## 1. Introduction

The city of Venice often experiences flooding events induced by abnormally high water levels at the three entrances of the lagoon. Piling up of water in the northern part of the Adriatic basin is usually produced by a depression pattern, typical of extratropical cyclones, which causes the surface pressure gradient to align with the major axis of the Adriatic Sea. The phenomenon is reinforced by the effect of local orography, forcing low-level winds to blow from the southeast along the same axis. As a consequence, water levels significantly higher than the expected astronomical tide level are reported several times a year, especially between October and January.

Moreover, during recent years subsidence has developed, partly as a by-product of urban and industrial development of the inner land: between 1900 and 1970, the whole area of the lagoon has “sunk” as much as 23 cm. Future prospects are not reassuring, and allow neither optimistic reliance on a reduction in the frequency of flooding events, nor understatement of the danger and costs implied by their intensity.

Due to the frequency of flood events in Venice, attention has been devoted to the development of a reliable warning system. A statistical model based on 50 predictors, represented by tidal levels and atmospheric pressure values at different stations, has been operative in Venice (Canestrelli and Pastore 1997) for more than 10 yr. However, this model is useful only for short-range forecasts, which could possibly be extended using the forecast atmospheric pressures as predictors. However, as this kind of model is based on the hypothesis of the analogs, it is hard to capture events not experienced before by the system.

As mentioned by Cavaleri (1999, section 9.2), a possible solution to overcome these problems is a forecast system based on the numerical integration of the dynamical equations. Such an approach had already been used by Finizio et al. (1972) to simulate the surge in the northern Adriatic Sea with a one-dimensional oceanic model. In recent years, more complex systems, based on the coupling among atmospheric and oceanic models, have been developed (Lionello 1995; Lionello et al. 1998a,b).

These systems consist of three modules: a limited area (LAM) atmospheric circulation model, a wave model, and a shallow water model. The regional atmospheric circulation model provides a high-resolution forcing for the wave model (surface wind) and for the shallow water model (pressure field and surface wind).

High-resolution (of the order of 10 km) forcing, not available from current general circulation models (GCMs), is needed mainly because the Mediterranean basin is surrounded by a complex orography that has a strong influence on the atmospheric flow. This influence, ranging from local to synoptic scales, can produce precipitating clouds through orographic lifting, triggering of convection, indirect effects of flow splitting or blocking, induced waves, and channeling of the wind.

Surge prediction systems have also been developed in other key areas. A numerical model for the western coast of Norway was developed by Martinsen et al. (1979), based on the depth-integrated shallow water equations. Their simulations show that the wind stress and the atmospheric pressure are of about equal importance in determining the largest storm surges.

The western coast of Alaska experiences coastal flooding events due to the storm surges associated with extratropical cyclones. A storm surge model forced by predicted large-scale atmospheric fields has been used by Blier et al. (1997) to simulate surge events, as a preliminary work for an operational implementation. In this case, the surge model is based on the depth-integrated quasi-linear shallow water equations, while the atmospheric forcing (mean sea level pressure and surface wind) is obtained from the National Centers for Environmental Prediction (NCEP) analysis for the hindcast experiments.

An area where the prediction of storm surges is even more crucial, since coastal floods are one of the major causes of loss of life, is the Bay of Bengal. A numerical model based on the nonlinear shallow water equations has been used for simulating storm surges in this area, on a grid covering both open sea and some estuarine channels (Flather 1994). A high-resolution shallow water model has instead been used by As-Salek (1997) to predict negative surges that destroy coastal aquaculture installations in the area of the Meghna estuary, in the northern part of the Bengal Bay.

Some recent papers (Hubbert et al. 1990; Tang et al. 1997) have been concerned with the study of the effect of tropical cyclones on storm surges on the Australian coasts, which are strongly related to the excitation of coastally trapped waves [a theoretical framework can be found in Fandry et al. (1984)]. Tang et al. (1997) have shown that a depth-integrated barotropic numerical model is appropriate both for the simulation of the continental shelf waves and of secondary effects, such as coastally trapped waves. Hubbert et al. developed a storm surge model using a depth-integrated shallow water model forced by wind stress and pressure gradients computed by a regional atmospheric model. In a successive work (Hubbert et al. 1991) the model developed into a real-time system for forecasting tropical cyclone storm surges.

