SUMMARYIn this work, we present a finite element model to approximate the modified Boussinesq equations. The objective is to deal with the major problem associated with this system of equations, namely, the need to use stable velocity-depth interpolations, which can be overcome by the use of a stabilization technique. The one described in this paper is based on the splitting of the unknowns into their finite element component and the remainder, which we call the subgrid scale. We also discuss the treatment of high-order derivatives of the mathematical model and describe the time integration scheme.

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Port infrastructure is strategic for local, regional and global economic growth and development. They play a crucial role as transportation hubs and gateways for the vast majority of goods transported around the world, linking local and national supply chains to global markets. Moreover, demands on ports are likely to grow in the light of expected increases in world freight volumes, due to shipping efficiency and its smaller carbon footprint compared to other modes of transport (Becker et al., 2012). Other economic activities, including industry, tourism and fisheries, also flourish around seaports. Thus, any significant disruption in the logistics of seaports can have significant economic implications (Chhetri et al., 2014). Service disruptions alone can cause considerable economic losses in the order of billions of dollars and may have important second-order consequences, not only for regional economies and the quality of life of those who depend directly on the port's functionality, but also for the operation of global supply-chains (Becker et al., 2013). Due to the type of businesses held around them, seaports are located in one of the most vulnerable areas to climate change impacts, i.e. coastal areas susceptible to sea level rise and increased storm intensity and/or mouths of rivers susceptible to flooding (Becker et al., 2012). Despite this, attention to climate-related impacts in ports is relatively recent (McEvoy et al., 2013). The first international benchmark studies consisted of an analysis of the most vulnerable to climate change port cities in 2070 (Nicholls et al., 2008) based on population and asset exposure to water levels defined as one hundred year storm surge, and a worldwide survey sent to Port Authorities to detect sectorial perceptions regarding port risks due to climate change (Becker et al., 2012), respectively. The first step in the evaluation of climate change impacts on ports involves reviewing all potential impacts and identifying the main marine variables and the databases available where this information is included (Sánchez