About UK oil spills:
Many phenomenon, such as oil spills, show a characteristic
frequency distribution of event sizes over time, with many small oil
spills, some medium sized events, and uncommon large oil spills. Other
hazardous phenomena which show this kind of frequency distribution
over time include forest fires, nuclear accidents, earthquakes, automobile
wrecks, landslides, and some volcanic eruptions. Other objects, such
as stream networks, veins in the body, and city streets, also show
this same size distribution. In general, objects (or phenomena) which
are self-similar in geometry ("fractal" or scale independent)
will show this characteristic frequency distribution.
Oil spills in the marine waters (open sea to closed
estuary) of the United Kingdom were analyzed from January 1989 to
December 1998 (9 years) in a comprehensive report by Safetec UK Ltd.
to DETRA (see below). The report contains a lot of great information
and analysis, including the sizes of every reported oil spill (in
metric tonnes) for spills greater than or equal to 1 tonne, for a
total of 261 oil spills.
The data have been reconfigured to express the
frequency of oil spills greater than or equal to a certain size category,
rather than the frequency of spills of a certain size range (the more
typical method of presenting frequency information). This data configuration
is analogous to cumulative frequency. There are a number of reasons
for expressing the data in this form. For example, if the sample is
not large, there may be bins (intervals) with no events of that size,
which can create problems when using logarithms.
If the object or phenomena is self-similar or
"fractal", then the object or phenomena will typically show
a "power law distribution" of sizes, with a linear relationship
between the logarithms of size and cumulative frequency. The UK oil
spill data seem to behave in this fashion; the students can do the
math, and determine the goodness of fit to a power law model. With
a bit of algebra, students can also calculate the parameters to the
power law model.
With the power law model in hand, students can
estimate the recurrence interval (by extrapolation) of very large
oil spills that may have not even occurred yet. For example, what
is the recurrence interval for an oil spill of 1 million tonnes in
Source: UK Department for Environment, Transport
and Regions Report on "Identification of Marine Environmental
High Risk Areas in the UK", Report # ST-8639-MI-1-Rev 01 . Appendix
3 has the data.