## Tuesday, January 5, 2010

### Warming in the Pipeline

How much "warming in the pipeline" is there? Is there a way to be sure? NASA GISS findings suggest it's about 0.6C.

I was contemplating a method of estimating "warming in the pipeline" from available temperature and CO2 data. It's sort of a heuristic method, with all this implies, but it's interesting that I get somewhat different results.

CO2 appears to be the main causal agent of recent temperature shifts. I've demonstrated that temperature fluctuations lag CO2 fluctuations by about 10 years. It comes to reason that observed temperature fluctuations lag equilibrium temperature fluctuations by about 10 years as well.

Imagine you have an equilibrium temperature series that looks like a sinusoid. Observed temperature will lag the hypothetical series, also looking like a sinusoid, by some number of years. If we use Newtonian cooling as an approximation, the expected rate of temperature change (R) will be given by:

`R = r·(T' - T)`

T' is the equilibrium temperature and T is the observed temperature. The constant r is something I will call the rate coefficient.

The question is: If you know the lag between the sinusoid series, can you estimate the value of the rate coefficient r? Then, if you know r, can you estimate "warming in the pipeline"? I think the answer is yes.

I gave up trying to solve it with calculus. Perhaps a reader can give it a shot. I instead solved it by means of a Monte Carlo simulation.

It turns out that the rate coefficient r depends on the period of the sinusoid and the lag between the series, but not the amplitude of the sinusoid.

The period of the CO2 sinusoid that results from the 3rd-order detrending of the CO2 series is about 85 years (pulsation is 0.074.) You can see that in the figure above. For this period, and a lag of 10 years, my simulations indicate that the rate coefficient r should be just about 0.08 in units of `year-1`.

Let's assume that the current rate of temperature change (without weather noise) is about 0.018 degrees Celcius per year. Then we have that:

`0.018 = 0.08·(T' - T)`

So the temperature imbalance is:

`ΔT = T' - T = 0.018 / 0.08 = 0.23°C`

This is not too bad. If correct, I'd take it as good news.

Climate Sensitivity

I'm essentially claiming that the global equilibrium temperature is knowable and that it's perhaps 0.7°C relative to the HadCRUT3 baseline. It also appears (based on various reconstructions) that the temperature in the 18th century was fairly stable at about -0.4°C. We can probably assume that's an equilibrium temperature. The difference is 1.1°C.

The concentration of CO2 in the 18th century was about 277 ppmv. The concentration as of 2008 is more like 385 ppmv. This means that:

`1.1 = k·ln(385/277)`

Therefore:

`k = 3.34`

We can estimate the climate sensitivity to CO2 doubling as follows:

`λ = k·ln(2) = 2.32°C`

This is actually a tad lower than the best estimates available. There are some uncertainties in the estimate, to be sure. For example, were temperatures really stable at -0.4°C in the 18th century? Then there are some errors that are immediately obvious. Some of the warming could be due to methane and other greenhouse gases. You also have cooling due to aerosols, which would confound the estimate in a manner whose magnitude is not well understood.