# Ship Route Oil Spill Modeling: A Case Study of the Northeast Brazil Event, 2019
## 2 Materials and Methods
### Oil Spill Model  
The OSCAR (Oil Spill Contingency And Response) model system, as detailed by [37; 38], serves as a tool for the objective analysis of alternative spill response strategies to contingency, offering valuable insight into hydrocarbon transport, oil fate, and effects during a release and spreading, enabling the simulation of different response strategies and configurations. Key features of OSCAR include three-dimensional modeling of oil in the water column, representation of oil by 25 pseudo-components, an extensive oil database with experimental weathering data, stochastic simulations, consideration of biological effects on marine organisms, and the interaction of oil with various shoreline types. Its applications encompass oil spill risk assessment, response planning, and the modeling of oil spill response operations. The model comprehensively considers weathering, as well as the physical, biological, and chemical processes affecting oil at sea, with a strong connection to laboratory activities at SINTEF focusing on oil weathering. The model conceptualizes oil as particles influenced by currents, winds, and turbulent diffusion, undergoing weathering processes such as evaporation, dissolution, and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Volume of Liquid** & **Cargo Tank** & **Average Tank Size** \\  & **Cargo (m\({}^{3}\))** & **Configuration** & **16** \\ \hline Panamax & 79,214 & 6 \(\times\) 2 & 5611 t (6601 m\({}^{3}\)) \\ Aframax & 122,779 & 6 \(\times\) 2 & 8697 t (10,232 m\({}^{3}\)) \\ Suezmax & 171,009 & 6 \(\times\) 2 & 12,113 t (14,251 m\({}^{3}\)) \\ VLCC & 340,015 & 5 \(\times\) 3 & 19,268 t (22,668 m\({}^{3}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensional parameters of the ships analyzed in oil spill simulations. Adapted from [16]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Volume of Two** & **Percent of the Total** & **Oil Spill Duration** \\  & **Tanks (m\({}^{3}\))** & **Capacity (\%)** & **(h)** \\ \hline Panamax & 13,202 & 16.7 & 3.3 \\ Aframax & 20,464 & 16.7 & 5.1 \\ Suezmax & 28,502 & 16.7 & 7.1 \\ VLCC & 45,336 & 13.3 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters used in oil dispersion modeling. dispersion, governed by process such as surface spreading, advection, entrainment, emulsification, and volatilization to determine transport and fate of oil at the surface. In the water column, horizontal and vertical advection and dispersion of entrained and dissolved hydrocarbons are simulated using random walk procedures. Vertical turbulence is influenced by wind speed (wave height) and depth. Wave height and period calculations derive from 10 m wind data using the JONSWAP spectrum, with fetch limited to 100 km. The model primarily represents local wind-driven waves, important for entrainment and mixing processes. OSCAR employs a stochastic differential equation to simulate transport, representing pollutants as particles sampled at the release location. Wave height is calculated as:  
\[H_{s}=MIN(h_{max},h_{nodim})u^{2}/g \tag{1}\]  
where  
\[h_{nodim}=h_{c}\sqrt{s/t^{2}} \tag{2}\]  
With constant \(h_{max}\) = 0.243, \(h_{c}\) = 0.0016, and \(g\) = 9.81 m s\({}^{-2}\). Fetch is calculated considering the presence of land and ice as in [39]. As referenced in the technical description of the OSCAR model, the transport is simulated as the superposition of a mean local velocity plus a random turbulent component. This is analogous to the advection-diffusion equation, where, in this case, the diffusive step is turbulent diffusion. To achieve transport, pollutants are represented through particles that are sampled at the release location. These particles represent individual solutions of a stochastic differential equation:  
\[dX(t)=(u+\delta_{x}K_{x}(x))dt+\sqrt{6K_{x}(x)}dW(t) \tag{3}\]  
where \(u\) is current velocity, \(K_{x}\) is diffusivity, and \(x\) represents any of the three spatial dimensions.