Predictable Components in Australian Daily Temperature Data

Abstract

ynamical components of Earth?s ice?ocean?atmosphere system evolve along characteristic trajectories, which make these components partly predictable. This paper reviews several methods for extracting these predictable components from space?time fields. These methods are optimal persistence analysis (OPA), slow feature analysis (SFA), principal trend analysis (PTA), average predictability time decomposition (APTD), and forecastable components analysis (ForeCA). These methods generally find a set of components that are ordered by their predictability, but each method uses a different measure of predictability. Also, a new bootstrap test for investigating the type of predictability exhibited by these components is introduced. This new test is based on an ?integrated red noise? hypothesis. The five methods and new test are applied to a dataset of Australian daily near-surface minimum air temperature, spanning 1910?2013. For all five methods, the two leading predictable components are a long-term trend and a low-frequency pattern that decreased in the first half of the twentieth century and increased after that. The third predictable component differs between the methods based on persistence (e.g., OPA) and those based on more general measures of predictability (APTD and ForeCA). In addition, the use of spectral entropy for analyzing time-dependent predictability is investigated. Further research is needed into the application of predictable component methods to specific problems, such as to fields that require regularization (i.e., using ridge regression), to fields with missing values, and to fields with propagating predictable components.