We present the approach which allows to construct nonlinear principal dynamic modes by multivariate time series. Similarly to nonlinear principal component analysis theory, we extend the definition of the principal component corresponding to single mode: from the projection of observed data on the principal line to the projection of the data on the principal curve determined by nonlinear parameterization. We apply the bayesian approach to find both time series of latent modes, and the parameters of nonlinear mapping of these time series on the data space. The simplest evolution law for each mode is included as prior information about the decomposition, which sets the prior smoothness of the principal components. The bayesian evidence criterion is proposed to find optimal structure parameters such as nonlinearity degree of the parameterization as well as prior limitations on the modes which are used in the approach.
The method is tested on strongly nonlinear two-dimensional model example and applied to spatially distributed sea surface temperature data over the Globe. It is shown that the nonlinearity of the modes improves the energy captured by them and allows to reduce the data dimension more efficiently than linear empirical orthogonal functions decomposition.