11 Applications of an Oil Drift and Fate Model for Fairway Design
375
The resulting trajectory ensemble is represented at any future instant t 1 by a particle
‘cloud’ as typical in ensemble modelling (Vandenbulcke et al. 2009). Summing up
and averaging each particle’s state vector over the particle cloud gives information
about the overall spill state: total volume, mean thickness, average position and
composition at that point in time.
The atmospheric and ocean models only resolve motions, the horizontal extension of which exceeds their grid size, but water particles and oil parcels are also
impacted by small-scale (turbulent) processes that are not resolved by the modelled basic forcing fields. There are many possible means to simulate the impact
of subgrid-scale processes on the statistics of calculated trajectories as described in
Chaps. 3, 7 or 10. Dick and Soetje (1990) introduced a pseudo-random, properly
scaled perturbation to the advection velocity to simulate the contribution of local
turbulence to the forcing fields. The perturbation is a vector sum of the impact of
the three-dimensional (3D) ocean current, wind drift (typically 3–3.5 % of the wind
speed at the surface, decreasing with depth), downward wave-induced mixing, and
a non-isotropic horizontal spreading velocity. The latter depends on the wind velocity and acts to elongate the particle cloud in the wind direction. A substitute of the
Brownian motion is also added to replicate the slow horizontal spreading of a spilled
substance with time as
√
t. This perturbation is active even in the total absence of
external forcing. The trajectories of oil parcels are three-dimensional and may reach
the sea bottom. When an oil particle sinks to the sea bed or reaches the shore, it
is assumed to settle and leave the water phase as in Höglund and Meier (2012). In
particular, all chemical processes come to a halt as the particle reaches the sea bed
or the shore.
For object tracking, the density of trajectories in such an ensemble may be interpreted as a probability distribution of the occurrence of this object at a particular location or time instant. For distributed substances, this ensemble is commonly
interpreted as representing natural spreading (or even splitting up) of the spill as
particles separate from each other. Each single trajectory may still be regarded as
being deterministic, pertaining to a certain fraction of the spill.
The trajectory approach reduces the ensemble prediction method to a manageable-size problem in real-time applications, where the calculation speed is an issue.
The key simplification is that it is only necessary to insert perturbations into the
advection velocity along trajectories. Weather or ocean model ensembles, in which
the entire flow field is perturbed and updated, typically have 20–50 members. Trajectory ensembles produced by drift models may be by 1–2 orders of magnitude
larger.
When the pollutant stems from a point or a line source, and within limited time,
the calculation of trajectories is much faster than the so-called grid point method
in which the spatio-temporal changes in the pollutant concentration are evaluated
basically for the entire basin. Apart from the replication of the general properties of
water masses (temperature, salinity), the grid point method is normally used to simulate spreading from more or less permanent point sources, e.g., river outlets which
supply the potential pollutants basically continuously, and these pollutants may influence the entire water body. The relevant calculations of advection and fate of, say,
375
The resulting trajectory ensemble is represented at any future instant t 1 by a particle
‘cloud’ as typical in ensemble modelling (Vandenbulcke et al. 2009). Summing up
and averaging each particle’s state vector over the particle cloud gives information
about the overall spill state: total volume, mean thickness, average position and
composition at that point in time.
The atmospheric and ocean models only resolve motions, the horizontal extension of which exceeds their grid size, but water particles and oil parcels are also
impacted by small-scale (turbulent) processes that are not resolved by the modelled basic forcing fields. There are many possible means to simulate the impact
of subgrid-scale processes on the statistics of calculated trajectories as described in
Chaps. 3, 7 or 10. Dick and Soetje (1990) introduced a pseudo-random, properly
scaled perturbation to the advection velocity to simulate the contribution of local
turbulence to the forcing fields. The perturbation is a vector sum of the impact of
the three-dimensional (3D) ocean current, wind drift (typically 3–3.5 % of the wind
speed at the surface, decreasing with depth), downward wave-induced mixing, and
a non-isotropic horizontal spreading velocity. The latter depends on the wind velocity and acts to elongate the particle cloud in the wind direction. A substitute of the
Brownian motion is also added to replicate the slow horizontal spreading of a spilled
substance with time as
√
t. This perturbation is active even in the total absence of
external forcing. The trajectories of oil parcels are three-dimensional and may reach
the sea bottom. When an oil particle sinks to the sea bed or reaches the shore, it
is assumed to settle and leave the water phase as in Höglund and Meier (2012). In
particular, all chemical processes come to a halt as the particle reaches the sea bed
or the shore.
For object tracking, the density of trajectories in such an ensemble may be interpreted as a probability distribution of the occurrence of this object at a particular location or time instant. For distributed substances, this ensemble is commonly
interpreted as representing natural spreading (or even splitting up) of the spill as
particles separate from each other. Each single trajectory may still be regarded as
being deterministic, pertaining to a certain fraction of the spill.
The trajectory approach reduces the ensemble prediction method to a manageable-size problem in real-time applications, where the calculation speed is an issue.
The key simplification is that it is only necessary to insert perturbations into the
advection velocity along trajectories. Weather or ocean model ensembles, in which
the entire flow field is perturbed and updated, typically have 20–50 members. Trajectory ensembles produced by drift models may be by 1–2 orders of magnitude
larger.
When the pollutant stems from a point or a line source, and within limited time,
the calculation of trajectories is much faster than the so-called grid point method
in which the spatio-temporal changes in the pollutant concentration are evaluated
basically for the entire basin. Apart from the replication of the general properties of
water masses (temperature, salinity), the grid point method is normally used to simulate spreading from more or less permanent point sources, e.g., river outlets which
supply the potential pollutants basically continuously, and these pollutants may influence the entire water body. The relevant calculations of advection and fate of, say,