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.

中文翻译：

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使用简化的物理方法改善大气模型中的时间步收敛：使用数学严格性避免参数化中的非物理行为

全球大气模型试图捕获各种时间和长度范围内的物理现象。为此，将时间或长度标度低于计算时间步长或网格像元大小的物理过程简化为一个或多个参数化。过度的过分简化会违反约束或破坏原始物理系统中的关系，从而导致意外的和物理上无效的行为。Wan等人的工作已经研究了这样一个问题的例子。（2020，https://doi.org/10.1029/2019MS001982）。通过重新研究参数化推导，这项工作从更基本的层面解决了这些问题。在非平均方程式（有时称为子网格方程式）中非平均冷凝率的推导，提供了与云生长/衰减相关的凝结/蒸发过程的清晰描述和更准确的量化，同时避免了早期研究中使用的简化方法。使用子网格重构（SGR）方法将未平均冷凝率与由全局模型求解的网格单元平均方程式联系起来。SGR方法和数值结果的分析提供了对离散配方不一致和非物理行为不一致的根本原因的见解。还表明，SGR方法论提供了解决此类不一致问题的灵活框架。这项工作可以证明，通过严格的数学推导避免了亚电网变异性参数化中的非物理行为，