Operational Oil Spill Modelling: From Science to Engineering Applications in the Presence of Uncertainty - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 104

Monte-Carlo simulation using a range of possible forecasts), but cannot be precisely
known a priori. However as a practical matter, once a modelling system has been
put into operation—that is, the science has been executed to minimize epistemic
uncertainty as much as practical for available resources—then any uncertainty in
the system, whether aleatoric or epistemic, is essentially irreducible. Thus, we need
practical methods for evaluating uncertainty during both model building (to focus
our efforts in uncertainty reduction) and model operation (to understand effects of
remaining uncertainty).
5.5 Model Design and Parameters Affecting Uncertainty
The generic forecast system of Fig. 5.1 includes models with a wide variety of para-
meters and settings that affect uncertainty. Many parameters are specific to particular
model designs; but the following provides an overview of some of the more common
parameters.
5.5.1 Oil Spill Model Time Step
The time step used for the Lagrangian integration of oil spill movement is a control
on the relationships between space, time, and the partitioning of transport between
advection and a stochastic model of diffusion. Coastal ocean studies have typically
used 30minute time steps consistent with their spatial resolution andwater velocities,
e.g. [ 22 , 39 ]. For higher-resolution models close to shore, smaller time steps are
typically necessary for velocity fields that are more highly variable in time and
space.
5.5.2 Numerical Scheme
Oil spill transport models can be coded with different options for transport. The
simplest Lagrangian models are 1st-order forward Euler transport, which use time n
velocity contributions at a particle position to compute the particle displacement, as
in Eq. ( 5.1 ) above. However, such simple models are recognized as having limited
accuracy [ 5 ]. The Runge-Kutta 4th-order (RK4) is a popular high-order method as it
takes into account the changing velocity field over a particle path. Although the RK4
itself is computationally efficient, its overall performance depends on the speed of
the interpolation scheme from the hydrodynamic model grid to an arbitrary particle
location. For an unstructured (triangular or generalized polyhedron) hydrodynamic
grid, this interpolation can be computationally expensive.