Stochastic Environmental Research and Risk Assessment

, Volume 17, Issue 1, pp 20–41

Robustness of spatial ranges of environmental chemicals to changes in model dimension

DOI: 10.1007/s00477-002-0107-3

Cite this article as:
Held, H. Stochastic Environmental Research and Risk Assessment (2003) 17: 20. doi:10.1007/s00477-002-0107-3


 A comparison is made between a circular and a more adequate spherical reaction-diffusion multi-media mass balance model. This comparison adds new aspects to ongoing debates about more effective assessments of potentially harmful substances including persistent organic pollutants (POPs). The circular model serves as a paradigm in investigations of persistence and spatial range of non-polar chemicals. An analytic solution of the spherical model is presented. It is utilized in order to establish circular spatial ranges as versatile approximations of their spherical counterparts for most cases. Deviations in the few exceptions are demonstrated as playing a minor role compared to sensitivities against parameter uncertainties which characterize these exceptional cases as well. The sensitivities are fundamentally linked to the multi-scale nature of the underlying system. Finally, the insensitivity of spatial ranges with respect to dimension – circle versus sphere – is further secured by extensive studies of the role of the mode of entry for which a set of rules is established.

Keywords: Risk assessment, Exposure, Spatial range, Reaction diffusion dynamics, Hypergeometric functions, Legendre Greens function, Uncertainty, Sensitivity, Mode of entry, Environmental chemical, Radioactivity, Precautionary principle

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • H. Held
    • 1
  1. 1.Department of Physics, University of California, Berkeley, CA 94720, USAUS