In this work, we describe an operational forecast system for the prediction of high water levels in the lagoon of Venice and of the state of the Mediterranean Sea, which has been recently developed at the National Environmental and Energy Agency (ENEA). The operative integrated system consists of a limited area model (the Bologna Limited Area Model, BOLAM), coupled with a wave model (WAM) and a high-resolution shallow water model (the two-dimensional Princeton Ocean Model, POM-2D) of the northern Adriatic Sea. Both BOLAM and WAM cover the whole Mediterranean basin. The atmospheric model is run over a wider domain at a resolution of 0.3°, using coarser boundary data from the European Centre for Medium-Range Weather Forecasts (ECMWF), and on a smaller nested domain at a resolution of 0.1° (see Fig. 1). In the operative configuration of the system, water levels at the entrances of the lagoon computed by POM are given as input to a finite-element model of the lagoon itself, to predict surface levels in Venice.

We concentrate, in particular, on the ability of the system to predict surge levels in the northern Adriatic Sea and focus on the POM-2D tuning needed to improve the prediction skill. A critical evaluation is given of the system performance for two relevant case studies.

This paper is organized as follows. In section 2 we describe the integrated forecast system and the models used. In section 3 there is a description of the two meteorological cases studies and of the WAM performance, while section 4 contains the results of the surge simulations. Section 5 summarizes the main conclusions of the study.

## 2. The modeling chain

The quality of the modeling chain's results depends on the quality of the atmospheric forcing (mean sea level pressure and surface wind). As mentioned in the introduction, this is strongly affected by the representation of the complex orographic features present in the area. International scientific programs such as the Alpine Experiment (ALPEX; Speranza et al. 1986), the Pyrennes Experiment (PYREX; Bougeault et al. 1990), and the Mesoscale Alpine Programme (MAP; Bougeault et al. 2001; http://www.map.ethz.ch/map-doc/) have been organized in the last 20 years in the European area with the aim of improving the understanding and the modeling of the impact of mountainous massifs on the atmospheric behavior. In the PYREX framework a direct comparison of analyses produced by the ECMWF GCM and by a mesoscale atmospheric model (PERIDOT) showed that the mesoscale model gives a more realistic representation of the orographic pressure drag (Lott 1995). The same mesoscale atmospheric model PERIDOT, run with a 10-km grid mesh and 40 sigma levels in the vertical, has been compared with observations of the PYREX campaign (Masson and Bougeault 1996), showing good skill by the model in reproducing the mesoscale features of the wind field.

In this study, in order to achieve a satisfactory representation of the orography surrounding the Adriatic and the central Mediterranean Sea, the limited area model BOLAM has been used. A nesting in two steps has been set, which allows a smooth transition from the coarser resolution of the boundary data (ECMWF analysis with a spectral truncation of T213) to a very high resolution (VHR) grid in the region of interest. Therefore the VHR BOLAM (10-km resolution) is driven by a high-resolution (HR) BOLAM (30-km resolution), which is in turn driven by the ECMWF analysis. Boundary data for the HR model are given every 6 h, and every 3 h for the VHR model. As we are using analyses as input for the LAM chain, the numerical experiments performed cannot be considered a forecast but a hindcast simulation. Both the HR and VHR models run with 40 sigma levels. Since we are mainly concerned with the POM model setup for an accurate prediction of the sea surge in the northern Adriatic Sea, the VHR domain is confined to the area between 29.5°–46°N and 9°–27°E, which is displayed in Fig. 2.

The HR and VHR model hindcasts start every day at 0000 UTC. For each VHR hindcast we skipped the first 6 h (spinup time) and we used the next 24 h to produce a continuous forcing dataset for the WAM and POM models. WAM is forced by the surface wind, while POM-2D is driven by the surface wind stress field computed by WAM and by the sea level pressure field computed by BOLAM.

