Faster Chemistry Solver Cuts Earth Model Costs by a Third

A two-stage Rosenbrock solver, known as ROS2, has been implemented in the US Department of Energy’s Energy Exascale Earth System Model version 1 (E3SMv1) and evaluated as an alternative way to integrate atmospheric chemistry. The result, reported in the journal Geoscientific Model Development by Rong-You Chien and Joshua S. Fu of the University of Tennessee, Knoxville, is a substantial computational saving: at the same 180-second chemistry timestep, ROS2 required roughly one third less chemistry integration time than the model’s original iterative implicit solver on the tested Cori/KNL CPU platform, while keeping one-year simulations stable and producing only small differences in simulated surface ozone.

The integration of stiff atmospheric chemical systems is one of the major computational costs in Earth system models. Atmospheric chemistry couples species whose lifetimes range from seconds or minutes for radical species to weeks or months for long-lived gases such as ozone, producing stiff ordinary differential equations that are expensive to solve. As models move toward higher spatial resolution, more comprehensive process coupling, and greater chemical complexity, the burden of solving these equations grows, motivating numerical methods that reduce cost without changing the underlying reaction mechanism.

Interactive chemistry, in which reaction rates respond dynamically to simulated meteorology such as temperature and radiation, improves internal consistency compared with prescribed-chemistry approaches but increases computational cost. Its adoption is still not universal: of the 60 coupled climate and Earth system models participating in CMIP6, 32 describe atmospheric chemistry components, and 11 of those used specified or prescribed oxidants in the configurations summarized by IPCC AR6. E3SMv1’s atmospheric component, the E3SM Atmosphere Model, is derived from the Community Atmosphere Model version 5 and uses a spectral-element dynamical core supporting global variable-resolution meshes.

In the default E3SMv1 configuration, the chemistry equations are integrated with an iterative implicit solver using a fixed chemistry timestep, an approach similar to that employed in other fully coupled chemistry-climate models such as WACCM. Iterative implicit solvers provide stable integration but can be limited by large timesteps when species lifetimes are minutes or seconds. Rosenbrock methods offer a different route: they are linearly implicit schemes designed for stiff systems that avoid costly nonlinear iterations. ROS2, a second-order two-stage variant developed by Verwer and colleagues, uses two intermediate stage solutions combined to advance the state, and with the stability parameter set to gamma equal to one plus the square root of two over two, the scheme is L-stable, which suits radical species with very short lifetimes.

The researchers tested ROS2 with two chemistry mechanisms adapted for E3SMv1 that differ substantially in size and structure. ChemUCI, based on the UC Irvine chemistry-transport formulation, contains 60 gas-phase and aerosol species, of which 53 are solved implicitly, with 90 reactions and 262 non-zero Jacobian elements after solver permutation. Trop_strat_mozart_mam4 represents more comprehensive tropospheric and stratospheric chemistry, with 155 species, 130 solved implicitly, 365 reactions, and 1232 non-zero Jacobian elements. The mechanisms were not compared as competing chemical representations; they served as numerically distinct testbeds for assessing solver behavior across different system sizes, sparsity patterns, and stiffness characteristics. The solver was inserted into the existing chemistry framework without modifying reaction mechanisms, species definitions, or transport, so any differences between simulations arise solely from the numerical integration method.

To assess accuracy under realistic conditions, the team built a box-model framework using actual chemical reaction rates and species interactions extracted from the full Earth system model, covering 48,602 atmospheric columns with 72 vertical layers from the first simulation day. Halving the timestep successively from 1800 seconds, they fitted log-log slopes of timestep-refinement differences as empirical convergence diagnostics. For chemUCI, the mean slopes were 0.34 for the implicit solver and 0.68 for ROS2; for trop_strat_mozart_mam4, 0.30 and 0.50. ROS2 therefore showed a steeper timestep-refinement trend in both mechanisms, although the authors caution these values should not be equated with the ideal first- and second-order limits, because the exact solution is unavailable and the stiff nonlinear system may not be in the asymptotic convergence regime at all sampled states. A sensitivity test reducing external NOx emissions by 20 percent changed the chemical state as expected, but within each emissions scenario the ozone distributions from the two solvers remained closely aligned.

