Low-dimensional manifolds and reduced chemical models for tropospheric chemistry simulations

The chemical component of a reactive pollution dispersion model often consumes much of the total computational effort involved. If savings can be made in the calculation of the chemical sub-model without significant loss of accuracy then higher resolution can be afforded in the spatial domain leading to better overall solution accuracy. The usual approach to reducing chemical models is by combining species with similar reactivities into single variables. Compact representations of atmospheric chemical mechanisms can be found of the order of 30–100 species. Dynamical systems analysis however shows that the long-term behaviour of chemical systems is usually restricted to much lower-dimensional manifolds in the total species space, due to many of the fast time-scales quickly reaching local equilibrium. This suggests that if appropriate representations can be found, further reductions can be made in the number of variables required to represent tropospheric chemistry. This paper will demonstrate using time-scale analysis that the intrinsic dimension of a typical tropospheric chemical model is low (varying between 2 and 9) and therefore by using a lower-dimensional representation of the chemistry, savings can be made in terms of the number of equations which need to be solved in the chemical sub-model of a dispersion code. An alternative method for chemical modelling will be described which uses simple difference equations rather than the solution of differential rate equations; a technique called repro-modelling. This technique defines difference equations representing species concentrations as functions of concentrations at previous time-points and important parameters, by fitting orthonormal polynomial functions to large data sets. The use of such fitted algebraic representations makes the repeated chemical kinetic simulations used in reactive dispersion codes more efficient. The paper will present a dimensional analysis of a reduced version of the Carbon-Bond scheme and will show that the scheme can be accurately represented over a wide range of concentration conditions using a nine-dimensional repro-model rather than the 90 variables in the original scheme.