Detection of probability distribution and regimes in nonlinear systems with nonlinear dimension reduction methods

大气系统是一个高维非线性系统，由于其高维性，对其变率进行简单的分析是不容易的。本研究采用非线性降维方法，从冬季极地平流层温度、降水等强非线性大气变率中提取低维流形。这些流形表现出物理量在正负值之间的不对称性，尽管这种不对称性不能用线性方法表示。此外，我估计了流形上状态变量和簇的存在概率分布，并获得了可能的状态，尽管它在统计上不显著。

The atmospheric system is a high dimensional nonlinear system and naive analyses of variability in the system is not easy due to the high dimensionality. In this study, I extract low dimensional manifolds from strongly nonlinear atmospheric variability, such as temperature in winter polar stratosphere and precipitation, with nonlinear dimension reduction methods. Those manifolds show asymmetry in physical quantities between positive and negative values, although the asymmetry cannot be represented with linear methods. Additionally I estimate existence probability distribution of state variables and clusters on the manifolds, and obtain possible regimes, though it is not statistically significant.