A few people have asked about the fascinating 2006 paper by Gerard Roe, In defense of Milankovitch.
Roe’s paper appears to show an excellent match between the rate of change of ice volume and insolation at 65°N in June. I’ve been puzzled by the paper for a while, because if this value of insolation does successfully predict changes in ice volume then case closed. Except we struggle to match glacial terminations with insolation (see earlier posts like Part Thirteen, Twelve, Eleven – End of the Last Ice age).
And we should also expect to find a 100 kyr period in the 65°N insolation spectrum. But we don’t.
To be fair to Roe, he does state:
The Milankovitch hypothesis as formulated here does not explain the large rapid deglaciations that occurred at the end of some of the ice age cycles
To be critical, it doesn’t seem like anyone is disputing that ice sheets wax and wane with at least some attachment to 40k (obliquity) and 20k (precession) cycles so what exactly does the paper demonstrate that is new? The missing bit of the puzzle is why ice ages start and end.
On the plus side, Roe points out:
Surprisingly, the [Milankovitch] hypothesis remains not clearly defined..
Which is the same point I made in Ghosts of Climates Past – Part Six – “Hypotheses Abound”.
One of the reasons I’ve spent quite a bit of time collecting and understanding datasets – see Part Fourteen – Concepts & HD Data – was for this kind of problem. Roe’s figure 2 spans half a page but covers 800,000 years. With the thick lines used I can’t actually tell if there is a match, and being poor at real statistics I want to see the data rather than just accept a correlation.
There’s not much point comparing SPECMAP (or LR04) with insolation because both of these datasets are “tuned” to summer 65°N insolation. If we find success then we accept that the producers of the dataset were competent in their objective. If we find lack of success we have to write to them with bad news. No one wants to do that.
Fortunately we have an interesting dataset from Peter Huybers (2007). This is an update of HW04 (Huybers & Wunsch 2004) which created a proxy for global ice volume from deep ocean cores without “orbital tuning”. It’s based on an autocorrelated sedimentation model, requiring that key turning points from many different cores all occur at the same time, and a key dateable event at around 800,000 years ago that shows up in most cores.
Some readers are wondering:
Why not use the ice cores you have been writing about?
Good question. The oxygen isotope (δ18O), or deuterium isotope (δD), in the ice is more a measure of local temperature than anything else (and it’s complicated). So Greenland and Antarctic ice cores provide lots of useful data, but not global ice volume. For that, we need to capture the δ18O stored in deep ocean sediments. The δ18O in deep ocean cores, to a first order, appears to be a measure of the amount of water locked up in global ice sheets. However, we have no easy way to objectively date the ocean cores, so some assumptions are needed.
Fortunately, Roe compared his theory with two datasets, the famous SPECMAP (warning, orbital tuning was used in the creation of this dataset) and HW04:
I downloaded the updated Huybers 2007 dataset. It is in 1 kyr intervals. I have calculated the insolation at all latitudes and all days for the last 500 kyrs using Jonathan Levine’s MATLAB program. This is also in 1 kyrs intervals. I used the values at 65N and June 21st (day 172 – thanks Climateer, for helping me with the basics of calendar days!).
I calculated change in ice volume in a very simple way – (value at time t+1 – value at time t) divided by time change. I scaled the resulting dataset to the same range as the insolation anomalies – so that they plot nicely. And I plotted insolation anomaly = mean(insolation) – insolation:
Figure 2 – Click to Expand
The two sets of data look very similar over the last 500 kyrs. I assume that some minor changes, e.g., at about 370 kyrs, are due to dataset updates. Note that insolation anomaly is effectively inverted to help match trends by eye – high insolation should lead to negative change in ice volume and vice-versa.
For reference, here is my calculation on its own (click to get the large version):
Figure 3 – Click to Expand
I did a Pearson correlation between the two datasets and obtained 0.08. That is, very little correlation. This just tells us what we can see from looking at the graph – the two key values are in phase to begin with then move out of phase and back into phase by the end.
Correlation between 0-100 kyrs: 0.66 (great)
Correlation between 101-200 kyrs: 0.51 (great)
Correlation between 201-300 kyrs: -0.72 (wrong direction)
Correlation between 301-400 kyrs -0.27 (wrong direction)
Correlation between 401-500 kyrs: 0.18 (wavering)
I’m a bit of a statistics amateur so comparing datasets except by looking is not my forte. Perhaps a rookie mistake somewhere.
