A solution to the trilemma of the moist Charney-Phillips staggering
A solution to the trilemma of the moist Charney-Phillips staggering
复制标题
潮湿的查尼-菲利普斯令人震惊的三难困境的解决方案
DOI：
10.1002/qj.4406
复制
发表时间：
2022
影响因子：
8.9
通讯作者：
Bendall T
中科院分区：
文献类型：
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作者：
Bendall T
在许多大气数值模型中使用的Charney-Phillips网格，涉及密度变量节点与熵型变量节点的垂直交错。当湿度包含在这样的模型中时，它要么与密度同位，这样湿度就可以与干质量保守一致地输送，要么与熵型变量同位，这样湿度和温度之间的耦合就可以很好地表示出来。这两种性质都是可取的，但起初似乎很难同时获得这两种性质。在这里，我们提出了一个框架来解决这个问题，通过将水分混合比与潜在温度一起定位，但将其传输表述为垂直移动网格上的密度。在此框架内，所涉及的操作人员的特定选择提供了所需的水分输送的保存和一致性。该框架是在有限元方法的背景下描述的。我们还提出了一个明确的龙格-库塔时间步进方案，适用于该框架。然后通过数值试验说明了该方法确实具有期望的守恒性和一致性。
The Charney–Phillips grid, used in many numerical models of the atmosphere, involves vertically staggering the nodes of the density variable with the nodes of the entropy‐type variable. When moisture is included in such a model, it is either co‐located with density so that moisture can be transported conservatively and consistently with dry mass, or with the entropy‐type variable so that the coupling between moisture and temperature can be represented well. Both properties are desirable, yet at first it appears difficult to obtain both simultaneously. Here, we present a framework to resolve this problem, by co‐locating the moisture mixing ratio with potential temperature but formulating its transport as that of a density on a vertically shifted mesh. Within this framework, particular choices of the operators involved provide the desired conservation and consistency properties of the moisture transport. The framework is described in the context of a finite‐element approach. We also present an explicit Runge–Kutta time‐stepping scheme that is appropriate for use within this framework. This approach is then illustrated through numerical tests, which demonstrate that it does indeed have the desired conservation and consistency properties.