Low-dimensional manifolds in tropospheric chemical systems

Abstract

Ordinary differential equations derived from large nonlinear systems of chemical reactions are computationally expensive to solve because of the large number of coupled species and the large range of time-scales present. The range of time-scales often spans several orders of magnitude leading to stiff systems of equations requiring implicit numerical techniques. The use of slow 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. The method exploits the existence of a low-dimensional manifold within a large-dimensional species phase space onto which the system quickly collapses. This paper investigates the existence of slow manifolds for nonlinear 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 including a subset of the Master Chemical Mechanism describing butane oxidation and the formation of ozone in the troposphere. It is shown that the intrinsic dimension of the slow manifold varies diurnally and depends on photolytic processes and the relative concentrations of major pollutants.