Then I checked lag correlations. The physical reasoning is that deep ocean concentration of 18O will take a few thousand years at least to respond to ice volume changes, simply due to the slow circulation of the major ocean currents. The results show there is a better correlation with a lag of 35,000 years, but there is no physical reason for this, it is probably just a better fit to a dataset with an apparent slow phase drift across the period of record. At a meaningful large ocean current lag of a few thousand years the correlation is worse (anti-correlated):
On the plus side, the first 200 kyrs look quite impressive, including terminations:
This has got me wondering.
What do we notice from the data for the first 200 kyrs (figure 6)? Well, the last two terminations (check out the last few posts) are easily identified because the rate of change of ice volume in proportion to insolation is about four times its value when no termination takes place.
Forgetting about the small problem of the Southern Hemisphere lead in the last deglaciation (Part Eleven – End of the Last Ice age), there is something interesting going on here. Almost like a theory that is just missing one easily identified link, one piece of the jigsaw puzzle that just needs to be fitted in, and the new Nature paper is waiting..
Onto some details.. it seems that T-II, if marked by the various radiometric dating values we saw Part Thirteen – Terminator II, would cause the 100k-200k values to move out of phase (the big black dip at about 125 kyrs would move about 15 kyrs to the left). So my next objective (see Sixteen – Roe vs Huybers II) is to set an age marker for Termination II from the radiometric dating values and “slide” the Huybers 2007 dataset to this and the current T1 dating. Also, the ice core proxies recorded in deep ocean cores must lag real ice volume changes by some period like say 1 – 3 kyrs (see note 1). This helps the Roe hypothesis because the black curves move to the left.
Let’s see what happens with these changes.
And hopefully, sharp-eyed readers are going to identify opportunities for improvement in this article, as well as the missing piece of the puzzle that will lead to the coveted Nature paper..
Articles in the Series
Part One – An introduction
Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz
Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory
Part Four – Understanding Orbits, Seasons and Stuff – how the wobbles and movements of the earth’s orbit affect incoming solar radiation
Part Five – Obliquity & Precession Changes – and in a bit more detail
Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name
Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago
Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers
Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover
Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs
Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs
Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age
Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2
Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland
Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II
Fourteen – Concepts & HD Data – getting a conceptual feel for the impacts of obliquity and precession, and some ice age datasets in high resolution
Sixteen – Roe vs Huybers II – remapping a deep ocean core dataset and updating the previous article
Seventeen – Proxies under Water I – explaining the isotopic proxies and what they actually measure
Eighteen – “Probably Nonlinearity” of Unknown Origin – what is believed and what is put forward as evidence for the theory that ice age terminations were caused by orbital changes
Nineteen – Ice Sheet Models I – looking at the state of ice sheet models
In defense of Milankovitch, Gerard Roe, Geophysical Research Letters (2006) – free paper
Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression, Peter Huybers, Quaternary Science Reviews (2007) – free paper
How long to oceanic tracer and proxy equilibrium?, C Wunsch & P Heimbach, Quaternary Science Reviews (2008) – free paper
Datasets for Huybers 2007 are here:
Insolation data calculated from Jonathan Levine’s MATLAB program (just ask for this data in Excel or MATLAB format)
Note 1: See, for example, Wunsch & Heimbach 2008:
The various time scales for distribution of tracers and proxies in the global ocean are critical to the interpretation of data from deep- sea cores. To obtain some basic physical insight into their behavior, a global ocean circulation model, forced to least-square consistency with modern data, is used to find lower bounds for the time taken by surface-injected passive tracers to reach equilibrium. Depending upon the geographical scope of the injection, major gradients exist, laterally, between the abyssal North Atlantic and North Pacific, and vertically over much of the ocean, persisting for periods longer than 2000 years and with magnitudes bearing little or no relation to radiocarbon ages. The relative vigor of the North Atlantic convective process means that tracer events originating far from that location at the sea surface will tend to display abyssal signatures there first, possibly leading to misinterpretation of the event location. Ice volume (glacio-eustatic) corrections to deep-sea d18O values, involving fresh water addition or subtraction, regionally at the sea surface, cannot be assumed to be close to instantaneous in the global ocean, and must be determined quantitatively by modelling the flow and by including numerous more complex dynamical interactions.