Predictable components in global speleothem δ18O

Abstract

The earth's ice–ocean–atmosphere system is made up of subsystems which have different dynamics and which evolve at different timescales. Examples include the slow dynamics of ice sheet growth and melting, the tropical response to precessional cycles (∼21,000 years), and the fast dynamics of Dansgaard–Oeschger cycles (∼1500 years). Since dynamical systems evolve along characteristic trajectories, they are, to some extent, predictable. Further, it should be possible to decompose any dynamical system that is made up of subsystems with discrete dynamics and characteristic timescales, into time series which capture those discrete components. This study reviews five methods which can potentially achieve this, including: Optimal Persistence Analysis (OPA), Slow Feature Analysis (SFA), Principal Trend Analysis (PTA), Average Predictability Time Decomposition (APTD) and Forecastable Components Analysis (ForeCA). These methods produce sets of components that are in some way predictable, such that each component is more predictable than the next component, but each method uses a different measure of predictability. The five methods are applied to a global dataset of speleothem δ18O spanning the period 22–0 ka BP. The two leading predictable components are a monotonic trend, and a low-frequency oscillation with a periodicity of ∼21,000 years. The methods ForeCA and PTA cleanly separate these two components from higher-frequency signals. The third predictable component consists predominantly of a peak which ramps up during Heinrich Stadial 1, and falls thereafter. Furthermore, predictable components analysis can be used not only to investigate the predictability within a field, but can be extended to exploring the predictability between fields, such as between the northern hemisphere field and the southern hemisphere field. Predictable components analysis allows a better insight into the dynamical components of climate fields, and hence should be a useful tool for improving the interpretation of paleo-isotope records and other climate proxies.