9 Statistics of Lagrangian Transport Reveals Hidden Features of Velocity Fields
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number of test particles and their initial separation are large enough. The limited
spreading of TRACMASS trajectories means that initially closely packed particles
will move together and the resulting trajectories will be strongly correlated. Therefore, it makes no sense to pack many test particles next to each other at a certain
time instant. This feature is accounted for in all described experiments that use
TRACMASS. The largest number of particles in one grid cell was 5 in Soomere
et al. (2011a), whereas Lu et al. (2012) seeded one particle into each fourth cell.
The trajectory models that contain an internal spreading scheme (that simulates
the impact of subgrid-scale motions) can easily make reasonable use of 10 trajectories per each grid point (Andrejev et al. 2010, 2011). Such schemes usually insert
a random disturbance to each trajectory after certain time intervals. This procedure
corrects certain statistical features of large pools of trajectories but obviously does
not improve the match of the resulting trajectories with the motion of real water particles. The best way to increase the number of trajectories is therefore to improve the
spatial resolution of the circulation model or to increase the time interval covered
by the circulation modelling.
9.3.7 Overlapping Simulations
Another feasible way of increasing the number of uncorrelated trajectories is to
restart the calculations with a given set of water particles already before the end of
the previous run. Restarting the calculations after very short time intervals should
be avoided as doing so would lead to equivalent trajectories and thus serially correlated results, and would not improve the final statistics. The surface current speed
in the test areas is typically well below 0.5 m/s and about 0.2–0.3 m/s in the Gulf of
Finland. Within one time step of the RCO velocity data (6 hours) a particle would
normally move by 4–6 km, that is, at least into a neighbouring grid cell. It is reasonable to assume that trajectories that are initially separated by a distance of about
the grid size of the circulation model (equivalently, start at least 6 hours after the
previous one in the case of the 2 nm resolution RCO model), can be treated as independent ones.
The use of a longer time lag between subsequent calculations leads to a decrease
in the chances for having equivalent (or strongly correlated) trajectories. As the resulting set of trajectories is smaller, doing so may still adversely affect the reliability
of the conclusions (Viikmäe et al. 2010). An analysis of the pools of trajectories
shows that the results are relatively insensitive with respect to variations in the time
lag t S from 1 to 10 days for the RCO data for 1987–1991 (Viikmäe et al. 2010).
This suggests that the accuracy and reliability of the results first of all depends on
the number of trajectories involved and less on how densely they are distributed in
time. This conjecture becomes important in the optimization of long-term calculations based on high-resolution simulations (Andrejev et al. 2010).
The presented estimates and their more exact specification in particular experiments only concern the reasonable values of different parameters necessary for the
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number of test particles and their initial separation are large enough. The limited
spreading of TRACMASS trajectories means that initially closely packed particles
will move together and the resulting trajectories will be strongly correlated. Therefore, it makes no sense to pack many test particles next to each other at a certain
time instant. This feature is accounted for in all described experiments that use
TRACMASS. The largest number of particles in one grid cell was 5 in Soomere
et al. (2011a), whereas Lu et al. (2012) seeded one particle into each fourth cell.
The trajectory models that contain an internal spreading scheme (that simulates
the impact of subgrid-scale motions) can easily make reasonable use of 10 trajectories per each grid point (Andrejev et al. 2010, 2011). Such schemes usually insert
a random disturbance to each trajectory after certain time intervals. This procedure
corrects certain statistical features of large pools of trajectories but obviously does
not improve the match of the resulting trajectories with the motion of real water particles. The best way to increase the number of trajectories is therefore to improve the
spatial resolution of the circulation model or to increase the time interval covered
by the circulation modelling.
9.3.7 Overlapping Simulations
Another feasible way of increasing the number of uncorrelated trajectories is to
restart the calculations with a given set of water particles already before the end of
the previous run. Restarting the calculations after very short time intervals should
be avoided as doing so would lead to equivalent trajectories and thus serially correlated results, and would not improve the final statistics. The surface current speed
in the test areas is typically well below 0.5 m/s and about 0.2–0.3 m/s in the Gulf of
Finland. Within one time step of the RCO velocity data (6 hours) a particle would
normally move by 4–6 km, that is, at least into a neighbouring grid cell. It is reasonable to assume that trajectories that are initially separated by a distance of about
the grid size of the circulation model (equivalently, start at least 6 hours after the
previous one in the case of the 2 nm resolution RCO model), can be treated as independent ones.
The use of a longer time lag between subsequent calculations leads to a decrease
in the chances for having equivalent (or strongly correlated) trajectories. As the resulting set of trajectories is smaller, doing so may still adversely affect the reliability
of the conclusions (Viikmäe et al. 2010). An analysis of the pools of trajectories
shows that the results are relatively insensitive with respect to variations in the time
lag t S from 1 to 10 days for the RCO data for 1987–1991 (Viikmäe et al. 2010).
This suggests that the accuracy and reliability of the results first of all depends on
the number of trajectories involved and less on how densely they are distributed in
time. This conjecture becomes important in the optimization of long-term calculations based on high-resolution simulations (Andrejev et al. 2010).
The presented estimates and their more exact specification in particular experiments only concern the reasonable values of different parameters necessary for the