5 Operational Oil Spill Modelling: From Science to Engineering Applications …
119
For the modelled conditions, it is clear that γ = 0.5 % should be preferred, and
that both decreasing or increasing the drag will increase the error. Note that the γ
derived herein is merely illustrative for the particular model and conditions, and
should not be taken as a recommended value for other models or conditions.
The “best” drag coefficient for an oil spill model is a subject of ongoing research,
and arguably depends on interactions between the modelled hydrodynamics and the
oil spill. That is, our operational goal is to predict the probable movement of an
oil spill, and the best γ is the one that compensates for the difference between the
modelled transport of near-surface currents (U current ) and the real transport. If the
hydrodynamic model poorly predicts the near-surface current effects, then the best
γ will be different than what would be used with a hydrodynamic model that has
better predictions. Thus γ will inherently be uncertain and a multi-model operational
system (Sect. 5.6) should include oil spill models with at least three γ values (low,
high, best) to cover a range of possible results. In particular, using a γ = 0 as a
lower bound provides the expected transport for subsurface oil, and can be useful for
oil spill models that are otherwise confined to modelling 2D surface transport (e.g.
GNOME, [58]).
5.8.3 Diffusivity
The physical diffusion of oil into water is a very slow process, and is generally
not represented in an oil spill model. Indeed, by definition the Lagrangian particles
used in oil spill models are unitary and cannot diffuse. Instead, the “diffusivity”
(or dispersion) model for Lagrangian particles is designed to represent the transport
processes and turbulence effects that are not resolved in either the hydrodynamic
model or the oil spill model itself [10]. A stochastic approach to diffusivity is to
modify Eq. (5.1) to include a diffusion term for each particle as
x
n+1
= x
n
+ Δt (U wind + U wave + U current ) + δx diff
(5.2)
where δx diff represents a vector random walk added to the deterministic particle
motion from the U terms. A diffusion rate (D) resulting in a normal distribution over
time Δt will have a variance σ 2 = 2DΔt, such that the standard deviation (σ ) is
an expected length scale for diffusive transport [8]. A random walk distance vector
can be modelled using the ratio of the variance of the diffusivity to the variance of a
random number generator, e.g. [25, 36], as:
δx diff = R
2D Δt
σ 2
(5.3)
where R is a uniform random number vector in the range [−1, 1] with a vanishing
mean and a variance of σ 2 = 1/3. Note that Δt here is the time step of the oil spill
model, which is not necessarily the same as the time step of the hydrodynamic model.
119
For the modelled conditions, it is clear that γ = 0.5 % should be preferred, and
that both decreasing or increasing the drag will increase the error. Note that the γ
derived herein is merely illustrative for the particular model and conditions, and
should not be taken as a recommended value for other models or conditions.
The “best” drag coefficient for an oil spill model is a subject of ongoing research,
and arguably depends on interactions between the modelled hydrodynamics and the
oil spill. That is, our operational goal is to predict the probable movement of an
oil spill, and the best γ is the one that compensates for the difference between the
modelled transport of near-surface currents (U current ) and the real transport. If the
hydrodynamic model poorly predicts the near-surface current effects, then the best
γ will be different than what would be used with a hydrodynamic model that has
better predictions. Thus γ will inherently be uncertain and a multi-model operational
system (Sect. 5.6) should include oil spill models with at least three γ values (low,
high, best) to cover a range of possible results. In particular, using a γ = 0 as a
lower bound provides the expected transport for subsurface oil, and can be useful for
oil spill models that are otherwise confined to modelling 2D surface transport (e.g.
GNOME, [58]).
5.8.3 Diffusivity
The physical diffusion of oil into water is a very slow process, and is generally
not represented in an oil spill model. Indeed, by definition the Lagrangian particles
used in oil spill models are unitary and cannot diffuse. Instead, the “diffusivity”
(or dispersion) model for Lagrangian particles is designed to represent the transport
processes and turbulence effects that are not resolved in either the hydrodynamic
model or the oil spill model itself [10]. A stochastic approach to diffusivity is to
modify Eq. (5.1) to include a diffusion term for each particle as
x
n+1
= x
n
+ Δt (U wind + U wave + U current ) + δx diff
(5.2)
where δx diff represents a vector random walk added to the deterministic particle
motion from the U terms. A diffusion rate (D) resulting in a normal distribution over
time Δt will have a variance σ 2 = 2DΔt, such that the standard deviation (σ ) is
an expected length scale for diffusive transport [8]. A random walk distance vector
can be modelled using the ratio of the variance of the diffusivity to the variance of a
random number generator, e.g. [25, 36], as:
δx diff = R
2D Δt
σ 2
(5.3)
where R is a uniform random number vector in the range [−1, 1] with a vanishing
mean and a variance of σ 2 = 1/3. Note that Δt here is the time step of the oil spill
model, which is not necessarily the same as the time step of the hydrodynamic model.