1) OpenOil model: This study uses OpenDrift’s OpenOil module to simulate the 2024 Tobago oil spill’s transport and weathering. OpenOil models oil as individual particles (Lagrangian elements) with properties like mass, viscosity, and density, enabling detailed tracking of oil behavior under Tobago’s conditions. Particle movement is driven by ocean currents, wind, Stokes drift, and random walk diffusion. The model includes physical processes such as wave entrainment [19] , turbulence-driven mixing [20] , buoyancy-driven resurfacing [21] , and emulsification [22] . Resurfacing depends on droplet size and density, with sinking velocity based on Stokes Law, making droplet size distribution critical [23] . Oil properties come from the ADIOS database, covering nearly 1000 oil types worldwide [24] .

2) Wind Data: Wind data were obtained from the Global Ocean Hourly Sea Surface Wind and Stress product, offering hourly wind and stress fields at 0.125˚ resolution. This dataset combines scatterometer data from Metop-B and Metop-C ASCAT with ECMWF model outputs, using temporally-averaged difference fields to correct model biases. It also includes divergence, curl, bias corrections, and variance measures [25] . Linear interpolation refined the data to 0.0045˚, but this higher resolution had minimal impact on oil particle movement while greatly increasing computational cost.

3) Hydrodynamic Data: The Operational Mercator Global Ocean Analysis and Forecast System provides daily-updated, 10-day 3D global ocean forecasts at 1/12˚ resolution. It aggregates data into a two-year sliding window, offering daily and monthly averages of temperature, salinity, currents, sea level, mixed layer depth, and ice conditions from surface to 5500 m depth across 50 vertical levels. Hourly surface data for sea level, temperature, and currents are also included. The data use a regular longitude/latitude projection. A specialized dataset, SMOC, merges surface currents with wave and tidal drift information [26] .

4) Wave Data: The Météo-France global ocean wave forecast system provides daily analyses and 10-day forecasts of sea surface waves at 1/12˚ resolution. It delivers 3-hourly fields for wave parameters like significant wave height, period, direction, and Stokes drift, including partitions for wind waves and primary/secondary swells. Based on the MFWAM third-generation model using ECWAM-IFS-38R2 code, it incorporates dissipation and bathymetry from ETOPO2/NOAA. The irregular grid spacing decreases near the poles, with ~1/10˚ spacing at the equator. Driven by 6-hourly ECMWF wind analyses and 3-hourly forecasts, the wave spectrum is discretized into 24 directions and 30 frequency bands (0.035 - 0.58 Hz). Altimeter data assimilation occurs every 6 hours. Analyses run four times daily, starting at 00:00 UTC [27] .

The simulations incorporate key physical processes affecting oil transport: 1) horizontal transport driven by currents, Stokes drift, and wind drift; and 2) vertical transport and mixing, including wave breaking, buoyancy-driven resurfacing, and turbulence-driven vertical movement.

Oil particles move horizontally due to advection by currents, wind, and waves. Whether submerged or at the surface, they follow ambient currents and experience wind drift, typically about 1% - 6% of surface wind speed (averaging 3%). They are also affected by surface Stokes drift, modeled using the Phillips spectrum [28] .

1) Wave entrainment: Wave entrainment refers to the process by which particles in the water are moved during stormy conditions and when waves break in the open sea. The mixing of oil near the surface in open seas is largely influenced by the energy from breaking waves [29] . To understand wave entrainment more thoroughly, several factors are considered, such as the thickness, density, and viscosity of the oil, the oil-water surface tension, water density, gravity, the energy available from breaking waves to lift the oil, and the extent of the sea surface affected by breaking waves [19] . The rate of oil entrainment, Q, is described using two dimensionless numbers: Weber (We) and Ohnesorge (Oh). The equation for entrainment is given by:

$Q=Q_0{F}_{bw}$ (1)

$Q_0=aW{e}^{b}O{h}^c$(2)

$Q=4.604\times {10}^{-10}W{e}^{1.805}O{h}^{-1.023}{F}_{bw}$(3)

$F_{bw}=\{\begin{array}{ll}{a}_{bw}\frac{U_{10m}-U_o}{T_p},\hfill & \text{if}{U}_{10m}>U_o\hfill \\ 0,\hfill & \text{if}{U}_{10m}\le U_o\hfill \end{array}$(4)

The Weber number (We) helps determine how much inertial forces and oil-water surface tension play a role [31] . It is calculated as:

$We=\frac{{\rho }_{sw}g{H}_s{d}_o}{{\sigma }_{ow}}$(5)

$d_o=4\sqrt{\frac{{\sigma }_{ow}}{g\left({\rho }_{sw}-{\rho }_{oil}\right)}}$(6)

The Ohnesorge number (Oh) describes the balance between viscous forces and inertial or surface tension forces [31] . It is calculated using the oil’s dynamic viscosity (μ_oil = 9.02 cPoise for Generic Light Crude), the oil density, the oil-water surface tension, and the Rayleigh-Taylor instability diameter:

