CMG: Statistical Analysis of Nonstationary and Nonlinear Paleoclimatic Time Series

Quantities that serve in paleoclimatology as proxy data for temperature, such as oxygen isotope ratios measured in seabed cores, reveal periodicities ranging from about 1000 to 100,000 years. These cycles are caused by a combination of external forcing by known changes in the Earth's orbital parameters (so-called Milankovitch forcing) and by little-understood, complex, nonlinear, and usually nonstationary interactions of different atmospheric and oceanic processes. To now, the statistical tools most commonly employed for analyzing the records have been spectral techniques and correlation analysis based on the assumption of statistical stationarity. This project examines the effects of nonlinear and nonstationary processes on the climate record of the last 5 million years by employing modern statistical techniques that have not previously seen much use in paleoclimatology. These include time-frequency analysis to characterize the non-stationarity in terms of frequency and phase modulation, and bispectral and cross-spectral analysis to different combinations of climate variables to recognize nonlinear couplings. One of the objectives of the project, which is supported jointly by the Division of Atmospheric Sciences and the Division of Mathematical Sciences, is to make these statistical methods available to the paleoclimate community by offering software to students and researchers and arranging a workshop devoted to the subject.