A DYI Climate Sensitivity Toolkit

A DYI Climate Sensitivity Toolkit


Guest disalarmism by David Middleton

Do you ever watch the DYI Network?  The TV network where they have all the “Do It Yourself” home improvement shows?  I don’t watch it because I can’t do anything like that myself.  If a home improvement or repair project is much beyond duct tape and bungee cords, I’m on the phone to a professional in a heartbeat.  When I was a bachelor, the pipe under my kitchen sink was leaking.  So I wrapped in in duct tape and put a bowl under it.  Whenever it started to leak again, I wrapped it with more duct tape.  I actually left the roll of duct tape attached to the pipe, so I could easily wrap more duct tape.  When I got married and we renovated the house, the plumbers actually took pictures of my “handiwork.”   Is it duct tape or duck tape?  But I digress…

I may not be able to fix things around the house, but it occurred to me that if the climate (e.g. average surface temperature of the Earth) is sensitive to atmospheric CO2, there ought to be a simple DYI way to demonstrate it.  So, I broke out two of my favorite data sets: Moberg et al., 2005 (a non-hockey stick 2,000 year northern hemisphere climate reconstruction) and MacFarling-Meure et al., 2006 (a fairly high resolution CO2 record from the Law Dome, Antarctica ice cores).

For the sake of this exercise, I am going to assume that the “greenhouse” warming effect of CO2 is logarithmic.  While this is not necessarily a safe assumption, it’s a good bet that it is a diminishing returns function… So a logarithmic function is probably good enough for a DYI project.

The first thing I did was to crossplot the Moberg temperature anomalies against the MacFarling-Meure CO2 values…


Figure 1. CO2 vs temperature 0-1979 AD. A really bad correlation below 285 ppm.

R² = 0.0741… not exactly a robust correlation.  Why is the correlation so bad below 285 ppm?  Well, that’s the data from the lower resolution DSS core.  What happens if we only use the data from the very high resolution DE08 core?


Figure 2. CO2 vs temperature 1850-1979. A much better correlation with a very low climate sensitivity.

R² = 0.1994… Roughly a 20% explained variance… Not too shabby for noisy climate data.  We also get a climate sensitivity that is in line with other recent observation-derived estimates: 1.23 °C per doubling of atmospheric CO2.  Note that this puts the “we’re all going to die” 2.0 °C limit out to about 720 ppm CO2 and the “women, children and poor people will die” 1.5 °C limit out to about 560 ppm CO2.  So, it’s not worse than we thought, unless you’re an alarmist.  Then it’s probably worse than you will believe.  1.23 °C is very close to the IPCC TAR estimate of 1.2 °C sans feedback mechanisms.

If the amount of carbon dioxide were doubled instantaneously, with everything else remaining the same, the outgoing infrared radiation would be reduced by about 4 Wm-2. In other words, the radiative forcing corresponding to a doubling of the CO2 concentration would be 4 Wm-2. To counteract this imbalance, the temperature of the surface-troposphere system would have to increase by 1.2°C (with an accuracy of ±10%), in the absence of other changes. In reality, due to feedbacks, the response of the climate system is much more complex. It is believed that the overall effect of the feedbacks amplifies the temperature increase to 1.5 to 4.5°C. A significant part of this uncertainty range arises from our limited knowledge of clouds and their interactions with radiation. To appreciate the magnitude of this temperature increase, it should be compared with the global mean temperature difference of perhaps 5 or 6°C from the middle of the last Ice Age to the present interglacial.

IPCC TAR, 2001

Things aren’t looking to good for feedback amplification.

The next thing I DIY’ed was to calculate a “CO2 temperature” using this equation:

T = 1.7714ln(CO2) – 10.305


Figure 3. Moberg temperature reconstruction, “CO2 temperature”, Moberg temperature minus CO2 effect and CO2.

The gray curve is the Moberg temperature reconstruction, the red dashed curve is Moberg at a constant 277 ppmv CO2.  Not much difference between the gray and red dashed curves.

