Normal forms for reduced stochastic climate models
Normal forms for reduced stochastic climate models
复制标题
DOI：
10.1073/pnas.0900173106
复制
发表时间：
2009-03
期刊：
影响因子：
--
通讯作者：
A. Majda;C. Franzke;D. Crommelin
中科院分区：
文献类型：
--
作者：
A. Majda;C. Franzke;D. Crommelin
从观测数据或综合性高维气候模式系统地发展低维随机气候模式是大气低频变率、气候敏感性和改进扩展范围预报的重要课题。在这里，从应用数学的技术被用来系统地推导出正规形式减少随机气候模式的低频变量。使用一些经验正交函数（EOF）（也称为主成分分析，Karhunen-Loéve和适当的正交分解）取决于观测数据，以跨越低频子空间，需要评估二元相互作用，除了更熟悉的三元组之间的相互作用的动态的低频和高频子空间。下图显示，二元和乘三元相互作用联合收割机与气候学线性算子相互作用同时产生强非线性耗散和相关加性和乘性（CAM）随机噪声。对于一个单一的低频变量的二元相互作用和气候线性算子单独产生一个正常的形式与CAM噪音从平流的大尺度的小尺度和同时强大的立方阻尼。这些正常的形式应该证明是有用的发展系统的战略，从气候数据的随机模型的估计。作为一个说明性的例子，下面将一维标准形应用于低频模式，如气候模式中的北大西洋涛动（NAO）。这里的结果也说明了最近提出的线性标量CAM噪声模型的低频变异性的短周期。
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 low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen–Loéve 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.