Sunday, January 23, 2011

Chaotic Climate and the Next Ice Age
Four items appeared on WUWT recently that started me on a small project.
1) Someone insisted that climate is chaotic. I think the drivers of climate are deterministic, but their combined results may appear chaotic.
2) There have been recent mentions of the end of the Holocene from Loutre & Berger (2003) at 50,000 years to Piers Corbyn - we are back in an ice age.
3) Don Easterbrooke contributed a somewhat controversial paper that included as Fig 5 an excellent GISP2 ice core graph.
4) Someone posted this link: to a paper by Roper that included as fig 2.1 an intriguing comparison of the Eemian with an Antarctic ice core, but GISP2 looks like a better comparison.
These inputs made me wonder if the recent Holocene could be approximated by a few simple variables, and if it might look a bit like the end of the Eemian. I chose 3 regularities that I had identified here: that are long enough to give very visible change, that appear with little variability for the last few thousand years, that have widely different frequencies, and that could be reasonably approximated with sine curves; the 60, 179 (Jose) and 1050 year cycles..
To generate a composite curve, I then had to choose both phase offsets and amplitudes, that wouldn’t be too arbitrary. I set the 60 and 179 year cycles to peak in the 1940 to 1945 period, with the 60 year leading a bit so that the recent 1938-1944 peak warming would be a bit higher than the more recent 1998-2006 peak warming. (I believe that if all of the warming biases in the surface instrument global average temperature calculations were corrected 1938-44 would be warmer). I then set the 1050 year cycle to peak about 1150 (MWP) and to bottom about 1675 (LIA). I then set amplitudes to be fairly similar, with a targeted increase of 0.45 degrees C from 1910 to 1944. Then using “MathGV” I was able to fiddle the following formulae and generate the curves as:
60 year cycle y = .15sin[5.23[x-.4]], Jose cycle y = .145cos[1.75[x+.3]] and the 1050 year cycle as y = .22sin[.299x], giving the following composite: 

The 1910-1944 excursion (just before the vertical axis) looks about right, and the MWP to LIA excursion is close to the spaghetti graphs and less than the Loehle reconstruction.
There is still too much regularity in the composite, but it looks pretty chaotic on a 300-400 year time scale. We can see the 1940-45 peak just before the Y axis, and the smaller 1998-2006 peak just after the Y axis, and both the MWP and LIA . Part of the problem is that in the real world these regularities are not sinusoidal. Based on the 20th century the 60 year cycle trend is more like - up for about 20 years then flat for 10 years, then sharply down for 10 years and flat for 20 years, with considerable fluctuation around the trend. Given the scale I have used, such detail would have little effect on the composite curve. From Geoff Sharp’s work the 179 year cycle seems to be a near 80 year high mean segment followed by a near 100 year low mean segment, with 20 year oscillations around the mean. Using such a representation would change the shape of the major peaks, but not the overall pattern. Now there are 2 more elements that need to be added that cannot be represented (approximated) so easily.
Here I need help from one of the computer whizzes out there. I need to add the Deep Grand Minimum (DGM) cycle of approx. 364 years (near 33 sunspot cycles), and a linear trend. I have done this manually on paper, and the results have a couple of very suggestive surprises. Can one of you wizards add these two elements so the resulting composite can be displayed electronically?
To get the trend, I simply took the downtrend from the Minoan optimum shown in the GISP2 curve, and halved it to represent a world trend. That gave me a downslope of 0.01 degrees C per century, applied from the peak of the MWP. The DGM is a little trickier. I took a 30 year linear temperature plunge at the beginning of a cycle (from +0.1 degrees C to -0.2 degrees C), followed by a ca 334 year linear rise to the peak before the next plunge. I located the current DGM by considering the peak of the 60 year curve, just to the left of the Y axis above, as 1940, and then moving right a little more than one cycle to start the 30 year down at about 2009. I then simply reproduced that cycle forward and back, using the 60 year curve to scale time on the X axis. With these two additions we have just 5 variables, (all of which are somewhat more regular than reality), and we start to get a temperature curve that looks pretty chaotic on any scale less than 500 years, and isn’t so far from reality. The biggest problem that appears is a severe cooling about 1850, that just didn’t happen, but then, looking at some of the SSB (careful, forbidden term) drivers there seems to have been what has been referred to as a “phase catastrophe” about 1850, which I have no way to factor in, so I have simply smoothed out the 1850 downspike in my manual composite, leaving the Dalton and the 1910 bottoms fairly clear. Given the different “spaghetti graph” depictions of the Holocene, this curve looks fairly good

For comparison of the MWP/LIA with an historic reconstruction see:

Some of the interesting results:
• The MWP and LIA extremes are clearly represented, with the LIA being relatively severe, and the MWP/LIA excursion is very close to the Loehle reconstruction.
• The 1998-2006 peak moves a little closer to the 1938-44 peak, but stays slightly cooler, which is probably realistic.
• The 1976-2006 supposed AGW is just a little insignificant shoulder on the long rise from the LIA, and we don’t max out until about 2300. The warmers “ain’t seen nothin’ yet”.
• The cooling we are now entering looks to be slightly colder than the Dalton, but way short of the LIA, with about 80 years of cool, followed by 280 more years of warm.
• At about AD 2300 we see the last warm peak before descending into cold about as deep as the LIA, but lasting unremittingly a lot longer, perhaps enough for the northern hemisphere albedo to grow to a “tipping point”, leading to the next glacial period.
So, here is a third ice age prediction. Should it be given even more than a moments consideration? Well there is one comparison that is kind of spooky. Go back to, fig 2.1, and zoom in to see detail for the Eemian. Consider that the Younger Dryas event, (I like the meteorite shower/Atlantic conveyer shutdown theory) simply blew the peak off the Holocene, without which we would look like an Eemian repeat. Looking at the GISP2 curve, we have 10 spikes at near 1000 year intervals. (The Minoan to the Roman is about 1300 years and the MWP to 2300 is about 1300 years). It is pretty easy to find 10 similar spikes of the Eemian. Just before the 10th Eemian peak, the downslope goes from about 0.04 degrees C/century to a bit more than 0.1 degrees C/century (.02 to .06 if divided by 2 as I did for the Holocene trend). My downslope from the Holocene Optimum  (ca 8000yrs BP) to 2300 is about 0.01 degrees C/century, and then it goes to about .07 degrees C/century.  My oversimplified model is better for curve shape than magnitudes and the slope change may be too abrupt, but the similarity to the Eemian is at least suggestive.

Note that Roper ascribes the long Holocene cooling trend to gradual reduction of polar summer insolation, particularly north polar, in his Fig 2.3. The total polar summer insolation is about to turn down as the north flattens at the bottom, and the south goes into the steep part of its decline. Since the Holocene Optimum north pole summer insolation has declined from about 565W/m2 to 521 W/m2, a drop of almost 8%, accompanying a GISP peak temperature cooling of nearly 1%K. Roper also suggests that we could be on the brink of the next major ice age.
My prediction – 2300-2310 for the last warm peak before we head into the next ice age.
My request – someone create the composite curve electronically, including the long cooling and the DGM effect as I have described above.
My hope – some good discussion, picking all of this apart, or adding something to it. Other reconstructions/projections welcome.