I know what you want to see: some half-arsed Climate Modelling!

The graph I showed in the last post wasn’t very good evidence for anthropogenic global warming. If I wanted to scare you, I would show you this graph instead.

This shows the correlation between carbon dioxide and temperature found in a brilliant set of data collected from ice cores at Vostok, Antarctica, where ‘0’ on the temperature axis is the average temperature for the last century or so. [Attribution to text files of raw data: J. R. Petit, J.M. Barnola, D. Raynaud, C. Lorius, Laboratoire de Glaciologie et de Geophysique de l'Environnement 38402 Saint Martin d'Heres Cedex, France; N. I. Barkov, Arctic and Antarctic Research Institute, Beringa Street 38, St. Petersburg 199226, Russia; J. Jouzel , G. Delaygue, Laboratoire des Sciences du Climat et de l'Environment (UMR CEA/CNRS 1572) 91191 Gif-sur-Yvette Cedex, France; V. M. Kotlyakov, Institute of Geography, Staromonetny, per 29, Moscow 109017, Russia]

I came to this data because I wanted to have a closer look at an assertion I have come across a number of times, that changes in carbon dioxide lag changes in temperature in ice core measurements. And yes, it does seem to, but it is a very unwise thing to base a full-blooded skepticism to global warming on. Because the lag is smaller than the uncertainty in the data. The age of the ice, and the age of the air trapped in the ice, is not the same: there is a difference of about 3000 years between the age of the trapped air and the age of the ice, which isn’t known with absolute accuracy, because it takes time for the snow and ice above a little bubble of air to be compact and impermeable enough to trap it there for good. The carbon dioxide content is obviously calculated from the air, while the temperature is calculated from the isotopic ratio of deuterium to hydrogen in the ice molecules. And the imprecision in aligning the exact times of these two sets of data is larger than the lag values that have been reported. It would be nice if this data gave a definitive answer as to how closely carbon dioxide and temperature changes track one another, but all we can say is that on a time scale of +/- 1000 years or so they move simultaneously.  I could just let you draw a line through the data extrapolating to the 400 ppm of carbon dioxide we have today, but I will do it myself.

This is a fit to the data assuming that all the change in temperature is due to radiative forcing by carbon dioxide, fixing T = 0 as 286 K and 284 ppm CO₂, with the log of the concentration change giving a change in absorption which has to be compensated by increasing the temperature of a black body radiator, with one adjustable parameter (an invariant non-CO₂ radiative forcing) adjusted to minimise the sum of the square of the differences between the fitted curve and the experimental data.

Scary, eh?

If this is the correct way to extrapolate the data, then we are about 6 degrees cooler than we should be, and are just in some sort of lag period - of some unknown length, but definitely less than a thousand years - waiting for this to happen.

I was on the brink of converting myself to global warming alarmism, but I thought I should have a look at the original papers first. Here are some great graphs from Petit et al., 'Climate and atmospheric history of the past 420,000 years from the Vostok ice core', Antarctica. Nature 399: 429-436.

Carbon dioxide is not the only thing that is correlated with temperature changes. Methane, another greenhouse gas, is correlated with temperature changes. (They did the maths in the paper, and r² is 0.71 for CO₂ and 0.73 for CH₄). The temperature changes are also closely correlated with the predicted insolation – the amount of sunlight incident on the Earth, varying according to irregularities in its orbit. Dust and sodium (a proxy for aerosols, which we know are cooling) are negatively correlated with temperature changes (r² is 0.70 for sodium). Ice volume (which is a proxy for water vapour, another powerful greenhouse gas) is positively correlated with temperature.

While insolation can only be a cause of warming, all of these other correlating things can be both a cause and an effect of increasing global temperature. We do not know, just by looking at this data, what is what. A sudden fall in dust and sodium, an increase in ice volume, and a sudden rise in CO₂ and CH₄ characterises the onset of all of the interglacial warm periods covered in this data. In the graph below I’ve fit the data again, but this time instead of adding an invariant radiative forcing by other things term have multiplied the carbon dioxide radiative forcing term by an adjustable constant to approximate the effect of all the other variables that are changing in synch with carbon dioxide. This constant turned out to be ‘41’ for the best fit, shown. So using this very crude fit, I can extrapolate the effects of *just* changing carbon dioxide concentration to 400 ppm, without any of those other things changing.(That's the line of green triangles hugging the axis from 300 to 410 ppm). This result seems absurdly Pollyanna-ish, even to me, and I'm sure I could make it looks scarier with a model for the experimental data with more adjustable parameters: but that's what the 'suck it and see' model gives me.

I've also put in the observed changes in modern times on this graph. It does make sense to attribute these to CO₂ with a little help from the other greenhouse gases we've been putting into the atmosphere. And because we're extrapolating beyond the bounds of the historical data, we may be in a strange and uncharted perturbation of the global climate system. So maybe there is still a significant lag for us to catch up with. Maybe.

But there is one other thing that emerges from this ice core data that suggests very strongly that carbon dioxide concentrations are much more an effect than a cause of global warming. Have another look at this figure:

At the end of each interglacial period, the temperature drops before the carbon dioxide concentration does. This is not a minor effect lost in the uncertainty, like the possible lag in carbon dioxide concentration at the beginning of warming periods; it is a big lag of many thousands of years. Insolation and methane don't behave like that: they rise and fall in lockstep with temperature. What this tells me is that carbon dioxide has historically not been sufficient, by itself, to maintain a warming trend. So we can completely discount any panic-mongering positive feedbacks.