Operational Oil Spill Modelling: From Science to Engineering Applications in the Presence of Uncertainty - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 100

turbulence in the ocean surface layer, and advective processes smaller than the grid
scale of the hydrodynamic model. Chemical processes lead to degradation and trans-
formation of the spill (e.g. spreading, emulsification, dissolution, evaporation [ 57 ]),
which can reduce the surface oil volume and change the oil response to physical
forcing. For example, emulsified oil “tarballs” take on the density of the surrounding
water and will sink below the water surface if advected into a region of warmer (less
dense) water. Near-surface submerged tarballs can be affected by currents diverging
from the surface currents, resulting in different transport paths.

5.2.4 Visualization and Analyses

The output from an oil spill model is the time evolution of the expected location,
composition, and extent of spilled oil. Ideally, an integrated operational systemwould
include visualization of a probability envelope for the future spill positions, much
as is done in the hurricane/typhoon forecasting community. However, present oil
spill visualizations are generally based on producing either a snapshot map of rep-
resentative oil spill particle trajectories (i.e. a “spaghetti” diagram), or a movie of
an evolving point cloud of particles. As Geographical Information Systems (GIS)
become more powerful and usable over mobile platforms (e.g. smart phones, tablets),
oil spill visualization systems should employ GIS standard formats for output data to
allow web-based access for emergency response personnel. Standardization within
a GIS also allows spill trajectories to be linked to existing Environmental Sensi-
tivity Indexes that classify sensitive coastal areas by their degree of exposure and
vulnerability [ 20 ].

5.3 Oil Spill Models

Oil spill models typically represent the spill as a collection of mass-less particles
moving passively with the water and without any particle-particle interaction. These
Lagrangian particles are advected based on modelled fields of the wind, waves, and
currents in a deterministic fashion: as the simplest example, given a position vector
of a single particle at time step n as x n , the position at succeeding time step n + 1is

given by

x n + 1 x n = + ʔ t ( U wind + U wave + U current ) (5.1)

where t is the particle transport time step and the U vectors are the modelled effects

of wind, waves and currents on the particle. Note these are not the wind, wave,
and current velocities themselves, but their modelled net effects with the underlying
assumption of linear superposition. More complex algorithms are often used in place
of the simple explicit Euler scheme above, e.g. the Runge-Kutta 4th-order (RK4) [ 6 ].
The U fields are typically based on coarse spatial and temporal scales relative to the

ʔ