geological Survey [USGS], 2020). The 2017 event occurred near the Turkey-Greece border and generated a moderate tsunami that caused damage in Bodrum Peninsula and in Kos Yalciner et al., 2017). The  tsunami was recorded by several tide gauges in the region ( Figure 1) and caused some moderate damage with no casualties. The tsunami was also recorded by a tide gauge in the Kasos Island, approximately 30 km to the east of Crete (i.e., station NOA-03) (Figure 1). The May 2020 tsunami occurred south of Crete Island, following an Mw 6.6 earthquake. There were no reports of injuries or casualties in the aftermath of this event. The earthquake generated a tsunami that hit the southern coast of Crete Island at around 15-20 min after the earthquake and was recorded at tide gauge NOA-04 with amplitudes of 15-20 cm (Figure 1).
In addition to earthquakes, tsunamis in the EMB are also generated by landslides and volcanic eruptions (Samaras et al., 2015;Yalciner et al., 2014).  studied 32 reliable cases of landslide tsunamis in the Mediterranean Sea. On 30 September 1650, a large tsunami occurred during the eruption of the submarine volcanic edifice Kolumbo in the Aegean Sea. It was generated by the submarine collapse of the volcanic cone (Dominey-Howes et al., 2000). The tsunami violently swept ships and fishing boats at Crete Island, and the wave overtopped the city's sea walls . Yalciner et al. (2014) studied generation and propagation of landslide tsunamis in the EMB.
For disaster mitigation purposes, it is important to design an observational system aimed at tsunami early warning. Tsunami data assimilation, a recent technology for tsunami warning, relies on Offshore Bottom Pressure Gauges (OBPGs) which monitor the sea surface elevation and report the data in real time (Heidarzadeh & Gusman, 2018;Maeda et al., 2015;Satake, 2014). In the Nankai Trough offshore west Japan, a dense array of OBPGs known as DONET (the Dense Oceanfloor Network system for Earthquakes and Tsunamis) (Kaneda, 2010;Wang et al., 2018) has been deployed and is available for tsunami warning system. However, in the EMB such observational system is presently unavailable. In this study, we propose a potential tsunami early warning system for Crete Island based on the deployment of OBPGs. The system forecasts the tsunami by data assimilation approach. We demonstrate that our designed OBPG network is useful for forecasting both seismogenic and landslide tsunamis, by conducting experiments with two hypothetical tsunamis and the real tsunami of 2 May 2020.

Criteria for Optimal Location of the OBPGs
The tsunami early warning system based on OBPGs should be able to detect the tsunami signals efficiently and forecast the tsunami waveforms in a timely manner. In this study, three criteria are followed to design the optimal location of the OBPGs: i. The network should have a large azimuthal coverage. ii. The OBPGs should be located at appropriate distance from the coast. iii. The OBPGs should be placed at the locations where the energetic dynamics occur.
We note that there might be some OBPGs that cannot meet the three criteria simultaneously, but we make sure that most OBPGs can satisfy these requirements. The tsunami early warning network needs to cover a large azimuthal coverage of the island, so that it can detect the tsunami signals from all directions. In this study, the design of OBPG locations is under the constraint that they surround the island with approximately 100 km interval. Moreover, in order to allow enough lead time for issuing warnings before the tsunami arrives at the coast, we also consider that the OBPGs are distanced at least 50 km from the coast.
In addition to these two criteria, the OBPGs should be placed at the locations where the energetic dynamics occur. To confirm the requirement of the third criterion, we apply Empirical Orthogonal Function (EOF) analysis. EOF is commonly used to decompose the data into spatial and temporal modes in earth science (Liu et al., 2018;Lorentz, 1956). The EOF spatial modes provide information about the areas where the modal activity is the highest, which correspond to the main energy distribution of a system (Cohen et al., 2003).
Assuming that there are n locations (grid points), and each location has a time series of length p, we create an n × p matrix Z that stores these data. The ith column of such a matrix contains the time series at the ith location (grid), while the jth row represents a snapshot of the whole region at the jth time step (Mulia et al., 2017;Navarrete et al., 2020). After removing the mean of each time series, the covariance matrix is formed by R = Z T Z. Then we solve the eigenvalue problem as formulated below: where C is the matrix of eigenvectors c i and Λ is a diagonal matrix containing the eigenvalues λ i . Each eigenvector presents a spatial mode, and the first EOF spatial mode is associated with the largest eigenvalue.
In our study, we select the region around Crete Island, within the geographical domain of 33-36°N, 22-28°E. We select the grids with a water depth of more than 300 m that cover the region of designed OBPGs. To perform the EOF analysis, we consider three tsunami scenarios which are called Mode Generating Scenarios (MGSs). The sources of the MGSs are adopted from the past real tsunami events in the EMB region, from west to east: the 2013 Platanos earthquake, the 1956 Amorgos earthquake, and the 2017 Bodrum-Kos earthquake (Figures 1 and 2). We adopt the same parameters of fault locations and focal mechanisms (Table 1) but amplify the slip values of each scenario (Table 1; last column) when computing the MGSs, in order to make the tsunami amplitude more evident in the EOF analysis area. The simulation of tsunami propagation and generation of three MGSs is described in section 2.2. After performing the EOF analysis, we check whether our designed OBPGs are placed at locations with large absolute EOF values.

