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

The chemical component of a reactive pollution dispersion model often consu mes much of the total computational effort involved. If savings can be made in the calculation of the chemical sub-model without significant loss of a ccuracy then higher resolution can be afforded in the spatial domain leadin g to better overall solution accuracy. The usual approach to reducing chemi cal models is by combining species with similar reactivities into single va riables. Compact representations of atmospheric chemical mechanisms can be found of the order of 30-100 species. Dynamical systems analysis however sh ows 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 chemist ry. This paper will demonstrate using time-scale analysis that the intrinsic di mension of a typical tropospheric chemical model is low (varying between 2 and 9) and therefore by using a lower-dimensional representation of the che mistry, 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 differen ce equations rather than the solution of differential rate equations; a tec hnique called repro-modelling. This technique defines difference equations representing species concentrations as functions of concentrations at previ ous time-points and important parameters, by fitting orthonormal polynomial functions to large data sets. The use of such fitted algebraic representat ions makes the repeated chemical kinetic simulations used in reactive dispe rsion codes more efficient. The paper will present a dimensional analysis o f a reduced version of the Carbon-Bond scheme and will show that the scheme can be accurately represented over a wide range of concentration condition s using a nine-dimensional repro-model rather than the 90 variables in the original scheme. (C) 2000 Elsevier Science Ltd. All rights reserved.