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

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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.