Simulation of Seismogenic Tsunamis
We adopt the analytical dislocation model of Okada (1985) to compute the seafloor deformation for seismogenic tsunamis. The sea surface displacement is assumed to be the same as the seafloor deformation and is used as the initial condition for tsunami simulation according to the common practice in tsunami science (e. g., Satake, 2015). Then, we apply a linear long-wave model to simulate tsunami propagation, using the simulation package JAGURS (Baba et al., 2015;Satake, 1995;Satake & Heidarzadeh, 2017). Tsunami computation is performed on the supercomputer of Earthquake Information Center, The University of Tokyo. For computing the tsunamis arising from our three MGSs, the simulation time is 60 min since the earthquake origin time, and the spatial variation of water surface is stored every 10 s, resulting in 360 snapshots.
The bathymetry and topography dataset are derived from the General Bathymetric Chart of the Ocean released in 2014 (GEBCO_2014; Weatherall et al., 2015). We use a grid size of 30 arc sec (equivalent tõ 925 m), and a time step of 1 s to satisfy the stability condition of Finite Difference Method. The simulated tsunami waveforms at the locations of the proposed OBPGs are used for data assimilation retrospectively. The waveforms recorded at tide gauges are employed for waveform comparison in order to examine the performance of our method. Four real and one artificial tide gauges around Crete Island are selected ( Figure 2) which are as follows: NOA-04, NOA-10, Soudhas, Paleochora, and Falasarna. The stations of NOA-04 and NOA-10 are operated by the National Observatory of Athens (NOA). The station Soudhas belongs to the Permanent Service for Mean Sea Level (PSMSL). The station Paleochora serves as an Inexpensive Device for Sea Level Measurement (IDSL), which is developed by the Joint Research Centre (JRC) of the European Commission. The station Falasarna is a virtual tide gauge, intended to evaluate the tsunami hazards of the west Crete Island in our study.

Simulation of Landslide Tsunamis
To assess the tsunami hazards in the EMB thoroughly, we also consider tsunamis triggered by landslides. We use a two-layer hydrodynamic model to simulate the generation and propagation of landslide tsunamis (Maeno & Imamura, 2011;Ren et al., 2020).
Here we assume that a submarine landslide occurs in the Cyclades region. We focus on a smaller region of 36.5-37.5°N, 25.0-26.0°E, and resample the GEBCO_2014 grid to a finer resolution of 6 arc sec. The time step is 0.1 s for modeling the generation phase of landslide tsunami. In our two-layer model, the slides are simulated as the bottom layer whose motion is fully coupled to that of the surrounding water. The submarine

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landslide layer is of arbitrary geometry and is represented as a dense Newtonian fluid. Additional information about landslide modeling process and associated hydrodynamic equations are given in Kawamata et al. (2005) and Ren et al. (2020). We simulate the landslide and the triggered tsunami for the first 5 min (i.e., the generation phase). Then, we continue the computation of the tsunami propagation in a larger region of 34.0-38.0°N, 24.0-28.0°E, with a resolution grid of 6 arc sec, and a time step of 0.25 s, using the two-layer/ JAGURS models. In the two layer-model, the surface elevation and the horizontal velocities at the end of landslide generation phase are used as the initial condition, while only the surface elevation was used in JAGURS model for tsunami propagation Satake, 2012). Comparison of these two models is shown in Supporting Information S1, which shows that they are similar. This might indicate the horizontal velocity at the end of landslide generation phase is negligible for tsunami propagation modeling. In our experiment of the hypothetical landslide tsunamis, we adopted the results of the two-layer model.

