Spill, Transport and Fate Model (STFM) is a new trajectory and weathering model for handling oil spills, which is under development for application in marine studies and environmental impact assessment (Zacharias et al. 2018). The model is suitable for both research and scientific activities, as well as engineering applications.

In Brazil, STFM is registered at the Instituto Nacional da Propriedade Industrial (INPI − Brazil) under contract: BR512021002447-8

It is a fully three-dimensional model based on Lagrangian elements (LE) that can be coupled in atmospheric, waves and hydrodinamic models. The current version reads the atmospheric and shoreline data directly from the Weather Research and Forecasting (WRF) Model, as also the currents, temperature, salinity, and depth data directlly from the Hybrid Coordinate Ocean Model (HYCOM).

STFM was successfully tested in the mysterious oil spill that occurred off the northeast coast of Brazil in 2019. The model was used in association with scenario trees, allowing the first estimate about the original volume of spilled oil and computationally confirming that the oil trajectory was a subsurface one. (Zacharias et al. 2021a; 2021b).

The behavior of an oil spill in the marine environment is initially governed by ocean and atmospheric conditions, which determine the transport and spread of the slick and by the physicochemical properties of the oil that determine the weathering (Fay, 1971).

The most common model sets involve spreading, advection, diffusion, evaporation, emulsification and dispersion, and they do not consider processes, such as oil dissolution, photo-oxidation, biodegradation and vertical mixing (**Figure 1**). Currently, the uncertainty estimates and timely response to oil spills are lacking in the new generation of oil spill models. Further improvements should emphasize better parametrizations of oil dissolution, biodegradation, entrainment, and prediction of oil particles size distribution.

**METHODOLOGY AND CONCEPTS**

STFM was designed to connect the concepts of particle and box-model, which means that each simulated Lagrangian Element (LE) is also a small box-model with its own mass balance, calculated independently for each LE. This design was particularly useful in simulating the 2019 oil spill off the Brazilian coast, to represent hundreds of small slicks that spread along the shore (Zacharias et al. 2021b).

Advection is the tridimensional transport of the LE caused by winds, currents, and vertical transport due to breaking waves and buoyancy. STFM uses the friction velocity from WRF to calculate the atmospheric drag coefficient and solve the advection (Lynch et al. 2015).

The buoyancy speed is based on Stokes’ law. This velocity is particularly important for undersurface spills or leaks (Mackay et al. 1980).

Spreading is the first effect solved by the STFM when the oil is released. It consists of a horizontal evolution of the slick, resulting from the action of gravity and buoyancy forces, facing the viscosity resistance (Fay 1971, Dodge et al. 1983, and Lynch et al. 2015).

The initial area evolves very quickly (a good number of minutes) compared to the oil slick's lifetime. After a certain moment, turbulent diffusion becomes predominant and spreading reduces to zero, following the increase in viscosity.

Turbulent diffusion is the mass transport inside the oil slick through random and chaotic motions. This effect is usually parameterized in different ways within the Lagrangian models to represent the subgrid scale effects of atmospheric and hydrodynamic models.

STFM solves the Brownian motion of the LE introduced by Langevin’s theory, using the Ornstein-Uhlenbeck process resulting in less abrupt changes in the velocity and position of the Lagrangian particles (Gillespie 1996 and Lynch et al. 2015).

The dissolution process consists in the losses of soluble fractions from the oil slick to the water column. The oil components dissolution rates are much lower than the other weathering effects. Analyzing the mass loss of the slick, dissolution is practically negligible (0-2% loss) when compared to its evaporation (30-90% loss), being this the reason why many models presented in literature do not include dissolution in their formulation (Keramea et al. 2021). However, some specific components, such as benzene, may be of special interest because of their higher dissolution rate and their levels of toxicity to marine life.

The dispersion process of the oil slick consists in the gradual entrance of oil fractions (droplets) in the vertical column of water, and, due to weathering of lighter fractions or the collision/coalescence process with suspended sediment, or the use of dispersants, these droplets no longer return to the surface.

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**PROBABILISTIC MODELS**

Probabilistic models are mathematical models that represent uncertainty or randomness in a system by using probability theory. These models are used to describe and analyze systems or processes where outcomes are not deterministic and can vary based on random variables or unknown factors. In probabilistic models, the emphasis is on capturing the likelihood or probability of different outcomes rather than providing precise predictions.

Probabilistic models make use of probability distributions to quantify and describe the uncertainty associated with different variables or parameters. These models can be used to estimate the likelihood of various events occurring, make predictions, or infer unknown values based on available data. They are widely used in various fields, including statistics, machine learning, artificial intelligence, finance, biology, and engineering.

Monte Carlo Methods: Monte Carlo methods use random sampling techniques to estimate unknown quantities or solve complex problems that involve probabilistic models. They involve generating random samples to approximate the behavior or distribution of interest.

Probabilistic models provide a powerful framework for decision making, risk analysis, and inference in situations where uncertainty plays a significant role. By explicitly accounting for uncertainty, these models enable more robust and realistic analysis of complex systems.

The STFM model was previously used in algorithm tests with offshore oil spill models. The STFM probabilistic model was used in this study to examine the plausibility of the initial areas obtained by LAMCE/COPPE/UFRJ; using particle reverse modeling (Al-Rabeh et al., 1989; Guo, 2017; Zacharias et al., 2018).

The probabilistic model used in this study is composed of several modules, which consist of a combination of hydrodynamic and atmospheric models, an STFM deterministic oil spill module, and a stochastic methodology (Guo, 2017).

The probabilistic model uses a weathering numerical scheme with simplified equations to guarantee computational performance in the face of a large number of simulations.