Cyclic exchanges and level of coupling between environmental media: intermedia feedback in multimedia fate models

The importance of cyclic transport of chemicals between media in the environment can be expressed in terms of the Feedback correction factor--a multiplier that accounts for the fraction of an emission that returns to the medium of release after transfer to other media. This factor is calculated analytically by explicitly solving the appropriate system of mass balance equations or using matrix techniques. It generalizes the concept of stickiness, the ratio between the net and the overall deposition rate constants, to multipathway feedback, while providing a clearer view of the level of coupling between media and analyzing the importance of coupling. This paper first shows the usefulness of the total removal rate coefficient in each media (sum of degradation rate and all intermedia transfer rates) as a baseline to determine the chemical mass in different media, the characteristic travel distance and to understand the cyclic behavior, rather than starting from the degradation lifetimes or the overall persistence in the environment. Starting from this baseline, the importance of feedback is limited for most organic chemicals. The predicted media concentrations are influenced by less than 10% due to the cyclic nature of the intermedia transport for more than 90% of the 317 tested chemicals in a 4-compartment, steady-state, closed-system multimedia model. The Feedback correction factor is always less than a factor of 5 with the greatest values when transfer fractions are important in both directions for adjacent media. This corresponds to a restricted range in the K(AW) and K(OA) space with long chemical lifetimes in both adjacent media. This analysis of the importance of the Feedback correction factor, in conjunction with resultant criteria for when cyclic exchanges between media are likely to be significant, facilitates a more transparent understanding of how substance masses are distributed in the modeled system. It is one of the important criteria to determine to what extent media can be independently modeled.