### a. The atmospheric limited area model: BOLAM

The atmospheric model used in the system was developed at Consiglio Nazionale delle Ricerche-Istituto per lo Studio dei Fenomeni Fisici e Chimici della Bassa ed Alta Atmosfera (CNR–FISBAT), Bologna, Italy (Buzzi et al. 1994). BOLAM is an explicit, primitive equation, hydrostatic, three-dimensional gridpoint model that uses pressure-like vertical coordinates (sigma coordinates). Horizontal discretization is performed on the Arakawa C grid, with rotated latitude and longitude as independent variables. The model integrates the equations of momentum, mass continuity, and energy conservation on a regular latitude–longitude grid. The prognostic variables are latitudinal and longitudinal wind components, potential temperature, specific humidity, and surface pressure. The time integration of the prognostic advection equations is performed using the forward–backward advection scheme (FBAS; Malguzzi and Tartaglione 1999). A fourth-order horizontal hyperdiffusion operator is applied to the prognostic variables, and divergence damping of momentum is used to reduce the growth of gravity waves. Both horizontal diffusion and divergence damping are computed using the Euler scheme. An adjustment loop has been implemented, using a forward–backward scheme with reduced time step, for those terms in the primitive equations describing fast gravity modes. Model physics includes vertical diffusion (Louis et al. 1981), soil water and energy balance, a two-band radiation scheme (Geleyn and Hollingsworth 1979), dry-adiabatic adjustment, cumulus convection (Emanuel 1991), and large-scale precipitation. Relaxation to boundary conditions is performed using the Davies scheme (Davies 1976), modified by Lehmann (1993), and is applied to all prognostic variables.

The model has been tested in a variety of different atmospheric situations (Buzzi et al. 1994) and has scored well in a comparison with other state-of-the-art LAMs in the context of the PYREX experiment (Georgelin et al. 2000).

### b. The WAM model

WAM is a third-generation wave model (WAMDI Group 1988). It describes the evolution of the wave spectrum by solving the wave energy transfer equation. It has no constraints on the spectral shape, whose evolution depends on the spatial divergence of the energy flux and on the local sources of energy. The WAM integration is forced by the atmospheric stress computed via the relation *τ*_{a} = *ρC*_{D}*U*^{2}_{10}*U*_{10} is the 10-m wind predicted by BOLAM, *C*_{D} is the drag coefficient, and *ρ* is density. WAM then calculates the wave contribution to the total stress (*τ*_{aw}), which, in turn, iteratively corrects the total atmospheric stress (*τ*_{a}). The resulting stress is used to force the POM integration. WAM is integrated on sea points of the regular latitude–longitude grid of the VHR domain (Fig. 2), at a resolution of 0.1°.

### c. The POM model: Shallow water version

POM (Blumberg and Mellor 1987; Mellor 1991) is a three-dimensional primitive equation ocean model. In this work, it has been operated in a 2D configuration solving the shallow water equations to compute surface elevation. We expect this approximation to be sufficient to capture the main features of the storm surges in the Mediterranean, since they are essentially the barotropic response of the basin to the atmospheric forcing (Blier et al. 1997). The 2D configuration of the POM model has been used in other studies dealing with storm surges in the northern Adriatic (Lionello 1995; Lionello et al. 1998b) and with the Indonesian Seas circulation (Burnett et al. 2000a,b). The horizontal discretization is performed on the Arakawa C grid. An explicit Orlanski condition (Orlanski 1976) for the elevation, with a restoring to a prescribed value, has been selected between the boundary conditions available in the model. However, since the Orlanski scheme does not conserve the total water mass of the basin (Palma and Matano 1998), it is necessary to locate the open boundary where the elevation is close to zero. The amphidromic points, in which the tidal range vanishes, can be identified by examining the barotropic modes of the Mediterranean basin. The first mode, computed by Schwab and Rao (1983) and by Beltrami Campagnani (2000), shows an oscillation of the western and eastern basins, with an amphidromic point in the Sicily channel (the Mediterranean mode). The second mode described by Beltrami Campagnani (2000) presents an amphidromic point in the Sicily channel and another one in the Strait of Otranto (the Adriatic mode). This mode divides the Mediterranean into three parts, the western basin, the eastern basin, and the Adriatic sea; the three basins oscillate around the amphidromic points.

Using a boundary condition located at Otranto the oscillation that involves both the Adriatic basin and the eastern basin cannot be entirely represented. For this reason an integration domain including at least the Adriatic and the eastern basin should be considered. Two domains have been used in the studies reported here: one including the Adriatic and the central part of the Mediterranean sea (Arc2 area; Fig. 3a), and the other covering the entire Mediterranean (MED; Fig. 3b). In the Arc2 domain the Levantine Sea is not included, since it accounts for a small part of the total water mass of the eastern basin.

