392
J. Murawski and J. Woge Nielsen
The resulting pathways thus represent a certain balance between attempts to maximize the integrated cost function and to minimize the path length. The resulting
optimum is generally relative rather than a global or absolute one. The gain (relative
performance) from the use of an optimum pathway can be evaluated in terms of the
ratio of the properly normalized integral of the cost function over its path and the
corresponding cost function for other pathways.
11.5.2 Environmentally Friendly Fairways
The four most important oil harbours in the eastern Gulf of Finland were selected for
the evaluation of the performance of the described technique: Saint Petersburg, Vyborg and Ust-Luga in Russia, and Sillamäe in Estonia. Given the extensive variability of the patterns of the oil residence time at sea and of the probability for landing,
we chose to develop the Monte Carlo based fairway optimizations for three basic
situations. The oil drift patterns for SW and SA seasons (discussed in Sect. 11.4.2)
are first analysed separately. These patterns are also combined for a joint analysis.
Seasonal ensembles of the cost function φ are formed for each release position X.
Ensemble averages are studied for the SW and SA designs (Fig. 11.7). The third
pattern, the basis for the combined (CMB) fairway design, was constructed to cover
all seasons (Fig. 11.7).
The two seasonal patterns can be merged in many ways. A simple way was to
produce annual averages that cover the complete set of monthly drift patterns. The
result was rather homogeneous and lacked the heterogeneity of the seasonal patterns and was thus unsuitable for the identification of distinct fairways. Instead, the
distribution of ensemble maxima was used for the development of CMB fairway
designs that can be used for all seasons. This distribution covers larger areas with
substantial values of the cost function as even single values at a certain instant may
contribute to this map. Namely, the distribution of ensemble maxima needs only
one value to highlight a particular release site whereas an ensemble average normally needs a much larger amount of high values to become significant. The results
in Fig. 11.7 confirm that the constructed annual pattern is a suitable basis for the
fairway optimization.
The results of the basic design evaluation in terms of the path length, path integral
of the cost function φ and their ratio (the normalized path integral of φ) (Table 11.1)
suggest that the SA design performs a little better than the SW design. Although the
gain of using a SA design is somewhat reduced by the longer path length, it is fully
compensated by much lower levels of environmental risks (expressed as the values of the integrated cost function). The performance of the SA design is, however,
rather low outside the spring and autumn seasons. A cross-seasonal evaluation reveals that the performance of the SW design is better balanced across the seasons.
The variability of the SA performance is larger, but the cross seasonal difference
is low. This means that the annual average performance of SW and SA designs are
nearly equal. The difference is generally less than ±0.01, except for Sillamäe, where
it is 0.06.
J. Murawski and J. Woge Nielsen
The resulting pathways thus represent a certain balance between attempts to maximize the integrated cost function and to minimize the path length. The resulting
optimum is generally relative rather than a global or absolute one. The gain (relative
performance) from the use of an optimum pathway can be evaluated in terms of the
ratio of the properly normalized integral of the cost function over its path and the
corresponding cost function for other pathways.
11.5.2 Environmentally Friendly Fairways
The four most important oil harbours in the eastern Gulf of Finland were selected for
the evaluation of the performance of the described technique: Saint Petersburg, Vyborg and Ust-Luga in Russia, and Sillamäe in Estonia. Given the extensive variability of the patterns of the oil residence time at sea and of the probability for landing,
we chose to develop the Monte Carlo based fairway optimizations for three basic
situations. The oil drift patterns for SW and SA seasons (discussed in Sect. 11.4.2)
are first analysed separately. These patterns are also combined for a joint analysis.
Seasonal ensembles of the cost function φ are formed for each release position X.
Ensemble averages are studied for the SW and SA designs (Fig. 11.7). The third
pattern, the basis for the combined (CMB) fairway design, was constructed to cover
all seasons (Fig. 11.7).
The two seasonal patterns can be merged in many ways. A simple way was to
produce annual averages that cover the complete set of monthly drift patterns. The
result was rather homogeneous and lacked the heterogeneity of the seasonal patterns and was thus unsuitable for the identification of distinct fairways. Instead, the
distribution of ensemble maxima was used for the development of CMB fairway
designs that can be used for all seasons. This distribution covers larger areas with
substantial values of the cost function as even single values at a certain instant may
contribute to this map. Namely, the distribution of ensemble maxima needs only
one value to highlight a particular release site whereas an ensemble average normally needs a much larger amount of high values to become significant. The results
in Fig. 11.7 confirm that the constructed annual pattern is a suitable basis for the
fairway optimization.
The results of the basic design evaluation in terms of the path length, path integral
of the cost function φ and their ratio (the normalized path integral of φ) (Table 11.1)
suggest that the SA design performs a little better than the SW design. Although the
gain of using a SA design is somewhat reduced by the longer path length, it is fully
compensated by much lower levels of environmental risks (expressed as the values of the integrated cost function). The performance of the SA design is, however,
rather low outside the spring and autumn seasons. A cross-seasonal evaluation reveals that the performance of the SW design is better balanced across the seasons.
The variability of the SA performance is larger, but the cross seasonal difference
is low. This means that the annual average performance of SW and SA designs are
nearly equal. The difference is generally less than ±0.01, except for Sillamäe, where
it is 0.06.