Optimized step size control within the Rosenbrock solvers for stiff chemical ODE systems in KPP version 2.2.3_rs4

Abstract. Numerical integration of multiphase chemical kinetics in atmospheric models is challenging. The underlying system of ordinary differential equations (ODEs) is stiff and thus difficult to solve. Rosenbrock solvers are a popular choice for such tasks. These solvers provide the desired stability and accuracy of results at an affordable yet large computational cost. The latter is crucially dependent on the efficiency of the step size control. Our analysis indicates that the local error, which is the key factor for the step size selection, is often overestimated, leading to very small sub-steps. In this study, we optimized the first-order step size controller most commonly employed in Rosenbrock solvers. Furthermore, we compared its efficiency to a second-order step size controller. We assessed the performance of the controllers in both a box and a global model for very stiff ODEs. Significant reductions of the computation time were accomplished with only marginal deviations in the results compared to the standard first-order controller. This was achieved not only for gas-phase chemistry but also for the more complex aqueous-phase chemistry in cloud droplets and deliquescent aerosols. Depending on the selected chemical mechanism, significant improvements were already achieved by simply adjusting heuristic parameters of the default controller. However, especially for the global model, the best results were achieved with the second-order controller, which reduced the number of function evaluations by 43 %, 27 % and 16 % for gas-phase, cloud and aerosol chemistry, respectively. The overall computational time was reduced by over 11 % while requiring only minimal adjustments to the original code. Analysis of a 1-year integration period showed that with the second-order controller, the deviations from the reference simulation stays below 1 % for the main tropospheric oxidants. The results presented here show the possibility of more efficient atmospheric chemistry simulations without compromising accuracy.