9 Statistics of Lagrangian Transport Reveals Hidden Features of Velocity Fields
307
this condition is violated, the uncertainty in the positioning of the particle caused
by subgrid-scale turbulence would be about the same size as the extension of the
open sea area and the related statistics of coastal hits could become meaningless.
Numerical simulations of Andrejev et al. (2010) assume that the typical spreading
rate is about 2 mm/s. Drifter experiments in the Baltic Proper (Kjellsson and Döös
2012) (see also Chap. 8) and in the Gulf of Finland (Soomere et al. 2011b) suggest
that this rate apparently is somewhat larger.
Therefore, the subgrid turbulence may separate the particles on average by 15 km
within about three weeks. This suggests that for time windows longer than about 20
days the final position of the particle would be basically random. As the majority
of coastal hits occurs much earlier and the actual rate of deviation of the modelled
path from the theoretically valid one is on average much smaller, the resulting distributions of the probabilities of coastal hits, the time it takes for the pollution to
reach the coast and net and bulk transport patterns evidently reflect well the reality
as simulated by the circulation model.
Summing up, the basic time scales for a reasonable calculation of the Lagrangian
trajectories, for current-induced semi-persistent features of transport of surface water and for the adequate location of the model boundary of the vulnerable areas
should be analysed separately for each basin. For the RCO model and the nonspreading version of the TRACMASS trajectory model it is appropriate to use a
nearshore area about 3 grid cells wide as a proper representation of the coastal zone.
A sensible length of time windows in calculations of coastal hits in the Gulf of Finland is at least 10–15 days. About 10 % of the released particles drift out of the gulf
and about one-third of the particles released in the central part of the gulf enter the
model nearshore during this time. 9
9.4.3 Temporal Scales for Transport Patterns in the Gulf
of Finland
We demonstrate several of the above-discussed issues and the importance of the
proper choice of the length of the time window for the example of areas of rapid net
and bulk Lagrangian transport in the Gulf of Finland. The net transport is defined as
the distance between the start and end positions of a trajectory (Fig. 9.12) and the
bulk transport as the length of the entire trajectory. Patterns of intense net transport
may become evident in many cases of current fields that have low overall long-term
persistency R p . A typical example is a system of coastal currents where the flow
direction alternates in weekly scales. They may rapidly and systematically relocate
patches of various substances between different domains even when the long-term
current system is almost perfectly random. Their location and magnitude can be
identified numerically using the above discretization of calculations into a sequence
of numerical simulations of Lagrangian trajectories of water particles.
9 The long-term average of this rate becomes explicitly evident below as the long-term average
probability of coastal hits for the entire basin, see Chap. 10.
307
this condition is violated, the uncertainty in the positioning of the particle caused
by subgrid-scale turbulence would be about the same size as the extension of the
open sea area and the related statistics of coastal hits could become meaningless.
Numerical simulations of Andrejev et al. (2010) assume that the typical spreading
rate is about 2 mm/s. Drifter experiments in the Baltic Proper (Kjellsson and Döös
2012) (see also Chap. 8) and in the Gulf of Finland (Soomere et al. 2011b) suggest
that this rate apparently is somewhat larger.
Therefore, the subgrid turbulence may separate the particles on average by 15 km
within about three weeks. This suggests that for time windows longer than about 20
days the final position of the particle would be basically random. As the majority
of coastal hits occurs much earlier and the actual rate of deviation of the modelled
path from the theoretically valid one is on average much smaller, the resulting distributions of the probabilities of coastal hits, the time it takes for the pollution to
reach the coast and net and bulk transport patterns evidently reflect well the reality
as simulated by the circulation model.
Summing up, the basic time scales for a reasonable calculation of the Lagrangian
trajectories, for current-induced semi-persistent features of transport of surface water and for the adequate location of the model boundary of the vulnerable areas
should be analysed separately for each basin. For the RCO model and the nonspreading version of the TRACMASS trajectory model it is appropriate to use a
nearshore area about 3 grid cells wide as a proper representation of the coastal zone.
A sensible length of time windows in calculations of coastal hits in the Gulf of Finland is at least 10–15 days. About 10 % of the released particles drift out of the gulf
and about one-third of the particles released in the central part of the gulf enter the
model nearshore during this time. 9
9.4.3 Temporal Scales for Transport Patterns in the Gulf
of Finland
We demonstrate several of the above-discussed issues and the importance of the
proper choice of the length of the time window for the example of areas of rapid net
and bulk Lagrangian transport in the Gulf of Finland. The net transport is defined as
the distance between the start and end positions of a trajectory (Fig. 9.12) and the
bulk transport as the length of the entire trajectory. Patterns of intense net transport
may become evident in many cases of current fields that have low overall long-term
persistency R p . A typical example is a system of coastal currents where the flow
direction alternates in weekly scales. They may rapidly and systematically relocate
patches of various substances between different domains even when the long-term
current system is almost perfectly random. Their location and magnitude can be
identified numerically using the above discretization of calculations into a sequence
of numerical simulations of Lagrangian trajectories of water particles.
9 The long-term average of this rate becomes explicitly evident below as the long-term average
probability of coastal hits for the entire basin, see Chap. 10.