论文标题
部分可观测时空混沌系统的无模型预测
Scaling approaches to quasi-geostrophic theory for moist, precipitating air
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Quasi-geostrophic (QG) theory is of fundamental importance in the study of large-scale atmospheric flows. In recent years, there has been growing interest in extending the classical QG plus Ekman friction layer model (QG-Ekman) to systematically include additional physical processes known to significantly contribute to real-life weather phenomena. This paper lays the foundation for combining two of these developments, namely Smith and Stechmann's family of \emph{Precipitating Quasi-Geostrophic} (PQG) models (J.\ Atmos.\ Sci, {\bfseries 74}, 3285--3303, 2017) on the one hand, and the extension of QG-Ekman for dry air by a strongly \emph{Diabatic Layer} (DL) of intermediate height (QG-DL-Ekman) in (J.\ Atmos.\ Sci, {\bfseries 79}, 887--905, 2022) on the other hand. To this end, Smith and Stechmann's PQG equations for sound-proof motions are first corroborated within a general asymptotic modeling framework starting from a full compressible flow model. The derivations show that the PQG model family is naturally embedded in the asymptotic hierarchy of scale-dependent atmospheric flow models introduced by one of the present authors in (Ann.\ Rev.\ Fluid Mech., {\bfseries 42}, 249--274). Particular emphasis is then placed on an asymptotic scaling regime for PQG that accounts for a generic Kessler-type bulk microphysics closure and is compatible with QG-DL-Ekman theory. The detailed derivation of a moist QG-DL-Ekman model is deferred to a future publication.
