On secondary spatial ranges of transformation products in the environment

Beside a domain of direct impact, environmental chemicals have a second, na turally more extended domain of influence due to their transformation produ cts. In order to estimate the spatial extent of the respective indirect eff ects. the concept of secondary spatial range of a pair of chemicals is intr oduced. Roughly speaking, the secondary spatial range is the typical distan ce of a molecule can reach from the position of release of its precursor be fore degrading itself in an isotropic environment with the same average geo chemical properties as the earth. Starting from a simple model covering glo bal long-range transport and (pseudo-) first-order degradation and/or conve rsion 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 large r of the two characteristic ranges rho (A) and rho (B), of A and B, respect ively: rho (AB) less than or equal to 1.4843 max {rho (A), rho (B)}. Second ly, 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 p ractical applications, we give a simple, yet highly precise approximation f ormula, allowing for rapid estimation of secondary ranges. By three typical examples, it is then demonstrated how secondary ranges can be estimated si mply by inserting 5 measurable constants for chemicals A and B, respectivel y, into a given formula. Finally, it is argued that secondary ranges should be adequately included in the environmental assessment of precursor compou nds. (C) 2000 Elsevier Science B.V. All rights reserved.