ERCIM News No.25 - April 1996 - CWI

Spatial Statistics and Oil Pollution in the North Sea

by Roelof Helmers

In a still ongoing project, commissioned by the North Sea Directorate of the Dutch Ministry of Transport and Public Works, the problem is to estimate the intensity of oil-pollution in the North Sea and to develop a reliable method for estimating the total amount of oil pollution in a given year.

The available real data sets consist of the locations and volumes of the oil spots observed in a given year. In the figure the oil spots observed in 1993 are plotted (with sizes proportional to the volumes of the oil spots).

The dashed area is the Dutch part of the continental shelf in the North Sea. The tiny triangles represent the locations of off-shore activities and the shaded areas correspond to the various shipping areas and also indicate the different shipping intensities in these areas.

Oil spots are observed by a surveillance aircraft with varying frequencies at different locations. A planar inhomogeneous Poisson point process with intensity function $\lambda(.,\theta)$- parametrized by a finite dimensional parameter ${\theta}$ - is used as a spatial (parametric) model for the locations of (the centres of) oil spots. The parametrization by the parameter vector ${\theta}$ enables one to incorporate the available a priori knowledge about oil pollution, such as the location of sources of oil pollution and the various shipping intensities. However, not much seems to be known about the distribution of the volumes of oil spots, but we can of course use the sizes of the observed oil spots to estimate it (nonparametric approach).

In this setup a simple semiparametric form of spatial bootstrapping was developed. The idea is to simulate many (a few thousands) realizations of an inhomogeneous planar Poisson process with estimated (from the real data at hand) intensity $\lambda\hat(.,\theta)$, where $\hat{\theta}$ is an estimate of ${\theta}$. In addition, we also resample the observed spot volumes in an appropriate manner. With the aid of these resampled datasets, we can obtain accurate bootstrap based confidence limits for the total amount of oil pollution in a given period of time (e.g. the year 1993).

This work is part of CWI's research programme Mathematics & the Environment.

Please contact:
Roelof Helmers - CWI
Tel: +31 20 592 4079

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