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Sunday, April 28, 2013

Greenland Red Noise

Tamino analyzed a paper by Chylek [1] who claimed to be able to extract a periodic signal out of Greenland ice core data (Dye3).

Tamino's post is comprehensive, but I wanted to check to see if I could extract any signal from the data myself.

The data is in the upper right of the following figure, and the FFT-based power spectral density (PSD) is in the lower left. 

FFT PSD lower left, Data upper right

The PSD is nondescript with a red noise envelope shown by the solid line. Red noise is the embodiment of the Ornstein-Uhlenbeck process.  This red noise shows very short correlation, at most a lag of one or two time units, as shown in the autocorrelation below.

Autocorrelation function, centered at 1/2 time series length

Hard pressed to find any real signal in such a time series.  A simulation of Ornstein-Uhlenbeck red noise is shown to the left below, with a slice of the Greenland data to the right.
Ornstein-Uhlenbeck red noise time series (left) and slice of data (right)
Chylek claims that he can see 20 year AMO (Atlantic Ocean) oscillations in the data. Like Tamino, I see nothing but garden variety noise.


P. Chylek, C. Folland, L. Frankcombe, H. Dijkstra, G. Lesins, and M. Dubey, “Greenland ice core evidence for spatial and temporal variability of the Atlantic Multidecadal Oscillation,” Geophysical Research Letters, vol. 39, no. 9, 2012.

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