338
T. Soomere
from about 0.4 (mostly in calm seasons) to values very close to 1. Their relative
fluctuations were, however, much smaller than similar variations in the forcing factors. For example, monthly averaged kinetic energy density of surface wind varied
by more than 10 times in the Gulf of Finland (Andrejev et al. 2011).
Both the cumulative quantities already closely matched their asymptotic values
¯
P (N max ) ≈ 0.67, ¯
A(N max ) ≈ 5.3 days after the first half-year of simulations and
revealed moderate variations after about two years of calculations. Their short-term
and seasonal fluctuations were very small (about 3 % from the average) from the
third year on and were almost negligible (below 1 %) after the fifth year. Therefore,
the cumulative measures in question calculated over >3 years reflect well long-term
internal properties of current-driven transport patterns even in a domain hosting
extensive seasonal variations in the forcing pattern such as the Gulf of Finland. This
time scale is close to the average ‘classical’ water age (equivalently, the time scale
of renewal of water masses) in the Gulf of Finland (Andrejev et al. 2004a) that also
revealed very small changes after three years of simulations.
The asymptotic values ¯
P (N max ) and ¯
A(N max ) can be used to roughly evaluate
whether the parameters of the developed procedure are sensible. The overall probability of coastal hits had a reasonable level ¯
P (N max ) ≈ 0.67, not very close to 1 and
also not small. It signifies that about 2/3 of the released particles have contributed
to the estimates of the environmental risk. The limit value of the particle age was
somewhat smaller than might be expected based on Viikmäe et al. (2010) where typically only 30–40 % of the particles released in the central part of the gulf reached
the nearshore within 10 days. Finally, we note that both P (N max ) and A(N max ) may
depend on the length of the time window t w in use. This dependence is usually much
stronger for A(N max ), as t w is assumed to be the age of all particles that have not
reached the coast (Soomere et al. 2011c, 2011d).
10.5.4 Spatial Distributions of Probability and Particle Age
The most important intermediate products of the technology are spatial distributions
of the measures of the environmental risk p ij (x, y) and a ij (x, y) associated with the
release of pollution. These maps can serve as starting points of various engineering
applications and decision support systems.
The average probability of a coastal hit for single cells p ij over the entire simulation period shows a rich spatial structure for the test areas (Fig. 10.4). The probabilities to the west of Paldiski (Fig. 10.2) in the Gulf of Finland are strongly affected
by the presence of the open boundary. The areas with smallest p ij < 0.4 are located
far offshore. The regions of small p ij have relatively small gradients. This is partially caused by the choice of the length of the time window (10 days) an increase
in which eventually would lead to larger contrasts in p ij (Soomere et al. 2011c).
A wide area where p ij ∼ 0.5–0.6 extends from Lahemaa almost to the island of
Gogland. Its bend to the south into Narva Bay obviously reflects the presence of
islands (that are ignored in the 2 nm simulations of Soomere et al. 2011c). Smaller
T. Soomere
from about 0.4 (mostly in calm seasons) to values very close to 1. Their relative
fluctuations were, however, much smaller than similar variations in the forcing factors. For example, monthly averaged kinetic energy density of surface wind varied
by more than 10 times in the Gulf of Finland (Andrejev et al. 2011).
Both the cumulative quantities already closely matched their asymptotic values
¯
P (N max ) ≈ 0.67, ¯
A(N max ) ≈ 5.3 days after the first half-year of simulations and
revealed moderate variations after about two years of calculations. Their short-term
and seasonal fluctuations were very small (about 3 % from the average) from the
third year on and were almost negligible (below 1 %) after the fifth year. Therefore,
the cumulative measures in question calculated over >3 years reflect well long-term
internal properties of current-driven transport patterns even in a domain hosting
extensive seasonal variations in the forcing pattern such as the Gulf of Finland. This
time scale is close to the average ‘classical’ water age (equivalently, the time scale
of renewal of water masses) in the Gulf of Finland (Andrejev et al. 2004a) that also
revealed very small changes after three years of simulations.
The asymptotic values ¯
P (N max ) and ¯
A(N max ) can be used to roughly evaluate
whether the parameters of the developed procedure are sensible. The overall probability of coastal hits had a reasonable level ¯
P (N max ) ≈ 0.67, not very close to 1 and
also not small. It signifies that about 2/3 of the released particles have contributed
to the estimates of the environmental risk. The limit value of the particle age was
somewhat smaller than might be expected based on Viikmäe et al. (2010) where typically only 30–40 % of the particles released in the central part of the gulf reached
the nearshore within 10 days. Finally, we note that both P (N max ) and A(N max ) may
depend on the length of the time window t w in use. This dependence is usually much
stronger for A(N max ), as t w is assumed to be the age of all particles that have not
reached the coast (Soomere et al. 2011c, 2011d).
10.5.4 Spatial Distributions of Probability and Particle Age
The most important intermediate products of the technology are spatial distributions
of the measures of the environmental risk p ij (x, y) and a ij (x, y) associated with the
release of pollution. These maps can serve as starting points of various engineering
applications and decision support systems.
The average probability of a coastal hit for single cells p ij over the entire simulation period shows a rich spatial structure for the test areas (Fig. 10.4). The probabilities to the west of Paldiski (Fig. 10.2) in the Gulf of Finland are strongly affected
by the presence of the open boundary. The areas with smallest p ij < 0.4 are located
far offshore. The regions of small p ij have relatively small gradients. This is partially caused by the choice of the length of the time window (10 days) an increase
in which eventually would lead to larger contrasts in p ij (Soomere et al. 2011c).
A wide area where p ij ∼ 0.5–0.6 extends from Lahemaa almost to the island of
Gogland. Its bend to the south into Narva Bay obviously reflects the presence of
islands (that are ignored in the 2 nm simulations of Soomere et al. 2011c). Smaller