Environmental Engineering Reference
In-Depth Information
model predictions, which can be used to develop probability contours for emergency
responders [ 39 ]. The present discussion is for a 2D oil spill confined to the water
surface, however there are no theoretical impediments for extension to 3D.
5.8.1 Geometric Uncertainty
A critical decision in the design of any operational oil spill forecast system is in the
choice of the model grids—both for the hydrodynamic model and the oil spill model.
For the hydrodynamic model, geometrical uncertainty is affected by interaction of
the numerical algorithm accuracy, the hydrodynamic model time step, and the grid
cell spacing. Further complexity is added by the choice of unstructured, curvilinear,
or Cartesian grids. The advantages and disadvantages of different grid methods for
hydrodynamics are subjects of ongoing debate; however, from the oil spill modelling
perspective the important issue is that finer model grids provide a more accurate
resolution of the spatio-temporal evolution of the surface currents, and hence reduce
the uncertainty in oil spill modelling associated with hydrodynamics. Unfortunately,
decreasing the grid length scale by 50% in each horizontal direction requires an
increase of the number of horizontal grid cells of 4
×
and a reduction in the model
time step by 50%, which leads to an 8
increase in computational requirements for
only a factor of two improvement in grid resolution. Thus, operational models are a
compromise betweenwhat is desirable andwhat is achievable with the computational
resources at hand. As discussed in Sect. 5.6 , for a practical system the hydrodynamic
model should be able to produce a set of velocities fields for the desired forecast
interval (e.g. 72h) in substantially less than the time between new updated forecasts.
This need inherently limits the practical grid resolution of the hydrodynamic model.
As further issue in geometrical uncertainty, Lagrangian particle transport oil spill
models are faster (and easier to code) for structured model grids (either Cartesian or
curvilinear) because Lagrangian particle models generally operate with each particle
defined by vector position s
×
c k in a 3D space (or 2D for surface models).
To move a particles through space/time, the velocity at the particle's present location
must be interpolated from the velocity field on the hydrodynamic model grid. If a
structured hydrodynamic grid is used, identifying the neighbour velocities is trivial;
however, for an unstructured grid the identification problem can be computation-
ally expensive. Nevertheless, unstructured hydrodynamic models are desirable for
many coastal oceans and embayments. One approach to simplifying the interface
between a Lagrangian particle and unstructured hydrodynamic grid is to “rasterize”
the velocity fields; i.e. interpolate the velocities to a structured grid before com-
puting the Lagrangian particle motion. This adds a second layer of interpolation
(hydrodynamics to raster, raster to Lagrangian particle) and hence another source of
uncertainty.
Geometrical uncertainty cannot be easily evaluated during run-time of an oper-
ational forecast system. Instead, the effects of geometrical uncertainty should be
analyzed during development of the system through model-model comparisons and
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