# Nature preservation acceptance model applied to tanker oil spill simulations

Peter Friis-Hansen, Ove Dalager Ditlevsen

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## Abstract

This paper emphazises the adverse event categorization principle in risk acceptance analysis, and suggests the use of a standard type risk profile of lognormal type for each category of adverse events. The risk profile for a specified category of adverse events and corresponding to a given operation time is defined as the complementary probability distribution function for the accumulated loss during the operation time. The suggestion of the lognormal standard risk profile is based on the following modeling: The sequence of rare adverse events in time is mathematically modeled as a homogeneous Poisson process. It is shown that there is a specific mathematical form of the risk profiles which is robust with respect to variation of distributional assumptions for the losses associated to the single adverse events. The effect of capitalization of the future losses to present time is that the risk profile asymptotically approaches a limit risk profile as the operation time increases. This asymptotic profile is well approximated by the lognormal profile as is the profile for shorter operation time if the single losses are assumed to have lognormal distribution. The risk profile modeling is exemplified by a study of oil spills due to simulated tanker collisions in the Danish straits. It is found that the distribution of the oil spill volume per spill is well represented by an exponential distribution both in Oeresund and in Great Belt. When applied in the Poisson model, a risk profile reasonably close to the standard lognormal profile is obtained. Moreover, based on data pairs (volume, cost) for world wide oil spills it is inferred that the conditional distribution of the costs given the spill volume is well modeled by a lognormal distribution. By unconditioning by the exponential distribution of the single oil spill, a risk profile for the costs is obtained that is indistinguishable from the standard lognormal risk profile.Finally the question of formulating a public risk acceptance criterion is addressed following Ditlevsen, and it is argued that a Nature Preservation Willingness Index can be defined in a similar way as the so-called Life Quality Index defined by Nathwani et al [Nathwani JS, Lind NC, Padey MD. Affordable safety by choice: the life quality method. Institute for Risk Research, University of Waterloo; Waterloo (Ontario, Canada):1997], and can be used to quantify the risk acceptance criterion for the pollution of the environment. This NPWI acceptance criterion is applied to the oil spill example.
Original language English Structural Safety 25 1 1-34 0167-4730 https://doi.org/10.1016/S0167-4730(02)00037-1 Published - 2003