The boundary condition for the domain covering the entire Mediterranean Sea has been imposed in the Atlantic region outside the Gibraltar Strait. The elevation to be imposed on this boundary has been derived, similarly to that done in Hubbert et al. (1990), by computing the difference between the boundary pressure and a reference Atlantic pressure, using an isostatic hypothesis for the Atlantic. This boundary condition allows the mass exchange between the Mediterranean Sea and the Atlantic Ocean. The initial elevation and current are set to zero for both the Arc2 and MED domains.

The effect of the initialization vanishes after different times for the two domains. In fact, the Arc2 is characterized by an extensive open boundary on which outflux of energy is allowed and the initial mean elevation is kept almost constant. Therefore, an initial perturbation of the elevation field with a low projection onto the main normal modes of the basin is rapidly radiated out of the boundary (in about 36 h for an experiment without forcing). On the other hand, the MED domain is almost closed and the main mechanism responsible for the loss of energy of an initial perturbation is dissipation. In this case the initialization effects, in an unforced experiment, last for more than 2 days. In defining the grids for the two domains we had to take into account the need of very high resolution (∼10^{3} m) in the northern part of the Adriatic Sea, which derives from the fact that, in the operative configuration, sea surface levels at the three close locations of Chioggia (45.23°N, 12.3°E), Malamocco (45.33°N, 12.32°E), and Lido (45.44°N, 12.42°E) have to be predicted.

_{0}, Lon

_{0}) = (48.73°N, 12.43°E). The distance of a generic point P is obtained via the equation

*η*

^{2}

_{p}

_{p}

_{0}

^{2}

_{p}

_{0}

^{2}

*ξ*

_{p}

_{p}

_{0}

_{p}

_{0}

*α*

_{0}

*α*

_{0}is defined by tan(

*α*

_{0}) = (Lat

_{sw}− Lat

_{0})/(Lon

_{sw}− Lon

_{0}) and (Lat

_{sw}, Lon

_{sw}) = (9.4°N, 28.9°E) (SW indicates the southwest extreme of the grid). The Mediterranean domain is defined by a latitude–longitude grid with nonuniform spacing. The grid spacing has a minimum at (44°N, 14°E) where the interval is 0.070° in latitude and 0.091° in longitude, respectively. Starting from this point the grid interval increases linearly by 1% per grid point in both directions.

## 3. Synoptic description and results from WAM: The two test cases

### a. The November 1996 event

The extreme surge events that took place during November 1996 were due to a cyclonic circulation over the Western Mediterranean region. The highest sea surface elevation in Venice was measured on 18 November at 0600 UTC. Two series of hindcasts at the two different resolutions were computed for November 1996, covering the period from the 11th to the 22rd. Figure 4 shows a sequence of ECMWF analyses of the mean sea level pressure field for the period starting at 1200 UTC 16 November, while the corresponding fields predicted by BOLAM-HR are shown in Fig. 5. A depression, initially located to the south of the Baleari Islands (Figs. 4a and 5a), moves slowly toward the east, reaching the Gulf of Genoa after 36 h (Figs. 4b and 5b). The pressure gradient aligns with the main axis of the Adriatic Sea and gives rise to a southeasterly wind. In the next 12 h the low covers the Alps while the strong gradient over the Adriatic Sea persists. Simulated and observed patterns are in good agreement, but the simulation reveals finer-resolution aspects, such as a split of the low at 0000 UTC 18 November. Surface wind during this period is directed along the Adriatic axis, blowing from the southeast. Figure 6 shows the wind field simulated by BOLAM-VHR for the same period: here the influence of the orography surrounding the Adriatic basin is evident.

To obtain a further experimental validation of the LAM results, we cannot use observations included in the assimilation cycle for the ECMWF analysis, such as those of coastal synoptic stations, that record the wind strength and direction. On the other hand, observational data over the sea should be preferred, due to the absence of the orographic influence. In the 1996 case, observational data of wind strength from the oceanographic tower located 15 km off the coast of Venice were available. The tower data (every 3 h), the corresponding simulated BOLAM-VHR wind (every 3 h) used to force the WAM and POM models, and the ECMWF analysis wind (every 6 h) are plotted in Fig. 7. Note that in the period from 1800 UTC November 14 to 0600 UTC November 17 observational data have not been recorded by the instrument.

