Using a two-stage Rosenbrock solver to increase computational efficiency in the DOE's Exascale Earth System Model version 1 (E3SMv1)

Abstract. The integration of stiff atmospheric chemical systems is a major computational cost in Earth System Models and poses challenges for numerical stability and scalability as chemical complexity and temporal resolution increase. Current implementations commonly rely on fully implicit Newton–Raphson-based solvers, which are robust but computationally expensive. In this study, we implement a semi-implicit two-stage Rosenbrock method (ROS2) in the Energy Exascale Earth System Model version 1 (E3SMv1) and evaluate its performance as an alternative chemistry time-integration scheme. The ROS2 solver is applied to two interactive chemical mechanisms of differing stiffness and size: chemUCI (60 prognostic species) and trop_strat_mozart_mam4 (155 prognostic species). Numerical experiments include short simulations to quantify computational cost and year-long integrations to assess numerical stability, solution consistency, and long-term behavior. Solver performance is evaluated under identical model configurations and timesteps. At a 180-second timestep, ROS2 reduces chemistry integration cost by approximately 33 % relative to the default implicit solver. Differences in global mean surface ozone concentrations are small (≤1.03 ppb), and no systematic drift or degradation in numerical stability is observed over one-year simulations. These results indicate that low-order Rosenbrock methods provide a computationally efficient and numerically stable alternative for stiff atmospheric chemistry integration in E3SMv1. The implementation offers a flexible framework for future model configurations with increased chemical complexity and resolution.