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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Normal Forms For Reduced Stochastic Climate Models
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Normal Forms For Reduced Stochastic Climate Models

机译：减少的随机气候模型的范式

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The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for iow-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen-Loeve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to low-frequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability.
机译：通过观测或综合性高维气候模型对低维随机气候模型进行系统开发是大气低频变化，气候敏感性和改进的扩展范围预报的重要课题。在这里，来自应用数学的技术被用来系统地推导用于低频变量的简化随机气候模型的正态形式。根据观察数据跨越低频子空间使用一些经验正交函数（EOF）（也称为主成分分析，Karhunen-Loeve和正确正交分解）需要对dyad相互作用进行评估，除了在三元组中更熟悉动力学的低频子空间和高频子空间之间的相互作用。如下所示，二元组和乘性三元组相互作用与气候线性算子相互作用相结合，以同时产生强非线性耗散和相关的加法和乘积（CAM）随机噪声。对于单个低频变量，二元相互作用和气候线性算子仅通过小规模的大尺度平流和强立方阻尼同时产生具有CAM噪声的正态形式。这些正常形式应被证明对开发用于从气候数据估算随机模型的系统策略很有用。作为说明性示例，一维范式在下面应用于气候模式中的低频模式，例如北大西洋涛动（NAO）。这里的结果还说明了其他地方针对低频可变性提出的最新线性标量CAM噪声模型的不足。

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