On secondary spatial ranges of transformation products in the environment

Beside a domain of direct impact, environmental chemicals have a second, naturally more extended domain of influence due to their transformation products. In order to estimate the spatial extent of the respective indirect effects. the concept of secondary spatial range of a pair of chemicals is introduced. Roughly speaking, the secondary spatial range is the typical distance of a molecule can reach from the position of release of its precursor before degrading itself in an isotropic environment with the same average geochemical properties as the earth. Starting from a simple model covering global long-range transport and (pseudo-) first-order degradation and/or conversion of a precursor A and its transformation product B, we first show that the secondary range rho (AB) is always smaller than 1.4843 times the larger of the two characteristic ranges rho (A) and rho (B), of A and B, respectively: rho (AB) less than or equal to 1.4843 max {rho (A), rho (B)}. Secondly, we give a closed formula for secondary ranges as a function of rho (A) and rho (B). Quite surprisingly, it turns out that the secondary range does not depend on the rate constant k(AB) of the reaction transforming A into B (In typical cases, usable values of k(AB) are difficult to obtain). For practical applications, we give a simple, yet highly precise approximation formula, allowing for rapid estimation of secondary ranges. By three typical examples, it is then demonstrated how secondary ranges can be estimated simply by inserting 5 measurable constants for chemicals A and B, respectively, into a given formula. Finally, it is argued that secondary ranges should be adequately included in the environmental assessment of precursor compounds. (C) 2000 Elsevier Science B.V. All rights reserved.