Test of two numerical schemes for use in atmospheric transport-chemistry models

Abstract

Two fast integration methods for chemical kinetics are tested. One is the Quasi-steady State Approximation (QSSA) method and the other is a new Euler Backward Iterative (EBI) method. The EBI method is based on iterative solution of the Euler backward approximation of a coupled system of nonlinear ordinary differential equations of chemical kinetics. The efficiency of the iteration process is increased by using analytical solutions for groups of species which are strongly coupled. The accuracy of both integration methods is evaluated by comparing the results with solutions obtained by a Gear method, the Livermore Solver for Ordinary Differential Equations (LSODE). The chemical scheme used is the Carbon-bond Mechanism IV (CBM-IV). The numerical methods are tested of three chemical scenarios: two scenarios without emissions and with constant reaction rates and one scenario with variable emissions and photodissociation rates. Using a short time step (50 s), both EBI and QSSA perform very well, even under extreme chemical conditions. For larger time steps the EBI method performs better than QSSA. In the case of more realistic chemical conditions, both methods perform well even with a time step of 900 s. The accuracy of QSSA depends highly on the iteration procedure. Without iterations the QSSA method performs poorly.

The great advantage of the EBI method is that concentrations are computed using linear operators only. Because of this, the method is mass conserving and can be used in air pollution transport models where higher moments of concentration distributions also need to be evaluated.

Both the QSSA and the EBI methods can be recommended for use in atmospheric transport-chemistry models, where accuracy as well as computational efficiency is important. In general, the new EBI method is, however, more efficient than QSSA with a constant number of iterations.