Optimal Persistence Patterns

Timothy DelSole
Center for Ocean-Land-Atmosphere Studies (COLA)

Absract

A major barrier to climate studies is the lack of an effective method for separating slowly varying components (i.e., droughts and heat waves) from rapidly varying components (i.e, daily weather). The usual approach of filtering time series and then computing principal components is problematic because the resulting structures may dominate variations on slow time scales simply because it dominates variations at all time scales. Other approaches based on computing long term means or trends do not efficiently capture space-time variations, or presume a slowly varying signal that is a linear function of time. In this talk I introduce a new technique, called optimal persistence analysis, which decomposes data by time scale. More precisely, this technique decomposes data in terms of spatial patterns and corresponding time series, ordered such that the first component maximizes the decorrelation time, the second maximizes the decorrelation time subject to being uncorrelated with the first, and so on. The decorrelation time is defined as the autocorrelation function of the time series. This method represents a substantial advance over previous methods, since it isolates slowly varying signals with a small number of spatial patterns and their corresponding time series, and allows time variations to be a nonlinear function of time. The results of applying optimal persistence analysis to surface temperature in observations, and in simulations conducted as part of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), will be discussed.