|Case study 13 - Isotope data and glacial cycles|
Data file: composite.dat
Oxygen isotope data from deep-sea cores give an excellent picture of temperature changes millions of years back in time. We will look at a data set compiled from several papers by Shackleton et al., found at http://delphi.esc.cam.ac.uk/coredata/v677846.html (also look at http://delphi.esc.cam.ac.uk/). In the file composite.dat, you will find the data for the last one million years, from the original six million years sequence. The very few data points that were marked as 'not available' in the original data set have been interpolated. The data set gives a composite sequence, constructed from two cores (V19-30 and ODP 677).
Open the file. Select the two columns, and choose 'Spectral analysis' in the 'Time menu'. You will get a spectrum where the upper half is a mirror image of the lower half, so you may want to set a lower 'X end' value to zoom in. The highest peak has a very high significance.
The peaks around 8 and 11 cycles/myr correspond to periods of 1/8=0.122 and 1/11=0.094 million years, respectively. These periods are in accordance with the 100 thousand year Milankovitch cycle (orbital eccentricity), or alternatively the inclination cycle (for information on this controversy, and the problems of the data set being 'astronomically tuned', see Muller & MacDonald 2000). The peak at 24 cycles/myr corresponds to the 41 thousand year Milankovitch cycle (obliquity), and the peak at 43 cycles/myr corresponds to the 23 thousand year cycle (precession).
More information about spectral analysis can be found in the manual.
The fit is not that bad, but these four sinusoids alone are obviously not enough to explain the data fully.
More information about sinusoidal fitting can be found in the manual.
This figure may not be very revealing, but it can be seen that we have relatively high correlations for lag times of around 30 and 39 samples. Each sample corresponds to 3000 years; this indicates a quasi-periodicity at 90 and 117 thousand years, in accordance with the two largest spectral peaks above.
More information about autocorrelation analysis can be found in the manual.
The vertical axis in the wavelet plot indicates logarithm of scale. For example, log2 s=3 means that we are observing the signal at a scale corresponding to 23=8 consecutive data points, which in our case again corresponds to 24000 years. Which periodicities can you identify in the wavelet plot?
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