It can be noted that the ECMWF analysis strongly underestimates the observed data all over the period. The BOLAM results are consistently better, particularly after 17 November, even if they are not able to reproduce some sharp peaks, such as those at 0600 UTC 17 November, 0600 UTC 20 November, and 1200 UTC 22 November. The bias values for BOLAM-VHR and ECMWF are, respectively, −1.96 and −6.20, while the rms errors are 4.9 and 7.5.

An indirect validation of the BOLAM surface wind field can be achieved through the analysis of the WAM performance in predicting significant wave height over the Adriatic basin (Cavaleri 1999, section 10.5). Experimental data from a wave measurement network of directional buoys managed by the National Department of Technical Services are available. Data from the oceanographic platform off the coast of Venice are also used. Two WAM runs were made over the VHR domain, at the resolution of 0.1°: one using as input the BOLAM-VHR wind fields, and another one using winds from the ECMWF analyses. Figures 8 and 9 display the significant wave height fields *H*_{S} at 0000 UTC 18 November for the two runs; in Fig. 9 the available buoy locations are also shown. It can be seen that the high resolution of the VHR field allows the WAM model to represent finer-scale features. Moreover, the VHR run produces larger areas where the significant wave height exceeds 2 m.

In Fig. 10 we compare significant wave height simulated by WAM, forced by VHR fields (filled circle) and by the ECMWF analyses (open square) with the wave height measured by buoys (open circle). Comparisons are shown for the following locations in the Adriatic Sea, indicated by numbers in Fig. 9: Venice (1), Pescara (2), Monopoli (3), and Crotone (4). Clearly, there is a very good simulation of the wave height at the two southern locations (Monopoli and Crotone). On the other hand, in Pescara and Venice the significant wave height peak on 15 November is almost completely missed. During these days a pressure gradient directed along the Adriatic Sea gives rise to a wind directed toward the NW. This situation is due to a low pressure area that is present over the Alps on 14 November and then slowly moves westward, covering a large area of the northern Tyrrenian Sea during the next day.

The comparison of wave heights at Venice is consistent with the results of the direct comparison of wind magnitudes (Fig. 7), which shows an underestimation in the simulated wind during the period 11–14 November.

In Table 1 the bias and the rms are shown both for the ECWMF and VHR simulations for all the available buoys. Data for Mazara (number 6 in Fig. 9) are not included because of the lack of measured data for most of the period. The wave height bias is negative in almost all the locations, but it is reduced when the input wind fields come from BOLAM-VHR. The rms values show an improvement using VHR forcing for the northern Adriatic buoys, while both the simulations display high rms values for the buoy of Ponza. This makes sense, since Ponza is close to the western boundary of the computational domain and the prevalent winds in the Tyrrenian Sea during the period of maximum wave height are from the west. This clearly leads to an underestimation of the swell part of the wave height.

### b. The October 1998 event

The October 1998 surge events are also characterized by a cyclonic circulation over the Western Mediterranean region. The cyclonic regime persists from 5 to 7 October, determining a pressure gradient along the main axis of the Adriatic Sea. The large-scale circulation shows for this period the development of an omega blocking. The 1996 and the 1998 events are quite similar in the synoptic development, even if the pressure minimum in the latter event is less pronounced. Another difference is related to the contribution of the tide to the elevation in Venice: in the October 1998 event the tide amplitude is close to its maximum, while in the November 1996 event it is less relevant. Therefore, in the 1998 event the correct simulation of the phase of the surge has the greatest importance.

Two series of hindcasts at the two different resolutions were computed for the period 3–9 October 1998. In Figs. 11a–d show the ECMWF analyses of the mean sea level pressure at 0600 UTC 5 October, 1200 UTC 5 October, 0600 UTC 7 October, and 1200 UTC 7 October. It can be seen that the depression located over the Gulf of Lion on 5 October moves to the east, covering the Italian peninsula and broadening during the two following days. The corresponding pressure gradient has a strong longitudinal component. These features are well reproduced in the results of the BOLAM-HR simulation shown in Figs. 12a–d. It should be noted, however, that on 7 October a stronger sea level pressure gradient is simulated in the Adriatic area. This discrepancy is particularly interesting, since the highest sea surface elevation in Venice was measured at 0800 UTC of the same day.

