Identifying signals from intermittent low-frequency behaving systems

An approach is presented to recover a true signal from an intermittent regime-like behaving noisy system given an estimate of the noise covariance C_N. The method is based on minimizing the noise probability distribution on isosurfaces of the data probability distribution and involves the spectrum of the matrix C_DC_N^-1 where C_D represents an estimate of the data covariance within a given regime. In single channel, i.e., one-dimensional, case the intermittent low-frequency time series is split according to the regime level. For each regime the obtained sub-sampled time series is first centred by removing its time mean and then projected onto a higher dimensional space using the method of the delay coordinates. The oscillation for each regime level is then obtained as the leading eigenvector of C_DC_N^-1. In the multi-channel case the signal pattern is obtained in the same way locally in each cluster forming the data. The approach is first tested with the Lorenz system yielding the correct oscillation. The method is then applied to the Pacific 500-hPa geopotential height from a set of multidecadal integrations with the General Circulation Model (GCM) of the Hadley Centre, forced with observed Sea Surface Temperature (SST), in order to identify the nonlinear atmospheric response associated with El Nino Southern Oscillation (ENSO).