Wednesday, January 6, 2010

Smoothing Splines and Law Dome CO2 Data

I've been reading about a paper by Ernst-Georg Beck where it is claimed that CO2 levels in the past 150 years have fluctuated widely. Apparently, when Mauna Loa measurements started, CO2 levels magically became more stable. It's not surprising these claims have been made fun of. But that's not what I really want to discuss.

Beck's paper got me thinking about the Law Dome ice-core data I've been using to associate CO2 with temperatures. I suspected it might actually be too smooth. You see, Etheridge et al. (1998) provides two convenience data sets: One is a 20-year smooth series spanning 1832-1978. The other is a 75-year smooth series spanning 1010-1975. They are obtained using smoothing splines.

You can actually see that the Etheridge et al. 20-year smooth data is even more smooth than Mauna Loa data (e.g. in this figure, before and after 1978.) The problem with smoothing out noise is that you can easily lose information.

I went ahead and calculated the natural spline interpolation of the raw data from Etheridge et al. (which I'm making available HERE.) The natural interpolation only uses the spline function to estimate data for years that are missing. It does not smooth out the raw data that is known. In the Etheridge et al. data set, what this will mean is that recent data will have most of the original noise, while old data will be smooth, but not 75-year smooth, hopefully.

Let's take a look at the 1850-1978 20-year smooth series provided by Etheridge et al. (1998), along with the natural interpolation of the raw data.



Interesting, isn't it? I think it makes a lot of sense. In particular, notice the flat CO2 trend between the years 1933 and 1952. That's 20 years without an increase in atmospheric CO2. With the smooth series, this is not so evident. You see perhaps 12 years of pause or so.

Is this important? Let's take a look at the HadCRUT3 temperature series along with the logarithm of the new CO2 series, from 1850 to 2008. (Mauna Loa data is added after 1978, minus a small offset.)



It would appear that the climate reacts rapidly to CO2 fluctuations, which again, argues for a small amount of "warming in the pipeline."

There are other things you can't see very well with the overly smooth data. Let's take a look at the time span between 1700 and 1900. For temperature, I will use the NH-SH average from the CPS temperature reconstruction of Mann et al. (2008).



Keeping in mind that both the temperature and CO2 data in the figure are reconstructed, I think this is pretty interesting. It suggests there might have been slight warming of about 0.1C right at the beginning of the industrial revolution. This is consistent with estimates of climate sensitivity.

1 comment:

charlie said...

I ran into the same concerns while I was putting together a graph of historical rates of change:

http://i1109.photobucket.com/albums/h428/csoeder/historical_Co2_rates.png

It looks to me like there is less variability in the calculated rate as the record goes back in time; for example, the Law Dome record appears to mostly stay in between +0.5 and -0.5 ppm/yr except for a dip to ~ -0.20ppm/yr around 1550-1600AD.

http://i1109.photobucket.com/albums/h428/csoeder/klimate/Law_Dome_Rate.png

The Taylor Dome record has variation from +0.5 to -0.5 ppm/yr, again showing decreased variation further back in time. And the Vostok record shows variation of about +/- 0.15 ppm/yr.

How would one work around the smoothing to reconstruct paleorates and error bars?