## 1. Introduction

[2] The lagoon of Venice is a wide, shallow tidal basin in the northeast of Italy. A large part of the lagoon is occupied by small islands and extensive tidal flats, which are dissected by an intricate network of channels departing from the three inlets of Lido, Malamocco, and Chioggia (Figure 1, see also *Fagherazzi et al.* [1999] for a description).

[3] Recent studies and field campaigns have shown that the salt marshes and tidal flats within the Venice lagoon are under erosion with a net sediment loss for the entire tidal basin [*Day et al.*, 1999; *Bettenetti et al.*, 1995, *D'Alpaos and Martini*, 2003; *Martini et al.*, 2003]. A further important trend within the lagoon is the flattening of the bottom topography, as proved by the gradual but persistent reduction of salt marshes and by the silting of the tidal channels. This trend is further enhanced by subsidence and sea level rise.

[4] Because of the above considerations it is clear that a correct description of local sediment resuspension is very important in understanding and assessing the evolution trend of the Venice lagoon.

[5] Tidal currents alone are unable to explain the erosion of salt marshes and the flattening of the lagoon bottom. Tidal currents produce shear stresses large enough to carry sediments into suspension only in the large channels near the three inlets, where velocities are high. In contrast, sediment resuspension on salt marshes and tidal flats is mainly caused by shear stresses induced by wind waves.

[6] Since shallow tidal basins have a very irregular morphology with large and sudden changes in bottom elevation, islands, and temporarily dry areas, a specific framework must be adopted to model wind wave propagation in these environments.

[7] Two alternative methods are available to model wind wave generation and propagation, i.e., a phase-resolving approach, based on mass and momentum balance equations (for a review, see *Dingemans* [1997]); or a phase-averaged approach that solves the energy or action balance equation [e.g., *Booij et al.*, 1999].

[8] Phase-resolving models reproduce the sea surface in space and time accounting for effects such as refraction and diffraction. Bottom friction and depth-induced wave breaking can be included in this framework but wind wave generation is usually absent or poorly reproduced. Phase-resolving models are thus unsuitable in enclosed basins, where storm conditions are important and local wave generation is a key process. Furthermore the space and time resolutions required by phase-resolving models are of the order of a fraction of the wavelength and period, respectively, thus limiting their practical application to small domains and short-duration events.

[9] For large-scale applications, such as for the modeling wind waves in the Venice lagoon, phase-averaged models are more suitable. There are two commonly used approaches to implement these models, i.e., the Lagrangian approach transporting wave energy along rays [*Collins*, 1972; *Cavaleri and Malanotte-Rizzoli*, 1981] and the Eulerian approach, where the wave energy is convected among cells of a prescribed computational grid. The latter is more efficient when nonlinear effects such as wave breaking must be reproduced.

[10] In the Eulerian approach the energy balance leads to a convective equation in which all the relevant processes of wave generation and dissipation are included in the source term.

[11] Many models that use the Eulerian phase-averaged approach have been developed since the pioneering work of *Gelci et al.* [1956]. Among them, the GLERL model developed by *Donelan* [1977] and revised by *Schwab et al.* [1984] for Great Lakes wave prediction, deserves to be mentioned here. GLERL is based on the solution of the local momentum balance equations, is time-dependent and can be applied to arbitrary bathymetries and wind conditions. However, shallow water wave effects are not included in this model.

[12] A successful extension of deep-water wave models to finite depth domains are the Hindcast Shallow water Waves model (HISWA model [see *Holthuijsen et al.*, 1989]), and its successor the Simulating Wave Nearshore (SWAN) model [*Booij et al.*, 1999; *Ris et al.*, 1999]. These models solve the wave action conservation equation using an implicit finite difference numerical scheme. The SWAN model accounts for refraction, shoaling, and wave breaking, and explicitly represents nonlinear wave-wave interactions.

