Residence times in reservoirs under non-steady-state conditions: application to atmospheric SO2 and aerosol sulfate

The definitions of the residence times describing the rate of removal of materials from natural reservoirs, i.e., the mean age, the mean transit time, and the turn-over time, have been extended to encompass time-dependent rates of introduction and removal. This treatment leads to two sets of such residence times, pertinent either to material present in the reservoir at a given observation time or to material that entered the reservoir at a given time of introduction. Whereas the former quantities reflect the time dependence of both the rates of introduction and removal processes, the latter quantities are properties only of the rates of removal processes. Relationships are examined among the several residence times, as well as to the burden of material in the reservoir attributable to a given rate of introduction. Additionally the several definitions are extended to encompass secondary materials, i.e., materials formed in sifu as a consequence of reactions of materials directly introduced. The above framework is applied to a consideration of the residence times and burdens of atmospheric SO, and sulfate aerosol, for assumed time-dependent rates of SO,-to-sulfate conversion and dry deposition. It is found that even for such rates exhibiting strong diurnal modulation, as expected from considerations of photochemical reaction rates and atmospheric stability, the turn-over times and atmospheric burdens of SO, and sulfate exhibit relatively little diurnal modulation, unless the fraction of SO, removed per day substantially exceeds 50%, a circumstance that is at variance with the present understanding of the fate of this material in the atmosphere. These considerations suggest that it may be adequate for many purposes to model the evolution of atmospheric sulfur compounds according to diurnal average rate coefficients. Regarding secondary materials one further useful quantity is the relative burden, or the ratio of the amounts of secondary to primary materials present in the reservoir. This quantity is directly comparable to ratio of the observed concentrations of these materials and thus serves as an additional condition that must be satisfied by models describing their transformation and removal.