PNNL

The Science                                

Numerical models can help researchers develop an understanding of atmospheric physics. However, results computed by numerical models may be misleading if their mathematical algorithms cause large inaccuracies. Computational scientists employ a diagnostic tool, called convergence testing, to help verify if the behavior of the numerical results is consistent with the characteristics of the underlying equations that describe the physics. In this study, researchers applied this tool to a sophisticated numerical model of turbulence and clouds. Such atmospheric physics parameterizations are not usually subjected to convergence testing of numerical discretization, partly because of the difficulty in identifying the cause of non-convergent results. However, guided by the convergence tests, the researchers identified and addressed issues in the numerical algorithms used in this physics parameterization, improving the overall fidelity of the results.

The Impact

When convergence testing suggests proper behavior, researchers can have more confidence that the numerical model, if it is run at adequate resolution, faithfully represents the physics described by the model equations. This is a necessary foundation for further work to increase numerical accuracy.

Summary

Atmospheric physics parameterizations are simplified descriptions of atmospheric processes that cost too much computing power to simulate in detail. Typically, parametrization development focuses on the formulation of underlying mathematical equations, rather than the numerical algorithms that solve those equations. Resolution convergence testing assesses the behavior of the numerical results by varying the resolution across a wide range. 

In this study, researchers applied resolution convergence testing to a sophisticated turbulence and cloud parameterization and found non-convergent behavior in several test cases. Through a close collaboration between atmospheric model developers and applied mathematicians, the team identified and reformulated problematic components of the numerical algorithms used in the parameterization. After reformulation, the model produced the expected convergence behavior in four test cases covering a diverse range of weather regimes. This enhances confidence in the trustworthiness of the numerical results. It also provides a necessary foundation for future improvements to the numerical accuracy. Both the method of testing and the numerical issues detected are expected to be relevant to other atmospheric models.

PNNL Contact

Hui Wan, Pacific Northwest National Laboratory, Hui.Wan@pnnl.gov

Funding

This research has been supported by the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) program via a partnership in Earth System Modeling between the Biological and Environmental Research and the Advanced Scientific Computing Research programs. Numerical simulations were carried out using the Department of Energy’s Earth System Modeling program area’s Compy computing cluster located at Pacific Northwest National Laboratory and using the Livermore Computing Center at Lawrence Livermore National Laboratory.