An alternative to PCA utilizing Dynamic Time Warping

The Earth’s system is warming due to natural and human driven climate change. Observing, analyzing and understanding the associated geophysical processes is important in order to improve prediction of future changes and mitigate impacts on society and infrastructure. Investigating individual climate processes, such as sea level change, often requires partitioning of the total signal for identifying sub-signals and drivers; in the sea level example these could be trend and seasonal signals or impacts from the El Niño Southern Oscillation (ENSO).

A commonly applied method is the (real) Principal Component Analysis (PCA), which factorizes a given input dataset into time-invariant Empirical Orthogonal Functions (EOF), i.e. spatial patterns, and time-variable Principal Components (PC) based on the most dominant eigenvalues. However, this real-EOF analysis assumes more or less static patterns over time and, thus, lacks the ability to capture temporal variations in the patterns. This can be circumvented by the application of complex or Hermitian EOF analysis, which also enables capturing phase shifts or in other words allows for time-varying spatial patterns.

Here, we present first results from a novel approach utilizing dynamic time warping (DTW) for extracting dominant modes in the form of spatially distributed amplitudes and lags with respect to a ‘base curve’. While classic PCA methods are sensitive to outlier influence on the partitioning, our approach represents a robust alternative. Furthermore, base curves are computed that represent spatial modes via traversal matrices, which act as extensions of the base curves to capture individual lag. We introduce our new approach, compare to complex/Hermitian EOF, explain the numerical scheme, and present some first results based on gridded sea level change data.