Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing

• Published in: Journal of advances in modeling earth systems 2023-05, Vol.15 (5), p.n/a
• Main Authors: Zhang, Shixuan, Vogl, Christopher J., Larson, Vincent E., Bui, Quan M., Wan, Hui, Rasch, Philip J., Woodward, Carol S.
• Format: Article
• Language: English
• Subjects: Atmosphere; Boundary conditions; Clouds; CLUBB cloud and turbulence parameterizations; Convergence; Cumulus clouds; Diffusion; Earth system modeling; General circulation models; GEOSCIENCES; Mathematical models; MATHEMATICS AND COMPUTING; Modelling; Noise; numerical convergence; numerical diffusion; numerical discretization; numerical limiters; Numerical models; Oscillations; Parameterization; Radiation; Simulation; Testing; Turbulence
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2023MS003633

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e., clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear artificial diffusion employed for improving numerical stability can introduce unintended small‐scale features into the solution of the model equations. Smoothing the limiters and using linear artificial diffusion reduces the noise and restores the expected first‐order convergence in CLUBB's solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high‐resolution simulations. The improvements in the results at coarser, near‐operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set. Plain Language Summary In order to detect pathologies in a numerical model of the atmosphere, a diagnostic test is used here that has been widely adopted in the applied mathematics community. The diagnostic test, if set up properly, proves to be effective at detecting the pathologies caused by issues associated with numerical discretization. Both the method of testing and the particular pathologies detected are expected to be relevant to other atmospheric models. Key Points Numerical limiters and nonlinear artificial diffusion can inject unintended small‐scale features into the solution of the model equations Improved treatment of limiters and artificial diffusion can reduce noise and improve the quality of solutions and numerical convergence Convergence testing is a valuable tool for detecting noise in the model solution, as wel