PNNL

Abstract

Global atmosphere 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. (2019). This work addresses the issues at a more fundamental level by revisiting the parameterization derivation. A derivation of the un-averaged equations, sometimes referred to as sub-grid 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 sub-grid reconstruction (SGR) methodology is used to connect the un-averaged equations 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 sub-grid variability is avoided through rigorous mathematical derivation, the resulting formulation can exhibit both better numerical convergence properties and significant impact on long-term climate.