## Tuesday, January 12, 2010

### Climate sensitivity

This is a graph of the natural logarithm of observed atmospheric carbon dioxide concentrations versus observed global annual temperatures since 1880, with the temperatures taken from GISS. Natural logarithm is used because the relationship of CO2 to temperature is not linear but logarithmic.

Using this graph, we can take a shot at working out what the climate sensitivity of the earth is.

First, what is climate sensitivity? Climate sensitivity in this case is basically how sensitive the climate is to changes in atmospheric concentrations of carbon dioxide. The standard way of describing it is how much the temperature will rise for a doubling of CO2.

The climate sensitivity usually suggested is 3 degrees plus or minus 1.5 degrees (centigrade). These numbers are the ones put forward by the IPCC.

The IPCC figure is for climate sensitivity at equilibrium - in other words, they are saying that the climate will have increased in temperature by somewhere between 1.5 and 4.5 degrees per doubling of CO2 once the earth settles into a stable state. This would presumably have to be some time after humans have ceased unsustainably pumping CO2 into the atmosphere.

The climate sensitivity that I will be examining here is the climate sensitivity when the earth is not yet at equilibrium. To do this, we need to look at the slope of the above graph.

The slope is 288. Given that GISS publishes its figures in 100ths of degrees celsius, we need to divide by 100. This gives us a figure of 2.88 degrees celsius.

However, this is an increase of 2.88 degrees per full point of increase in the natural logarithm of CO2. To determine the increase per doubling of CO2, we need to multiply the slope by .7. This is because the natural logarithm of 2 is .7.

The result is 2.01 - we may as well round to 2.

So, the observed non-equilibirum temperature sensitivity from 1880 to 2009 was 2 degrees per doubling.

I will post in a little while on whether or not this is a good way of calculating temperature sensitivity.

1. Interesting work.

You need to include anthropogenic sulfates. These mask part of the signal from anthropogenic CO2. (You can get it from here).

Even then, it may not be a simple 1-1 relationship as you have assumed, because of the delay in temporal response to a change in C. (Lucia has some work on a 2-box model that is apropos to this.)

Finally, Arthur P. Smith has a response that he wrote to Lord Monkton that contains a similar result (he fit the CO2 curve by eye to the temperature curve).

2. Carrick,

I am having a look at some of the issues that you raise - I have been sent some information on the 2-box model idea, and done some more reading. I will be gradually discussing some of these things in the future (at the moment, I am struggling with autocorrelation ...).

3. On autocorrelation, hopefully, Lucia will explain her method at some point. I'd like to learn the technique.

The only way I know to handle autocorrelation in a fairly rigorous fashion is to compute the spectrum for the noise, then use that to produce multiple instances of the noise and fit to each of these and histogram the trend estimates from the individual runs... What this involves of course is an application of the Monte Carlo method with a noise model that matches the characteristics of your observed noise.

You probably know the trick for generating the noise time series, I'll repeat it here just in case, you use the measured amplitude of the spectrum, but use random phases for each frequency component, inverse FFT to get the time series. It doesn't hurt to smooth the amplitude of the spectrum (for example if the spectral amplitude resembles 1/f use 1/f).

According to the two-box modeling stuff, the time constant for the ocean-atmosphere system is about 30 years if that helps.