296
T. Soomere
9.3.3 Reconstruction of Trajectories of Water Particles
Calculation of a Lagrangian trajectory of a particle, carried passively by sea currents, is equivalent to solving the Cauchy problem for a simple system of differential
equations
dX
dt
= u,
dY
dt
= v,
dZ
dt
= w,
X t=t 0 = x 0 ,
Y t=t 0 = y 0 ,
Z t=t 0 = z 0 ,
(9.2)
where (X, Y, Z) is the instantaneous location of the particle, (x, y, z) are spatial
coordinates, (u, v, w) are the velocity components, t is time and (x 0 , y 0 , z 0 ) is the
location of the particle at the starting time instant t 0 (Chap. 7). The results of such
calculations obviously depend on the quality and spatial and temporal resolution of
the underlying velocity fields. It is therefore crucial to use the best available circulation models and forcing and boundary conditions in order to obtain an adequate
representation of the statistics of the modelled Lagrangian trajectories.
As mentioned above, in this and the following chapter we only use the horizontal
velocities (u, v) in the uppermost model layer to model the Lagrangian transport of
selected water particles. The vertical velocity w and the equation for Z(x, y, t) are
ignored. Thus the resulting trajectories are not truly Lagrangian (except for areas
where w ≥ 0 in this layer) and essentially represent the transport of particles or
substances that are locked within the uppermost layer.
Although both wind drag and wave-driven impact on the trajectories of drifting
objects could be substantial (Rohrs et al. 2012), we focus on the problem of statistics of purely current-driven transport. In other words, the impact of wind drag on
the floating objects (lost containers, debris, litter, oil spill, algae, etc.) is ignored
as well as wave-driven Stokes drift and other wave-induced effects (Breivik et al.
2011). A partial reason for this simplification is that the impact of wind and waves
is very site- and object-specific (Breivik et al. 2012; Rohrs et al. 2012). The realistic
behaviour and fate of oil spill under the joint impact of currents, wind and waves is
studied in Chap. 11.
There is extensive evidence that the drift of oil spills (and eventually other substances that form a thin film on the sea surface) usually differs considerably from
the trajectories of other objects, incl. the devices specifically designed to follow
the oil spill (Fingas 2011). This situation calls for us to take a step back and make
more efforts towards a better understanding of current-driven transport, which still
seems to be the largest source of uncertainties in the prediction of surface-layer drift
(Vandenbulcke et al. 2009).
The use of the output of circulation models for solving Eqs. (9.2) is justified
for many occasions in several domains of the World Ocean. This setup is generally
applicable for studies of contaminants or dissolved radioactive substances in a thin
surface layer of lighter water overlying denser water masses. Hydrometeorological
conditions supporting such a manner of transport occur, for example, regularly and
during relatively long time periods in the Gulf of Finland. In the spring season the
wind is normally very weak there (Mietus 1998) and the uppermost well-mixed
T. Soomere
9.3.3 Reconstruction of Trajectories of Water Particles
Calculation of a Lagrangian trajectory of a particle, carried passively by sea currents, is equivalent to solving the Cauchy problem for a simple system of differential
equations
dX
dt
= u,
dY
dt
= v,
dZ
dt
= w,
X t=t 0 = x 0 ,
Y t=t 0 = y 0 ,
Z t=t 0 = z 0 ,
(9.2)
where (X, Y, Z) is the instantaneous location of the particle, (x, y, z) are spatial
coordinates, (u, v, w) are the velocity components, t is time and (x 0 , y 0 , z 0 ) is the
location of the particle at the starting time instant t 0 (Chap. 7). The results of such
calculations obviously depend on the quality and spatial and temporal resolution of
the underlying velocity fields. It is therefore crucial to use the best available circulation models and forcing and boundary conditions in order to obtain an adequate
representation of the statistics of the modelled Lagrangian trajectories.
As mentioned above, in this and the following chapter we only use the horizontal
velocities (u, v) in the uppermost model layer to model the Lagrangian transport of
selected water particles. The vertical velocity w and the equation for Z(x, y, t) are
ignored. Thus the resulting trajectories are not truly Lagrangian (except for areas
where w ≥ 0 in this layer) and essentially represent the transport of particles or
substances that are locked within the uppermost layer.
Although both wind drag and wave-driven impact on the trajectories of drifting
objects could be substantial (Rohrs et al. 2012), we focus on the problem of statistics of purely current-driven transport. In other words, the impact of wind drag on
the floating objects (lost containers, debris, litter, oil spill, algae, etc.) is ignored
as well as wave-driven Stokes drift and other wave-induced effects (Breivik et al.
2011). A partial reason for this simplification is that the impact of wind and waves
is very site- and object-specific (Breivik et al. 2012; Rohrs et al. 2012). The realistic
behaviour and fate of oil spill under the joint impact of currents, wind and waves is
studied in Chap. 11.
There is extensive evidence that the drift of oil spills (and eventually other substances that form a thin film on the sea surface) usually differs considerably from
the trajectories of other objects, incl. the devices specifically designed to follow
the oil spill (Fingas 2011). This situation calls for us to take a step back and make
more efforts towards a better understanding of current-driven transport, which still
seems to be the largest source of uncertainties in the prediction of surface-layer drift
(Vandenbulcke et al. 2009).
The use of the output of circulation models for solving Eqs. (9.2) is justified
for many occasions in several domains of the World Ocean. This setup is generally
applicable for studies of contaminants or dissolved radioactive substances in a thin
surface layer of lighter water overlying denser water masses. Hydrometeorological
conditions supporting such a manner of transport occur, for example, regularly and
during relatively long time periods in the Gulf of Finland. In the spring season the
wind is normally very weak there (Mietus 1998) and the uppermost well-mixed