356
T. Soomere
demonstrates how sensitive the resulting optimum fairway may be with respect to
seemingly small variations in the method.
10.7.4 Nearly Optimal Solutions
The issues of robustness and possible uncertainties are closely related to the question
of sensitivity of the optimum fairways calculated using different options (Soomere
et al. 2011c). A convenient way to quantify the sensitivity of the environmental risks
associated with optimum solutions with respect to small variations is to construct a
‘corridor’ surrounding the optimum sailing line. In such a corridor the underlying
measure of risk (probability for a coastal hit, particle age or ˆ
p) is allowed to vary to
some extent compared to its optimum value. The shape of such corridors together
with the values for the gradients of the underlying fields provides information about
the flexibility of shipping and characterizes the degree of freedom for captains (or
for the decision-making in general) to choose the sailing line with a reasonable
increase in the environmental risks. The along-gulf variations in the width of such
corridors may also highlight sea regions with different internal dynamics.
The spatial variability of such corridors with a predefined total area (equivalently,
with a fixed average width of 15 km in the Gulf of Finland) is analysed in Soomere
et al. (2011c) using the 2 nm RCO model, the TRACMASS code and the five specifications of the optimum solution found from the cross-sections of the underlying
distributions as described in the previous section. Within such a corridor the probability of coastal hits (or the particle age) is allowed to differ to some extent from the
relevant minimum (maximum).
A corridor with an average width of 15 km (8.1 nm) corresponds to an increase
in the probability of coastal hits by up to 0.0293 (or to a decrease in the particle
age by up to 0.54136 days) for each longitude compared to the optimum value.
The corridor’s border lines were determined from an analysis of the cross-sections
of the underlying distributions as described above. The locations of the probability
p = p min + 0.293 (p min is the minimum probability for the particular longitude) or
the particle age of a = a max − 0.54136 days were found for each latitude. The curve
consisting of such points was smoothed over five neighbouring points.
The resulting corridors were quite wide at the entrance to the Gulf of Finland,
relatively narrow in the Tallinn–Helsinki region (Fig. 10.17), widened substantially
in the eastern part of the gulf in the vicinity of Gogland and become very narrow
again in the area to the north of Luga Bay. The minimum and maximum widths
were 7.35/9.6 km and 29.1/42 km, respectively, for Methods III/IVa.
Similar corridors were defined as the sea area between the equiprobability lines
corresponding to ˆ
p = ±0.11189 for the direct method I and to ˆ
p = ±0.09542 for
the smoothing method II. The fields of ˆ
p had a very steep north–south slope in the
central part of the bay in both cases. The corridor for the direct method (Fig. 10.18)
had a minimum width of only 2.1 km. The slope was very small at the entrance of the
gulf where the resulting corridor was up to 48.6 km wide. The equiprobability line
T. Soomere
demonstrates how sensitive the resulting optimum fairway may be with respect to
seemingly small variations in the method.
10.7.4 Nearly Optimal Solutions
The issues of robustness and possible uncertainties are closely related to the question
of sensitivity of the optimum fairways calculated using different options (Soomere
et al. 2011c). A convenient way to quantify the sensitivity of the environmental risks
associated with optimum solutions with respect to small variations is to construct a
‘corridor’ surrounding the optimum sailing line. In such a corridor the underlying
measure of risk (probability for a coastal hit, particle age or ˆ
p) is allowed to vary to
some extent compared to its optimum value. The shape of such corridors together
with the values for the gradients of the underlying fields provides information about
the flexibility of shipping and characterizes the degree of freedom for captains (or
for the decision-making in general) to choose the sailing line with a reasonable
increase in the environmental risks. The along-gulf variations in the width of such
corridors may also highlight sea regions with different internal dynamics.
The spatial variability of such corridors with a predefined total area (equivalently,
with a fixed average width of 15 km in the Gulf of Finland) is analysed in Soomere
et al. (2011c) using the 2 nm RCO model, the TRACMASS code and the five specifications of the optimum solution found from the cross-sections of the underlying
distributions as described in the previous section. Within such a corridor the probability of coastal hits (or the particle age) is allowed to differ to some extent from the
relevant minimum (maximum).
A corridor with an average width of 15 km (8.1 nm) corresponds to an increase
in the probability of coastal hits by up to 0.0293 (or to a decrease in the particle
age by up to 0.54136 days) for each longitude compared to the optimum value.
The corridor’s border lines were determined from an analysis of the cross-sections
of the underlying distributions as described above. The locations of the probability
p = p min + 0.293 (p min is the minimum probability for the particular longitude) or
the particle age of a = a max − 0.54136 days were found for each latitude. The curve
consisting of such points was smoothed over five neighbouring points.
The resulting corridors were quite wide at the entrance to the Gulf of Finland,
relatively narrow in the Tallinn–Helsinki region (Fig. 10.17), widened substantially
in the eastern part of the gulf in the vicinity of Gogland and become very narrow
again in the area to the north of Luga Bay. The minimum and maximum widths
were 7.35/9.6 km and 29.1/42 km, respectively, for Methods III/IVa.
Similar corridors were defined as the sea area between the equiprobability lines
corresponding to ˆ
p = ±0.11189 for the direct method I and to ˆ
p = ±0.09542 for
the smoothing method II. The fields of ˆ
p had a very steep north–south slope in the
central part of the bay in both cases. The corridor for the direct method (Fig. 10.18)
had a minimum width of only 2.1 km. The slope was very small at the entrance of the
gulf where the resulting corridor was up to 48.6 km wide. The equiprobability line