Three numerical configurations were compared in fully coupled one-day and one-year simulations: the original implicit solver at 1800 seconds (IMP_1800), the implicit solver at 180 seconds (IMP_180), and ROS2 at 180 seconds (ROS2_180). All simulations used identical initial conditions, emissions, boundary conditions, and physical parameterizations, and all ran on the now-decommissioned Cray XC-40 Cori system at NERSC with Intel Knights Landing processors, using 693-core and 1350-core configurations. For trop_strat_mozart_mam4, ROS2_180 required 67.64 percent of the IMP_180 computational time on 693 cores and 67.20 percent on 1350 cores; for chemUCI, the corresponding values were 67.38 and 67.66 percent. The similar percentage reductions across the two mechanisms should not be read as a mechanism-independent scaling law, and standalone box-model tests showed a broader improvement range of roughly 20 to 48 percent. IMP_1800 remained the least expensive configuration overall because it takes one chemistry step for every ten steps at 180 seconds, so the demonstrated advantage applies specifically to the same-timestep comparison.

Over one-year integrations, ROS2_180 showed no evidence of numerical instability. Global-mean surface-ozone differences relative to IMP_1800 were small: about +0.11 parts per billion for chemUCI and about -1.03 ppb for trop_strat_mozart_mam4. Spatial differences in ozone, NO, NO2, and OH were species- and mechanism-dependent, with no common-sign systematic response evident across the evaluated gas-phase species. For chemUCI, ozone differences were generally small with modest positive features over parts of the Northern Hemisphere, while for trop_strat_mozart_mam4, ROS2_180 produced lower surface ozone over much of the globe with larger negative differences over North Africa. Diurnal cycles retained similar timing and day-night structure, but the comparisons diagnose numerical sensitivity rather than rank accuracy, since no exact reference solution exists for the fully coupled simulations.

The authors are careful to define the limits of the study. The experiments were not designed to provide observational validation of either chemistry mechanism or an absolute accuracy ranking among the tested configurations, and the timing results are controlled same-platform benchmarks rather than evidence of performance on contemporary GPU-accelerated or exascale architectures. Regional differences among configurations can reflect interactions among precursor abundance, radical chemistry, photolysis, transport, and meteorology, and a process-budget analysis would be needed to attribute them. Additional timestep-refinement tests and benchmarking on current CPU and GPU systems are needed to quantify coupled-model convergence and performance portability.

Within those limits, the message is practical and concrete. When E3SM chemistry must operate at short timesteps, whether to resolve fast photochemistry or to support finer vertical resolution and stronger coupling constraints, ROS2 offers a lower-cost alternative to the current implicit integrator, cutting same-timestep chemistry integration cost by about a third on the tested hardware while preserving stability over a full simulated year. As Earth system models advance toward CMIP7-era simulations with higher resolution and richer chemistry, efficient and numerically robust stiff-chemistry solvers of this kind become increasingly relevant, and the ROS2 implementation in E3SMv1 provides a tested starting point for that transition.

Subject of Research: Implementation and evaluation of a two-stage Rosenbrock chemistry solver in the E3SMv1 Earth system model

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

Article References: Chien, R.-Y., & Fu, J. S. (2026). Using a two-stage Rosenbrock solver to increase computational efficiency in the DOE's Exascale Earth System Model version 1 (E3SMv1). Geoscientific Model Development, 19(20), 10309-10320. https://doi.org/10.5194/gmd-19-10309-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-10309-2026

Keywords: E3SMv1, Rosenbrock solver, ROS2, atmospheric chemistry, stiff ODEs, computational efficiency, Earth system modeling, chemistry-climate model, numerical methods, surface ozone, timestep, high-performance computing