| 28 Apr 2026
Using a two-stage Rosenbrock solver to improve surface ozone prediction and 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.
This manuscript introduces a two-stage Rosenbrock solver (ROS2) into the E3SMv1 model to address the significant computational bottleneck associated with atmospheric chemistry integration. By evaluating the solver across two chemical mechanisms of varying complexity (chemUCI and trop_strat_mozart_mam4), the authors demonstrate that the ROS2 solver can reduce the computational cost by approximately 33% at a 180-second timestep, while maintaining a remarkably low global mean surface ozone bias compared to the default fully implicit solver.
Overall, this paper addresses a critical challenge in Earth System Modeling. The implications of improving the computational efficiency of atmospheric chemistry are broad and highly significant for the development of next-generation, high-resolution climate models. The motivation is strong, the methodology is novel, and the manuscript is generally well-written and clearly structured. I recommend this manuscript for publication after the authors address the following comments.
1. The core contribution of this paper is the enhancement of computational efficiency for atmospheric chemistry modeling within Earth System Models (ESMs), which has broad implications for the modeling community. However, the current Introduction and Conclusion seem to focus too heavily on ozone right from the beginning. I suggest revising the opening paragraphs of both sections to frame the narrative around the broader context, challenges, and historical development of atmospheric chemistry modules in ESMs. Ozone can then be introduced subsequently as a key metric for evaluation, rather than the primary motivation of the paper.
2. The authors note that at a 180-second timestep, the ROS2 solver achieves a ~33% efficiency improvement for both the MOZART and chemUCI mechanisms. Given the significant difference in complexity (number of species and reactions) between these two mechanisms, is this identical 33% reduction a coincidence? Or does it imply that the relative efficiency gain of the ROS2 solver, compared to the default implicit solver, is independent of the chemical network's size? The authors should discuss the theoretical or practical computational reasons behind this consistent scaling.
3. While the global mean surface ozone bias is small, Figure 5 reveals substantial regional discrepancies. The current manuscript lacks a detailed discussion on what drives these specific regional differences (e.g., are they related to specific emission hotspots or distinct meteorological regimes?). Furthermore, focusing almost exclusively on ozone provides a somewhat limited perspective. The spatial differences of other critical atmospheric components, such as NO2, OH and aerosols should also be presented and discussed. I highly recommend strengthening this section to provide a more comprehensive spatial evaluation of the solver’s performance.
4. Although the baseline simulation shows small bias for ozone, the sensitivity of the chemical system to non-linear responses might show larger difference when using the two solvers. To ensure the ROS2 solver behaves consistently with the implicit solver under perturbed conditions, I suggest conducting a simple sensitivity test. For instance, the authors could run a short test where global NOx emissions are reduced by 20%. Comparing the ozone response between the two solvers under this perturbed scenario would robustly demonstrate whether the acceptable bias holds true for non-linear chemical regimes.
Technical Comments: The x and y axes are currently missing Fig.1 labels. I believe they represent the number or index of the chemical species. Please add appropriate axis labels to clarify what is being plotted.