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T. Soomere
10.7.1 Quantification of the Benefit
The simplest estimates of the benefit for a stationary location of a potentially dangerous activity that has to be carried out in the open sea are the ratio of the minimum probability min(p ij ) and the average probability ¯
P (N max ), and the difference
between the maximum max(a ij ) and average particle age ¯
A(N max ). The typical values of ¯
P (N max ) are in the range from 0.62 to 0.67 in the Gulf of Finland (Andrejev
et al. 2011; Soomere et al. 2011c) whereas the minima of the probability extend
well below 0.3. In realistic conditions there exist many constraints for the location
of such spots and the benefit has to be estimated by comparing the extrema of the
particular measure with its average values over the technically suitable sea domain.
For certain choices of measures only the additional ‘costs’ of the consequences
can be estimated. An example is that the equiprobability line only divides equally
the potential loss between the opposite coasts. The relevant measure ˆ
p ij contains
very limited information about the actual probability of the coastal hit. The benefit
from its use can be measured to some extent as the average value of ˆ
p (either for a
particular location or for a fairway roughly following this line) showing the added
risk for one side.
Similarly the potential benefit from the use of an optimum sailing line substantially depends on the underlying measure, the value system and additional constraints. The simplest way to estimate the benefit from the use of the sailing line
that provides a reduced level of probability of coastal hits in case of possible accidents can be roughly evaluated in terms of the decrease in the probability of such a
hit compared with a ‘random’ location of the fairway. A convenient measure is the
ratio p opt / ¯
P (N max ) of this probability p opt calculated along the optimum fairway
over the average probability for the entire sea. In these terms the benefit is quite substantial. For example, for the 2 nm RCO model the average probability ¯
P (N max ) for
a coastal hit in the Gulf of Finland within 20 days is 0.62. The similar average value
along the optimum fairway is 0.347, giving a gain of 44 % (Soomere et al. 2011c).
For the 1 nm OAAS model and 10 days long trajectories ¯
P ≈ 0.67 and p opt ≈ 0.4
(that is, about 40 % lower) along the optimum fairways shown in Fig. 10.13.
In the same vein the benefit can be expressed in terms of an increase in the time
elapsed from the release of the adverse impact until it reaches the coast. The average
particle age is 8.7 days in the Gulf of Finland for the 2 nm RCO model and 20day long trajectories (Soomere et al. 2011c). The average over the points lying on
the optimum fairway to the eastern end of the gulf is 12.4 days. The gain is thus
up to 42.5 %. The values of a opt and ¯
A(N max ) are much shorter (5.3 and 9 days,
respectively) for calculations using 10-day long trajectories and the 1 nm OAAS
model (Andrejev et al. 2011).
It is remarkable that the potential in increase in the time available for combating
the pollution is almost the same, slightly below 4 days, for radically different model
setups. This invariance could suggest that the potential increase in time is largely
independent on the particular length of the trajectories (provided the number of hits
to the vulnerable area leads to adequate statistics) and possibly is an intrinsic feature
of the current-driven dynamics of the particular domain.
T. Soomere
10.7.1 Quantification of the Benefit
The simplest estimates of the benefit for a stationary location of a potentially dangerous activity that has to be carried out in the open sea are the ratio of the minimum probability min(p ij ) and the average probability ¯
P (N max ), and the difference
between the maximum max(a ij ) and average particle age ¯
A(N max ). The typical values of ¯
P (N max ) are in the range from 0.62 to 0.67 in the Gulf of Finland (Andrejev
et al. 2011; Soomere et al. 2011c) whereas the minima of the probability extend
well below 0.3. In realistic conditions there exist many constraints for the location
of such spots and the benefit has to be estimated by comparing the extrema of the
particular measure with its average values over the technically suitable sea domain.
For certain choices of measures only the additional ‘costs’ of the consequences
can be estimated. An example is that the equiprobability line only divides equally
the potential loss between the opposite coasts. The relevant measure ˆ
p ij contains
very limited information about the actual probability of the coastal hit. The benefit
from its use can be measured to some extent as the average value of ˆ
p (either for a
particular location or for a fairway roughly following this line) showing the added
risk for one side.
Similarly the potential benefit from the use of an optimum sailing line substantially depends on the underlying measure, the value system and additional constraints. The simplest way to estimate the benefit from the use of the sailing line
that provides a reduced level of probability of coastal hits in case of possible accidents can be roughly evaluated in terms of the decrease in the probability of such a
hit compared with a ‘random’ location of the fairway. A convenient measure is the
ratio p opt / ¯
P (N max ) of this probability p opt calculated along the optimum fairway
over the average probability for the entire sea. In these terms the benefit is quite substantial. For example, for the 2 nm RCO model the average probability ¯
P (N max ) for
a coastal hit in the Gulf of Finland within 20 days is 0.62. The similar average value
along the optimum fairway is 0.347, giving a gain of 44 % (Soomere et al. 2011c).
For the 1 nm OAAS model and 10 days long trajectories ¯
P ≈ 0.67 and p opt ≈ 0.4
(that is, about 40 % lower) along the optimum fairways shown in Fig. 10.13.
In the same vein the benefit can be expressed in terms of an increase in the time
elapsed from the release of the adverse impact until it reaches the coast. The average
particle age is 8.7 days in the Gulf of Finland for the 2 nm RCO model and 20day long trajectories (Soomere et al. 2011c). The average over the points lying on
the optimum fairway to the eastern end of the gulf is 12.4 days. The gain is thus
up to 42.5 %. The values of a opt and ¯
A(N max ) are much shorter (5.3 and 9 days,
respectively) for calculations using 10-day long trajectories and the 1 nm OAAS
model (Andrejev et al. 2011).
It is remarkable that the potential in increase in the time available for combating
the pollution is almost the same, slightly below 4 days, for radically different model
setups. This invariance could suggest that the potential increase in time is largely
independent on the particular length of the trajectories (provided the number of hits
to the vulnerable area leads to adequate statistics) and possibly is an intrinsic feature
of the current-driven dynamics of the particular domain.