The Estimation of Intrinsic Low Dimensional Manifold Dimension in Atmospheric Chemical Reaction Systems

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Abstract

Detailed chemical sub-systems are computationally expensive to solve both because of the large number of coupled species and the large range of time-scales present. Intermediate radical species may have fast relaxation times leading to stiff systems of equations requiring implicit numerical techniques. The use of low dimensional manifolds for the description of long time-scale chemical processes has two advantages in that it reduces the number of variables required and also the stiffness of the chemical system by assuming that the fast time-scales are in local equilibrium with respect to the slower ones. This method, referred to as the ILDM (Intrinsic Low Dimensional Manifold), has already been used extensively in combustion related problems. This paper describes the existence of low dimensional manifolds for tropospheric chemical systems and presents a simple method for estimating the local dimension of the manifold using linear perturbation theory. The method is demonstrated for several tropospheric mechanisms over diurnal simulations. It is shown for a Carbon Bond mechanism that the intrinsic dimension of the manifold varies diurnally and is highly dependent on photolytic processes and relative concentrations of the major pollutants. Comments about the implications of diurnal behaviour for applications of ILDM’s in chemically reactive atmospheric dispersion models are made.