Terrain methods on spectral analysis for paleoclimate interpretations: A novel visualization technique using python

Abstract

Spectral analysis techniques are valuable tools at the disposal of paleoclimate scientists in their research of cyclical phenomena potentially responsible for past climatic fluctuations. Advances in computing and an increased availability of climate time series have helped to consolidate this approach. Yet the visual representation of spectral analysis results has not improved at the same pace. Time-frequency analysis aims to identify periodic signals that vary over time using 2-D color graphs, depicting spectral bands theoretically discernible from the image background. The paleoclimate literature is full of examples such as the continuous wavelet analysis, the evolutionary fast Fourier transform (FFT) spectrogram, or even the more recent synchrosqueezing transform. Our approach is based on the stack of non-evolutive (assuming stationary behaviour) spectral analysis results from thousands of fixed interval time series, previously split from a longer and unevenly spaced (irregular sampling) paleoclimate time series. As illustrative examples, the targeted time series are derived from the LR04 Global Pliocene-Pleistocene Benthic δ18O stack and from the 65 ◦N summer insolation for the last 5.3 Myr, by means of the Lomb-Scargle periodogram technique. Enhanced and clearer visualization is achieved through the novel incorporation of the terrain analysis techniques: slope, hillshading and color mapping, and posterior blending of the individual images, using Python code. The result consists of a high resolution graphical output, allowing for better qualitative and quantitative interpretations of the obtained cyclicity, as the code incorporates the import of the achieved confidence levels from the spectral technique and the option to obscure the pixels under a certain threshold value. The application of terrain analysis techniques on visualization of spectral analysis results has the purpose of improving previous graphical representations of paleoclimate time-series, especially those time-frequency aspects of the involved phenomena. New developments of our approach may be applied to time-frequency analysis directly, supporting present and future paleoclimate studies.