Operational Oil Spill Modelling: From Science to Engineering Applications in the Presence of Uncertainty - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 102

5.4.1 Structural Uncertainty

Choices made in governing equations (e.g. use of hydrostatic instead of
non-hydrostatic equations for a hydrodynamic model) and choices made in develop-
ing a discrete version of the equations (e.g. grid scale, time step, numerical solution
method) contribute to an underlying structural uncertainty, which imposes limitations
on how well the model can represent the actual physics. This structural uncertainty
exists for both geophysical and oil spill models.

5.4.2 Empirical Parameter Uncertainty

Any oil spill modelling system has dozens, if not hundreds, of parameters; e.g. coef-
ficients for sub-models of turbulence, wind/wave drag, and oil spreading. Parameters
are typically selected based on combinations of laboratory studies, prior field studies,
theory, and modelling experience. Unfortunately, one can never be sure of having the
exactly “correct” set of parameters—even if we simply define “correct” as the set of
parameters for a given model structure that provides a prediction within some desired
accuracy. To add further complexity, parameters are often used to compensate for
model structural errors and thus cannot always be taken from experiments or theory
without considering the model formulation. For example the turbulent eddy diffusion
coefficient in a hydrodynamic model is typically a function of the local shear stress;
at different grid scales the resolved shear will have different values and hence needs
different eddy diffusion coefficients to match real-world physics. Furthermore, if
the hydrodynamic eddy diffusion coefficient is overestimated then a corresponding
underestimate of oil spill diffusion might be necessary for a highly-accurate predic-
tion. We generally do not know whether a particular parameter is over- or under-
estimated, so it is impossible to specifically set compensating parameters; as a result,
there are multiple layers of interaction between parameter uncertainties.

5.4.3 Initial Condition Uncertainty

The output from an oil spill forecast system is subject to initial condition (IC) uncer-
tainty for both the oil spill event and the geophysical forcing models. The IC uncer-
tainty for the oil spill includes the initial volume [ 55 ] and the near-field forces that
give shape to the initial slick. In some cases the chemical composition of the oil
might also be uncertain at the time of the spill [ 37 ]. In contrast to this irreducible oil
spill IC uncertainty, the geophysical forcing IC uncertainty can be readily addressed
by having geophysical models that are continuously (or periodically) running. When
a hydrodynamic model is started at some time t 0, the initial velocity field over

the entire model domain is typically zero because we do not have sufficient data
for anything more complex. There is some spin-up time that it takes a model to

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