Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves
Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves
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DOI：
10.1175/jas-d-18-0092.1
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发表时间：
2018-08
影响因子：
3.1
通讯作者：
Z. Kuang
中科院分区：
文献类型：
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作者：
Z. Kuang
提出了一种系统地构建潮湿对流大气线性稳定性简单模型的程序。首先，由云系统解析模型构建的积云系综的线性响应函数与表示二维大规模线性波动力学的矩阵耦合。对于辐射-对流平衡参考状态，该模型给出了不稳定模式的两个分支：传播对流耦合波分支和与柱积分湿静态能量（MSE）存储相关的静止分支。静止支路仅在有辐射反馈时才不稳定，而对流耦合波支路受辐射反馈影响较小。通过控制理论中的模块化降阶过程，基于线性响应函数的模型被简化为六个常微分方程组，同时仍然捕获不稳定模式的基本特征（特征值和结构）。然后六维系统被分成慢流形和快流形。慢流形（同样是反射柱 MSE 存储）对于稳态模式至关重要，但对于对流耦合波则不然。然后，快速流形被转换为类似于先前对流耦合波的简单模型的形式，从而使这些模型和从中得出的见解奠定了更坚实的基础。该过程还可以更好地量化此类简单模型的参数，并允许更好地理解不同参考状态之间的稳定性差异。
A procedure is presented to systematically construct simple models for the linear stability of moist convecting atmospheres. First, linear response functions of a cumulus ensemble constructed from cloud-system-resolving models are coupled with matrices expressing two-dimensional large-scale linear wave dynamics. For a radiative–convective equilibrium reference state, this model gives two branches of unstable modes: a propagating convectively coupled wave branch and a stationary branch related to storage of column-integrated moist static energy (MSE). The stationary branch is unstable only when radiative feedback is included, while the convectively coupled wave branch is less affected by radiative feedback. With a modular order-reduction procedure from control theory, the linear-response-function-based model is reduced to a system of six ordinary differential equations while still capturing the essential features of the unstable modes (eigenvalues and structures). The six-dimensional system is then split into a slow and a fast manifold. The slow manifold (again, reflecting column MSE storage) is essential for the stationary mode but not for the convectively coupled waves. The fast manifold is then transformed into a form similar to that of prior simple models of convectively coupled waves, thus placing those models and the insights derived from them on a firmer footing. The procedure also better quantifies the parameters of such simple models and allows the stability difference between different reference states to be better understood.