In Fig. 13 we show significant wave heights simulated by WAM, forced by VHR wind fields (filled circle) and by ECMWF analysis fields (empty square), and wave heights measured by buoys (empty circle), for four locations: Pescara, Monopoli, Crotone, and Catania (number 5 in Fig. 9). The Venice data are not available for this event.

The results are discussed for each of the locations, starting from the northern buoy (Pescara). The peak in the VHR simulation is correct both in amplitude and in time, but there is a clear underestimation during the previous two days. During 6 October the mean energy of the measured waves is directed westward, with a mean frequency of about 0.15 Hz, while wind waves frequently change direction. This suggests that the mean energy is related to the swell component. Therefore, the observed underestimation could be due to an insufficient quality of the simulated wind far from the station.

The VHR simulated height at Monopoli is larger than the observed one during 7 and 8 October. Analyzing the components of the simulated significant wave height, it is found that the wind waves are predominant during this period. Then the strong positive bias could be connected to an overestimation of local wind by the model. For both the two southern locations (Catania and Crotone) the growing phase in the VHR simulation is in good agreement with observed values, but stops too early (9 h before the observation).

Table 2 presents values of bias and root-mean square for each buoy, both for the simulation using BOLAM-VHR input and for that using ECMWF input. In general, the finer wind resolution corresponds to a better result; the ECMWF run always provides an underestimation of wave heights. The only exception is represented by Monopoli where the rms error is higher for the VHR run, due to the overestimation explained before.

## 4. The surge events

### a. Surge simulation: 1996 event

The period we are studying was characterized by several flooding events with a maximum surge of 85 cm on 18 November. Including the effects of the astronomical tide and the 23 cm of subsidence in the lagoon, gives a total elevation of 128 cm. Experimental data of sea elevation are available from the oceanographic tower near Venice and from a network of altimeters managed by the National Department of Technical Services.

The elevations of sea level at Venice and Bari resulting from the shallow water model integration are plotted in Figs. 14a and 14b. The integration is on the Arc2 area and covers the period 11–22 November 1996. The model has been initialized with prognostic fields set to zero. Tide values have been subtracted from elevation data to obtain pure surge. It can be seen from Fig. 14a that the main peaks for Venice are well simulated in amplitude but not in phase, with a lag ranging from 2 to 4 h. The discrepancy in the period 13–16 November, as already observed in section 3a, can be explained by a deficiency in the simulated wind field. On the other hand, Fig. 14b shows that, with the exception of the two major peaks, the simulation gives an underestimation of the elevation for Bari.

In Fig. 15, we present the elevation at Venice obtained from analogous experiments in which the POM integration is extended over the entire Mediterranean domain. Both the results of a run with BOLAM-HR forcing at the resolution of 0.3° and of a run using ECMWF analyses forcing are presented. The results obtained using the BOLAM-HR forcing show very good agreement, both in amplitude and in phase, with the observed elevation, while the general underestimation for the run forced by ECMWF analysis is evident. The lag problem observed at Venice in the experiment with the Arc2 domain (Fig. 14a) has been overcome; in particular, the phase error at 0700 UTC 18 November has disappeared and a similar improvement has been obtained for the secondary peaks. The strong overestimation of the minimum absolute values, present in the Arc2 run, is significantly reduced in the new simulation.

*η*

^{2}

_{LF}

*η*

^{2}

_{HF}

The amplitude ratio analysis shows a predominance of the low-frequency component over the high-frequency component: the low-frequency amplitude ratios range from 0.84 to 0.87, which has to be compared with a value of 0.9 for the measured data. It can be noted that the low-frequency component in the simulated data always has a negative bias with respect to the observed values. Looking at the correlation coefficients, two things can be observed. There is an evident improvement going from the Arc2 to the MED experiment, that is, extending the integration domain over the whole basin. Bias and rms errors are strongly reduced and the correlation coefficient grows up to 71%. On the other hand, it should be noted that the ECMWF experiment shows the highest values of bias and the worst correlation coefficient.

