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

Abstract

A numerical method t o 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.

Sulfur chemistry in the National Center for Atmospheric Research Community Climate Model: Description, evaluation, features, and sensitivity to aqueous chemistry

“…Because R4 is nonlinear and the diurnally averaged rate of reaction does not equal the reaction rate of diurnally averaged HO2 mixing ratios, the H O2 mixing ratios are adjustcd by the amount of daylight at any given latitude. The rates of the sulfur reactions are determined by the effective first-order rate coefficient and using a quasi-steady state approximation [Hesstvedt et al, 1978]. The H20= concentration determined from the gas-phase reactions is calculated using an Euler forward approximation.…”

Benchmarking stiff ode solvers for atmospheric chemistry problems-I. implicit vs explicit

“…where this is illustrated for the EUSMOG problem), but have the disadvantage of being problem dependent. With lumping we mean here the technique of grouping species into chemical families to reduce, for example, the stiffness, or to enforce conservation for a chemical family (see Hesstvedt et al (1978) where this form oflumping was proposed first for the QSSA method). Hence our comparison emphasizes the numerical properties and performance of the solvers applied.…”

“…There are many such solvers in use in atmospheric models. Often the numerical methods are adapted for a particular chemistry scheme, like QSSA methods Hesstvedt et al, 1978;Verwer and Simpson, 1995). In such a case a change in the chemistry scheme necessitates a reconsideration of the numerical scheme as well, which is a disadvantage.…”

Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

“…• Chemistry-deposition part: An improved version of the QSSA (Quasi Steady-State Approximation) [8].…”