Let’s now apply this to the HadCRUT4 northern hemisphere temperature series (via Wood for Trees).


Figure 4. HadCRUT4 northern hemisphere (1979-2017), “CO2 temperature” and HadCRUT 4 minus “CO2 temperature.”

Northern hemisphere warming since 1979

  • Total: 0.91 °C (0.1 to 0.92)
  • CO2-driven: 0.33 °C (0.0 to 0.33)
  • Not CO2-driven: 0.58 °C (0.1 to 0.59)

This would suggest that anthropogenic CO2 emissions are only responsible for 36% of the warming since 1979.

Let’s now look at some RCP (representative concentration pathways) scenarios.


Figure 5. “CO2 temperature calculations for RCP 4.5, 6.0 and Bad SyFy 8.5 along with an extrapolation of MLO CO2 and HadCRUT4 31-yr average.

With a 1.23 °C climate sensitivity, not even the Bad SyFy RCP8.5 exceeds the “we’re all going to die” 2.0 °C limit and RCP4.5 and 6.0 pretty well stay below the “women, children and poor people will die” 1.5 °C limit.  Note than an exponential extrapolation of MLO CO2 basically tracks RCP4.5.  Also note that HadCRUT4 clearly exhibits a ~60-yr cyclical variation and continued warming from the Little Ice Age (part of a ~1,000-yr cyclical variation).  For those math purists who object to my geological use of the word “cyclical,” pretend that I wrote “quasi-periodic fluctuation.”

The Phanerozoic Eon

This is all well and good for the Late Holocene; but what about the rest of the Phanerozoic Eon?  Thanks to Bill Illis, I have this great set of paleoclimate spreadsheets.  One of the paleo temperature data sets was the pH-corrected version of Veizer’s Phanerozoic reconstruction from Royer et al., 2004.  The Royer temperature series was smoothed (spline fit?) to a 10 million year sample interval matching Berner’s GeoCarb III,  thus facilitating crossplotting.


Figure 6. Phanerozoic CO2 vs temperature.

Shocking!!! It yields a climate sensitivity of 1.28 °C.  Royer’s pH corrections were derived from CO; so it shouldn’t be too much of a surprise that the correlation was so good (R² = 0.6701)… But the low climate sensitivity is truly “mind blowing”… /Sarc.


Berner, R.A. and Z. Kothavala, 2001. GEOCARB III: A Revised Model of Atmospheric CO2 over Phanerozoic Time, American Journal of Science, v.301, pp.182-204, February 2001.

Hadley Centre.  Data from Hadley Centre.  http://www.metoffice.gov.uk/hadobs/hadcrut4/data/download.html Data processed by http://www.woodfortrees.org

Illis, B. 2009. Searching the PaleoClimate Record for Estimated Correlations: Temperature, CO2 and Sea Level. Watts Up With That?

MacFarling Meure, C., D. Etheridge, C. Trudinger, P. Steele, R. Langenfelds, T. van Ommen, A. Smith, and J. Elkins (2006), Law Dome CO2, CH4 and N2O ice core records extended to 2000 years BP, Geophys. Res. Lett., 33, L14810, doi:10.1029/2006GL026152.

Moberg, A., D.M. Sonechkin, K. Holmgren, N.M. Datsenko and W. Karlén. 2005.
Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature, Vol. 433, No. 7026, pp. 613-617, 10 February 2005.

NOAA. Data from NOAA Earth System Research Laboratory. http://www.esrl.noaa.gov/gmd/ccgg/trends/ Data processed by http://www.woodfortrees.org

Royer, D. L., R. A. Berner, I. P. Montanez, N. J. Tabor and D. J. Beerling. CO2 as a primary driver of Phanerozoic climate.  GSA Today, Vol. 14, No. 3. (2004), pp. 4-10

Featured image from Wikipedia.

The DYI Climate Sensitivity Toolkit



Superforest,Climate Change

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