The better results observed in the MED simulation could be due to a better representation of the barotropic oscillation of the Mediterranean Sea caused by the pressure forcing. To test this hypothesis two experiments using only pressure forcing for Arc2 and MED have been performed (Fig. 16). The Arc2 experiment shows two strong minima at the same times of the experiment with total forcing (Fig. 14a). In the MED experiment these minima are drastically reduced. This strong improvement can be explained as follows. If a normal mode decomposition is applied, the forcing for the *N*th normal mode coefficient equation is computed by the spatial integration of the forcing times the *N*th normal mode. Since the first gravitational modes have non-negligible amplitudes in the area outside the Arc2 domain (Beltrami Campagnani 2000), including this area is important for a precise determination of the coefficients.

The improvement in phase can also be explained by looking at the normal modes. In fact, in a recent study (Briganti 2000) the normal mode frequencies have been calculated for the Arc2 basin both for a closed boundary and for a zero elevation boundary. In the case of a zero elevation boundary, an anomalous principal gravitational mode, characterized by only one amphidromic point near the boundary, with an oscillation period of 23.3 h is observed. This spurious mode can interact with the first Adriatic gravitational mode, characterized by two amphidroms and a period of 22 h, producing an error in the phase of the simulated oscillation.

### b. Surge simulation: 1998 event

The flooding events of October 1998 were relevant in the recent history of Venice surges, because the maximum elevation of 57 cm at 0800 UTC 7 October was in phase with a high value of the astronomical tide. Including also the lagoon subsidence, the sea level reached 120 cm.

Due to these characteristics it is crucial to predict both the correct amplitude and phase of the maximum peaks. In Fig. 17a the simulated sea elevation values at Venice obtained using the Arc2 domain are compared with the observed values. The principal peak at 1100 UTC 7 October is underestimated and presents a phase lag of about 3 h. The peaks at 2000 UTC 5 October and at 1800 UTC 6 October are well simulated, while the peak observed at 1200 UTC 8 October is considerably underestimated. The comparison for the Bari station (Fig. 17b) shows a quite good agreement in the second part of the simulation, while in the first part the underestimation is principally related to the 36-h spinup time.

Similarly to the 1996 event, better results are given by the simulation over the entire Mediterranean domain (Fig. 18). Both the amplitude and the phase improve with respect to the Arc2 experiment (Fig. 17a); in particular, the 1100 UTC 7 October and 1200 UTC 8 October peaks are now well reproduced. The ECMWF experiment shows a general underestimation and a phase lag for the peaks at 2000 UTC 5 October and at 1800 UTC 6 October.

Table 4 gives a summary of the bias, root-mean-square error, and correlation coefficient for the sea surface elevation at the Venice station for the 1998 case. As in the 1996 event, the amplitude ratio comparison shows a predominance of the low-frequency component, and all the experiments show a tendency to underestimate the observed values. Again, a significant improvement is observed going from the Arc2 to the MED configuration. The bias is similar for the two experiments, but the rms error for MED is reduced and the correlation coefficient goes from 61% to 91%. Instead, the ECMWF experiment shows higher bias and rms error values, even if in this case the correlation coefficient is quite good, with a value of about 80%.

The improvement observed using the Mediterranean domain suggests that the pressure could play an important role in the surge phenomenon. Two experiments to evaluate the relevance of the pressure forcing on the elevation in Venice have been performed, using the stress and pressure forcing separately. In Fig. 19 we show the elevation in Venice for the run with stress only (open squares), for the run with pressure forcing only (filled circles), and for the observations (open circles). It can be seen looking at the main peaks that the contribution of the pressure forcing to the surge on the northern Adriatic Sea is comparable with that coming from the stress.

Finally, since forcing at different resolutions have been used for the Mediterranean experiments (0.3°) and the Arc2 simulations (0.1°), we want to verify if this has had an impact on the results. In order to do that, we perform an experiment over the Arc2 domain, using the lower forcing resolution, for the 1998 case, where the differences between Arc2 and MED were more pronounced. In Fig. 20 results for the 0.3° resolution forcing applied to the Arc2 area are shown, for the October 1998 period. The comparison with the results obtained for the same domain with higher-resolution forcing does not show substantial differences.

## 5. Summary and conclusions

Two storm surge events in the northern Adriatic Sea have been simulated using an integrated forecast system developed for the prediction of the Mediterranean Sea state and of the surge in the lagoon of Venice.

The forecasting system consists of a limited area model (BOLAM) for the simulation of the atmospheric conditions, of a wave model (WAM) for the simulation of the stress field, and of a shallow water model (POM) for the simulation of the sea elevation. WAM is forced by the surface wind computed by BOLAM, while POM-2D is driven by the surface wind stress computed by WAM and by the sea level pressure field computed by BOLAM.

