Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling

Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: Using Mathematical Rigor to Avoid Nonphysical Behavior in a Parameterization

TitleImproving Time Step Convergence in an Atmosphere Model With Simplified Physics: Using Mathematical Rigor to Avoid Nonphysical Behavior in a Parameterization
Publication TypeJournal Article
Year of Publication2020
JournalJournal of Advances in Modeling Earth Systems
Volume12
Number10
Abstract / Summary

Global atmospheric models seek to capture physical phenomena across a wide range of time and length scales. For this to be a feasible task, the physical processes with time or length scales below that of a computational time step or grid cell size are simplified as one or more parameterizations. Inadvertent oversimplification can violate constraints or destroy relationships in the original physical system and consequently lead to unexpected and physically invalid behavior. An example of such a problem has been investigated in the work of Wan et al. (2020, https://doi.org/10.1029/2019MS001982). This work addresses the issues at a more fundamental level by revisiting the parameterization derivation. A derivation of an unaveraged condensation rate in the unaveraged equations, sometimes referred to as subgrid equations, provides a clear description and more accurate quantification of the condensation/evaporation processes associated with cloud growth/decay, while avoiding simplifications used in earlier studies. A subgrid reconstruction (SGR) methodology is used to connect the unaveraged condensation rate with the grid cell averaged equations solved by the global model. Analyses of the SGR method and the numerical results provide insights into root causes of inconsistent discrete formulations and nonphysical behavior. It is also shown that the SGR methodology provides a flexible framework for addressing such inconsistencies. This work serves as a demonstration that when nonphysical behavior in a parameterization of subgrid variability is avoided through rigorous mathematical derivation, the resulting formulation can exhibit both better numerical convergence properties and significant impact on long‐term climate.

URLhttp://dx.doi.org/10.1029/2019ms001974
DOI10.1029/2019ms001974
Journal: Journal of Advances in Modeling Earth Systems
Year of Publication: 2020
Volume: 12
Number: 10
Publication Date: 10/2020

Global atmospheric models seek to capture physical phenomena across a wide range of time and length scales. For this to be a feasible task, the physical processes with time or length scales below that of a computational time step or grid cell size are simplified as one or more parameterizations. Inadvertent oversimplification can violate constraints or destroy relationships in the original physical system and consequently lead to unexpected and physically invalid behavior. An example of such a problem has been investigated in the work of Wan et al. (2020, https://doi.org/10.1029/2019MS001982). This work addresses the issues at a more fundamental level by revisiting the parameterization derivation. A derivation of an unaveraged condensation rate in the unaveraged equations, sometimes referred to as subgrid equations, provides a clear description and more accurate quantification of the condensation/evaporation processes associated with cloud growth/decay, while avoiding simplifications used in earlier studies. A subgrid reconstruction (SGR) methodology is used to connect the unaveraged condensation rate with the grid cell averaged equations solved by the global model. Analyses of the SGR method and the numerical results provide insights into root causes of inconsistent discrete formulations and nonphysical behavior. It is also shown that the SGR methodology provides a flexible framework for addressing such inconsistencies. This work serves as a demonstration that when nonphysical behavior in a parameterization of subgrid variability is avoided through rigorous mathematical derivation, the resulting formulation can exhibit both better numerical convergence properties and significant impact on long‐term climate.

DOI: 10.1029/2019ms001974
Citation:
Vogl, C, H Wan, S Zhang, C Woodward, and P Stinis.  2020.  "Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: Using Mathematical Rigor to Avoid Nonphysical Behavior in a Parameterization."  Journal of Advances in Modeling Earth Systems 12(10).  https://doi.org/10.1029/2019ms001974.