Long-range memory in temperature reconstructions from ice cores; glacial vs interglacial climate conditions
Abstract:The presence of long-range memory (LRM) in climatic records is well documented in the geophysics literature. The power spectral density (PSD) of LRM time series follows a power law; limf→0 S(f) ∝ f−β, where 0 < β < 3. An uncorrelated white noise has β=0, while a typical model for an LRM stochastic process is the persistent fractional Gaussian noise (fGn). This is a stationary process with 0 < β < 1. The cumulative integral (or sum) of such a process has the PSD of the form S(f) ∼ f−β, but with β→β+2. Such a process with 1<β<3 is a non-stationary LRM process called a fractional Brownian motion (fBm). The power-law behavour of the PSD indicates the absence of a characteristic scale in the time record; the record is scale-invariant or just scaling. For this reason, β is often referred to as the scaling exponent.
Time series from the Holocene and from the last glacial period are extracted from ice cores from Greenland and from Antarctica. The scaling exponent β is then estimated for each time period separately by using the Lomb-Scargle periodogram. For the Holocene period, we find (β ≈ 0 for time scales < 103 years for both the GRIP and EPICA ice core, and β ≈ 0.8 for longer time scales. We suggest that the scale break at 103 years marks a transition between fluctuations dominated by local/regional variability to fluctuations on time scales dominated by global variability. For the last glacial period, the results are different for the individual cores and also different from the Holocene climate. For GRIP we find β ≈ 1.5 for time scales longer than 102 years, while the Dansgaard-Oeschger events most likely affect the power spectrum on shorter time scales. For EPICA we find β ≈ 0.6 for time scales 102 < τ < 103 years, and β ≈ 1.8 in the range 103 < τ < 104 years. From this study, we suggest that the scaling properties of glacial and interglacial climate are different, so that long, paleoclimate time series combining the two climate conditions should be divided into sequences before studying the scaling and drawing conclusions about a specific period such as the Holocene.