The November 1996 and October 1998 surge events were associated with a persistent omega blocking on the large scale and with a cyclonic circulation over the Western Mediterranean region, determining a pressure gradient along the main axis of the Adriatic Sea. The two events differ in the tide contribution: while in November 1996 it is less relevant, in October 1998 the tide amplitude is close to its maximum, making crucial a correct phase prediction. The comparison with wind strengths measured at the CNR tower off the coast of Venice shows good performance of the simulation with BOLAM at higher resolution; the same comparison shows a general underestimation for the ECMWF wind analysis. Similar conclusions are reached evaluating the WAM performance in predicting significant wave height over several locations in the Adriatic basin.

Two domains corresponding to the entire Mediterranean basin and to the Adriatic–Ionian basin (Arc2), respectively, have been used in the POM-2D simulations. Concerning the Arc2 experiments, it is found, after comparison with measurements of elevation in the Adriatic Sea at Venice and Bari, that the amplitudes are reasonably reproduced, with an underestimation of some of the main peaks and some discrepancies in the corresponding phases. The same comparison for the MED experiment shows clear improvements, with a good representation of the maximum and minimum values of elevation and an almost-perfect phase simulation. The computation of the normal modes on the Arc2 domain shows a spurious mode (Briganti 2000) that can cause the phase lag problem found in running POM over this domain. This is overcome in the experiment using the Mediterranean basin, in which the main barotropic modes are correctly represented.

Another advantage in using the entire Mediterranean basin as a computational domain is a correct accounting of the total effect of pressure forcing. The experiment performed to check the importance of pressure forcing on the Mediterranean basin has shown that the pressure forcing and the stress forcing are of about equal importance in determining the sea elevation amplitude at Venice. Similar results were found by Martinsen and Gjevik (1979), in a study on storm surge along the Norway coast. An evaluation of the relative importance of the two forcings in the Mediterranean context, based on scaling arguments, is given in the appendix.

## Acknowledgments

The authors wish to acknowledge P. Malguzzi (CNR–FISBAT), P. Lionello (UN–PADOVA), R. Iacono (ENEA), and two anonymous referees for their helpful suggestions and comments. We wish to thank L. Cavaleri and A. Tomasin for the CNR platform data of Venice, and the National Department of Technical Services (DSTN) for the oceanographic data. This work has been supported by the DSTN.

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## APPENDIX

### Scale Analysis

*ζ*in an ocean of constant depth

*h,*as in Fandry et al. (1984):where

*c*=

*gh*

*f*is the Coriolis parameter. The forcing term includes the surface wind stress (

*τ*) and the atmospheric pressure (

*p*

_{a}):where

*ρ*

_{w}is the water density.

*ρ*

_{a}is the air density, ‖

*V*‖ is the module of the wind vector,

*C*

_{D}is the drag coefficient,

*A*is defined as (−1/

*ρ*

_{a}

*f*) ∇

^{2}

*p*

_{a}, and a term involving the derivative of ‖

*V*‖ has been neglected. The importance of pressure versus stress can be assessed by computing the ratio between the two forcing terms:Scaling ∂

*A*/∂

*t*as

*A*/Δ

*t,*with Δ

*t*≅ 10

*f*

^{−1}, we obtain

If we assign the values *f* ≅ 10^{−4} s^{−1}, ‖*V*‖ ≅ 10 m s^{−1}, *C*_{D} ≅ 10^{−3}, the ratio of wind stress forcing to pressure forcing is of order of 1 if *h* ≅ 10^{3} m (mean Mediterranean depth), or of order of 10 if *h* ≅ 10^{2} m (mean northern Adriatic depth). This is consistent with the numerical findings.

Bias and rms error for wave height at buoys (see Fig. 9), using ECMWF and VHR results. For Nov 1996

Bias and rms error for wave height at buoys (see Fig. 9), using ECMWF and VHR results. For Oct 1998

Bias, rms error, correlation coefficient, and amplitude ratio for sea elevation at Venice, for the Nov 1996 case. The values are computed separately for high and low frequencies (threshold value is 18 h). Experiments shown for Arc2, MED, and ECMWF domains

Same as in Table 3 for the Oct 1998 case