Tests on Combined Projection/forward Differencing Integration for Stiff Photochemical Family Systems at Long Time Step

Abstract Accurate estimates of final tracer concentrations guide adjustment of individual species levels so that forward integration of stiff families can proceed at time steps an order of magnitude larger than inherent loss constants. Maintenance of a unified concentration vector in the solver ensures mass conservation. The sequence was perfected by raising the step size upward from 100 s in a standard 25 family 45 species stratospheric box model with explicit Euler numerics. Projections were inserted as instabilities arose. Ultimately, a uniform Δt of 1 h was achieved from 20–50 km at mid-latitudes. Results were compared over five equinoctial diurnal cycles with runs at 0.1 and 1 s steps in which every constituent other than the individual atoms, CHO and CH3O, was handled separately. Agreement was better than 10−2 for the major reservoirs in almost all cases, and was equally close for radicals between 6 a.m. and 6 p.m., provided that photolysis constants were time averaged. The few exceptions were due to experimentation with a linearized implicit concentration predictor, or to the approximations underlying family partitioning recipes. CPU timings extrapolated to a hypothetical GCM grid suggest that 3-D modeling will be possible at the level of chemical resolution in the programs.