On a fundamental problem in implementing flux‐form advection schemes for tracer transport in 3‐dimensional general circulation and chemistry transport models
On a fundamental problem in implementing flux‐form advection schemes for tracer transport in 3‐dimensional general circulation and chemistry transport models
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关于在三维大气环流和化学输运模型中实施示踪剂输运通量形式平流方案的基本问题
DOI：
10.1002/qj.49712757318
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发表时间：
2001
影响因子：
8.9
通讯作者：
B. Eaton
中科院分区：
文献类型：
--
作者：
P. Jöckel;R. Kuhlmann;M. Lawrence;B. Steil;C. Brenninkmeijer;P. Crutzen;P. Rasch;B. Eaton
解决了 3D 模型中的一个基本困难，该困难可能是由于平流方案和风之间的不一致而引起的。结果表明，当通过风的平流方案计算的密度场与基于表面压力和西格玛（或混合）坐标的隐含密度场不同时，模型将无法满足 3D 输运模型所需的某些基本标准。为了进行严格的数学公式，重点是模型中质量通量平流方案的示例，其中风和表面压力来自不同的平流方案（例如气候模型或天气中心模型中的光谱方案）；然而，原则上，该讨论几乎适用于模型中压力水平发生变化的任何情况。为了说明此类问题的潜在严重性，构建了质量守恒网格到网格转换方案，该方案仅使用当前示踪剂质量混合比分布。结果表明，只有一种解决方案对任意示踪剂分布全面有效，并且这种类型的校正在模型传输中引入了额外的不需要的人工垂直扩散分量，该分量随着示踪剂质量混合比梯度的增加而增加，并且可能超过物理垂直传输本身。事实证明，任何补充修复的结果，无论是质量修复器还是网格到网格转换，对于全局建模应用程序来说通常都是不可接受的。由此得出的结论是，能够为任意示踪剂产生可靠结果的唯一替代方案是在整个模型时间步长中保持一致的网格，其中由于模拟平流引起的压力水平的所有变化与下一时间步长的表面压力所暗示的变化完全匹配。尽管这已经在一些模型中完成，但这需要对平流方案的结构或其输入风场在其他几个当代大气环流和化学输运模型中进行重大改变。
A fundamental difficulty in 3‐D models is addressed which can arise due to inconsistencies between advection schemes and winds. It is shown that a model will fail to meet certain basic criteria, desired of 3‐D transport models, when the density field computed by the advection scheme from the winds differs from the implied density field based on the surface pressure and the sigma (or hybrid) coordinates. To allow a rigorous mathematical formulation, the focus is on the example of a mass flux advection scheme in a model where the winds and surface pressure are derived from different advection schemes (e.g. a spectral scheme in a climate model or a weather centre model); however, in principle the discussion applies to nearly any situation in which the pressure levels change in a model. To illustrate the potential severity of such problems, a mass conserving gridto‐grid transformation scheme is constructed which only uses the current tracer mass mixing‐ratio distribution. It is shown that only one solution exists that is comprehensively valid for any arbitrary tracer distribution, and that this type of correction introduces an additional undesired artificial vertical diffusion component into the model transport that increases with increasing tracer mass mixing‐ratio gradients and may exceed the physical vertical transport itself. It is demonstrated that the results of any supplementary fix, either mass fixer or grid‐to‐grid transformation, are generally unacceptable for global modelling applications. From this, it is concluded that the only alternative which can produce reliable results for any arbitrary tracer is to maintain a consistent grid throughout the entire model time step, where all changes in pressure levels due to modelled advection exactly match the changes implied by the surface pressure at the next time step. Although this is already done in some models, this would require significant changes in the structure of the advection scheme or its input wind fields in several other contemporary general circulation and chemistry transport models.