334
T. Soomere
a substantial part of the motions with periods from 2 to 36 h are strongly circularly
polarized (Lilover et al. 2011). This feature was accounted for by perturbing the xcomponent of velocity based on the magnitude of the y-component and vice versa
(Andrejev et al. 2010). They chose u = crv, v = cru, where the random variable r
was uniformly distributed within the interval [−0.5, 0.5] and c was a tunable coefficient reflecting the intensity of spreading.
Setting c = 0.5 in Andrejev et al. (2010) resulted in the average spreading rate
of 10-day long trajectories in December 1990–November 1991 of about 176 m/day
(∼2 mm/s) for the 1 nm model and 10 particles per each grid cell (with a typical initial distance of ∼500 m between particles). This value matches the estimates from
drift of surface buoys in 2011 for the separation rate of particles initially located
at a distance of 50–150 m from each other (Soomere et al. 2011e). The resulting
statistics apparently somewhat underestimates the actual spreading rate. The introduced spreading was, though, reasonable to ensure a high enough rate of hits to
the nearshore (that was defined as the pool of wet points directly adjacent to the
land points): about 2/3 of all released particles entered this zone during 10 days of
propagation (Andrejev et al. 2011).
Each method has its advantages and disadvantages (Chap. 7). The on-line method
allows the use of the integration time step of the circulation model for solving the
trajectory equations and leads to more exact formal reproduction of single trajectories. This is, however, no real advantage as subgrid-scale effects deform the real
trajectories in a manner that can be only reproduced statistically. The set of online simulations is severely limited as re-running of a high-resolution circulation
model is usually very time-consuming. The accuracy of the trajectories from the
off-line method suffers from the coarse temporal resolution of the saved velocity
data (usually once in a few hours). This shortcoming is partially balanced by a
much larger flexibility: off-line trajectory calculations are much faster, it is easy
to re-parameterize the impact of subgrid motions, the already calculated trajectories
can be used for differently set problems, etc.
10.5 Quantification of the Risk of Coastal Pollution
The applications described in this book have assumed that a hit of any part of long
sections of the nearshore is equally undesired. This is equivalent to introducing a
constant cost function: reaching any section of the nearshore by a particle is ‘bad’
(optionally with a sign) and staying in the open sea (or leaving the test area towards
the North Sea or the Baltic Proper) is mostly considered ‘neutral.’
10.5.1 Launching the Particles
The basic requirements concerning the number of trajectories in order to create reliable statistics of coastal hits have been discussed in Chap. 9 and in Viikmäe et al.
T. Soomere
a substantial part of the motions with periods from 2 to 36 h are strongly circularly
polarized (Lilover et al. 2011). This feature was accounted for by perturbing the xcomponent of velocity based on the magnitude of the y-component and vice versa
(Andrejev et al. 2010). They chose u = crv, v = cru, where the random variable r
was uniformly distributed within the interval [−0.5, 0.5] and c was a tunable coefficient reflecting the intensity of spreading.
Setting c = 0.5 in Andrejev et al. (2010) resulted in the average spreading rate
of 10-day long trajectories in December 1990–November 1991 of about 176 m/day
(∼2 mm/s) for the 1 nm model and 10 particles per each grid cell (with a typical initial distance of ∼500 m between particles). This value matches the estimates from
drift of surface buoys in 2011 for the separation rate of particles initially located
at a distance of 50–150 m from each other (Soomere et al. 2011e). The resulting
statistics apparently somewhat underestimates the actual spreading rate. The introduced spreading was, though, reasonable to ensure a high enough rate of hits to
the nearshore (that was defined as the pool of wet points directly adjacent to the
land points): about 2/3 of all released particles entered this zone during 10 days of
propagation (Andrejev et al. 2011).
Each method has its advantages and disadvantages (Chap. 7). The on-line method
allows the use of the integration time step of the circulation model for solving the
trajectory equations and leads to more exact formal reproduction of single trajectories. This is, however, no real advantage as subgrid-scale effects deform the real
trajectories in a manner that can be only reproduced statistically. The set of online simulations is severely limited as re-running of a high-resolution circulation
model is usually very time-consuming. The accuracy of the trajectories from the
off-line method suffers from the coarse temporal resolution of the saved velocity
data (usually once in a few hours). This shortcoming is partially balanced by a
much larger flexibility: off-line trajectory calculations are much faster, it is easy
to re-parameterize the impact of subgrid motions, the already calculated trajectories
can be used for differently set problems, etc.
10.5 Quantification of the Risk of Coastal Pollution
The applications described in this book have assumed that a hit of any part of long
sections of the nearshore is equally undesired. This is equivalent to introducing a
constant cost function: reaching any section of the nearshore by a particle is ‘bad’
(optionally with a sign) and staying in the open sea (or leaving the test area towards
the North Sea or the Baltic Proper) is mostly considered ‘neutral.’
10.5.1 Launching the Particles
The basic requirements concerning the number of trajectories in order to create reliable statistics of coastal hits have been discussed in Chap. 9 and in Viikmäe et al.