Quasi‐steady‐state approximations in air pollution modeling: Comparison of two numerical schemes for oxidant prediction

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Abstract
A numerical method to solve the set of differential equations which describes the chemical development in polluted air is presented. The photochemical lifetimes, continuously monitored for all compounds, determine how the integrations are performed at all times. Components with lifetimes less than 10% of the time step, which is taken as 30 sec, are assumed to be in photochemical equilibrium, while compounds with photochemical lifetimes greater than 100 times the time step are computed according to Euler's method. All other components are calculated from the exponential solution of the continuity equation. The computational accuracy may be improved by iteration on components assumed to be determined by the instant values of other components. The convergence of the iteration is speeded up by ordering the short‐lived compounds in a hierarchical sequence. Since computational errors connected with QSSA methods are difficult to assess, comparison with an automatic scheme is necessary. Our method has been compared with Gear's method for a range of model mixtures of hydrocarbons, nitrogen oxides, and air, thought to cover most conceivable situations of atmospheric pollution. The agreement with Gear's method is within a few percent for all components all the time, in most cases even within 1%. No accumulation of deviations occur during long‐term integrations (e.g., 48 hr with day and night shiftings), and differences which appear during periods with strong concentration gradients (e.g., after sunrise) vanish when the activity has culminated. The method presented here is considerably more efficient than Gear's method, with respect to both computer time and storage.