The Earth’s system dynamics has an intrinsically multi-scale and nonlinear nature, which fundamentally affects the ability to perform weather forecasting and climate projections. In the face of complex dynamics, conventional data analysis techniques (such as EOF analysis) have frequently ambiguous physical interpretation. Moreover, validation of the extracted signals against observations is oftentimes limited by the time span of the observational record, which can be shorter than the timescales of interest, and also significantly altered by anthropogenic factors. Here, we introduce a new data analysis technique for complex dynamical systems and demonstrate its potential by investigating Indo-Pacific climate variability in models and observations. Through this technique, drawbacks associated with ad-hoc filtering are avoided as the extracted signals span many temporal scales without pre-processing the input data. In addition, we discuss the applicability of our approach in non-stationary signals (i.e. trends), and also describe a modification suitable for skillful extraction of coherent patterns in systems lacking spatiotemporal separability (e.g. turbulence). As an extension of this work, we present a framework for data assimilation and forecasting of non-linear time series.