Tsunami Data Assimilation
Tsunami data assimilation is a tsunami early warning approach which does not require information about initial condition but is directly applied to sea surface elevation data during tsunami propagation for forecast (Gusman et al., 2016;Maeda et al., 2015). It successively assimilates the real-time offshore sea surface observation and estimates the regional tsunami status.  applied this approach to the 2015 Torishima volcanic tsunami earthquake retrospectively and successfully forecasted the tsunami height and arrival time based only on offshore sea surface observations. Recently, this approach is also taken into consideration when designing the offshore observational devices. For example, Heidarzadeh et al. (2019) proposed a potential deployment of OBPGs in the western Mediterranean Sea. Navarrete et al. (2020) designed a network of tsunameters off the Chilean coast based on tsunami data assimilation.
The tsunami status at nth time step is represented as: where h is the sea surface height, M and N are horizontal flow fluxes in the x and y directions, respectively, and Δt is the time step for numerical simulations. Assuming that the total grid number is L and the number of OBPGs is m, the tsunami status vector x n will be a 3L × 1 column vector. M and N are defined as M = u(d + h) and M = v(d + h) where u and v are horizontal velocities in the x and y directions, respectively, and d is water depth. The tsunami status is forecasted by multiplying the tsunami status of last time step with a propagation matrix F (3L × 3L), which is built from the tsunami propagation model (Equation 2). Here the superscripts f and a refer to forecasted (before correction) and assimilated (after correction) tsunami status, respectively.
where matrix H (m × 3L) is a sparse matrix that extracts the forecasted tsunami height of the corresponding stations, matrix W (3L × m) is a weight matrix for smoothing which is used to bring the forecasted tsunami status closer to the real wavefield, and y n is real tsunami observation data that is obtained from the OBPGs. More details about the weight matrix W are described in Maeda et al. (2015). In Equation 3, the forecasted tsunami status (i.e., x f n ) is corrected by observation. The offshore OBPGs provide the data of tsunami height (h); then, tsunami flow velocities (u and v) are reconstructed during the assimilation process. After correction, we obtain the assimilated tsunami status x a n , and it will be used for further forecasting in the next time step. During the assimilation process, Equations 2 and 3 are iterated repeatedly at each time step. Therefore, we are able to forecast the tsunami status based on the observation of OBPGs. In order to improve the efficiency of data assimilation, we adopt the technique of Green's Function-based Tsunami Data Assimilation (GFTDA; Furumura et al., 2018;Wang et al., 2017). We calculate the Green's functions between the proposed OBPGs and the tide gauges (Figures 3a-3c), and we use them to synthesize the forecasted tsunami waveforms during the assimilation process.

OBPG Locations and EOF Results
A total number of 12 OBPGs are selected for the observational network. They are located around Crete Island with an approximately 100 km interval and cover all directions (Figures 3 and 4). They are also 10.1029/2020JB020293 Journal of Geophysical Research: Solid Earth located at least 50 km from the coast to allow enough lead time for tsunami early warning. The first EOF spatial modes for three MGSs are plotted in Figure 4. For each EOF mode, there is a value of variance which represents its contribution to the total energy (Lorentz, 1956). For the three MGSs, that is, the 2013-like event, the 1956-like event, and the 2017-like event, the variances of the first EOF mode are 36.8%, 51.1%, and 41.2%, respectively. Since the variance of the first EOF mode is considerably larger than that of subsequent EOF modes (e.g., the second and third modes), using only the first EOF mode is sufficient to quantify the total energy of the tsunami dynamics in deep water . It can be seen that most OBPGs are located at the areas with a large absolute EOF value for at least one MGS (Figures 4a-4c). For stations E06 and E07, they appear in the areas with large absolute values in both MGS1 and MGS2. The station E05 is located in the energetic regions of both MGS1 and MGS3. We note that the EOF energy is not maximum at the locations of E08, E09, and E10. However, EOF analysis is not the only criterion for designing the locations of OBPGs as discussed in section 2.1. The criteria of azimuthal coverage and distance to coast are other two criteria.
We note that the OBPG network is designed for providing warning to Crete Island as a pilot location. Therefore, in case the target of the warning system is another coastal location or a combination of locations, the same criteria can be applied to design an optimal OBPG network for those cases.

