Fugacity superposition: a new approach to dynamic multimedia fate modeling

The fugacities, concentrations, or inventories of pollutants in environmental compartments as determined by multimedia environmental fate models of the Mackay type can be superimposed on each other. This is true for both steady-state (level III) and dynamic (level IV) models. Any problem in multimedia fate models with linear, time-invariant transfer and transformation coefficients can be solved through a superposition of a set of n independent solutions to a set of coupled, homogeneous first-order differential equations, where n is the number of compartments in the model. For initial condition problems in dynamic models, the initial inventories can be separated, e.g. by a compartment. The solution is obtained by adding the single-compartment solutions. For time-varying emissions, a convolution integral is used to superimpose solutions. The advantage of this approach is that the differential equations have to be solved only once. No numeric integration is required. Alternatively, the dynamic model can be simplified to algebraic equations using the Laplace transform. For time-varying emissions, the Laplace transform of the model equations is simply multiplied with the Laplace transform of the emission profile. It is also shown that the time-integrated inventories of the initial conditions problems are the same as the inventories in the steady-state problem. This implies that important properties of pollutants such as potential dose, persistence, and characteristic travel distance can be derived from the steady state.