$Oh=\frac{{\mu }_{oil}}{\sqrt{{\rho }_{oil}{\sigma }_{ow}{d}_o}}$(7)

2) Oil resurfacing: Oil droplets in the water can rise back to the surface due to buoyancy, resulting in either resurfaced or submerged droplets depending on their size and density difference relative to the surrounding water [31] . The rate at which droplets rise is governed by their radius and the density contrast between oil and seawater. According to Tkalich and Chan [21] , different formulas apply depending on droplet size: small droplets follow Stokes’ law, while larger droplets are calculated using Reynolds’ law. The vertical terminal velocity w is given by:

$w\left(r\right)=\{\begin{array}{ll}\sqrt{\frac{16}{3}g\left(1-\rho \right)r},\hfill & \text{if}Re>50\hfill \\ \frac{2g\left(1-\rho \right)}{9v_{sw}}{r}^2,\hfill & \text{if}Re\le 50\hfill \end{array}$(8)

Typical rise velocities vary greatly with droplet size and density. For example, a droplet with a diameter of 0.01 mm and density 900 kg/m³ may rise at around 1 cm per hour, while a 0.5 mm droplet can ascend at up to 30 meters per hour [31] . Liu et al. [32] further reported that a 4 mm droplet with a density of 870 kg/m³ can achieve a rise speed as high as 0.095 m/s.

3) Oil droplet distribution: When an oil droplet is released during a subsea blowout, it begins a slow ascent toward the surface. At such depths, droplet sizes vary considerably—ranging from as small as 0.1 mm (100 µm) to as large as 0.5 mm (500 µm) [33] . The rate at which these droplets rise is strongly influenced by their size: larger droplets ascend more rapidly due to greater buoyancy, while smaller droplets tend to remain suspended and are more readily transported by deep-sea currents. Research by Johansen et al. [34] and Li et al. [19] indicates that the distribution of oil droplet sizes is best described by a lognormal distribution. In this framework, the volume-based median droplet diameter ( $D_{50}^V$) serves as a key parameter to characterize the size spectrum. According to Li et al. [19] , $D_{50}^V$ can be calculated using the following equation:

$D_{50}^V=d_o{r}_e{\left(1+10Oh\right)}^{p}W{e}^q$(9)

The size distribution follows a lognormal distribution, where the probability density function (PDF) is given by:

$PDF=\frac{1}{ds\sqrt{2\pi }}\exp \left(-\frac{{\left(\ln d-\ln D_{50}^V\right)}^2}{2s^2}\right)$(10)

Finally, the volume size distribution, as described by Delvigne and Sweeney [35] , is:

$V\left(d\right)=d^{-0.7},d\in \left[d_{\min },d_{\max }\right]$(11)

4) Turbulent mixing: Turbulent mixing plays a critical role in redistributing oil droplets vertically in the water column, driven by factors such as wind speed, current shear, stratification, and the dissipation of wave energy. The strength of this vertical mixing is quantified by the vertical eddy diffusivity coefficient, K(z), as described by Visser [36] . In Lagrangian particle tracking models, the vertical movement of oil droplets is commonly simulated using a random walk approach. This stochastic method accounts for both deterministic and random influences on particle displacement. The vertical displacement of a droplet (∆z) over a time interval (Δt) can be calculated as:

$\Delta z=K^{\prime }\left(z_n\right)\Delta t+R\sqrt{\frac{2}{r_s}K\left(z_n+\frac{K^{\prime }\left(z_n\right)\Delta t}{2}\right)\Delta t}$(12)

OpenOil integrates advanced parameterizations of key oil weathering processes, including 1) dispersion, 2) evaporation, 3) emulsification, and 4) biodegradation. These processes are modeled using oil properties sourced from NOAA’s ADIOS (Automated Data Inquiry for Oil Spills) Oil Library. The evaporation rate varies considerably depending on oil type and environmental conditions such as wind speed [31] . Both evaporation and emulsification substantially alter the oil’s density, viscosity, and interfacial tension, which in turn affect the droplet size distribution [23] .

1) Dispersion: The dispersion process simulates the entrainment of oil droplets into the water column, primarily driven by turbulence generated at the ocean surface by wind and waves [37] . In OpenOil, dispersion is modeled using the Delvigne and Sweeney [35] approach, which estimates wave energy dissipation—the energy lost due to wave breaking—calculated as:

$D_e=0.0034\times g{\rho }_{sw}{H}_s^2$(13)

A critical parameter is the wave energy dissipation coefficient (c_disp), representing the fraction of dissipated energy contributing to oil dispersion:

$c_{disp}={\left(D_e\right)}^{0.57}{f}_{bw}$(14)

The oil dispersion rate into the water column (q_disp) is then computed as:

$q_{disp}=\frac{c_{Roy}{c}_{disp}{V}_{entrain}}{{\rho }_{oil}}$(15)

2) Evaporation: OpenOil adjusts its evaporation modeling based on the prevailing conditions of the oil slick [24] . Under calm weather, when the slick remains smooth and undisturbed, evaporation is simulated using Mackay’s analytical model [38] . In contrast, during rough sea states, OpenOil applies a more detailed approach based on the ADIOS2 framework, which employs a pseudo-component evaporation model [39] . In this model, crude oils and refined products are represented by a limited set of discrete, non-interacting components, each characterized by its own vapor pressure. The evaporation rate of each component depends on factors including wind speed, sea surface temperature, slick thickness, the component’s molar fraction, and its volume. The molar volume of each pseudo-component is estimated using empirical correlations with alkane boiling points, enabling the calculation of vapor pressure through Antoine’s equation [40] .