Early Warning for Hypothetical Seismogenic Tsunamis
Our first test of data assimilation is for a relatively far-field tsunami originating from the east Sicily, at the distance of approximately 900 km from Crete Island. The hypothetical earthquake (Mw 7.9) in east Sicily has a fault with a dimension of 95.0 km × 45.0 km, and its epicenter is located at 37.266°N, 15.686°E. The depth is

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35.0 km. The strike, dip, and rake angles of the hypothetical earthquake are 20°, 42°, and 121°, respectively, with a slip of 7.0 m. Figure 5a shows the initial sea surface deformation produced by this earthquake. It generates a tsunami that propagates towards the EMB (Figures 5b-5d). The rationale for this scenario is based on the study by Soloviev (1990) who informed that east Sicily is a major tsunamigenic zone in the EMB. Crete Island is along the direction of the short axis of the seismic fault (i.e., fault width), and thus, the tsunami energy is more concentrated towards this island. The tsunami waveforms obtained through forward tsunami simulation are called "synthetic waveforms" here which are shown in Figure 5e. The first tsunami peak arrives at the stations E02 and E01 at 59 min and 64 min after the earthquake, respectively (Figure 5e). The arrival times are 67 min and 69 min at the tide gauges Falasarna and Paleochora, respectively. The maximum tsunami amplitude of 19.3 cm is recorded at the tide gauge Falasarna. It has a comparatively smaller effect (<10.0 cm) on the tide gauge NOA-10, because it is located on the eastern side of the island ( Figure 6).
The tsunami waveforms are forecasted using data assimilation approach and are updated continuously during the data assimilation process. The tsunami waveforms obtained by data assimilation are called "forecasted waveforms" here ( Figure 6; red waveforms), which are compared with synthetic waveforms (Figure 6; black waveforms). The dashed line in Figure 6 indicates the end of data assimilation process. Therefore, the time interval between the end of the assimilation (i.e., dashed line in Figure 6) and the arrival of the tsunami at each tide gauge is the lead time for issuing tsunami warnings. At tide gauges NOA-4, NOA-10, and Soudhas, the lead time for tsunami warning is approximately 20 min. At Paleochora and Falasarna, the warning lead time is relatively shorter (i.e., approximately 10 min) due to the relatively short distance between the tide gauge and the OBPGs. Figure 6 indicates that our data assimilation approach forecasts the tsunami arrival times and first-peak amplitudes at all tide gauges well, with a warning leading time of 10-20 min. At NOA-04, NOA-10, and Soudhas, the amplitude of the first tsunami peak is accurately predicted by data assimilation. But at Falasarna, the forecasted amplitude (i.e., 11.0 cm) is smaller than the synthetic amplitude that is used for comparison (19.3 cm). The reason is that the tsunami arrives at Falasarna at an early time, even before it arrives at most OBPGs. We do not have much tsunami waveform data for assimilation. To the contrary, the stations on the middle or eastern part of Crete Island show a better match between the synthetic and forecasted waveforms. According to the performance quality index of Tsushima et al. (2012), the tsunami forecast accuracy (i.e., percentage of success) is calculated by: Here, O i and F i are the first-peak amplitude of the synthetic (used as observation) and forecasted tsunamis, respectively. Overall, the accuracy of data assimilation process for tsunami forecasting is 88.5% for a tsunami source in east Sicily. Though the maximum tsunami amplitude may come in later phase for far-field event at some stations (e.g., NOA-04 and Soudhas), which is not well predicted at a warning leading time of 10-20 min, we note that our tsunami early warning system is mainly aimed at forecasting the first wave).

Early Warning for Hypothetical Landslide Tsunamis
The tsunami generated by a landslide in Cyclades mainly affects the northern side of Crete Island (Figures 7a  and 7d). We assume that a submarine landslide occurs at 37.0°N and 25.7°E. The region of the landslide is assumed to be a circle with a diameter of 1.5 km. The total amount of landslide volume is assumed to be 0.3 km 3 , and the average thickness of the sliding mass is 170 m. The rationale for this scenario is based on

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the studies by Soloviev (1990) and Samaras et al. (2015) who showed that seismic activities in the Aegean Sea region have triggered tsunamigenic submarine landslides such as the events of the 1650 (M 6.3) and the 1968 (M 6.8).
The designed OBPGs on the north of Crete Island (E04-E07) received evident tsunami signals from this hypothetical landslide tsunami, but the tsunami heights of other OBPGs are less than 2.0 cm (Figure 7). Compared to the seismogenic tsunami, the landslide tsunami has a shorter wavelength, and there are more high-frequency components and dispersive characteristics in their waveforms. Hence, it is challenging to distinguish the arrival time of the first tsunami peak. Assuming the time of the landslide initiation as

