ANALYTIC SOLUTIONS OF REACTION-DIFFUSION EQUATIONS AND IMPLICATIONS FOR THE CONCEPT OF AN AIR PARCEL

In the atmosphere, hydroxyl radical concentrations can be estimated by considering the relative change in the concentration of two hydrocarb ons of differing reactivity. This approach is based on three assumptio ns: (1) that background concentrations of the two hydrocarbon are zero ; (2) that transport processes will influence all hydrocarbon concentr ations equally; that is, hydrocarbon changes can be separated into the product of a chemical term and a transport term; and (3) that hydroca rbons have the same spatial and temporal emission pattern. In this pap er, analytical solutions to a steady state reaction diffusion equation are derived. The general solutions to this problem are nonseparable, with the degree of nonseparability defined by a single parameter that is a simple function of the system's intrinsic timescales. When this p arameter is evaluated for diffusivities typical of the boundary layer (similar to 10(2) m(2)/s) and hydrocarbon reactivities that are suffic iently slow to be practically useful, it can be readily shown that for all practical purposes, separability can be assumed. This separabilit y influences the spatial distribution of loss but not the net global l oss. Thus even under nonseparable conditions, although the apparent lo cal loss rate may be considerably less than the actual kinetic loss ra te implied by hydrocarbon reactivity, when the apparent local loss rat es are integrated to deduce a global loss rate, there will be no under estimate in the global loss rate, since the chemical loss rate is a li near function of hydrocarbon concentrations. It is conjectured that wh en much higher dispersion rates common in photochemical transport mode ls (similar to 10(5)-10(6) m(2)/s) are invoked, local photochemical ba lances may be perturbed when chemical loss rates are either spatially inhomogeneous or influenced by reactant concentrations. Thus in highly diffusive models the influence of highly reactive chemical species ma y be extended further from the source regions than is realistic, even though the globally averaged loss rates would still be consistent with the magnitude of the globally averaged sink.