The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine surface oil slick numerical model and rewrites the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particle variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998, 2006; Zodiatis et al., 2008a). Part 2 of this paper describes the applications of the model to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.

In this paper we use MEDSLIK-II, a Lagrangian marine surface oil spill model described in Part 1 (De Dominicis et al., 2013), to simulate oil slick transport and transformation processes for realistic oceanic cases, where satellite or drifting buoys data are available for verification. The model is coupled with operational oceanographic currents, atmospheric analyses winds and remote sensing data for initialization. The sensitivity of the oil spill simulations to several model parameterizations is analyzed and the results are validated using surface drifters, SAR (synthetic aperture radar) and optical satellite images in different regions of the Mediterranean Sea. It is found that the forecast skill of Lagrangian trajectories largely depends on the accuracy of the Eulerian ocean currents: the operational models give useful estimates of currents, but high-frequency (hourly) and high-spatial resolution is required, and the Stokes drift velocity has to be added, especially in coastal areas. From a numerical point of view, it is found that a realistic oil concentration reconstruction is obtained using an oil tracer grid resolution of about 100 m, with at least 100 000 Lagrangian particles. Moreover, sensitivity experiments to uncertain model parameters show that the knowledge of oil type and slick thickness are, among all the others, key model parameters affecting the simulation results. Considering acceptable for the simulated trajectories a maximum spatial error of the order of three times the horizontal resolution of the Eulerian ocean currents, the predictability skill for particle trajectories is from 1 to 2.5 days depending on the specific current regime. This suggests that re-initialization of the simulations is required every day.

Coastal vegetation can reduce extreme water levels during storm events, but the controlling factors and processes in complex estuary or delta systems are still unclear. This limits an effective implementation of nature-based coastal defences in delta mega-cities in low-lying coastal areas. Here we have numerically modelled how mangroves can offer coastal protection to the large coastal cities located in the Pearl River Delta (China), such as Guangzhou and Shenzhen, during strong typhoons, like Hato (2017). Water level attenuation by mangroves is effective during extreme water level conditions and differences in mangrove forests’ properties drive their coastal protection function. The local (within-wetland) attenuation of extreme water levels is more effective with wide vegetation patches and higher vegetation drag. Narrower vegetation patches can still provide non-local (upstream) water level attenuation if located in the upper estuary channels, but their design needs to avoid amplification of water levels in other delta areas.

The Pearl River Delta contains the world's largest urban area in both size and population. It is a low‐lying flood‐prone coastal environment exposed to sea level rise (SLR) and extreme water levels caused by typhoons. A Finite Volume Community Ocean Model implementation for the South China Sea and the Pearl River Delta is used to understand how future SLR, tides, and typhoon storm surges will interact and affect coastal inundation. The SLR signal and extreme surge levels provide the major contributions to flooding; however, amplification of tides could exceed 0.5 m for 2.1 m SLR and should be considered when planning future coastal defences. On the other hand, if typhoons like Hato or Mangkhut, the latest and strongest ones hitting the area, were to happen in the future, a surge level reduction up to 0.5 m could be expected in coastal areas.