9 Statistics of Lagrangian Transport Reveals Hidden Features of Velocity Fields
299
medium-resolution RCO model does not reproduce many local bathymetric features
(cf. Andrejev et al. 2010). The use of a proper representation of the nearshore for
the TRACMASS model (three grid cells, see below) means that the offshore of the
Gulf of Finland is only represented by about 10 grid points in its narrowest part.
The temporal resolution of saved velocity data (6 hours for the RCO model data)
evidently distorts the impact of inertial oscillations and only partially accounts for
the mesoscale motions.
The control over other parameters is still in the hands of the operator of the
technology. The resulting discrete problem contains three intrinsic time scales:
• Duration of single trajectories (time window t W );
• Selection of water particles in time (time lag t S between subsequent simulations);
• Time interval [t 0 , t 0 + t D ] covered by the calculations.
Additionally, several other parameters may affect the appearance and reliability
of the results:
• Number of trajectories used for statistical estimates;
• Numerical representation of the vulnerable areas;
• Target function (e.g., whether or not the climatologically valid solution is targeted, see Chap. 11).
Several items in the list can be specified by a suitable choice of time scales (e.g.,
for which semi-persistent patterns may be important in the particular basin, or the
typical time for coastal hits). The use of very short propagation times (trajectory
lengths less than a few hours) is normally imprudent as no adverse impact can reach
remote areas during such a short time. The propagation time should be long enough 7
to allow for a significant number of particles to reach the vulnerable area(s). Also,
the hidden properties of Lagrangian transport can only be revealed by trajectories
that are long enough to highlight net dislodgements of surface water.
A rough estimate of the reasonable time scales could be extracted from a comparison of the appearance of the Eulerian and Lagrangian transport in various environments. For a rectilinear flow (a generalisation of a stationary jet current in the
sea) the Eulerian and Lagrangian velocities and transport are equivalent and a proper
time scale should match the lifetime of the jet currents.
These velocities and the relevant transport rates are usually very different in environments containing numerous synoptic eddies. In the core of a stationary eddy the
Eulerian speed is constant and the Eulerian transport increases linearly with time.
The water particles ideally exert circular motions and periodically return to their
initial locations. The direction of the motion of a water particle (equivalently, its
Lagrangian velocity) varies periodically in time but the relevant speed is constant.
Its displacement (Lagrangian transport) periodically varies from zero to a certain
maximum value. Consequently in eddy-dominated (and even in eddy-containing)
7 It is, however, equally unwise to trace the trajectories during very long time intervals as shortliving patterns will be smoothed out and the properties of the tracked items or substances eventually
will change.
299
medium-resolution RCO model does not reproduce many local bathymetric features
(cf. Andrejev et al. 2010). The use of a proper representation of the nearshore for
the TRACMASS model (three grid cells, see below) means that the offshore of the
Gulf of Finland is only represented by about 10 grid points in its narrowest part.
The temporal resolution of saved velocity data (6 hours for the RCO model data)
evidently distorts the impact of inertial oscillations and only partially accounts for
the mesoscale motions.
The control over other parameters is still in the hands of the operator of the
technology. The resulting discrete problem contains three intrinsic time scales:
• Duration of single trajectories (time window t W );
• Selection of water particles in time (time lag t S between subsequent simulations);
• Time interval [t 0 , t 0 + t D ] covered by the calculations.
Additionally, several other parameters may affect the appearance and reliability
of the results:
• Number of trajectories used for statistical estimates;
• Numerical representation of the vulnerable areas;
• Target function (e.g., whether or not the climatologically valid solution is targeted, see Chap. 11).
Several items in the list can be specified by a suitable choice of time scales (e.g.,
for which semi-persistent patterns may be important in the particular basin, or the
typical time for coastal hits). The use of very short propagation times (trajectory
lengths less than a few hours) is normally imprudent as no adverse impact can reach
remote areas during such a short time. The propagation time should be long enough 7
to allow for a significant number of particles to reach the vulnerable area(s). Also,
the hidden properties of Lagrangian transport can only be revealed by trajectories
that are long enough to highlight net dislodgements of surface water.
A rough estimate of the reasonable time scales could be extracted from a comparison of the appearance of the Eulerian and Lagrangian transport in various environments. For a rectilinear flow (a generalisation of a stationary jet current in the
sea) the Eulerian and Lagrangian velocities and transport are equivalent and a proper
time scale should match the lifetime of the jet currents.
These velocities and the relevant transport rates are usually very different in environments containing numerous synoptic eddies. In the core of a stationary eddy the
Eulerian speed is constant and the Eulerian transport increases linearly with time.
The water particles ideally exert circular motions and periodically return to their
initial locations. The direction of the motion of a water particle (equivalently, its
Lagrangian velocity) varies periodically in time but the relevant speed is constant.
Its displacement (Lagrangian transport) periodically varies from zero to a certain
maximum value. Consequently in eddy-dominated (and even in eddy-containing)
7 It is, however, equally unwise to trace the trajectories during very long time intervals as shortliving patterns will be smoothed out and the properties of the tracked items or substances eventually
will change.