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@ARTICLE{Dreger:1044264,
      author       = {Dreger, Raphael and Kirfel, Timo and Pozzer, Andrea and
                      Rosanka, Simon and Sander, Rolf and Taraborrelli, Domenico},
      title        = {{O}ptimized step size control within the {R}osenbrock
                      solvers for stiff chemical ordinary differential equation
                      systems in {KPP} version $2.2.3_rs4$},
      journal      = {Geoscientific model development},
      volume       = {18},
      number       = {13},
      issn         = {1991-959X},
      address      = {Katlenburg-Lindau},
      publisher    = {Copernicus},
      reportid     = {FZJ-2025-03134},
      pages        = {4273 - 4291},
      year         = {2025},
      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 substeps. 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 in 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 $13 \%$ 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
                      stay below $1 \%$ for the main tropospheric oxidants. The
                      results presented here show the possibility of more
                      efficient atmospheric chemistry simulations without
                      compromising accuracy.},
      cin          = {ICE-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)ICE-3-20101013},
      pnm          = {2111 - Air Quality (POF4-211)},
      pid          = {G:(DE-HGF)POF4-2111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001528724000001},
      doi          = {10.5194/gmd-18-4273-2025},
      url          = {https://juser.fz-juelich.de/record/1044264},
}