3) Emulsification: OpenOil simulates emulsification following the approach of Lehr et al. [24] , incorporating key factors such as oil weathering, evaporation, water content, and droplet size distribution. Once emulsification initiates, the model calculates the growth of the oil–water interfacial area over time, driven by wave energy and wind speed. This interfacial area is capped by a maximum value (S_max) of 5.4 × 10⁷ m², determined by the oil’s properties and droplet characteristics. The water fraction (Y) within the emulsion is dynamically updated based on the relationship between interfacial area and droplet size, expressed as:

$Y=\frac{S{d}_w}{6+S{d}_w}$(16)

4) Biodegradation: Biodegradation plays a critical role in the natural attenuation of marine oil spills, gradually reducing their environmental impact. The rate of biodegradation depends on factors such as hydrocarbon type, temperature, microbial communities, and the availability of oxygen and nutrients. In OpenOil, the biodegradation process follows the model proposed by Adcroft et al. [41] , emphasizing the influence of temperature. The total biodegradation time (R⁻¹), expressed in days, is calculated as:

$R^{-1}=12\text{days}\times 3^{\left(20˚\text{C}-T\right)/10˚\text{C}}$(17)

The numerical simulation for oil spill dispersion was conducted using the OpenOil model, a Lagrangian particle-tracking system integrated with atmospheric and oceanographic forcing data. The case study examined a continuous oil spill caused by a shipwreck off the coast of Tobago on February 7, 2024 ( Figure 1 ). The model incorporated multiple environmental datasets—including wind fields, ocean currents, bathymetry, and wave data—to simulate the trajectories of oil particles and their interaction with the marine environment. The spill involved an estimated 35,000 barrels of oil. Using a standard conversion factor (1 barrel = 0.1589872949 m³) and the given oil density of 854.2 kg/m³, this volume corresponds to approximately 5564.56 cubic meters (m³) of oil. An overview of the input parameters and data sources is provided in Table 1 .

To analyze the transport characteristics of simulated oil particles, we implemented a computational approach within the OpenOil python framework. This involved extracting movement data, calculating directional trends, and assessing key transport metrics such as distance and velocity. Longitude and latitude coordinates were retrieved at each time step, and their differences were used to compute displacement, movement angles, and the dominant movement direction. Trajectory characteristics, including total distance traveled, segment-wise distances, and particle velocities, were derived and stored for further analysis. Mean speed and travel distance were also calculated, excluding stationary particles to ensure accuracy. The initial release point of the Tobago shipwreck oil spill was derived from the Trinidad and Tobago Weather Center [13] .

To validate the simulated oil spill trajectories, high-resolution satellite imagery was obtained from the Copernicus Data Space Ecosystem. Both optical and radar datasets were selected to coincide with critical dates in the spill’s progression.

In both cases, photointerpretation techniques were employed to manually delineate the extent of the surface oil slicks. The affected areas were digitized based on variations in tone, texture, and spatial context, informed by knowledge of local wind and current conditions. The delineated areas were exported as vector shapefiles and reprojected to a common coordinate system (WGS84). The resulting masks served as ground truth for quantitative comparison with OpenOil simulation outputs.

To assess the performance of the OpenOil model, the forecasted oil slick coverage was compared with the actual oil slick extent observed through in situ observations, Sentinel-1 and Sentinel-2 images. The comparison led to the establishment of two key performance metrics. While the first have been widely used in flood modeling for comparing model results with satellite data [42] , the second metric has recently been introduced to oil spill modeling [43] [44] .

1) Success Rate (SR): The SR measures the overlap between the model’s predicted oil spill area and the actual spill area as derived from observations and satellite images. It is calculated as:

$SR=\frac{Overlappedarea}{Totalactualarea}$ (18)

2) Centroid Skill Score (CSS): The Centroid Skill Score (CSS) evaluates how closely the predicted centroid of the oil spill matches the observed centroid. It begins by calculating the Initial Centroid Displacement Index (CI), which measures the distance between the centroids of the actual and modeled oil spill areas. The CI is defined as:

$CI=\frac{\Delta x_{centroid}}{L_{box}}$(19)

The Centroid Skill Score (CSS) is then calculated as:

$CSS=\{\begin{array}{ll}1-\frac{CI}{C_{thr}}\hfill & \text{if}CI<C_{thr}\hfill \\ 0\hfill & \text{if}CI\ge C_{thr}\hfill \end{array}$(20)