Careful Mathematical Choices Help More Rapidly Reduce Errors in Simulations

More accurate methods provide better results in numerical simulations of atmospheric clouds by avoiding accidental contradictions.

The Science

Numerical weather and climate predictions unfailingly contain errors that can be traced to the various finite resolutions of the underlying numerical models. At higher temporal resolutions, a numerical model recalculates the properties of the atmosphere more often and provides more accurate results by better capturing the detailed features of rapidly evolving phenomena. Earlier studies revealed that small-scale physical phenomena, such as the formation of clouds and rain, act as bottlenecks for achieving higher error reduction rates as a global atmospheric model’s temporal resolution increases. This study shows that improving the mathematical assumptions about individual small-scale phenomena and carefully choosing methods for numerically coupling different atmospheric processes can help improve the internal consistency of the simulations, which in turn can help produce higher error reduction rates.

The Impact

By better-reducing errors, the numerical models will converge at more accurate answers faster. This allows for more efficient use of computing resources as model resolution continues to increase. Improved physical realism also provides a more solid basis for the eventual weather and climate predictions made with the results of numerical models. This makes the predictions, ranging from near-term local rain events to regional and global-scale temperature changes over the next few decades, more accurate.


Assessing error reduction with respect to model resolution is routinely performed for atmospheric processes resolved by numerical weather and climate models. However, it is rarely done for the small-scale and unresolvable, yet impactful processes, such as the formation of clouds and rain. Earlier studies revealed these small-scale processes can be primary culprits of slow error reduction, but the cause remained unclear. In this study, researchers conducted simulations using an idealized configuration created to facilitate the investigation, and a more sophisticated configuration, similar to those used for actual applications, of a state-of-the-art global climate model. The results indicate that overly simplified assumptions about small-scale processes, and simplistic choices made during the assembly of a complete model, can lead to model behaviors that are not only physically invalid, but also mathematically problematic (e.g., singular and/or discontinuous). Addressing these issues at their roots should lead to a model with better internal consistency and higher numerical accuracy as the temporal resolution of a simulation is refined.


Principal Investigator(s)

Hui Wan
Pacific Northwest National Laboratory


This work was supported by the U.S. Department of Energy (DOE) Office of Science through the Office of Biological and Environmental Research and through the Office of Advanced Scientific Computing Research via its Scientific Discovery through Advanced Computing program. Computing resources were provided by National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science user facility supported by the DOE Office of Science under Contract DE- AC02-05CH11231. Additional computing resources were provided by Livermore Computing at Lawrence Livermore National Laboratory and Research Computing at Pacific Northwest National Laboratory.


Wan, H. et al. “Improving time step convergence in an atmosphere model with simplified physics: The impacts of closure assumption and process coupling.Journal of Advances in Modeling Earth Systems 12(10), e2019MS001982 (2020). DOI:10.1029/2019MS001982