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Journal of Geophysical Research: Solid Earth t = 0, the first tsunami peak arrives at t = 55 min at tide gauge NOA-10 with an amplitude of 3.0 cm (Figure 8). The maximum peak, which is 9.7 cm in amplitude, arrives later at NOA-10. At tide gauge Soudhas, the first peak arrives at t = 72 min with an amplitude of 3.3 cm. The tsunami heights are smaller (<3 cm) at tide gauges NOA-04 and Falasarna. Almost no tsunami signal can be seen at Paleochora.
The waveforms are forecasted at 10 min before the arrival of the tsunami's first peak by data assimilation approach (Figure 8). At both NOA-10 and Soudhas, the tsunami waveforms that are forecasted by data assimilation are consistent with the simulations (Figure 8), though the forecasted waveforms have less high-frequency components. At NOA-10, the tsunami arrival time and the first-peak amplitude are predicted accurately, but the maximum amplitude is not forecasted well. At Soudhas, the first-peak amplitude and the maximum amplitude are precisely forecasted. At NOA-04, our forecasted waveforms generally match with the simulation, but at Falasarna, it fails to predict the tsunami waveforms with a very small amplitude (i. e., <3 cm). Overall, considering the waveforms at tide gauges except for Paleochora, the forecast accuracy of our data assimilation approach for a hypothetical landslide tsunami is 87.3%.
Because the source size of landslide tsunamis is smaller than the seismogenic tsunamis, we make additional tests for landslide tsunamis and present them in the supporting information. They are the effects of noise in the OBPG waveforms (Supporting Information S2) and of station interval and the characteristic distance of data assimilation (Supporting Information S3) on the forecast. In our synthetic experiments presented above, we assumed that OBPG waveforms are noise-free, because OBPG is capable of detecting tsunamis of less than 1 cm , indicating that the associated noise level is relatively low. However, OBPG records can be affected by several natural interferences, particularly for landslide tsunamis because of the short period. In our Supporting Information S2, we conduct additional experiments by incorporating noise into the OBPG waveforms. We also examine the effect of shorter characteristic distance (5 km) than used in our data assimilation (20 km). The characteristic distance is the size of Gaussian-shape source for GFTDA (Figure 3b; . Because the forecast accuracy is affected by both the characteristic distance and the station interval, we also change the station interval from 100 km to 25 km in the additional experiments (Supporting Information S3).

Early Warning for the May 2020 Off the Crete Tsunami
Besides hypothetical experiments, we also retrospectively use the tsunami generated by the 2 May 2020 earthquake (Mw 6.6) offshore Crete Island as a test case. The tsunami was recorded by the tide gauge NOA-04 on Crete Island ( Figure 1). As there are no OBPGs located off the coast, we use the synthetic waveforms as the input for data assimilation. To compute the synthetic waveforms at OBPGs, we invert the tsunami data recorded at NOA-04 and estimate the source model of the 2020 event. A single fault with a   Figure 9a shows the initial sea surface deformation caused by this earthquake.
Figures 9b-9d demonstrate the propagation of the tsunami and its wavefield. The tsunami arrives at E10 at around 5 min after the earthquake whereas it arrives at the southern coast of Crete Island at around 15 min after the earthquake. The tsunami waveforms at OBPGs obtained through numerical simulation are used for data assimilation (Figure 9e). In Figure 9e, we only plot the waveforms of the OBPGs where the tsunami arrives earlier than at tide gauge NOA-04. This means we apply only three OBPG records of E09, E10, and E11 for forecasting the tsunami at the coastal location NOA-04. The data assimilation process ends at 8 min after the earthquake, which is indicated by the dashed line in Figures 9e-9f.
The forecasted waveform using data assimilation is compared with the real observation and the synthetic waveform ( Figure 9f). The synthetic waveform is consistent with the real observations for the first few waves, proving the validity of our source model and that the waveforms at OBPGs are reliable for tsunami data assimilation. Our assimilation predicts the tsunami arrival at tide gauge NOA-04 accurately, and it fairly forecasts the tsunami amplitude as well. For the first tsunami peak, the observed and forecasted amplitudes are 5.0 and 4.5 cm, which yields an accuracy of 99.0% calculated by the equation of quality index (Tsushima et al., 2012), and the observed and forecasted arrival times are 18 and 19 min, respectively. For the later phase, the forecasted waveform has a longer wavelength, but it fairly predicts the tsunami peaks at~28 and 35 min. Because the assimilation process ends at 8 min, the tsunami warning lead time is~10 min for the May 2020 event. Overall, the performance of the OBPG network in predicting the real May 2020 tsunami appears to be satisfactory despite its rather short arrival time of~20 min. In this study, the size of the tsunami source is shorter than the distance between the two adjacent OBPGs (Figure 9a). In many cases of data assimilation efforts in the past, the size of a tsunami source spans at least several OBPGs. Therefore, it is believed that the result shown in Figure 9 for the May 2020 event is very important because it proves the success of the method even for small tsunamis.

