Glacial Cycles, part 1

There’s really no doubt that astronomical cycles have influenced the growth and decay of ice on planet earth for the last 5 million years or so. The subject came up recently, and there seems to be a lot of confusion on the issue, so let’s take a closer look at the influence of astronomical factors on earth’s cryosphere.

First, how can we be sure that astronomical cycles have any influence at all? The answer is, that the growth and decay of ice shows cyclic influences with the same periods as astronomical cycles. The statistical significance is so high, and the synchronization so persistent, that frankly it’s pretty much impossible that there’s no relationship. And I think we can safely conclude that it’s not earth’s glacial changes that are causing the astronomical cycles.

For instance, here’s the data for delta-oxygen-18 from a stack of 57 ocean sediment cores, which is considered an excellent proxy for global ice volume, known as the “LR04 stack” (from Lisiecki, L.E., & Raymo, M.E. 2005. A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records. Paleoceanography, 20, 1003–1019, doi:10.1029/2004PA001071). Up is less ice (so generally warmer conditions), down is more (generally cooler), the distant past is on the left and the present is to the right:

Over the last 5 million years, the very-long-term trend is of a gradual increase in global ice. Let’s remove the very-long-term trend by subtracting a cubic polynomial fit, leaving this:

This emphasizes that over the last 5 million years, we’ve also seen an increase in the size of the fluctuations of global ice volume. The glacial cycles have been a lot bigger over the last million years, than they were prior to that.

If we Fourier analyze the detrended data we get this (sorry, the x-axis is mis-labeled “period” when it’s actually “frequency”):

I’ve indicated the important cylic (and pseudo-cyclic) peaks in the Fourier periodogram. The strongest is at frequency 0.024 cycles/kyr, period about 41,000 years. This is the same as the cycle of obliquity, the tilt angle of the earth’s spin axis relative to its orbit. We can see it plainly in a Fourier periodogram of earth’s obliquity over the last 5 million years:

There’s also a cluster of small peaks in the range 0.042 to 0.045 cycles/kyr (periods 22,000 to 24,000 years) and a small peak at 0.053 cycles/kyr (period 19,000 years) that are all coincident with periods in the changes of precession, the orientation of earth’s spin axis relative to the longitude of perihelion (closest approach to the sun) of earth’s orbit. We can see these peaks in the Fourier periodogram of the earth’s precession factor (we’ll define that precisely in the next installment) over the last 5 million years:

I also adorned the first periodogram with an arrow labelled “???”. This is a broadband response around frequency 0.01 cycle/kyr (period about 100,000 years), but its attribution is unclear.

Some may object that ice-core and sediment-core records are often “tuned” to orbital variations, i.e., the timing is adjusted to match orbital changes. However, the presence of orbital-cycle variations has (time and again) been confirmed in records which are not orbitally tuned (see e.g. Huybers, P. 2007. Glacial variability over the last two million years: an extended depth-derived age model, continuous obliquity pacing, and the Pleistocene progression. Quaternary Science Rev., 26, 37-55, doi:10.1016/j.quascirev.2006.07.013) — there’s just no doubt about it, these astronomical cycles are clearly imprinted on paleoclimate data. Both obliquity and precession have an undeniable effect on glacial changes.

We can identify the times at which these fluctuations are stronger and weaker with a wavelet analysis. Here’s the logarithm of the wavelet power (using the WWZ, or “weighted wavelet Z-transform”) as a function of time and frequency (NOTE: in this graph, unlike those preceding, time goes from right to left so the present day is at the far left):

There’s stronger response recently (especially in the last 800,000 years or so). In part it’s a purely statistical effect, due to the fact that we have more data points for more recent times. But there’s also a stronger response due to truly stronger periodic fluctuations recently, especially for the precession frequencies and the unidentified 100,000-year fluctuation. Only the 41,000-year fluctuation is ubiquitous in this data set, in fact before about 800,000 years ago it dominates glacial changes, which leads to that period being called the “41kyr world” (Raymo, M.E., and Nisancioglu, K. 2003. The 41 kyr world: Milankovitch’s other unsolved mystery. Paleoceanography, 18, 1011-1016, doi:10.1029/2002PA000791).

We can even use the wavelet analysis to estimate changes over time in the strength of the astronomical cycles. We can do this for obliquity and precession themselves, to gauge the changing strength of the driving influence, and to the LR04 stack to gauge the strength of the glacial response. Here, for example, is normalized amplitude of the 41kyr obliquity changes compared to normalized amplitude of the 41kyr response in the LR04 stack (time goes from left to right, with the present at the far right):

There’s a lot of commonality to the changes, not only on long (million-year) time scales but even on very brief (100,000-year) time scales as well (interesting to refer to 100,000-year time scales as “brief”). However, there’s less match between the amplitude changes in the most recent million years or so, yet another indicator that the response of glacial changes to astronomical cycles is itself changing over time.

So without doubt astronomical cycles (specifically, obliquity and precession) have profoundly affected glacial changes — essentially, Milankovitch’s overall thesis has been proved correct. The question remains, how do they do so? And why does the 41kyr obliquity cycle dominate most of the time? And wherefore has the glacial response changed over time? And what is the cause of that 100,000-year pseudoperiodic response over the last 800,000 years or so? Stay tuned — we’ll look into those questions in our next installment.