One-way and two-way coupling

When working in coastal areas the interaction between the wind, waves and currents fields is not negligible, and therefore it is recommendable to couple the different models. Various types of coupling are available, that will be discussed in this chapter. A one-way coupling (also known as offline coupling) is the simplest option that consists in getting results from one model and introduce them as an input into another model. Additionally, there is the option to execute a two-way coupling (or online coupling), so that for each time step both models run in parallel, and every so often they share physical parameters such as the wave height, the current intensity or the atmospheric pressure, thus being able to reproduce more realistically the physical behaviour in coastal areas.

The last decades, the scientific community has begun to consider the currents fields in the wave modelling. Jorda et al. (2007) quantified the importance of cur- rents fields when modelling the waves in a shelf ocean domain. In this study, he concluded that under storm conditions, a decisive contribution of currents on waves is observed, basically due to the wave refraction. Few years later, Benetazzo et al. (2013) modelled the waves coupled to the circulation model for the semi-enclosed Gulf of Venice, obtaining considerably variations of the significant wave height and an increase/decrease of wave spectral energy in situation of opposite/following cur- rents respectively. Some experimental studies have been carried out by Rusu and Soares (2011), compared to wave simulations under different current conditions.

The interaction between surface winds and waves was studied by Charnock (1995). An estimation of the surface drag created by the waves as a function of the wind speed was proposed. More recent studies have revisited the topic propos- ing new parameterizations (e.g Johnson et al., 1998). Few years later, studies using atmospheric and wave models have focused on case studies that analyse many as- pects of the ocean and atmospheric feedbacks (e.g. Warner et al., 2010), which make difficult to generalize results regarding the potential benefit in the lower level wind simulation and its effect on wave forecast as a result of coupling atmospheric and wave models.

The contributions presented above, although quantifying processes related to the three fields (waves-circulation-atmosphere), treat each phenomena separately (which is usually called one-way coupling). This is performed running the different models sequentially and introducing some of the results as inputs for the other models.

Chapter 4. The effect of coupling on the wave modelling in the Catalan Coast

concurrently, using a coupling toolkit to allow the transfer of information between models, which is usually called two-way coupling. Warner et al. (2008a) implemented the SWAN wave model and the circulation model ROMS (Regional Ocean Modelling System; Haidovel et al., 2008; Shchepetkin and Williams, 2005, 2009) coupled in a two-way manner. This coupling was undertaken with the tool Model Coupling Toolkit(MCT; http://www-unix.mcs.anl.gov/mct/ ; Larson et al., 2004; Jacob et al., 2005) and is valid for riverine areas, estuaries, coastal and ocean platform. In this case, the proposed system implements, compiles and executes a parallel models tak- ing into account the influence of currents on waves and waves on currents, but it was not coupled with the atmosphere. The coupling of the three fields at the same time was finally implemented and applied by Warner et al. (2010) under the name of COAWST system (Coupled Ocean-Atmosphere-Wave-Sediment Transport mod- elling system), which executes a system where the three models run concurrently: the wave model SWAN, the circulation modelling ROMS and the non-hydrostatic meteorological model WRF (Weather Research and Forecasting; Skamarock et al., 2005).

Furthermore, some other models have been coupled in a two-way manner with also good results. Bola˜nos et al. (2011) improved the coupling between the cir- culation model POLCOMS (Proudman Oceanographic Laboratory Coastal-Ocean Modelling System; Holt and James, 2001) and the waves model WAM (WAMDI- group, 1988). The previous version (Osuna and Wolf, 2005) worked with a two-way coupled system in two dimensions (with depth-averaged momentum equations) and considered the wave refractions by currents, the bottom friction modification due to wave and current fields, and the increase of the wind stress due to waves. The new version also includes the effects of Stokes drift in the currents and the distri- bution of the surface tension between the waves and currents. This system was evaluated in the North-western Mediterranean sea and the results conclude that currents, typically small in this region, do not have a great effect on the waves while the currents generated by waves, usually caused by a change in wind stress due to the surface roughness of the sea, are not negligible. Other system that has been used to study the circulation and waves in a coupled manner is formed by the wave model STWAVE (STeady State Spectral WAVE; Smith et al., 2001) and the circu- lation mode MOHID (Santos, 1995) implemented in a coastal lagoon off the coast of Portugal (Malhadas et al., 2010). In this case performing a one-way coupling in which the STWAVE wave model results are introduced as an input into the MOHID model, where currents are calculated. Dietrich et al. (2011b) have integrated the SWAN model working with unstructured grids with the circulation and storm surge model ADCIRC (Luettich and Westerink, 1994b) for two hurricane events in the Gulf of Mexico, demonstrating the importance of the wave-circulation interactions

4.2. Background: model coupling

under those conditions.