[13] Further shallow water wave models are the WAVAD model [*Resio*, 1987; *Resio and Pierre*, 1989], and the Automated Coastal Engineering System (ACES) model, empirically derived from limited field data sets using dimensional analysis [*Leenknecht et al.*, 1992].

[14] *Lin et al.* [1998] tested all the models mentioned above against a wind and wave data set collected in the northern Chesapeake Bay during September 1992, when the tropical storm Danielle passed over the area. They found that no single model seems to be good at predicting all aspects of the surface wave field in the Chesapeake Bay, but the GLERL and SWAN models were the most promising. A further comparison of these two models against a more complete wind and wave data set collected in Chesapeake Bay is presented by *Lin et al.* [2002]. Both SWAN and GLERL correctly reproduce the change in wave direction due to a sudden wind variation. The models overpredict significant wave height (SWAN overpredicts more than GLERL does) and both underpredict the peak period. Using the SWAN model, *Lin et al.* [2002] also performed a model data spectral analysis that supported what was found in the previous comparison.

[15] The above discrepancies between measured and modeled waves will be enhanced in a shallower and more irregular basin like the Venice lagoon. In particular, in Chesapeake Bay there are not the deep channels, the extensive salt marshes, and the islands typical of the Venice lagoon. Moreover, Chesapeake Bay is deep enough (average water depth of 8.5 m against a depth of approximately 1 m in the Venice lagoon) to prevent the emergence of tidal flats during low tide.

[16] Even though the evaluation of nonlinear terms as triad interactions is important for the calculation of wave spectra in shallow waters, the SWAN model is in better agreement with shallow water flume experiments when the triad interactions are neglected [see *Wood et al.*, 2001; *Feola*, 2002].

[17] The detailed calculation of the spectral evolution of wind waves is also computationally expensive [see *Lin et al.*, 2002] thus hindering the applicability of these models to midterm and long-term studies.

[18] Moreover, the instantaneous value of the local water depth is crucial to correctly predict the wave field, since water depths strongly affects wave propagation. Wave prediction can therefore be accomplished only by coupling a hydrodynamic model with a wave model.

[19] A recent attempt to couple a hydrodynamic model with a wave model for the Venice lagoon was made by *Umgiesser et al.* [2002, 2004]. They combined a two-dimensional finite elements model [*Umgiesser and Bergamasco*, 1993] with the finite difference SWAN model run in stationary mode. The hydrodynamic model uses an unstructured mesh reproducing the Venice lagoon comprising 4359 nodes and 7845 triangular elements and a grid size ranging from 50m to 1 km. The SWAN model uses a 100 m regular grid. For consistency, all the results produced by the hydrodynamic model are interpolated to the grid of the wave model, thus introducing significant numerical approximations. It is also worth noting that the coarse grid used by *Umgiesser et al.* [2004] does not allow for an accurate resolution of wave refraction.

[20] Given the irregular bathymetry of the Venice lagoon and the uncertainties affecting the modeling of non linear wave interactions, a simplified, computationally efficient model, which propagates a monochromatic wave, is presented herein. The model reproduces the wind wave generation and propagation inside the lagoon of Venice by solving the wave action conservation equation on an unstructured triangular mesh of arbitrary shape with a first-order finite volume explicit scheme. The wave model is coupled with a hydrodynamic model for tide propagation inside the basin based on a finite element scheme [*D'Alpaos and Defina*, 1995]. Both models share the same computational grid, enabling us to accurately reproduce irregular domains and to correctly account for the interactions between waves and tides. In the model special attention is given to describing all the physical phenomena producing or dissipating wave energy. Wind waves are then combined to tidal currents in order to determine bottom shear stresses necessary to describe erosion patterns in tidal basins.

[21] Numerical simulations reproducing the wind wave field inside the Venice lagoon under different wind and tidal conditions are presented and the results are compared with recent data collected in two field stations. Finally, bottom shear stress distributions are evaluated to assess the potential for sediment resuspension in shallow tidal basins due to the combined action of tidal currents and wind waves.