R. Taylor writes in to Tips and Notes to WUWT with this. Anthony: If you shift Vostok temperatures by reasonable time lags, and use reasonable parameters for an equilibrium between temperature and CO2, you get predicted values for CO2 that closely match CO2 measurements in Vostok. Really simple and conclusive, but I don’t think anyone has done it before.
I’m always interested in posting others research, so here it is. – Anthony
Atmospheric Temperature and Carbon Dioxide: Feedback or Equilibrium?
For several years, the suggestion that there is positive feedback between atmospheric temperature (T) and carbon-dioxide concentration (CO2) has dominated the scientific literature, and has become a fundamental assumption of climate science. Alternatively, the relationship between T and CO2 might be one of equilibrium. We can test models of each type by comparison with the Vostok record, first published by Petit, et al. (1999). The Vostok record contains about 3,300 determinations of T and 280 determinations of CO2, spanning the last 420,000 years.
Figure 1 shows the Vostok record; for clarity, the dates and measurements of T have been averaged in groups of 10, and those after 0 BCE are not shown (cf. Figure 4).
Figure 1: Temperature and Carbon Dioxide Inferred from the Vostok Ice-core.
T ranges through about 13 °C in the record, and CO2 ranges through about 120 ppm. There are peaks and valleys of various amplitudes and durations, and changes in T precede corresponding changes in CO2 (Mudelsee, 2001). The resolution of the record improves as measurements become more recent.
The first quantitative model comparable to the Vostok record with feedback between T and CO2 seems to be that of Hogg (2008). Hogg simulated insolation and other factors over a given interval of 500,000 years to predict values of T and CO2. Figure 2 is rescaled from Hogg’s figure 2a, so T and CO2 have approximately equal amplitude.
Feedback systems typically have characteristic amplitude and period. For this model, 1.7 °C is the characteristic amplitude of T, and 100,000 years is about the characteristic period. Adjusting the parameters of the model will change its amplitude and period, but these will be characteristic for any given set of parameters: Other amplitudes and periods will be suppressed.
Since the model assumes that CO2 has a significant effect on T, changes in CO2 happen before corresponding changes in T through a substantial portion of its cycle, viz. the latter portion of the rises to the peaks (cf. Hogg) and through essentially all of the subsequent declines. As previously mentioned, however, the Vostok record shows that changes in CO2 happen after corresponding changes in T. This lag is shown most clearly by large-amplitude features in the more recent portion of the record: CO2 rises hundreds of years after T rises, and falls thousands of years after T falls.
The substantially inverted lag of this feedback model confirms what is self-evident in an equilibrium model: A lagging entity can have no significant effect on a leading entity. For example, CO2 at a given time cannot affect the level of T that existed hundreds-to-thousands of years earlier.
A model of equilibrium between T and CO2 can be based on balance between temperature dependent processes that (i) release CO2 into the atmosphere and (ii) absorb it into the surface of the earth. If the temperature dependency is simply linear, we can express our model as:
CO2(t+l) = mT(t) + b
where t is time, l is the length of time required for CO2 to regain equilibrium after a change in T, m is the number of units that CO2 changes for a unit change in T, and b is the constant offset between units of CO2 and units of T.
Using this equation, we can predict a value for CO2 at some time in the future from each value of T. If we give l a value of 50 years after a rise in temperature and 8000 years after a fall in temperature, m a value of 10 and b a value of 270, and average the times and predicted values of CO2 in groups of 10, we obtain the predicted values shown in figure 3. The figure also shows the measured values of CO2 for comparison.
The output of the equilibrium model is consistent with the lag, spectrum and amplitudes of the record. The correspondence between predicted and measured values of CO2 indicates that CO2 is in temperature-dependent time-lagged equilibrium, and that the temperature dependence of CO2 is essentially linear through the Vostok range.
Let us turn our attention to the last 11,000 years, during which humans have disturbed the equilibrium between T and CO2. The most recent CO2 determination from the ice-core has a date of about 340 BCE. We can add an early-industrial-era value of 290 ppm at 1800 CE and a value of 365 ppm at 2000 CE to provide figure 4. The scaling in the figure is consistent with the
equilibrium model that fits the overall Vostok record, where a change of 1 °C in T causes a change of 10 ppm in CO2.
T and CO2 appear to have been in equilibrium until about 3,000 BCE. Over the 5,000 years since then, CO2 has risen increasingly above its natural equilibrium. By 1,800 CE, CO2 had risen to a level comparable to the highest in the Vostok record. During this time, T declined at a rate of 0.1 °C per thousand years, indicating again that CO2 has no apparent effect on T. The trends of this 5,000-year interval of excess CO2 are consistent with the equilibrium model, in
which T is independent of CO2.
The last 5,000 years are trivial compared to the 420,000 years of the Vostok record; of even less significance are the last 1,200 years. However, climate science has put great emphasis on the features of this interval, even though they fit within the noise-envelope. The “medieval warm period” spanned 800 CE to 1,200 CE; Vostok shows it wasn’t really warm, but wasn’t really cold either. The “little ice age” followed (although average T was barely lower), and ended after the low of -1.84 °C around 1,770 CE. By the early 1800s, T was higher than it is at present, and it has fluctuated within levels typical of the last 11,000 years since then. It is remarkable that climate hysteria should be based on noise-level changes in T over the last 200 years, which is an eye-blink in the Vostok record. It seems to be the superstition of our time.
In summary, the Vostok record indicates that CO2 is in lagged equilibrium with T and that, for the range of T in Vostok, the dependency of CO2 on T is essentially linear. Unnaturally high CO2 for the last 5,000 years has had no apparent effect on T. This empirical evidence supports a conclusion that there cannot be any significant feedback between CO2 and T. Such feedback would cause predicted T and CO2 to show fundamental disagreement with the lag, spectrum and amplitudes evident in the Vostok record.
It is impossible to say how enduring the feedback fallacy will be. However, any such model proposed in the future can be regarded as qualitative if it does not specify lag, characteristic amplitude and period, and as speculative if it cannot be compared to the Vostok record. Accordingly, any such model can be ignored.
If we may depart for a moment from objectivity, any such model should be ignored if its proponents declare that it shows polar bears are in peril, and you can save them by painting your roof white and burning nuts and corn in your car.
Hogg, A.M., 2008, Glacial cycles and carbon dioxide: A conceptual model. Geophysical
Research Letters, 35, L01701 (5 pp.).
Mudelsee, M., 2001, The phase relations among atmospheric CO2 content, temperature and global ice volume over the past 420 ka. Quaternary Science Reviews, 20, 583-589. Petit, J.R., Jouzel, J., Raynaud, D., Barkov, N.I., Barnola, J.-M., Basile, I., Bender, M., Chappellaz, J., Davis, M., Delaygue, G., Delmotte, M., Kotlyakov, V.M., Legrand, M., Lipenkov, V.Y., Lorius, C., Pépin, L., Ritz, C., Saltzman, E. and Stievenard, M., 1999, Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 399, 429-436. http://www.ncdc.noaa.gov/paleo/icecore/antarctica/vostok/vostok_data.html provides on-line data.
Code with data:
Is available upon request.