Convergence testing is a common practice in the development of dynamical cores of atmospheric models but is not as often exercised for the parameterization of subgrid physics. An earlier study revealed that the stratiform cloud parameterizations in several predecessors of the Energy Exascale Earth System Model (E3SM) showed strong time step sensitivity and slower‐than‐expected convergence when the model's time step was systematically refined. In this work, a simplified atmosphere model is configured that consists of the spectral‐element dynamical core of the E3SM atmosphere model coupled with a large‐scale condensation parameterization based on commonly used assumptions. This simplified model also resembles E3SM and its predecessors in the numerical implementation of process coupling and shows poor time step convergence in short ensemble tests. We present a formal error analysis to reveal the expected time step convergence rate and the conditions for obtaining such convergence. Numerical experiments are conducted to investigate the root causes of convergence problems. We show that revisions in the process coupling and closure assumption help to improve convergence in short simulations using the simplified model; the same revisions applied to a full atmosphere model lead to significant changes in the simulated long‐term climate. This work demonstrates that causes of convergence issues in atmospheric simulations can be understood by combining analyses from physical and mathematical perspectives. Addressing convergence issues can help to obtain a discrete model that is more consistent with the intended representation of the physical phenomena.

中文翻译：

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用简化的物理方法改善大气模型中的时间步收敛：封闭假设和过程耦合的影响

收敛测试是大气模型动力学核心开发中的一种常见实践，但对于亚网格物理参数化却不那么频繁地进行。一项较早的研究表明，在能量百亿地球系统模型（E3SM）的几个前身中，层状云参数化显示出较强的时间步敏感性，并且当系统地改进时间步时，收敛速度慢于预期。在这项工作中，配置了一个简化的大气模型，该模型由E3SM大气模型的光谱元素动态核心以及基于常用假设的大规模冷凝参数化组成。这个简化的模型在过程耦合的数值实现中也类似于E3SM及其前身，并在短期整体测试中显示出较差的时间步收敛性。我们提出一种形式上的误差分析，以揭示预期的时间步收敛速度以及获得这种收敛的条件。进行数值实验以研究收敛问题的根本原因。我们表明，使用简化模型对过程耦合和闭合假设进行的修订有助于提高短期仿真的收敛性；对全大气层模型进行的相同修改会导致模拟的长期气候发生重大变化。这项工作表明，可以通过组合物理和数学角度的分析来理解大气模拟中收敛问题的原因。解决收敛问题可以帮助获得与物理现象的预期表示更加一致的离散模型。