Today I was reviewing and re-reading the nonlinear time series technical literature I have, seeking ideas on how to go about using the statistical ensemble learning technique called “boosting” with them. (See the very nice book, R. E. Schapire, Y. Freund, Boosting: Foundations and Algorithms, 2010, The MIT Press.) There have been attempts, and I’m reviewing those as well. My progress on that, intending to be used for my work on Town of Sharon hydrological series and others, will be documented here some other day. During the review, I decided to go over the famous convergent cross mapping (“CCM”) ideas from George Sugihara and team (Ye, May, Hsieh, Fogarty, Munch, Clark, Isbell, Deyle, Cowles, Tilman, and colleagues Maher and Hernandez with their work on CauseMap). I have mentioned and written about this development in three places on this blog already,

• “All I do is complain, complain …“
• “Tsonis, Swanson, chaos, and “s__t happens” (slightly revised and expanded)
• “Detecting Causality in Complex Ecosystems“

And, along the way, I read another article, “Spatial ‘convergent cross mapping’ to detect causal relationships from short time-series”, by Clark, Ye, Isbell, Deyle, Cowles, Tilman, and Sugihara, which appeared late in December 2014 in the journal Ecology, and the striking paper in PNAS, by Ye, et al, “Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling“. But today I found an article I missed, from earlier in 2015, pertaining to climate change, which has not, as far as I can tell, gotten much play. And it should.

That article appeared in March 2015 in Nature Climate Change, and is by Egbert van Nes, Marten Scheer, Victor Brovkin, Timothy Lenton, Hao Ye, Ethan Deyle, and George Sugihara, and is titled “Causal feedbacks in climate change“.

One of the favorite lines heard in science denier circles about climate change regards an observation that in the paleoclimate record temperature rises appear to lead increases in CO₂ production and, so, they conclude, CO₂ increases cannot cause temperature rises. The paleoclimate record demonstrates a very strong association and then geophysicists argue case by case in paleohistory what happened in each event, generally suggesting that the two series, temperature and CO₂ concentration, are dynamically interrelated and mutually re-enforcing as a coupled system of differential equations. All that’s true. And, if even in the past, temperature rise occurred first, that does not in any way mean that an abrupt increase in CO₂ concentration now would not result in abrupt increases in temperature.

But the remarkable result from van Nes, et al (2015) is that, by applying their CCM method to the two series of temperature and CO₂ concentration, they conclusively demonstrate that, yes, indeed, the increase in CO₂ concentration is in fact causing the increase in temperature, even there remains an enhancement of CO₂ production by increases in temperature. That enhancement proves to be both much weaker than the forcing in the other direction, although it definitely exists. And, to top off the paper, van Nes, et al show “direct confirmation that internal Earth system mechanisms rather than orbital forcing have controlled climate dynamics over the Pleistocene cycles”.

The figure below is a reproduction of Figure 3 from their paper. There is more detail in supplementary online information.

(Click on figure to see larger image. Use your browser Back button to return to article in blog.)

Another denier claim is now neatly relegated to the trash, without the need for roundabout explanation.

Update, 2015-01-22

Professor Robert May illustrates the key ideas in empirical dynamic modeling in the video below:

Update, 2016-07-24

Berner, et al do “Stochastic parameterization”.