Discussion
Unlike trans-Pacific tsunamis, tsunamis in the EMB propagate in a narrow and confined region (e.g., Heidarzadeh & Satake, 2013), and thus, tsunamis could propagate across the Mediterranean Sea in a short time (<1 h) and arrive at the coastal areas. The OBPGs designed in our study for the EMB are located in the narrow water body of the Mediterranean Sea and are aimed at detecting tsunamis and assimilating the observed data into early warning in a short time, mostly less than 30 min. For the data assimilation approach, we need sufficient observational data in order to provide accurate forecasts. In our test of the

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Journal of Geophysical Research: Solid Earth real tsunami of 2 May 2020, the earthquake occurred in the near-field at the distance of~100 km from the coast, and the proposed OBPG station E10 is very close to the source region. In some cases, if the OBPG is located within the source regions, it cannot record the initial ocean surface displacement directly, because of the seismic waves and that fact that the ocean surface displacement is almost the same as the ocean bottom deformation (Saito et al., 2019;Saito & Tsushima, 2016;Tsushima et al., 2012). To overcome this problem, we could use the method developed by Tanioka (2018) to reproduce the tsunami height distribution correctly and make it available for tsunami data assimilation.
The early warning system that we proposed is applicable not only to seismogenic tsunamis, but also to landslide and volcanic tsunamis. This is extremely helpful in the EMB, due to its potential for a large variety of tsunamigenic sources (Soloviev, 1990). Traditional tsunami early warning systems based on seismic observations may fail to provide appropriate warnings for non-seismic tsunamis. Our approach is also useful in other regions worldwide where tsunamis are also generated by landslide or volcano eruption, like Indonesia and Japan (Heidarzadeh et al., 2020;Maeno & Imamura, 2011;Satake, 2007). For landslide tsunamis, the real practice of OBPGs for tsunami detection requires more caution. As discussed by Saito and Kubota (2020), the pressure induced by short-period waves on OBPGs deviates from hydrostatic relation if the wavelength of the sea-bottom deformation is not much greater than the sea depth. Last but not least, our designed early warning system aims to solely protect Crete Island, where high potential of tsunami damage exist. In case the warning system is aimed at protecting other regions such as Cyprus and west Turkey region, a new network of OBPG should be designed.

Conclusion
We proposed a potential early tsunami warning system based on tsunami data assimilation in the Eastern Mediterranean Basin (EMB). Twelve Offshore Bottom Pressure Gauge (OBPGs) are designed around Crete Island, and their locations are confirmed by performing Empirical Orthogonal Function (EOF) analysis. Our proposed warning system is able to forecast tsunami arrival time and first-peak amplitude in Crete Island accurately at 10-20 min before the tsunami arrival. The forecasting accuracy of the hypothetical seismogenic tsunami in east Sicily is 88.5%. It also works well for landslide tsunamis, though the high-frequency components of landslide-generated waves are not fully captured by the OBPG network. The forecasting accuracy of our data assimilation approach for the hypothetical landslide tsunami is 87.3%. Moreover, the retrospective study of the real tsunami event of 2 May 2020, generated by an Mw 6.6 earthquake off Crete Island, shows that our approach is able to predict the tsunami fairly well though it is a near-field tsunami with travel time of~20 min. The observed and forecasted first-peak amplitudes are 5.0 and 4.5 cm, while the arrival times are 18 and 19 min, respectively. A warning lead time of~10 min was obtained for the May 2020 event. We conclude that the deployment of OBPGs is helpful to tsunami early warning for Crete Island for both near-field and far-field tsunamis in the EMB. We recommend this method for other tsunamigenic zones in the EMB region such as the Aegean Sea and west Turkey and for beyond EMB such as Indonesia.