The astronomical theory and data compared - Ice Ages and Interglacials: Measurements, Interpretation, and Models - page 302

framework of the hypothesis of Stott and Timmerman (2011). They discuss
various aspects of their concept at some length, yet the details seem somewhat
ephemeral. They concluded:

''Our hypothesis does not necessarily account for the entire glacial/
interglacial CO 2 change. However, it would reconcile the lack of evidence for
an isolated deepwater mass during glacials that is otherwise required to explain
the large d 14 C excursion during the last deglaciation. It would also explain why
atmospheric CO 2 began to rise very soon after the Southern Ocean began to
warm . A comprehensive test of our CO 2 hypothesis requires a more thorough

assessment of the present-day CO 2 flux at sites of active magmatism and the
extent of liquid and hydrate CO 2 accumulations. There is also need to trace the
flow of 14 C-depleted waters during the last deglaciation to determine where it was
ventilated to the atmosphere. In the meantime, the hypothesis presented here
offers an important opportunity to reexamine the causes of glacial/interglacial
CO 2 variations and the sequence of events that punctuated the last deglaciation.''

...

10.3 SPECTRAL ANALYSIS

10.3.1 Introduction

M&M provided an extensive detailed discussion of spectral analysis. Only a very
brief discussion is given here. Spectral analysis is based on the mathematical
principle that almost any function (in particular, time series for ice core or ocean
sediment climate data) can be expressed as a sum of sine and cosine functions that
oscillate with variable frequency. If the time series oscillates in a regular fashion
with time, the coecient of the sine or cosine function with the frequency that
most closely matches the frequency of the time series will be the dominant term in
the expansion over all sine and cosine functions. Even though the time series
may be noisy and somewhat irregular, if its underlying structure contains regular
oscillations with time the spectrum of coecients vs. frequency will show peaks at
the frequencies that most closely match an appropriate sine or cosine function.
Thus, by expressing the time series as an expansion over all sine and cosine func-
tions with variable frequency, one can identify the most important underlying
frequencies (or time periods) that govern the variability of the time series. A plot
of the square of the coecients in the expansion in cosines and sines vs. frequency
will then reveal the underlying tempo of the variability of the time series.
However, there are a few caveats that must be mentioned here. First, there are
many procedures for estimating the principal frequencies underlying a time series,
and they do not always agree with one another. Second, low frequencies might not
show themselves clearly if the time series oscillates rapidly. Third, in comparing
solar variability with time series variability, it is insucient to compare principal
frequencies on their own. The phasing of the two functions is critical in establish-
ing a putative cause-effect relationship. Finally, to the extent that tuning was used